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A microservices architecture is the gold standard for building scalable web applications. Gartner estimates that 74% of organizations use microservices for their web applications, with another 23% planning to use them soon. If you’re an IT leader, architect, or developer, you might have experienced the faster deployments, better fault isolation, and easier scaling that come with microservices. However, the old maxim, “there’s no such thing as a free lunch,” rings true here. Because microservices can also lead to significant operational overhead and complexity. Microservices sprawl, unclear component dependencies, service duplication, and anti-patterns like circular dependencies are all part of the chaos that comes hand-in-hand with microservices. Perhaps you’ve seen some of the common symptoms of this microservices chaos: Engineering velocity drastically slows down
Onboarding new developers grows more difficult
Mean time to recovery (MTTR) for outages or performance issues increases
Overall system resiliency diminishes, putting business outcomes at risk While it’s still best practice to modernize monolithic applications by breaking them into microservices, it’s also best practice to proactively guard against the issues that microservices introduce. Architecture Governance to Control the Chaos The best way to proactively guard against these problems is by using architecture governance — a collection of rules, processes, and practices that manage and control your software architecture. With proper software architecture governance, you can reduce microservices complexity, ramp up developers faster, reduce MTTR, and improve the resiliency of your system, all while building a culture of intentionality. (Note that we’re talking about software architecture governance in this article, not enterprise architecture governance, which has been around for some time and is concerned with the policies, processes, and procedures of enterprise architecture strategies.) But exactly how do you build architecture governance? Governance, whether we’re talking about access, data, or architecture, is often just establishing a set of rules. But for architecture governance, you need more than just rules. You must start with architectural observability. Architectural Observability: The Foundation of Good Governance To implement effective governance, you first need comprehensive visibility into your software architecture. Architectural observability gives you a continuous, real-time view of your architecture. It provides your team with the necessary insights to manage the architecture and interconnectedness of distributed applications. Architectural observability provides documentation from a working system, it shows you systems flows, dependencies, what’s changing, and how your systems interact. It gives your team a thorough understanding of how the architecture works, how it drifts from release to release, and how its changes impact dependent services and resources. Without this visibility, you’re in trouble. If you’ve built a microservices project, you’ve probably encountered the results of a lack of visibility: Microservices that are difficult to manage
Unclear component dependencies
Service duplication
Anti-patterns such as circular dependencies that increase the risk of outages
Performance issues Your overall application resiliency, scalability, and engineering velocity are at high risk. And it only gets worse — the longer you let this lack of visibility continue, the more complex and unmanageable your architecture becomes. Good Observability Equals Good Governance However, with good architectural observability, you can visualize your architecture layer in real-time, gain an understanding of how your system works, and monitor changes as your architecture evolves. With observability, your team can proactively address issues, such as service sprawl and dependency mismanagement — before they lead to technical debt or system failures. And once you have that observability in place — once you know what’s happening and what’s changing — you can now create and enforce your rules of governance. You can implement a governance program that sits over your architecture, monitors, and controls changes, and allows you to build and manage microservices effectively by proactively applying standards and rules to your architecture and codebase as it evolves. Sounds great! But how do you actually build this? Let’s look at an example of how to build this in the real world. Implementing Architectural Observability and Governance First, you need to implement your architectural observability. The domain of architectural observability is new and rapidly evolving. For our example, we’ll use one of the platforms at the forefront — vFunction. vFunction is an AI-driven platform that provides visualizations of software architecture. vFunction leverages AI and OpenTelemetry tracing to enable teams to track every aspect of their architecture and monitor changes between releases. It can quickly identify complex flows, architectural, technical debt, and architectural drift. For example, vFunction allows you to better understand your distributed applications: Visualize the architecture and automatically create exportable sequence diagrams of all system and data flows.
Identify drift, such as new services or dependencies.
Identify resource exclusivity changes (such as multiple new services accessing the same database table) versus previous releases.
Identify circular dependencies between services that could impact resiliency.
Identify duplicate functionality/services that may be merged to remove complexity.
Maintain an up-to-date, real-time view of the global microservices ecosystem. vFunction uses the same data that APM tools use (so it’s straightforward to install) but uses a different layer of intelligence to address the architectural root cause of issues. This is especially important for managing the sprawl and complexity that result from the rapid and frequent deployment of microservices. Implementing Rules to Maintain Standards After implementing your observability, you’re ready to create and enforce your rules of governance. vFunction allows you to create architecture rules and tags and then monitor your architecture in real time against those rules, enforcing your critical governance policies. Any time a deployment or merge request breaks these rules, you can block that action. What type of rules might your governance enforce? You could enforce rules such as: Dependency requirements. For example, certain services should or should not communicate with other services.
Restricted resources.
Multiple services should not depend on the same database table.
Changes should not increase service interdependencies.
Restrictions on new multi-hop flows that could impact performance and resiliency. vFunction can watch and send alerts for all of the above. By implementing a focused set of rules and tags, you can create adaptive governance that guides developers in maintaining an optimal, clean, and efficient architecture. You can build architecture governance into your code and your culture. Conclusion Microservices chaos can threaten to derail development velocity, system resiliency, and operational efficiency. Architecture governance offers a way out of this chaos — a way to regain control over your architecture and steer it toward greater scalability and stability. Whether your organization is just starting to scale with microservices or is already in the depths of microservices sprawl, it’s the right time to introduce architecture governance to ensure that your architecture is efficient and resilient — and ready to support your next phase of growth. A microservices architecture is the gold standard for building scalable web applications. Gartner estimates that 74% of organizations use microservices for their web applications , with another 23% planning to use them soon. 74% of organizations use microservices for their web applications If you’re an IT leader, architect, or developer, you might have experienced the faster deployments, better fault isolation, and easier scaling that come with microservices. However, the old maxim, “ there’s no such thing as a free lunch ,” rings true here. Because microservices can also lead to significant operational overhead and complexity. Microservices sprawl, unclear component dependencies, service duplication, and anti-patterns like circular dependencies are all part of the chaos that comes hand-in-hand with microservices. there’s no such thing as a free lunch Perhaps you’ve seen some of the common symptoms of this microservices chaos: Engineering velocity drastically slows down Onboarding new developers grows more difficult Mean time to recovery (MTTR) for outages or performance issues increases Overall system resiliency diminishes, putting business outcomes at risk Engineering velocity drastically slows down Onboarding new developers grows more difficult Mean time to recovery (MTTR) for outages or performance issues increases Overall system resiliency diminishes, putting business outcomes at risk While it’s still best practice to modernize monolithic applications by breaking them into microservices, it’s also best practice to proactively guard against the issues that microservices introduce . it’s also best practice to proactively guard against the issues that microservices introduce Architecture Governance to Control the Chaos The best way to proactively guard against these problems is by using architecture governance — a collection of rules, processes, and practices that manage and control your software architecture. architecture governance With proper software architecture governance, you can reduce microservices complexity, ramp up developers faster, reduce MTTR, and improve the resiliency of your system, all while building a culture of intentionality. (Note that we’re talking about software architecture governance in this article, not enterprise architecture governance, which has been around for some time and is concerned with the policies, processes, and procedures of enterprise architecture strategies.) But exactly how do you build architecture governance? Governance, whether we’re talking about access, data, or architecture, is often just establishing a set of rules. But for architecture governance, you need more than just rules. You must start with architectural observability. Architectural Observability: The Foundation of Good Governance To implement effective governance, you first need comprehensive visibility into your software architecture . comprehensive visibility into your software architecture Architectural observability gives you a continuous, real-time view of your architecture. It provides your team with the necessary insights to manage the architecture and interconnectedness of distributed applications. Architectural observability Architectural observability provides documentation from a working system, it shows you systems flows, dependencies, what’s changing, and how your systems interact. It gives your team a thorough understanding of how the architecture works, how it drifts from release to release, and how its changes impact dependent services and resources. Without this visibility, you’re in trouble. If you’ve built a microservices project, you’ve probably encountered the results of a lack of visibility: Microservices that are difficult to manage Unclear component dependencies Service duplication Anti-patterns such as circular dependencies that increase the risk of outages Performance issues Microservices that are difficult to manage Unclear component dependencies Service duplication Anti-patterns such as circular dependencies that increase the risk of outages Performance issues Your overall application resiliency, scalability, and engineering velocity are at high risk. And it only gets worse — the longer you let this lack of visibility continue, the more complex and unmanageable your architecture becomes. Good Observability Equals Good Governance However, with good architectural observability, you can visualize your architecture layer in real-time, gain an understanding of how your system works, and monitor changes as your architecture evolves. with With observability, your team can proactively address issues, such as service sprawl and dependency mismanagement — before they lead to technical debt or system failures. And once you have that observability in place — once you know what’s happening and what’s changing — you can now create and enforce your rules of governance. You can implement a governance program that sits over your architecture, monitors, and controls changes, and allows you to build and manage microservices effectively by proactively applying standards and rules to your architecture and codebase as it evolves. Sounds great! But how do you actually build this? Let’s look at an example of how to build this in the real world. Implementing Architectural Observability and Governance First, you need to implement your architectural observability. The domain of architectural observability is new and rapidly evolving. For our example, we’ll use one of the platforms at the forefront — vFunction . vFunction is an AI-driven platform that provides visualizations of software architecture. vFunction vFunction leverages AI and OpenTelemetry tracing to enable teams to track every aspect of their architecture and monitor changes between releases. It can quickly identify complex flows, architectural, technical debt, and architectural drift. OpenTelemetry For example, vFunction allows you to better understand your distributed applications: Visualize the architecture and automatically create exportable sequence diagrams of all system and data flows. Identify drift, such as new services or dependencies. Identify resource exclusivity changes (such as multiple new services accessing the same database table) versus previous releases. Identify circular dependencies between services that could impact resiliency. Identify duplicate functionality/services that may be merged to remove complexity. Maintain an up-to-date, real-time view of the global microservices ecosystem. Visualize the architecture and automatically create exportable sequence diagrams of all system and data flows. Identify drift, such as new services or dependencies. Identify resource exclusivity changes (such as multiple new services accessing the same database table) versus previous releases. Identify circular dependencies between services that could impact resiliency. Identify duplicate functionality/services that may be merged to remove complexity. Maintain an up-to-date, real-time view of the global microservices ecosystem. vFunction uses the same data that APM tools use (so it’s straightforward to install) but uses a different layer of intelligence to address the architectural root cause of issues. This is especially important for managing the sprawl and complexity that result from the rapid and frequent deployment of microservices. Implementing Rules to Maintain Standards After implementing your observability, you’re ready to create and enforce your rules of governance. vFunction allows you to create architecture rules and tags and then monitor your architecture in real time against those rules, enforcing your critical governance policies. Any time a deployment or merge request breaks these rules, you can block that action. What type of rules might your governance enforce ? You could enforce rules such as: What type of rules might your governance enforce Dependency requirements. For example, certain services should or should not communicate with other services. Restricted resources. Multiple services should not depend on the same database table. Changes should not increase service interdependencies. Restrictions on new multi-hop flows that could impact performance and resiliency. Dependency requirements. For example, certain services should or should not communicate with other services. Restricted resources. Multiple services should not depend on the same database table. Changes should not increase service interdependencies. Restrictions on new multi-hop flows that could impact performance and resiliency. vFunction can watch and send alerts for all of the above. vFunction can watch and send alerts By implementing a focused set of rules and tags, you can create adaptive governance that guides developers in maintaining an optimal, clean, and efficient architecture. You can build architecture governance into your code and your culture. Conclusion Microservices chaos can threaten to derail development velocity, system resiliency, and operational efficiency. Architecture governance offers a way out of this chaos — a way to regain control over your architecture and steer it toward greater scalability and stability. Whether your organization is just starting to scale with microservices or is already in the depths of microservices sprawl, it’s the right time to introduce architecture governance to ensure that your architecture is efficient and resilient — and ready to support your next phase of growth.

