Arithmetic engages in internet-based advertising business.

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Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type ...

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Computer Arithmetic is a successful, profitable, and fast growing company in the Software development and consulting industry. It is through its continuing commitment to excellence that we have achieved this success. Their solutions change the way users operate, improve their productivity, ...

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Arithmos supports the Life Science companies to embrace digital transformation and value-added business services.

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Services across Clinical Development, Regulatory, Quality Management, PV, and Medical Affairs domains for pharma, biotech and medical device companies.

Arithmos | Consulting, Technology and Services for Life Sciences

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Arithmix Company Profile: Acquisition & Investors | PitchBook

Information on acquisition, funding, investors, and executives for Arithmos. Use the PitchBook Platform to explore the full profile.

Arithmos Company Profile: Acquisition & Investors | PitchBook

Arithmix allows anyone to build the ideal app to run numbers, unite the team, and make the perfect moves together.

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Arith Company Ltd. - Governors America Corp.

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Arithmo | 39 followers on LinkedIn. Arithmo makes bookkeeping quick, simple and cost effective. Its easy to use interface means even a complete beginner can be up and running in minutes, without any accountancy training. At the same time, Arithmo is very powerful online accounting software, ...

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And we encourage anyone, any use case, to pick it up and start running numbers in minutes · Arithmix co-founders Jack Binks and Bruno Nicoletti reinvented CGI/visual effects for movies and television by streamlining multidimensional data (image) modeling. Their software enabled visual artists ...

About Us

This year Arithmos is celebrating its 10th anniversary. Founded in 2010, Arithmos was born as an innovative IT solutions provider with a specific focus on the Life Sciences value chain. Since then the company has grown to an international business that offers...

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Arithmix was founded because we know there&#x27;s untapped potential in your numbers - potential that gets unlocked when everyone in the team understands what these numbers are showing them. With Arithmix, anyone can build the ideal app to run their num...

Arithmix, Inc. - Current Openings

With Buzzfile, clients can search Buzzfile&#x27;s vast database of 18 million companies, 50 million contacts and 6 million places to uncover more prospects, close more deals, and do it in less time. Buzzfile also provides unique productivity tools for Telecommunications professionals.

Arith Inc. in Palo Alto, CA - (408) 439-0412 - Company Profile

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STMicroelectronics announces completion of acquisition of Arithmos ...

From Proto-Indo-European *h₂rey-. Cognates include Old Irish rím, Old English rīm (English rhyme), and perhaps Latin rītus. Also compare νήριτος (nḗritos, “countless”) · ᾰ̓ρῐθμός • (arithmós) m (genitive ᾰ̓ρῐθμοῦ); second declension (Epic, Attic, Ionic, ...

