IntroductionIn mathematics and theoretical computer science, a fixed point of an operator $F$ is an entity $x$ such that $F(x) = x$. Fixed-point results appear across many domains: for example, Banach’s Fixed-Point Theorem guarantees a unique fixed point for any contraction mapping on a complete metric space, and the Knaster–Tarski Theorem ensures that every monotone function on a complete lattice has a fixed point. These classical theorems establish existence (and sometimes uniqueness) of solutions to $x = F(x)$ under various conditions. In recursive and computational settings, fixed points enable self-referential definitions – a recursive function can be seen as a fixed point of a functional that “unwinds” one step of the recursion. For instance, the Y-combinator in lambda calculus provides a fixed-point combinator $Y$ such that for any function $W$, $Y(W)$ is a term satisfying $Y(W) = W(Y(W))$. This yields recursive definitions (like the factorial function) as solutions to self-referential equations.This article develops a fully formal framework for recursive fixed points – fixed points obtained via an iterative or recursive process. We focus on the convergence of a sequence (possibly transfinite) of transformations to a self-consistent state. Intuitively, we start with an initial approximation and repeatedly apply a transformation $\phi$; if this process approaches a stable state that no longer changes under $\phi$, we have reached a fixed point. Formally, one may consider an iterative sequence $x_0, x_1 = \phi(x_0), x_2 = \phi(x_1), \dots$ and seek a limit $x_{\infty}$ such that $\phi(x_{\infty}) = x_{\infty}$. Such a limit, if it exists, is a recursive fixed point – the result of infinitely (or transfinitely) many applications of $\phi$. This idea can be generalized beyond simple sequences, using the machinery of ordinal-indexed recursion and category theory to rigorously construct $\phi^\infty$, the outcome of transfinitely many iterations of $\phi$.Recent research by Alpay (2025) introduced Alpay Algebra, a category-theoretic framework where transfinite recursive fixed points play a central role. In this framework, an endofunctor $\phi$ (an operator on objects in a category) can be iterated through ordinal numbers to yield a stable initial fixed point denoted $\phi^{\infty}$. The existence of $\phi^{\infty}$ under broad conditions and its universal properties have been proven with mathematical rigor. The fixed point $\phi^{\infty}$ is recursive in that it is obtained as the limit of an ordinal-indexed chain of iterative approximants (often called the initial chain). Notably, this $\phi^{\infty}$ is not just any solution to $X \cong \phi(X)$; it is the smallest or initial solution, meaning it is generated by the recursive process itself and any other fixed point admits a unique morphism from $\phi^{\infty}$. In other words, $\phi^{\infty}$ encapsulates the “ultimate outcome” of the transformation $\phi$ applied repeatedly without end – a self-consistent structure that remains invariant under $\phi$.This manuscript provides a formal exposition of recursive fixed points. We begin by establishing the mathematical preliminaries (category-theoretic foundations and definitions of transfinite iteration). We then prove the existence and uniqueness of the transfinite fixed point $\phi^{\infty}$ under appropriate conditions, drawing on recent developments in Alpay Algebra. We illustrate these concepts with examples ranging from classical structures (natural numbers, infinite streams) to logic (fixed-point semantics of recursive theories) and AI systems (iterative embedding alignment) to demonstrate the ubiquity of recursive fixed points in theory and practice. Throughout, we use a formal style with symbolic notation – emphasizing symbols over prose – to maximize precision and semantic weight. By the end, we will see that recursive fixed points not only exist, but in fact serve as universal invariants in many self-referential systems, providing a rigorous backbone for understanding phenomena like emergent consistency, identity of processes, and convergence of iterative algorithms.Preliminaries: Category-Theoretic FrameworkOur development uses the language of category theory to formalize recursive processes. We briefly summarize the