Mastering Microservices: Building Effective Architecture Governance for Scalability and Stability

Author:
(1) Lothar Moeller, SubCom, Eatontown, NJ 07724, USA, lmoeller@subcom.com. Table of Links Abstract and Introduction GPS Long-Term Stabilized RF Phase Meter Simple and Accurate models for tides Latency Variations on Transpacific Cable Poisson effect on pressurized cables Conclusions, Acknowledgments, and References 2. GPS LONG-TERM STABILIZED RF PHASE METER The key idea behind our experiment is to assess path length changes by measuring the phase delay of an RF signal that propagates on an optical carrier through the cable. An ultra-stable phase meter compares the arrival phase of an RF signal at the cable output with a stable local reference (btb) as sketched in Fig.1a. Any delay variation in path 1 would be captured as a varying phase difference. Contrariwise, a varying phase difference does not automatically point to a length fluctuation; but could also originate from a frequency drift in the RF signal. Typically, signal propagations last over ~100 ms and recordings run weeks. Therefore, a correspondingly stable frequency synthesizer is essential in these experiments. Our Rubidium-controlled OCXO synthesizer locks to a 10-MHz standard, derived from a GPS signal and ensures excellent short-, medium-, and long-term stability. The synthesizer drives an optical LiNbO3 (Fig.1b) modulator connected via a PM fiber to a cw external cavity laser (ECL). A weak optical feedback keeps it locked to the null of its characteristic curve. The modulator driven at 10 MHz imprints a 20 MHz RF tone on the carrier (~10 m RF-wavelength). Chromatic dispersion converts any wavelength drift of the carrier into latency variations of the received signal, i.e. creating an artifact. Tapped signals fed into a wavemeter and an O/E converter enable us to study the impact of the remaining ECL’s - drift in measurements and serve as btb signal for the phase meter, respectively. The probe combined with a 100 GHz wide ASE gap spectrum enters the wet plant at ~ -5 dBm (Fig.1c). The ASE loading carries most of the repeater output power to ensure linear propagation of the probe, which then gets optically looped back at the other end of the cable and is received using an amplifier/ filter cascade, followed by a PIN receiver. Our commercially available phase meter samples the received probe and the btb signal at about 30 S/s. Its intrinsic noise is negligibly small. A fast polarization scrambler mitigates link PDL and PMD impacts. We assume that an optical path length change equals twice the cable length change. This paper is available on arxiv under CC BY 4.0 DEED license. Author: (1) Lothar Moeller, SubCom, Eatontown, NJ 07724, USA, lmoeller@subcom.com. Author: Author: (1) Lothar Moeller, SubCom, Eatontown, NJ 07724, USA, lmoeller@subcom.com. Table of Links Abstract and Introduction Abstract and Introduction GPS Long-Term Stabilized RF Phase Meter GPS Long-Term Stabilized RF Phase Meter Simple and Accurate models for tides Simple and Accurate models for tides Latency Variations on Transpacific Cable Latency Variations on Transpacific Cable Poisson effect on pressurized cables Poisson effect on pressurized cables Conclusions, Acknowledgments, and References Conclusions, Acknowledgments, and References 2. GPS LONG-TERM STABILIZED RF PHASE METER The key idea behind our experiment is to assess path length changes by measuring the phase delay of an RF signal that propagates on an optical carrier through the cable. An ultra-stable phase meter compares the arrival phase of an RF signal at the cable output with a stable local reference (btb) as sketched in Fig.1a. Any delay variation in path 1 would be captured as a varying phase difference. Contrariwise, a varying phase difference does not automatically point to a length fluctuation; but could also originate from a frequency drift in the RF signal. Typically, signal propagations last over ~100 ms and recordings run weeks. Therefore, a correspondingly stable frequency synthesizer is essential in these experiments. Our Rubidium-controlled OCXO synthesizer locks to a 10-MHz standard, derived from a GPS signal and ensures excellent short-, medium-, and long-term stability. The synthesizer drives an optical LiNbO3 (Fig.1b) modulator connected via a PM fiber to a cw external cavity laser (ECL). A weak optical feedback keeps it locked to the null of its characteristic curve. The modulator driven at 10 MHz imprints a 20 MHz RF tone on the carrier (~10 m RF-wavelength). Chromatic dispersion converts any wavelength drift of the carrier into latency variations of the received signal, i.e. creating an artifact. Tapped signals fed into a wavemeter and an O/E converter enable us to study the impact of the remaining ECL’s - drift in measurements and serve as btb signal for the phase meter, respectively. The probe combined with a 100 GHz wide ASE gap spectrum enters the wet plant at ~ -5 dBm (Fig.1c). The ASE loading carries most of the repeater output power to ensure linear propagation of the probe, which then gets optically looped back at the other end of the cable and is received using an amplifier/ filter cascade, followed by a PIN receiver. Our commercially available phase meter samples the received probe and the btb signal at about 30 S/s. Its intrinsic noise is negligibly small. A fast polarization scrambler mitigates link PDL and PMD impacts. We assume that an optical path length change equals twice the cable length change. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

How the Moon Impacts Subsea Communication Cables: GPS Long-Term Stabilized RF Phase Meter

Trust-based Currencies on Blockchain: Trustlines Network, Circles UBI, and Karma

Blockchain-də etimad əsaslı valyutalar: Trustlines Network, Circles UBI və Karma

Валюты на аснове даверу на блокчейне: сетка Trustlines, Circles UBI і Karma

ব্লকচেইনে বিশ্বাস-ভিত্তিক মুদ্রা: ট্রাস্টলাইন নেটওয়ার্ক, সার্কেল ইউবিআই, এবং কর্ম

Monedas basadas en la confianza en la cadena de bloques: Trustlines Network, Circles UBI y Karma

Luottamukseen perustuvat valuutat Blockchainissa: Trustlines Network, Circles UBI ja Karma

מטבעות מבוססי אמון בבלוקצ'יין: Trustlines Network, Circles UBI ו-Karma

ブロックチェーン上の信頼に基づく通貨: Trustlines Network、Circles UBI、Karma

Waluty oparte na zaufaniu w Blockchain: Trustlines Network, Circles UBI i Karma

Meny založené na dôvere na blockchaine: Trustlines Network, Circles UBI a Karma

Trust-based Currencies paBlockchain: Trustlines Network, Circles UBI, uye Karma

Асъорҳои боваринок дар Blockchain: Шабакаи Trustlines, Circles UBI ва Karma

Tiền tệ dựa trên sự tin cậy trên Blockchain: Trustlines Network, Circles UBI và Karma

