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Neural Network for Valuing Bitcoin: Numerical Results, Implementation and Discussion

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Hyerin Cho (조혜린), Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA;
(2) Ben S. Prather, CCS-2, Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA;
(3) Ramesh Narayan, enter for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA;
(4) Priyamvada Natarajan, Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA, Department of Astronomy, Yale University, Kline Tower, 266 Whitney Avenue, New Haven, CT 06511, USA and Department of Physics, Yale University, P.O. Box 208121, New Haven, CT 06520, USA;
(5) Kung-Yi Su, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA;
(6) Angelo Ricarte, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA;
(7) Koushik Chatterjee, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA. Table of Links Abstract and Introduction Numerical Methods Hydrodynamic Bondi Accretion Magnetized Bondi Accretion Feedback Via Reconnection-Driven Convection Summary and Conclusions Acknowledgements Appendix A. GRMHD Primer and Definitions B. Numerical Set-up C. Resolution and Initial Condition Study References 2. NUMERICAL METHODS Our numerical scheme utilizes the GRMHD code KHARMA[1], a performance-portable C++ implementation based on iharm3D (Prather et al. 2021); iharm3D is itself an extension of HARM, an efficient secondorder conservative finite-volume scheme for solving MHD equations on Eulerian meshes in stationary curved space-times (Gammie et al. 2003). KHARMA offers a more flexible, portable, and scalable implementation suitable for multiple uses, by leveraging the Parthenon Adaptive Mesh Refinement Framework and the Kokkos programming model (Grete et al. 2023; Trott et al. 2022). [1] https://github.com/AFD-Illinois/kharma [2] A few details of the numerical method are given in Section B. A complete description is deferred to a future paper. This paper is available on Arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. Authors: (1) Hyerin Cho (조혜린), Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (2) Ben S. Prather, CCS-2, Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA; (3) Ramesh Narayan, enter for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (4) Priyamvada Natarajan, Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA, Department of Astronomy, Yale University, Kline Tower, 266 Whitney Avenue, New Haven, CT 06511, USA and Department of Physics, Yale University, P.O. Box 208121, New Haven, CT 06520, USA; (5) Kung-Yi Su, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (6) Angelo Ricarte, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (7) Koushik Chatterjee, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Hyerin Cho (조혜린), Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (2) Ben S. Prather, CCS-2, Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA; (3) Ramesh Narayan, enter for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (4) Priyamvada Natarajan, Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA, Department of Astronomy, Yale University, Kline Tower, 266 Whitney Avenue, New Haven, CT 06511, USA and Department of Physics, Yale University, P.O. Box 208121, New Haven, CT 06520, USA; (5) Kung-Yi Su, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (6) Angelo Ricarte, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (7) Koushik Chatterjee, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA. Table of Links Abstract and Introduction Abstract and Introduction Numerical Methods Numerical Methods Hydrodynamic Bondi Accretion Hydrodynamic Bondi Accretion Magnetized Bondi Accretion Magnetized Bondi Accretion Feedback Via Reconnection-Driven Convection Feedback Via Reconnection-Driven Convection Summary and Conclusions Summary and Conclusions Acknowledgements Acknowledgements Appendix Appendix A. GRMHD Primer and Definitions A. GRMHD Primer and Definitions B. Numerical Set-up B. Numerical Set-up C. Resolution and Initial Condition Study C. Resolution and Initial Condition Study References References 2. NUMERICAL METHODS Our numerical scheme utilizes the GRMHD code KHARMA[1], a performance-portable C++ implementation based on iharm3D (Prather et al. 2021); iharm3D is itself an extension of HARM, an efficient secondorder conservative finite-volume scheme for solving MHD equations on Eulerian meshes in stationary curved space-times (Gammie et al. 2003). KHARMA offers a more flexible, portable, and scalable implementation suitable for multiple uses, by leveraging the Parthenon Adaptive Mesh Refinement Framework and the Kokkos programming model (Grete et al. 2023; Trott et al. 2022). [1] https://github.com/AFD-Illinois/kharma [2] A few details of the numerical method are given in Section B. A complete description is deferred to a future paper. This paper is available on Arxiv under CC 4.0 license. This paper is available on Arxiv under CC 4.0 license. Arxiv

The Numerical Methods We Used to Study Black Holes

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Jihoon Chung;
(2)  Zhenyu (James) Kong. Table of Links Abstract & Introduction
Review of Related Work
Proposed Research Methodology
Numerical Case Studies
Real-World Simulation Case Studies
Conclusion
References IV. NUMERICAL CASE STUDIES This section provides numerical studies to compare the performance between the proposed method and benchmark methods. The studies evaluate the performance by varying the correlations (ki in Eq. (7)) between the KCCs in nonstationary process faults. All the numerical case studies consist of 20 independent trials. The code of the proposed algorithm is implemented in Matlab 2021. The CPU used in case studies is an Intel® Core™ Processor i7-8750H. This section compares the proposed method with the following benchmark methods. • User Grouping Sparse Bayesian Learning (i.e., UGSBL) proposed in [2] is an SBL method that clusters the KPCs samples into groups sharing the same process faults in sparse estimation. • Spatially Correlated Bayesian Learning (i.e., SCBL) proposed in [8] is an SBL method to diagnose process faults by exploiting the spatial correlation of KCCs. • [10] proposed the SBL method that considers prior knowledge of the process faults in sparse estimation. • MSBL proposed in [32] is a basic SBL method that assumes the independence of KCCs and stationarity of process faults. Performance Evaluation: To evaluate the effectiveness of the proposed method, two performance measures are used in this paper. The first measure evaluates the process fault detection capability, and the second measure is related to estimation accuracy. Each measure is evaluated by varying the correlation coefficients of spatially correlated KCCs. Fault Detection Capability: First, the proposed method requires correctly identifying process faults whose KCCs have excessive variance. In order to assess the capability of detecting process faults under sparse conditions, the area under the receiver operating characteristics (ROCs) curve (AUC) is utilized [46]. AUC is widely used for evaluating the accuracy of binary classification. Specifically, AUC measures the quality of the classification accuracy between process faults and non process faults irrespective of the threshold of variance. In other words, AUC accounts for the trade-off between the type 1 and type 2 errors. When the method is capable of achieving perfect classification results, the resulting AUC value will be 1. However, the AUC with a value close to 0.5 denotes that the estimated variances of KCCs from the method are similar between the process faults and non-process faults. Table I represents that the proposed method always achieves the best performance of AUC in the various spatial correlation between KCCs. Specifically, the AUC of the proposed method is close to 1.0 at every correlations levels, representing the perfect classification between the process faults and nonprocess faults in terms of estimated variance. Since UGSBL clusters the KPCs samples that share the same process faults, the method shows a comparable result to the proposed method  when the spatial correlation of KCCs is relatively low and moderate. However, the performance degrades in the high spatial correlation since the method assumes independence between all KCCs. The performance of SSBL is robust to correlations. This is because SSBL utilizes the correlation of correlated KCCs in its estimation. However, SSBL performs worse than the proposed method since this method assumes the same process faults between all KPCs samples, which are unsuitable for dealing with nonstationary process faults. MSBL and [10] show poor performances since these methods assume the independence of KCCs and stationarity of process faults. 2) Estimation Accuracy: In addition to correctly identifying the process fault, the method needs to accurately estimate the variance of process faults. After the process faults are identified, the practitioners are interested in how large the variances are to make decisions for the maintenance of the process. To achieve this objective, this paper provides the normalized mean squared error (NMSE) between true and estimated variance. Table II represents that the proposed method achieves the best performance in the estimation accuracy of the variance in most of the correlations. It implies that the proposed method is useful not only for the process faults identification but also for measuring how severe the process faults are. Compared to benchmark methods, the effectiveness of the proposed method in the NMSE results is noticeable in the presence of high spatial correlations between KCCs. Unlike AUC performance, the NMSE of SSBL increases as the correlation increases. It implies that SSBL successfully identifies the process faults utilizing the correlation information but cannot accurately estimate the variance since SSBL assumes the stationary process faults over KPC samples. The performance of UGSBL, MSBL, and [10] represent similar trends to the performance of AUC. This paper is available on arxiv under CC 4.0 license. Authors: (1) Jihoon Chung; (2)  Zhenyu (James) Kong. This paper is available on arxiv under CC 4.0 license. Authors: (1) Jihoon Chung; (2)  Zhenyu (James) Kong. Table of Links Abstract & Introduction Review of Related Work Proposed Research Methodology Numerical Case Studies Real-World Simulation Case Studies Conclusion References Abstract & Introduction Abstract & Introduction Review of Related Work Review of Related Work Proposed Research Methodology Proposed Research Methodology Numerical Case Studies Numerical Case Studies Real-World Simulation Case Studies Real-World Simulation Case Studies Conclusion Conclusion References References IV. NUMERICAL CASE STUDIES This section provides numerical studies to compare the performance between the proposed method and benchmark methods. The studies evaluate the performance by varying the correlations (ki in Eq. (7)) between the KCCs in nonstationary process faults. All the numerical case studies consist of 20 independent trials. The code of the proposed algorithm is implemented in Matlab 2021. The CPU used in case studies is an Intel® Core™ Processor i7-8750H. This section compares the proposed method with the following benchmark methods. • User Grouping Sparse Bayesian Learning (i.e., UGSBL) proposed in [2] is an SBL method that clusters the KPCs samples into groups sharing the same process faults in sparse estimation. • Spatially Correlated Bayesian Learning (i.e., SCBL) proposed in [8] is an SBL method to diagnose process faults by exploiting the spatial correlation of KCCs. • [10] proposed the SBL method that considers prior knowledge of the process faults in sparse estimation. • MSBL proposed in [32] is a basic SBL method that assumes the independence of KCCs and stationarity of process faults. Performance Evaluation: To evaluate the effectiveness of the proposed method, two performance measures are used in this paper. The first measure evaluates the process fault detection capability, and the second measure is related to estimation accuracy. Each measure is evaluated by varying the correlation coefficients of spatially correlated KCCs. Performance Evaluation: Fault Detection Capability: First, the proposed method requires correctly identifying process faults whose KCCs have excessive variance. In order to assess the capability of detecting process faults under sparse conditions, the area under the receiver operating characteristics (ROCs) curve (AUC) is utilized [46]. AUC is widely used for evaluating the accuracy of binary classification. Specifically, AUC measures the quality of the classification accuracy between process faults and non process faults irrespective of the threshold of variance. In other words, AUC accounts for the trade-off between the type 1 and type 2 errors. When the method is capable of achieving perfect classification results, the resulting AUC value will be 1. However, the AUC with a value close to 0.5 denotes that the estimated variances of KCCs from the method are similar between the process faults and non-process faults. Fault Detection Capability: First, the proposed method requires correctly identifying process faults whose KCCs have excessive variance. In order to assess the capability of detecting process faults under sparse conditions, the area under the receiver operating characteristics (ROCs) curve (AUC) is utilized [46]. AUC is widely used for evaluating the accuracy of binary classification. Specifically, AUC measures the quality of the classification accuracy between process faults and non process faults irrespective of the threshold of variance. In other words, AUC accounts for the trade-off between the type 1 and type 2 errors. When the method is capable of achieving perfect classification results, the resulting AUC value will be 1. However, the AUC with a value close to 0.5 denotes that the estimated variances of KCCs from the method are similar between the process faults and non-process faults. Table I represents that the proposed method always achieves the best performance of AUC in the various spatial correlation between KCCs. Specifically, the AUC of the proposed method is close to 1.0 at every correlations levels, representing the perfect classification between the process faults and nonprocess faults in terms of estimated variance. Since UGSBL clusters the KPCs samples that share the same process faults, the method shows a comparable result to the proposed method  when the spatial correlation of KCCs is relatively low and moderate. However, the performance degrades in the high spatial correlation since the method assumes independence between all KCCs. The performance of SSBL is robust to correlations. This is because SSBL utilizes the correlation of correlated KCCs in its estimation. However, SSBL performs worse than the proposed method since this method assumes the same process faults between all KPCs samples, which are unsuitable for dealing with nonstationary process faults. MSBL and [10] show poor performances since these methods assume the independence of KCCs and stationarity of process faults. 2) Estimation Accuracy: In addition to correctly identifying the process fault, the method needs to accurately estimate the variance of process faults. After the process faults are identified, the practitioners are interested in how large the variances are to make decisions for the maintenance of the process. To achieve this objective, this paper provides the normalized mean squared error (NMSE) between true and estimated variance. Table II represents that the proposed method achieves the best performance in the estimation accuracy of the variance in most of the correlations. It implies that the proposed method is useful not only for the process faults identification but also for measuring how severe the process faults are. Compared to benchmark methods, the effectiveness of the proposed method in the NMSE results is noticeable in the presence of high spatial correlations between KCCs. Unlike AUC performance, the NMSE of SSBL increases as the correlation increases. It implies that SSBL successfully identifies the process faults utilizing the correlation information but cannot accurately estimate the variance since SSBL assumes the stationary process faults over KPC samples. The performance of UGSBL, MSBL, and [10] represent similar trends to the performance of AUC.

