Apsy has unveiled the pioneering AI-powered app builder, enabling users to transform their ideas into functional apps just by speaking their minds, guided by the AI for customization

Apsy

Welcome to HackerNoon’s interview series. This section is curated by our Editorial team to spotlight bold and disruptive startups across the globe. If you’ve been nominated, and answer these questions Startups-Of-The-Year create a brand profile here. Hey Hackers, Apsy has been nominated in HackerNoon's annual Startup of the Year awards in Los Angeles, US. Please vote for us . here Read more about us below to understand why we deserve your vote. Meet Apsy Our start-up is called , a cool name rooted in Apps, but to us, it means “making app-building a breeze!” We are the first to introduce a fully AI-powered app builder. Our users speak their minds as our AI builds them. Apsy What makes us a different startup from others who offer tools to build apps is that we're all about letting your ideas flow while our AI does the heavy lifting. You dream it, speak it, and our AI builds it. Unlike traditional DIY tools, we take care of all the techy stuff, so our users don't have to. With Apsy, your creativity is the only limit. My Role Tooraj, a double Ph.D. dynamo in Economics and Computer Science, is a seasoned tech exec with a penchant for AI algorithms. A Y-Combinator and Techstars alumni is now driving his second startup, Apsy, towards reimagining software development. With a vision to make it simpler and cost-effective through AI, Tooraj is steering tech's future. How We're Disrupting/Improving the app development industry Building an app with traditional methods feels like a tough mountain to climb, right? But at Apsy, we're turning that hike into a fun walk in the park! Just chat with our AI about your brilliant app idea, answer a few clever questions it throws at you, and ta-da! Your app is up and running in a snap - we're talking hours, not months! We're shaking up the app-making game, making it a piece of cake for everyone, not just the coding wizards. Apsy isn't just transforming app development but the whole software landscape and tech entrepreneurship. Exciting times are ahead! Standing Out from The Crowd Do you remember how difficult building an app was in the good old days? Costly developers, scary DIY journeys, and months of learning only to end up with an 'okay-ish' app. Well, not anymore! We Apsy all you need to do is share your big idea, answer a few questions from our smarty-pants AI, and boom! It starts crafting screen options for you. And the best part? You can add your finishing touches and have a fabulous, tailor-made app ready to shine in just a few hours. And all this without burning a hole in your pocket! Building an app has never been this fun and easy, right? Our Predictions/Thoughts on the App Development Industry in 2023 The tech industry, specifically app development, is experiencing a significant shift towards no-code and low-code solutions. However, their complexity often presents challenges. Here, AI-driven platforms like Apsy come into play, simplifying app creation without needing users to be coding experts. As we move further into 2023 and beyond, we predict a surge in AI integration into app development owing to the rising demand for rapid, cost-effective digital solutions. The growth of AI sophistication will enable a better understanding of user needs and the delivery of high-quality, personalized apps. This AI infusion will transform the technological landscape and democratize the digital space, fostering innovation and promoting tech entrepreneurship. As Apsy, we're excited to pioneer this transformative journey, making app development more accessible and enjoyable. What word defines the state of app development in 2023? If you're asking about the vibe of app development in 2023, it's all 'Mind-to-Machine'! Just picture this - you come up with a killer app idea, chat about it, and voila, our AI buddy gets it done. No fuss, no code, just pure creativity! This exciting 'Mind-to-Machine' era is giving everyone the power to turn their app dreams into reality. It's like having a chat with a friend who happens to be a coding genius. So, buckle up, folks! We're on a fun-filled, game-changing journey that's turning the tech world on its head! Why we decided to participate in HackerNoon's Startup of the Year awards We jumped into HackerNoon's Startup of the Year awards because we're shaking things up with our 'Mind-to-Machine' tech at Apsy and wanted to share this cool innovation with fellow tech enthusiasts. Plus, who doesn't love a good challenge? We saw it as a great chance to learn, grow, and have some fun while competing with other innovative startups. So, here we are, all set to dazzle at the awards. Fingers crossed, folks! Final Thoughts At Apsy, we're on an exciting mission in 2023, transforming app development and making it accessible for all. We're thrilled to bring our innovation to HackerNoon's Startup of the Year awards, showcasing our approach, learning from peers, and embracing challenges. So, we invite you to on this thrilling journey, where we'll turn dreams into digital realities together! join us Don’t forget to ! Vote for us today

