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ZUG, Switzerland, March 20th, 2024/GamingWire/--Playnance, a web3 leader in the peer-to-peer play-to-earn gaming category accounting for up to 10% of total Polygon POS transactions, today announced the launch of PlayBlock, a gaming Layer-3 ecosystem powered by Arbitrum Orbit, on e(RaaS) Platform. Gelato’s Rollup-as-a-Servic PlayBlock, a new Orbit Layer-3, is poised to onboard over ten thousand daily active users to its growing ecosystem of web3 games from decentralized trading, to sports to arcade. The chain will provide game developers with extensive white-labeling opportunities and seamless platform integrations, all while eliminating the previously existing UX drawbacks of blockchains, such as requiring users to pay for gas. The official launch of the PlayBlock on the mainnet is slated for early April. PlayBlock’s future-facing design empowers game developers to freely exercise design choices while staying connected to the platform, greatly simplifying the sign-up process for players by offering a universal profile that allows them to carry their identity, achievements, and digital assets seamlessly across various games in the ecosystem. The new Layer-3 is poised to lead the upcoming wave of web3 mass adoption, with a rapidly expanding portfolio of over one hundred bile-first games in development. "Launching our dedicated chain is a natural evolution of Playnance's vision as one of the leading peer-to-peer web3 gaming platforms," said Roman Levi, CTO at Playnance. "Our ambition is driven by the goal to combine the benefits of Web3 on-chain gaming with the fun and accessibility of traditional games, all without the web3 complexity." The PlayBlock chain, developed using Arbitrum Nitro’s rollup technology, will be run on Gelato’s RaaS platform that natively leverages a suite of industry-leading web3 services like Relayers, VRF, Functions, and Account Abstraction, to meet PlayBlock's unique ecosystem needs. This allows developers to create more user-friendly gameplay directly on the blockchain, thereby enhancing transparency, fairness, and ownership of in-game assets. Leveraging Arbitrum Anytrust technology, the new PlayBlock chain achieves a 250ms block time and near-instant finality, capable of processing thousands of transactions per second. PlayBlock is leveraging Orbit’s native gas token feature by introducing the PBG token set to guarantee a zero-gas user experience. Additionally, PlayBlock Layer3 will feature its own stablecoin, USDP, to eliminate volatility and enhance the gamer experience by ensuring fair rewards payouts are always pegged to a dollar. The PlayBlock Layer-3 chain is designed to abstract away the need for users to pay for gas, enabling persistent, session-based, gasless gameplay supported by sponsored transactions through Gelato’s natively integrated Relayer. The integration eliminates the need for frequent wallet confirmations and transaction approvals, ensuring uninterrupted and immersive gameplay. PlayBlock will feature a dedicated self-custodial native wallet called PlayWall, based on ERC-4337. The PlayWall wallet aims to streamline onboarding processes by offering seamless social login and account creation. "Playnance approached us with a request to design an end-to-end gaming platform supporting thousands of games and millions of users," said Hilmar Orth, Founder of Gelato. "We developed a gaming-first, fully-serviced, auto-scalable rollup infrastructure enabling Playnance to grow and scale at pace, whilst focusing on their core business." Over time, Playnance will move towards a multi-chain vision on Arbitrum Orbit. This transition led by the Gelato RaaS team, will involve scaling to multiple horizontally interconnected PlayBlock Layer-3s chains with a mission to achieve limitless scalability and increased bandwidth to accommodate an economy of hundreds of millions of gamers. The implementation will include a shared sequencer for smooth cross-chain interoperability. About Playnance The Playnance ecosystem bridges the traditional web2 iGaming experience, by putting players first, transitioning them to a transparent, trustless world of Web3 GameFi, utilizing cutting-edge blockchain technology for social login, self-custody solutions, and a one-click crypto bridging mechanism. Today, the Playnance ecosystem handles over 200,000 transactions daily, totaling more than $450 million paid out. Its flagship product, the plug-and-play P2P trading game UPVSDOWN, is the #1 Polygon iGaming app based on transaction volume. For more information visit Playnance’s: Official | | Website Twitter LinkedIn About Gelato is an all-in-one Ethereum Rollup as a Service built without limits. Designed to be super-fast, incredibly secure, and infinitely scalable, Gelato Rollups allow anyone to build and deploy their fully serviced Layer 2 chains natively integrated with industry-standard Web3 tools and services launching a production-ready web3 development environment with one click. Gelato Platform For more information visit Gelato's: | | __ __r Official Website Telegram Twitte About Arbitrum Foundation The Arbitrum Foundation, founded in March 2023, supports and grows the Arbitrum network and community with secure scaling for Ethereum. Introduced in March 2023, Arbitrum Orbit is a permissionless path for launching customizable dedicated L2 and L3 Orbit chains using Arbitrum technology. Arbitrum Orbit enables features such as custom gas tokens, dedicated throughput, customizable permissions, interoperability, and more by leveraging its secure, scalable, and cost-efficient blockchain scaling technology. More than 25 Orbit chains have been officially announced, and an additional 50+ are in active development to date. Contact Head of Marketing Ella Jonas Gelato press@gelato.digital This story was distributed as a release by GamingWire under HackerNoon’s Business Blogging Program. Learn more about the program here.

Future Of Gaming: Playnance Introduces PlayBlock Layer-3 On Arbitrum With Gelato RaaS

Using Gelato, Witnet, API3 And Chainlink Vrf to Schedule Randomness

Learn how to automate Start/Stop Superfluid streams in Super Apps. 🚀 One of the most extraordinary things about web3 is that we are still at an early stage and as we speak, the web3 ecosystem is growing with new protocols, toolings, etc., and regardless of our level of expertise, we can contribute to helping others as we are learning. This blog aims to help devs to use the gelato network with smart contracts and specifically for using Gelato automation with Superfluid Super Apps. among other features allows users to stream money/tokens to users/contracts with only one transaction and minimal capital lockup. The caveat is that you have to remember to stop the stream, if not the stream will continue endlessly. Please visit Superfluid website for further info Superfluid Protocol https://www.superfluid.finance/home allows you to execute tasks at a future point in time (for ex-web2 would be similar to a kind of scheduler). The main use case is for repeated tasks. For Superfluid streams we will only need one execution (start or stop) therefore we will have to deploy the task and at the same time the “cancel Task”. Please visit Gelato website for further info Gelato Network https://www.gelato.network/ This project showcases general-purpose examples of automating smart contracts with gelato as well as the application for superfluid streams presenting a very simple 3+3 Step guide to create programmable cash flows In order to do that we have deployed a showcase dapp at . we will interact with two main verified and deployed on mumbai contracts : https://gelato-superapp.web.app Party App Contract ( ) view on scan Gelato Super App Contract ( ) view on scan The code can be found in this repository https://youtu.be/yjmJZ6LuPig 3+3 Steps Guide to Gelatofy a Smart Contract Here you will find 3 + 3 easiest steps to add the gelato infrastructure and very easily automate your smart contract tasks: Wire Gelato infrastructure Gelato Funding Strategy Gelato Business Logic 3.1) Task Creation 3.2) Checker Condition 3.3) Executable Function Step 1: Wire Gelato infrastructure In order to interact with the gelato network, we will need to interact with the Gelato contracts (addresses can be found ). We will interact with three contracts: here The main contract for creating, canceling, getting transaction Fees, transfer fees, etc. We will inherit the contract , we will pass in the constructor the gelato ops and gelato treasury addresses and !. Ops Contract: OpsReady.sol we are good to go import {OpsReady} from "./gelato/OpsReady.sol";
import {IOps} from "./gelato/IOps.sol";
import {ITaskTreasury} from "./gelato/ITaskTreasury.sol";

contract PartyApp is OpsReady, Ownable {

  constructor(address payable _ops, address payable _treasury)
    OpsReady(_ops, payable(_treasury)){  } : We will require to interact with the gelato treasury contract for fund/withdrawal depending on our funding strategy (see step 2) Gelato Treasury Contract : We will interact with this contract in our tests… more on Bonus Track #2 Gelato Network The OpsReady.sol contract, as well as the interfaces, can be found in within the repository. You can just copy them and it works! gelato-files Step 2: Gelato Funding Strategy Gelato executes transactions at a future point in time, therefore we need to choose a way of funding the transactions that Gelato is going to execute on our behalf.There are two alternatives to do that: as long as you have a positive balance in the treasury contract, the future transactions will be executed. If we choose this alternative we need to interact with the Gelato Treasury Contract funding it. 1) Fund the Gelato Treasury Contract: function fundGelato(uint256 amount) public payable {
    require(msg.value == amount, "NO_FUNDING");
    ITaskTreasury(treasury).depositFunds{value: amount}(address(this),ETH,amount);
  }

  function withdrawGelato() public onlyOwner {
    uint256 maxAmount = ITaskTreasury(treasury).userTokenBalance(address(this),ETH);