Sparse Bayesian Learning: Numerical Case Studies

Efficient Neural Network Approaches for Conditional Optimal Transport: Numerical Experiments

This paper is under CC 4.0 license. available on arxiv Authors: (1) Amir Noorizadegan, Department of Civil Engineering, National Taiwan University; (2) D.L. Young, Core Tech System Co. Ltd, Moldex3D, Department of Civil Engineering, National Taiwan University & dlyoung@ntu.edu.tw; (3) Y.C. Hon, Department of Mathematics, City University of Hong Kong; (4) C.S. Chen, Department of Civil Engineering, National Taiwan University & dchen@ntu.edu.tw. Table of Links Abstract & Introduction Neural Networks PINN for Solving Inverse Burgers’ Equation Residual Network Numerical Results Results, Acknowledgments & References 5 Numerical Results 1. Mean Square Error: The training errors shown in the plotted graphs, relative to the iteration number, are computed using the mean square error criterion. 2. Relative L2 Norm Error: The validation errors, calculated over the test data and presented in the plotted graphs concerning the iteration number, are measured using the relative L2 norm error metric. 3. Maximum Absolute Error: When visualizing errors across the entire domain, whether in 2D or 3D scenarios, the error represented on the contour error plot is referred to as the maximum absolute error. It is important to note that the contour bars are scaled according to the largest error in the plot. Maximum Absolute Error = max |u − N| These error metrics provide valuable insights into the accuracy and convergence of the methods used in this study. In this section four methods will be investigated. 1. Plain NN: A conventional neural network without any additional modifications or residual connections (see Fig. 2(a)). 2. ResNet: A residual neural network architecture where the output of each layer is obtained by adding the residual to the layer’s output (see Fig. 2(b)). 3. SkipResNet: An extension of ResNet, where the residual connection is applied every other layer, alternating between including and excluding the residual connection (see Fig. 2(c) where p = 1). 4. SQR-SkipResNet: An innovative variation of the ResNet architecture, where the squared residual is added every other layer. In this approach, the output of each alternate layer is obtained by squaring the previous layer’s output and adding the squared residual to it (see Fig. 2(c)-(d) where p = 2). The numerical experiments were executed on a computer equipped with an Intel(R) Core(TM) i9-9900 CPU operating at 3.10GHz with a total of 64.0 GB of RAM. For the first example, three test functions are investigated and depicted in Fig. 3. The top panel of Fig. 3 displays the 3D surface plot of the test functions, while the bottom panel presents the corresponding contour plots. F1 is a smooth function, originally introduced by Franke [9], which has been extensively used for studying radial basis function (RBF) interpolation. On the other hand, F2 and F3 are non-smooth functions [10]. Example 1 Our observations from these plots are as follows: 1. Plot (a) indicates that the ResNet is not accurate enough compared to the other three networks, both during training and validation. This pattern has been consistently observed in various examples, and we will no longer investigate the ResNet performance. 2. As indicated by the plot, it can be observed that the Plain NN necessitates approximately 2400 iterations for convergence, whereas the proposed SQR-SkipResNet achieves convergence in a significantly reduced 1400 iterations. Additionally, the latter method exhibits higher accuracy compared SQR-SkipResNet. 3. Plot (a) also shows that SkipResNet performs somewhat between Plain NN and SQR-SkipResNet. This behavior has been observed in different examples conducted by the authors, but we do not plan to further investigate to the former. 4. Contour error plots for both Plain NN and SQR-SkipResNet are presented in plots (b) and (c) respectively. These plots highlight that the maximum absolute error achieved with SQR-SkipResNet exhibits a remarkable improvement of approximately 60% compared to Plain NN. Therefore, a higher accuracy and better convergence are observed when using SQRSkipResNet compared to other algorithms. More investigations on the performance of the SQR-SkipResNet has been done by interpolating the non-smooth functions F2 and F3. Figure 6 presents the interpolation results for F2 on the top panel and F3 on the bottom panel with n = 1000. The corresponding training and validation error with respect to the epoch are shown in the Table 1: Example 1: Maximum absolute errors and CPU time (t) for F2-F3. The second and third columns show the interpolated surface using Plain NN and SQR-SkipResNet, respectively. Clearly, a better surface interpolation has been carried using the proposed method. More details are listed in Table 1. This table shows that the accuracy using the SQR-SkipResNet is slightly better than Plain NN, however it is worth nothing that these functions are non-smooth and a slightly changes in error would affect the quality of interpolation tremendously as shown in Fig. 6. However to reach a better accuracy, the SQR-SkipResnet requires larger number of iterations and consequently the higher CPU time. This can be seen as the trade-off that SQRSkipResNet makes for interpolating non-smooth functions to obtain better accuracy, in contrast to the smaller CPU time it requires for interpolating smooth functions. In this example, we demonstrate the performance of the proposed method in a real case study. Specifically, we interpolate the Mt. Eden or Maungawhau volcano in Auckland, NZ, as depicted in Fig. 7(a) [11]. The available data consists of 5307 elevation points uniformly distributed in a mesh grid area of size 10 by 10 meters. Plot (b) shows the 3D surface, and plot (c) presents the contour plot of the volcano. Example 2 Figure 7: Example 2: (a) An image showcasing the Mt. Eden or Maungawhau volcano located in Auckland, New Zealand [11]. (b) A 3D surface representation generated from a dataset containing n = 5307 data points. (c) A contour plot providing insights into the topography of Mt. Eden. Additionally, we provide more details on the interpolated surface and accuracy in Fig. 8. The second row shows the interpolated surface using Plain NN, while the third row shows the results obtained with SQR-SkipResNet. Specifically, plots 8(b) and 8(e) depict the interpolated surfaces for Plain NN and SQR-SkipResNet, respectively. Similarly, plots 8(c) and 8(f) display the contour plots for both methods. Finally, plots 8(d) and 8(g) represent the contour error plots, measured by the maximum absolute error, for Plain NN and SQR-SkipResNet, respectively. Clearly, the results using SQR-SkipResNet significantly outperform those from Plain NN. The accuracy of Plain NN, specifically in terms of the maximum absolute error, improves significantly (500%) when using the SQR-SkipResNet architecture. This underscores the superiority of SQR-SkipResNet in achieving more accurate and reliable interpolation results. In our second experiment, we repeat the the previous example but this time we use Adam optimizer with the learning rate of 1.0E-3, and 10k iteration. The organization of plots are as the previous example. Plot 9(a) shows that SQR-SkipResNet works much more accurate from the beginning of the iterations with much less fluctuation compare with Plain NN (compare plots 9 (b) and 9(e), respectively, and its corresponding contour plots in 9(c) and 9(f)). We also see that the interpolated surface when using the SQRSkipResNet (plot 9(g)) can be completely better than Plain NN (plot 9(d)). The accuracy with respect to the maximum absolute error for the latter one is about 462% better than the Plain NN. A comparisopn between these two optimizers, L-BFGS-B (Fig. 8 and Fig. 9) shows a better performance using Adam for both Plain NN and proposed SQRSkipResNet. Finally we see that in all cases, SQR-SkipResNet led to better accuracy compare to Plain NN. In the concluding example regarding the interpolation problems, we analyze the effectiveness of the proposed neural network in a 3D example, specifically using the Stanford bunny model, as depicted in Fig. 10(a). The entire bunny model has been scaled by a factor of 10. A distribution of points over the bunny’s surface is illustrated in Fig. 10(b), comprising a total of 8171 data points. The validation error is performed using the following test function (refer to [12], F4): Example 3 Figure 11: Example 3: Error profile comparison for the Stanford Bunny model using LBFGS-B (top panel) and Adam optimizers (bottom panel). Training errors are indicated by the dotted line, and validation errors are represented by the solid line. In Fig. 11, the training process (dotted line) is depicted with 500 data values, while the remaining 7671 points are reserved for validation error assessment (solid line). The top panel showcases results obtained using the L-BFGS-B optimizer, while the bottom panel displays outcomes achieved through the Adam optimizer. As demonstrated in Fig. 11(a), the SQR-SkipResNet surpasses the Plain NN in terms of accuracy and convergence rate across both the training and test datasets. The recorded CPU times amount to 35 seconds for Plain NN and 15 seconds for SQR-SkipResNet. Plots (b) and (c) offer insight into the maximum absolute error, highlighting an accuracy improvement of approximately 70% when implementing the proposed network architecture. Moreover, the lower panel of the figure reveals that the efficacy of the SQR-SkipResNet method persists even when utilizing the Adam optimizer. Plot (a) illustrates a more rapid convergence rate for the proposed method when evaluated against test data. The plots (b) and (c) portraying the maximum absolute error clearly exhibit significantly improved accuracy achieved through the proposed approach. This consistent superiority serves to highlight the distinct advantages of the SQR-SkipResNet approach over its alternatives. In comparing the L-BFGS-B and Adam optimizers, it becomes evident that the former displays enhanced performance in both accuracy and CPU time, accomplishing the desired accuracy level more efficiently. To illustrate this aspect, we emphasize the significance of network depth in neural networks, as shown in Fig. 12, specifically focus focusing on F4 with One might wonder about the advantages of employing deep neural networks and their computational implications. = 500 data points and employing the L-BFGS-B optimizer. The results presented here encompass scenarios with 5, 10, and 20 hidden layers, each consisting of 50 neurons. n Conversely, in the case of SQR-SkipResNet, a deeper network correlates with improved convergence rate and enhanced accuracy. This suggests that deeper hidden layers can identify features when embedded within an appropriate neural network architecture for this particular example. This stands in contrast to our findings in the second example (Table 2), which highlighted the problem-dependent nature of selecting an optimal number of layers. In this context, the recorded CPU times for models with 5 and 20 hidden layers amount to 19 and 16 seconds, respectively. This observation suggests that deeper networks may not necessarily result in longer CPU times; rather, they can potentially expedite training due to improved convergence rates, as evident in this case. Comparing the two plots, we observe that the accuracy difference between Plain NN and SQR-SkipResNet becomes more pronounced as the network size increases. This emphasizes the crucial role of architecture selection in achieving stable results.