Vote for Apsy in HackerNoon's Startups of the Year 2023

To help researchers and developers in academia and beyond, Alibaba has now published its Cluster Data V2018 for all to explore In IT articles about internet applications, you will often find words such as “large scale” and “mass requests”. These applications all run in large-scale data centers, and readers generally have many questions about those environments. For example, what is the operating status of each machine in the data center? What kinds of applications are running? What are the characteristics of these applications? With the exception of a few senior experts, it is rare for students and corporate researchers to understand these details. Today, Alibaba shares a real dataset for computer clusters: (attached at the end of article). This dataset provides a full record of details for the servers and running tasks in Alibaba’s production cluster. With the release of this data, Alibaba hopes to engage its peers in academia and the wider industry and to promote further development within the industry. Alibaba Cluster Data V2018 Drawing on insights from Lin Shi, a technical expert at the Ali System Software Division, this article offers an in-depth introduction to this unique dataset, as well as findings from academic research with the previous year’s data. Releasing the Dataset: A Resource for Exploration In 2015, Alibaba tried to deploy latency insensitive batch computing tasks and latency sensitive online services to the same batch of machines in its data center, with the goals of allowing redundant resources to be fully utilized and improving the overall utilization of these machines. After more than three years of trial demonstrations, structural adjustments, and optimization of resource isolation, this program has now moved into the mass production phase. Average resource utilization of clusters has since increased from 10% to 45% using colocation technology (i.e. the technology that allows running online service and batch workloads on same machine). In addition, through various optimization methods, more tasks can now be run in the data center, and the average transaction cost of the 11.11 Global Shopping Festival has been reduced by 17% per 10,000 transactions. Though some readers will understand this achievement and how it was accomplished, many are likely to have questions such as what exactly the computer cluster looks like after optimization, or what colocation means and why it matters. In releasing the Alibaba Cluster Data V2018 dataset, Alibaba hopes to help interested students and researchers answer those questions and better understand large-scale data centers. Using the dataset, individuals can learn more about how Alibaba has increased resource utilization to 45% via colocation; how many tasks Alibaba runs each day; and what the resource requirements of the business are. How individuals use this dataset depends entirely on their needs. Making Use of the Data At 50 GB compressed and 270 GB uncompressed, Alibaba Cluster Data V2018 is a large dataset with many different uses. In six files, it has data for 4000 servers, corresponding online application containers, and operation of offline computing tasks for up to eight days. With Alibaba Cluster Data V2018, individuals can do the following: · Understand the servers and the characteristics of running tasks in today’s advanced data centers. · Experiment with various algorithms for task management and cluster optimization in scheduling and operations, and write papers about them. · Use the data to learn how to conduct data analysis, and reveal more techniques and methodologies that have not yet been discovered. The following are examples of questions the data can be used to answer: · E-commerce businesses face different pressures during daytime and nighttime. How can we improve overall resource utilization with these peaks and valleys? · How many dependencies does Alibaba’s longest DAG have? · How long does a container typically exist? · What is the typical lifetime of a computational task? · Multiple instances of a task are theoretically similar to each other, but do they all run at the same time? In fact, academics have already used Alibaba cluster data for a range of crucial analysis and research. In 2017 and 2018, a number of prominent academic papers were published based on of the first wave of data shared in Alibaba Cluster Data V2017. The following sections show examples of academic uses of the dataset, many of which have been featured in academic conferences such as OSDI. LegoOS: A Disseminated, Distributed OS for Hardware Resource Disaggregation — Yizhou Shan, Yutong Huang, Yilun Chen, and Yiying Zhang; Purdue University. (OSDI’18 Best Paper Award recipient) Imbalance in the Cloud: An Analysis on Alibaba Cluster Trace — Chengzhi Lu et al. (BIGDATA 2017) Characterizing Co-located Datacenter Workloads: An Alibaba Case Study — Yue Cheng, Zheng Chai, Ali Anwar. (APSys2018) The Elasticity and Plasticity in Semi-Containerized Co-locating Cloud Workload: a View from Alibaba Trace — Qixiao Liu and Zhibin Yu. (SoCC2018) Looking Forward: Updates in V2018 There are two major differences that distinguish the new V2018 dataset from the previous year’s V2017 dataset featured in the above research. First, the V2018 dataset includes the DAG information of some of our production batch workloads. This means that offline computing tasks like those commonly used in Map Reduce, Hadoop, Spark, and Flink are arranged in the form of a Directed Acyclic Graph (DAG), which shows parallelism, dependencies between tasks, and so on. As such, this dataset is the now the largest available DAG dataset from an actual production environment. The following figure illustrates and example of a DAG: Second, the V2018 dataset is considerably larger in scale than the previous set, which contained data for approximately 1300 machines over a 24-hour period. The new version includes data for 4000 machines over a period of 8 days. With so much having been accomplished using V2017 dataset, Alibaba looks forward to the developments to come as researchers begin work with the new dataset in 2019. (The original article is written by Ding Haiyang丁海洋) Alibaba Cluster Data V2018 Download link: [machine_meta]( http://clusterdata2018pubus.oss-us-west-1.aliyuncs.com/machine_meta.tar.gz) [machine_usage]( http://clusterdata2018pubus.oss-us-west-1.aliyuncs.com/machine_usage.tar.gz) [container_meta]( http://clusterdata2018pubus.oss-us-west-1.aliyuncs.com/container_meta.tar.gz) [container_usage]( http://clusterdata2018pubus.oss-us-west-1.aliyuncs.com/container_usage.tar.gz) [batch_task]( http://clusterdata2018pubus.oss-us-west-1.aliyuncs.com/batch_task.tar.gz) [batch_instance]( http://clusterdata2018pubus.oss-us-west-1.aliyuncs.com/batch_instance.tar.gz) Alibaba Tech First hand and in-depth information about Alibaba’s latest technology → Facebook: . Twitter: . “Alibaba Tech” “AlibabaTech”