ἀριθμός - Wiktionary, the free dictionary

Arithmikis in the AI Infrastructure Industry

Arithmik

Author:
(1) Yitang Zhang. Table of Links Abstract & Introduction
Notation and outline of the proof
The set Ψ1
Zeros of L(s, ψ)L(s, χψ) in Ω
Some analytic lemmas
Approximate formula for L(s, ψ)
Mean value formula I
Evaluation of Ξ11
Evaluation of Ξ12
Proof of Proposition 2.4
Proof of Proposition 2.6
Evaluation of Ξ15
Approximation to Ξ14
Mean value formula II
Evaluation of Φ1
Evaluation of Φ2
Evaluation of Φ3
Proof of Proposition 2.5 Appendix A. Some Euler products Appendix B. Some arithmetic sums References Appendix B. Some arithmetic sums Proof of Lemma 15.1. Put First we claim that Since χ = µ ∗ ν, it follows that Hence This together with Lemma 3.2 yields (B.1). Next we claim that This yields (B.2). By (B.1) and (B.2), for µ = 2, 3, We proceed to prove theassertion with µ = 2. Since for σ > 1 and it follows that For µ = 1 the proof is therefore reduced to showing that By (4.2) and (4.3), the left side of (B.3) is equal to By a change of variable, for 0.5 ≤ z ≤ 0.504, Hence, in a way similar to the proof of, we find that the left side of (B.3) i Proof of Lemma 17.1. By Lemma 3.1, The sum on the right side is equal to Assume σ > 1. We have If χ(p) = 1, then (see [19, (1.2.10)]) if χ(p) = −1, then if χ(p) = 0, then Hence In a way similar to the proof of, by (A) and simple estimate, we find that the integral (14) is equal to the residue of the function at s = 0, plus an acceptable error O, which is equal to This paper is available on arxiv under CC 4.0 license. Author: (1) Yitang Zhang. Author: Author: (1) Yitang Zhang. Table of Links Abstract & Introduction Notation and outline of the proof The set Ψ1 Zeros of L(s, ψ)L(s, χψ) in Ω Some analytic lemmas Approximate formula for L(s, ψ) Mean value formula I Evaluation of Ξ11 Evaluation of Ξ12 Proof of Proposition 2.4 Proof of Proposition 2.6 Evaluation of Ξ15 Approximation to Ξ14 Mean value formula II Evaluation of Φ1 Evaluation of Φ2 Evaluation of Φ3 Proof of Proposition 2.5 Abstract & Introduction Abstract & Introduction Notation and outline of the proof Notation and outline of the proof The set Ψ1 The set Ψ1 Zeros of L(s, ψ)L(s, χψ) in Ω Zeros of L(s, ψ)L(s, χψ) in Ω Some analytic lemmas Some analytic lemmas Approximate formula for L(s, ψ) Approximate formula for L(s, ψ) Mean value formula I Mean value formula I Evaluation of Ξ11 Evaluation of Ξ11 Evaluation of Ξ12 Evaluation of Ξ12 Proof of Proposition 2.4 Proof of Proposition 2.4 Proof of Proposition 2.6 Proof of Proposition 2.6 Evaluation of Ξ15 Evaluation of Ξ15 Approximation to Ξ14 Approximation to Ξ14 Mean value formula II Mean value formula II Evaluation of Φ1 Evaluation of Φ1 Evaluation of Φ2 Evaluation of Φ2 Evaluation of Φ3 Evaluation of Φ3 Proof of Proposition 2.5 Proof of Proposition 2.5 Appendix A. Some Euler products Appendix A. Some Euler products Appendix B. Some arithmetic sums Appendix B. Some arithmetic sums References References Appendix B. Some arithmetic sums Proof of Lemma 15.1. Put Proof of Lemma 15.1. First we claim that Since χ = µ ∗ ν, it follows that Hence This together with Lemma 3.2 yields (B.1). Next we claim that This yields (B.2). By (B.1) and (B.2), for µ = 2, 3, We proceed to prove theassertion with µ = 2. Since for σ > 1 and it follows that For µ = 1 the proof is therefore reduced to showing that By (4.2) and (4.3), the left side of (B.3) is equal to By a change of variable, for 0.5 ≤ z ≤ 0.504, Hence, in a way similar to the proof of, we find that the left side of (B.3) i Proof of Lemma 17.1. By Lemma 3.1, Proof of Lemma 17.1. The sum on the right side is equal to Assume σ > 1. We have If χ(p) = 1, then (see [19, (1.2.10)]) if χ(p) = −1, then if χ(p) = 0, then Hence In a way similar to the proof of, by (A) and simple estimate, we find that the integral (14) is equal to the residue of the function at s = 0, plus an acceptable error O , which is equal to s O This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Discrete Mean Estimates and the Landau-Siegel Zero: Appendix B. Some Arithmetic Sums

This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) Minghao Yan, University of Wisconsin-Madison; (2) Hongyi Wang, Carnegie Mellon University; (3) Shivaram Venkataraman, myan@cs.wisc.edu. Table of Links Abstract & Introduction Motivation Opportunities Architecture Overview Proble Formulation: Two-Phase Tuning Modeling Workload Interference Experiments Conclusion & References A. Hardware Details B. Experimental Results C. Arithmetic Intensity D. Predictor Analysis C ARITHMETIC INTENSITY The arithmetic intensity of a 2D convolution layer can be computed by the following equation: The notations used in equation 1 can be found in table 8. The FLOPs term captures the total computation of each workload, while the arithmetic intensity term captures how much computation power and memory bandwidth will affect the final performance. Combining the aforementioned features with an intercept term, which captures the fixed overhead in neural network inference, we can build a model that predicts inference latency if the hardware operating frequency is stable.