Physics-Informed with Power-Enhanced Residual Network: Numerical Results

This paper is available on arxiv under CC 4.0 license. Authors: (1) Ulysse Gazin, Universit´e Paris Cit´e and Sorbonne Universit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation, (2) Gilles Blanchard, Universit´e Paris Saclay, Institut Math´ematique d’Orsay, (3) Etienne Roquain, Sorbonne Universit´e and Universit´e Paris Cit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation. Table of Links Abstract & Introduction Main results Application to prediction intervals Application to novelty detection Conclusion, Acknowledgements and References Appendix A: Exact formulas for Pn,m Appendix B: Numerical bounds and templates Appendix C: Proof Appendix D: Explicit control of (16) for α=0 Appendix E: Proof of Corollary 4.1 Appendix F: The Simes inequality Appendix G: Uniform FDP bound for AdaDetect Appendix H:  Additional experiments B Numerical bounds and templates The bound proposed in Theorem 2.3 are explicit and elegant, but can be conservative in some cases and we develop here the numerical approach mentioned in Remark 2.5. Hence, let us consider

Transductive Conformal Inference With Adaptive Scores: Numerical Bounds and Templates

This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Flor Ortiz, University of Luxembour; (2) Juan A. Vasquez-Peralvo, University of Luxembour; (3) Jorge Querol, University of Luxembour; (4) Eva Lagunas, University of Luxembour; (5) Jorge L. Gonzalez Rios, University of Luxembour; (6) Marcele O. K. Mendonc¸a, University of Luxembour; (7) Luis Garces, University of Luxembour; (8) Victor Monzon Baeza, University of Luxembour; (9) Symeon Chatzinotas, University of Luxembou. Table of Links Abstract & Introduction System Model and Problem Statement Antenna Design and Training Data Generation Supervised Learning for Adaptive Beamforming Numerical Results Conclusions, Acknowledgment, and References V. NUMERICAL RESULTS The neural networks are trained offline, so they are used only for onboard satellite inference which drastically decreases the execution time, as explained in [10]. Both approaches are suitable for real-time beamforming adaptation due to the speed where Precision measures the model’s ability not to misclassify negative instances, and Recall measures the model’s ability to find all positive instances. Figure 2 shows the average KPIs obtained for the three approaches: Genetic Algorithm, Multi-Label Classification Neural Network (Approach 1), and Clustering and Classification Neural Network (Approach 2) after running and testing the three approaches iteratively with a sample size greater than 50,000 samples. The Genetic Algorithm outperforms almost all the evaluated KPIs. However, the time required for execution and obtaining the beamforming matrix makes this algorithm unsuitable for real-time applications. On the other hand, both supervised learning-based approaches significantly reduce the execution time by more than a thousand times. This is because after training the ML models, they can be used for inference with almost immediate response times, making them suitable for real-time adaptation. Additionally, both ML-based approaches consistently maintain system performance above 90 Regarding classification metrics, Approach 2 outperforms Approach 1 because binary classification is typically less complex than multi-label classification. However, in terms of overall system performance, Approach 1 performs better than Approach 2.

Supervised Learning Based Real-Time Adaptive Beamforming On-board: Numerical Results

Authors: (1) Davide Viviano, Department of Economics, Harvard University; (2) Lihua Lei, Graduate School of Business, Stanford University; (3) Guido Imbens, Graduate School of Business and Department of Economics, Stanford University; (4) Brian Karrer, FAIR, Meta; (5) Okke Schrijvers, Meta Central Applied Science; (6) Liang Shi, Meta Central Applied Science. Table of Links Abstract & Introduction Setup (When) should you cluster? Choosing the cluster design Empirical illustration and numerical studies Recommendations for practice References A) Notation B) Endogenous peer effects C) Proofs 5 Empirical illustration and numerical studies In this section we illustrate the properties of the procedure in two empirical applications, one using unique data from the Facebook friendship and messaging graphs, and one using data from an experiment conducted in rural China by Cai et al. [2015]. We provide further evidence supporting our theoretical analysis using simulated networks in Section 5.3. 5.1 Clustering on Facebook graphs We first study the procedure’s properties for two clustering algorithms implemented at scale on social networks owned by Meta: Louvain algorithm [Blondel et al., 2008], Balanced Partitioning [Kabiljo et al., 2017]. We consider two graphs owned by Meta. In each graph, edges are continuous variables. In the first graph, edges capture the strength of the friendship in the Facebook graph, and in the second graph they capture connections based on messaging on Facebook, in both cases the data was aggregated and de-identified. We compute our statistics by setting the edges to be zero if below the 5th, 10th, and 50th percentile. We will refer to these graphs obtained as dense, moderate (mod), and sparse after thresholding (graphs all have a bounded maximum degree). We report the bias and variance, with the variance weighted by a parameter ξn, defined respectively as Louvain and Balanced Partitioning clustering produce a hierarchical clustering structure with a growing number of clusters. We consider three “types” of such algorithms, corresponding to three levels in the clustering structure hierarchy (i.e., different numbers of clusters), defined as Type 1, 2, and 3, respectively. For Louvain clustering, higher-order types denote more clusters, whereas it is the opposite for Balanced Partitioning. For each clustering, we report log(Kn/n), log-ratio of the number of clusters over the population size. Table 2 collects each of these algorithms’ worst-case bias and variance and the number of clusters per individual. Louvain algorithm dominates Balanced Partitioning both in worstcase variance and bias. A larger number of clusters increases the bias but decreases the variance, which we observe throughout all graphs. The bias increases for sparser networks because the denominator |Ni | decreases. Figure 3 reports the objective function for different graphs, Louvain algorithms, and degrees of sparsity. For ξn ≈ 1, the Louvain algorithm with the largest number of clusters (Type 3) dominates the other two algorithms in all but one case. This result provides some interpretable comparisons for the number of clusters. We also observe a trade-off between the number of clusters and the degree of sparsity of the adjacency matrix as ξn decreases. Louvain clustering with the largest number of clusters (Type 1) is optimal for a dense graph with ξn ≫ 1. Such clustering, however, is sub-optimal as the graph becomes more sparse. This result is intuitive: for denser networks, a larger number of clusters may best control the estimator’s bias relative to the bias induced by other clustering algorithms. These comparisons motivate trade-offs in the choice of the graph (and its density) and the clustering algorithm. We recommend practitioners compare clustering by averaging objective functions over different sparsity thresholding. For example, it is possible to compare clustering based on the average objective across different graphs using some priors on the degree of sparsity without affecting our theoretical results. Finally, note that using Theorem 3.6 it is possible to compute the smallest values of the spillover effects that would motivate using a cluster instead of Bernoulli design. From Theorem 3.6, researchers should prefer a cluster over a Bernoulli design if In summary, our results shed light on using clustering algorithms for large-scale implementation on online platforms. These results suggest that Louvain clustering with possibly many clusters performs best in practice. It confirms intuitive arguments in Karrer et al. [2021] who also recommend Louvain clustering based on AA-tests. 5.2 Clustering in the field We consider as an application the problem of informing individuals to increase insurance takeup studied in Cai et al. [2015]. The authors collected network information in approximately 184 villages in rural China from 48 larger regions. We use network data collected by Cai et al. [2015] to study the properties of the proposed method, where we assume that two individuals are connected if at least one of the two indicates the other as a friend. Because we do not require information from end-line outcomes, we construct a network using information from surveyed individuals as well as their friends. The network has in total 7649 nodes, once we also include individuals who are friends of surveyed individuals (but do not necessarily live in their same village or were surveyed in the experiment). Individuals between villages present on average 50% of their connections outside their village. On the other hand, individuals in different regions (with approximately 50 regions) have 99% of their connections within the same region. We use an adjacency matrix a “weak ties” adjacency matrix, where two individuals are connected if either indicates the other has a friend. We study clustering within each region and report results for different clustering algorithms. Clustering within each region is performed as in Algorithm 1, where we first estimate Xˆ (K) via semi-definite programming, use K-means algorithm to retrieve the clusters from Xˆ (K) and iterate to estimate the optimal number of clusters K. We report the frontier with respect to the absolute bias consistently with Algorithm 1. 5.2.1 How many clusters should we choose? Figure 4 presents the main results. The left-hand side panel reports the average number of estimated clusters, estimated by the proposed method divided by the population size in a given cluster. Different choices of ξn justify a different number of clusters. For ξn = 1, the number of clusters is 7%, the total population size, whereas for ξn = 15, the number of clusters is roughly half the population size. To gain further intuition of its practical implication, take ψ¯ = 0.24 approximately equal to the outcomes’ variance in Cai et al. [2015] and ϕ¯ n = 0.27 as in Table 2 in Cai et al. [2015]. A recommended choice of ξn is approximately ψ/¯ ϕ¯2 n = 3.29. This choice puts slightly more weight on the bias than the variance when λ = 1, and therefore can be considered a conservative choice for the number of clusters.[13] Even with such a conservative choice, the suggested number of clusters is large relative to the population size. In this case, the optimal number of clusters is around 15% of the overall population size, approximately 600 clusters with a surveyed sample size of 3600 individuals. This number is consistent (in scale) with the choice in the number of clusters in other applications in development, such as Egger et al. [2022], Alatas et al. [2012], but larger than the number of villages that we have in the application in Cai et al. [2015]. 5.2.2 Comparison with other clustering methods Next, we compare the procedure (denoted as “Causal Clustering”) with the following alternative clustering algorithms: ε-net clustering as in Eckles et al. [2017] with ε = 3 as suggested in Eckles et al. [2017]; spectral clustering with a fixed number of clusters equal to n/3, where n is the population size in a given region (note that spectral clustering do not optimize over the number of clusters); Louvain clustering with default parameters selected by the R-package igraph; clustering based on village identity of each individual (creating one additional cluster for those individuals whose village is missing in the data). We contrast the objective function with alternative algorithms in the right-hand side of Figure 4. The proposed method achieves the smallest objective function across all competitors, providing suggestive evidence that Algorithm 1 (with a semi-definite relaxation) works particularly well in practice. For a smaller number of clusters the method is closer to the Louvain clustering algorithm, while for a larger number of clusters the objective of the algorithm is close to the objective of the spectral algorithm. Interestingly, clustering based on village identity leads to the largest loss function. This is because individuals are connected within and between villages in this application. Finally, in Figure 5 (first three panels), we report the mean-squared error obtained by simulating the model in Cai et al. [2015] (Table 2, Column 4) and vary the variance of the residuals σ 2 ∈ {1/4, 1/2, 1} to emulate settings with high, medium and low signal to noise ratio. The model in Cai et al. [2015] assumes that individual outcomes depend on neighbors’ treatments, consistently with our Assumption 1. Our method uniformly outperforms competitors in terms of mean-squared error, except for the Louvain algorithm when the signal-to-noise ratio is particularly high, but not in the remaining settings. In the last panel, we consider settings where the local interference assumption is violated, and we calibrate our model to the specification in Cai et al. [2015] (Column 4, Table 5), where the individual outcome depends on the neighbors’ outcomes, violating Assumption 1 and introducing global dependence. We fix the residuals’ variance to be σ 2 = 1/4, whereas the results are robust as we increase σ 2 . In this setup, we observe a larger mean-squared error of all methods, with the proposed method achieving the lowest mean-squared error. 5.3 A numerical study Next, we illustrate the properties of the method in numerical studies. We consider three different data generating processes for the network formation: a geometric network formation, Albert Barabasi network and Erdos-Renyi graph. The geometric network takes the form Ai,j = 1{|Xi,1 − Xj,1|/2 +|Xi,2 − Xj,2|/2 ≤ rn} where rn = p 4/2.75n similarly to simulations in Leung [2020]. Here, Xi,1, Xi,2 are drawn independently from a uniform distribution between [−1, 1]. For the Albert-Barabasi network we first draw n/5 edges uniformly according to Erdos-Renyi graph with probabilities p = 10/n, and second, we draw sequentially connections of the new nodes to the existing ones with probability equal to the number of connection of each pre-existing node divided by the overall number of connections. Finally, the Erdos-Renyi graph is generated with probability of connection p = 2/n. We study the properties of the proposed method and of the same competitors discussed in Section 5.2. Figure 6 showcases that the proposed procedure leads to the lowest objective function. This result is consistent with our theoretical findings. Figure 7 showcases that the number of clusters increases in the sample size, varies substantially across different data generating processes, and increases in ξn. [13] This follows from the fact that ξn is proportional to ψ/¯ ϕ¯2 n for clusters whose bias is of order O(ϕ¯ n), and researcher’s goal is to minimize the worst-case mean squared error (λ = 1). This paper is under CC 1.0 license. available on arxiv