Authors:
(1) Timothy R. McIntosh;
(2) Teo Susnjak;
(3) Tong Liu;
(4) Paul Watters;
(5) Malka N. Halgamuge. Table of Links Abstract and Introduction Background: Evolution of Generative AI The Current Generative AI Research Taxonomy Innovative Horizon of MOE Speculated Capabilities of Q* Projected Capabilities of AGI Impact Analysis on Generative AI Research Taxonomy Emergent Research Priorities in Generative AI Practical Implications and Limitations of Generative AI Technologies Impact of Generative AI on Preprints Across Disciplines Conclusions, Disclaimer, and References V. SPECULATED CAPABILITIES OF Q* In the burgeoning realm of AI, the anticipated Q* project stands as a beacon of potential breakthroughs, heralding advancements that could redefine the landscape of AI capabilities (Fig. 5). A. Enhanced General Intelligence Q*’s development in the arena of general intelligence represents a paradigm shift from specialized to holistic AI, indicating a broadening of the model’s cognitive abilities akin to human intelligence. This advanced form of general intelligence involves integrating diverse neural network architectures and machine learning techniques, enabling the AI to process and synthesize multifaceted information seamlessly. The universal adapter approach, mirroring models like T0, could endow Q* with the capability to rapidly assimilate knowledge from various domains. This method allows Q* to learn adaptable module plugins, enhancing its ability to tackle new data types while preserving existing skills, leading to an AI model that combines narrow specializations into a comprehensive, adaptive, and versatile reasoning system. The corresponding quasi-mathematical formulation can be expressed as: Such advancements in AI suggest the emergence of an intelligence that not only parallels but potentially exceeds human cognitive flexibility, with far-reaching implications in facilitating cross-disciplinary innovations and complex problem-solving. The speculated capabilities of Q* bring forth complex ethical implications and governance challenges. As AI systems approach higher levels of autonomy and decision-making, it is crucial to establish robust ethical frameworks and governance structures to ensure responsible and transparent AI development. This involves mitigating potential risks associated with advanced AI capabilities, emphasizing the need for comprehensive and dynamic ethical guidelines that evolve in tandem with AI advancements. B. Advanced Self-Learning and Exploration In the realm of advanced AI development, Q* is anticipated to represent a significant evolution in self-learning and exploration capabilities. It is speculated to utilize sophisticated Policy Neural Networks (NNs), similar to those in AlphaGo, but with substantial enhancements to handle the complexities of language and reasoning tasks. These networks are expected to employ advanced reinforcement learning techniques like Proximal Policy Optimization (PPO), which stabilizes policy updates and improves sample efficiency, a crucial factor in autonomous learning. The integration of these NNs with cutting-edge search algorithms, potentially including novel iterations of Tree or Graph of Thought, is predicted to enable Q* to autonomously navigate and assimilate complex information. This approach might be augmented with graph neural networks to bolster meta-learning capacities, allowing Q* to rapidly adapt to new tasks and environments while retaining previously acquired knowledge. The corresponding quasi-mathematical formulation can be represented as: ASLE(Q∗) = RL(P NN, SA) × GNN Where: • ASLE: “Advanced Self-Learning and Exploration” • RL: to reinforcement learning algorithms, particularly Proximal Policy Optimization (PPO). • PNN: Policy Neural Networks, adapted for language and reasoning tasks. • SA: sophisticated search algorithms, like Tree or Graph of Thought. • GNN: the incorporation of Graph Neural Networks for meta-learning. • ×: the cross-functional enhancement of RL with GNN. Such capabilities indicate a model not limited to understanding existing data but equipped to actively seek and synthesize new knowledge, effectively adapting to evolving scenarios without the need for frequent retraining. This signifies a leap beyond current AI models, embedding a level of autonomy and efficiency previously unattained. C. Superior Human-Level Understanding Q*’s aspiration to achieve superior human-level understanding is speculated to hinge on an advanced integration of multiple neural networks, including a Value Neural Network (VNN), paralleling the evaluative components found in systems like AlphaGo. This network would extend beyond assessing accuracy and relevance in language and reasoning processes, delving into the subtleties of human communication. The model’s deep comprehension capabilities may be enhanced by advanced natural language processing algorithms and techniques, such as those found in transformer architectures like DeBERTa. These algorithms would empower Q* to interpret not just the text but also the nuanced socio-emotional aspects such as intent, emotion, and underlying meanings. Incorporating sentiment analysis and natural language inference, Q* could navigate layers of socio-emotional insights, including empathy, sarcasm, and attitude. The corresponding quasi-mathematical formulation can be expressed as: Where: • SHLU: “Superior Human-Level Understanding”. • VNN: the Value Neural Network, similar to evaluative components in systems like AlphaGo. • NLP: a set of advanced NLP algorithms. • ⊕: the combination of VNN evaluation with NLP algorithms. • alg: individual algorithms within the NLP set. This level of understanding, surpassing current language models, would position Q* to excel in empathetic, context aware interactions, thus enabling a new echelon of personalization and user engagement in AI applications. D. Advanced Common Sense Reasoning Q*’s anticipated development in advanced common sense reasoning is predicted to integrate sophisticated logic and decision-making algorithms, potentially combining elements of symbolic AI and probabilistic reasoning. This integration aims to endow Q* with an intuitive grasp of everyday logic and an understanding akin to human common sense, thus bridging a significant gap between artificial and natural intelligence. Enhancements in Q*’s reasoning abilities might involve graphstructured world knowledge, incorporating physics and social engines similar to those in models like CogSKR. This approach, grounded in physical reality, is expected to capture and interpret the everyday logic often absent in contemporary AI systems. By leveraging large-scale knowledge bases and semantic networks, Q* could effectively navigate and respond to complex social and practical scenarios, aligning its inferences and decisions more closely with human experiences and expectations. The corresponding quasi-mathematical formulation can be represented as: Where: • ACSR: “Advanced Common Sense Reasoning”. • LogicAI and ProbAI: symbolic AI and probabilistic reasoning components, respectively. • WorldK: the integration of graph-structured world knowledge. • ⊙: the integrated operation of these elements for common sense reasoning. E. Extensive Real-World Knowledge Integration edge is speculated to involve the use of advanced formal verification systems, which would provide a robust basis for validating its logical and factual reasoning. This method, when coupled with sophisticated neural network architectures and dynamic learning algorithms, would enable Q* to engage deeply with the complexities of the real world, transcending conventional AI limitations. Additionally, Q* might employ mathematical theorem proving techniques for validation, ensuring that its reasoning and outputs are not only accurate but also ethically grounded. The incorporation of Ethics classifiers in this process further strengthens its capacity to deliver reliable and responsible understanding and interaction with real-world scenarios. The corresponding quasi-mathematical formulation can be represented as: Where: • ERWKI: “Extensive Real-World Knowledge Integration”. • F V S: Formal Verification Systems. • NN: neural network architectures. • LT P: mathematical theorem proving for logical and factual validation. • EC: the incorporation of Ethics classifiers. • ⊗: the comprehensive integration for knowledge synthesis and ethical alignment. Furthermore, the speculated capabilities of Q* have the potential to significantly reshape the job market and labor dynamics. With its advanced functionalities, Q* could automate complex tasks, leading to a shift in job requirements and the emergence of new skill demands. This necessitates a reevaluation of workforce strategies and educational paradigms, aligning them with the evolving technological landscape and ensuring that the workforce is equipped to interact with and complement these advanced AI systems. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) Timothy R. McIntosh; (2) Teo Susnjak; (3) Tong Liu; (4) Paul Watters; (5) Malka N. Halgamuge. Authors: Authors: (1) Timothy R. McIntosh; (2) Teo Susnjak; (3) Tong Liu; (4) Paul Watters; (5) Malka N. Halgamuge. Table of Links Abstract and Introduction Abstract and Introduction Background: Evolution of Generative AI Background: Evolution of Generative AI The Current Generative AI Research Taxonomy The Current Generative AI Research Taxonomy Innovative Horizon of MOE Innovative Horizon of MOE Speculated Capabilities of Q* Speculated Capabilities of Q* Projected Capabilities of AGI Projected Capabilities of AGI Impact Analysis on Generative AI Research Taxonomy Impact Analysis on Generative AI Research Taxonomy Emergent Research Priorities in Generative AI Emergent Research Priorities in Generative AI Practical Implications and Limitations of Generative AI Technologies Practical Implications and Limitations of Generative AI Technologies Impact of Generative AI on Preprints Across Disciplines Impact of Generative AI on Preprints Across Disciplines Conclusions, Disclaimer, and References Conclusions, Disclaimer, and References V. SPECULATED CAPABILITIES OF Q* In the burgeoning realm of AI, the anticipated Q* project stands as a beacon of potential breakthroughs, heralding advancements that could redefine the landscape of AI capabilities (Fig. 5). A. Enhanced General Intelligence A. Enhanced General Intelligence Q*’s development in the arena of general intelligence represents a paradigm shift from specialized to holistic AI, indicating a broadening of the model’s cognitive abilities akin to human intelligence. This advanced form of general intelligence involves integrating diverse neural network architectures and machine learning techniques, enabling the AI to process and synthesize multifaceted information seamlessly. The universal adapter approach, mirroring models like T0, could endow Q* with the capability to rapidly assimilate knowledge from various domains. This method allows Q* to learn adaptable module plugins, enhancing its ability to tackle new data types while preserving existing skills, leading to an AI model that combines narrow specializations into a comprehensive, adaptive, and versatile reasoning system. The corresponding quasi-mathematical formulation can be expressed as: Such advancements in AI suggest the emergence of an intelligence that not only parallels but potentially exceeds human cognitive flexibility, with far-reaching implications in facilitating cross-disciplinary innovations and complex problem-solving. The speculated capabilities of Q* bring forth complex ethical implications and governance challenges. As AI systems approach higher levels of autonomy and decision-making, it is crucial to establish robust ethical frameworks and governance structures to ensure responsible and transparent AI development. This involves mitigating potential risks associated with advanced AI capabilities, emphasizing the need for comprehensive and dynamic ethical guidelines that evolve in tandem with AI advancements. B. Advanced Self-Learning and Exploration B. Advanced Self-Learning and Exploration In the realm of advanced AI development, Q* is anticipated to represent a significant evolution in self-learning and exploration capabilities. It is speculated to utilize sophisticated Policy Neural Networks (NNs), similar to those in AlphaGo, but with substantial enhancements to handle the complexities of language and reasoning tasks. These networks are expected to employ advanced reinforcement learning techniques like Proximal Policy Optimization (PPO), which stabilizes policy updates and improves sample efficiency, a crucial factor in autonomous learning. The integration of these NNs with cutting-edge search algorithms, potentially including novel iterations of Tree or Graph of Thought, is predicted to enable Q* to autonomously navigate and assimilate complex information. This approach might be augmented with graph neural networks to bolster meta-learning capacities, allowing Q* to rapidly adapt to new tasks and environments while retaining previously acquired knowledge. The corresponding quasi-mathematical formulation can be represented as: ASLE(Q∗) = RL(P NN, SA) × GNN Where: • ASLE : “Advanced Self-Learning and Exploration” ASLE • RL : to reinforcement learning algorithms, particularly Proximal Policy Optimization (PPO). RL • PNN : Policy Neural Networks, adapted for language and reasoning tasks. • PNN • SA : sophisticated search algorithms, like Tree or Graph of Thought. • SA • GNN : the incorporation of Graph Neural Networks for meta-learning. • GNN • ×: the cross-functional enhancement of RL with GNN. Such capabilities indicate a model not limited to understanding existing data but equipped to actively seek and synthesize new knowledge, effectively adapting to evolving scenarios without the need for frequent retraining. This signifies a leap beyond current AI models, embedding a level of autonomy and efficiency previously unattained. C. Superior Human-Level Understanding C. Superior Human-Level Understanding Q*’s aspiration to achieve superior human-level understanding is speculated to hinge on an advanced integration of multiple neural networks, including a Value Neural Network (VNN), paralleling the evaluative components found in systems like AlphaGo. This network would extend beyond assessing accuracy and relevance in language and reasoning processes, delving into the subtleties of human communication. The model’s deep comprehension capabilities may be enhanced by advanced natural language processing algorithms and techniques, such as those found in transformer architectures like DeBERTa. These algorithms would empower Q* to interpret not just the text but also the nuanced socio-emotional aspects such as intent, emotion, and underlying meanings. Incorporating sentiment analysis and natural language inference, Q* could navigate layers of socio-emotional insights, including empathy, sarcasm, and attitude. The corresponding quasi-mathematical formulation can be expressed as: Where: • SHLU : “Superior Human-Level Understanding”. SHLU • VNN : the Value Neural Network, similar to evaluative components in systems like AlphaGo. VNN • NLP : a set of advanced NLP algorithms. NLP • ⊕: the combination of VNN evaluation with NLP algorithms. • alg : individual algorithms within the NLP set. alg This level of understanding, surpassing current language models, would position Q* to excel in empathetic, context aware interactions, thus enabling a new echelon of personalization and user engagement in AI applications. D. Advanced Common Sense Reasoning D. Advanced Common Sense Reasoning Q*’s anticipated development in advanced common sense reasoning is predicted to integrate sophisticated logic and decision-making algorithms, potentially combining elements of symbolic AI and probabilistic reasoning. This integration aims to endow Q* with an intuitive grasp of everyday logic and an understanding akin to human common sense, thus bridging a significant gap between artificial and natural intelligence. Enhancements in Q*’s reasoning abilities might involve graphstructured world knowledge, incorporating physics and social engines similar to those in models like CogSKR. This approach, grounded in physical reality, is expected to capture and interpret the everyday logic often absent in contemporary AI systems. By leveraging large-scale knowledge bases and semantic networks, Q* could effectively navigate and respond to complex social and practical scenarios, aligning its inferences and decisions more closely with human experiences and expectations. The corresponding quasi-mathematical formulation can be represented as: Where: • ACSR : “Advanced Common Sense Reasoning”. • ACSR • LogicAI and ProbAI : symbolic AI and probabilistic reasoning components, respectively. • LogicAI ProbAI • WorldK : the integration of graph-structured world knowledge. • WorldK • ⊙: the integrated operation of these elements for common sense reasoning. E. Extensive Real-World Knowledge Integration E. Extensive Real-World Knowledge Integration edge is speculated to involve the use of advanced formal verification systems, which would provide a robust basis for validating its logical and factual reasoning. This method, when coupled with sophisticated neural network architectures and dynamic learning algorithms, would enable Q* to engage deeply with the complexities of the real world, transcending conventional AI limitations. Additionally, Q* might employ mathematical theorem proving techniques for validation, ensuring that its reasoning and outputs are not only accurate but also ethically grounded. The incorporation of Ethics classifiers in this process further strengthens its capacity to deliver reliable and responsible understanding and interaction with real-world scenarios. The corresponding quasi-mathematical formulation can be represented as: Where: • ERWKI : “Extensive Real-World Knowledge Integration”. • ERWKI • F V S: Formal Verification Systems. • F V S: • NN : neural network architectures. • NN • LT P : mathematical theorem proving for logical and factual validation. • LT P • EC : the incorporation of Ethics classifiers. • EC • ⊗: the comprehensive integration for knowledge synthesis and ethical alignment. Furthermore, the speculated capabilities of Q* have the potential to significantly reshape the job market and labor dynamics. With its advanced functionalities, Q* could automate complex tasks, leading to a shift in job requirements and the emergence of new skill demands. This necessitates a reevaluation of workforce strategies and educational paradigms, aligning them with the evolving technological landscape and ensuring that the workforce is equipped to interact with and complement these advanced AI systems. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