PolyThrottle: Energy-efficient Neural Network Inference on Edge Devices: Arithmetic Intensity

Algebra and statistics are members of the same family. Undoubtedly they are tough and complex but we cannot deny their significance in our daily life. What is a sequence? Before understanding the arithmetic sequence we will first understand we mean be sequences. In a classroom, the students sitting represent the sequence they are sitting in the same manner and hence make a sequence. They are in order! And each student present in the sequence called “series” let’s put this common concept in a technical example: We have the list of some numbers which are: 4, 3, 4, 65, 7, 6, 4 8, 5, 3, 1, 5, 5 What do you think? These numbers in sequence or not? You got it right! These numbers are “not” in the sequence. Because in a sequence it is compulsory to be in an “order” just like the students wearing the same uniform, in the same grade, represents the sequence in the classroom. So the sequence will be: 1, 3, 5, 7, 9… 2, 4, 6, 8, 10… These two lists are in a sequence because each list represents the sequence of “same order” the first row represents the odd numbers and the second shows even numbers. The simplest way to predict whether a given list in a sequence or not? In a sequenced series we can always predict the next number. Just like in the above examples we can predict the next even or odd number came in series. What is an arithmetic sequence? Just like a simple sequence, in the arithmetic sequence, we look towards order or the constant value. It is a specific type of sequence in which the difference between two terms is “constant”. We can write the arithmetic sequence as: {a, a+2d, a+3d,} In the above expression, we see that “a” is the first term and “d” will be the difference in the terms but remember this difference will be a common difference and this sequence can also be termed as arithmetic progression. And the difference between the terms will always remain constant. For example, in a sequence (1, 3, 5, 7, 9,) the difference is two and it is continuous to infinity and the nth term in the series will be: An = a1 + (n - 1) d You can use an for quick operation. Arithmetic sequence calculator What does “limit of function” mean? You will be surprised to know that the concept of limit is thousand years old but the definition came in the 19th century and the purpose to introduce the “limit” is to show whether a sequence or function approach to a “stable” when its index goes to the fixed point. The limit of a function simply means that the given function has a limit at a specific point. To understand it more clearly let’s consider a function (f) in which f is the real-valued function and b is a continuous quantity. Limit→ bf(x) =L This limit of the function shows us that the function f(x) can be set close to L if we have arranged the values of x close to b. In a given example, x=1, x2-1/x-1 = 12-1/ 1-1 = 0/0 In the above example, we can arrange the value of x very close to 1 and get our desired result. We can set it to 0.25 and ultimately the final answer will be: X (2-1) = 1.0625/X-1 Similarly, if we set the value of x to 0.45 the resultant value will be 1.205, and if we set x=0.9 the function will be 1.810. The reason to give multiple examples is to throw light on the fact as we are setting the value closer to 1 the final answer of the function becomes closer to 2. Hence we can say that: Limit measures the change or the rate of change of a given function by the approximations to get the possible value. You can use a limit calculator to calculate it easily, saving your time. How are these two concepts used in real life? If we have talked about the arithmetic sequence, it is used in: Filling something… Stacking chairs, tables, etc. To find, to suggest, or fill any pattern Because in every case you will focus on one thing “order” Similarly, the limit of a function is used: Specifically by engineers to design the engines of cars. To make calculations by approximating a function by applying small differences and calculate by having smaller spacing in the functions.