Design of Cluster Experiments: Empirical Illustration and Numerical Studies

The Story-book of Science by Jean-Henri Fabre, is part of the HackerNoon Books Series. You can jump to any chapter in this book here . A NUMEROUS FAMILY CHAPTER VII. A NUMEROUS FAMILY “APLANT-LOUSE, we will suppose,” resumed Uncle Paul, “has just established itself on the tender shoot of a rosebush. It is alone, all alone. A few days after, young plant-lice surround it: they are its sons. How many are there? Ten, twenty, a hundred? Let us say ten. Is that enough to assure the preservation of the species? Don’t laugh at my question. I know well that if the plant-lice were missing from the rosebushes, the order of things would not be sensibly changed.” “The ants would be the most to be pitied,” said Emile. “The round earth would continue to turn just the same, even when the last plant-louse was dying on its leaf; but it is not, in truth, an idle question to ask if ten plant-lice suffice to preserve the race; for science has no higher object than the quest of providential means for maintaining everything in a just measure of prosperity. “Well, ten plant-lice coming from one would be far too many if we did not have to take account of destructive agencies. One replacing one, the population remains the same; ten replacing one, in a short time the number increases beyond all possible limits. Think of the dervish’s grain of wheat doubled sixty-four times, so that it becomes a bed of wheat of a finger’s depth over the whole earth. What would it be if it had been multiplied ten times instead of doubled! In like manner, after a few years, the descendants of a first plant-louse, continually multiplied tenfold, would be in straitened circumstances in this world. But there is the great reaper, death, which puts an invincible obstacle to overcrowding, counterbalances life in its overgrowing fecundity, and, in partnership with it, keeps all things in a perpetual youth. On a rosebush apparently most peaceful there is death every minute. But the small, the humble, and weak, are the habitual pasture, the daily bread, of the large eaters. To how many dangers is not the plant-louse exposed, so tiny, so weak, and without any means of defense! No sooner does a little bird, hardly out of the shell, discover with its piercing eyes a spot haunted by the plant-lice, than, merely as an appetizer, it will swallow hundreds. And if a worm, far more rapacious, a horrible worm expressly created and put into the world to eat you alive, joins in, ah! my poor plant-lice, may God, the good God of little creatures, protect you; for your race is indeed in peril. “This devourer is of a delicate green with a white stripe on its back. It is tapering in front, swollen at the back. When it doubles itself up it takes the shape of a tear-drop. They call it the ants’ lion because of the ravages it makes in the stupid herd. It establishes itself among them. With its pointed mouth, it seizes one, the biggest, the plumpest; it sucks it and throws away the skin, which is too hard for it. Its pointed head is lowered again, a second plant-louse seized, raised from the leaf, and sucked. Then another and another, a twentieth, a hundredth. The foolish herd, whose ranks are thinning, do not even seem to perceive what is going on. The trapped plant-louse kicks between the lion’s fangs; the others, as if nothing were happening, continue to feed peacefully. It would take a good deal more than that to spoil their appetite! They eat while they are waiting to be eaten. The lion has had enough. He squats amidst the herd to digest at his ease. But digestion is soon over and already the greedy worm has its eye on those that he will soon crunch. After two weeks of continual feasting, after having browsed as it were on whole herds of plant-lice, the worm turns into an elegant little dragon-fly with eyes as bright as gold, and known as the hemerobius. Ladybug (a) larva (b) pupa (c) first joint of larva “Is that all? Oh, no. Here is the lady-bug, the good God’s bug. It is round and red, with black spots. It is very pleasing; it has an innocent air. Who would take it also to be a devourer, filling its stomach with plant-lice? Look at it closely on the rosebush, and you will see it at its ferocious feasting. It is very pretty and innocent-looking; but it is a glutton, there is no denying the fact, so fond is it of plant-lice. “Is that all? Oh, no. Those poor plant-lice are manna, the regular diet of all sorts of ravagers. Young birds eat them, the hemerobius eats them, lady-birds eat them, gluttons of all kinds eat them; and still there are always plant-lice. Ah! that is where, in the fight between fecundity which repairs and the rough battle of life which destroys, the weak excel by opposing legions and legions to the chances of annihilation. In vain the devourers come from all sides and pounce upon their prey; the devoured survive by sacrificing a million to preserve one. The weaker they are, the more fruitful they are. “The herring, cod, and sardine are given over as pasturage for the devourers of the sea, earth, and sky. When they undertake long voyages to graze in favorable spots, their extermination is imminent. The hungry ones of the sea surround the school of fish; the famished ones of the sky hover over their route; those of the earth await them on the shore. Man hastens to lend a strong hand to the killing and to take his share of the sea food. He equips fleets, goes to the fish with naval armies in which all nations are represented; he dries in the sun, salts, smokes, packs. But there is no perceptible diminution in the supply; for him the weak are infinite in number. One cod lays nine million eggs! Where are the devourers that will see the end of such a family?” “Nine million eggs!” exclaimed Emile. “Is that a great many?” “Just to count them, one by one, would take nearly a year of ten working hours each day.” “Whoever counted them had lots of patience,” was Emile’s comment. “They are not counted,” replied Uncle Paul; “they are weighed, which is quickly done; and from the weight the number is deduced. “Like the cod in the sea, the plant-lice are exposed on their rosebushes and alders to numerous chances of destruction. I have told you that they are the daily bread of a multitude of eaters. So, to increase their legions, they have rapid means that are not found in other insects. Instead of laying eggs, very slow in developing, they bring forth living plant-lice, which all, absolutely all, in two weeks have obtained their growth and begin to produce another generation. This is repeated all through the season, that is to say at least half the year, so that the number of generations succeeding one another during this period cannot be less than a dozen. Let us say that one plant-louse produces ten, which is certainly below the actual number. Each of these ten plant-lice borne by the first one bears ten more, making one hundred in all; each of these hundred bears ten, in all one thousand; each of the thousand bears ten, in all ten thousand; and so on, multiplying always by ten, eleven times. Here is the same calculation as the dervish’s grain of wheat, which grew with such astonishing rapidity when they multiplied it by two. For the family of the plant-lice the increase is much more rapid, as the multiplication is made by ten. It is true that the calculation stops at the twelfth instead of going on to the sixty-fourth. No matter, the result would stupefy you; it is equal to a hundred thousand millions. To count a cod’s eggs, one by one, would take nearly a year; to count the descendants of one plant-louse for six months would take ten thousand years! Where are the devourers that would see the end of the miserable louse? Guess how much space these plant-lice would cover, as closely packed as they are on the elder branch.” “Perhaps as large a place as our garden,” suggested Claire. “More than that; the garden is a hundred meters long and the same in width. Well, the family of that one plant-louse would cover a surface ten times larger; that is to say, ten hectares. What do you say to that? Is it not necessary that the young birds, little lady-bugs, and the dragon-fly with the golden eyes should work hard in the extermination of the louse, which if unhindered would in a few years overrun the world? “In spite of the hungry ones which devour them, the plant-lice seriously alarm mankind. Winged plant-lice have been seen flying in clouds thick enough to obscure the daylight. Their black legions went from one canton to another, alighted on the fruit trees, and ravaged them. Ah! when God wishes to try us, the elements are not always unchained. He sends against us in our pride the paltriest of creatures. The invisible mower, the feeble plant-louse, comes, and man is filled with fear; for the good things of the earth are in great peril. “Man, so powerful, can do nothing against these little creatures, invincible in their multitude.” Uncle Paul finished the story of the ants and their cows. Several times since, Emile, Jules, and Claire have talked of the prodigious families of the plant-louse and the cod, but rather lost themselves in the millions and thousand millions. Their uncle was right: his stories interested them much more than Mother Ambroisine’s tales. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Jean-Henri Fabre (2018). The Story-book of Science. Urbana, Illinois: Project Gutenberg. Retrieved https://www.gutenberg.org/cache/epub/56795/pg56795-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org , located at https://www.gutenberg.org/policy/license.html.