Open Season for Research: Alibaba Releases Cluster Data from 4000 Servers

Designed for developers at the intersection of curiosity and professional growth, this primer aims to illuminate how asynchronous programming can elevate application performance, scalability, and responsiveness. By focusing on the universal principles of non-blocking operations and event loops, we venture beyond specific technologies like AsyncIO, Node.js, or Go. This exploration is crafted for software developers eager to grasp the efficiencies driving modern software without the complexity of technical jargon. Think of how a single thread handling requests is like a single-lane road in a busy city: each request is a car, and when there's only one lane, cars line up, causing delays. But what if our city — our service — could manage traffic more cleverly? That's where the magic of an asynchronous runtime comes into play. It's like adding an intelligent traffic system to our city, guiding cars through multiple lanes and intersections without waiting. This system keeps traffic flowing smoothly, ensuring no car (or task) waits too long, which is precisely how an asynchronous runtime keeps our software running efficiently. Let's consider an example of a service that completes I/O operations synchronously. For clarity, these operations are shown outside the main flow of execution in the diagram: Blocking I/O during your service's startup phase might be acceptable, but avoiding this approach when processing external requests is advisable. The following diagram illustrates how service efficiency can be enhanced through the adoption of non-blocking I/O operations: These examples highlight scenarios where the server's performance gains are maximized. Nevertheless, the advantage of non-blocking operations persists across any frequency of incoming requests. Even in less-than-ideal conditions, performance benefits from integrating dedicated I/O threads into the processing workflow. The total time required to process a request (from the client's initial request to the final response, as depicted by the blue number on the right) will invariably decrease, provided there are sufficient threads to handle all requests. In the worst-case scenario, this duration will not surpass that of synchronous processing methods. We then encounter a practice that might seem counterintuitive to many developers. When I/O operations constitute a significant portion of request processing time, optimizing other code segments may yield slight improvement. The duration to fetch data from a cache might align closely with the time dedicated to business logic and template rendering. Employing caching or an in-process database can reduce data retrieval times compared to other processing activities. To segment code effectively and facilitate callback execution, one can instruct the runtime to proceed to the next event loop cycle. Below is an illustrative example of how this concept is applied: // blocking callbacks
function func1_cb(str, cb) {
 var res = func1(str);
 cb(res);
}

function func2_cb(str, cb) {
 var res = func2(str);
 cb(res);
}

// non-blocking callbacks
function func1_cb(str, cb) {
 var res = func1(str);
 process.nextTick(function () {
   cb(res);
 });
}

function func2_cb(str, cb) {
 var res = func2(str);
 process.nextTick(function () {
   cb(res);
 });
}

// usage example
func1_cb(content, function (str) {
 func2_cb(str, function (result) {
   // work with result
 });
}); By adopting this methodology to split two parts of calculations, the overall processing time for scenarios with nearly concurrent request arrivals remains the same. However, the response to the first request is delayed: This scenario represents the least favorable outcome when employing the “next tick” strategy. As shown in the initial example, the “next tick” method proves benign for infrequent requests. Should requests arrive at a moderate pace, leveraging this technique enhances processing speed by allowing the initiation of new requests and the start of non-blocking operations to be interleaved during execution breaks. This approach effectively reduces both the total processing time and the average time per request: In conclusion, adopting non-blocking I/O is crucial for enhancing application performance and beneficial in environments with both sparse and heavy incoming request volumes. Additionally, effectively sequencing the execution flow — illustrated by concepts similar to the "next tick" technique — significantly improves server efficiency. Embracing these asynchronous programming practices offers clear advantages over traditional, synchronous methods.