Introduction to Arithmetic Sequences

the search for fast complex numbers in c99 and c++ For quite some time, I’ve used complex number definition in C++. Mostly out of misplaced distrust for std::complex. I have a co-worker who’s done the same. Recently he wanted to move to using the complex number support introduced in C99 for reasons of simplicity. my own After awhile he came back and reported that the built in complex numbers were approximately ten times slower than the one he was already using, so he was going to stick with that. He showed me the benchmarks, which I’ve reproduced . It compares a plain c99 complex float, a std::complex<float> along with my cfloat_t and a trivial complex class that merely defines addition and multiplication. Using this benchmark, we’ll try to pin down exactly the cause of this performance difference. here Compiling with g++ 4.8.5 (same g++ that ships with RHEL7). The results are, indeed, disheartening. Note: from this point on all benchmarks are run on my core i7–2600k. I turned isolcpus=2,3 on during kernel boot and ran benchmarks using a taskset on the isolated CPUs. Benchmarks themselves are 1000 iterations of a 1 million element vector operation ‘vec = const*vec + const*vec + vec’ > g++ -I. test.cc -O3 -o test> taskset -c 2 ./test# c99time stltime mytime cftime<snip># mean: 0.018774 0.018836 0.003292 0.003289# stddev: 2.872722e-04 1.511633e-04 1.248804e-04 1.259614e-04 Ouch, the built-in types perform similarly (expected because GCC’s STL uses C99’s complex type). But they’re almost six times slower than the custom solutions. We didn’t have an obvious reason or solution, so it was generally agreed he should continue using his custom complex class and move on. It wasn’t until about a month later that the dark truth was revealed. If you’re like me, sometime in middle school you learned about complex numbers. In particular the rules for multiplying them. You probably learned something similar to the following, which uses the FOIL rule to expand the product out, then simplifies to get back into canonical complex form: (a+bi) * (c+di) = (ac-bd) + (ad + bc)i Do you know how C99 defines complex multiplication? Page 470 of the (Annex G) provides the answer, I’ll reproduce it here: C99 standard <a href="https://medium.com/media/5f6090b67bf61339b10dfbd40b0d104e/href">https://medium.com/media/5f6090b67bf61339b10dfbd40b0d104e/href</a> That … looks more complex. The goal here seems to be rigorously correct behavior with regards to inf and NaN results. At the very least, there’s a NaN check followed by an extra branch, assuming the first NaN check fails. That and perhaps missed optimization opportunities because of the required checks might explain the 6x slowdown. So what can be done? After fiddling with some settings we eventually decided to try setting -ffast-math (-Ofast works for gcc ≥ 4.7) in the hopes that forcing finite math, and perhaps re-ordering of operations would give us some win. And lo and behold: > g++ -I. test.cc -Ofast -o test> taskset -c 2 ./test# c99time stltime mytime cftime<snip># mean: 0.003191 0.003109 0.003184 0.003270# stddev: 4.600097e-05 2.530775e-05 1.377464e-05 9.412087e-06 The performance difference disappears! After a little more digging, looking at the flags that -ffast-math actually implies, we settled on -fcx-limited-range, which explicitly disables the NaN checking for complex multiply and divide. And sure enough, that’s sufficient to recover the performance: > g++ -I. test.cc -O3 -fcx-limited-range -o test> taskset -c 2 ./test# c99time stltime mytime cftime<snip># mean: 0.003269 0.003328 0.003277 0.003287# stddev: 4.911105e-05 2.076989e-05 1.038577e-05 1.047159e-05 Finally, I wanted to make sure there weren’t any other regressions, so I installed a range of gcc compilers on my machine, and ran the benchmark for each (with -O3 and -fcx-limited-range). The results were as follows: <a href="https://medium.com/media/320e780c29ff5da86963e76084c8f76e/href">https://medium.com/media/320e780c29ff5da86963e76084c8f76e/href</a> These look good, everything is comparable performance-wise, when we hit GCC5, however, the vectorizer finally gets the loop and gives us ~33% boost in performance, but no regressions across complex number types. Except, what’s that hiding in the corner of g++4.4’s results? Did it… actually make my two custom classes slower than the built-ins? $#%$*, It did and not a little slower, either, 3.5x slower. Well, let’s look at a little assembly from the innerloop for the c99 complex and my cfloat: <a href="https://medium.com/media/fa26e54447525a5569a48e6833d68910/href">https://medium.com/media/fa26e54447525a5569a48e6833d68910/href</a> I don’t know what’s really going on here, other than it’s clear the compiler failed to optimize the cfloat.h code very well, which causes very poor performance. The takeway from all of this is that: If you’re relying on c99 complex or std::complex and fast complex operations, and you don’t have -fcx-limited-range or -ffast-math turned on, you should probably consider this a bug in your project. It’s not sufficient to write your own and stick with that, as some (admittedly older, but still in wide use) compilers seem to have trouble optimizing as well as the built in types. But, if you’re not running on g++(4.4.7) (no RHEL6 support?) you can roll your own custom type with some confidence. I haven’t reproduced it here, but I have run into a situation with a similar benchmark (on g++4.4.7) where the built-in complex types were vectorized, while the others were not, causing a large difference in performance. I haven’t seen anything going the other way, where user types were vectorized, but built-in types weren’t. And, finally, don’t think newer compilers will save you either, with g++7 without -fcx-limited-range: > g++ -I. test.cc -O3 -o test> taskset -c 2 ./test# c99time stltime mytime cftime<snip># mean: 0.017414 0.017436 0.002254 0.002277# stddev: 2.660802e-04 1.467618e-04 2.559226e-05 2.129554e-05 Here, g++ happily vectorized the custom structs, while abandoning the built-ins to their default performance. This time it’s an almost 8x difference in speed, even worse than what we started with g++4.4.7. Trust nothing, and stay frosty.