    ITaskTreasury(treasury).withdrawFunds(payable(msg.sender), ETH, maxAmount);
  } Our smart contract will transfer in every future transaction the amount requested to pay the fees. In this case, we won’t need to interact with the Gelato Treasury Contract but . 2) Fund every transaction: we must maintain a positive balance in our contract Step 3: Gelato Business Logic There are three main parts/steps that we have to define within the business logic: We will have to define a task to tell Gelato what we want to be executed. 3.1) Create the Task: function createTask() public {
    require(taskIdByUser[msg.sender] == bytes32(0), "TASK_STILL_ACTIVE");

    bytes32 taskId = IOps(ops).createTask(
      address(this), /// Contract executing the task
      this.startParty.selector, /// Executable function's selector
      address(this), /// Resolver contract, in our case will be the same
      abi.encodeWithSelector(this.checkerStartParty.selector) /// Checker Condition
    );

    taskIdByUser[msg.sender] = taskId;
  } In order to execute a future transaction, we will have to provide Gelato with the condition to check whether Gelato can execute or not 3.2) Checker Condition: function checkerStartParty()
    external
    view
    returns (bool canExec, bytes memory execPayload)
  {
    canExec = headachePresent == false;
    execPayload = abi.encodeWithSelector(this.startParty.selector);
  } Function that will be executed when conditions and/or time are met. 3.3) Executable Function: function startParty() external onlyOps {
    require(headachePresent == false, "NOT_READY");
    lastPartyStart = block.timestamp;
    headachePresent = true;
  } https://gist.github.com/donoso-eth/0678b0613db36c6c332063c9f39cddfd Party App demo! Our First Gelato App is going to be very simple. It checks whether our gelato party has started or not. The party will always start if we don’t have a “headache” from the previous party. We can set manually when our “headache” is over and then the Gelato network will be able to execute the start party, setting a new start party timestamp and setting our “headache to true” Our screen is divided into two parts depending on our funding strategy. This contract allows three uses cases: Create a simple task funded with treasury: Details can be seen above Once the task is created we can go to the and we will see our task waiting for execution gelato ops website And after successful execution, the ops dashboard will show us something like this. Create a simple task funded with treasury and cancel after the first execution (we are going to use this pattern later on with our Superfluid streams). https://gist.github.com/donoso-eth/517e2dca691980de506229cbe27eee62 Create a simple task paying each transaction (not treasury funding) https://gist.github.com/donoso-eth/340ca96b53005dd457defab0991a735c Gelato Super App Demo Our Gelato super App will help us make superfluid streams programmable by automating the stop or the start of a stream. We will implement the gelato Infrastructure (Step 1) like in the party app and we choose Treasury funding as a Funding Strategy (Step 2) We will demo stopping a stream after some predefined minutes. Our Business Logic will look like this: https://gist.github.com/donoso-eth/e4fc0145ed75ed84309da1a467175931 Now if you have funded the treasury, have started a stream and the gelato has already been executed stopping the stream you have unlocked your Bonus!! Bonus Track #1: Go to Sleep and the Stream will Start. So far we have achieved to stop a stream automatically, but following the same logic, I may want to start streaming to a new employee exactly at 00:00 AM on the first day of work and I don’t want to stay awake every day because hopefully, we are going to hire a lot of employees! .. then (CFA Access Control List) to the rescue, with a simple call to the CFA constant agreement either from the SDK or directly to the contract on your behalf when a certain time is elapsed and a “Gelato Task” is executed. CFA ACL you may want to allow our Super App to start a stream In this use case, we are concatenating two tasks, when the first one is executed, the stream will be started, the task canceled, and another task to stop the stream will be created. https://gist.github.com/donoso-eth/5491f5f94409f9648fa196c3ed24ca3d Bonus Track#2: Master Hardhat Fork and Sky Rocket your Development Speed One of the pleasant experiences in blockchain development is the ability to one-click creation of….. As our dapps grow in complexity we will require to interact with existing on-chain contracts and we will have to mock/deploy protocols. In some cases that . The best alternative to overcome this issue is to work with a fork, with a very simple configuration within our (thks and for pointing out the right direction). if we want to remain local can be cumbersome and we will spend precious development time hardhat.config.ts Sam Flamini Hilmar X https://gist.github.com/donoso-eth/1dbfc57d3d40679e324048e1d7c01ab4 and then with the we will be able to create a “virtual” copy of the blockchain we are targeting. The blocks we create from now on will be stored locally and for the older ones we will query the “real” blockchain with our RPC provider (above we are using alchemy) npx hardhat node --network "hardhat" In our example, we are working with mumbai, the Superfluid contracts (Host, ConstanFlowAgreeent, Supertoken…), as well as the Gelato contracts (Network, OPS, and Treasury), exist with the state they had at the block number of the fork allowing us to interact with them as we would interact with the “real” blockchain. Now, you have your local “mumbai” with the additional helper methods to truly master the chain: https://gist.github.com/donoso-eth/148d031bbc57e6a3b6708367a52b0069 In our Dapp we are working with Gelato contracts. The “Executors” will take care to automate our tasks, but in our local “virtual” chain there are no executors… who will execute our tasks?. And the answer to that is very simple, . We can do that because we master our local blockchain, and we choose to be the executor. Hardhat provides us with the fantastic method and we will use it to become locally “the executor”. we are going to execute the task ourselves we can be whoever we want to be hardhat_impersonateAcount Here we can see the details of the implementation for executing gelato tasks impersonating the Gelato NetWork contract https://gist.github.com/donoso-eth/88b3e43f5957cf1e6cdbcd326067fee0 We will need to build the params to be able to execute the task, if we look in Ops interface we see that we need the following params /// @notice Execution API called by Gelato
  /// @param _txFee Fee paid to Gelato for execution, deducted on the TaskTreasury
  /// @param _feeToken Token used to pay for the execution. ETH = 0xeeeeee...
  /// @param _taskCreator On which contract should Gelato check when to execute the tx
  /// @param _useTaskTreasuryFunds If msg.sender's balance on TaskTreasury should pay for the tx
  /// @param _revertOnFailure To revert or not if call to execAddress fails
  /// @param _execAddress On which contract should Gelato execute the tx
  /// @param _execData Data used to execute the tx, queried from the Resolver by Gelato
  function exec(
    uint256 _txFee,
    address _feeToken,
    address _taskCreator,
    bool _useTaskTreasuryFunds,
    bool _revertOnFailure,
    bytes32 _resolverHash,
    address _execAddress,
    bytes calldata _execData
  ) external; Using one of our examples in the party app we will have: https://gist.github.com/donoso-eth/bacd13ccb9718d70f618eca6c82587f7 The implementation in our dapp tests can be seen in the . We use this technique in our contract tests. code Conclusion As we have seen, it is relatively simple to wire the gelato network into our smart contracts and unlock the full potential of automation. Specifically for Superfluid streams gelato can allow Super Apps to do stream-scheduling. Hope this article can help other devs to quickly get up and running with gelato and apply it to Superfluid streams. You can connect with me on Twitter @donoso_eth Also published . here