A NUMEROUS FAMILY

: offers the , a tool to help Data Scientists automate their weekly submission pipeline for the Numerai tournament. This CLI configures a in and automatically deploys your model to it. tl;dr Numerai numerai-cli Numerai Prediction Node Amazon Web Services (AWS) . 🚀 This guide describes how I set up my own weekly submission pipeline from scratch, using for free Microsoft Azure and python 🤖 Just give me the code: https://github.com/papaemman/azure-functions-with-python What is Numerai? is a quant hedge founded in San Francisco, CA, in 2015, built on thousands of crowdsourced machine learning models. Every week, Numerai gives away data so that Data Scientists worldwide have free, hedge-fund quality data to develop their Machine Learning (ML) / Deep Learning (DL) models — data they would otherwise not have access to. Numerai At the beginning of each round, competitors can stake (a cryptocurrency issued by Numerai) on the predictions they submit if they want to get paid (or "burnt") based on the predictive accuracy of their models. Staking on a model is fundamentally a type of "bet" competitors take towards the performance of their own model's predictions. NMR tokens Numerai Compute CLI Competing in Numerai is an ongoing, never-ending challenge because competitors need to download the new data every week and submit their predictions based on them. is a framework aiming to help participants automate their weekly submission workflow. Using the , participants can "provision" their cloud infrastructure in and deploy their pre-trained models as a Prediction Node that can Numerai Compute numerai-cli Amazon Web Services (AWS) be triggered by Numerai every weekend download new tournament data run the ML models and upload predictions to Numerai The configures a Numerai Prediction Node in Amazon Web Services (AWS). This solution is architected to cost less than on average, but actual costs may vary. numerai-cli $5/month You need 4 things to use Numerai CLI: , , , and . Docker Python Numerai API Keys AWS API Keys Why not just use Numerai Compute? 1. Cost Last week was tough for the crypto market. carried away the whole crypto market. Currently (May 2022), the NMR token has a price of around . Therefore, saving per month and investing them in buying more NMR to stake in your models is an appealing idea. The massive crash of LUNA 13$ 5$ 2. Learn something new When building something from scratch, you have the opportunity to understand how it works under the hood. Last year, I deep-dived into Microsoft Azure cloud technologies, and I wanted to test if my skills were enough to build a real-world solution. 4. Don't have an AWS account Many professionals prefer to work with other Cloud providers than AWS, such as or Google Cloud Platform. Setting up a new AWS account, adding billing information, and finding your way into the AWS console might seem like a lot of work. *, this guide is for you.* Microsoft Azure If you prefer to use Azure Goal Automate my weekly submission pipeline, for the Numerai Tournament, using Azure and python, with zero cost. Azure offers many services adequate to solve this task, but I decided to use Azure Functions after some research. is a cloud service available on-demand that provides all the continually updated infrastructure and resources needed to run your applications. You focus on the pieces of code that matter most to you, and Functions handles the rest. Functions provides serverless compute for Azure. Azure Functions Going for a is a great way to because you don't need to pay for the infrastructure you don't use. And if you already have the code you want to run, setting up an Azure function is . Also, Azure offers a which is more than enough for this project's scope. serverless architecture save money and time easy free tier, Thus my goal was to create an Azure Function that will: ⏲️ be triggered every Sunday 🔋interact with the Numerai API to download numerai_live_data and upload my predictions 💾 interact with Azure Storage to read and store and data pre-trained ML/DL models numerai_live_data numerai_predictions 📥 send a fun email notification after the submission 😊 allow me to enjoy my weekend MS Azure Architecture Design Technical Implementation Prerequisites Azure Account and VSCode Azure Extension Python 3.8 Azure Functions Core Tools Azure Storage Explorer Numerai API Keys Trained ML/DL models and inference python code Setup 1. Setup all prerequisites Download and install the required software Create your accounts in Azure and Numerai 2. Open VSCode and create a new local Azure function project While you don't have any workspace opened in VSCode, go to the extension, find and select _Create New Project…- S_elect , , and a to create a virtual environment- Select the template, give a name to the function, and set up the timer to run every [* 0 0 * * SUN]. You don't need to set up the function to run in short time intervals. Azure functions support " . Azure FUNCTIONS Directory Language (Python) python interpreter Time Trigger Sunday Execute Function now…" to trigger it manually within VSCode for testing purposes 3. Then, the VSCode will create a with a time-trigger function sample code. automatically Local project ## Azure function project codebase structure
.
├── .venv                     # Python Virtual environment
├── .vscode                   # Configuration options for VSCode
├── host.json                 # Configuration options that affect all functions in a function app instance
├── local.settings.json       # Maintains settings used when running functions locally.These settings aren't used when running in Azure
|
├── AzureFunction_1
│ ├── function.json           # Azure Function Settings
│ ├── __init__.py             # Python Code
│ └── readme.md               # Documentation
|
├── AzureFunction_2
│ ├── function.json           
│ ├── __init__.py             
│ └── readme.md               
|
└── requirements.txt          # Package dependencies (Open VSCode and Press F5 or 4. Run the Function locally Run →Start Debugging) To debug, you must select a storage account for internal use by the Azure Functions runtime: Select a , create a , create a and select a for resources. Keep in mind that this is a . subscription new storage account new resource group, location temporary resource group Go to extension, find and go to . Find the function, right-click, and select Azure FUNCTIONS Local Project Execute Function now… Examine functions' logs Stop the function (ctrl+c) Delete the resource group Important note ⚠️ ”, update the extensionBundle “version”: “[2.*, 4.0.0)” If you get an error “connect ECONNREFUSED 127.0.0.1:9091 to version , in host.json file. 5. Publish the project to Azure Go to extension_,_ find and select Azure FUNCTIONS, Deploy to Function App… Select a and subscription create a new function App Select a and for the new resource runtime stack location This will create a new resource group with an App Service Plan, a Function App, a Storage Account, and an Application Insights service. 6. Run the Function in Azure Go to extension, find , open the related and find the function app. Azure FUNCTIONS subscription Open the function app, find the specific function and select This will run the function to the Azure environment. Execute Function now…. You can see the function logs in the Live metrics tab using the Application Insights resource. 7. Download the function app settings Open VSCode and download remote settings in the Local environment for the function App ( and select Azure Functions: Download Remote Settings) F1 This will update the file with info about App service Plan, Function App, Storage Account, and Application Insights. local.settings.json 8. Setup the Azure Storage account. Open the connect with your Azure account and find the related storage account inside the newly created resource group. Azure Storage Explorer, Create a new Blob container called and upload all your pre-trained ML models there. production-models Create a new Blob container called to store numerai_live_data for every round. live-data Create a new Blob container called to store numerai_predictions for every round. predictions-files 9. Purchase the Twilio SendGrid SaaS offering from Microsoft Azure Marketplace To send a notification email every time the function triggered and submitted predictions, I decided to use the Twilio SendGrid's Email API Purchase the Twilio SendGrid offer (free tier) from Microsoft Azure Marketplace and configure your account on their platform. Get API keys from Twilio SendGrid 10. Configure Function App Having the and hardcoded in the source code is a terrible practice. Azure Functions offers a dedicated Function's App configuration to store environmental variables and secrets. Numerai API Keys Twillio Seng Grid API keys Open the , find the and go to . The complete set of Environment Variables is stored in the Application settings by default. This helps developers define input/output bindings with other resources in Azure. Azure portal Function App service Configuration Create 2 new application settings and store Numeai API Keys and SendGridKeys NumeaiAPIKeys →secret_key=***;public_id=***” SendGridKeyss →*** Open VSCode and re-download remote settings to the local environment ( and ) to get the new Application Settings into the file. F1 Azure Functions: Download Remote Settings local.settings.json 11. Write the Python code Now it's time to write (or copy-paste) the python code responsible for reading the numerai live data & pre-trained ML/DL models and submitting predictions using Numerai API. The input and output configurations (configurations and paths to load and store files) are the only thing you have to modify in your previous python code (running locally) to run it as an Azure Function. Instead of local paths, you should use the newly created Storage Account. For this, you need to use the . Azure Storage Python SDK Go to the file and replace your python code. .py init 12. Run the Function locally and verify that it is working Run the locally ( F5 or Run → Start Debugging), go to A_zure extension,_ find the Function in , and select ` Function Local Project ExecutFunctionon now… Check Function's logs and the connection with the Azure Storage Account Stop the Function (ctrl+c) 13. Redeploy and verify the updated App Go to extension, find , and select Azure FUNCTIONS Deploy to function App… After the deployment completes, find the Function under the respective subscription in VSCode, right-click to function, and select Execute Function now… Check Function's logs in the Metrics tab for this Function. Conclusions Last Sunday, I woke up to this fun email from myself, letting me know that everything went as planned. The Azure Function was triggered on Sunday at 00:00:00 UTC, the Numerai submissions were successful, and I was able to enjoy my day! 🌞 Email Notification for successful submission PS. Check the awesome quote at the end. I added a random quote generator inside the function creating the email notification just to spark things up ✨ Get in touch I hope you liked this guide. If you have any questions or just want to introduce yourself, don't hesitate to reach out! Panagiotis Papaemmanouil 📧 papaemman.pan@gmail.com 💬 https://www.linkedin.com/in/panagiotis-papaemmanouil/ 🌐 https://papaemman.com/ 🔥 Check my under the name Numerai Models PAPAEMMAN https://numer.ai/papaemman1 Also Published here

Automate Submissions for the Numerai Tournament Using Azure Functions and Python

is not only a crypto trading platform with a great name, it also has its own coin called crypto.com coin. Crypto.com Crypto.com platform which supports its own coin is fast becoming one of the popular platforms to buy and sell your cryptocurrency.  From its , Crypto.com has been making strides to differentiate itself and take a slice of the market. inception in 2016 Currently, the Singapore exchange company supports over 10 million users and 3,000 employees.  It has secured some very impressive partnerships deals with the , , , ., , , and the most notable is the purchase of naming right to the . UFC Formula one Lega Series A Paris Saint-Germains F.C the Philadelphia 76ers Montreal Canadiens Los Angeles Staples Center The deal with the Los Angeles Staples Center was a reported that changes the name of the center to Crypto.com for 20 years. 700 million dollar acquisition Considering the aforementioned achievements, it is appropriate to question why crypto.com is currently at and yet to demolish the one-dollar mark. 0.7507 One can become even more worried for crypto.com when juxtaposed with its competitor . Binance Binance started just one year after Crypto.com in 2017, it also has its own coin called Binance coin. However, the Binance coin is currently at with a market cap of . Those numbers show a clear difference from Crypto.com. $631.52 per coin $103 billion Price Disparity Between Crypto coin and Binance coin. What could be the cause of such huge price disparity between Binance coin and Crypto coin?  There are several factors, but I will point out some critical ones. One possible factor is that Binance is still a private company that has a total of , with still the largest shareholder. $1B in funding CEO CZ Zhao The company also only uses one-fifth of profits to repurchase and permanently in their treasury. burn Binance coins Lastly, Binance has been aggressively acquiring new markets by securing to operate all over the world. licenses Crypto.com on the contrary is a public company that has raised a relatively meager total of $26.7 million in round one funding. It also raised an additional $200 million under its crypto fund.  However, it is evident that most of those funds, including their profits may have been diverted into potentially lucrative partnership deals. With such strategic partnerships, I believe that in five years, Crypto.com coin will surpass the top trading platforms such as Binance and . Coinbase Also published here: https://libranews.com/2021/11/26/will-crypto-com-coin-meet-expected-growth-after-sponsorship-deals/

Is Crypto.com Poised for Growth After Numerous Partnership Deals?

Technology is progressing, so are the cyberattacks. Do you know that there is a new cyberattack every ? Innocent people came across 2,200 attacks every single day. For every lock, there is always someone out there who is trying to break in or pick it. Cyberattacks are not what makes the cold war cold. As a strategic matter, they do not differ fundamentally from older tools of sabotage and espionage. 39 seconds These are evolving with the speed of light and will keep on evolving. Nearly 95% of all digital data breaches are due to human error. But will the tech giants let these cases evolve? cyberattacks Are they acquiring appropriate measures to combat these counterfeits and unauthorized access? It’s high time for enterprises and financial infrastructures to invest a hefty amount for the enhancement of safety and security measures. Organizations of all sizes deal with different sorts of people and data each day. Enhancement of cybersecurity measures is crucial because it protects all categories of data from unauthorized access and damages. “The Biden administration is coming up with a $100 billion investment plan as cybersecurity spending as permit receipts will be required to source from credible vendors. ” Recent Cyberattacks Recap A single vulnerability is more than enough for a hacker to break into the system. The United States of America faced a series of attacks. Let’s have a quick look at all of them. A wide range of organizations were potentially compromised after the cyberattack on the Microsoft exchange. The cybercriminal utilized previously known vulnerabilities in the email software and some stolen passwords to access the targeted network. Microsoft claimed that the cybercriminals are state-sponsored. Microsoft also affirmed that hackers were operating out of China.  While it was priorly considered that the number of hackers had been limited, it has since then reported the progressive utilization of sophisticated tactics. Hackers are piling up to benefit from the current public vulnerabilities before systems are patched. While talking of cyberattacks, let’s not forget talking about the SolarWinds attack. On , the president of the United States Joe Biden signed an executive order staggering fresh sanctions on Russia over a pattern of malicious cyberattacks against the United States and allies, including the SolarWind Attack that occurred in December 2020, that has now formally attributed to Cosy Bear or Russian state-backed APT29. 15th April 2021 Talking of recent incidents, the shut down its operations and notified federal agencies that it has fallen victim to a ransomware attack. This act was carried out by the cyber group called DarkSide and forced the company to shut down approximately 5,500 miles of pipeline, resulting in the disruption of almost half of the east coast fuel supply of the nation. colonial pipeline The ransomware attack involves malware and that encrypts files, resulting in making the system inoperable. $2 Trillion Infrastructure Plan Considering these evolving cyberattacks, the Biden administration explains their recent cybersecurity spending, which involved a $2.3 trillion plan. That plan involves $20 billion in energy infrastructure investments for tribal, state, and local governments that are unforeseeable on cybersecurity modernization. The White House that: claimed “Modernization block grants will be specifically utilized for the enhancement of technology, energy, and security standards in the 21st century.  The eligibility of such grants will be fortuitous on such policies that require the installation of technology, which proves to be beneficial for the detection and inspection of malicious cyberattacks on operational and informational security networks, which was consistent with privacy protection.” The plan of this infrastructure involves the investment of $200 billion, making services more reliable, secure, and affordable for the nation of America. Prior, the Biden administration secured more than $1 billion in American Rescue Plan funding for the modernization of the cybersecurity infrastructure of the federal government. Related stocks involve CrowdStrike (NASDAQ: ), CyberArk (NASDAQ: ), and FireEye (NASDAQ: ). Biden signed an executive based on cybersecurity last week for the enhancement of cybersecurity protocols of the nation and modernizing the nation’s defenses. CRWD CYBR FEYE The announcement came after the Colonial Pipeline breach encountered by RaaS group Darkside. My Opinion Businesses and infrastructures deal with different sorts of sensitive data and the protection of that data is crucial. Having said that, a hefty investment for the enhancement of cybersecurity protocols is mandatory for tech giants to dodge cybercriminals. I personally believe that the Biden step for the acquisition of $2T infrastructure is a splendid measure to keep in view progressing ransomware and cyberattacks that are occurring in a series. There is no doubt that cyberattacks are never going to stop but appropriate measures and solutions can be acquired to dodge them. Cybercriminals are always crawling to find sophisticated tactics to have unauthorized access to the network. As a result, the network lost billions and trillions of dollars along with data breaches. Infrastructure from all across the globe must attain lessons from the $2T infrastructure plan of the United States of America and invest a hefty amount for the modernization of cybersecurity infrastructure. There exists a vast range of products that provides real-time, reliable, and robust AI-powered that provides KYC/AML compliance, biometric authentication, face verification, OCR data extraction, document verification, age verification, and more. Hence infrastructures must not think twice when it comes to the enhancement of security protocols and must not compromise in that aspect at all. identity verification