complex arithmetic is complicated

Teaching High School Students Software Engineering: Project Implementation

Authors:
(1) Joseph Latessa, Department of Computer Science Wayne State University, Detroit MI USA (jlatessa@wayne.edu);
(2) Aadi Huria, Senior, Salem High School Canton, MI USA (huria.aadi@gmail.com);
(3) Deepak Raju, Senior, Salem High School, Canton MI USA (Deepak.Raju294@outlook.com). Table of Links Abstract and Introduction Related Work Project Prerequisites Project Implementation Insight and Reflections Conclusions, Acknowledgement and References 3 PROJECT PREREQUISITES We will now take a closer look at each part of the project’s development. Throughout the summer, our meetings took place using Zoom at intervals of one or two meetings per week and each session lasted between one and two hours. 3.1 Tools and Installation After introductions, a discussion about scheduling, and a discussion about what we planned to accomplish over the summer, we decided upon and installed our development tools to ensure a consistent development environment. This involved stepping through the WSL installation process and setting up Ubuntu user accounts. We then installed Windows Terminal as our command line application and Visual Studio Code as our preferred text editor. We then visited github.com to explore GitHub’s features and establish user accounts. 3.2 Linux Shell Familiarization At our next meeting, we explored Windows Terminal and entered basic commands to navigate the directory structure. Basic commands such as ls, pwd, cd, mkdir, touch, mv, cp, and clear were discussed and demonstrated. We practiced creating directories, creating files, moving files, and displaying a directory’s contents. In addition to navigating the command line on one’s local machine, automation with GitHub Actions requires command line navigation on GitHub’s runners. A familiarity with the command line will therefore be needed later in the project. 3.3 Introducing Version Control For the next few meetings, we focused on learning version control. To assist with this learning and because the students had previous experience writing Python, we implemented a simple calculator application in Python. The main function provided a menu for users to choose arithmetic operations and to input operands. Each operation such as addition, subtraction, and raising a number to a power was a separate function that received the requisite operands as parameters and returned the result. A skeleton of the Python code was provided, with unimplemented function stubs that all returned zero. The students learned to create a new repository on GitHub and clone the new repository to a directory on their local machine. Git was introduced using terminal commands rather than through a GUI to provide further command line practice, which will be useful when executing commands on GitHub’s runners. Upon cloning the remote repository, we discussed the concepts of distributed versus centralized version control and discussed the pros and cons of each system. The students added the new calculator skeleton to the repository and pushed it to the remote. The Git commands clone, pull, status, log, add, commit, and push were introduced and applied. Since two students were working on the project, one student implemented the addition function, and the other implemented the subtraction function. Each committed their local changes and pushed those changes to the remote. Each screen-shared while implementing the changes, and we noted how the second person to push needed to pull the changes already made to the remote before pushing one’s own. It was also noted that having made changes to different functions, the differences could be reconciled automatically without giving rise to a merge conflict. We next discussed the concept of branching and the benefits of developing features on specific feature branches. We created separate branches for the implementation of the multiplication and power functions. One student implemented multiplication and the other implemented power. Continuing to practice staging and committing files, we committed our local feature branches and learned to establish remote tracking for new branches. git diff was also introduced to compare un-staged changes with the most recent local commit and to compare other commits using the relevant commit hash. We then applied git merge to locally merge our feature back into our local main branch. Since each student had changed different parts of the code, it was again noted that the merge was automatic and gave rise to no merge conflict. Next, we specifically edited the code to create and demonstrate a merge conflict. Having both edited the same section of the code, the students learned to manually resolve merge conflicts. We concluded our introduction to version control with a look at pull requests and forks. In addition to merging branches locally, we discussed a typical workflow in which a developer without push access to the main branch would propose changes by submitting a pull request. We also looked at creating repository forks and saw how pull requests could be submitted across forks. The final calculator function, a square root function, was merged into the main branch through the submission and approval of a pull request. To prepare for the next phase of our project, the students created their own forks of the JETSCAPE [1] and GOMC [2] application repositories as well as the JETSCAPE and GOMC website repositories. Most of the time spent writing these tests would pertain to the website repositories. 