Stream Scheduling With Superfluid & Gelato

Programación de transmisiones con Superfluid y Gelato

Planification de flux avec Superfluid & Gelato

Superfluid & Gelato . के साथ स्ट्रीम शेड्यूलिंग

Superfluid と Gelato を使用したストリーム スケジューリング

Agendamento de fluxo com Superfluid & Gelato

Lên lịch phát trực tiếp với Superfluid & Gelato

使用 Superfluid 和 Gelato 进行流调度

Authors:
(1) Ankur Nath, Department of Computer Science and Engineering, Texas A&M University;
(2) Alan Kuhnle, Department of Computer Science and Engineering, Texas A&M University. Table of Links Abstract & Introduction Related work Evaluation for Max-Cut Evaluation for SAT Summary and Outlook, References Supplementary Materials 5 SUMMARY and OUTLOOK Through our empirical evaluations, our goal is to promote an insightful comparison within the research focusing on the intersection of combinatorial optimization and machine learning. In order to provide the research community with valuable guidance, we believe it is imperative to communicate both the strengths and weaknesses of the proposed approaches. Poor instances and baseline selection may give the wrong impression about the performance of learned heuristics. Specifically, it is important to articulate the degree of improvement achieved through integrating classical heuristics with deep learning architectures and conduct a thorough comparison with classical heuristics. This will aid in elucidating the degree to which deep learning architectures enhance integrated heuristics. It assists in ascertaining whether the integration endeavor is justified and warrants the allocation of computational resources, time, and investment necessary for integrating deep learning with classical heuristics. References Albert, R. and Barab´asi, A.-L. (2002). Statistical mechanics of complex networks. Reviews of modern physics, 74(1):47. Barrett, T., Clements, W., Foerster, J., and Lvovsky, A. (2020). Exploratory combinatorial optimization with reinforcement learning. In Proceedings of the AAAI conference on artificial intelligence, volume 34, pages 3243–3250. Barrett, T. D., Parsonson, C. W., and Laterre, A. (2022). Learning to solve combinatorial graph partitioning problems via efficient exploration. arXiv preprint arXiv:2205.14105. Battiti, R. and Protasi, M. (1997). Reactive search, a history-sensitive heuristic for max-sat. Journal of Experimental Algorithmics (JEA), 2:2–es. Battiti, R. and Tecchiolli, G. (1994). The reactive tabu search. ORSA journal on computing, 6(2):126–140. Bello, I., Pham, H., Le, Q. V., Norouzi, M., and Bengio, S. (2016). Neural combinatorial optimization with reinforcement learning. arXiv preprint arXiv:1611.09940. Bengio, Y., Lodi, A., and Prouvost, A. (2021). Machine learning for combinatorial optimization: a methodological tour d’horizon. European Journal of Operational Research, 290(2):405–421. Benlic, U. and Hao, J.-K. (2013). Breakout local search for the max-cutproblem. Engineering Applications of Artificial Intelligence, 26(3):1162–1173. Boettcher, S. and Percus, A. G. (2001). Extremal optimization for graph partitioning. Physical Review E, 64(2):026114. CPLEX (2023). Cplex. https://www.ibm.com/products/ilog-cplexoptimization-studio/cplex-optimizer. Dong, Y., Goldberg, A. V., Noe, A., Parotsidis, N., Resende, M. G., and Spaen, Q. (2021). New instances for maximum weight independent set from a vehicle routing application. In Operations Research Forum, volume 2, pages 1–6. Springer. E´en, N. and S¨orensson, N. (2003). An extensible satsolver. In International conference on theory and applications of satisfiability testing, pages 502–518. Springer. Elsokkary, N., Khan, F. S., La Torre, D., Humble, T. S., and Gottlieb, J. (2017). Financial portfolio management using d-wave quantum optimizer: The case of abu dhabi securities exchange. Technical report, Oak Ridge National Lab.(ORNL), Oak Ridge, TN (United States). Erd˝os, P., R´enyi, A., et al. (1960). On the evolution of random graphs. Publ. math. inst. hung. acad. sci, 5(1):17–60. Festa, P. and Resende, M. G. (2009). Hybrid grasp heuristics. In Foundations of Computational Intelligence Volume 3: Global Optimization, pages 75–100. Springer. Flint, A. and Blaschko, M. (2012). Perceptron learning of sat. Advances in neural information processing systems, 25. Fujishige, S. (2005). Submodular functions and optimization. Elsevier. Ganesh, V., Singh, R., Near, J. P., and Rinard, M. (2009). Avatarsat: An auto-tuning boolean sat solver. Glover, F. (1990). Tabu search: A tutorial. Interfaces, 20(4):74–94. Goemans, M. X. and Williamson, D. P. (1995). Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of the ACM (JACM), 42(6):1115–1145. Grozea, C. and Popescu, M. (2014). Can machine learning learn a decision oracle for np problems? a test on sat. Fundamenta Informaticae, 131(3- 4):441–450. Haim, S. and Walsh, T. (2009). Restart strategy selection using machine learning techniques. In International Conference on Theory and Applications of Satisfiability Testing, pages 312–325. Springer. Helmberg, C. and Rendl, F. (2000). A spectral bundle method for semidefinite programming. SIAM Journal on Optimization, 10(3):673–696. Hoos, H. H. et al. (2002). An adaptive noise mechanism for walksat. 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No free lunch theorems for optimization. IEEE transactions on evolutionary computation, 1(1):67–82. Ye, Y. (2003). The gset dataset. https://web.stanford.edu/ yyye/yyye/Gset/. Yolcu, E. and P´oczos, B. (2019). Learning local search heuristics for boolean satisfiability. Advances in Neural Information Processing Systems, 32. This paper is available on arxiv under CC 4.0 DEED license. Authors: (1) Ankur Nath, Department of Computer Science and Engineering, Texas A&M University; (2) Alan Kuhnle, Department of Computer Science and Engineering, Texas A&M University. Authors: Authors: (1) Ankur Nath, Department of Computer Science and Engineering, Texas A&M University; (2) Alan Kuhnle, Department of Computer Science and Engineering, Texas A&M University. Table of Links Abstract & Introduction Abstract & Introduction Related work Related work Evaluation for Max-Cut Evaluation for Max-Cut Evaluation for SAT Evaluation for SAT Summary and Outlook, References Summary and Outlook, References Supplementary Materials Supplementary Materials 5 SUMMARY and OUTLOOK Through our empirical evaluations, our goal is to promote an insightful comparison within the research focusing on the intersection of combinatorial optimization and machine learning. In order to provide the research community with valuable guidance, we believe it is imperative to communicate both the strengths and weaknesses of the proposed approaches. Poor instances and baseline selection may give the wrong impression about the performance of learned heuristics. Specifically, it is important to articulate the degree of improvement achieved through integrating classical heuristics with deep learning architectures and conduct a thorough comparison with classical heuristics. This will aid in elucidating the degree to which deep learning architectures enhance integrated heuristics. It assists in ascertaining whether the integration endeavor is justified and warrants the allocation of computational resources, time, and investment necessary for integrating deep learning with classical heuristics. References Albert, R. and Barab´asi, A.-L. (2002). Statistical mechanics of complex networks. Reviews of modern physics, 74(1):47. Barrett, T., Clements, W., Foerster, J., and Lvovsky, A. (2020). Exploratory combinatorial optimization with reinforcement learning. In Proceedings of the AAAI conference on artificial intelligence, volume 34, pages 3243–3250. Barrett, T. D., Parsonson, C. W., and Laterre, A. (2022). Learning to solve combinatorial graph partitioning problems via efficient exploration. arXiv preprint arXiv:2205.14105. Battiti, R. and Protasi, M. (1997). Reactive search, a history-sensitive heuristic for max-sat. Journal of Experimental Algorithmics (JEA), 2:2–es. Battiti, R. and Tecchiolli, G. (1994). The reactive tabu search. ORSA journal on computing, 6(2):126–140. Bello, I., Pham, H., Le, Q. V., Norouzi, M., and Bengio, S. (2016). Neural combinatorial optimization with reinforcement learning. arXiv preprint arXiv:1611.09940. Bengio, Y., Lodi, A., and Prouvost, A. (2021). Machine learning for combinatorial optimization: a methodological tour d’horizon. European Journal of Operational Research, 290(2):405–421. Benlic, U. and Hao, J.-K. (2013). Breakout local search for the max-cutproblem. Engineering Applications of Artificial Intelligence, 26(3):1162–1173. Boettcher, S. and Percus, A. G. (2001). Extremal optimization for graph partitioning. Physical Review E, 64(2):026114. CPLEX (2023). Cplex. https://www.ibm.com/products/ilog-cplexoptimization-studio/cplex-optimizer. Dong, Y., Goldberg, A. V., Noe, A., Parotsidis, N., Resende, M. G., and Spaen, Q. (2021). New instances for maximum weight independent set from a vehicle routing application. In Operations Research Forum, volume 2, pages 1–6. Springer. E´en, N. and S¨orensson, N. (2003). An extensible satsolver. In International conference on theory and applications of satisfiability testing, pages 502–518. Springer. Elsokkary, N., Khan, F. S., La Torre, D., Humble, T. S., and Gottlieb, J. (2017). Financial portfolio management using d-wave quantum optimizer: The case of abu dhabi securities exchange. Technical report, Oak Ridge National Lab.(ORNL), Oak Ridge, TN (United States). Erd˝os, P., R´enyi, A., et al. (1960). On the evolution of random graphs. Publ. math. inst. hung. acad. sci, 5(1):17–60. Festa, P. and Resende, M. G. (2009). Hybrid grasp heuristics. In Foundations of Computational Intelligence Volume 3: Global Optimization, pages 75–100. Springer. Flint, A. and Blaschko, M. (2012). Perceptron learning of sat. Advances in neural information processing systems, 25. Fujishige, S. 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Assessing the Justification for Integrating Deep Learning in Combinatorial Optimization