Surveying the Evolution and Future Trajectory of Generative AI - Speculated Capabilities of Q*

Authors:
(1) Timothy R. McIntosh;
(2) Teo Susnjak;
(3) Tong Liu;
(4) Paul Watters;
(5) Malka N. Halgamuge. Table of Links Abstract and Introduction Background: Evolution of Generative AI The Current Generative AI Research Taxonomy Innovative Horizon of MOE Speculated Capabilities of Q* Projected Capabilities of AGI Impact Analysis on Generative AI Research Taxonomy Emergent Research Priorities in Generative AI Practical Implications and Limitations of Generative AI Technologies Impact of Generative AI on Preprints Across Disciplines Conclusions, Disclaimer, and References IV. INNOVATIVE HORIZON OF MOE The MoE model architecture represents a pioneering advancement in transformer-based language models, offering unparalleled scalability and efficiency (Fig. 4). As evidenced by recent models like the 1.6 trillion parameter Switch Transformer [285] and the 8x7B parameter Mixtra [286], MoEbased designs are rapidly redefining the frontiers of model scale and performance across diverse language tasks. A. Core Concept and Structure MoE models represent a significant innovation in neural network design, offering enhanced scalability and efficiency in training and inference [287], [288], [110]. At their core, MoE models utilize a sparsity-driven architecture by replacing dense layers with sparse MoE layers comprising multiple expert networks, where each expert is dedicated to a specific subset of the training data or task, and a trainable gating mechanism dynamically allocates input tokens to these experts, thereby optimizing computational resources and effectively adapting to the task’s complexity [94], [21], [110]. MoE models demonstrate a substantial advantage in terms of pretraining speed, outperforming dense models [94], [287]. However, they face challenges in fine-tuning and require substantial memory for inference due to the necessity of loading all experts into Video Random Access Memory (VRAM) [289], [290], [110]. The structure of MoE involves alternating transformer layers with router layers containing gating networks for expert routing, leading to an architecture that allows significant parameter scaling and advanced specialization in problem-solving [291], [21]. A distinguishing characteristic of MoE models is their flexibility in managing large datasets, capable of amplifying model capacity by over a thousand times while only experiencing minor reductions in computational efficiency [289], [292]. The Sparsely-Gated Mixture-of-Experts Layer, a key component of these models, comprises numerous simple feed-forward expert networks and a trainable gating network responsible for expert selection, which can facilitate the dynamic and sparse activation of experts for each input instance, maintaining high computational efficiency [293], [294], [110]. Recent advancements in MoE models, such as those in the Switch Transformer, have highlighted the significant benefits of intelligent routing, when the router’s ability to intelligently route tokens to appropriate experts confers considerable advantages to MoE models, allowing them to scale up model sizes while keeping compute time constant [295], [296], [297]. Experimental evidence suggests that routers learn to route inputs according to data clusters, demonstrating their potential in real-world applications [295], [289]. The core concept and structure of MoE models lie in their dynamic routing and specialization capabilities, offering promising avenues for scaling up neural networks and enhancing their efficiency and adaptability in various tasks, but the robustness of the router must be protected against adversarial attacks [289], [298]. B. Training and Inference Efficiency MoE models, notably Mixtral 8x7B, are renowned for their superior pretraining speed compared to dense models, yet they face hurdles in fine-tuning and demand considerable VRAM for inference, owing to the requirement of loading all experts [289], [290], [110]. Recent advancements in MoE architecture have resulted in notable training cost efficiencies, especially in encoder-decoder models, with evidence showing cost savings of up to fivefold in certain contexts when compared to dense models [21], [289], [298], [287]. Innovations like DeepSpeedMoE [287] offered new architectural designs and model compression, decreasing the MoE model size by approximately 3.7x and optimizing inference to achieve up to 7.3x better latency and cost efficiency. The progression in distributed MoE training and inference, notably with innovations like Lina [299], has effectively tackled the all-to-all communication bottleneck by enhancing tensor partitioning, which not only improves all-to-all communication and training step time, but also optimizes resource scheduling during inference, leading to a substantial reduction in training step time by up to 1.73 times and lowering the 95th percentile inference time by an average of 1.63 times compared to existing systems. These developments have marked a crucial shift in the large model landscape, from dense to sparse MoE models, expanding the potential applications of AI by training higher-quality models with fewer resources. C. Load Balancing and Router Optimization Effective load balancing is essential in MoE models to guarantee a uniform distribution of computational load among experts, with the router network in MoE layers, responsible for selecting the appropriate experts for processing specific tokens, playing a pivotal role in achieving this balance, which is fundamental to the stability and overall performance of MoE models [293], [289], [288], [300], [110]. Developments in router Zloss regularization techniques plays a crucial role in addressing expert imbalance in MoE models by fine-tuning the gating mechanism, ensuring a more equitable workload distribution across experts and fostering a stable training environment, thereby enhancing model performance and reducing training time and computational overhead [301], [302]. Concurrently, the integration of expert capacity management strategies, emerges as a crucial approach in MoE models to regulate the processing abilities of individual experts by setting thresholds on the number of tokens each can handle, effectively averting bottlenecks and ensuring a more efficient and streamlined model operation, leading to improved training processes and heightened performance during complex computational tasks [293], [303], [289]. D. Parallelism and Serving Techniques Recent developments in MoE models highlighted their efficiency in parallelism and serving techniques, significantly influencing large-scale neural networks. DeepSpeed-MoE, for instance, introduces advanced parallelism modes like data parallelism, tensor-slicing for non-expert parameters, and expert parallelism for expert parameters, enhancing model efficiency, as their approach optimizes both latency and throughput in MoE model inference, offering scalable solutions in production environments using multiple Graphics Processing Unit (GPU) devices [287]. MoE models, versatile in applications like multilingual tasks and coding, demonstrated impressive capabilities in handling complex tasks due to their ensemblelike structure within a single framework [304], [305], [306]. Notably, models like Mixtral and Switch Transformer, with over 1.6 trillion parameters, achieved computational efficiency equivalent to a 10 billion-parameter dense model, because they benefited from the sublinear scaling of MoE compute versus model size, leading to substantial accuracy gains within fixed compute budgets [21], [289], [287], [110]. Moreover, DeepSpeed-MoE included model compression techniques, reducing model size by up to 3.7x while maintaining accuracy, and an end-to-end MoE training and inference solution, part of the DeepSpeed library, which was instrumental in serving large-scale MoE models with enhanced speed and costefficiency [287]. These innovations open new directions in AI, shifting from dense to sparse MoE models, where training and deploying higher-quality models with fewer resources become more widely achievable. E. Future Directions and Applications Emerging research on MoE architectures could focus on advancing sparse fine-tuning techniques, exploring instruction tuning methods, and improving routing algorithms to fully utilize performance and efficiency gains. As models scale over one billion parameters, MoE represents a paradigm shift for vastly expanding capabilities across scientific, medical, creative, and real-world applications. Frontier work could also aim to refine auto-tuning of hyperparameters during finetuning to optimize accuracy, calibration, and safety. MoE research continues to push model scale limits while maintaining specialization for transfer learning. Adaptive sparse access allows coordinating thousands of experts to cooperate on tasks ranging from reasoning to open domain dialogue. Continued analysis of routing mechanisms seeks to balance load across experts and minimize redundant computation. As the AI community further investigates MoE methods at scale, these models hold promise for new breakthroughs in language, code generation, reasoning, and multimodal applications. There is great interest in evaluating implications across education, healthcare, financial analysis, and other fields. Outcomes may yield insights not only into model optimization but also for understanding principles behind combinatorial generalization. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) Timothy R. McIntosh; (2) Teo Susnjak; (3) Tong Liu; (4) Paul Watters; (5) Malka N. Halgamuge. Authors: Authors: (1) Timothy R. McIntosh; (2) Teo Susnjak; (3) Tong Liu; (4) Paul Watters; (5) Malka N. Halgamuge. Table of Links Abstract and Introduction Abstract and Introduction Background: Evolution of Generative AI Background: Evolution of Generative AI The Current Generative AI Research Taxonomy The Current Generative AI Research Taxonomy Innovative Horizon of MOE Innovative Horizon of MOE Speculated Capabilities of Q* Speculated Capabilities of Q* Projected Capabilities of AGI Projected Capabilities of AGI Impact Analysis on Generative AI Research Taxonomy Impact Analysis on Generative AI Research Taxonomy Emergent Research Priorities in Generative AI Emergent Research Priorities in Generative AI Practical Implications and Limitations of Generative AI Technologies Practical Implications and Limitations of Generative AI Technologies Impact of Generative AI on Preprints Across Disciplines Impact of Generative AI on Preprints Across Disciplines Conclusions, Disclaimer, and References Conclusions, Disclaimer, and References IV. INNOVATIVE HORIZON OF MOE The MoE model architecture represents a pioneering advancement in transformer-based language models, offering unparalleled scalability and efficiency (Fig. 4). As evidenced by recent models like the 1.6 trillion parameter Switch Transformer [285] and the 8x7B parameter Mixtra [286], MoEbased designs are rapidly redefining the frontiers of model scale and performance across diverse language tasks. A. Core Concept and Structure A. Core Concept and Structure MoE models represent a significant innovation in neural network design, offering enhanced scalability and efficiency in training and inference [287], [288], [110]. At their core, MoE models utilize a sparsity-driven architecture by replacing dense layers with sparse MoE layers comprising multiple expert networks, where each expert is dedicated to a specific subset of the training data or task, and a trainable gating mechanism dynamically allocates input tokens to these experts, thereby optimizing computational resources and effectively adapting to the task’s complexity [94], [21], [110]. MoE models demonstrate a substantial advantage in terms of pretraining speed, outperforming dense models [94], [287]. However, they face challenges in fine-tuning and require substantial memory for inference due to the necessity of loading all experts into Video Random Access Memory (VRAM) [289], [290], [110]. The structure of MoE involves alternating transformer layers with router layers containing gating networks for expert routing, leading to an architecture that allows significant parameter scaling and advanced specialization in problem-solving [291], [21]. A distinguishing characteristic of MoE models is their flexibility in managing large datasets, capable of amplifying model capacity by over a thousand times while only experiencing minor reductions in computational efficiency [289], [292]. The Sparsely-Gated Mixture-of-Experts Layer, a key component of these models, comprises numerous simple feed-forward expert networks and a trainable gating network responsible for expert selection, which can facilitate the dynamic and sparse activation of experts for each input instance, maintaining high computational efficiency [293], [294], [110]. Recent advancements in MoE models, such as those in the Switch Transformer, have highlighted the significant benefits of intelligent routing, when the router’s ability to intelligently route tokens to appropriate experts confers considerable advantages to MoE models, allowing them to scale up model sizes while keeping compute time constant [295], [296], [297]. Experimental evidence suggests that routers learn to route inputs according to data clusters, demonstrating their potential in real-world applications [295], [289]. The core concept and structure of MoE models lie in their dynamic routing and specialization capabilities, offering promising avenues for scaling up neural networks and enhancing their efficiency and adaptability in various tasks, but the robustness of the router must be protected against adversarial attacks [289], [298]. B. Training and Inference Efficiency B. Training and Inference Efficiency MoE models, notably Mixtral 8x7B, are renowned for their superior pretraining speed compared to dense models, yet they face hurdles in fine-tuning and demand considerable VRAM for inference, owing to the requirement of loading all experts [289], [290], [110]. Recent advancements in MoE architecture have resulted in notable training cost efficiencies, especially in encoder-decoder models, with evidence showing cost savings of up to fivefold in certain contexts when compared to dense models [21], [289], [298], [287]. Innovations like DeepSpeedMoE [287] offered new architectural designs and model compression, decreasing the MoE model size by approximately 3.7x and optimizing inference to achieve up to 7.3x better latency and cost efficiency. The progression in distributed MoE training and inference, notably with innovations like Lina [299], has effectively tackled the all-to-all communication bottleneck by enhancing tensor partitioning, which not only improves all-to-all communication and training step time, but also optimizes resource scheduling during inference, leading to a substantial reduction in training step time by up to 1.73 times and lowering the 95th percentile inference time by an average of 1.63 times compared to existing systems. These developments have marked a crucial shift in the large model landscape, from dense to sparse MoE models, expanding the potential applications of AI by training higher-quality models with fewer resources. C. Load Balancing and Router Optimization C. Load Balancing and Router Optimization Effective load balancing is essential in MoE models to guarantee a uniform distribution of computational load among experts, with the router network in MoE layers, responsible for selecting the appropriate experts for processing specific tokens, playing a pivotal role in achieving this balance, which is fundamental to the stability and overall performance of MoE models [293], [289], [288], [300], [110]. Developments in router Zloss regularization techniques plays a crucial role in addressing expert imbalance in MoE models by fine-tuning the gating mechanism, ensuring a more equitable workload distribution across experts and fostering a stable training environment, thereby enhancing model performance and reducing training time and computational overhead [301], [302]. Concurrently, the integration of expert capacity management strategies, emerges as a crucial approach in MoE models to regulate the processing abilities of individual experts by setting thresholds on the number of tokens each can handle, effectively averting bottlenecks and ensuring a more efficient and streamlined model operation, leading to improved training processes and heightened performance during complex computational tasks [293], [303], [289]. D. Parallelism and Serving Techniques D. Parallelism and Serving Techniques Recent developments in MoE models highlighted their efficiency in parallelism and serving techniques, significantly influencing large-scale neural networks. DeepSpeed-MoE, for instance, introduces advanced parallelism modes like data parallelism, tensor-slicing for non-expert parameters, and expert parallelism for expert parameters, enhancing model efficiency, as their approach optimizes both latency and throughput in MoE model inference, offering scalable solutions in production environments using multiple Graphics Processing Unit (GPU) devices [287]. MoE models, versatile in applications like multilingual tasks and coding, demonstrated impressive capabilities in handling complex tasks due to their ensemblelike structure within a single framework [304], [305], [306]. Notably, models like Mixtral and Switch Transformer, with over 1.6 trillion parameters, achieved computational efficiency equivalent to a 10 billion-parameter dense model, because they benefited from the sublinear scaling of MoE compute versus model size, leading to substantial accuracy gains within fixed compute budgets [21], [289], [287], [110]. Moreover, DeepSpeed-MoE included model compression techniques, reducing model size by up to 3.7x while maintaining accuracy, and an end-to-end MoE training and inference solution, part of the DeepSpeed library, which was instrumental in serving large-scale MoE models with enhanced speed and costefficiency [287]. These innovations open new directions in AI, shifting from dense to sparse MoE models, where training and deploying higher-quality models with fewer resources become more widely achievable. E. Future Directions and Applications E. Future Directions and Applications Emerging research on MoE architectures could focus on advancing sparse fine-tuning techniques, exploring instruction tuning methods, and improving routing algorithms to fully utilize performance and efficiency gains. As models scale over one billion parameters, MoE represents a paradigm shift for vastly expanding capabilities across scientific, medical, creative, and real-world applications. Frontier work could also aim to refine auto-tuning of hyperparameters during finetuning to optimize accuracy, calibration, and safety. MoE research continues to push model scale limits while maintaining specialization for transfer learning. Adaptive sparse access allows coordinating thousands of experts to cooperate on tasks ranging from reasoning to open domain dialogue. Continued analysis of routing mechanisms seeks to balance load across experts and minimize redundant computation. As the AI community further investigates MoE methods at scale, these models hold promise for new breakthroughs in language, code generation, reasoning, and multimodal applications. There is great interest in evaluating implications across education, healthcare, financial analysis, and other fields. Outcomes may yield insights not only into model optimization but also for understanding principles behind combinatorial generalization. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

