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Funding for drains, embankments and other measures is part £45.4bn five-year investment plan

Network Rail to spend £2.8bn to cope with effects of climate crisis | Network Rail | The Guardian

The government-owned company&#x27;s chief has described climate change as the &quot;biggest challenge our railway faces&quot; and the investment will fund projects such as installing CCTV in sites at risk of flooding.

Network Rail to invest £2.8bn on protecting railways from climate change and extreme weather | UK News | Sky News

Michael Macartney, 50, confessed to the BBC his role in an extreme monkey torture network.

Ringleader of global monkey torture network, 'The Torture King', is charged - BBC News

Bus will provide to provide an alternative to the unfunded £10bn Bakerloo line extension to the Tube

Sadiq Khan unveils plans for 'Bakerloop' extension to the Superloop bus network | Evening Standard

How to Raise VC Financing for Your Video Game Startup

Why Do We Need to Secure Networks? Networks are constantly under attack and can be infiltrated via various tactics, including malware, spoofing, packet sniffing, and much more. If a network is not protected from these tactics and is intruded upon, it could have a catastrophic impact on the organization. Consider one of such intrusion tactics, denial of service (DoS) attacks. What Is a Denial of Service Attack? A denial of service, or DoS, attack is an attack that targets a network or server and floods it with network traffic. The objective of this attack is to disrupt normal business operations by overloading an organization’s network with the goal of sending so much information that the network crashes or is unable to respond to legitimate users. Types of DoS Attacks Distributed Denial of Service (DDoS) Attack: This type of DoS attack uses multiple devices or servers, in different locations to flood the target network with unwanted traffic. This attack archives effectiveness by exploiting devices such as computers, IoT devices, and other networked resources. Network-level DoS Attacks: These DoS attacks target network bandwidths on a server to slow traffic. Types of these attacks include: SYN (synchronize) flood attack: To understand this attack, you have to understand the process used to establish a transmission control protocol (TCP) connection between devices and a server. This process is often called the handshake process.

The handshake process begins when a device sends a synchronize request to the server. The server responds with a SYN/ACK packet, acknowledging the receipt of the device’s request and leaves a port open for the final step of the handshake.
Upon receiving the final ACK packet from the device, the server establishes that the TCP connection is established.

Attackers understand this process and use SYN flood attacks to simulate TCP connections and flood a server with SYN packets. When the number of requests is larger than the number of available ports on the server, the server will crash and be unable to function.

Internet Control Message Protocol (ICMP) flood attack: This is a type of DoS attack where ICMP packets are repeatedly sent to a network server, forcing the server to send an ICMP in response, which eventually uses all the bandwidth for incoming and outgoing traffic, causing the server to crash.

The Internet control message protocol (ICMP) is an Internet protocol used by devices to tell each other about data transmission errors across a network.
Learn more about ICMP here Ping of Death: This is a type of DoS attack caused when a hacker pings a system by sending it an oversized ICMP packet that is bigger than 64kb (the maximum size for a currently formed ICMP packet). This causes the server to crash. Conclusion You are now aware of how a denial of service attack works and the different types associated with it. How do you keep yourself and your data safe from these attacks. How do you go about navigating these vulnerabilities? Do you have answers or suggestions? Feel free to share your thoughts in the comment section. GodSpeed Why Do We Need to Secure Networks? Networks are constantly under attack and can be infiltrated via various tactics, including malware, spoofing, packet sniffing, and much more. If a network is not protected from these tactics and is intruded upon, it could have a catastrophic impact on the organization. Consider one of such intrusion tactics, denial of service (DoS) attacks. What Is a Denial of Service Attack? A denial of service, or DoS, attack is an attack that targets a network or server and floods it with network traffic. The objective of this attack is to disrupt normal business operations by overloading an organization’s network with the goal of sending so much information that the network crashes or is unable to respond to legitimate users. Types of DoS Attacks Distributed Denial of Service (DDoS) Attack: This type of DoS attack uses multiple devices or servers, in different locations to flood the target network with unwanted traffic. This attack archives effectiveness by exploiting devices such as computers, IoT devices, and other networked resources. Network-level DoS Attacks: These DoS attacks target network bandwidths on a server to slow traffic. Types of these attacks include: SYN (synchronize) flood attack: To understand this attack, you have to understand the process used to establish a transmission control protocol (TCP) connection between devices and a server. This process is often called the handshake process.

The handshake process begins when a device sends a synchronize request to the server. The server responds with a SYN/ACK packet, acknowledging the receipt of the device’s request and leaves a port open for the final step of the handshake.
Upon receiving the final ACK packet from the device, the server establishes that the TCP connection is established.

Attackers understand this process and use SYN flood attacks to simulate TCP connections and flood a server with SYN packets. When the number of requests is larger than the number of available ports on the server, the server will crash and be unable to function. Internet Control Message Protocol (ICMP) flood attack: This is a type of DoS attack where ICMP packets are repeatedly sent to a network server, forcing the server to send an ICMP in response, which eventually uses all the bandwidth for incoming and outgoing traffic, causing the server to crash.

The Internet control message protocol (ICMP) is an Internet protocol used by devices to tell each other about data transmission errors across a network.
Learn more about ICMP here SYN (synchronize) flood attack: To understand this attack, you have to understand the process used to establish a transmission control protocol (TCP) connection between devices and a server. This process is often called the handshake process. The handshake process begins when a device sends a synchronize request to the server. The server responds with a SYN/ACK packet, acknowledging the receipt of the device’s request and leaves a port open for the final step of the handshake.
Upon receiving the final ACK packet from the device, the server establishes that the TCP connection is established. Attackers understand this process and use SYN flood attacks to simulate TCP connections and flood a server with SYN packets. When the number of requests is larger than the number of available ports on the server, the server will crash and be unable to function. SYN (synchronize) flood attack: To understand this attack, you have to understand the process used to establish a transmission control protocol (TCP) connection between devices and a server. This process is often called the handshake process . handshake process The handshake process begins when a device sends a synchronize request to the server. The server responds with a SYN/ACK packet, acknowledging the receipt of the device’s request and leaves a port open for the final step of the handshake. Upon receiving the final ACK packet from the device, the server establishes that the TCP connection is established. The handshake process begins when a device sends a synchronize request to the server. The server responds with a SYN/ACK packet, acknowledging the receipt of the device’s request and leaves a port open for the final step of the handshake. Upon receiving the final ACK packet from the device, the server establishes that the TCP connection is established. Attackers understand this process and use SYN flood attacks to simulate TCP connections and flood a server with SYN packets. When the number of requests is larger than the number of available ports on the server, the server will crash and be unable to function. Internet Control Message Protocol (ICMP) flood attack: This is a type of DoS attack where ICMP packets are repeatedly sent to a network server, forcing the server to send an ICMP in response, which eventually uses all the bandwidth for incoming and outgoing traffic, causing the server to crash. The Internet control message protocol (ICMP) is an Internet protocol used by devices to tell each other about data transmission errors across a network.
Learn more about ICMP here Internet Control Message Protocol (ICMP) flood attack: This is a type of DoS attack where ICMP packets are repeatedly sent to a network server, forcing the server to send an ICMP in response, which eventually uses all the bandwidth for incoming and outgoing traffic, causing the server to crash. The Internet control message protocol (ICMP) is an Internet protocol used by devices to tell each other about data transmission errors across a network. Learn more about ICMP here The Internet control message protocol (ICMP) is an Internet protocol used by devices to tell each other about data transmission errors across a network. Learn more about ICMP here here Ping of Death: This is a type of DoS attack caused when a hacker pings a system by sending it an oversized ICMP packet that is bigger than 64kb (the maximum size for a currently formed ICMP packet). This causes the server to crash. Ping of Death: This is a type of DoS attack caused when a hacker pings a system by sending it an oversized ICMP packet that is bigger than 64kb (the maximum size for a currently formed ICMP packet). This causes the server to crash. Conclusion You are now aware of how a denial of service attack works and the different types associated with it. How do you keep yourself and your data safe from these attacks. How do you go about navigating these vulnerabilities? Do you have answers or suggestions? Feel free to share your thoughts in the comment section. GodSpeed GodSpeed