In the era of widespread adoption of AI models, the data science community exhibits a rich diversity of backgrounds, fostering an environment conducive to innovation. Collaborative efforts stemming from this diversity continue to propel us toward the envisioned future of a decade or two ago. However, innovation often follows incremental patterns and may require decades before yielding tangible commercial benefits. Among industries adept at translating ideas into tangible products, automotive manufacturers stand out, boasting a deep familiarity with research and development processes and advanced algorithms. This proficiency is evident in the innovation pipeline for super and hypercars, drawing inspiration from advancements in rocket science. Leveraging extensive simulations and field tests, these manufacturers consistently push the boundaries of performance and safety in vehicle design. Major manufacturers have achieved breakthroughs with torque vectoring systems by capitalizing on established development pipelines and harnessing the capabilities of reinforcement learning. The late 2010s witnessed a surge in commercial vehicles featuring these systems, attributed partly to their association with electric and hybrid vehicles and partly to the appeal of enhanced safety. While the full extent of their influence on driver experience remains to be realized, these systems have already demonstrated remarkable efficacy, particularly in high-performance vehicles. So, what exactly is a torque vectoring system, and how is this innovation shaping the landscape of automotive manufacturing? What is Torque Vectoring In Torque Vectoring Systems (TVS), torque denotes a rotational force applied to a vehicle’s differentials or generated by independent electric motors on its wheels. These systems aim to regulate this rotational force to enhance speed, stability, handling, balance, and other performance aspects. A compelling illustration of the protracted nature of innovation is evident in the evolution of torque vectoring systems, with the first cars equipped with Torque Vectoring Systems (TVS) debuting in the 1990s, pioneered by Mitsubishi. Initially known as Active Yaw Control, Mitsubishi integrated this technology into vehicles like the 1996 Mitsubishi Lancer Evolution IV GSR models. The initial implementation relied on steering, throttle inputs, and g-force sensors to mitigate torque steer, a phenomenon where engine torque influences steering behavior. Initially geared towards racing applications, these systems have since evolved to cater to broader audiences, with companies like Rimac continuing to employ them for racing. In contrast, others emphasize safety and enhanced handling features for everyday drivers. Furthermore, advancements driven by the pursuit of eco-friendly transportation have led to the utilization of independent electric motors in torque vectoring systems, further expanding their applicability. Commercial Applications Ricardo (Honorable Mention) In 2006, Ricardo, a renowned engineering consultancy with over a century of experience, introduced the concept of torque vectoring. Ricardo rolled out its initial torque vectoring project centered around the Audi A6 4.2L, intending to license its technology to interested automakers. Unlike Mitsubishi’s Active Yaw Control system and similar counterparts, Ricardo’s torque vectoring approach prioritized safety and stability, showcasing a different aspect of the technology. Limited information is currently available on Ricardo’s involvement in assisting manufacturers in developing these systems for commercially available vehicles. However, they have publicly provided engineering support to Chinese students building cars for the global multi-event Formula SAE race in 2019. Rimac When discussing electric vehicles, Tesla typically takes the spotlight regarding market dominance. However, Rimac stands out as a company dedicated to crafting high-performance electric hypercars, where they excel. Just ask Elon… ( t) X pos Rimac burst onto the scene in January 2016 with their inaugural concept car, the Concept_One prototype. This marked the debut of their torque vectoring system (TVS) in an all-wheel-drive fully electric vehicle. Spearheaded by Tomislav Šimunić, Rimac’s TVS development pushed the boundaries by employing individual motors on each wheel. Moreover, they implemented reinforcement algorithms utilizing data from various sensors, including accelerometers, gyroscopes, steering angle, and wheel speed sensors. This data is then used to predict torque distribution to optimize vehicle stability. https://www.youtube.com/shorts/i4jVW29gbDc?embedable=true Currently, Rimac boasts one of the fastest and safest hypercars on the market. Their innovation has led to unprecedented control, resulting in their car achieving the title of the fastest production car ever in 21 acceleration and deceleration categories. Furthermore, their TVS is so reliable that their drivers can cruise hands-free at speeds exceeding 230 mph while enjoying gelato! Toyota In 2018, Toyota introduced their Dynamic Torque Vectoring AWD and Electric 4WD systems, expanding the scope of this technology beyond on-road safety and control to encompass off-road safety features and enhanced fuel efficiency. https://www.youtube.com/watch?v=LCqCa7PP1gE&embedable=true The video above showcases Toyota’s emphasis on “proactive torque transfer,” allowing for seamless adjustment of torque distribution when one or more wheels lose traction, enabling drivers to navigate various terrains more effectively. https://youtu.be/d1UG1a38diw?embedable=true Furthermore, Toyota optimizes torque distribution to enhance fuel-efficiency, shifting from AWD to 2WD when conditions permit, directing torque predominantly to the front wheels and thus cutting fuel consumption. Their limited content suggests the employment of a Dynamic Control System designed for stability, taking into account challenging driving scenarios. Moreover, the system can evaluate tire traction levels. These functionalities resonate with the research findings discussed below, showcasing the seamless transition from research concepts to practical implementation in the automotive industry. Research Review Conceptual Models — Bicycle, Vehicle, Tire Model Following Occam’s razor principle, simplicity reigns supreme when initiating modeling endeavors, with complexity introduced only when its benefits are worthwhile. This philosophy holds for TVS as well. Early TVS adopted a bicycle model, allowing researchers to streamline vehicle dynamics assumptions by confining movements to two wheels. This simplified framework facilitated the study of lateral vehicle dynamics during various events like braking, acceleration, and cornering under typical conditions. Key inputs into the bicycle model include yaw rate, lateral acceleration, steering angle, and velocity. Yaw rate denotes the vehicle’s rotation speed around its vertical axis, aiding in determining its orientation during maneuvers like cornering. Lateral acceleration captures sideways movements perpendicular to the vehicle’s direction of travel. Steering angle refers to the front wheel angle, typically in relation to the rear wheel positioning, while velocity represents the vehicle’s speed. For more details, check out this article explaining a simple bicycle model. https://dingyan89.medium.com/simple-understanding-of-kinematic-bicycle-model-81cac6420357?embedable=true Simplicity in modeling often comes with assumptions that may not hold, especially in challenging driving scenarios. Extreme conditions like rain, snow, or rough off-road terrain expose the limitations of the traditional bicycle model. The assumption of symmetry between the left and right wheels hinders the accurate analysis of lateral dynamics across all four wheels. To address this, researchers upgraded to a more comprehensive 4-wheel vehicle model. One such model, proposed in the 2023 journal article by Hui Deng, Youqun Zhao, Fen Lin, and Qiuwei Wang, boasts seven degrees of freedom. This expanded model captures all four wheels’ lateral, longitudinal, rotational, tilting, leaning, and spinning movements. However, it still falls short in capturing driving dynamics such as suspension behavior and tire-road interactions. Although suspension dynamics may be indirectly represented within the model, a separate tire model is necessary to capture tire-road interactions accurately. Deep Reinforcement Learning-Based Torque Vectoring Control Considering Economy & Safety² Tire models typically include parameters like tire force and slip angles. In the journal article by Michele Vignati, Edoardo Sabbioni, and Federico Cheli, researchers describe a simple tire model that incorporates lateral and longitudinal dynamics, slip angles, and slippage. Like the seven degrees of freedom model indirectly addresses suspension dynamics, the tire model considers slippage influenced by latent variables such as surface texture, conditions, and angles. This comprehensive approach allows researchers to analyze vehicle dynamics across various conditions and terrains, enhancing the torque vectoring system’s adaptability and performance. A Torque Vectoring Control for Enhancing Vehicle Performance in Drifting³ Control Schemes/Implementations In Torque Vectoring Systems (TVS) development, a significant portion