Surveying the Evolution and Future Trajectory of Generative AI - Innovative Horizon of MOE

Customers aren’t waiting for Black Friday to start holiday shopping, nor should your company. Most shoppers already work to gather holiday gifts in November or even October, holiday shopping trends start well before Thanksgiving in the United States. Customers are shopping early, looking for great deals, and spending their money carefully. Understanding recent holiday shopping insights can empower companies to make data-driven decisions. After all, consumer feedback allows businesses to optimize marketing strategies, improve customer service, and manage inventory more effectively. Is Holiday Shopping Still a Big Deal? Black Friday happens later in November this year, and consumers are shopping earlier. Does that mean that the traditional holiday shopping window is less important? Definitely not. Holiday shopping trends might have consumers in stores looking for gifts early this Autumn. Still, spending is only projected to go up. Holiday shopping data from Deloitte suggests holiday sales will rise by 3.3% this year. The timing may shift a bit as to when purchases are made, but holiday shopping is still very much a big deal. Early Shopping vs Last Minute Deals While last-minute deals will certainly still occur with holiday shopping, 2024 data shows that consumers are not waiting to shop. They are already in stores starting to collect gift ideas. Holiday shopping statistics show that 60% of shoppers start their holiday shopping in November or as early as October. The survey also “noted a significant drop” in holiday shopping closer to the holidays, with increases in other sales periods. Shoppers are planning and budgeting for purchases, taking advantage of sales. In fact, December is the least popular month to start holiday shopping, making last-minute shopping less popular than in years past. For retailers who enjoy sales closer to December 25, there is a silver lining. Consumers spend $47 billion in the two weeks after Christmas, and 50% of the time, shoppers are buying for themselves, creating a great secondary opportunity for holiday shopping after the traditional season closes. Budgets are Getting Tighter Holiday shopping survey data suggests that 2024 will have a slightly different feel than previous holiday seasons. What is the force behind the change in holiday shopping in 2024? Tighter budgets, more internet-savvy consumers, and inflation. In fact, according to a recent PissedConsumer.com survey, 74.1% of consumers feel inflation might impact their holiday shopping. So, shoppers are looking to save money this holiday season, with 56.8% waiting for sales and 38% planning to buy fewer gifts. Fortunately, according to a McKinsey survey, despite the higher prices caused by previous inflation, consumers are also feeling more optimistic. Consumers plan to spend more in the coming three months, and 41% of respondents felt more optimistic about the economy and spending, likely due in part to stabilizing prices. Flexible Payment Options Are on Its Top With so many consumers planning ahead, looking for deals, and working with a budget in 2024, it’s no surprise that flexible payment options are also extremely popular. By now, pay later (BNPL) options are big this year, especially on mobile devices and through apps. Adobe currently forecasts that Cyber Monday will be the top day of BNPL shopping, with consumers spending about $993 million. Roughly 75% of that spending will likely be through mobile devices. Consumers Are Less Likely to Shop In-Store The move to online shopping has been accelerating for years, and 2024 will not be an exception. While the ability to see, touch, and test items will always keep the brick-and-mortar experience alive and well, shoppers are mixing it up. 7% of shoppers will only buy online, and all but roughly 18% of consumers shop online at least some of the time. Online shopping is expected to increase by 8.4% over last year, equating to a record $240.8 billion spent in the United States. Most of that spending, at 53.2%, will be through mobile devices, creating tremendous opportunities for online retailers. Holiday Shopping Insights to Remember The 2024 holiday shopping data shows customers are budgeting, planning, and already hard at work shopping for the holidays, often through mobile devices using delayed payments. The holiday season starts early, but a secondary season happens in the weeks after Christmas, presenting plenty of opportunities for retailers to tap into a $240 billion market. Customers aren’t waiting for Black Friday to start holiday shopping, nor should your company. Most shoppers already work to gather holiday gifts in November or even October, holiday shopping trends start well before Thanksgiving in the United States. Customers are shopping early, looking for great deals, and spending their money carefully. Understanding recent holiday shopping insights can empower companies to make data-driven decisions. After all, consumer feedback allows businesses to optimize marketing strategies, improve customer service, and manage inventory more effectively. Is Holiday Shopping Still a Big Deal? Black Friday happens later in November this year, and consumers are shopping earlier. Does that mean that the traditional holiday shopping window is less important? Definitely not. Holiday shopping trends might have consumers in stores looking for gifts early this Autumn. Still, spending is only projected to go up. Holiday shopping data from Deloitte suggests holiday sales will rise by 3.3% this year. The timing may shift a bit as to when purchases are made, but holiday shopping is still very much a big deal. Early Shopping vs Last Minute Deals While last-minute deals will certainly still occur with holiday shopping, 2024 data shows that consumers are not waiting to shop. They are already in stores starting to collect gift ideas. Holiday shopping statistics show that 60% of shoppers start their holiday shopping in November or as early as October. The survey also “noted a significant drop” in holiday shopping closer to the holidays, with increases in other sales periods. 60% of shoppers 60% of shoppers Shoppers are planning and budgeting for purchases, taking advantage of sales. In fact, December is the least popular month to start holiday shopping, making last-minute shopping less popular than in years past. For retailers who enjoy sales closer to December 25, there is a silver lining. Consumers spend $47 billion in the two weeks after Christmas, and 50% of the time, shoppers are buying for themselves, creating a great secondary opportunity for holiday shopping after the traditional season closes. $47 billion $47 billion Budgets are Getting Tighter Holiday shopping survey data suggests that 2024 will have a slightly different feel than previous holiday seasons. What is the force behind the change in holiday shopping in 2024? Tighter budgets, more internet-savvy consumers, and inflation. In fact, according to a recent PissedConsumer.com survey , 74.1% of consumers feel inflation might impact their holiday shopping. So, shoppers are looking to save money this holiday season, with 56.8% waiting for sales and 38% planning to buy fewer gifts. PissedConsumer.com survey PissedConsumer.com survey Fortunately, according to a McKinsey survey , despite the higher prices caused by previous inflation, consumers are also feeling more optimistic. Consumers plan to spend more in the coming three months, and 41% of respondents felt more optimistic about the economy and spending, likely due in part to stabilizing prices. McKinsey survey McKinsey survey Flexible Payment Options Are on Its Top With so many consumers planning ahead, looking for deals, and working with a budget in 2024, it’s no surprise that flexible payment options are also extremely popular. By now, pay later (BNPL) options are big this year, especially on mobile devices and through apps. Adobe currently forecasts that Cyber Monday will be the top day of BNPL shopping, with consumers spending about $993 million. Roughly 75% of that spending will likely be through mobile devices. Adobe currently forecasts Adobe currently forecasts Consumers Are Less Likely to Shop In-Store The move to online shopping has been accelerating for years, and 2024 will not be an exception. While the ability to see, touch, and test items will always keep the brick-and-mortar experience alive and well, shoppers are mixing it up. 7% of shoppers will only buy online, and all but roughly 18% of consumers shop online at least some of the time. 7% of shoppers 7% of shoppers Online shopping is expected to increase by 8.4% over last year , equating to a record $240.8 billion spent in the United States. Most of that spending, at 53.2%, will be through mobile devices, creating tremendous opportunities for online retailers. 8.4% over last year 8.4% over last year Holiday Shopping Insights to Remember The 2024 holiday shopping data shows customers are budgeting, planning, and already hard at work shopping for the holidays, often through mobile devices using delayed payments. The holiday season starts early, but a secondary season happens in the weeks after Christmas, presenting plenty of opportunities for retailers to tap into a $240 billion market.