3.4 Introducing Continuous Integration To introduce the concept of continuous integration, we created a simple Python script that uses the requests.get method to query a website and return a status code. The script can be run manually at the command line and accepts a URL as a command line argument. If the status code returned is 200, a success message is printed, and the program exits normally. If another code is returned or if there is no response from the server, the program terminates having raised an exception. We tested the program manually on popular websites like google.com and on URLs we knew to be invalid. We then discussed the usefulness of having a test run automatically either on a set schedule or whenever there are changes to a specified branch. Since there are two students and two websites (JETSCAPE [1] and GOMC [2]), each student focused on a specific website and worked on their locally cloned fork. We committed the Python script that checks for reachability and discussed the YAML file steps required to generate the automation. We decided that the test should run on push operations and pull requests to the main branch and run once per day at a specific time. We discussed the job steps including running on ubuntu-latest, checking out the current repository using GitHub’s checkout action, and executing terminal commands on GitHub’s runners to install the requests library using pip. We discussed that this step would be performed every time the workflow executes because each job runs on a new instance of ubuntu-latest. We then added the job steps to navigate to the tests/ folder on the runner and to execute the python3 command calling the URL reachability script. The students committed, pushed to the remote forks, and checked the Actions tabs on GitHub to review the running tests and their respective logs. Equipped with prior knowledge of the Python language and having now gained a familiarity with the command line, version control, and automating workflows with GitHub Actions, the students were ready to start researching and experimenting with writing and deploying the automated tests. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) Joseph Latessa, Department of Computer Science Wayne State University, Detroit MI USA (jlatessa@wayne.edu); (2) Aadi Huria, Senior, Salem High School Canton, MI USA (huria.aadi@gmail.com); (3) Deepak Raju, Senior, Salem High School, Canton MI USA (Deepak.Raju294@outlook.com). Authors: Authors: (1) Joseph Latessa, Department of Computer Science Wayne State University, Detroit MI USA (jlatessa@wayne.edu); (2) Aadi Huria, Senior, Salem High School Canton, MI USA (huria.aadi@gmail.com); (3) Deepak Raju, Senior, Salem High School, Canton MI USA (Deepak.Raju294@outlook.com). Table of Links Abstract and Introduction Abstract and Introduction Related Work Related Work Project Prerequisites Project Prerequisites Project Implementation Project Implementation Insight and Reflections Insight and Reflections Conclusions, Acknowledgement and References Conclusions, Acknowledgement and References 3 PROJECT PREREQUISITES We will now take a closer look at each part of the project’s development. Throughout the summer, our meetings took place using Zoom at intervals of one or two meetings per week and each session lasted between one and two hours. 3.1 Tools and Installation After introductions, a discussion about scheduling, and a discussion about what we planned to accomplish over the summer, we decided upon and installed our development tools to ensure a consistent development environment. This involved stepping through the WSL installation process and setting up Ubuntu user accounts. We then installed Windows Terminal as our command line application and Visual Studio Code as our preferred text editor. We then visited github.com to explore GitHub’s features and establish user accounts. 3.2 Linux Shell Familiarization At our next meeting, we explored Windows Terminal and entered basic commands to navigate the directory structure. Basic commands such as ls, pwd, cd, mkdir, touch, mv, cp, and clear were discussed and demonstrated. We practiced creating directories, creating files, moving files, and displaying a directory’s contents. In addition to navigating the command line on one’s local machine, automation with GitHub Actions requires command line navigation on GitHub’s runners. A familiarity with the command line will therefore be needed later in the project. 