An Overview of Network Intrusion Tactics: Denial of Service (DOS) Attacks

You can jump to any part of the United States International Cyberspace & Digital Policy Strategy here. This part is 12 of 38. Line of Effort 1: Promote Development and Adoption of Open, Inclusive, Secure, and Resilient Telecommunication Networks 5G applications are rapidly evolving—expanding digital connectivity in new ways and creating new cybersecurity vulnerabilities. Telecommunication networks should be built using products from trusted suppliers that operate, and have supply chain partners that operate, primarily in countries that respect rights through consistent application of the law through an independent judiciary, in accordance with the principles reflected in the Organisation for Economic Co-operation and Development (OECD) Declaration on Government Access to Personal Data Held by Private Sector Entities. Telecommunications networks should not be built using products from suppliers subject to the control or influence of an authoritarian regime, and without meaningful, independent checks and balances or judicial recourse against government demands. International 5G-related principles, such as the Prague Proposals on 5G Security and Prague Proposals on Telecommunications Supplier Diversity, support market competitiveness and the diversity of trusted 5G equipment vendors. These efforts also extend to the Partnership for Global Infrastructure and Investment’s Digital Infrastructure pillar. Recognizing that cost is often the primary driving factor in ICT procurements, the United States is supporting governments, middle-mile internet infrastructure providers, and Internet service providers to develop greater competition and diversity in telecommunications supply chains, particularly through the Digital Connectivity and Cybersecurity Partnership (DCCP). DCCP is a whole-of-government effort, led by the Department of State, to provide capacity building, technical assistance, and project design and financing in support of an open Internet and enhanced cybersecurity. In addition, the CHIPS and Science Act allocated $500 million to the International Technology Security and Innovation (ITSI) Fund for the Department of State to support the development and adoption of secure semiconductor supply chains and telecommunications networks. The United States will use this funding to continue to work with partners to put in place policy and regulatory frameworks for secure ICT ecosystems and to level the playing field for secure and trustworthy vendors. Along with helping build secure networks, digital solidarity is also expressed through efforts to build digital infrastructure that promotes competition, advances consumer choice, and puts communities and individuals in charge of their digital lives and resources. Recognizing the need to attract capital and de-risk potential digital infrastructure investment, USAID—with funding from DCCP—launched a blended finance program called Digital Invest that partners with fund managers and project developers to expand access to Internet connectivity and digital financial services in emerging markets worldwide. To date, Digital Invest’s 13 partners have leveraged an initial $8.45 million in Department of State and USAID funding to raise over $300 million in investment capital for digital finance and Internet service providers in emerging markets that use secure network equipment, catalyzing an additional $1.15 billion in follow-on funding from third-party investors. U.S. foreign assistance programs will also increase competition in the market and promote telecommunications supplier diversity by advancing the development of open and interoperable interfaces and protocols, such as Open Radio Access Networks (Open RAN). This open network architecture eases the ability for new suppliers to enter the market, lowers costs for deployment, and speeds innovation. Open RAN presents opportunities for emerging economies to participate directly in the supply chain, such as through local assembly and software development. Just as important, Open RAN offers alternatives for the reliance on technology from untrusted vendors. As a result, the Department of State will continue to support efforts such as funding commercial trials, feasibility studies, reverse trade missions, and workforce education and awareness activities that promote Open RAN. The United States will continue collaborating with the governments of Australia, Canada, Japan, and the United Kingdom on telecommunications supply chain diversification and related issues through the Global Coalition on Telecommunications, launched in October 2023. Working with other governments and the private sector, the United States is also preparing for a new wave of innovation. Within the next decade, 6G will within the next decade bring even higher speeds, larger capacity, and lower latency to wireless communication. Building open and interoperable network architectures such as Open RAN into 6G development from the beginning will help ensure supplier diversity and supply chain resilience. In February 2024, the United States—with Australia, Canada, the Czech Republic, Finland, France, Japan, the Republic of Korea, Sweden, and the United Kingdom—endorsed shared principles for the research and development of 6G wireless communication systems. Continue Reading Here. This post was originally published on May 6, 2024, by the U.S Department of State You can jump to any part of the United States International Cyberspace & Digital Policy Strategy here. This part is 12 of 38. You can jump to any part of the United States International Cyberspace & Digital Policy Strategy here . This part is 12 of 38. here Line of Effort 1: Promote Development and Adoption of Open, Inclusive, Secure, and Resilient Telecommunication Networks 5G applications are rapidly evolving—expanding digital connectivity in new ways and creating new cybersecurity vulnerabilities. Telecommunication networks should be built using products from trusted suppliers that operate, and have supply chain partners that operate, primarily in countries that respect rights through consistent application of the law through an independent judiciary, in accordance with the principles reflected in the Organisation for Economic Co-operation and Development (OECD) Declaration on Government Access to Personal Data Held by Private Sector Entities. Telecommunications networks should not be built using products from suppliers subject to the control or influence of an authoritarian regime, and without meaningful, independent checks and balances or judicial recourse against government demands. International 5G-related principles, such as the Prague Proposals on 5G Security and Prague Proposals on Telecommunications Supplier Diversity, support market competitiveness and the diversity of trusted 5G equipment vendors. These efforts also extend to the Partnership for Global Infrastructure and Investment’s Digital Infrastructure pillar. Recognizing that cost is often the primary driving factor in ICT procurements, the United States is supporting governments, middle-mile internet infrastructure providers, and Internet service providers to develop greater competition and diversity in telecommunications supply chains, particularly through the Digital Connectivity and Cybersecurity Partnership (DCCP). DCCP is a whole-of-government effort, led by the Department of State, to provide capacity building, technical assistance, and project design and financing in support of an open Internet and enhanced cybersecurity. In addition, the CHIPS and Science Act allocated $500 million to the International Technology Security and Innovation (ITSI) Fund for the Department of State to support the development and adoption of secure semiconductor supply chains and telecommunications networks. The United States will use this funding to continue to work with partners to put in place policy and regulatory frameworks for secure ICT ecosystems and to level the playing field for secure and trustworthy vendors. Along with helping build secure networks, digital solidarity is also expressed through efforts to build digital infrastructure that promotes competition, advances consumer choice, and puts communities and individuals in charge of their digital lives and resources. Recognizing the need to attract capital and de-risk potential digital infrastructure investment, USAID—with funding from DCCP—launched a blended finance program called Digital Invest that partners with fund managers and project developers to expand access to Internet connectivity and digital financial services in emerging markets worldwide. To date, Digital Invest’s 13 partners have leveraged an initial $8.45 million in Department of State and USAID funding to raise over $300 million in investment capital for digital finance and Internet service providers in emerging markets that use secure network equipment, catalyzing an additional $1.15 billion in follow-on funding from third-party investors. U.S. foreign assistance programs will also increase competition in the market and promote telecommunications supplier diversity by advancing the development of open and interoperable interfaces and protocols, such as Open Radio Access Networks (Open RAN). This open network architecture eases the ability for new suppliers to enter the market, lowers costs for deployment, and speeds innovation. Open RAN presents opportunities for emerging economies to participate directly in the supply chain, such as through local assembly and software development. Just as important, Open RAN offers alternatives for the reliance on technology from untrusted vendors. As a result, the Department of State will continue to support efforts such as funding commercial trials, feasibility studies, reverse trade missions, and workforce education and awareness activities that promote Open RAN. The United States will continue collaborating with the governments of Australia, Canada, Japan, and the United Kingdom on telecommunications supply chain diversification and related issues through the Global Coalition on Telecommunications, launched in October 2023. Working with other governments and the private sector, the United States is also preparing for a new wave of innovation. Within the next decade, 6G will within the next decade bring even higher speeds, larger capacity, and lower latency to wireless communication. Building open and interoperable network architectures such as Open RAN into 6G development from the beginning will help ensure supplier diversity and supply chain resilience. In February 2024, the United States—with Australia, Canada, the Czech Republic, Finland, France, Japan, the Republic of Korea, Sweden, and the United Kingdom—endorsed shared principles for the research and development of 6G wireless communication systems. Continue Reading Here. Continue Reading Here . Here This post was originally published on May 6, 2024, by the U.S Department of State This post was originally published on May 6, 2024, by the U.S Department of State by the U.S Department of State

Strengthening Telecommunication Networks: Promoting Openness and Security in 5G and Beyond