Holiday Shopping Trends Shaping 2024 Retail Strategies

In today’s fast-paced financial landscape, the conversation around cash versus digital payments has never been more pressing. As digital transactions continue to dominate daily life, offering unprecedented speed and convenience, many have questioned the future of physical currency. But despite the growing prevalence of digital payments, cash remains a critical player in the global economy—particularly in moments of crisis. When natural disasters, geopolitical unrest, or cyberattacks disrupt the infrastructure that supports digital transactions, cash suddenly becomes indispensable. Yet, cash itself is not without flaws. In uncertain times, its value can plummet, leaving essential goods like food and fuel far more valuable. This has driven some people to invest in agricultural land—an enduring, tangible asset that provides both security and resources when conventional money systems break down. Cash—A Reliable Standby in Crisis Cash has been a cornerstone of commerce for centuries. Its simplicity and universal acceptance make it a reliable option in even the most remote or technologically underserved regions. But its true value shines through during times of crisis—when digital infrastructure fails and people are cut off from their bank accounts or mobile wallets. In 2024, the Federal Emergency Management Agency (FEMA) reported 81 major disaster declarations in the U.S., double the number from just two years ago. Widespread power outages rendered digital payment systems unusable, but cash remained a dependable option for people to access essential goods like food, water, and fuel. When you can’t swipe a card or tap a phone, having cash in your pocket is often the only way to get what you need. The same story plays out in areas affected by war or political instability. During conflict, cash demand spikes as people seek something tangible in the midst of chaos. The European Central Bank reported a surge in euro cash demand near conflict zones as both locals and refugees turned to it as a secure, reliable option. In such times, cash is viewed as a lifeline. But despite its resilience, cash has its weaknesses. It can be easily lost or stolen, and in the face of severe instability, it can lose value quickly. In war economies, for instance, the worth of cash plummets as food and supplies become the real currency. In these situations, people start to look for alternatives to safeguard their wealth—and that’s where investments like agricultural land come into play. Digital Payments—Convenience with Vulnerabilities On the other side of the coin, digital payments have transformed how we handle money. With just a few taps, you can send or receive money across the globe in seconds, buy groceries, or even pay your bills. Digital payments are fast, efficient, and increasingly secure, thanks to encryption and two-factor authentication. For many, they’ve become the go-to for nearly every transaction. But this convenience has its limits. Digital payments depend entirely on an infrastructure that can fail during times of crisis. In 2024, 72% of Americans experienced at least one extreme weather event. In these moments—when power lines are down and the internet is inaccessible—those who rely solely on digital payments find themselves cut off. Cash, on the other hand, continues to circulate. Cybersecurity is another growing concern. As financial systems become increasingly digital, they are also more vulnerable to attacks. A major data breach or ransomware attack can leave millions without access to their accounts. When things go wrong with digital systems, cash remains a safe and reliable alternative. Finding Balance—Cash, Digital Payments, and Crisis-Proof Investments As we move forward in an increasingly unpredictable world, finding a balance between cash and digital payments is more important than ever. Each form of currency has its strengths. Digital payments excel in speed and convenience during stable times, but cash proves invaluable when infrastructure crumbles. Having both options available ensures that people can navigate through both normal and extreme conditions with ease. In moments of extreme uncertainty—whether from natural disasters, political upheaval, or economic collapse—cash might not always be enough. This has driven some to invest in more permanent, crisis-proof assets like agricultural land. Farmland, whether for crops or livestock, offers a level of security that cash and digital payments cannot. No matter the state of the economy, well-managed land can yield valuable resources, ensuring both financial stability and sustenance during hard times. The Land of Tomorrow In a world marked by technological advances and growing uncertainties, the need for both cash and digital payments is clear. Digital transactions will continue to dominate in convenience, but cash will always have a role in times of crisis. As we’ve seen time and again, when the infrastructure supporting digital payments falters, cash becomes the lifeline people turn to. At the same time, in truly unstable times, it may not be cash or even digital payments that hold the most value. Assets like agricultural land—capable of producing essential goods like food—often become the ultimate form of security. Looking forward, it’s not about choosing one form of currency over the other, but rather understanding how both cash and digital payments can coexist and support each other, while also recognizing that tangible investments like land provide a level of resilience that neither can match. In the end, being prepared for an uncertain future means diversifying—both in how we handle our money and how we invest in long-term, crisis-resistant resources. In today’s fast-paced financial landscape, the conversation around cash versus digital payments has never been more pressing. As digital transactions continue to dominate daily life, offering unprecedented speed and convenience, many have questioned the future of physical currency. But despite the growing prevalence of digital payments, cash remains a critical player in the global economy—particularly in moments of crisis. When natural disasters, geopolitical unrest, or cyberattacks disrupt the infrastructure that supports digital transactions, cash suddenly becomes indispensable. Yet, cash itself is not without flaws. In uncertain times, its value can plummet, leaving essential goods like food and fuel far more valuable. This has driven some people to invest in agricultural land—an enduring, tangible asset that provides both security and resources when conventional money systems break down. Cash—A Reliable Standby in Crisis Cash—A Reliable Standby in Crisis Cash has been a cornerstone of commerce for centuries. Its simplicity and universal acceptance make it a reliable option in even the most remote or technologically underserved regions. But its true value shines through during times of crisis—when digital infrastructure fails and people are cut off from their bank accounts or mobile wallets. In 2024, the Federal Emergency Management Agency (FEMA) reported 81 major disaster declarations in the U.S., double the number from just two years ago. Widespread power outages rendered digital payment systems unusable, but cash remained a dependable option for people to access essential goods like food, water, and fuel. When you can’t swipe a card or tap a phone, having cash in your pocket is often the only way to get what you need. 81 major disaster declarations The same story plays out in areas affected by war or political instability. During conflict, cash demand spikes as people seek something tangible in the midst of chaos. The European Central Bank reported a surge in euro cash demand near conflict zones as both locals and refugees turned to it as a secure, reliable option. In such times, cash is viewed as a lifeline. surge in euro cash demand But despite its resilience, cash has its weaknesses. It can be easily lost or stolen, and in the face of severe instability, it can lose value quickly. In war economies, for instance, the worth of cash plummets as food and supplies become the real currency. In these situations, people start to look for alternatives to safeguard their wealth—and that’s where investments like agricultural land come into play. Digital Payments—Convenience with Vulnerabilities Digital Payments—Convenience with Vulnerabilities On the other side of the coin, digital payments have transformed how we handle money. With just a few taps, you can send or receive money across the globe in seconds, buy groceries, or even pay your bills. Digital payments are fast, efficient, and increasingly secure, thanks to encryption and two-factor authentication. For many, they’ve become the go-to for nearly every transaction. But this convenience has its limits. Digital payments depend entirely on an infrastructure that can fail during times of crisis. In 2024, 72% of Americans experienced at least one extreme weather event . In these moments—when power lines are down and the internet is inaccessible—those who rely solely on digital payments find themselves cut off. Cash, on the other hand, continues to circulate. 72% of Americans experienced at least one extreme weather event Cybersecurity is another growing concern. As financial systems become increasingly digital, they are also more vulnerable to attacks. A major data breach or ransomware attack can leave millions without access to their accounts. When things go wrong with digital systems, cash remains a safe and reliable alternative. Finding Balance—Cash, Digital Payments, and Crisis-Proof Investments Finding Balance—Cash, Digital Payments, and Crisis-Proof Investments As we move forward in an increasingly unpredictable world, finding a balance between cash and digital payments is more important than ever. Each form of currency has its strengths. Digital payments excel in speed and convenience during stable times, but cash proves invaluable when infrastructure crumbles. Having both options available ensures that people can navigate through both normal and extreme conditions with ease. In moments of extreme uncertainty—whether from natural disasters, political upheaval, or economic collapse—cash might not always be enough. This has driven some to invest in more permanent, crisis-proof assets like agricultural land. Farmland, whether for crops or livestock, offers a level of security that cash and digital payments cannot. No matter the state of the economy, well-managed land can yield valuable resources, ensuring both financial stability and sustenance during hard times. The Land of Tomorrow In a world marked by technological advances and growing uncertainties, the need for both cash and digital payments is clear. Digital transactions will continue to dominate in convenience, but cash will always have a role in times of crisis. As we’ve seen time and again, when the infrastructure supporting digital payments falters, cash becomes the lifeline people turn to. At the same time, in truly unstable times, it may not be cash or even digital payments that hold the most value. Assets like agricultural land—capable of producing essential goods like food—often become the ultimate form of security. Looking forward, it’s not about choosing one form of currency over the other, but rather understanding how both cash and digital payments can coexist and support each other, while also recognizing that tangible investments like land provide a level of resilience that neither can match. In the end, being prepared for an uncertain future means diversifying—both in how we handle our money and how we invest in long-term, crisis-resistant resources.