Asynchronous Runtimes: A Primer for the Perplexed Developer

Async/await in C# is a framework used for writing asynchronous C# code that is both readable and maintainable. These tips will help you to integrate async/await programming more effectively in the # projects: 1. ValueTask for Lightweight Operations Use ValueTask instead of Task for asynchronous methods that often complete synchronously, reducing the allocation overhead. public async ValueTask<int> GetResultAsync()
    {
        if (cachedResult != null)
            return cachedResult;
        int result = await ComputeResultAsync();
        cachedResult = result;
        return result;
    } 2. ConfigureAwait for Library Code Use ConfigureAwait(false) in the library code to avoid deadlocks by not capturing the synchronization context. public async Task SomeLibraryMethodAsync()
    {
        await SomeAsyncOperation().ConfigureAwait(false);
    } 3. Avoiding async void Prefer async Task over async void except for event handlers, as async void can lead to unhandled exceptions and is harder to test. public async Task EventHandlerAsync(object sender, EventArgs e)
    {
        await PerformOperationAsync();
    } 4. Using IAsyncDisposable For asynchronous cleanup, implement IAsyncDisposable and use await to ensure resources are released properly. public async ValueTask DisposeAsync()
    {
        await DisposeAsyncCore();
    }
    
    private async ValueTask DisposeAsyncCore()
    {
        if (resource != null)
        {
            await resource.DisposeAsync();
        }
    } 5. Efficiently Combine Tasks Use Task.WhenAll for running multiple tasks in parallel and waiting for all to complete, which is more efficient than awaiting each task sequentially public async Task ProcessTasksAsync()
    {
        Task task1 = DoTask1Async();
        Task task2 = DoTask2Async();
        await Task.WhenAll(task1, task2);
    } 6. Cancellation Support Support cancellation in asynchronous methods using CancellationToken. public async Task DoOperationAsync(CancellationToken cancellationToken)
    {
        await LongRunningOperationAsync(cancellationToken);
        cancellationToken.ThrowIfCancellationRequested();
    } 7. State Machine Optimization For performance-critical code, consider structuring your async methods to minimize the creation of state machines by separating synchronous and asynchronous paths. public async Task<int> FastPathAsync()
    {
        if (TryGetCachedResult(out int result))
        {
            return result;
        }
        return await ComputeResultAsync();
    } 8. Avoid Blocking Calls Avoid blocking on async code with .Result or .Wait(). Instead, use asynchronous waiting through the stack. public async Task WrapperMethodAsync()
    {
        int result = await GetResultAsync();
    } 9. Eliding Async/Await In simple passthrough scenarios or when returning a task directly, you can elide the async and await keywords for slightly improved performance. public Task<int> GetResultAsync() => ComputeResultAsync(); 10. Custom Task Schedulers For advanced scenarios, like limiting concurrency or capturing synchronization contexts, consider implementing a custom TaskScheduler. public sealed class LimitedConcurrencyLevelTaskScheduler : TaskScheduler
    {
        // Implement the scheduler logic here.
    } 11. Using Asynchronous Streams Leverage asynchronous streams with IAsyncEnumerable<T> for processing sequences of data asynchronously, introduced in C# 8.0. public async IAsyncEnumerable<int> GetNumbersAsync()
    {
        for (int i = 0; i < 10; i++)
        {
            await Task.Delay(100); // Simulate async work
            yield return i;
        }
    } 12. Avoid Async Lambdas in Hot Paths Async lambdas can introduce overhead. In performance-critical paths, consider refactoring them into separate async methods. // Before optimization
    Func<Task> asyncLambda = async () => await DoWorkAsync();
    
    // After optimization
    public async Task DoWorkMethodAsync()
    {
        await DoWorkAsync();
    } 13. Use SemaphoreSlim for Async Coordination SemaphoreSlim can be used for async coordination, such as limiting access to a resource in a thread-safe manner. private readonly SemaphoreSlim semaphore = new SemaphoreSlim(1, 1);
    
    public async Task UseResourceAsync()
    {
        await semaphore.WaitAsync();
        try
        {
            // Access the resource
        }
        finally
        {
            semaphore.Release();
        }
    } 14. Task.Yield for UI Responsiveness Use await Task.Yield() in UI applications to ensure the UI remains responsive by allowing other operations to process. public async Task LoadDataAsync()
    {
        await Task.Yield(); // Return control to the UI thread
        // Load data here
    } 15. Asynchronous Lazy Initialization Use Lazy<Task<T>> for asynchronous lazy initialization, ensuring the initialization logic runs only once and is thread-safe. private readonly Lazy<Task<MyObject>> lazyObject = new Lazy<Task<MyObject>>(async () =>
    {
        return await InitializeAsync();
    });
    