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

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com];
(2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za];
(3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za];
(4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction
Methodology
Neural Network Methodology
Numerical results, implementation and discussion
Conclusion, Acknowledgments, and Funding
Availability of data, code and materials, Contributions and Declarations
References 5. Conclusion This paper has considered the valuation of the bitcoin call option when the bitcoin price dynamics follow a bivariate Merton jump-diffusion model. This research generally provided a novel pricing framework that described the behaviour of bitcoin prices and the model parameter estimation with the intent of pricing the corresponding derivatives. Since bitcoin is normally affected by investors’ attention and sentiment, we used the continuous-time stochastic jump-diffusion process to capture the dynamics of the bitcoin prices and the transaction volumes affecting the price. In the methodological aspect of the research, we extended the classical Black-Scholes model in order to obtain the extended Black-Scholes equation for the bitcoin options. By introducing the artificial NN, we proposed a trial solution that solves the associated BlackScholes PDE for the bitcoin call options with European features. As a result, the original constrained optimization problem was transformed into an unconstrained one. The numerical results considered both the normal Black-Scholes model and the Merton jump-diffusion model, and it was observed that the latter resulted in a more efficient valuation process. Hence, we can conclude that the NN can be employed efficiently in solving complex PDE-related problems and can be applied to pricing certain financial derivatives without analytical forms. For the Model I and II comparison, we noted that the Black-Scholes used in connection with Model II showed the out-of-the-money feature of the call option. The option absolutely pays off when the underlying price falls below the strike price. The JMD overprices the out-of-the-money options for Model II, whereas the BlackScholes overprices the call options in Model I. Hence, one of the limitations of this research lies in finding the optimal neural network configuration which ensures the fair pricing of bitcoin options using the proposed two models. This optimal feature will be incorporated to avoid over-pricing or under-pricing of these option values, and future research will focus on this. One of the limitations of the approach used in this paper is that it may be prone to artificial Google searches affecting sentiment-based data analysis and decisions. Even though search-based measures appear to be more transparent than other social media-driven measures, they seem limited as the volume of data is concerned. Social media like Twitter provides high-frequency data (second, minute, hour, daily, . . . ), which can provide meaningful and instantaneous insights into the price dynamics of cryptocurrencies and bitcoin in particular. Our future work will first examine the correlation between search-based data and tweets data, then compare their performance when included in the valuation process. The tweets sentiment scores will be computed using the stateof-the-art Lexicon-based sentiment analyzer Valence Aware Dictionary and sEntiment Reasoner (VADER). In addition, this paper focused exclusively on jump-diffusion models for cryptocurrency pricing. Levy processes allow the modelling of heavy-tailed return distributions and large deviations from the mean. Expanding the set of stochastic processes considered would provide a more thorough treatment of cryptocurrency dynamics. Processes like variance gamma, normal inverse Gaussian, and generalized hyperbolic Levy motions have shown promise in modelling assets with frequent extreme moves. Given Bitcoin’s volatility clustering and significant outliers, applying Levy processes could potentially improve model fitting. We acknowledge the limitations of only exploring a jumpdiffusion framework presently. Incorporating alternatives like Levy processes would strengthen the generalizability and robustness of the modelling approach. Building on the initial foundation proposed here, researchers could examine a wider set of stochastic processes for capturing empirically observed features. Comparative testing using historical data would elucidate the relative effectiveness of diffusions, Levy processes, and other probabilistic models. Extending this work to Levy processes represents a valuable progression for future research. The flexibility of Levy’s motions shows potential for modelling emerging cryptocurrency returns. We hope this paper provides a starting point that can be incrementally improved by incorporating innovations like heavy-tailed processes. Evaluating a range of stochastic models will ultimately enhance financial engineering techniques tailored specifically to cryptocurrencies. Acknowledgement The second author thanks the Research Centre of AIMS-Cameroon for hosting him during the preparation of this manuscript. Funding This research received no external funding. This paper is available on arxiv under CC 4.0 license. Authors: (1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com]; (2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com]; (2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction Methodology Neural Network Methodology Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations References Abstract and Introduction Abstract and Introduction Methodology Methodology Neural Network Methodology Neural Network Methodology Numerical results, implementation and discussion Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations Availability of data, code and materials, Contributions and Declarations References References 5. Conclusion This paper has considered the valuation of the bitcoin call option when the bitcoin price dynamics follow a bivariate Merton jump-diffusion model. This research generally provided a novel pricing framework that described the behaviour of bitcoin prices and the model parameter estimation with the intent of pricing the corresponding derivatives. Since bitcoin is normally affected by investors’ attention and sentiment, we used the continuous-time stochastic jump-diffusion process to capture the dynamics of the bitcoin prices and the transaction volumes affecting the price. In the methodological aspect of the research, we extended the classical Black-Scholes model in order to obtain the extended Black-Scholes equation for the bitcoin options. By introducing the artificial NN, we proposed a trial solution that solves the associated BlackScholes PDE for the bitcoin call options with European features. As a result, the original constrained optimization problem was transformed into an unconstrained one. The numerical results considered both the normal Black-Scholes model and the Merton jump-diffusion model, and it was observed that the latter resulted in a more efficient valuation process. Hence, we can conclude that the NN can be employed efficiently in solving complex PDE-related problems and can be applied to pricing certain financial derivatives without analytical forms. For the Model I and II comparison, we noted that the Black-Scholes used in connection with Model II showed the out-of-the-money feature of the call option. The option absolutely pays off when the underlying price falls below the strike price. The JMD overprices the out-of-the-money options for Model II, whereas the BlackScholes overprices the call options in Model I. Hence, one of the limitations of this research lies in finding the optimal neural network configuration which ensures the fair pricing of bitcoin options using the proposed two models. This optimal feature will be incorporated to avoid over-pricing or under-pricing of these option values, and future research will focus on this. One of the limitations of the approach used in this paper is that it may be prone to artificial Google searches affecting sentiment-based data analysis and decisions. Even though search-based measures appear to be more transparent than other social media-driven measures, they seem limited as the volume of data is concerned. Social media like Twitter provides high-frequency data (second, minute, hour, daily, . . . ), which can provide meaningful and instantaneous insights into the price dynamics of cryptocurrencies and bitcoin in particular. Our future work will first examine the correlation between search-based data and tweets data, then compare their performance when included in the valuation process. The tweets sentiment scores will be computed using the stateof-the-art Lexicon-based sentiment analyzer Valence Aware Dictionary and sEntiment Reasoner (VADER). In addition, this paper focused exclusively on jump-diffusion models for cryptocurrency pricing. Levy processes allow the modelling of heavy-tailed return distributions and large deviations from the mean. Expanding the set of stochastic processes considered would provide a more thorough treatment of cryptocurrency dynamics. Processes like variance gamma, normal inverse Gaussian, and generalized hyperbolic Levy motions have shown promise in modelling assets with frequent extreme moves. Given Bitcoin’s volatility clustering and significant outliers, applying Levy processes could potentially improve model fitting. We acknowledge the limitations of only exploring a jumpdiffusion framework presently. Incorporating alternatives like Levy processes would strengthen the generalizability and robustness of the modelling approach. Building on the initial foundation proposed here, researchers could examine a wider set of stochastic processes for capturing empirically observed features. Comparative testing using historical data would elucidate the relative effectiveness of diffusions, Levy processes, and other probabilistic models. Extending this work to Levy processes represents a valuable progression for future research. The flexibility of Levy’s motions shows potential for modelling emerging cryptocurrency returns. We hope this paper provides a starting point that can be incrementally improved by incorporating innovations like heavy-tailed processes. Evaluating a range of stochastic models will ultimately enhance financial engineering techniques tailored specifically to cryptocurrencies. Acknowledgement The second author thanks the Research Centre of AIMS-Cameroon for hosting him during the preparation of this manuscript. Funding This research received no external funding.

Neural Network for Valuing Bitcoin: Conclusion, Acknowledgments, and Funding

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com];
(2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za];
(3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za];
(4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction
Methodology
Neural Network Methodology
Numerical results, implementation and discussion
Conclusion, Acknowledgments, and Funding
Availability of data, code and materials, Contributions and Declarations
References Availability of data, code and materials Please contact the corresponding author for request. Contributions All authors contributed equally to the paper. All authors read and approved the final manuscript. Declarations Conflict of interest: All authors declare that they have no conflict of interest. Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors. This paper is available on arxiv under CC 4.0 license. Authors: (1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com]; (2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com]; (2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction Methodology Neural Network Methodology Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations References Abstract and Introduction Abstract and Introduction Methodology Methodology Neural Network Methodology Neural Network Methodology Numerical results, implementation and discussion Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations Availability of data, code and materials, Contributions and Declarations References References Availability of data, code and materials Please contact the corresponding author for request. Contributions All authors contributed equally to the paper. All authors read and approved the final manuscript. Declarations Conflict of interest: All authors declare that they have no conflict of interest. Conflict of interest: Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors. Ethical approval:

Neural Network for Valuing Bitcoin: Availability of Data, Code and Materials, Contributions