Biden Administration Prioritizes Cybersecurity Funding After Numerous Cyberattacks

A is a symbol or group of symbols that represents a number. The symbols “11(decimal)”, “1011(binary)” and “B(hexadecimal)” are numerals, all representing the number. The number is the idea, the numeral is anything that represents that idea. numeral Numerals are not the same as numbers just as words are not the same with the things they refer to. different same A positional numeral system denotes usually the extension to any of the (or ). In a more general sense, a positional system is a numeral system in which the to the value of a number is the . base Hindu–Arabic numeral system decimal system contribution of a digit value of the digit multiplied by a factor determined by the position of the digit In modern positional systems, such as the , the of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five , five , and five , respectively, due to their different in the digit string. decimal system position hundreds tens units positions According to its of occurrence in the number, each digit is . Towards the left, the weights increase by a constant factor equivalent to the or . With the help of the radix point (‘.’), the positions corresponding to integral weights (1) are differentiated from the positions corresponding to fractional weights (<1). position weighted base radix Any integer value that is greater than or equal to two can be used as the base or . radix The digit position ’ ’ has weight . . n r ^n The largest value of digit position is always 1 less than the base value The value of a number is a weighted sum of its digits. For example: Decimal (0–9 digits with radix 10) 2056 value breakdown Hexadecimal(0–9 & A-F digits with radix 16) 171B value breakdown The general form of value breakdown, where b is the base or radix of the numeral system The Idea to package Quick Link I wanted to be able to and play around with without having to worry about the semantics of each system. At the end of the day, as we mentioned before can represent the . So even operations between numerals from different systems shouldn’t be an issue when they can be translated to represent the same numbers. implement any numeral system the representation of numbers multiple different numerals same number For some reason, an image from the movie flashed in my head. The where machine, the , came to life and the mechanical rotors started spinning. Imitation Game beloved moment in human history Alan Turing’s bombe A digit in any positional numeral system can be by the it can take. Each state has a and a . The of the is the while producing a . represented possible states next state previous state next state last state first state carry-over A data structure like a can effectively represent what we mentioned in the above paragraph. circular list , . In a doubly-linked circular list the next pointer of the last node points to the first node, and the previous pointer of the first node points to the last node making the circular in both directions Here comes Go’s . With the ring, we can easily represent of by filling it with the possible ordered states and an initial value. ring any single digit any positional numeral system { r := ring.New( (values)) _, e := values {
      r.Value = e
      r = r.Next()
   } indexOf(state, values) == { , fmt.Errorf( , state, values)
   } values { r.Value == state { }
      r = r.Next()
   } r, } // newDigit creates and initializes a new digit (ring). func newDigit (values [] , state ) rune rune (*ring.Ring, error) // initialize a new empty ring len // fill the ring with values for range if -1 return nil "invalid digit. value: %v does not exist in possible values: %v" // roll the ring in desired "state" position. for range if break return nil What happens when a numeral contains more than one digit? That can easily be solved by having a whose elements would be consisted of doubly-linked list doubly-linked circular list s. This way we can easily create positional representation of any number. any { number := Numeral{
      digits:      list.New(),
      digitValues: values,
   } i := ; i < (initial); i++ {
      digit, err := newDigit(values, (initial[i])) err != { , err
      }
      number.digits.PushBack(digit)
   } &number, } // NewNumeral initializes a numeral by providing the initial number in strings // along with the possible values that each digit can have. func NewNumeral (values [] , initial ) rune string (*Numeral, error) // initialise a new number. // add digits to the number along with their state. for 0 len rune if nil return nil return nil Every time a resets back to the “first” state it would trigger a to the next most valuable digit. Pretty simple right? digit Next() In the case that our digits are all full and we want to increment, we can just create a new ring, initialize it and link it to the left side of our list. Think of an example, a hypothetical numeral system with which has a , and also imagine that we want to have a 4 “digit numeral” like “2z3r”. symbols [0–9,a-z] radix of 36 Numeral {
   digits      *list.List
   digitValues [] } // Numeral represents a numeral that is consisted by its digits // and digit values. type struct rune By defining a number like this all you need to have is a you want to your number . slice of the symbols represent in the order they will have to exist values= [] { , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , } var rune '0' '1' '2' '3' '4' '5' '6' '7' '8' '9' 'a' 'b' 'c' 'd' 'e' 'f' 'g' 'h' 'i' 'j' 'k' 'l' 'm' 'n' 'o' 'p' 'q' 'r' 's' 't' 'u' 'v' 'w' 'x' 'y' 'z' Then you need a “constructor” to generate numerals at will. { number := Numeral{
      digits:      list.New(),
      digitValues: values,
   } i := ; i < (initial); i++ {
      digit, err := newDigit(values, (initial[i])) err != { , err
      }
      number.digits.PushBack(digit)
   } &number, } // NewNumeral initializes a numeral by providing the initial number in strings // along with the possible values that each digit can have. func NewNumeral (values [] , initial ) rune string (*Numeral, error) // initialise a new number. // add digits to the number along with their state. for 0 len rune if nil return nil return nil Initializing a numeral after we have reached this point is pretty straightforward. number, _ := numeral.NewNumeral(values, ) "2z3r" Performing Simple Operations This approach makes +1 and -1 operations since always know their next and previous node. very fast lists (either circular or not) For example: Incrementing a numeral by needs to execute The result is “12d5”. Hexadecimal “12d4” one 1 next() to the rightmost ring, that's all. Incrementing a numeral “ ” by needs to execute . The result is “e000”. Hexadecimal dfff one 4 next() calls on the 3 rightmost rings and one last on the 4th most significant ring Decrementing1will operate in a similar way. { e := n.digits.Back(); e != ; e = e.Prev() { r := e.Value.(*ring.Ring) r = r.Next()
      e.Value = r r.Value != n.digitValues[ ] { } e.Prev() == {
         d, _ := newDigit(n.digitValues, n.digitValues[ ])
         n.digits.PushFront(d)
      }
   } } // Increment performs a +1 to the Numeral. func (n *Numeral) Increment () error // take the first digit from the right and keep going if there are any arithmetic holdings. for nil // get current ring. // rotate and update. // if the digit is not being reset (no arithmetic holdings) then there is no need to // proceed in adding on the others. if 0 break // If needed add an extra new digit on the left side. if nil 0 return nil Adding and Subtracting can also happen efficiently even between numerals that are based on different systems by using the most known numbers of the decimal system that our computers easily understand. will just require both of those to , add them and generate a new numeral from the . The result numeral can even be on a different numeral system easily by generating it from an integer. Adding 2 numerals converting decimal integers result Converting any numeral to integer is easy by performing a value breakdown {
   dec := di := d := n.digits.Back(); d != ; d = d.Prev() { r := d.Value.(*ring.Ring) i := indexOf(r.Value.( ), n.digitValues) dec = dec + i*powInt( (n.digitValues), di)
      di++
   } dec
} // Decimal converts a numeral to a decimal integer. func (n *Numeral) Decimal () int 0 0 for nil // get current ring. // get the index of the ring. rune // Add digit's decimal counterpart to the decimal sum. len return Let’s Talk Numbers Running some on the method for for different initial values (small and big) results in some very nice results. The average execution time of the Increment function for binary numerals after 1 billion increments is around 7.6ns / op. benchmarks Increment() 3 different numeral systems As one may expect, therefore the transitions that need to happen are (increments/decrements)which results in better performance. selecting a numeral system with a higher numeral range results in carryovers appearing less frequently, fewer goos: linux
goarch: amd64
pkg: github.com/slysterous/numeral
cpu: Intel(R) Core(TM) i7– CPU @ GHz
BenchmarkNumeralIncrementDecimalSmall ns/op
BenchmarkNumeralIncrementDecimalLarge ns/op
BenchmarkNumeralIncrementBinarySmall ns/op
BenchmarkNumeralIncrementBinaryLarge ns/op
BenchmarkNumeralIncrementHexSmall ns/op
BenchmarkNumeralIncrementHexLarge ns/op 7700 3.60 -8 1000000000 4.604 -8 1000000000 4.574 -8 1000000000 7.644 -8 1000000000 7.655 -8 1000000000 4.427 -8 1000000000 4.652 How about converting numerals into decimal integers? From the benchmarks that I performed on Hex and Binary numerals, the process takes . The opposite process, converting from decimal ints to any numeral is similar. less than 1 μsecond Since converting to decimals , it’s easy to reach the conclusion that , . This can also be reflected in the below benchmark. requires traversing through every digit to sum its weight the more digits there are the slower the process will be go test -bench=NumeralDecimal -benchtime= s
goos: linux
goarch: amd64
pkg: github.com/slysterous/numeral
cpu: Intel(R) Core(TM) i7– CPU @ GHz
BenchmarkNumeralDecimalFromHex0– ns/op
BenchmarkNumeralDecimalFromHexfffff ns/op
BenchmarkNumeralDecimalFromHexffffffffff ns/op
BenchmarkNumeralDecimalFromHexffffffffffffffffffff ns/op
BenchmarkNumeralDecimalFromBinary0– ns/op
BenchmarkNumeralDecimalFromBinary10000– ns/op
BenchmarkNumeralDecimalFromBinary1000000000– ns/op
BenchmarkNumeralDecimalFromBinary1000000000000000000– ns/op 60 7700 3.60 8 1000000000 8.182 -8 252367634 284.8 -8 250184980 286.0 -8 100000000 616.6 8 1000000000 7.818 8 837013039 84.98 8 337445121 214.8 8 158028769 455.9 Alright, one last check. How does adding numerals of different systems perform? Remember, I’m using decimal integers as the intermediate common base to perform operations. Turns out adding is also relatively fast since it to perform an average addition takes roughly around 8 μseconds Additions are a bit trickier in terms of performance. At least 2 conventions have to happen, both numbers are translated to decimal and in the end, the result is converted back to the final desired numeral system. This on the . relies heavily performance of the conversion of a numeral to decimal int go test -bench=NumeralAdd -benchtime= s
goos: linux
goarch: amd64
pkg: github.com/slysterous/numeral
cpu: Intel(R) Core(TM) i7– CPU @ GHz
BenchmarkNumeralAddBinaryOnHex ns/op
BenchmarkNumeralAddHexOnHex ns/op
BenchmarkNumeralAddDecOnDec ns/op
BenchmarkNumeralAddSumBinaryOnHex ns/op
BenchmarkNumeralAddSumHexOnHex ns/op
BenchmarkNumeralAddSumDecOnDec ns/op 60 7700 3.60 -8 9691966 8651 -8 9144648 8290 -8 11384712 7014 -8 11281405 6237 -8 12745245 5873 -8 12672326 5849 In conclusion, is now a Go package. It gives you the ability to create custom (positional) numeral systems and perform operations on them. Feel free to contribute and don’t hesitate to reach out for any questions. numeral Also published on Medium's slysterous