needed notions (for a comprehensive background, see Mac Lane, 1971). We assume a category $\mathcal{A}$ with an initial object $\varnothing$ (an object with a unique morphism from it to any other object). An endofunctor $\phi: \mathcal{A} \to \mathcal{A}$ is an operator that maps objects to objects and morphisms to morphisms within $\mathcal{A}$. Intuitively, $\phi$ represents one step of a generative or transformative process on the structures in $\mathcal{A}$. We are interested in objects $X$ that satisfy an isomorphism $X \cong \phi(X)$ – such objects are fixed points of the functor $\phi$ (also called $\phi$-algebras that are self-consistent).Transfinite Ordinals and Chains: To capture recursive (potentially infinite) iteration, we consider ordinal numbers $0, 1, 2, \dots, \omega, \omega+1, \dots$ which extend the natural numbers into the transfinite. An ordinal-indexed chain(or transfinite sequence) in $\mathcal{A}$ is a family of objects ${X_{\alpha}}{\alpha < \lambda}$ for some ordinal $\lambda$, together with morphisms connecting them, such that $X{0} = \varnothing$ (the initial object), and for each ordinal $\beta < \lambda$:Successor step: If $\beta = \alpha+1$ is a successor, then $X_{\beta} = \phi(X_{\alpha})$. In other words, each step applies the functor $\phi$ to the previous object.Limit step: If $\beta$ is a limit ordinal (zero is the minimal ordinal, any non-zero ordinal with no immediate predecessor is a limit), then $X_{\beta}$ is defined as the colimit (categorical limit of the diagram) of all earlier $X_{\alpha}$ for $\alpha < \beta$. Intuitively, at a limit stage, $X_{\beta}$ is the “union” or limit of the prior approximations $X_{0}, X_{1}, ..., X_{\alpha}, (\alpha<\beta)$.This process yields an initial chain:X0→ X1=ϕ(X0)→ X2=ϕ2(X0)→ ⋯→ Xω=colim{Xn:n<ω}→ Xω+1=ϕ(Xω)→ ⋯Each stage $X_{\alpha}$ is built “recursively” from the previous ones. We say $\phi$ is continuous (or $\kappa$-accessible) if it preserves colimits of chains of length $<\kappa$ for some regular cardinal $\kappa$ (for example, $\omega$-continuous means it preserves countable colimits). Under such conditions, one can show that the initial chain eventually reaches a stage where applying $\phi$ does not produce a new object. Formally, there exists some ordinal $\mu$ (often $\mu = \kappa$ or earlier) such that $X_{\mu} \cong X_{\mu+1} = \phi(X_{\mu})$. When this first occurs, $X_{\mu}$ is a fixed point of $\phi$. By construction, it is the minimal or initial fixed point, since it arose from the smallest starting object by iterative application of $\phi$. We denote this object as $\mu \phi$ or $\phi^{\infty}$ (Alpay’s notation). It is also called the initial $\phi$-algebra in category-theoretic terms.Definition: The recursive fixed point of $\phi$, denoted $\phi^{\infty}$, is the object (if it exists) at which the transfinite iterative chain stabilizes. Concretely, $\phi^{\infty}$ is an object such that $\phi(\phi^{\infty}) \cong \phi^{\infty}$ and for some ordinal $\mu$, $\phi^{\infty} = X_{\mu}$ with $X_{\mu} \cong \phi(X_{\mu})$, where ${X_{\alpha}}$ is the initial chain defined above.Because $\phi^{\infty}$ arises by iterating $\phi$ starting from the smallest object, it intuitively represents the “limit of applying $\phi$ forever.” This aligns with the idea of a recursive process converging to a fixed point. The existence of $\phi^{\infty}$ is not automatic in every category or for every functor $\phi$; it typically requires conditions like completeness of the category or continuity of $\phi$ as mentioned. The Alpay Algebra framework explicitly assumes such conditions (e.g., working in well-behaved categories with transfinite colimits and $\phi$ preserving those colimits). In fact, Alpay Algebra I establishes that $\phi^{\infty}$ exists for every initial object under ZFC set theory assumptions without additional axioms. All proofs are carried out within standard category-theoretic foundations (following Mac Lane’s paradigm).Existence of the Recursive Fixed Point ($\phi^{\infty}$)We now state and prove (in outline) the Existence Theorem for recursive fixed points. This corresponds to the fixed-point existence results found in Alpay’s work and is analogous to the classical results (Knaster-Tarski, etc.) but in a transfinite categorical setting.Theorem 