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com];
(2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za];
(3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za];
(4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction
Methodology
Neural Network Methodology
Numerical results, implementation and discussion
Conclusion, Acknowledgments, and Funding
Availability of data, code and materials, Contributions and Declarations
References 2. Methodology Jump-diffusion models are continuous-time stochastic processes introduced in quantitative finance by Merton [34], extending the work on option pricing by Black and Scholes [3]. These models reproduce stylized facts observed in asset price dynamics, such as mean-reversion and jumps. There are two ways to expound the description of jump processes. 1. One is to describe the jump in absolute terms (this is useful if we are focusing on prices or interest rates), 2. The other is to describe the jump in proportional terms (this is more useful if our focus is on returns, as in this study). In addition to jump-diffusion models, Levy processes appear as an alternative for capturing large deviations in asset prices. Levy processes allow sample paths with frequent discontinuities, enabling them to generate heavy-tailed distributions. Some key examples include variance gamma processes, normal inverse Gaussian processes, and generalized hyperbolic processes. [51] demonstrated that Bitcoin returns exhibit heavy tails and proposed using a variance gamma process to model the price dynamics. [25] found evidence that variance gamma processes fit cryptocurrency log returns compared to classical diffusion. Levy processes have also been employed to model stochastic volatility in Bitcoin prices [5]. Overall, Levy processes provide an alternative class of models with more flexibility to account for extreme deviations. They have shown promise in fitting the empirical distributional properties of cryptocurrency returns. As this work focuses initially on extending jump-diffusion models, exploring Levy processes represents a worthwhile direction for future research. However, their ability to capture heavy tails and discontinuities suggests that Levy processes could serve as a valuable modelling technique in this domain. Theorem 2.1. In the market model described previously, the following holds: 2.1. Strengths and limitations of the proposed model The bivariate jump-diffusion model provides an essential first step in applying financial engineering techniques to this new domain. By capturing stochastic volatility, discrete jumps, and a sentiment indicator, it incorporates several salient features of cryptocurrencies. The preliminary pricing and derivatives valuation framework can be built upon as the market evolves. While the assumptions require validation as more data emerges, the model offers valuable inputs for investment analysis at present. We acknowledge the need to refine techniques as cryptocurrency finance matures into its own field. This paper aims to provide the initial modelling foundation, which can be improved incrementally as research progresses. Future enhancements may include more flexible return distributions, multifactor models to capture additional risks, regime-switching models to reflect market phases, and calibration of the sentiment factor from various data sources. In addition, the current proposed model offers a useful starting point, we recognize this initial framework may require modifications over time to align with market realities. As more cryptocurrency data becomes available, the distributional properties and other intricacies of these markets will become clearer. If the actual return distributions exhibit higher kurtosis than the normal distribution assumed, the model may need to be adjusted accordingly. Furthermore, if inefficiencies and arbitrage opportunities remain prevalent, the dynamics may diverge from a pure jump-diffusion process. As researchers expand their knowledge of the microstructure, behavioural components, and risks in cryptocurrency markets, our modelling approach can be enhanced. In summary, we emphasize this work represents a starting point for modelling cryptocurrencies and enabling financial applications. The proposed bivariate jump-diffusion model and sentiment indicator capture essential dynamics but may require adjustments as knowledge develops. We welcome future research to build on these initial techniques for pricing and valuation of cryptocurrency-denominated assets. 2.2. Applications This extended Black-Scholes PDE poses challenges for analytical solutions due to the unbounded upside of the European call payoff. Therefore, numerical methods are often used to approximate the solution. Two standard techniques are finite difference methods and Monte Carlo simulation. Finite difference methods involve discretizing the price domain and time dimensions and replacing the derivatives with finite difference approximations. This transforms the PDE into a system of algebraic equations that can be solved recursively. Various finite difference schemes can be employed, such as explicit, implicit, and Crank-Nicolson. Monte Carlo simulation generates sample paths of the underlying price using the assumed stochastic process. The discounted payoffs from each sample path are averaged to estimate the option price. Variance reduction techniques like antithetic sampling and control variates can improve efficiency. Both methods have tradeoffs regarding accuracy, speed, and implementation complexity. Our proposed neural network approach serves as an alternative way to numerically solve the pricing PDE without discretizing the domain. This offers benefits in terms of generalization and scaling. This paper is available on arxiv under CC 4.0 license. Authors: (1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com]; (2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com]; (2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction Methodology Neural Network Methodology Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations References Abstract and Introduction Abstract and Introduction Methodology Methodology Neural Network Methodology Neural Network Methodology Numerical results, implementation and discussion Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations Availability of data, code and materials, Contributions and Declarations References References 2. Methodology Jump-diffusion models are continuous-time stochastic processes introduced in quantitative finance by Merton [34], extending the work on option pricing by Black and Scholes [3]. These models reproduce stylized facts observed in asset price dynamics, such as mean-reversion and jumps. There are two ways to expound the description of jump processes. 1. One is to describe the jump in absolute terms (this is useful if we are focusing on prices or interest rates), 2. The other is to describe the jump in proportional terms (this is more useful if our focus is on returns, as in this study). In addition to jump-diffusion models, Levy processes appear as an alternative for capturing large deviations in asset prices. Levy processes allow sample paths with frequent discontinuities, enabling them to generate heavy-tailed distributions. Some key examples include variance gamma processes, normal inverse Gaussian processes, and generalized hyperbolic processes. [51] demonstrated that Bitcoin returns exhibit heavy tails and proposed using a variance gamma process to model the price dynamics. [25] found evidence that variance gamma processes fit cryptocurrency log returns compared to classical diffusion. Levy processes have also been employed to model stochastic volatility in Bitcoin prices [5]. Overall, Levy processes provide an alternative class of models with more flexibility to account for extreme deviations. They have shown promise in fitting the empirical distributional properties of cryptocurrency returns. As this work focuses initially on extending jump-diffusion models, exploring Levy processes represents a worthwhile direction for future research. However, their ability to capture heavy tails and discontinuities suggests that Levy processes could serve as a valuable modelling technique in this domain. Theorem 2.1. In the market model described previously, the following holds: Theorem 2.1. 2.1. Strengths and limitations of the proposed model 2.1. Strengths and limitations of the proposed model The bivariate jump-diffusion model provides an essential first step in applying financial engineering techniques to this new domain. By capturing stochastic volatility, discrete jumps, and a sentiment indicator, it incorporates several salient features of cryptocurrencies. The preliminary pricing and derivatives valuation framework can be built upon as the market evolves. While the assumptions require validation as more data emerges, the model offers valuable inputs for investment analysis at present. We acknowledge the need to refine techniques as cryptocurrency finance matures into its own field. This paper aims to provide the initial modelling foundation, which can be improved incrementally as research progresses. Future enhancements may include more flexible return distributions, multifactor models to capture additional risks, regime-switching models to reflect market phases, and calibration of the sentiment factor from various data sources. In addition, the current proposed model offers a useful starting point, we recognize this initial framework may require modifications over time to align with market realities. As more cryptocurrency data becomes available, the distributional properties and other intricacies of these markets will become clearer. If the actual return distributions exhibit higher kurtosis than the normal distribution assumed, the model may need to be adjusted accordingly. Furthermore, if inefficiencies and arbitrage opportunities remain prevalent, the dynamics may diverge from a pure jump-diffusion process. As researchers expand their knowledge of the microstructure, behavioural components, and risks in cryptocurrency markets, our modelling approach can be enhanced. In summary, we emphasize this work represents a starting point for modelling cryptocurrencies and enabling financial applications. The proposed bivariate jump-diffusion model and sentiment indicator capture essential dynamics but may require adjustments as knowledge develops. We welcome future research to build on these initial techniques for pricing and valuation of cryptocurrency-denominated assets. 2.2. Applications 2.2. Applications This extended Black-Scholes PDE poses challenges for analytical solutions due to the unbounded upside of the European call payoff. Therefore, numerical methods are often used to approximate the solution. Two standard techniques are finite difference methods and Monte Carlo simulation. Finite difference methods involve discretizing the price domain and time dimensions and replacing the derivatives with finite difference approximations. This transforms the PDE into a system of algebraic equations that can be solved recursively. Various finite difference schemes can be employed, such as explicit, implicit, and Crank-Nicolson. Monte Carlo simulation generates sample paths of the underlying price using the assumed stochastic process. The discounted payoffs from each sample path are averaged to estimate the option price. Variance reduction techniques like antithetic sampling and control variates can improve efficiency. Both methods have tradeoffs regarding accuracy, speed, and implementation complexity. Our proposed neural network approach serves as an alternative way to numerically solve the pricing PDE without discretizing the domain. This offers benefits in terms of generalization and scaling.