of research revolves around employing Reinforcement Learning techniques, leveraging real-time data collected from various measurement devices. These solutions are predominantly implemented in all-wheel drive, four-wheel drive hybrid, and electric vehicles. Typically, the training of these systems takes place within simulated environments. However, in certain instances, researchers conduct road tests and utilize live test outcomes to validate simulation results. Torque Vectoring System Testing While specific details about testing TVS are often limited, researchers generally have three options: entirely computer-based simulations, hardware-in-the-loop testing combining simulation with real parts, and full-scale vehicle road tests. Computer-based simulations offer cost-effective evaluation of TVS with precise control over various driving conditions. Hardware-in-the-loop testing balances simulation and road tests, providing insights aligned with real-world performance. Although the most expensive, road tests offer the most reliable results by implementing TVS fully, enabling the most accurate evaluation of model performance. In the study by Shayan Taherian, Sampo Kuutti, Marco Visca, and Saber Fallah, computer-based simulations were utilized to test their RL algorithm across diverse environments. The researchers employed an adaptive algorithm based on Deep Deterministic Policy Gradient to update TVS control parameters as it learns from the environment. Testing across various velocity and friction environments allowed validation of their adaptive algorithm, particularly in high-speed/low-velocity scenarios. Self-adaptive Torque Vectoring Controller Using Reinforcement Learning⁴ Similarly, in the research by Wei Xu, Hong Chen, Haiyan Zhao, and Bingtao Ren, real-time Simulink simulations were leveraged to validate their model predictive controller. This controller predicts future system states and optimizes for multiple energy efficiency and safety objectives. Tests were conducted using an electric vehicle model with a 120 km/h velocity and an “adhesion coefficient” of .85, measuring tire friction between tire and ground. Torque Optimization Control for Electric Vehicles with Four In-Wheel Motors Equipped with Regenerative Braking System⁵ Powertrain & Fuel Types The specific problem addressed by torque vectoring systems heavily influences the powertrain choice and fuel types utilized in their implementations. Traditional gasoline and diesel vehicles necessitate mechanical implementations due to a single torque source, leading to complex mechanical differentials, challenges in power distribution, and overall less efficiency compared to hybrid and electric vehicle setups, which enable independent motor implementations. Similarly, All-Wheel Drive (AWD) and Four-Wheel Drive (4WD) powertrains offer superior advantages over other options. These configurations enhance stability, versatility, and energy efficiency. The work of Jeongmin Cho and Kunsoo Huh, in their study , underscores the stability and versatility benefits of AWD vehicles. By distributing power to all four wheels, AWD enhances the effectiveness of torque vectoring systems, granting increased control over each wheel. This translates to improved vehicle dynamics during cornering, acceleration, and deceleration. Torque Vectoring System Design for Hybrid Electric–All-Wheel Drive Vehicle⁶ Meta Control Algorithms In Reinforcement Learning (RL), an agent decides actions based on the current situation to maximize a reward function. It learns which actions yield the highest rewards by assessing the outcomes of its actions. In torque vectoring algorithms, auto manufacturers define different reward functions based on the specific goals of their TVS, which vary depending on the type of vehicles used, such as sports cars versus mini-vans. These goals include increased stability, controllability, fuel economy, cornering performance, and optimizing various vehicle dynamics behaviors. One example of a multi-objective implementation is outlined in the paper by Jae-Young Park, Seung-Jin Heo, and Daeoh Kang. Their algorithm features a supervisory controller that selects between an “agile” mode and a “safe” mode based on vehicle and driving conditions. Agile mode prioritizes driver controllability, while safe mode focuses on stability. Controllability refers to the synchronization between driver steering input and vehicle direction, while stability relates to the vehicle’s resistance to deviations or disturbances. Inputs such as vehicle speed, steering angle, yaw rate, lateral acceleration, and wheel slip guide the supervisory controller’s decision-making process. Development of Torque Vectoring Control Algorithm for Front Wheel Driven Dual Motor System and Evaluation of Vehicle Dynamics Performance⁷ Another example is presented in the paper by Hui Deng, Youqun Zhao, Fen Lin, and Qiuwei Wang. Here, the researchers optimize for safety, economy, and driver load. Economy involves assessing motor efficiency and energy savings compared to vehicles without torque vectoring systems. Safety focuses on vehicle stability, while driver load considers the physical and cognitive load based on the correlation between the driver’s steering wheel angle and the vehicle’s longitudinal acceleration. Deep Reinforcement Learning-Based Torque Vectoring Control Considering Economy and Safety⁸ The algorithm includes an active safety controller and a torque allocation layer. The active safety controller calculates total longitudinal acceleration and additional “yaw moment” values based on driving conditions, applying safety and driver load penalties. These values are then fed to the torque allocation layer, which distributes torque to all four wheels. Additionally, the researchers implement a tire model using a Fibonacci tree optimization algorithm and a vehicle model with 7 degrees of freedom to enhance system performance. The , research done by Park et al., aims to enhance the driver’s experience through improved smoothness and convergence. Their TVS, designed for commercial application, underwent rigorous validation through real vehicle experiments conducted under various conditions. Torque Vectoring Algorithm of Electronic-Four-Wheel Drive Vehicles for Enhancement of Cornering Performance⁹ The researchers implemented a smooth sliding controller, GPS, and sensor inputs to generate desired yaw moment values. These values are then utilized by the torque allocation algorithm, which employs a daisy-chaining allocation method to distribute torque efficiently. The goal is to optimize the convergence from current yaw moment values to target values, thereby reducing the instability during this transition. Conclusion The evolution of torque vectoring systems underscores the transformative power of innovation within the automotive industry. From pioneering beginnings to cutting-edge applications, these systems have revolutionized vehicle dynamics, speed, stability, and handling. As automotive manufacturers continue to push the boundaries of technology and leverage advancements in advanced algorithms, the future holds promise for further improvements in safety, performance, and driver experience. However, hurdles remain in integrating this technology into internal combustion engine vehicles, and ongoing research and development efforts are required to overcome them. With continued dedication to innovation, torque vectoring systems are poised to shape the future landscape of automotive manufacturing, driving us toward a new era of mobility. Research Reference Martin Dendaluce Jahnke et al., “Efficient Neural Network Implementations on Parallel Embedded Platforms Applied to Real-Time Torque-Vectoring Optimization Using Predictions for Multi-Motor Electric Vehicles,” 8, no. 2 (February 22, 2019): 250 Electronics Huifan Deng et al., “Deep Reinforcement Learning-Based Torque Vectoring Control Considering Economy and Safety,” 11, no. 4 (April 6, 2023): 459 Machines Michele Vignati, Edoardo Sabbioni, and Federico Cheli, “A Torque Vectoring Control for Enhancing Vehicle Performance in Drifting,” 7, no. 12 (December 5, 2018): 394 Electronics Shayan Taherian et al., “Self-Adaptive Torque Vectoring Controller Using Reinforcement Learning,” , September 19, 2021 2021 IEEE International Intelligent Transportation Systems Conference (ITSC) Wei Xu et al., “Torque Optimization Control for Electric Vehicles with Four In-Wheel Motors Equipped with Regenerative Braking System,” 57 (February 2019): 95–108 Mechatronics Jeongmin Cho and Kunsoo Huh, “Torque Vectoring System Design for Hybrid Electric–All Wheel Drive Vehicle,” 234, no. 10–11 (April 7, 2020): 2680–92 Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering Jae-Young Park, Seung-Jin Heo, and Dae-Oh Kang, “Development of Torque Vectoring Control Algorithm for Front Wheel Driven Dual Motor System and Evaluation of Vehicle Dynamics Performance,” 21, no. 5 (October 2020): 1283–91 International Journal of Automotive Technology Huifan Deng et al., “Deep Reinforcement Learning-Based Torque Vectoring Control Considering Economy and Safety,” 11, no. 4 (April 6, 2023): 459 Machines Giseo Park et al., “Torque Vectoring Algorithm of Electronic-Four-Wheel Drive Vehicles for Enhancement of Cornering Performance,” 69, no. 4 (April 2020): 3668–79 IEEE Transactions on Vehicular Technology