1 (Existence of $\phi^{\infty}$): Let $\phi: \mathcal{A} \to \mathcal{A}$ be an endofunctor on a category $\mathcal{A}$ that admits all colimits of chains of length up to some regular ordinal $\Lambda$, and assume $\phi$ preserves these colimits (i.e. $\phi$ is $\Lambda$-continuous). If $\mathcal{A}$ has an initial object $X_0$, then the initial chain $(X_{\alpha}){\alpha < \Lambda}$ defined by $X{0} = \varnothing$ and $X_{\alpha+1} = \phi(X_{\alpha})$ (with $X_{\lambda} = \mathrm{colim}{\alpha<\lambda} X{\alpha}$ for limit ordinals $\lambda < \Lambda$) will converge to a fixed point. In other words, there exists some ordinal $\mu < \Lambda$ such that $X_{\mu} \cong \phi(X_{\mu})$. This object $X_{\mu}$ is the recursive fixed point $\phi^{\infty}$. Moreover, $\phi^{\infty}$ is an initial algebra for $\phi$: the unique $\phi$-algebra generated by this transfinite iteration.Proof Sketch: Because $\Lambda$ is regular and $\phi$ preserves colimits of chains of length $<\Lambda$, the chain cannot continue to produce strictly larger (non-isomorphic) objects at every stage without end; if it did, one could take the colimit at stage $\Lambda$ (contradicting regularity or continuity). Thus there must be some stage where stabilization occurs. Formally, consider the sequence of inclusions (morphisms) $X_0 \to X_1 \to X_2 \to \cdots$. Either this sequence continues strictly (no stabilization) for all ordinals $<\Lambda$, or else there is a stage $\mu$ where $X_{\mu} \to X_{\mu+1}$ is an isomorphism. The former scenario is ruled out by a cardinality/cumulativity argument: if no stabilization occurs before $\Lambda$, then $X_{\Lambda} = \mathrm{colim}{\alpha<\Lambda} X{\alpha}$ is a fixed point of $\phi$ at stage $\Lambda$, because $\phi(X_{\Lambda}) = \phi(\mathrm{colim}{\alpha<\Lambda} X{\alpha}) \cong \mathrm{colim}{\alpha<\Lambda} \phi(X{\alpha}) = \mathrm{colim}{\alpha<\Lambda} X{\alpha+1} = \mathrm{colim}{\alpha<\Lambda} X{\alpha} = X_{\Lambda}$ (using continuity of $\phi$). Thus $X_{\Lambda}$ itself would be a fixed point, effectively $X_{\Lambda} \cong \phi(X_{\Lambda})$, achieving stabilization at $\Lambda`. In either case, we obtain some least ordinal $\mu$ (possibly $\mu=\Lambda$ if no earlier stage) such that $X_{\mu} \cong \phi(X_{\mu})$. Define $\phi^{\infty} := X_{\mu}$. By construction, $\phi^{\infty}$ satisfies $\phi(\phi^{\infty}) \cong \phi^{\infty}$. Furthermore, for any $\phi$-algebra $(X,\alpha: \phi(X)\to X)$ (any other fixed structure), we have by initiality of the chain that there is a unique homomorphism from each $X_{\alpha}$ into $X$ commuting with the $\phi$-action; at the limit, this yields a homomorphism $h: \phi^{\infty} \to X$. Thus $\phi^{\infty}$ is the initial object among all solutions of $X \cong \phi(X)$. ∎This theorem formalizes the existence of a transfinitely attained fixed point. In plainer terms, if one keeps applying $\phi$ starting from the simplest object, eventually (perhaps after an infinite number of steps) one stops getting new structures and hits a self-consistent one. That endpoint is $\phi^{\infty}$. All the intermediate steps $X_0 \to X_1 \to \cdots \to X_{\mu}=\phi^{\infty}$ are essentially building up a solution to the equation $X = \phi(X)$ piece by piece (like successive approximations). The condition of $\phi$ preserving colimits ensures that no information is lost in the limit process and that $\phi^{\infty}$ truly is a fixed point.In the context of Alpay Algebra (a formal system introduced by Faruk Alpay), Theorem 1 is a central pillar: it guarantees that for the self-referential processes defined in that framework, a stable identity emerges as a fixed point. Specifically, Alpay Algebra treats $\phi^\infty$ as representing the intrinsic identity of a generative process, since it is the unique invariant state that the process converges to. The existence theorem above matches statements in Alpay’s work such as: “We prove that the fixed point $\phi^\infty$ exists for every initial object ... and [that] $\phi$-iterates converge under regular cardinals”. The iterative construction of $\phi^\infty$ is sometimes called an ordinal-indexed fold or transfinite induction on the functor.It is worth noting that this categorical result generalizes classical fixed-point constructions. For