Neural Network for Valuing Bitcoin: Methodology

Neural Network for valuing Bitcoin: References 

Neural Network for Valuing Bitcoin: Abstract and Introduction

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com];
(2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za];
(3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za];
(4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction
Methodology
Neural Network Methodology
Numerical results, implementation and discussion
Conclusion, Acknowledgments, and Funding
Availability of data, code and materials, Contributions and Declarations
References 3. Neural Network Methodology The neural network (NN) algorithm is used for solving problems relating to dimensionality reduction [42, 49], visualization of data [31], clustering [11, 52] and classification issues [37, 40]. It is also used in regression [2, 21, 45] in solving regression problems since they do not require prior knowledge about the distribution of the data. The NN algorithm often has the tendency to predict with higher accuracy than other techniques due to the NN’s capability to fit any continuous functions [18]. Mathematically, the NN can be referred to as a directed graph having neurons as vertices and links as edges. Different forms of NN depend on the connectivity of their neurons, and the simplest one is the Multi-layer perceptron, also known as the feedforward NN. Basically, a NN can have only one input and one output layer in its simplest form, and this can be written as: where m is the number of input variables, Φ is the activation function, wi,k is the weight of the input layer i with respect to the output k, b is the bias, and the input vector x is connected to the output k (denoting the kth neuron in the output layer) through a biased weighted sum. In the presence of hidden layers positioned between the input layers and the output layers, the output can be written as: where m1 is the number of input variables, m2 is the number of nodes in the hidden layer, Φ : R → R refers to non-linear activation functions for each of the layers in the brackets, and Φout is the possibly new output function. Recently, the NN has become an indispensable tool for learning the solutions of differential equations, and this section will utilize the potential of the NN in solving PDE-related problems [1, 10, 20, 50]. Also, the NN has been implemented in solving equations without analytical solutions. For instance, Nwankwo et al. [38] considered the solution of the American options PDE by incorporating the Landau transformation and solving the corresponding transformed function via a neural network approach. In many scientific and industrial contexts, there is a need to solve parametric PDEs using NN techniques and Khoo et al. [24] developed such a technique which solves PDE with inhomogeneous coefficient fields. For high-dimensional parametric PDE, [14] analyzed the deep parametric PDE method to solve high-dimensional parametric PDEs with much emphasis on financial applications. In the following, we describe the Bitcoin options with the corresponding Black-Scholes pricing PDE: The above equation which is a non-homogeneous PDE can be re-written as Standard theorems guarantee a classical smooth solution exists for the pricing PDE (3.13) given the assumed dynamics. The continuity and linear growth conditions on the coefficient functions ensure they satisfy Lipschitz continuity. Contingent claims theory shows that Lipschitz continuity is sufficient for existence and uniqueness under the stochastic process specifications. In particular, the smooth past price dependence in the diffusion coefficient allows the application results for delayed Black-Scholes equations. Therefore, the Cauchy problem is well-posed under the model assumptions, and a smooth pricing solution is guaranteed to exist based on the theorems. This provides the theoretical foundation for using a neural network to approximate the price function numerically. Thus, employing the ANN to solve the PDE, we introduce an approximating function ζ(t, S : θ) with parameter set θ. The loss or cost function associated with this training is measured by how well the approximation function satisfies the differential operator, boundary conditions and the terminal condition of the option pricing PDE. These are given respectively as Suppose L(ζ) = 0, then ζ(t, S : θ) is a solution of the PDE in equation (3.13). The major aim is to obtain a set of parameters θ such that the function ζ(t, S : θ) minimizes the observed error of L(ζ). The procedure for seeking a good parameter set by minimizing this loss function using the stochastic gradient descent (SGD) optimizer is called “training”. Thus, using a Machine Learning approach, and in this case, the artificial NN, it will be feasible to minimize the function L(ζ) by applying the SGD approach on the sequence of asset and time points which are drawn at random. A part of the input samples, fully dependent on the mini-batch size, is drawn within each iteration to estimate the gradient of the given objective function. The gradient is then estimated over these mini-batches due to the limitations of the computer memory [30]. The training of NN is classified into first identifying the network’s hyperparameters, that is, the architectural structure and the loss function of the network. Next, use the SGD to optimize or estimate the loss minimizer, and then the derivatives of the loss function are computed using the backpropagation techniques. Essentially, the process of searching and identifying the best θ parameter by minimizing the loss function using the gradient descent-based optimizers is referred to as “training”. The whole procedure is well illustrated in the algorithm below [46], and can be implemented in solving the PDE in equation (3.13): The learning rate α is employed to scale the intensity of the parameter updates during the gradient descent. Choosing the learning rate, as the descent parameter α, in the network training is crucial since this factor plays a significant role in aiding the algorithm’s convergence to the true solution in the gradient descent. It equally affects the pace at which the algorithm learns and whether or not the cost function is minimized. When α implies divergence, and thus, the optimal point can be missed. Also, a fixed value of α can most likely make the local optima overshoot after some iterations, leading to divergence. Defining the learning rate as a dynamic decreasing function is preferable since it allows the algorithm to identify the needed point rapidly. Another limitation in employing the gradient descent method is obtaining the value of the initial parameters of the loss function. If the value is significantly close to the local optimum, then the slope of the loss function reduces, thereby leading to the optimal convergence. Otherwise, there will be no convergence as the solution explodes abnormally. 3.1. Solution of bitcoin option pricing PDE While the pricing PDE has a proven smooth solution under the model dynamics, obtaining the analytical form is intractable. Numerical methods must be used to approximate the solution. Neural networks provide a flexible parametric approach based on their universal approximation theoretical results. Given sufficient network capacity, neural networks can represent a wide class of functions, including solutions to PDEs like the pricing equation. However, challenges remain in finding the optimal network parameters to recover the true solution robustly. While existence is guaranteed, the non-convex optimization of neural networks does not assure convergence to global optimality. Care must be taken in specifying the network architecture, loss function, regularization, and training methodology to promote the learning of the pricing function. Subject to these caveats, neural networks present a promising computational technique for approximating smooth pricing solutions, circumventing discretization of the domain. We note the limitations of using neural networks as function approximators. However, their generalization capabilities provide a methodology for data-driven extraction of the pricing mapping across the entire domain. This avoids the constraints of methods like grid-based techniques that rely on local consistency. Future work should explore neural network training enhancements and theoretical guarantees to ensure robust solutions. This paper is available on arxiv under CC 4.0 license. Authors: (1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com]; (2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [edsonpindza@gmail.com]; (2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction Methodology Neural Network Methodology Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations References Abstract and Introduction Abstract and Introduction Methodology Methodology Neural Network Methodology Neural Network Methodology Numerical results, implementation and discussion Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations Availability of data, code and materials, Contributions and Declarations References References 3. Neural Network Methodology The neural network (NN) algorithm is used for solving problems relating to dimensionality reduction [42, 49], visualization of data [31], clustering [11, 52] and classification issues [37, 40]. It is also used in regression [2, 21, 45] in solving regression problems since they do not require prior knowledge about the distribution of the data. The NN algorithm often has the tendency to predict with higher accuracy than other techniques due to the NN’s capability to fit any continuous functions [18]. Mathematically, the NN can be referred to as a directed graph having neurons as vertices and links as edges. Different forms of NN depend on the connectivity of their neurons, and the simplest one is the Multi-layer perceptron, also known as the feedforward NN. Basically, a NN can have only one input and one output layer in its simplest form, and this can be written as: where m is the number of input variables, Φ is the activation function, wi,k is the weight of the input layer i with respect to the output k, b is the bias, and the input vector x is connected to the output k (denoting the kth neuron in the output layer) through a biased weighted sum. In the presence of hidden layers positioned between the input layers and the output layers, the output can be written as: where m1 is the number of input variables, m2 is the number of nodes in the hidden layer, Φ : R → R refers to non-linear activation functions for each of the layers in the brackets, and Φout is the possibly new output function. Recently, the NN has become an indispensable tool for learning the solutions of differential equations, and this section will utilize the potential of the NN in solving PDE-related problems [1, 10, 20, 50]. Also, the NN has been implemented in solving equations without analytical solutions. For instance, Nwankwo et al. [38] considered the solution of the American options PDE by incorporating the Landau transformation and solving the corresponding transformed function via a neural network approach. In many scientific and industrial contexts, there is a need to solve parametric PDEs using NN techniques and Khoo et al. [24] developed such a technique which solves PDE with inhomogeneous coefficient fields. For high-dimensional parametric PDE, [14] analyzed the deep parametric PDE method to solve high-dimensional parametric PDEs with much emphasis on financial applications. In the following, we describe the Bitcoin options with the corresponding Black-Scholes pricing PDE: The above equation which is a non-homogeneous PDE can be re-written as Standard theorems guarantee a classical smooth solution exists for the pricing PDE (3.13) given the assumed dynamics. The continuity and linear growth conditions on the coefficient functions ensure they satisfy Lipschitz continuity. Contingent claims theory shows that Lipschitz continuity is sufficient for existence and uniqueness under the stochastic process specifications. In particular, the smooth past price dependence in the diffusion coefficient allows the application results for delayed Black-Scholes equations. Therefore, the Cauchy problem is well-posed under the model assumptions, and a smooth pricing solution is guaranteed to exist based on the theorems. This provides the theoretical foundation for using a neural network to approximate the price function numerically. Thus, employing the ANN to solve the PDE, we introduce an approximating function ζ(t, S : θ) with parameter set θ. The loss or cost function associated with this training is measured by how well the approximation function satisfies the differential operator, boundary conditions and the terminal condition of the option pricing PDE. These are given respectively as Suppose L(ζ) = 0, then ζ(t, S : θ) is a solution of the PDE in equation (3.13). The major aim is to obtain a set of parameters θ such that the function ζ(t, S : θ) minimizes the observed error of L(ζ). The procedure for seeking a good parameter set by minimizing this loss function using the stochastic gradient descent (SGD) optimizer is called “training”. Thus, using a Machine Learning approach, and in this case, the artificial NN, it will be feasible to minimize the function L(ζ) by applying the SGD approach on the sequence of asset and time points which are drawn at random. A part of the input samples, fully dependent on the mini-batch size, is drawn within each iteration to estimate the gradient of the given objective function. The gradient is then estimated over these mini-batches due to the limitations of the computer memory [30]. The training of NN is classified into first identifying the network’s hyperparameters, that is, the architectural structure and the loss function of the network. Next, use the SGD to optimize or estimate the loss minimizer, and then the derivatives of the loss function are computed using the backpropagation techniques. Essentially, the process of searching and identifying the best θ parameter by minimizing the loss function using the gradient descent-based optimizers is referred to as “training”. The whole procedure is well illustrated in the algorithm below [46], and can be implemented in solving the PDE in equation (3.13): The learning rate α is employed to scale the intensity of the parameter updates during the gradient descent. Choosing the learning rate, as the descent parameter α, in the network training is crucial since this factor plays a significant role in aiding the algorithm’s convergence to the true solution in the gradient descent. It equally affects the pace at which the algorithm learns and whether or not the cost function is minimized. When α implies divergence, and thus, the optimal point can be missed. Also, a fixed value of α can most likely make the local optima overshoot after some iterations, leading to divergence. Defining the learning rate as a dynamic decreasing function is preferable since it allows the algorithm to identify the needed point rapidly. Another limitation in employing the gradient descent method is obtaining the value of the initial parameters of the loss function. If the value is significantly close to the local optimum, then the slope of the loss function reduces, thereby leading to the optimal convergence. Otherwise, there will be no convergence as the solution explodes abnormally. 3.1. Solution of bitcoin option pricing PDE 3.1. Solution of bitcoin option pricing PDE While the pricing PDE has a proven smooth solution under the model dynamics, obtaining the analytical form is intractable. Numerical methods must be used to approximate the solution. Neural networks provide a flexible parametric approach based on their universal approximation theoretical results. Given sufficient network capacity, neural networks can represent a wide class of functions, including solutions to PDEs like the pricing equation. However, challenges remain in finding the optimal network parameters to recover the true solution robustly. While existence is guaranteed, the non-convex optimization of neural networks does not assure convergence to global optimality. Care must be taken in specifying the network architecture, loss function, regularization, and training methodology to promote the learning of the pricing function. Subject to these caveats, neural networks present a promising computational technique for approximating smooth pricing solutions, circumventing discretization of the domain. We note the limitations of using neural networks as function approximators. However, their generalization capabilities provide a methodology for data-driven extraction of the pricing mapping across the entire domain. This avoids the constraints of methods like grid-based techniques that rely on local consistency. Future work should explore neural network training enhancements and theoretical guarantees to ensure robust solutions.

Neural Network for Valuing Bitcoin: Neural Network Methodology

Metamorphosis Commenced: Network States v0.01

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Adaptive Graph Neural Networks for Cosmological Data Generalization: Acknowledgements and Disclosure

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Andrea Roncoli, Department of Computer, Science (University of Pisa);
(2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago);
(3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory);
(4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute);
(5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Data and Methods Results Conclusions Acknowledgments and Disclosure of Funding, and References Additional Plots 4 Conclusions We propose and demonstrate a method for unsupervised DA for cosmological inference with GNNs. We use an MMD-based loss to enable the domain-invariant encoding of features by the GNN. This approach enhances cross-domain robustness: compared to previous methods, DA-GNNs reduce prediction error and improve uncertainty estimates. Limitations The cross-domain accuracy remains worse when compared to single-domain performance. Although reaching the same accuracy might not be possible, more flexible approaches such as adversarial-based DA techniques [20, 36], instead of distance-based ones such as MMD, might yield better results. Moreover, due to computational and time constraints, our models have been trained and tested only on two of the four available CAMELS simulation suites. Using more suites would yield better cross-domain efficacy and reliability at assessment time. These limitations will be addressed in future work. This paper is available on arxiv under CC 4.0 license. Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). This paper is available on arxiv under CC 4.0 license. available on arxiv Authors: Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Abstract and Intro Data and Methods Data and Methods Results Results Conclusions Conclusions Acknowledgments and Disclosure of Funding, and References Acknowledgments and Disclosure of Funding, and References Additional Plots Additional Plots 4 Conclusions We propose and demonstrate a method for unsupervised DA for cosmological inference with GNNs. We use an MMD-based loss to enable the domain-invariant encoding of features by the GNN. This approach enhances cross-domain robustness: compared to previous methods, DA-GNNs reduce prediction error and improve uncertainty estimates. Limitations The cross-domain accuracy remains worse when compared to single-domain performance. Although reaching the same accuracy might not be possible, more flexible approaches such as adversarial-based DA techniques [20, 36], instead of distance-based ones such as MMD, might yield better results. Moreover, due to computational and time constraints, our models have been trained and tested only on two of the four available CAMELS simulation suites. Using more suites would yield better cross-domain efficacy and reliability at assessment time. These limitations will be addressed in future work. Limitations