Introduction to Numeral Systems in Go

At , we deliver software development services for two Houston-based clients. A few weeks ago, I was discussing the pros and cons of Houston startup ecosystem with , Clever Box Company Founder. Altalogy Dommonic Nelson The following point was made “When it comes to startups and tech in Texas, Austin outperforms Houston by order of magnitude”. I was a bit surprised by that fact and decided to see how other cities in Texas compare. As a source of information, I selected Angel List. I’m fully aware of the bias that some companies may not be present there though. The comparison includes 4 Largest Cities — Houston, San Antonio, Dallas, and Austin. Disclaimer: I live in Central Europe 7 hours time zone away from Texas, and the only time I’ve seen the Lone Star State myself was from an aircraft window. So, pardon me, Texas natives, for trying to analyze your state without even being there :) Houston With a population exceeding 2 million people, Houston is the 4th largest city in the United States and most populated metropolitan area in Texas. The city also has a global economy and only New York City has more Fortune 500 headquarters. This fact should make for a great, global startup hub — let’s have a look at the numbers. As you can see above, there are 1861 startups in Houston according to Angel List. Is a good or bad result? We’ll find out later on. In the last eight months (Jun 2018 — January 2019), 166 companies were registered on Angel List which is nearly 9% of all Houston-based startups listed on angel.co. San Antonio San Antonio is the second largest city in Texas. Its economy revolves around defense, healthcare, and the financial services sectors. With almost 1.5 million inhabitants, it does make me curious why only 507(!) startups are located there according to Angel List. I’m not sure what the reason is behind such a tiny ecosystem but I’m not going to try digress on that matter. Let’s move forward to Dallas. Dallas Most people around the world know Dallas mostly for what happened in ’63. It is the third largest city in texas(~1.3 M). The economy of Dallas is considered diverse, with dominant sectors including defense, financial services, information technology, telecommunications, and transportation. We can see it performs better than Houston regarding the total number of startups. The average salary is lower, but not significantly. Austin Finally, let’s look at the smallest brother (<1M inhabitants) of the big four Texas cities. According to various sources, the Texas capital is hailed as a high-tech mecca calling it “The Silicon Hills.” Not to mention named Austin the #1 place to live in the U.S. for 2017 and 2018. U.S. News & World Report There are over twice as many startups as in Houston, and four times more jobs than in Dallas. “The Silicon Hills” nickname is legitimate, undoubtedly. Comparison Ecosystem Austin plays in a different league than Houston, Dallas, and San Antonio. 45 startups per 10 000 inhabitants put the city in pursuit of locations like Boston. Number of startups per 10 000 inhabitants Salary Regarding salaries, Dallas and Houston are quite similar. Austin salaries are higher by $15k per year. Unfortunately, the data for San Antonio is missing, but that might be the case due to the low number of companies. Average salary (source: Angel List) Growth rate Dallas is our winner when comes to the growth rate. Austin seems to perform a little weaker but on the other hand — it already has an established position as a tech hub so the growth pace might not be as relevant here. Growth rate for the last eight months (June 2018-January 2019) Conclusion Austin is the place to be in Texas for entrepreneurs. It is itself home to more startups than Houston, San Antonio and Dallas combined. But can we assume that the market is already saturated there and the city will leave more room for the rest of the cities to develop?It’s tricky to answer that question since Austin is also the fastest growing large city in the United States. Dallas, on the other hand, performs best regarding growth rate, which shows it is gaining momentum. I think Houston has huge potential thanks to its population and age distribution(45% of the population is between 18–44). As it is already a large corporate hub, it requires certain incentives and motivation to trigger the transition — the resources are already there. For me, the most surprising fact is San Antonio’s poor result. I’d love to hear your suggestions what might be the reason for such a low number of young companies there. In the end, I would like to emphasize the potential bias. Those data are collected manually from Angel List, and might not be accurate. My purpose was to find a criterion that applies correspondingly to all cases. Last but not least: Do you find this story valuable? Is there any crucial factor I accidentally skipped in the comparison? Would you like me to write about other states/regions too? I encourage you to share your feedback in the comments section below. Thanks for reading!

A Brief Numerical Overview of the Texas Startup Ecosystem

Today, while using a Ledger Nano S — I was shocked to see this scary message after I left my ledger nano s for few minutes while a transaction was confirming. The message was scrolling horizontally saying “ ” Vires in Numeris If the Auto-Lock feature is activated, your Nano S will enter into stand-by mode after a delay you can choose (1, 3, 5 or 10 minutes). Then, each time your Nano S will be connected and not used during this selected delay, it will run stand-by mode. When you want to use again your device, you will have to press both buttons and re-enter your PIN code. Open the “Settings” of the Nano S Select “Security” Select “Auto-lock” Scroll to choose your favorite delay and press both buttons to validate or select OFF if you do not want to set this mode If this article has helped you feel relieved, Give some claps and share it across. Follow me on medium and twitter for more informational articles about Cryptocurrency, Blockchain and UI/UX for web/mobile products Disclosure: This article is based on information provided on and few reddit posts. Worked for me — It is for informational and educational purposes only. I am not responsible for any effects or loss of your funds. Ledger Nano FAQs

It’s perfectly fine to see “Vires in Numeris” message on Ledger Nano S

If you believe that action and practice are better than theory and have little to no experience in the field of and quantitative analysis (but a healthy interest) , this might be the post for you, for the rest it is a look into a probable future where one more thing could become decentralized and open sourced: . machine learning Wall Street There are 2 main ideas at play here, so I’ll try giving you a birds eye view of both : Within the world of finance, hedge funds are a group of investors that plunk money into a basket of financial instruments and investments with hopes of having a return, a $3 Trillion Dollar competitive industry. Within this industry is one of the first experiments in open sourcing at some level the management and decision of buying and selling investments. Numerai: Numerai Quantitative analysis in finance employs statistical & mathematical models to predict and evaluate the price and value of financial instruments, in a nutshell various numbers representing some feature of the instrument go in, and a prediction or score comes out, said prediction or valuation then informs the decision making on the funds capital (buying,selling, holding etc) Machine learning which is everywhere these days is but the latest tool in making sense of the numbers; to a researcher like me or someone more interested in different A.I. problems like pattern recognition this type of analysis is just a new, fun and probably profitable application. Quantitavie Analysis & Machine Learning: Numerai bridges both worlds and adds a crowdfunded twist by providing the raw data and asking you and me to provide a better estimate, these predictions are then used to control capital and the top performing ones get paid real money for their contribution, additionally there are incentives in the form of staking your own funds ( in the form of numerais own cryptocurrency) which in essence is a reward and punishment system for keeping your predictions novel and useful. This is a complex but interesting part which I will sidestep for now to focus on getting started. For the money, for the glory, and for the fun , but mostly for the money. In my experience it will take a novice data scientist, coder, or hobbyist a few weeks to get off the ground, at the end of this very short period you will have practical knowledge on applying various statistical and A.I. concepts to a real problem on a platform that you can then expand to your own interests, the competitive aspect and financial incentives can help you stay focused and motivated while learning although I should mention that making a dollar might take months. If you are not planning on participating but came for the whole open source wall street thing you can skip the following 2 sections. Hands on: This is but one path ( the one I took ) yours might be different depending on your starting point. Sign up to Numerai, read the documentation, get thoroughly intimidated by the documentation, the forums, the slack channel and the sinking feeling that even though you thought you were a smart cookie, this will require learning quite a few new things, take a deep breadth. Download the data set, it consists of multiple files which you will use, here’s what the latest one looks like: These files might make perfect sense if you’ve done some , if not I’ll try giving you a quick overview/introduction: data science Numerai is kind enough to provide 2 fully functioning and working examples, these are perfectly good springboards and working examples of a base implementation in R and Python, 2 very popular languages for big data analysis and machine learning, I went with Python since I had some experience with it, although I foolishly tried making a neural net on excel at first, my computer is still recovering. example_model.py & example_model.r : There are a few things to this file, so let’s start by looking at what’s inside: numerai_tournament_data.csv : Importantly there are various types of elements or categories ( id’s) divided into validation,live and test types, and each one has features, and some date information in the form of eras; the target column is what your model will predict in the form of a binary number (1 or 0). Numerai obfuscates the data, so even though we are assuming these are financial instruments (could be volume, open,close price, etc) there is nothing explicitly apparent, feature 11 on id 12546 could represent stock price at close date last week (era2) or something else, a dataset representing cancer rates or pixels in a dog recognition problem would look the same ! numerai_training_data.csv: An additional dataset, the training set is also provided, if you are familiar with it will be obvious what this dataset represents and how it is used. In a nutshell, you are given a problems definition and it’s solution, ( ), you a model to it and then generalize the solution to new data ( ) and make your predictions. It is the equivalent of learning to ride a bicycle with training wheels ( here you are the model ) and then trying your skill (predicting) by riding on a bicycle without them, if you fall you have a bad model. cross validation the training set fit the blank test and live rows on the tournament dataset This is an example of what you will be submitting, a column of id’s ( the same id’s from numerai_tournament_data.csv) and a probabilistic prediction that the id will be of class 1, so while the target of your model is a binary number, it needs to output probabilities on said target. example_predictions.csv : Once you have these files, you now need to set up your environment for making, predicting, keeping track of and submitting predictions. In my case it involved installing python plus setting up my editor ( I use Atom with script for running python) and creating a few spreadsheets to test,tweak and keep track of predictions, this is time consuming and will probably take a few weeks if not months to streamline. As mentioned, the example models provided by numerai are an excellent way to get started making predictions and working with models, the code does everything for you (read files, divide data, define a model, train,predict, write to file ) provided you have the right libraries installed, pandas and numpy for dealing with the data and sklearn for the statistical models for instance. Models : Numerai has a weekly tournament and after each one the clock resets and a new dataset is provided, you can have 3 models submitting predictions and are limited to uploading 25 per day (it’s usually plenty once you learn how to calculate logloss and other metrics on your own). They also provide an API if you choose to automate the download/upload. The Tournament : Once you have successfully submitted a model, you will be in the leaderboard and your predictions will be scored across various dimensions : At this point the algorithms for originality,concordance and consistency are not open source, but they are described as follows ( ) you also need to meet a specific treshold to qualify for the tournament and control capital Logloss across era, explanation forthcoming. ( ) Consistency: 75% an up Somehow controversial since it might favor early submitters; a check to see if your predictions/model were already submitted. ( a pass/ fail flag) Originality : A check to see if one model was applied to all data_types. ( a pass/fail flag) Concordance : Once your model is prequalified by these metrics, you are then scored by your logloss against live data in order to actually win money, a process that takes 4 weeks, the scoreboard is then not a reflection of the actual place your model will place in the tournament. Numerai is not telling the specifics, but they hint at a meta model based on the top predictions, those closests in logloss to their own model and their live data, the time period also plays into favoring models and predictions over a longer time span, since logloss is the main ranking metric, it’s important to know about it. is a graded statistical measure of confidence over your predictions, in real terms something like 0.50 would represent a random guess and 0.00 a perfectly confident prediction, it is graded because the more confident you are about a certain outcome ( I will not fall of the bicycle) the more it penalizes you if in fact you fall of the bicycle. In the case Numerai it could be understood as I am certain to this degree about my predictions. Logloss : ( or logarithmic loss ) And that’s it, once you have your setup ready you are welcome to try any of the multiple statistical models that are open source, and any technique and combination of parameters for analyzing this data, a good place to start is the sklearn library and all their models. I should also mention that ranking within the 100 or so models that are paid is difficult and requires a lot of experimenting, applying advanced techniques and in general getting to know the dataset, so using out of the box models will probably not get you very far. : Folks interested on the whole open source Wall Street thing continue reading here Beyond a great way to get into applied machine learning and quantitative analysis, Numerai might become something bigger and arguably better for the world of finance, it is early days and it is on the experimental side like many startups, but the upside potential is there. The hedge fund and banking industry have traditionally been elite,closed and secretive places with a bad reputation, in the same way that Hollywood and the TV networks were once the only source for movies and shows, Youtube has provided a new avenue for both consumers and content creators. A distributed and open source wall street would allow diverse talent and ideas to contribute, a self taught analyst in a developing country that does not like wearing a suit and the heavy handed bro atmosphere of wall street could make a living and contribute to a hedge fund. A researcher in academia might not want to abandon his full time job or research, but might be able to contribute part time. The consumers of the hedge fund industry as a whole would also benefit if the experiment proves successful, this bet hinges on the wisdom of the collective quant crowd vs the existing industry and the performance of these new types of funds. I am personally somehow optimistic, but I am also aware that consistent positive performance in the hedge fund industry (and other investments) usually favors an index approach vs stock picking and active management, so in the end a quant approach, even an open sourced one might not be all that profitable. Finally, I believe the hedge fund industry will probably have nothing to fear,but will coexist peacefully and even contribute if the experiment resolves favorably, established banks might even one day foster this type of funds, competition wise, I also think there is room for everyone since there is plenty of untapped investment capital facilitated by the new ecosystems (cryptocurrencies,globalization, the web) which numerai an other similar ventures might be better positioned to capture; if there is a point of concern for the hedge fund industry, is that of cost, the current fee structure ( 2 percent on assets and 20% on profits ) is pricey for 2 reasons, the cost of having an infrastructure (brokers, analysts, researchers, back office, etc) and the walled garden of finance that limits participation, it is in this space that a desentralized open source hedge fund can lower costs and compete, so as mentioned we could very well see a new more competitive type of hedge fund appear and the existing ones would need to adapt. 2 and 20 Parting Words I left a few things out for lack of space and because I wanted to focus this short piece as a both an alternative way of onboarding, which I struggled with and to discuss albeit briefly what this type of fund could herald. You can read about staking via this , and keep up with numerai at their . whitepaper blog I should also mention and other writings on , and here on medium as a way to start and further your learning (as well as mine). kaggle numerai machine learning quantitative analysis Small Update: (Oct 1st 2017)The dataset has been changed, there is now roughly twice the features and 10–20 K more rows, this means that if you are on basic hardware ( I am on a i3 4GB RAM HD windows machine) you will most likely experience memory errors on some models, the solution is to subsample. Also, I got my first NMR by ranking within the first 100 ! Medium sized Update: (Dec 25 2017 ) Numerai has now released the source for scoring predictions and streamlined the API for automatic submissions along with some other minor changes and a vision statement & road map, read more here : Most importantly, payouts have now changed in nature (more NMR, less usd). I personally have been doing great ranking in the top 50 – 60 more or less consistently. Numerai’s Master Plan. Early 2018 Update — Breaking changes: Payouts for the tournament have changed once more, the only way to win both NMR and USD . This means that in order to compete you need to have NMR to stake , and in order to have NMR you have to buy them or have been part of the original distribution, it is early to know how this will affect the project, but in my eyes the project has changed in nature, moving the bar higher and making it harder for newcomers, time will tell if this breaks the project. is through staking Mid 2018 Update — More changes: There are now 5 different tournaments and the payout structure has gone through a number of complex rule changes, consult the Numerai page for the current ones, there is also a new reputation system that rewards you with 0.1 NMR every time you beat benchmark, ( there was also a sweet reputation bonus for previously submitted performant models ); so now you have a path to stake NMR without buying them, I think it’s perhaps too small an amount, but understand there are issues in giving out more (like bots). I’ve been consistently ranking in the top 20 but earnings are now tied to how much you stake, your confidence level and that of other players,coupled with the current cryptocurrency slump, my earnings have been low ; there have also been problems with bots taking advantage of airdrops and players exploiting rules, these have all been progressively addressed by Numerai resulting in added complexity and rules. Disclaimer : I just took a short term contract position with Numerai (August 2018-Oct 2018) I will be helping them with Front End,UX and enything else I can. I won’t be competing during the duration… April 2019 Update : There’s been quite a few new things in the world of Numerai since I left and went back to being a competitor, there’s new data, new tournaments ( still only 5 though) and a new measuring metric (AUC) instead of logloss, it has also become much more competitive ( ), mostly pay to play and payouts per participant have gone down, ( although general prize pools are bigger now). I rank top 100-200 now Thanks ! Keno About the Author : Born Eugenio Noyola Leon (Keno) I am a Designer,Web Developer/programmer, Artist and Inventor, currently living in Mexico City, you can find me at www.k3no.com