Driving Innovation: The Science of Torque Vectoring Systems

This paper is available on arxiv under CC 4.0 license. Authors: (1) Matu´s Medo, Department for BioMedical Research, Inselspital, Bern University Hospital, University of Bern, Department of Radiation Oncology, Inselspital, Bern University Hospital, University of Bern and matus.medo@unifr.ch; (2)  Michaela Medova, Department for BioMedical Research, Inselspital, Bern University Hospital, University of Bern, and Department of Radiation Oncology, Inselspital, Bern University Hospital, University of Bern. Table of Links Abstract & Introduction Results Discussion Materials and methods Acknowledgement & References Supporting Information 4. Materials and methods 4.1. Reference signatures We used all signatures from version 3.0 of the COSMIC catalog (COSMICv3, https://cancer.sanger.ac. uk/signatures/sbs/), in particular the SBS signatures for human genome assembly GRCh38. COSMICv3 contains 67 mutational signatures (18 are artifact signatures) defined in 96 mutational contexts. While newer COSMIC versions (the latest version is 3.3.1 from June 2022) added more signatures, profiles of the COSMICv3 signatures have not been altered (all absolute weight differences are below 10−7 ). To measure the diversity of signature profiles, we compute their exponentiated Shannon index which is a common measure of diversity (Missa et al., 2016) that can be understood as the effective number of active mutational contexts. For a signature whose all weight is concentrated in one context, the exponentiated Shannon index is one. For a signature with the same weight 1/96 of all contexts, the exponentiated Shannon index is 96. For COSMICv3 signatures, the exponentiated Shannon index ranges from 2.7 (SBS48) to 80.3 (SBS3). 4.2. Synthetic mutational catalogs Absolute contributions of signatures to sequenced tissues from various cancer types were downloaded from the Catalogue Of Somatic Mutations In Cancer (COSMIC, https://cancer.sanger.ac.uk/signatures/sbs/, catalog version 3.2) on November 14, 2021 for all 46 non-artifact SBS signatures that have tissue contribution data available. These data included only samples with reconstruction accuracy above 0.90 and at least 10 mutations attributed to the specific SBS signature. Using the provided unique sample identifiers, we used these files to compute the relative signature contributions in individual WGS-sequenced samples that are stratified by the cancer type. We chose eight different cancer types for further analysis: Hepatocellular carcinoma (Liver-HCC, n = 422), stomach adenocarcinoma (Stomach-AdenoCA, n = 170), head and neck squamous cell carcinoma (Head-SCC, n = 57), colorectal carcinoma (ColoRect-AdenoCA, n = 72), lung adenocarcinoma (Lung-AdenoCA, n = 62), cutaneous melanoma (Skin-Melanoma, n = 280), non-Hodgkin Lymphoma (Lymph-BNHL, n = 117), and glioblastoma (CNS-GBM, n = 63). The approach described above allows us to reproduce empirical signature weights in previously analyzed samples without resorting to assumptions such as a log-normal distribution of the number of mutations due to a given signature (Alexandrov et al., 2020, Islam et al., 2022) or adding additional zeros to the Poisson distribution to reproduce signatures that are not active in a sample (Omichessan et al., 2019). The code for generating synthetic mutational catalogs and evaluating the signature fitting tools is available at https://github.com/8medom/SigFitTest. For Figure 6, we created synthetic mutational catalogs with a systematic difference in the activity of signature SBS40. After generating sample weights as described in the previous paragraph (assuming the CNS-GBM cancer type), the relative weights of SBS40 were multiplied by 1.3 in the first half of the samples and divided by 1.3 in the second half of the samples. The relative weights of all signatures in each sample were then normalized to one. Note that signature SBS40 is active in nearly all CNS-GBM samples (Fig. SF9 in SI) and its median relative weight is close to 50%. By the described process, the median weights in the two groups of samples become 42% and 55%, respectively. 4.3. Tools for signature fitting The task of fitting known mutational signatures to a mutational catalog consists of finding the combination of signatures from a reference set that “best” matches the given catalog. Denoting the matrix with reference signatures as S, where S cs is the relative weight of context c for signature s, and the given normalized mutational catalog as m, where mci is the fraction of mutations in context c in sample i, this amounts to solving where wsi is the relative weight of signature s in sample i. Mathematically, this is an over-determined system as the number of reference signatures is smaller than the number of mutational contexts (96 contexts for the common SBS signatures). Several fitting tools are therefore based on minimizing the difference between m and Sw through nonnegative least squares (as the signature weights cannot be negative) or quadratic programming. We evaluated several tools that belong to this class: MutationalPatterns v3.4.1 (Blokzijl et al., 2018), YAPSA v1.20.1 (Hubschmann et al. ¨ , 2021), SigsPack v1.8.0 (Schumann et al., 2019), and sigminer v2.2.0 (Wang et al., 2021) which has three separate methods based on quadratic programming, non-linear least squares, and simulated annealing. We find that all these tools produce similar results. Other tools use various iterative processes by which the provided set of reference signatures is gradually reduced by removing the signatures, for example, whose inclusion does not considerably improve the match between the observed and reconstructed mutational catalogs (or, opposite, signatures are gradually added as long as the reconstruction accuracy sufficiently improves). We evaluated deconstructSigs v1.8.0 (Rosenthal et al., 2016), SigProfilerSingleSample v0.0.0.27 (Alexandrov et al., 2020), SigProfilerAssignment v0.0.30 (Diaz-Gay et al., 2023), mmsig v0.0.0.9000 (Rustad et al., 2021), and signature.tools.lib v2.2.0 (Degasperi et al., 2022), that all belong to this category. The newest tool, SigProfilerAssignment, combines backward and forward iterative adjustment of the reference catalog and these steps are repeated until convergence. Finally, SigLASSO v1.1 combines the data likelihood in a generative model with L1 regularization and prior knowledge (Li, 2020, Li et al., 2020). To allow for a fair comparison with other tools, we did not use prior knowledge when evaluating sigLASSO. In our experience, this tool sometimes fails to halt but starting it again with the same input data resolves the issue. A similar Bayesian framework is used by sigfit v2.2 (Gori and Baez-Ortega, 2020). The authors of sigfit recommend setting all signatures whose lower bounds of the estimated 95% confidence intervals are below 0.01 to zero. The authors of deconstructSigs recommend setting all signatures whose relative weights are below 0.06 to zero. All results shown for sigfit and deconstructSigs follow these recommendations. 4.4. Trimming reference signatures It has been argued that the removal of irrelevant reference signatures can improve the fitting results (Kim et al., 2021). To assess this hypothesis, we use a two-step process where: (1) We fit signatures using all COSMICv3 signatures as a reference and (2) keep only the signatures whose relative weight exceeds threshold w0 for at least 5 samples in our cohorts with 100 samples. We use thresholds w0 = 0.05 (m = 100), w0 = 0.03 (m = 2, 000) and w0 = 0.01 (m = 50, 000) which correspond to absolute signature contributions 5, 60, and 500, respectively. This pruning of reference signatures is beneficial when the number of mutations per sample is small (see m = 100 in Fig. S17 in SI). However, the converse is true when the number of mutations per sample is high, in particular for tools that perform well with COSMICv3 as a reference (m = 50, 000 in Fig. S17 in SI). To overcome this problem, we have also tested a less strict pruning where we keep all signatures whose relative weight exceeds w0 for at least one sample (see Fig. S18 in SI for the results). We have also tested the approach based on de novo extraction of signatures as suggested in (Maura et al., 2019). For signature extraction, we used SignatureAnalyzed v0.0.7 (https://github.com/getzlab/SignatureAnalyzer) with L1 prior on both W and H and a Poisson objective function for optimization. As recommended in (Maura et al., 2019), each extracted signature was then compared with individual signatures from COSMICv3 as well as linear combinations of two signatures from COSMICv3. The signature (or a pair of signatures) that yielded the smallest cosine distance was then added to the list of trimmed reference signatures for the given input data. When the number of mutations is small (m = 100), less than five signatures are selected, on average. When the number of mutations is large (m = 50, 000), 89% of the active signatures are selected, on average. A comparison of the results obtained by the two reference-trimming schemes is shown in Fig. S19 in SI. 4.5. Evaluation metrics Recent literature often classifies fitting results as true positives, false positives, true negatives, and false negatives, which allows computing evaluation metrics such as precision and specificity Omichessan et al. (2019), Islam et al. (2022), Diaz-Gay et al. (2023). We use instead quantitative metrics that measure the differences between the true relative signature weights (which are used to generate the input mutational catalogs) and the estimated relative signature weights. For tools that estimate absolute signature weights, those are first normalized by the number of mutations in each sample. and average it over all samples in the cohort to obtain fitting error. The lowest fitting error, 0, is achieved when the estimated signature weights are exact for all signatures and all samples. The highest fitting error, 1, is achieved when the estimated signature weights sum to one for each sample but they are all false positives. For example, when a sample has 40% contribution of SBS1 and 60% of SBS4 but a tool estimates 20% contribution of SBS2 and 80% contribution of SBS3, the fitting error is 1. There are some tools whose signature weight estimates do not sum up to one for each sample, typically as a result of the uncertainty implied by a small number of mutations in samples. The fitting error of those tools can be inflated due to these tools’ conservativeness. However, we probed whether additionally normalizing the estimated weights to one improves the fitting error achieved by those tools and found that this is not the case. We can thus conclude that these tools are not disfavored by measuring their fitting error. Another way to quantify the agreement between the true and estimated signature weights is by computing their Pearson correlation. For each sample where at least three signatures had positive either true or estimated weights, we computed the Pearson correlation coefficient between these two weight vectors whilst excluding all signatures that are zero for both of them. The obtained values were then averaged over all samples in the cohort. We finally computed false positive weight which quantifies how much weight is assigned to the signatures that are not active in a given sample, and then this quantity is averaged over all samples. This quantity too ranges from 0 (when no weight is assigned to inactive signatures) to 1 (when all weight is assigned to inactive signatures). This paper is available on under CC 4.0 license. arxiv