Adaptive Graph Neural Networks for Cosmological Data Generalization: Conclusions

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Andrea Roncoli, Department of Computer, Science (University of Pisa);
(2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago);
(3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory);
(4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute);
(5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Data and Methods Results Conclusions Acknowledgments and Disclosure of Funding, and References Additional Plots 3 Results Latent space organization Isomaps are two-dimensional projections of the multi-dimensional latent space [35]. Figure 1 shows the difference in the latent space structure without (top row) and with (bottom row) DA. Ellipses in the top right isomap highlight how the two distributions are encoded in different regions of the latent space. Without the MMD loss, the model encodes samples with very different values of Ωm close to each other, if they originate from different simulations (circles and triangles of different colors are overlapping). This scenario leads to the fragility of the regressor, which cannot learn to output different values for the same latent space encodings. On the contrary, the DA-GNN (bottom right plot) correctly encodes the samples in a domain-invariant way. Visually, circle and triangle distributions are overlapping, which indicates domain mixing. Furthermore, the direction in the color gradient shows that the DA-GNN encodes information such that the regressor can now more correctly predict cosmological parameters based on the encodings of both simulations. [5] In [41], authors get slightly better results for the same domain, and slightly worse for the cross-domain tests. We impute these differences to choices such as batch sizes and optimization techniques we took due to computational and time constraints. [6] In Appendix A, the IllustrisTNG counterpart of this plot is presented. This paper is available on arxiv under CC 4.0 license. Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). This paper is available on arxiv under CC 4.0 license. available on arxiv Authors: Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Abstract and Intro Data and Methods Data and Methods Results Results Conclusions Conclusions Acknowledgments and Disclosure of Funding, and References Acknowledgments and Disclosure of Funding, and References Additional Plots Additional Plots 3 Results Latent space organization Isomaps are two-dimensional projections of the multi-dimensional latent space [35]. Figure 1 shows the difference in the latent space structure without (top row) and with (bottom row) DA. Ellipses in the top right isomap highlight how the two distributions are encoded in different regions of the latent space. Without the MMD loss, the model encodes samples with very different values of Ωm close to each other, if they originate from different simulations (circles and triangles of different colors are overlapping). This scenario leads to the fragility of the regressor, which cannot learn to output different values for the same latent space encodings. On the contrary, the DA-GNN (bottom right plot) correctly encodes the samples in a domain-invariant way. Visually, circle and triangle distributions are overlapping, which indicates domain mixing. Furthermore, the direction in the color gradient shows that the DA-GNN encodes information such that the regressor can now more correctly predict cosmological parameters based on the encodings of both simulations. [5] In [41], authors get slightly better results for the same domain, and slightly worse for the cross-domain tests. We impute these differences to choices such as batch sizes and optimization techniques we took due to computational and time constraints. [6] In Appendix A, the IllustrisTNG counterpart of this plot is presented.

Adaptive Graph Neural Networks for Cosmological Data Generalization: Results

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Andrea Roncoli, Department of Computer, Science (University of Pisa);
(2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago);
(3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory);
(4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute);
(5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Data and Methods Results Conclusions Acknowledgments and Disclosure of Funding, and References Additional Plots 2 Data and Methods 2.1 Domain Adaptation Optimization and Computing Resources We performed experiments on NVIDIA A100 40GB GPU. For each of the models, implemented using PyTorch Geometric [19], we perform a hyperparameter search using the Optuna library [1], with 50 trials per model. More details on code performance, model implementations, and selected hyperparameters can be found in the publicly available code[4]. 2.2 Evaluation [1] https://arepo-code.org/ [2] http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.html [3] CAMELS dataset documentation: https://camels.readthedocs.io/en/latest/index.html [4] GitHub repository will be added after the anonymous review stage. This paper is available on arxiv under CC 4.0 license. Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). This paper is available on arxiv under CC 4.0 license. available on arxiv Authors: Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Abstract and Intro Data and Methods Data and Methods Results Results Conclusions Conclusions Acknowledgments and Disclosure of Funding, and References Acknowledgments and Disclosure of Funding, and References Additional Plots Additional Plots 2 Data and Methods 2.1 Domain Adaptation Optimization and Computing Resources We performed experiments on NVIDIA A100 40GB GPU. For each of the models, implemented using PyTorch Geometric [19], we perform a hyperparameter search using the Optuna library [1], with 50 trials per model. More details on code performance, model implementations, and selected hyperparameters can be found in the publicly available code[4]. Optimization and Computing Resources 2.2 Evaluation [1] https://arepo-code.org/ [2] http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.html [3] CAMELS dataset documentation: https://camels.readthedocs.io/en/latest/index.html [4] GitHub repository will be added after the anonymous review stage.

Adaptive Graph Neural Networks for Cosmological Data Generalization: Data and Methods

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Andrea Roncoli, Department of Computer, Science (University of Pisa);
(2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago);
(3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory);
(4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute);
(5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Data and Methods Results Conclusions Acknowledgments and Disclosure of Funding, and References Additional Plots Abstract 1 Introduction Accurate determination of cosmological parameters using big data from astronomical surveys is a task of paramount importance in modern science. Historically, the extraction of valuable cosmological information has relied on computing summary statistics [31, 16, 15]. More recently, deep learning methods, such as 2D and 3D Convolutional Neural Networks (CNNs), showed great promise in extracting rich non-linear information that summary statistics struggle to capture [32, 39, 29]. However, CNNs lack scale-invariance, as their analysis is firmly anchored to the grid size of the convolutional kernels, while any information on scales below that is lost. Choosing a superfine grid to avoid information loss, though, would simply yield almost entirely zeros in case of sparse and irregular data, such as galaxy clusterings. Thus, CNNs result in an inadequate method for structured sparse data. In contrast, Graph Neural Networks (GNNs) [23, 4, 49, 46] can handle structured cosmic web data in a scale-free manner [41, 14]. As with any other model, the typical procedure is to train GNNs on labeled data (like simulations) and then infer cosmological parameters from unlabeled data (like observations). However, there is a significant risk of these models not generalizing in the presence of the domain shift between simulations and observations. Systematic biases have been demonstrated even in experiments that train and test on simulations with different subgrid physics [41]. Domain adaptation (DA) techniques [11, 43, 18, 27] can be used to increase model robustness to this type of domain shift. Here we propose the use of Domain Adaptive Graph Neural Networks (DA-GNNs) and investigate the utility of distance-based DA losses i.e., Maximum Mean Discrepancy (MMD) [6]. MMD is an unsupervised DA technique because it does not require labeled data, which is paramount for future applications on observations. We show that our domain-adaptive models achieve stronger generalization across datasets than regular GNN models. Our work is a significant step towards building future models trained on simulations, yet robust enough to work on observational data. Related Work GNNs have shown great potential for extracting information from large sparse datasets, such as the distribution of galaxies, galaxy clusters, and cosmic large-scale structures [25, 28, 41, 33, 42, 14]. Unfortunately, due to the complexity of most deep learning models, they often learn dataset-specific features, which renders them useless when testing on a different dataset (different simulations or astronomical observations). In astronomy, it has been shown that DA techniques applied to different types of CNNs can substantially improve model performance in cross-dataset applications [8, 10, 9, 37, 21, 2]. Recently, it has been shown that DA can be used on other types of deep learning algorithms such as GNNs [12, 24, 45, 47, 7, 44, 17]. However, DA on GNNs has not been used for any astrophysics or cosmology applications. This paper is available on arxiv under CC 4.0 license. Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). This paper is available on arxiv under CC 4.0 license. available on arxiv Authors: Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Abstract and Intro Data and Methods Data and Methods Results Results Conclusions Conclusions Acknowledgments and Disclosure of Funding, and References Acknowledgments and Disclosure of Funding, and References Additional Plots Additional Plots Abstract 1 Introduction Accurate determination of cosmological parameters using big data from astronomical surveys is a task of paramount importance in modern science. Historically, the extraction of valuable cosmological information has relied on computing summary statistics [31, 16, 15]. More recently, deep learning methods, such as 2D and 3D Convolutional Neural Networks (CNNs), showed great promise in extracting rich non-linear information that summary statistics struggle to capture [32, 39, 29]. However, CNNs lack scale-invariance, as their analysis is firmly anchored to the grid size of the convolutional kernels, while any information on scales below that is lost. Choosing a superfine grid to avoid information loss, though, would simply yield almost entirely zeros in case of sparse and irregular data, such as galaxy clusterings. Thus, CNNs result in an inadequate method for structured sparse data. In contrast, Graph Neural Networks (GNNs) [23, 4, 49, 46] can handle structured cosmic web data in a scale-free manner [41, 14]. As with any other model, the typical procedure is to train GNNs on labeled data (like simulations) and then infer cosmological parameters from unlabeled data (like observations). However, there is a significant risk of these models not generalizing in the presence of the domain shift between simulations and observations. Systematic biases have been demonstrated even in experiments that train and test on simulations with different subgrid physics [41]. Domain adaptation (DA) techniques [11, 43, 18, 27] can be used to increase model robustness to this type of domain shift. Here we propose the use of Domain Adaptive Graph Neural Networks (DA-GNNs) and investigate the utility of distance-based DA losses i.e., Maximum Mean Discrepancy (MMD) [6]. MMD is an unsupervised DA technique because it does not require labeled data, which is paramount for future applications on observations. We show that our domain-adaptive models achieve stronger generalization across datasets than regular GNN models. Our work is a significant step towards building future models trained on simulations, yet robust enough to work on observational data. Related Work GNNs have shown great potential for extracting information from large sparse datasets, such as the distribution of galaxies, galaxy clusters, and cosmic large-scale structures [25, 28, 41, 33, 42, 14]. Unfortunately, due to the complexity of most deep learning models, they often learn dataset-specific features, which renders them useless when testing on a different dataset (different simulations or astronomical observations). In astronomy, it has been shown that DA techniques applied to different types of CNNs can substantially improve model performance in cross-dataset applications [8, 10, 9, 37, 21, 2]. Recently, it has been shown that DA can be used on other types of deep learning algorithms such as GNNs [12, 24, 45, 47, 7, 44, 17]. However, DA on GNNs has not been used for any astrophysics or cosmology applications. Related Work