3.3 Introducing Version Control For the next few meetings, we focused on learning version control. To assist with this learning and because the students had previous experience writing Python, we implemented a simple calculator application in Python. The main function provided a menu for users to choose arithmetic operations and to input operands. Each operation such as addition, subtraction, and raising a number to a power was a separate function that received the requisite operands as parameters and returned the result. A skeleton of the Python code was provided, with unimplemented function stubs that all returned zero. The students learned to create a new repository on GitHub and clone the new repository to a directory on their local machine. Git was introduced using terminal commands rather than through a GUI to provide further command line practice, which will be useful when executing commands on GitHub’s runners. Upon cloning the remote repository, we discussed the concepts of distributed versus centralized version control and discussed the pros and cons of each system. The students added the new calculator skeleton to the repository and pushed it to the remote. The Git commands clone, pull, status, log, add, commit, and push were introduced and applied. Since two students were working on the project, one student implemented the addition function, and the other implemented the subtraction function. Each committed their local changes and pushed those changes to the remote. Each screen-shared while implementing the changes, and we noted how the second person to push needed to pull the changes already made to the remote before pushing one’s own. It was also noted that having made changes to different functions, the differences could be reconciled automatically without giving rise to a merge conflict. We next discussed the concept of branching and the benefits of developing features on specific feature branches. We created separate branches for the implementation of the multiplication and power functions. One student implemented multiplication and the other implemented power. Continuing to practice staging and committing files, we committed our local feature branches and learned to establish remote tracking for new branches. git diff was also introduced to compare un-staged changes with the most recent local commit and to compare other commits using the relevant commit hash. We then applied git merge to locally merge our feature back into our local main branch. Since each student had changed different parts of the code, it was again noted that the merge was automatic and gave rise to no merge conflict. Next, we specifically edited the code to create and demonstrate a merge conflict. Having both edited the same section of the code, the students learned to manually resolve merge conflicts. We concluded our introduction to version control with a look at pull requests and forks. In addition to merging branches locally, we discussed a typical workflow in which a developer without push access to the main branch would propose changes by submitting a pull request. We also looked at creating repository forks and saw how pull requests could be submitted across forks. The final calculator function, a square root function, was merged into the main branch through the submission and approval of a pull request. To prepare for the next phase of our project, the students created their own forks of the JETSCAPE [1] and GOMC [2] application repositories as well as the JETSCAPE and GOMC website repositories. Most of the time spent writing these tests would pertain to the website repositories. 3.4 Introducing Continuous Integration To introduce the concept of continuous integration, we created a simple Python script that uses the requests.get method to query a website and return a status code. The script can be run manually at the command line and accepts a URL as a command line argument. If the status code returned is 200, a success message is printed, and the program exits normally. If another code is returned or if there is no response from the server, the program terminates having raised an exception. We tested the program manually on popular websites like google.com and on URLs we knew to be invalid. We then discussed the usefulness of having a test run automatically either on a set schedule or whenever there are changes to a specified branch. Since there are two students and two websites (JETSCAPE [1] and GOMC [2]), each student focused on a specific website and worked on their locally cloned fork. We committed the Python script that checks for reachability and discussed the YAML file steps required to generate the automation. We decided that the test should run on push operations and pull requests to the main branch and run once per day at a specific time. We discussed the job steps including running on ubuntu-latest, checking out the current repository using GitHub’s checkout action, and executing terminal commands on GitHub’s runners to install the requests library using pip. We discussed that this step would be performed every time the workflow executes because each job runs on a new instance of ubuntu-latest. We then added the job steps to navigate to the tests/ folder on the runner and to execute the python3 command calling the URL reachability script. The students committed, pushed to the remote forks, and checked the Actions tabs on GitHub to review the running tests and their respective logs. Equipped with prior knowledge of the Python language and having now gained a familiarity with the command line, version control, and automating workflows with GitHub Actions, the students were ready to start researching and experimenting with writing and deploying the automated tests. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