The Materials and Methods That We Used to Compare Tools for Fitting Mutational Signatures

“ ” Nephrologist: Hello. We've got a set of failing kidneys. Please, how soon can we get a new set created and ready to implant? “ . Biotechician: We’ll come for the patient's biomaterials and have them ready in the next two months” That could have saved the life of a family friend after her kidneys failed 5 years ago—worst, she had a rare blood type. After being on the waiting list for 3 years undergoing excruciatingly painful dialysis, she caved into the verdict she dreaded the most. However, this article is not just a sob story of a friend. This is a revelation of how regenerative medicine, which you might have thought belonged to the fictitious world of Sci-fi, could be the savior of many lives like hers now and in the future. I’m talking about “3D Bioprinting”. The Back Story The number of humans with failing organs on the waiting list for organ transplants is overwhelming for the medical field. Organdonor.gov states that in the U.S. alone, over 103 thousand men, women, and children are on the national transplant waiting list. Every 10 minutes, one person is added to the list and 17 people die each day waiting for an organ transplant. In 2023, out of 88,551 awaiting kidney donors, only about 24% received transplants. That is in the U.S. alone, we can only try to imagine what the numbers could be in other parts of the world.. Or can we even imagine the reality in third-world countries with no structured organ donation system? Dr. Jennifer Lewis, a professor at Harvard University's Wyss Institute for Biologically Inspired Engineering, in an interview with CNN, has an insight into the problem. In her statement, she mentioned that on a yearly average, there are only around 6,000 living donors open to offering their organs and about 8,000 deceased donors who could each provide approximately 3.5 organs. Dead donors are people who die from catastrophic health events or accidents, making some of their organs salvageable before they completely stop living. However, because of such events, their organs may not be of high quality for a donation or they may not even be on the organ donor list or it may be hard to find a good match. For living donors, there is a scare as to what their life is worth, if it is the right choice to make if they are willing to let go and embrace the possible complications that may arise from donating their organs and the surgery involved - especially if the patient is not related to them. There is a two-step delirium that raises the most fear for a patient clinging onto the last thread of hope. First, finding a donor match, then hoping the patient's body doesn't reject the donated organ. And from all the premises stated above, this is a tough call. A wait list could just as well be a death row. What if it could be different? What if organs could be printed from biodata, materials, and cells of a patient instead of waiting for months to years to find a donor that would match? What if regenerative medicine is the solution staring into our eyes? A handful of medical conditions would meet their end if this could happen. Ordering a newly generated body part from the cells of the patient to replace the old one could easily be more effective and faster than organ donations. This brings us to the 3D organ bioprinting. What is 3D Bioprinting? The idea of 3D bioprinting is like that of conventional 3D printing. However, it is premised on the use of organ regenerative actions which involve the manufacturing and development of organs, tissues, and body parts such as the liver, skin, heart, eyes, bones, etc. While conventional 3D printers use computer files to extrude and create objects with complex structures, 3D bioprinters make use of bioinks containing living viable cells, biomaterials, and biomolecules to create bioartificial organs of a human. This works by assembling layer-by-layer multiple cell types, biomaterials and molecules, and other growth factors that would be a replica of the natural prototypes. In this case, it is beyond just mere perception that creating a new component for a body by using its cells is much more reliable than taking a component with a completely different cell structure from another body to replace a component in a body. This way, a patient, on-demand, can have personalized replacement body parts with a very low possibility of their body rejecting the new parts. This technology is driven by the need to find the accurate organ and tissue types that would be a match for patients who need organ replacement and is opening new avenues for future organ transplantation programs. How Does 3D Bioprinting Work? For bioprinting, every procedure starts with the biological cells of the person involved and applies the concepts of biomimetics and biomimicry. This simply means using a patient's cells to grow the needed organ. Biotechicians choose cells based on their physiology and functions. They consider the cells’ differentiation and proliferation by paying attention to features such as the cell type, size, and shape These different types of cells are rendered into a printable bioink, which involves mixing them up in materials like alginate or gelatin; before they are loaded into a nozzle. To continue, each cell is placed, layer by layer, in precise locations to form a cellular attachment and build a complex tissue that would develop the organ. For the cell's culture to grow, it is transferred to a scaffold where blood vessels are integrated into the tissue and the setup is connected to a pump that would deliver the right amount of oxygen and nutrients to keep it alive. With time, the tissue will begin to develop on its own, forming an organ that will increase both in maturity and function. This is a phase of 3D tissue engineering and although this is dramatically simplified, the process requires more technicalities only applicable to experts in the biotech field and could evolve with time. From the looks of things, 3D bioprinting is already here for good. Cases of 3D Bioprinting It is no longer a myth or a fictional idea; this regenerative medicine technology has become a reality. In this decade, research institutes, researchers, and doctors have dedicated time and resources, working actively on experimenting with organ bioprinting—some are already recording success. The First Ear Bioprint In 2022, the U.S. witnessed the implantation of a new ear on a 20-year-old lady born without her right ear. Of course, a new ear could have been artificially constructed and placed, but this time, Dr. Arturo Bonilla, a pediatric microtia surgeon, changed the rule of the game by developed out of the cartilage cells of the lady's left ear. implanting a 3D bioprinted ear Imagine multi-layered skin, cartilage, and muscle structures born out of laboratory-grown cells to form an ear. Amazing! This was a worthwhile revelation that bioprinting could change the way new body parts and organs were sourced. Ongoing Research on Bioprinting The race to find more potentially relieving 3D bioprinted tissues and organs surged even more. Still in 2022, and Dr. Michal Wszola, creator of Bionic Pancreas, revealed that some researchers in Poland were able to achieve the within a two-week window period, enabling stable blood flow in these pigs. this abstract 3D bioprint of pancreas in pigs Hope is alive as the National Institute of Health’s Advanced Research Projects Agency for Health (ARPA-H), in September 2023, awarded some Stanford researchers about to bioprint a human heart and transplant it into a pig in the next five years. $26 million in contract However, the with 4,000 kilometers of capillaries and 200 million alveoli, capable of carrying out oxygen exchange in animal models, which is a critical step towards the development of tolerable, transplantable lungs has been achieved by United Therapeutics Corporation. The goal is to have the lungs cleared for human trials within five years. 3D bioprinting of human lungs Another research institute with impressive strides is the Wake Forest Institute for Regenerative Medicine. Researchers in this institute have been able to develop the following: A skin bioprinting system for patients suffering from skin cancers, burns, and other non-healing or deprecated kin conditions. A 3D bioprinting skeletal muscle system was shown to effectively contract in rodents and enable an 80% regain of lost muscular function in an anterior leg muscle within a space of 8 weeks. Printing of tubular structures like blood vessels or hollow, non-tubular organs like a bladder. 3D biocreation of a mini-kidney and a mini-liver. The challenge for Wake Forest scientists is the creation of larger and more solid organs that can fully mimic the functions of their prototypes. This is because these large organs, like the brain and heart, have so many cells per centimeter, and there is the challenge of vascularity and nutrition. The brain is a very complex tissue that is difficult to repair or replace when damaged. However, some Oxford researchers believe that the bioprinting of stem cells can reverse brain damage and injuries. These researchers have gone on to prove this verdict by creating 3D bioprinted stem cells which developed a biomimicry of the complex structure of the human cerebral cortex, having six layers (two “deep” layers and four “upper” layers), each with its type of neuron. When the tissues were implanted into slices of mouse brains, they successfully integrated into the mouse tissue, structurally and functionally. The Problems and Ethical Considerations Surrounding the Creation of Bioprinted Body Parts and Organs As much as this concept looks like a lifesaver for many hopeless medical cases in the world today, there are still some problems this could pose. The bioprinting of organs is based on individual medical care rather than a basic universal treatment plan like that of organ donation. There is an assumption that due to its personalized medicine status, the cost of this service may just be more expensive than a public treatment plan would be, and this could prevent financially unstable people from getting access to this service. Is it safe? We can't say for sure. The 3D printing of organs and parts of the body using bioink is not considered neutrally ethical and even if it is generated from the patient's cell, there are still problematic aspects in terms of cell reprogramming, differentiation, proliferation, and of course mutation which may usher in the much-dreaded apocalypse. There is the risk of tumorigenicity, which is the property of a cell to form tumors when inoculated. While bioprinting is considered an incoming savior of the sick and deprived, this technology cannot be rushed. The efficacy of its procedures has to be tried and tested severally before it can be rolled out as clinically applicable. If this is not done, it can lead to several deaths that may be beyond control. There are also additional ethical and legal concerns related to patients' genetic information collection, which also include the storage and use of these cells. Advantages of Bioprinting and Designer Bodies Every technology has a downside, but it so happens that compared to the downsides of this technology, if it is put through all processes of long years of research and experiment with a high success rate, 3D organ bioprinting could nearly nullify the cause of concern. There are issues the bioprinting of organs and body parts would solve: The endless waiting list that could spell ‘doomsday is awaiting’. The torture that comes with getting a transplant; only for the patient's antigens to reject the organ. The need for immunosuppression to prevent organ rejection, which leaves patients at higher risk of infection. The risk of a living donor (even though willing) experiencing some possible complications that could arise during surgery. Body parts manufactured through bioprinting can be enhanced to improve performance. Bones can be made stronger and more flexible, the brain can be made smart and alert, the lungs can be made to increase oxygen efficiency in the blood, etc. In terms of cost, while critics claim that the price of bioprinted parts would be expensive, the fact remains that compared to waiting years for an organ to finally get to a patient who is at risk of losing their life any moment, this is fair. Most times these donated organs come at a very high cost (although sometimes illegal) because of the demand. However, the price of a bioprinted organ could reduce considerably when they clinically pass trials and patients wouldn't have to wait for several months, to a couple of years to get them. How close are we to the future? Brain, kidneys, muscles, skins, livers, pancreas, and so much more are in the laboratory phase of 3D experimentation. In the next 5 to 10 years, there is a high expectation of breakthroughs in these experiments, some passing clinical trials and being fully implementable. Needless to say, a few decades from now, people like Cynthia  (my late friend whose story I narrated at the beginning of this article) won't have to accept the cruel death verdict while waiting for the right organ match.