    public async Task<MyObject> GetObjectAsync() => await lazyObject.Value; 16. Combining async and LINQ Be cautious when combining async methods with LINQ queries; consider using asynchronous streams or explicitly unwrapping tasks when necessary. public async Task<IEnumerable<int>> ProcessDataAsync()
    {
        var data = await GetDataAsync(); // Assume this returns Task<List<int>>
        return data.Where(x => x > 10);
    } 17. Error Handling in Async Streams Handle errors gracefully in asynchronous streams by encapsulating the yielding loop in a try-catch block. public async IAsyncEnumerable<int> GetNumbersWithErrorsAsync()
    {
        try
        {
            for (int i = 0; i < 10; i++)
            {
                if (i == 5) throw new InvalidOperationException("Test error");
                yield return i;
            }
        }
        catch (Exception ex)
        {
            // Handle or log the error
        }
    } 18. Use Parallel.ForEachAsync for Asynchronous Parallel Loops Utilize Parallel.ForEachAsync in .NET 6 and later for running asynchronous operations in parallel, providing a more efficient way to handle CPU-bound and I/O-bound operations concurrently. await Parallel.ForEachAsync(data, async (item, cancellationToken) =>
    {
        await ProcessItemAsync(item, cancellationToken);
    }); 22. Avoid Excessive Async/Await in High-Performance Code In performance-critical sections, minimize the use of async/await. Instead, consider using Task.ContinueWith with caution or redesigning the workflow to reduce asynchronous calls. Task<int> task = ComputeAsync();
    task.ContinueWith(t => Process(t.Result)); 23. Async Main Method Utilize the async entry point for console applications introduced in C# 7.1 to simplify initialization code. public static async Task Main(string[] args)
    {
        await StartApplicationAsync();
    } 24. Optimize Async Loops For loops performing asynchronous operations, consider batching or parallelizing tasks to improve throughput. var tasks = new List<Task>();
    for (int i = 0; i < items.Length; i++)
    {
        tasks.Add(ProcessItemAsync(items[i]));
    }
    await Task.WhenAll(tasks); More Cheatsheets Cheat Sheets - .Net C# Programming🚀 Thank you for being a part of the C# community! Before you leave: Follow us: | | | Visit our other platforms: More content at Youtube X LinkedIn Dev.to GitHub C# Programming Also published . here

Async/Await For Basic to Advanced C# Developers: 24 Essential Tips

Introduction The article highlights the importance of limiting the concurrent asynchronous operations, which in turn improves performance. Learning Objectives The common mistake all developers do How to use limit concurrent async operations Best Practices Prerequisites for Developers Basic understanding of C# programming language Basic understanding of asynchronous programming using async await Getting Started The common mistake all developers do Consider an example where the user wants to load data asynchronously within a method, and it highlights the common mistake developers make. (async item => await ProcessItem(item));
/// <summary>
/// Old approach with classic async await 
/// </summary>
/// <returns></returns>
public async static Task OldApproach(List<string> items)
{
    var tasks = items.Select(async item => await ProcessItem(item));
    await Task.WhenAll(tasks);
} The approach may look clean and simple, but it initiates tasks for each item in the collection concurrently. This can cause system strain under heavy List<string> items, which will produce poor application performance. Optimized approach with Concurrency Limit Let’s transform the above method using SemaphoreSlim to limit the number of concurrent asynchronous operations. The following code snippet demonstrates the more refined approach. /// <summary>
/// Optimized approach with limit concurrency
/// </summary>
/// <returns></returns>
public static async Task OptimizedApproachAsync(List<string> items, int maxConcurrency = 10)
{
    using (var semaphore = new SemaphoreSlim(maxConcurrency))
    {
        var tasks = items.Select(async item =>
        {
            await semaphore.WaitAsync(); // Limit concurrency by waiting for the semaphore.
            try
            {
                await ProcessItem(item);
            }
            finally
            {
                semaphore.Release(); // Release the semaphore to allow other operations.
            }
        });