Numerai walkthrough: Quantitative Analysis & Machine learning for fun and profit.

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Hyerin Cho (조혜린), Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA;
(2) Ben S. Prather, CCS-2, Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA;
(3) Ramesh Narayan, enter for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA;
(4) Priyamvada Natarajan, Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA, Department of Astronomy, Yale University, Kline Tower, 266 Whitney Avenue, New Haven, CT 06511, USA and Department of Physics, Yale University, P.O. Box 208121, New Haven, CT 06520, USA;
(5) Kung-Yi Su, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA;
(6) Angelo Ricarte, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA;
(7) Koushik Chatterjee, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA. Table of Links Abstract and Introduction Numerical Methods Hydrodynamic Bondi Accretion Magnetized Bondi Accretion Feedback Via Reconnection-Driven Convection Summary and Conclusions Acknowledgements Appendix A. GRMHD Primer and Definitions B. Numerical Set-up C. Resolution and Initial Condition Study References C. RESOLUTION AND INITIAL CONDITION STUDY This paper is available on Arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. Authors: (1) Hyerin Cho (조혜린), Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (2) Ben S. Prather, CCS-2, Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA; (3) Ramesh Narayan, enter for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (4) Priyamvada Natarajan, Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA, Department of Astronomy, Yale University, Kline Tower, 266 Whitney Avenue, New Haven, CT 06511, USA and Department of Physics, Yale University, P.O. Box 208121, New Haven, CT 06520, USA; (5) Kung-Yi Su, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (6) Angelo Ricarte, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (7) Koushik Chatterjee, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA. This paper is available on arxiv under CC 4.0 license. Authors : Authors (1) Hyerin Cho (조혜린), Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (2) Ben S. Prather, CCS-2, Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA; (3) Ramesh Narayan, enter for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (4) Priyamvada Natarajan, Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA, Department of Astronomy, Yale University, Kline Tower, 266 Whitney Avenue, New Haven, CT 06511, USA and Department of Physics, Yale University, P.O. Box 208121, New Haven, CT 06520, USA; (5) Kung-Yi Su, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (6) Angelo Ricarte, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (7) Koushik Chatterjee, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA. Table of Links Abstract and Introduction Abstract and Introduction Numerical Methods Numerical Methods Hydrodynamic Bondi Accretion Hydrodynamic Bondi Accretion Magnetized Bondi Accretion Magnetized Bondi Accretion Feedback Via Reconnection-Driven Convection Feedback Via Reconnection-Driven Convection Summary and Conclusions Summary and Conclusions Acknowledgements Acknowledgements Appendix Appendix A. GRMHD Primer and Definitions A. GRMHD Primer and Definitions B. Numerical Set-up B. Numerical Set-up C. Resolution and Initial Condition Study C. Resolution and Initial Condition Study References References C. RESOLUTION AND INITIAL CONDITION STUDY This paper is available on Arxiv under CC 4.0 license. This paper is available on Arxiv under CC 4.0 license. Arxiv

The Resolution to Our Black Hole Study

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Hyerin Cho (조혜린), Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA;
(2) Ben S. Prather, CCS-2, Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA;
(3) Ramesh Narayan, enter for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA;
(4) Priyamvada Natarajan, Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA, Department of Astronomy, Yale University, Kline Tower, 266 Whitney Avenue, New Haven, CT 06511, USA and Department of Physics, Yale University, P.O. Box 208121, New Haven, CT 06520, USA;
(5) Kung-Yi Su, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA;
(6) Angelo Ricarte, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA;
(7) Koushik Chatterjee, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA. Table of Links Abstract and Introduction Numerical Methods Hydrodynamic Bondi Accretion Magnetized Bondi Accretion Feedback Via Reconnection-Driven Convection Summary and Conclusions Acknowledgements Appendix A. GRMHD Primer and Definitions B. Numerical Set-up C. Resolution and Initial Condition Study References REFERENCES Angl´es-Alc´azar, D., Quataert, E., Hopkins, P. F., et al. 2021, ApJ, 917, 53, doi: 10.3847/1538-4357/ac09e8 Anile, A. M. 1989, Relativistic fluids and magneto-fluids: With applications in astrophysics and plasma physics Bisnovatyi-Kogan, G. S., & Ruzmaikin, A. A. 1974, Ap&SS, 28, 45, doi: 10.1007/BF00642237 Bondi, H. 1952, MNRAS, 112, 195, doi: 10.1093/mnras/112.2.195 Booth, C. 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Prather, CCS-2, Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA; (3) Ramesh Narayan, enter for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (4) Priyamvada Natarajan, Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA, Department of Astronomy, Yale University, Kline Tower, 266 Whitney Avenue, New Haven, CT 06511, USA and Department of Physics, Yale University, P.O. Box 208121, New Haven, CT 06520, USA; (5) Kung-Yi Su, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (6) Angelo Ricarte, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (7) Koushik Chatterjee, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA. This paper is available on arxiv under CC 4.0 license. Authors : Authors (1) Hyerin Cho (조혜린), Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (2) Ben S. Prather, CCS-2, Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545, USA; (3) Ramesh Narayan, enter for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (4) Priyamvada Natarajan, Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA, Department of Astronomy, Yale University, Kline Tower, 266 Whitney Avenue, New Haven, CT 06511, USA and Department of Physics, Yale University, P.O. Box 208121, New Haven, CT 06520, USA; (5) Kung-Yi Su, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (6) Angelo Ricarte, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA; (7) Koushik Chatterjee, Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA and Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA. Table of Links Abstract and Introduction Abstract and Introduction Numerical Methods Numerical Methods Hydrodynamic Bondi Accretion Hydrodynamic Bondi Accretion Magnetized Bondi Accretion Magnetized Bondi Accretion Feedback Via Reconnection-Driven Convection Feedback Via Reconnection-Driven Convection Summary and Conclusions Summary and Conclusions Acknowledgements Acknowledgements Appendix Appendix A. GRMHD Primer and Definitions A. GRMHD Primer and Definitions B. Numerical Set-up B. Numerical Set-up C. Resolution and Initial Condition Study C. Resolution and Initial Condition Study References References REFERENCES Angl´es-Alc´azar, D., Quataert, E., Hopkins, P. F., et al. 2021, ApJ, 917, 53, doi: 10.3847/1538-4357/ac09e8 Anile, A. M. 1989, Relativistic fluids and magneto-fluids: With applications in astrophysics and plasma physics Bisnovatyi-Kogan, G. S., & Ruzmaikin, A. 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