Adaptive Graph Neural Networks for Cosmological Data Generalization: Abstract and Intro

Omnity Network, the first fully on-chain Bitcoin asset hub, plans to provide Bitcoin liquidity and security to any connected chain. The Bitcoin interoperability hub, launched after the Bitcoin halving, was the first protocol to support Runes interoperability with its Red Envelope HOPE YOU GET RICH Runes token ($RICH.) Omnity's omnichain hub is built on the Internet Computer (ICP). ICP's Chain Fusion Technology allows Omnity to read and write directly to the Bitcoin network, sidestepping the congestion and high user fees. Ordinal NFT and Runes asset standards have increased Bitcoin's potential as a general-purpose settlement layer, but these assets can bottleneck the Bitcoin network. Omnity says it has solved this problem without compromising security or decentralization. It is now expanding its scope to include Bitcoin staking and shared security to become the "Liquidity and Security Hub of the Bitcoin Ecosystem." Omnity's novelty lies in its ability to achieve a user experience comparable to trust-based bridges without relying on off-chain witnesses or relayers due to its 100% end-to-end on-chain tech stack. As the liquidity and security hub of the Bitcoin ecosystem, Omnity's goal is to support Bitcoin Shared Security Services for execution chains or Layer-2s (L2s) by providing L2s multibillion-dollar-level security at a modest cost. Any end-user-facing, highly usable blockchain that deals with Bitcoin assets and needs to peg security to the Bitcoin Network could then be connected through Omnity. Armed with ICP's Chain Fusion, Omnity acts as the "bond" between the Bitcoin settlement layer and unlimited execution layers, ready to handle massive transactions because ICP is infinitely scalable. Omnity's roadmap includes the launch of Bitcoin Staking in Q3 2024, followed by Bitcoin Shared Security in Q4 2024. Omnity's Service Nervous System (SNS) governance token, $OT, will also be released in Q4, granting voting rights via $OT SNS staking. The SNS framework is the Internet Computer's built-in solution for creating and maintaining decentralized autonomous organizations (DAOs) to govern Dapps. Omnity’s SNS DAO shall implement voting rights for determining protocol upgrades, blockchain connections to the Omnity Interoperability Network, and Bitcoin L2 connections to use Omnity's shared security. "We hope that Bitcoin will be the settlement layer for the world economy because it is a common good. No one can control Bitcoin. It's an impartial and non-abusable settlement layer," said Louis Liu, Founder of Omnity. "Similarly, Omnity is an ‘unopinionated infrastructure.’ We don't care what type of blockchain it is. We care about what our users are willing to use. If it can bring some utility, entertainment, or profit to Bitcoin asset holders, Omnity will direct Bitcoin assets to that blockchain." From a technical perspective, Omnity relies on ICP's Bitcoin integration to bring Bitcoin assets, BTC, or Runes to ICP. A dedicated subnet has made ICP an impartible part of the Bitcoin network. Dfinity Foundation has a world-class cryptography research team that supported the development of Chain Key Cryptography, the cornerstone of ICP and the Bitcoin integration, safeguarding assets worth billions in USD. However, connections to all other blockchains rely fully on the Omnity team's extensive experience with IBC Protocol implementations and on-chain light clients. "As the only team to implement IBC-ICS 28 on Rust/Wasm chains, Omnity has transplanted many kinds of on-chain light clients, such as Tendermint, Substrate, and NEAR light clients, to enable trustless interoperability,” says Liu. Omnity can immediately support Tendermint-based, Substrate-based, and Polygon CDK-based blockchains, with plans to include OP stack-based L2s and others. Omnity Network , the first fully on-chain Bitcoin asset hub, plans to provide Bitcoin liquidity and security to any connected chain. The Bitcoin interoperability hub, launched after the Bitcoin halving, was the first protocol to support Runes interoperability with its Red Envelope HOPE YOU GET RICH Runes token ($RICH.) Omnity Network Omnity Network Omnity's omnichain hub is built on the Internet Computer (ICP). ICP's Chain Fusion Technology allows Omnity to read and write directly to the Bitcoin network, sidestepping the congestion and high user fees. Internet Computer Internet Computer Chain Fusion Technology Chain Fusion Technology Ordinal NFT and Runes asset standards have increased Bitcoin's potential as a general-purpose settlement layer, but these assets can bottleneck the Bitcoin network. Omnity says it has solved this problem without compromising security or decentralization. It is now expanding its scope to include Bitcoin staking and shared security to become the "Liquidity and Security Hub of the Bitcoin Ecosystem." Omnity's novelty lies in its ability to achieve a user experience comparable to trust-based bridges without relying on off-chain witnesses or relayers due to its 100% end-to-end on-chain tech stack . As the liquidity and security hub of the Bitcoin ecosystem, Omnity's goal is to support Bitcoin Shared Security Services for execution chains or Layer-2s (L2s) by providing L2s multibillion-dollar-level security at a modest cost. 100% end-to-end on-chain tech stack 100% end-to-end on-chain tech stack Any end-user-facing, highly usable blockchain that deals with Bitcoin assets and needs to peg security to the Bitcoin Network could then be connected through Omnity. Armed with ICP's Chain Fusion, Omnity acts as the "bond" between the Bitcoin settlement layer and unlimited execution layers, ready to handle massive transactions because ICP is infinitely scalable. Omnity's roadmap includes the launch of Bitcoin Staking in Q3 2024, followed by Bitcoin Shared Security in Q4 2024. Omnity's Service Nervous System (SNS) governance token, $OT, will also be released in Q4, granting voting rights via $OT SNS staking. The SNS framework is the Internet Computer's built-in solution for creating and maintaining decentralized autonomous organizations (DAOs) to govern Dapps. Omnity’s SNS DAO shall implement voting rights for determining protocol upgrades, blockchain connections to the Omnity Interoperability Network, and Bitcoin L2 connections to use Omnity's shared security. Service Nervous System (SNS) Service Nervous System (SNS) "We hope that Bitcoin will be the settlement layer for the world economy because it is a common good. No one can control Bitcoin. It's an impartial and non-abusable settlement layer," said Louis Liu, Founder of Omnity. "Similarly, Omnity is an ‘unopinionated infrastructure.’ We don't care what type of blockchain it is. We care about what our users are willing to use. If it can bring some utility, entertainment, or profit to Bitcoin asset holders, Omnity will direct Bitcoin assets to that blockchain." From a technical perspective, Omnity relies on ICP's Bitcoin integration to bring Bitcoin assets, BTC, or Runes to ICP. A dedicated subnet has made ICP an impartible part of the Bitcoin network. Dfinity Foundation has a world-class cryptography research team that supported the development of Chain Key Cryptography , the cornerstone of ICP and the Bitcoin integration, safeguarding assets worth billions in USD. Dfinity Foundation Dfinity Foundation Chain Key Cryptography Chain Key Cryptography However, connections to all other blockchains rely fully on the Omnity team's extensive experience with IBC Protocol implementations and on-chain light clients. "As the only team to implement IBC-ICS 28 on Rust/Wasm chains, Omnity has transplanted many kinds of on-chain light clients, such as Tendermint, Substrate, and NEAR light clients, to enable trustless interoperability,” says Liu. IBC Protocol IBC Protocol Omnity can immediately support Tendermint-based, Substrate-based, and Polygon CDK-based blockchains, with plans to include OP stack-based L2s and others.

Omnity Network's Fully Onchain Hub Announces Bitcoin Staking and Shared Security

ওমনিটি নেটওয়ার্কের সম্পূর্ণ অনচেইন হাব বিটকয়েন স্টেকিং এবং শেয়ার্ড সিকিউরিটি ঘোষণা করেছে

Der vollständig Onchain-Hub von Omnity Network kündigt Bitcoin-Staking und gemeinsame Sicherheit an

El centro totalmente en cadena de Omnity Network anuncia participación y seguridad compartida de Bitcoin

Le hub entièrement en chaîne d'Omnity Network annonce le jalonnement Bitcoin et la sécurité partagée

ओम्निटी नेटवर्क के पूर्णतः ऑनचेन हब ने बिटकॉइन स्टेकिंग और साझा सुरक्षा की घोषणा की

オムニティネットワークの完全オンチェーンハブがビットコインのステーキングと共有セキュリティを発表

Omnity Network의 완전 온체인 허브, 비트코인 스테이킹 및 공유 보안 발표

Hub Fully Onchain da Omnity Network anuncia piquetagem de Bitcoin e segurança compartilhada

Полностью ончейн-концентратор Omnity Network объявляет о стейкинге биткойнов и общей безопасности

Omnity Network'ün Tamamen Zincir Üzerindeki Merkezi, Bitcoin Staking ve Paylaşımlı Güvenliği Duyurdu

Trung tâm Onchain hoàn chỉnh của Omnity Network công bố đặt cọc Bitcoin và bảo mật chia sẻ