        await Task.WhenAll(tasks);
    }
} The aforementioned code prevents the system from being choked by too many concurrent tasks. Best Practices Please find below the best practices Limit Concurrency To balance system load and resources, it is recommended to use SemaphoreSlim Avoid Blocking Calls Avoid using  .Result or .Wait(), as they can lead to deadlocks and degrade performance. Async all the way Avoid mixing async and sync code. Ensure all methods are async from top to bottom to prevent deadlock and make optimal use of resources. Conclusion Asynchronous programming in C# involves more than just understanding the async and await keywords; it requires more features like concurrency, resource utilization, and code structure Complete Code on GitHub GitHub — ssukhpinder/30DayChallenge.Net C# Programming🚀 Thank you for being a part of the C# community! Before you leave: If you’ve made it this far, please show your appreciation with a clap and follow the author! 👏️️ Follow us: | | | | | X LinkedIn Dev.to Hashnode Newsletter Tumblr Visit our other platforms: | | | | GitHub Instagram Tiktok Quora Daily.dev More content at C# Programming Also published . here

The 30-Day .NET Challenge Day 14: Limit Concurrent Async Operations

This paper is available on arxiv under CC 4.0 license. Authors: (1) Vianney Brouard, ENS de Lyon, UMPA, CNRS UMR 5669, 46 All´ee d’Italie, 69364 Lyon Cedex 07, France; E-mail: vianney.brouard@ens-lyon.f. Table of Links Abstract & Introduction and presentation of the model Main results and biological interpretation First-order asymptotics of the mutant sub-populations for an infinite mono-directional grap First-order asymptotics of the mutant sub-populations for a general finite trait space (Theorem 2.1) Convergence for the stochastic exponents (Theorem 2.2) Acknowledgements & References 3 First-order asymptotics of the mutant sub-populations for an infinite mono-directional grap In this section consider the model described in Section 1 in the particular following infinite monodirectional grap Assume in the case of the infinite mono-directional graph that A graphical representation of the model can be found in Figure 5. In particular it means that any Compared to the general finite graph, for any trait i ∈ N there is only one path from trait 0 to i for this mono-directional graph. In particular it implies that Notice in particular that with such a construction it immediately follows the monotone coupling Denote by see [12] Section 1.1, or [11] Theorem 1. 3.1 The wild-type dynamics Using Ito’s formula and (18) it follows Solving this equation we obtain for all t ≥ 0 Similarly we have Consequently combining (21), (22) and (23) gives that Finally we have which concludes the proof. Proof of Lemma 3.2. Let ε > 0 and for all n ∈ N introduce the event We start by showing that for all 0 < δ1 < δ2 Step 1: from which we obtain Remark 3.1. From Lemma 3.2, it follows the useful result 3.2 The mutant sub-populations dynamics in the deterministic time-scale (Theorem 2.1 (i)) In this subsection, Equations (11) and (12) are proven for the mono-directional graph. It will be done in two steps. The first one will consist in showing the result for a fixed s ∈ R and uniformly in the parameter t. Then in the second step, the result will be proved uniformly in the parameter 3.2.1 Uniform control on the time parameter In this subsection we are going to prove the following proposition, which is a less refine result of (11) and (12), because the result is not uniform on the parameter s. The proof is done by induction on i ∈ N. As long as the proof is similar for the initialization and the inductive part the step considered will not be specified. To make the proof the clearer possible it is cut using several lemmas. All the results are obtained using a martingale approach. In the next Lemma the martingales that are considered for all the mutant sub-populations are introduced, and their quadratic variations are computed. Lemma 3.3. For all i ∈ N define Proof of Proposition 3.1. Let i ∈ N ∗ . For i ≥ 2 assume that Proposition 3.1 is true for i − 1. We start by showing the result when i is a neutral trait, that is to say we are going to prove (27). All the lemmas that we are mentioning in the proof are free from such neutral assumption, and work also for deleterious mutant traits. We are going to show that (33), (34) and (35) converges to 0 when n goes to infinity. (33): Step 1: Convergence to 0 of = 1: (i) Case i Using Equation (38) we have that (40) For i = 1 we prove without condition. It allows to write (44) For i = 1 we prove without condition. Let Proof of Lemma 3.6. Using similar computations as in (46) and (47), it follows (45). First, a natural upper bound on the mean of the growth of each mutant sub-population can be easily obtained. This is stated in the next Lemma. Second, using both the expression of the quadratic variation of the martingale associated to a mutant sub-population given in Equation (30) and the previous Lemma 3.7, a natural upperbound on its mean is obtained and summed up in the next Lemma. First notice that the function is a non-decreasing function implying that Notice that Then for n large enough, and remembering that θ(i) = θ(i − 1) + 1 we have And we have Then for large enough, and remembering that 1) we have n θ(i) = θ(i − Then by hypothesis on (ψn(i), γn(i)) it follows that (41) converges to 0. (35): Step 3: Convergence to 0 of Notice that for all t ≥ t(i) Then it allows to write Then combining (52) and (53) we get as θ(i) ≥ 1 since the vertex i is assumed to be neutral. It ends the proof of the convergence to 0 of the term (49). The term (50) converges to 0 according to the following Lemma. Lemma 3.9. Assume Equation (15). Let i ∈ N, T ≥ t(i) and s ∈ R. For i ≥ 2 we prove that if Proposition 3.1 is true for i − 1 then (54) For i = 1, we prove without condition. Our aim is to prove that for all ε > 0 = 1: We have (i) Case i Let us set 3.2.2 Uniform control on the parameter s In this subsection we will prove (11) and (12) from (27) and (28) using an idea from the proof of Lemma 3 of [15]. We start by showing (12). We will use that It gives that Hence we get for sufficiently large n from which (12) is obtained. Indeed the term (63) converges to 0 according to Equation (28) and (64) converges to 0 since W is finite almost surely (see (20)). We now show Equation (11). We have Finally using (65) and (66) we obtain for all (t, s) ∈ [0, T] × [−M, M] Then it follows that where the different convergences to 0 are obtained in the following way: 3.3 First-order asymptotics of the mutant sub-populations in the random time-scale (Theorem 2.1 (ii))