The Great Debate: Cash vs. Digital Payments in a Crisis-Driven World

Hello all, I have recently read through the Startup Playbook and will give a quick take on it based on my experience. I would say reading The Startup Playbook by Sam Altman became this new look into the world of startups. Being a Middle Eastern chemical engineering student in Arizona, I found insight and connected things relevant to me in particular. Although my field is technical, the insights on how to actually build something users really love caught my full attention. Similar to engineering, entrepreneurship can be very complicated, and one could think that sometimes big is always better. Still, Altman insists on the power of starting small: focus on something a few people love, not something lots of people like. There's almost something universal about this advice, possibly beyond startups themselves. What did lead was how he spoke to the notion of risk: growing up in a culture that sometimes puts such high value on stability, the notion of taking risks felt a little paradigm-shifting. Conclusion: This playbook makes it plain and simple that, yes, starting a venture is hard, but playing it safe rather than passionate might be the riskier play over the long term. This really made me reflect on the opportunities available to me after graduation, whether through traditional chemical engineering paths or, I don't know, maybe something a little more entrepreneurial-perhaps even in sustainability or energy. Altman's point about clarity of thought and clarity of communication also parallels to my engineering education. While we are taught to solve the most complicated problems, solution communication is equally important. Whether it is to sell an idea, design a product, or to solve a chemical process problem, clarity makes the difference. Here is the reference: https://playbook.samaltman.com/ Hello all, I have recently read through the Startup Playbook and will give a quick take on it based on my experience. I would say reading The Startup Playbook by Sam Altman became this new look into the world of startups. Being a Middle Eastern chemical engineering student in Arizona, I found insight and connected things relevant to me in particular. Although my field is technical, the insights on how to actually build something users really love caught my full attention. Similar to engineering, entrepreneurship can be very complicated, and one could think that sometimes big is always better. Still, Altman insists on the power of starting small: focus on something a few people love, not something lots of people like. There's almost something universal about this advice, possibly beyond startups themselves. What did lead was how he spoke to the notion of risk: growing up in a culture that sometimes puts such high value on stability, the notion of taking risks felt a little paradigm-shifting. Conclusion: This playbook makes it plain and simple that, yes, starting a venture is hard, but playing it safe rather than passionate might be the riskier play over the long term. This really made me reflect on the opportunities available to me after graduation, whether through traditional chemical engineering paths or, I don't know, maybe something a little more entrepreneurial-perhaps even in sustainability or energy. Altman's point about clarity of thought and clarity of communication also parallels to my engineering education. While we are taught to solve the most complicated problems, solution communication is equally important. Whether it is to sell an idea, design a product, or to solve a chemical process problem, clarity makes the difference. Here is the reference: https://playbook.samaltman.com/ https://playbook.samaltman.com/