Omnity Network 的 Fully Onchain Hub 宣布推出比特币质押和共享安全

PANAMA CITY, Panama, May 2nd, 2024/Chainwire/--AppLayer, has unveiled the fastest and most robust infrastructure for scaling Ethereum-based applications, a cutting-edge blockchain that not only delivers lightning-fast transaction speeds but also offers a new approach to Ethereum Virtual Machine (EVM) development for both DeFi and GameFi developers. AppLayer offers an EVM network that's 10 times faster than standard Golang based EVM networks and an even more amazing 65 times execution speed boost with C++ stateful pre-compiles. Imagine having both the speediest EVM in the game and the best tools to build on it – that's what AppLayer brings to the table! The Game Changer: Stateful Pre-compiled Smart Contracts AppLayer is not only a speed powerhouse but also allows for comprehensive composability with game-changing stateful pre-compiles that are a cornerstone of this release, offering an unmatched ability to process complex smart contracts at unprecedented speeds. But what does this mean for everyday users and developers? It's simple: AppLayer’s network brings the power of advanced blockchain technology right to the user's fingertips. Developers can now create their own stateful pre-compiles as smart contracts with features and syntax that are identical to Solidity, but with the added turbo-charge of C++ performance. The real excitement stems from the intricate workings of AppLayer’s network with these Stateful Pre-compiles. Solidity smart contracts no longer function in isolation but interact with and build upon these ultra-fast pre-compiles. This enhances the sophistication, power, and efficiency of blockchain applications, marking a significant shift in the landscape of decentralization. The best part for developers is the ease of transition to this high-performance environment. AppLayer allows developers to effortlessly convert their existing Solidity code into C++ with nearly identical syntax, unlocking the potential for more complex and scalable dApps. This feature is especially vital for blockchain projects hitting performance limitations in traditional EVM environments. AppLayer takes it further with rdPoS (random deterministic Proof of Stake) – a unique consensus mechanism that amplifies network security while ensuring ultra-efficient transaction processing. This ingenious combination of stateful pre-compiles and rdPoS turns AppLayer into a robust platform perfect for handling high-scale and intricate applications. As Itamar Carvalho, CTO at AppLayer, stated at ETHDenver 2024, “AppLayer is not just an upgrade; it’s a revolution. We’re empowering developers to build without boundaries, pushing the limits of what's possible in blockchain application development.” AppLayer stands as a testament to innovation, redefining the standards of blockchain development and opening new horizons in the gaming sector, decentralized finance, and beyond. With its combination of speed, efficiency, and developer-friendly features, AppLayer is poised to become a leading force in the blockchain space. Expanding EVM Horizons with the Testnet Launch The next exciting phase for AppLayer is the deployment of its testnet, complete with a front-end user portal coming in June and up to $1.5 million in incentives available now. This stage invites developers to push the boundaries of their existing Solidity code into a more robust, scalable environment. The more unique and intricate the transactions, the greater the reward, fostering a creative and efficient ecosystem. AppLayer is now inviting developers to participate in its incentivized testnet. With a unique rewards system based on user activity and creativity, AppLayer is fostering a vibrant and innovative developer community. “We are excited to see what developers will build on AppLayer. This is an opportunity to reshape the landscape of blockchain applications,” said Carvalho. The AppLayer testnet not only represents a pivotal moment for blockchain innovation but also a unique opportunity for both crypto enthusiasts and developers. Whether the user is looking to explore cutting-edge projects on the fastest EVM or the user is a developer eager to build on this revolutionary platform, AppLayer's testnet is their gateway to opportunity and rewards. Build on the AppLayer Testnet to Unlock Grants Developers, on the other hand, are invited to bring their creativity and technical skills to the forefront. Build on AppLayer, the fastest EVM network, and receive $APPL token grants as recognition of the user's innovative contributions. With up to 100,000,000 $APPL tokens available for allocation to projects, the potential for reward is substantial. Additionally, for every $APPL token a project distributes to users, an equal amount is granted back to the project, forming a cycle of innovation and reward that continues through to the mainnet launch. The most engaging and interacted-with projects may be eligible for additional allocations, incentivizing not just development but also user engagement. This is a testnet that rewards utilization and creativity, pushing for more unique and complex smart contracts. For more information on the Grants Program and how to participate, users can fill out an application to get started and become a part of this transformative phase in blockchain development. Users can discover, build, and earn with AppLayer – where the future of blockchain is being shaped today. About AppLayer: AppLayer (formerly SparqNet) is a C++ based Ethereum scaling solution where developers can deploy Solidity smart contracts and C++ programmed stateful pre-compiles as smart contracts. In AppLayer, Solidity smart contracts are 10 times faster than those in Golang-based competing networks, and stateful pre-compiles are 65 times faster. Website: https://applayer.com/ Twitter: https://twitter.com/AppLayerLabs Discord: https://discord.gg/6dsUebskfA Telegram: https://t.me/AppLayerLabs Contact CEO Michael Weinrub AppLayer michael@applayer.com This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here. PANAMA CITY, Panama, May 2nd, 2024/Chainwire/--AppLayer, has unveiled the fastest and most robust infrastructure for scaling Ethereum-based applications, a cutting-edge blockchain that not only delivers lightning-fast transaction speeds but also offers a new approach to Ethereum Virtual Machine (EVM) development for both DeFi and GameFi developers. AppLayer offers an EVM network that's 10 times faster than standard Golang based EVM networks and an even more amazing 65 times execution speed boost with C++ stateful pre-compiles. Imagine having both the speediest EVM in the game and the best tools to build on it – that's what AppLayer brings to the table! The Game Changer: Stateful Pre-compiled Smart Contracts AppLayer is not only a speed powerhouse but also allows for comprehensive composability with game-changing stateful pre-compiles that are a cornerstone of this release, offering an unmatched ability to process complex smart contracts at unprecedented speeds. But what does this mean for everyday users and developers? It's simple: AppLayer’s network brings the power of advanced blockchain technology right to the user's fingertips. Developers can now create their own stateful pre-compiles as smart contracts with features and syntax that are identical to Solidity, but with the added turbo-charge of C++ performance. The real excitement stems from the intricate workings of AppLayer’s network with these Stateful Pre-compiles. Solidity smart contracts no longer function in isolation but interact with and build upon these ultra-fast pre-compiles. This enhances the sophistication, power, and efficiency of blockchain applications, marking a significant shift in the landscape of decentralization. The best part for developers is the ease of transition to this high-performance environment. AppLayer allows developers to effortlessly convert their existing Solidity code into C++ with nearly identical syntax, unlocking the potential for more complex and scalable dApps. This feature is especially vital for blockchain projects hitting performance limitations in traditional EVM environments. AppLayer takes it further with rdPoS (random deterministic Proof of Stake) – a unique consensus mechanism that amplifies network security while ensuring ultra-efficient transaction processing. This ingenious combination of stateful pre-compiles and rdPoS turns AppLayer into a robust platform perfect for handling high-scale and intricate applications. As Itamar Carvalho, CTO at AppLayer, stated at ETHDenver 2024, “AppLayer is not just an upgrade; it’s a revolution. We’re empowering developers to build without boundaries, pushing the limits of what's possible in blockchain application development.” As Itamar Carvalho, CTO at AppLayer, stated at ETHDenver 2024, “AppLayer is not just an upgrade; it’s a revolution. We’re empowering developers to build without boundaries, pushing the limits of what's possible in blockchain application development.” AppLayer stands as a testament to innovation, redefining the standards of blockchain development and opening new horizons in the gaming sector, decentralized finance, and beyond. With its combination of speed, efficiency, and developer-friendly features, AppLayer is poised to become a leading force in the blockchain space. Expanding EVM Horizons with the Testnet Launch The next exciting phase for AppLayer is the deployment of its testnet, complete with a front-end user portal coming in June and up to $1.5 million in incentives available now . This stage invites developers to push the boundaries of their existing Solidity code into a more robust, scalable environment. $1.5 million in incentives available now $1.5 million in incentives available now The more unique and intricate the transactions, the greater the reward, fostering a creative and efficient ecosystem. AppLayer is now inviting developers to participate in its incentivized testnet. With a unique rewards system based on user activity and creativity, AppLayer is fostering a vibrant and innovative developer community. “We are excited to see what developers will build on AppLayer. This is an opportunity to reshape the landscape of blockchain applications,” said Carvalho. “We are excited to see what developers will build on AppLayer. This is an opportunity to reshape the landscape of blockchain applications,” said Carvalho. The AppLayer testnet not only represents a pivotal moment for blockchain innovation but also a unique opportunity for both crypto enthusiasts and developers. Whether the user is looking to explore cutting-edge projects on the fastest EVM or the user is a developer eager to build on this revolutionary platform, AppLayer's testnet is their gateway to opportunity and rewards. Build on the AppLayer Testnet to Unlock Grants Developers, on the other hand, are invited to bring their creativity and technical skills to the forefront. Build on AppLayer, the fastest EVM network, and receive $APPL token grants as recognition of the user's innovative contributions. With up to 100,000,000 $APPL tokens available for allocation to projects, the potential for reward is substantial. Additionally, for every $APPL token a project distributes to users, an equal amount is granted back to the project, forming a cycle of innovation and reward that continues through to the mainnet launch. The most engaging and interacted-with projects may be eligible for additional allocations, incentivizing not just development but also user engagement. This is a testnet that rewards utilization and creativity, pushing for more unique and complex smart contracts. For more information on the Grants Program and how to participate, users can fill out an application to get started and become a part of this transformative phase in blockchain development. Users can discover, build, and earn with AppLayer – where the future of blockchain is being shaped today. fill out an application to get started fill out an application to get started About AppLayer: AppLayer (formerly SparqNet) is a C++ based Ethereum scaling solution where developers can deploy Solidity smart contracts and C++ programmed stateful pre-compiles as smart contracts. In AppLayer, Solidity smart contracts are 10 times faster than those in Golang-based competing networks, and stateful pre-compiles are 65 times faster. AppLayer AppLayer Website: https://applayer.com/ https://applayer.com/ https://applayer.com/ Twitter: https://twitter.com/AppLayerLabs https://twitter.com/AppLayerLabs https://twitter.com/AppLayerLabs Discord: https://discord.gg/6dsUebskfA https://discord.gg/6dsUebskfA https://discord.gg/6dsUebskfA Telegram: https://t.me/AppLayerLabs https://t.me/AppLayerLabs https://t.me/AppLayerLabs Contact CEO Michael Weinrub AppLayer michael@applayer.com This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here. This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here . here here

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