First-order Asymptotics of the Mutant Sub-populations for an Infinite Mono-directional Grap

This paper is available on arxiv under CC 4.0 license. Authors: (1) Vianney Brouard, ENS de Lyon, UMPA, CNRS UMR 5669, 46 All´ee d’Italie, 69364 Lyon Cedex 07, France; E-mail: vianney.brouard@ens-lyon.f. Table of Links Abstract & Introduction and presentation of the model Main results and biological interpretation First-order asymptotics of the mutant sub-populations for an infinite mono-directional grap First-order asymptotics of the mutant sub-populations for a general finite trait space (Theorem 2.1) Convergence for the stochastic exponents (Theorem 2.2) Acknowledgements & References 4 First-order asymptotics of the mutant sub-populations for a general finite trait space (Theorem 2.1) Notice that with such a construction it immediately follows the monotone coupling In the next definition, we are going to introduce an equivalence relation on Γ(V ). Two paths are said to be equivalent if they are the same up to cycles (in particular cycles formed by backward mutations are taken into account). More precisely, that there exists a minimal path, from which the two previous paths are using all the edges, but potentially also some other edges forming cycles. The aim of this equivalence relation is to say that among one class of equivalence, only the path with the minimal length may contribute for the asymptotic of the mutant sub-population sizes Now we have all the preliminary results and definitions to prove Theorem 2.1. We show Equation (11). The proof of Equation (12) is similar and is left to the reader. Proof of Theorem 2.1. And the last term of the r.h.s converges to 0 because

First-order Asymptotics of the Mutant Sub-populations for a General Finite Trait Space (Theorem 2.1)