A Review of Sam Altman's Startup Playbook

Table of Links Abstract and 1. Introduction 1.1 Option Pricing 1.2 Asymptotic Notation (Big O) 1.3 Finite Difference 1.4 The Black-Schole Model 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.6 Our Contribution Literature Review
Methodology 3.1 Model Assumption 3.2 Theorems and Model Discussion Result Analysis
Conclusion and References 5. CONCLUSION The research findings have demonstrated that finite difference methods offer a powerful tool for approximating option prices and hedging parameters, especially in cases where closed-form solutions are unavailable or impractical. The asymptotic analysis conducted in this study has provided valuable insights into the convergence properties and accuracy of finite difference approximations, shedding light on the optimal choice of discretization schemes and grid sizes for different option contracts. Furthermore, the combination of finite difference methods and Monte Carlo simulation with variance reduction techniques offers a comprehensive approach to hedge error analysis in option pricing. By leveraging the strengths of both methodologies, financial practitioners can obtain more robust and reliable estimates of option prices and hedge parameters, thereby enhancing their risk management capabilities and decision-making processes. It is important to acknowledge the limitations of this study and areas for future research. While the asymptotic analysis provides valuable theoretical insights, further empirical validation is warranted to assess the robustness of the findings across different market conditions and asset classes. Additionally, exploring alternative variance reduction techniques and incorporating more sophisticated models of market dynamics could yield further improvements in hedge error analysis and option pricing accuracy. this study has advanced our understanding of the factors influencing hedge errors and provided practical tools for mitigating their impact on derivative pricing and risk management. As financial markets continue to evolve, the insights gained from this research will remain valuable for academics, practitioners, and policymakers striving to enhance the efficiency and stability of global financial systems. REFERENCES [1] C. W. Smith, “Option pricing. A review,” J. financ. econ., vol. 3, no. 1–2, pp. 3–51, 1976, doi: 10.1016/0304-405X(76)90019-2. [2] S. Guernsey, “an Introduction To the Black-Scholes Pde Model,” 2013. [3] B. Peeters, C. L. Dert, and A. Lucas, “Black Scholes for Portfolios of Options in Discrete Time,” SSRN Electron. J., no. 03, 2005, doi: 10.2139/ssrn.469022. [4] J. He, “A Study on Analytical and Numerical Solutions of Three Types of Black-Scholes Models,” Int. J. Trade, Econ. Financ., vol. 13, no. 2, 2022, doi: 10.18178/ijtef.2022.13.2.720. [5] A. S. Shinde and K. C. Takale, “Study of BlackScholes model and its applications,” Procedia Eng., vol. 38, pp. 270–279, 2012, doi: 10.1016/j.proeng.2012.06.035. [6] Y. Zhang, “The value of Monte Carlo model-based variance reduction technology in the pricing of financial derivatives,” PLoS One, vol. 15, no. 2, pp. 1–13, 2020, doi: 10.1371/journal.pone.0229737. [7] P. L. Bonate, “A brief introduction to Monte Carlo simulation,” Clin. Pharmacokinet., vol. 40, no. 1, pp. 15–22, 2001, doi: 10.2165/00003088- 200140010-00002. [8] D. R. Tobergte and S. Curtis, “Importance sampling for high speed statistical Monte-Carlo simulations,” J. Chem. Inf. Model., vol. 53, no. 9, pp. 1689–1699, 2013. [9] E. C. Anderson and M. Stephens, “Importance Sampling and (MC)^3,” Sisg 2020, vol. 2, no. July, pp. 1–29, 2020. [10] I. N. Medvedev, “Vector estimators of the Monte Carlo method with a finite variance,” Russ. J. Numer. Anal. Math. Model., vol. 28, no. 3, pp. 231– 244, 2013, doi: 10.1515/rnam-2013-0014. [11] E. Saliby and R. J. Paul, “A farewell to the use of antithetic variates in monte carlo simulation,” J. Oper. Res. Soc., vol. 60, no. 7, pp. 1026–1035, 2009, doi: 10.1057/palgrave.jors.2602645. [12] P. W. Glynn and R. Szechtman, “Some New Perspectives on the Method of Control Variates,” Monte Carlo Quasi-Monte Carlo Methods 2000, pp. 27–49, 2002, doi: 10.1007/978-3-642-56046-0_3. [13] W. Gustafsson, “Evaluating the Longstaff-Schwartz method for pricing of American options,” 2015. [14] L. Andersen and M. Broadie, “Primal-dual simulation algorithm for pricing multidimensional American options,” Manage. Sci., vol. 50, no. 9, pp. 1222–1234, 2004, doi: 10.1287/mnsc.1040.0258. [15] E. Wipplinger, Jim Gatheral: The volatility surface, a practitioner’s guide, vol. 22, no. 1. 2008. doi: 10.1007/s11408-007-0072-4. [16] M. Avellaneda and S. Stoikov, “High-frequency trading in a limit order book,” Quant. Financ., vol. 8, no. 3, pp. 217–224, 2008, doi: 10.1080/14697680701381228. [17] S. Mayoral, D. Moreno, and A. Zareei, “Using a hedging network to minimize portfolio risk,” Financ. Res. Lett., vol. 44, no. April, p. 102044, 2022, doi: 10.1016/j.frl.2021.102044. [18] S. Gayathri Devi, K. Selvam, and S. P. Rajagopalan, “An abstract to calculate big o factors of time and space complexity of machine code,” IET Conf. Publ., vol. 2011, no. 583 CP, pp. 844–847, 2011, doi: 10.1049/cp.2011.0483. [19] M. S. H. Mojumder, M. N. Haque, and M. J. Alam, “Efficient Finite Difference Methods for the Numerical Analysis of One-Dimensional Heat Equation,” J. Appl. Math. Phys., vol. 11, no. 10, pp. 3099–3123, 2023, doi: 10.4236/jamp.2023.1110204. [20] I. R. Khan and R. Ohba, “Taylor series based finite difference approximations of higher-degree derivatives,” J. Comput. Appl. Math., vol. 154, no. 1, pp. 115–124, 2003, doi: 10.1016/S0377- 0427(02)00816-6. [21] S. Danho, “Pricing Financial Derivatives with the Finite Difference Method,” p. 237, 2017. [22] G. Connor and T. Lasarte, “An Introduction to Hedge Funds Strategies. Introductory Guide,” pp. 1–16, 2004, [Online]. Available: http://eprints.lse.ac.uk/24675/1/dp477.pdf [23] M. Nurul Anwar and L. Sazzad Andallah, “A Study on Numerical Solution of Black-Scholes Model,” J. Math. Financ., vol. 08, no. 02, pp. 372–381, 2018, doi: 10.4236/jmf.2018.82024. [24] J. Akahori, F. Barsotti, and Y. Imamura, “Hedging error as generalized timing risk,” Quant. Financ., vol. 23, no. 4, pp. 693–703, 2023, doi: 10.1080/14697688.2022.2154255. [25] R. C. A. Oomen and G. J. Jiang, “Hedging Derivatives Risks - A Simulation Study,” SSRN Electron. J., no. May, 2005, doi: 10.2139/ssrn.302525. [26] K. A. Froot, “Hedging Portfolios with Real Assets,” J. Portf. Manag., vol. 21, no. 4, pp. 60–77, 1995, doi: 10.3905/jpm.1995.409527. [27] H. E. LELAND, “Option Pricing and Replication with Transactions Costs,” J. Finance, vol. 40, no. 5, pp. 1283–1301, 1985, doi: 10.1111/j.1540- 6261.1985.tb02383.x. [28] T. Hayashi and P. A. Mykland, “Evaluating hedging errors: An asymptotic approach,” Math. Financ., vol. 15, no. 2, pp. 309–343, 2005, doi: 10.1111/j.0960-1627.2005.00221.x. [29] J.-L. Prigent, R. Hentati, and A. Kaffel, “Dynamic versus static optimization of hedge fund portfolios: the relevance of performance measures,” Int. J. Bus., vol. 15, no. 156, pp. 1–17, 2010. [30] R. A. Jarrow, D. Lando, and F. Yu, “Default Risk and Diversification : Theory and Empirical Implications * Default Risk and Diversification: Theory and Empirical Implications Abstract,” no. 607, 2003. [31] S. Kim, D. Jeong, C. Lee, and J. Kim, “Finite difference method for the multi-asset black-scholes equations,” Mathematics, vol. 8, no. 3, pp. 1–17, 2020, doi: 10.3390/math8030391. [32] D. Jeong, M. Yoo, and J. Kim, “Finite Difference Method for the Black–Scholes Equation Without Boundary Conditions,” Comput. Econ., vol. 51, no. 4, pp. 961–972, 2018, doi: 10.1007/s10614-017- 9653-0. [33] T. Guo, Black-Scholes Process and Monte Carlo Simulation-Based Options Pricing. Atlantis Press International BV, 2023. doi: 10.2991/978-94-6463- 010-7_75. [34] P. Glasserman, “Monte Carlo Methods in Financial Engineerring,” J. Chem. Inf. Model., vol. 53, no. 9, pp. 1689–1699, 2013. [35] Q. Jiang*, “Comparison of Black–Scholes Model and Monte-Carlo Simulation on Stock Price Modeling,” vol. 109, no. Icemci, pp. 135–137, 2020, doi: 10.2991/aebmr.k.191217.025. [36] E. Derman and E. K, “Stochastic Caclulus for Finance,” pp. 1–63, 2000. Authors:
(1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com);
(2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in);
(3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Abstract and 1. Introduction 1.1 Option Pricing 1.1 Option Pricing 1.2 Asymptotic Notation (Big O) 1.2 Asymptotic Notation (Big O) 1.3 Finite Difference 1.3 Finite Difference 1.4 The Black-Schole Model 1.4 The Black-Schole Model 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.6 Our Contribution 1.6 Our Contribution Literature Review Methodology Literature Review Literature Review Literature Review Methodology Methodology 3.1 Model Assumption 3.1 Model Assumption 3.2 Theorems and Model Discussion 3.2 Theorems and Model Discussion Result Analysis Conclusion and References Result Analysis Result Analysis Result Analysis Conclusion and References Conclusion and References Conclusion and References 5. CONCLUSION The research findings have demonstrated that finite difference methods offer a powerful tool for approximating option prices and hedging parameters, especially in cases where closed-form solutions are unavailable or impractical. The asymptotic analysis conducted in this study has provided valuable insights into the convergence properties and accuracy of finite difference approximations, shedding light on the optimal choice of discretization schemes and grid sizes for different option contracts. Furthermore, the combination of finite difference methods and Monte Carlo simulation with variance reduction techniques offers a comprehensive approach to hedge error analysis in option pricing. By leveraging the strengths of both methodologies, financial practitioners can obtain more robust and reliable estimates of option prices and hedge parameters, thereby enhancing their risk management capabilities and decision-making processes. It is important to acknowledge the limitations of this study and areas for future research. While the asymptotic analysis provides valuable theoretical insights, further empirical validation is warranted to assess the robustness of the findings across different market conditions and asset classes. Additionally, exploring alternative variance reduction techniques and incorporating more sophisticated models of market dynamics could yield further improvements in hedge error analysis and option pricing accuracy. this study has advanced our understanding of the factors influencing hedge errors and provided practical tools for mitigating their impact on derivative pricing and risk management. As financial markets continue to evolve, the insights gained from this research will remain valuable for academics, practitioners, and policymakers striving to enhance the efficiency and stability of global financial systems. REFERENCES [1] C. W. Smith, “Option pricing. A review,” J. financ. econ., vol. 3, no. 1–2, pp. 3–51, 1976, doi: 10.1016/0304-405X(76)90019-2. [2] S. Guernsey, “an Introduction To the Black-Scholes Pde Model,” 2013. [3] B. Peeters, C. L. Dert, and A. Lucas, “Black Scholes for Portfolios of Options in Discrete Time,” SSRN Electron. J., no. 03, 2005, doi: 10.2139/ssrn.469022. [4] J. He, “A Study on Analytical and Numerical Solutions of Three Types of Black-Scholes Models,” Int. J. Trade, Econ. Financ., vol. 13, no. 2, 2022, doi: 10.18178/ijtef.2022.13.2.720. [5] A. S. Shinde and K. C. Takale, “Study of BlackScholes model and its applications,” Procedia Eng., vol. 38, pp. 270–279, 2012, doi: 10.1016/j.proeng.2012.06.035. [6] Y. Zhang, “The value of Monte Carlo model-based variance reduction technology in the pricing of financial derivatives,” PLoS One, vol. 15, no. 2, pp. 1–13, 2020, doi: 10.1371/journal.pone.0229737. [7] P. L. Bonate, “A brief introduction to Monte Carlo simulation,” Clin. Pharmacokinet., vol. 40, no. 1, pp. 15–22, 2001, doi: 10.2165/00003088- 200140010-00002. [8] D. R. Tobergte and S. Curtis, “Importance sampling for high speed statistical Monte-Carlo simulations,” J. Chem. Inf. Model., vol. 53, no. 9, pp. 1689–1699, 2013. [9] E. C. Anderson and M. Stephens, “Importance Sampling and (MC)^3,” Sisg 2020, vol. 2, no. July, pp. 1–29, 2020. [10] I. N. Medvedev, “Vector estimators of the Monte Carlo method with a finite variance,” Russ. J. Numer. Anal. Math. Model., vol. 28, no. 3, pp. 231– 244, 2013, doi: 10.1515/rnam-2013-0014. [11] E. Saliby and R. J. Paul, “A farewell to the use of antithetic variates in monte carlo simulation,” J. Oper. Res. Soc., vol. 60, no. 7, pp. 1026–1035, 2009, doi: 10.1057/palgrave.jors.2602645. [12] P. W. Glynn and R. Szechtman, “Some New Perspectives on the Method of Control Variates,” Monte Carlo Quasi-Monte Carlo Methods 2000, pp. 27–49, 2002, doi: 10.1007/978-3-642-56046-0_3. [13] W. Gustafsson, “Evaluating the Longstaff-Schwartz method for pricing of American options,” 2015. [14] L. Andersen and M. Broadie, “Primal-dual simulation algorithm for pricing multidimensional American options,” Manage. Sci., vol. 50, no. 9, pp. 1222–1234, 2004, doi: 10.1287/mnsc.1040.0258. [15] E. Wipplinger, Jim Gatheral: The volatility surface, a practitioner’s guide, vol. 22, no. 1. 2008. doi: 10.1007/s11408-007-0072-4. [16] M. Avellaneda and S. Stoikov, “High-frequency trading in a limit order book,” Quant. Financ., vol. 8, no. 3, pp. 217–224, 2008, doi: 10.1080/14697680701381228. [17] S. Mayoral, D. Moreno, and A. Zareei, “Using a hedging network to minimize portfolio risk,” Financ. Res. Lett., vol. 44, no. April, p. 102044, 2022, doi: 10.1016/j.frl.2021.102044. [18] S. Gayathri Devi, K. Selvam, and S. P. Rajagopalan, “An abstract to calculate big o factors of time and space complexity of machine code,” IET Conf. Publ., vol. 2011, no. 583 CP, pp. 844–847, 2011, doi: 10.1049/cp.2011.0483. [19] M. S. H. Mojumder, M. N. Haque, and M. J. Alam, “Efficient Finite Difference Methods for the Numerical Analysis of One-Dimensional Heat Equation,” J. Appl. Math. Phys., vol. 11, no. 10, pp. 3099–3123, 2023, doi: 10.4236/jamp.2023.1110204. [20] I. R. Khan and R. Ohba, “Taylor series based finite difference approximations of higher-degree derivatives,” J. Comput. Appl. Math., vol. 154, no. 1, pp. 115–124, 2003, doi: 10.1016/S0377- 0427(02)00816-6. [21] S. Danho, “Pricing Financial Derivatives with the Finite Difference Method,” p. 237, 2017. [22] G. Connor and T. Lasarte, “An Introduction to Hedge Funds Strategies. Introductory Guide,” pp. 1–16, 2004, [Online]. Available: http://eprints.lse.ac.uk/24675/1/dp477.pdf http://eprints.lse.ac.uk/24675/1/dp477.pdf [23] M. Nurul Anwar and L. Sazzad Andallah, “A Study on Numerical Solution of Black-Scholes Model,” J. Math. Financ., vol. 08, no. 02, pp. 372–381, 2018, doi: 10.4236/jmf.2018.82024. [24] J. Akahori, F. Barsotti, and Y. Imamura, “Hedging error as generalized timing risk,” Quant. Financ., vol. 23, no. 4, pp. 693–703, 2023, doi: 10.1080/14697688.2022.2154255. [25] R. C. A. Oomen and G. J. Jiang, “Hedging Derivatives Risks - A Simulation Study,” SSRN Electron. J., no. May, 2005, doi: 10.2139/ssrn.302525. [26] K. A. Froot, “Hedging Portfolios with Real Assets,” J. Portf. Manag., vol. 21, no. 4, pp. 60–77, 1995, doi: 10.3905/jpm.1995.409527. [27] H. E. LELAND, “Option Pricing and Replication with Transactions Costs,” J. Finance, vol. 40, no. 5, pp. 1283–1301, 1985, doi: 10.1111/j.1540- 6261.1985.tb02383.x. [28] T. Hayashi and P. A. Mykland, “Evaluating hedging errors: An asymptotic approach,” Math. Financ., vol. 15, no. 2, pp. 309–343, 2005, doi: 10.1111/j.0960-1627.2005.00221.x. [29] J.-L. Prigent, R. Hentati, and A. Kaffel, “Dynamic versus static optimization of hedge fund portfolios: the relevance of performance measures,” Int. J. Bus., vol. 15, no. 156, pp. 1–17, 2010. [30] R. A. Jarrow, D. Lando, and F. Yu, “Default Risk and Diversification : Theory and Empirical Implications * Default Risk and Diversification: Theory and Empirical Implications Abstract,” no. 607, 2003. [31] S. Kim, D. Jeong, C. Lee, and J. Kim, “Finite difference method for the multi-asset black-scholes equations,” Mathematics, vol. 8, no. 3, pp. 1–17, 2020, doi: 10.3390/math8030391. [32] D. Jeong, M. Yoo, and J. Kim, “Finite Difference Method for the Black–Scholes Equation Without Boundary Conditions,” Comput. Econ., vol. 51, no. 4, pp. 961–972, 2018, doi: 10.1007/s10614-017- 9653-0. [33] T. Guo, Black-Scholes Process and Monte Carlo Simulation-Based Options Pricing. Atlantis Press International BV, 2023. doi: 10.2991/978-94-6463- 010-7_75. [34] P. Glasserman, “Monte Carlo Methods in Financial Engineerring,” J. Chem. Inf. Model., vol. 53, no. 9, pp. 1689–1699, 2013. [35] Q. Jiang*, “Comparison of Black–Scholes Model and Monte-Carlo Simulation on Stock Price Modeling,” vol. 109, no. Icemci, pp. 135–137, 2020, doi: 10.2991/aebmr.k.191217.025. [36] E. Derman and E. K, “Stochastic Caclulus for Finance,” pp. 1–63, 2000. Authors: (1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com); (2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in); (3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). Authors: Authors: (1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com); (2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in); (3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv available on arxiv

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