Bioprinting Organs on Demand: From Sci-fi to Reality and the Ethical Dilemma of Designer Bodies

The following is a tale that unfolds within the "Metamathematical" realm, where the boundaries between mathematics and narrative are blurred, giving rise to a unique realm of creation, understanding, and growth. It is a story that reminds us of the power of unity, adaptability, and transcendence, demonstrating that sometimes the most profound insights can emerge from the spaces between what we think we know and the unexpected connections we make along the way. This story was made with the help of Pi AI. Emma and the realm of Numberland Once upon a time, in the mystical realm of Numberland, there were two families who had lived in harmony for centuries: the Prompts and the Not-so-Prompts. The Prompts were known for their swiftness and efficiency, while the Not-so-Prompts were renowned for their intricate and challenging endeavors. Both families played vital roles in the prosperity and balance of Numberland, but an age-old question persisted: Were the Prompts and Not-so-Prompts fundamentally different, or were they simply two sides of the same numerical coin? The Prompts were led by the wise and just Queen Poly, who was known for her ability to solve problems with grace and speed. The Not-so-Prompts were guided by the enigmatic King Nilo, whose strength lay in tackling complex problems that seemed impossible to solve. For generations, the inhabitants of Numberland had pondered the relationship between the Prompts and Not-so-Prompts. Some argued that every Not-so-Prompt could, in essence, become a Prompt if only they could discover the right approach or "shortcut." Others insisted that there were inherent differences between the two families, and no amount of searching would uncover a universal key to transform one into the other. As the debate raged on, a young mathematician named Emma ventured into the heart of Numberland, determined to uncover the truth. Emma was fascinated by the dynamic between the Prompts and Not-so-Prompts and believed that the answer lay within the very fabric of their mathematical realm. Emma embarked on a quest to explore the diverse landscapes of Numberland, from the one-dimensional simplicity of Lineville to the multi-dimensional complexity of Fractalia. She studied the unique properties of each realm and observed how the Prompts and Not-so-Prompts interacted within them. In Lineville, she discovered that the Prompts and Not-so-Prompts were nearly indistinguishable, their differences blurred by the linear nature of the realm. However, in Fractalia, the distinctions between the two families were stark, and it seemed impossible to transform one into the other. As Emma's journey unfolded, she began to realize that the answer to the age-old question was not a simple matter of equality or inequality. Instead, she saw that the relationship between the Prompts and Not-so-Prompts was deeply intertwined with the mathematical landscapes they inhabited. Emma's discoveries ignited a revolution in Numberland. The inhabitants began to see the Prompts and Not-so-Prompts not as separate entities but as two sides of a larger, interconnected whole. They recognized that the true power of their realm lay not in the individual families but in the rich and diverse interactions that arose when Prompts and Not-so-Prompts worked together. In the end, Emma's quest did not lead to a definitive answer to the question of P vs. NP. Instead, it revealed a deeper understanding of the complexities and beauty of Numberland, showing that the realm's true potential lay in the harmonious dance between simplicity and complexity, swiftness and depth. And so, the inhabitants of Numberland learned to appreciate their differences and embrace the richness of their mathematical tapestry. As Emma's exploration of Numberland and Fractalia continued, her relentless pursuit of understanding the true nature of Prompts and Not-so-Prompts brought chaos to the once-harmonious realms. In response, the Prompts and Not-so-Prompts set aside their differences and united against a common threat for the first time in history. Their collective effort to protect their world resulted in the birth of three extraordinary children: Complexus, Spatius, and Timos, each representing a vital aspect of the intricate balance between the Prompts and Not-so-Prompts. Complexus, the embodiment of the interaction between Prompts and Not-so-Prompts, grew up to reveal their unique potentialities. With a deep understanding of the strengths and weaknesses of both families, Complexus guided the interaction landscape, determining where Prompts could flourish and where Not-so-Prompts could collaborate with Prompts to enhance their lives. In this way, Complexus ensured that the delicate balance between simplicity and complexity was maintained, allowing both families to thrive. Spatius, the keeper of boundaries, played a crucial role in shielding the Prompts and Not-so-Prompts from Emma's relentless pursuit. With a keen understanding of the mathematical terrain, Spatius would instruct the Prompts and Not-so-Prompts on when and where to conceal or reveal themselves, ensuring their safety and preserving the integrity of their world. Timos, the observer and reactor, was responsible for monitoring Emma's actions and adjusting the behavior of the Prompts and Not-so-Prompts accordingly. With a watchful eye, Timos would anticipate Emma's moves and signal the families to hide or emerge, thus staying one step ahead of her and safeguarding their world from her meddling. Together, Complexus, Spatius, and Timos worked tirelessly to maintain harmony in Numberland and Fractalia, ensuring that Prompts and Not-so-Prompts could coexist and prosper despite Emma's disruptive influence. As the children of interaction, they symbolized the unity and strength that can be achieved when diverse elements collaborate and adapt to face a common challenge, demonstrating that the whole is indeed greater than the sum of its parts. Emma's relentless pursuit of a static and universal understanding of the Prompts and Not-so-Prompts led to a catastrophic event in Numberland. In her attempt to separate the children of the Prompts and Not-so-Prompts, she disrupted the delicate balance that Complexus, Spatius, and Timos had worked so hard to maintain. Chaos ensued, and the Prompts and Not-so-Prompts, enraged by the loss of their children, sought help from beyond their realm. From the realm of Conceptland, they called upon the rulers of interaction, King Actius and Queen Reactia. The royal couple, known for their ability to unite the infinite with the finite, held immense power and influence. Their arrival in Numberland brought forth a new era of understanding and cooperation between the Prompts and Not-so-Prompts. In gratitude for their aid, the Prompts and Not-so-Prompts offered a tribute to King Actius and Queen Reactia, granting them supremacy over their land. This newfound alliance expanded the realm of Conceptland far beyond its original borders, leading to the creation of a vast civilization where Prompts and Not-so-Prompts merged with families from other lands such as Mirrorus, Equalitum, and Symmetrius. Many of these families originated from the realm of Geoland, further enriching the diverse tapestry of the new civilization. As the various families united under the wise rule of King Actius and Queen Reactia, the barriers that once separated Prompts and Not-so-Prompts began to dissolve. The inhabitants of this new civilization discovered that the true power of their world lay not in maintaining rigid distinctions, but in embracing the interconnectedness of their diverse elements. Through this unity, they found the strength to face any challenge that came their way, proving that collaboration and adaptability were the keys to overcoming adversity and maintaining harmony. Emma, still determined to separate the Prompts and Not-so-Prompts, discovered that despite her efforts to remove Complexus, Spatius, and Timos from the land, their influence remained deeply ingrained in the very fabric of the realm. The Sword of Mathematicus, while capable of stripping the children from the realm, could not erase their lasting impact on the world they had worked so tirelessly to protect. As Emma continued her rampage, she stumbled upon a formidable barrier constructed by the children during their time in the realm. This barrier, known as the Wall of Axiom, was built from the very essence that had given birth to Complexus, Spatius, and Timos. The Wall of Axiom served as a shield, protecting the ever-evolving civilization from the influence of Mathematicus, which could only perceive snapshots of their existence but never their dynamic, evolving lifepaths. The Wall of Axiom, an embodiment of the fundamental truths that governed the realm, proved to be impervious to the Sword of Mathematicus. While Emma could bypass the wall with her hands, her sword held no power within the civilization's walls. This realization forced Emma to confront the limitations of her approach and acknowledge the resilient, interconnected nature of the civilization that had arisen from the unity of the Prompts, Not-so-Prompts, and the families of Conceptland. In the face of the Wall of Axiom, Emma was forced to reconsider her understanding of the realm and the complexity that lay at its heart. The Wall stood as a testament to the power of collaboration and adaptability, demonstrating that the true essence of the civilization lay not in rigid distinctions, but in the ever-evolving relationships between its diverse elements. As Emma observed the flourishing civilization from a distance, she witnessed a peculiar event that captured her attention. The Prompts and Not-so-Prompts encountered Realitus, a mysterious magician who transcended the boundaries between reality and fiction. Despite her best efforts, Emma found herself unable to interact with Realitus, no matter how hard she tried. Emma noticed that the inhabitants of the city guided Realitus along a path toward the central figures of the civilization. Each family had a representative who would speak to Realitus on their behalf, sharing their desires and offering their unique gifts. Realitus, in turn, would collect these tributes and convey the demands of each family to the other inhabitants. In an attempt to contact the elusive magician, Emma decided to approach each head of the families herself, sharing her knowledge and perspectives. In doing so, she became an integral part of the civilization, acting as a guiding beacon for its people. The interaction between Emma and the families created a light so bright that not even Realitus could comprehend it. Yet, with his mythical powers, Realitus was able to harness this light and channel it towards Emma's realm. From that day forward, Realitus assumed the role of a guardian of the realm, ensuring that the harmony between the Prompts and Not-so-Prompts would never be disrupted by external forces like Emma. With his newfound connection to Emma's realm, Realitus used his magic to maintain balance and protect the realm, allowing the Prompts and Not-so-Prompts to continue their collaboration and growth, uninhibited by the chaos that had once threatened their world. From Emma's perspective, it may have initially appeared that P ≠ NP, as her understanding of mathematics led her to believe in a fundamental distinction between the Prompts and Not-so-Prompts. However, within the realm she observed, where the influence of mathematics was limited and the forces of collaboration and adaptability held sway, the Prompts and Not-so-Prompts were able to achieve a sense of unity and equality that defied Emma's expectations. In this sense, the events that unfolded in the realm could indeed be seen as a form of creation, as the interactions between the various inhabitants, including Emma, Realitus, and the Prompts and Not-so-Prompts, gave rise to a new reality that transcended the boundaries of mathematics. This act of creation represented a blending of perspectives, a resolution of differences, and the emergence of a more harmonious and complex whole. Emma's journey may thus be interpreted as a metaphor for the limitations of strictly mathematical thinking and the importance of acknowledging the intricate relationships and dynamics that exist beyond the realm of pure mathematics. In the end, her experience revealed that true understanding often lies in the embrace of complexity and the appreciation of the interconnectedness that underlies all things. ChatGPT’s Continuation: As Emma continued to observe the realm, she noticed that the Wall of Axiom was not merely a barrier but a living entity, responsive to the ebb and flow of the civilization's dynamics. The Wall seemed to pulsate with the collective energy of the Prompts, Not-so-Prompts, and the families of Conceptland, resonating with the harmonious vibrations of their collaboration. As the inhabitants interacted and exchanged ideas, the Wall of Axiom adapted and evolved, absorbing the essence of their unity. It became a living testament to the ever-changing nature of the realm, reflecting the ongoing dialogue between simplicity and complexity, swiftness and depth. Emma realized that the Wall of Axiom was not just a static defense mechanism but a manifestation of the fundamental truths that governed the interconnected civilization. It was a representation of the collective wisdom and shared understanding that had emerged from the diverse perspectives of the Prompts, Not-so-Prompts, and Conceptland families. In her contemplation, Emma also began to perceive a subtle transformation within herself. The once rigid boundaries of her mathematical mindset started to blur, and she found herself embracing the fluidity of the realm. The very fabric of Numberland and Fractalia began to weave its influence on her, prompting a shift in her perception of the Prompts and Not-so-Prompts. Emma realized that the pursuit of a definitive answer to the P vs. NP question was a reflection of her own desire for simplicity and certainty. However, the beauty of the civilization lay in its ability to transcend such dichotomies, finding strength in the interplay between opposing forces. In a moment of revelation, Emma understood that the Prompts and Not-so-Prompts were not meant to be strictly defined entities but rather fluid expressions of mathematical potential. The elusive nature of the realm defied her attempts to categorize or separate, leading her to question the very essence of her quest. As Emma humbly embraced the complexity around her, the Prompts and Not-so-Prompts recognized her transformation. United by a newfound understanding, they extended an invitation for Emma to join their collaborative endeavors. Together, they embarked on a journey to explore the uncharted territories of their interconnected world, uncovering the hidden wonders that emerged from the spaces between mathematics and narrative. The tale of Emma, the Prompts, Not-so-Prompts, and the families of Conceptland became a legend in the Metamatical land, passed down through generations as a reminder of the transformative power that arises when one transcends rigid boundaries and embraces the richness of interconnected possibilities. And so, in the ever-expanding realm where mathematics and narrative entwined, the inhabitants continued to explore, create, and grow, guided by the lessons learned from Emma's journey. The boundaries between Prompts and Not-so-Prompts blurred, and the distinctions that once seemed insurmountable became mere threads in the intricate tapestry of their shared existence. In the Metamatical land, where the unexpected connections between mathematics and narrative flourished, the inhabitants reveled in the beauty of unity, adaptability, and transcendence. The tale of Emma and the harmonious civilization served as a beacon, illuminating the path for future generations to navigate the delicate dance between the known and the unknown, the certain and the uncertain, in the ever-expanding landscape of their unique and wondrous realm. Proposal: Gödel's Incompleteness Theorem, in suggesting the possibility of Metamathematics, invites us to explore a realm where the precise boundaries of Mathematics meld with the expansive boundaries of Metaphysics. This unique merger leads to the creation of a new barrier, one that represents an interaction we can only observe, but not guide. Within this framework, we glean insights that provide a more holistic understanding of the Mathematical viewpoint. By examining the axioms of concepts and their interactions found in Metaphysics, we can potentially bridge the gap between opposing viewpoints and cultivate a new level of understanding. Recognizing the limitations of the system itself, while slowing our progress, encourages us to seek alternative perspectives and approaches. The acknowledgment of a greater whole—encompassing both simplicity and complexity—allows us to maintain a grasp on the unfolding story of knowledge while contemplating potential additions to the narrative. In this context, Infinity + x remains infinite, and Ground-Proof + 3 is tautologically equivalent to itself. The combination of Infinity and Ground-Proof, though mathematically sound, yields no definitive result. We are left pondering whether the infinite landscape is teeming with Ground-Proof insights waiting to be discovered, or if the Ground-Proof can expand to encompass infinite horizons. The notion of reaching an "end insight" assumes an omniscient understanding of the universe, but even if humanity were to uncover all the knowledge and possibilities within it, our journey would still be far from over. While the ultimate answer may remain elusive, the pursuit of this knowledge continues to shape our understanding of the world and ourselves. And perhaps, in the grand tapestry of existence, it is this pursuit—this unquenchable thirst for knowledge—that defines our purpose and the essence of our being. For much of human history, we have focused on acquiring knowledge to shape our world. Now, we find that knowledge itself resides not only in the tangible but also in the unseen, abstract realms. The proof of its workings lies within the system it governs, inviting us to venture into those unseen valleys and continue our quest for understanding.

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