Teaching High School Students Software Engineering: Prerequisites

Survey and Analysis of Smart Contract Quality Assurance: Defense Methodologies

Author:
(1) Sima Mehri, Farzanegan High School. Table of Links Abstract and 1 Introduction and Description of Results 2. Proof of Results and References 2. Proof of Results In the proof of both theorems, we use induction. using properties of Pascal triangle, we get The statement for k + 1 is also true, and the proof is completed. using properties of the trinomial coefficients, we get The statement for k + 1 is also true, and the proof is completed. The hockey stick theorem in the trinomial triangles has been proved. This theorem can be translated in Pascal pyramid as follows : Other similar theorems might be obtained for Pascal’s four dimensional and even n-dimensional pyramid. References 1] G. Andrews, Euler’s ’Exemplum Memorabile Inductionis Fallacis’ and Trinomial Coefficients J. Amer. Math. Soc. 3 (1990), 653-669. [2] P. Hilton and J. Pedersen, Looking into Pascal Triangle, Combinatorics, Arithmetic and Geometry Mathematics Magazine, Vol. 60, No. 5 (Dec., 1987), 305-316. [3] Eric W.Weisstein, Trinomial Coefficient From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/TrinomialTriangle.html [4] Eric W.Weisstein, Trinomial Triangle From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/TrinomialTriangle.html This paper is available on arxiv under CC BY 4.0 DEED license. Author: (1) Sima Mehri, Farzanegan High School. Author: Author: (1) Sima Mehri, Farzanegan High School. Table of Links Abstract and 1 Introduction and Description of Results Abstract and 1 Introduction and Description of Results 2. Proof of Results and References 2. Proof of Results and References 2. Proof of Results In the proof of both theorems, we use induction. using properties of Pascal triangle, we get The statement for k + 1 is also true, and the proof is completed. using properties of the trinomial coefficients, we get The statement for k + 1 is also true, and the proof is completed. k The hockey stick theorem in the trinomial triangles has been proved. This theorem can be translated in Pascal pyramid as follows : Other similar theorems might be obtained for Pascal’s four dimensional and even n-dimensional pyramid. References 1] G. Andrews, Euler’s ’Exemplum Memorabile Inductionis Fallacis’ and Trinomial Coefficients J. Amer. Math. Soc. 3 (1990), 653-669. [2] P. Hilton and J. Pedersen, Looking into Pascal Triangle, Combinatorics, Arithmetic and Geometry Mathematics Magazine, Vol. 60, No. 5 (Dec., 1987), 305-316. [3] Eric W.Weisstein, Trinomial Coefficient From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/TrinomialTriangle.html [4] Eric W.Weisstein, Trinomial Triangle From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/TrinomialTriangle.html This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

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