Events and event handlers aren’t necessarily the most common language feature being used if you’re focused on web development in ASP.NET Core… but if you’re building applications in WinForms, WPF, Maui — or anything with a user interface really — it’s almost guaranteed you’ll be using these. Given how pervasive async await code is now, that also suggests you’re probably going to run into async event handlers in C# at some point too. Async event handlers have their challenges. They’re essentially two things that conceptually fit nicely together, but the language features of C# break down for us right where these two things intersect. In this article, I’ll explain why there are risks, what those risks are, and what you can try and do to make things better. Understanding Async Event Handlers in C# Async event handlers in C# allow you to handle asynchronous events that occur during the execution of a program. These events can include user input, network requests, or any other asynchronous operations. These methods are marked with the keyword, indicating that they contain asynchronous operations, and therefore we can await other calls within them. When an event is triggered, the async event handler is invoked and runs concurrently with the rest of the program. async A traditional synchronous event handler in C# has the following syntax: void MyEventHandler(object sender, EventArgs e)
{
    // TODO: handle the event
} But if we need one to run asynchronously, it will look like this: async void MyEventHandler(object sender, EventArgs e)
{
    // TODO: handle the event, running the asynchronous code we can await on
} Keeping in mind that event handlers in C# *must* have a void return type, what kind of problem do we have here? What Makes Async Event Handlers in C# Dangerous? While async event handlers offer great flexibility and improved responsiveness, they also introduce a set of potential dangers and risks that you need to be aware of. And I don’t blame you if either you weren’t aware of these or you were aware but weren’t sure the best way to navigate these issues… because it’s a very awkward intersection of event handler syntax and async-await code. Fundamentally, issues arise because of the declaration of the event handler. When we start using async await, we’re told early on that using async void is a big no-no. async void And why is that? It eliminates the possibility for us to await the asynchronous operation — that’s what Task allows us to do. When we’re unable to leverage a task to await, we lose the ability to manage the execution of the task, including exception handling. That means if your event handler goes boom, then your app is going to go boom somewhere else. And you won’t be able to gracefully deal with it. Key Risks With Async Event Handlers in C# Now that you understand what makes them dangerous in general, here are a few key risks associated with async event handlers in C#: Unobserved exceptions: When an async event handler encounters an exception during its execution, it can cause an unhandled exception if the error is not properly handled. This can lead to unexpected program behavior or even crashes. It’s important to handle exceptions appropriately to prevent these issues. This was the focus of the previous section. Concurrency concerns: Async event handlers run concurrently with the rest of the program, making it important to consider potential concurrency issues. Concurrent access to shared resources can lead to race conditions, data corruption, or inconsistent state. When we’re doing async await, sure, we are dealing with concurrency… But now we just have an async body of code running off potentially into outer space that we can’t align with. And of course, the async flavor of event handlers in C# carries the same potential memory-leak issue. We’ll skip the details here but just remember to unhook events when you’re done requiring the registration and properly manage your event and event handler lifetimes! Handling Async Event Handlers Safely in C# Async event handlers in C# can introduce some potential issues if not handled properly. I’ve tried coming up with alternative solutions in the past to async void code as well as helpers that could clean up the syntax when trying to write safe event handlers. Ultimately, these are either incredibly complex or in the simple case the syntax just feels a bit off. This section will detail some general simple strategies you can employ to make these less of a headache — but the responsibility is still on you to add them! Wrap Async Event Handlers with Try/Catch If we accept that we’re stuck using for event handlers, the biggest concern for us to address is catching exceptions. Once an exception bubbles up and hits that async void boundary, it’s game over. There’s not going to be an elegant way for your application to handle that. The current call stack will be unable to properly catch this even if you wrapped the event invocation in a try/catch. [async void](https://www.devleader.ca/2023/01/27/async-void-how-to-tame-the-asynchronous-nightmare/) To mitigate this risk, use a block at the top level of your event handler. Make it the first and last thing that your event handler does so there’s no way for code to throw exceptions without being wrapped with a catch block: try-catch async Task MyEventHandler(object sender, EventArgs e)
{
    try
    {
        // TODO: do the async code
    }
    catch (Exception)
    {
        // Handle cancellation
    }
} This still sucks because it’s manual, but maybe someone could make a Roslyn analyzer to enforce this?! Also, notice that I’m catching *all* exceptions here… But what are we expecting to do about it? Truly, unless we’re ready for our application to crash or experience weird behavior, we need to stop exceptions from bubbling out of an async void method. Maybe logging or telemetry? But not a lot of great options by default. Force Timeout on Async Event Handlers Here’s a not-so-silver-bullet option you could add to the mix for working with async event handlers. Sometimes, async operations within an event handler can take longer to complete than expected. Recall that we can’t easily manage this async void call because we can’t await it and we don’t have a task object to work with. But if we could do *something* to help keep these from running away with resources in some sort of infinite loop, we could introduce a cancellation token timed with some maximum allowable time. See the example below which includes the suggestion from the previous section: async void MyEventHandler(object sender, EventArgs e)
{
    using (var cts = new CancellationTokenSource(TimeSpan.FromSeconds(5)))
    {
        try
        {
            // Continue with async operation, pass in cancel token
        }
        catch (OperationCanceledException)
        {
            // Handle cancellation
        }
        catch (Exception ex)
        {
            // TODO: how should we handle these?
        }
    }
} In the code above, we simply try to limit execution to no longer than 5 seconds. As long as the async code we implement within here takes advantage of the cancellation token, then they should be able to handle canceling properly. But that does mean that *someone* still needs to carry that responsibility. Wrapping Up Async Event Handlers in C# In summary, understanding and safely managing async event handlers in C# is important for C# developers. Async event handlers have their own set of dangers and complexities that need to be addressed to ensure the stability and efficiency of software applications. These can be challenging to be aware of in the first place, but even once you’re aware… what’s the best way to solve them? Hopefully from this article you understand why these are challenging and some strategies to help. If you found this useful and you’re looking for more learning opportunities, consider and check out my ! subscribing to my free weekly software engineering newsletter free videos on YouTube Also published here.

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