example, in domain theory (a branch of theoretical computer science and math), a special case of this theorem states that any continuous endofunction on a complete partial order has a least fixed point (by taking the $\omega$-chain of iterates starting from the bottom element). That is essentially the $\omega$-continuous case of the above, corresponding to Kleene’s Fixed-Point Theorem for monotone operators on CPOs (which is itself an instance of Tarski’s theorem for lattices). Our transfinite approach extends this idea: even if $\omega$ steps are not enough, one allows transfinite steps until convergence. The result is a powerful guarantee: if the process can keep going without inconsistency, it will find a fixed point. In practical terms, this means any self-referential or recursive definition, under broad conditions, “bottoms out” at a well-defined semantics or structure that does not further change under the defining transformation.Uniqueness and Universal PropertyHaving established existence, we examine the uniqueness and universal property of the recursive fixed point $\phi^{\infty}$. Uniqueness here means $\phi^{\infty}$ is essentially the only fixed point that can be obtained through the recursive construction – if there were another built in the it would be to $\phi^{\infty}$. $\phi^{\infty}$ is the smallest fixed point, and every other fixed point of $\phi$ out” of $\phi^{\infty}$ in a unique and In the of Theorem 1, the recursive fixed point $\phi^{\infty}$ is unique up to isomorphism. Moreover, $\phi^{\infty}$ has the initiality for any object $X$ with an isomorphism \cong \phi(X)$ (i.e. any other fixed point of there exists a unique morphism \phi^{\infty} \to (a the appropriate In any other fixed-point object $X$ admits a unique from $\phi^{\infty}$, which is an isomorphism if $X$ is also obtained via a iterative Sketch: Uniqueness up to isomorphism is a standard category-theoretic argument: if and are initial $\phi$-algebras fixed then by initiality of there is a unique homomorphism I \to and by initiality of a unique homomorphism \to The I \to must the identity on (by uniqueness of the on and = Thus and are \cong This any solutions of the transfinite recursion are we can of the $\phi^{\infty}$ up to the universal any other fixed point we can $X$ with a $\phi$-algebra structure and to Specifically, \to can serve as the structure on \cong is there is a unique $\phi$-algebra homomorphism \phi^{\infty} \to such that = Intuitively, maps the fixed into any fixed structure $X$ in the only with $\phi$. If $X$ itself built by a iterative limit process (e.g., another chain that also a fixed then will be an isomorphism $\phi^{\infty}$, cannot into a end up the and formal terms, there is only one smallest self-consistent structure generated by $\phi$, and any other self-consistent structure a from this smallest one. This $\phi^{\infty}$ the universal fixed point or the identity of the process $\phi$. other solution of $X \cong \phi(X)$ through $\phi^{\infty}$ in a unique The morphism \phi^{\infty} \to can be seen as the or the fixed point $\phi^{\infty}$ into the fixed point If $X$ is not not be or but it exists and is universal property that $\phi^{\infty}$ the of all of the recursive process. In Alpay’s terms, $\phi^{\infty}$ as the of the a fixed point that every other fixed point in a This is analogous to the least fixed point in a lattice is in (or maps every other fixed point in that of Recursive Fixed illustrate the theory with recursive fixed points in various the functor = 1 on the category is a $\phi$-algebra is \to which provides a point (the of the and a function \to (the on the $X$ $X \cong 1 in yields the result that $X$ must be a infinite set to the natural numbers (with the point corresponding to and the function corresponding to the starting from the initial object and iterating $\phi$: $X_0 = = 1 \cong (a = 1 1 \cong = 1 \cong ... one \cong and the colimit as \to is \cong $\omega$ we have \cong 1 has a point and the is to is a fixed point of $\phi$. 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We that $\phi^{\infty}$ is the smallest solution to $X = \phi(X)$ and that every other solution through its universal Our examples from mathematics numbers as fixed point, as fixed logic fixed point semantics of recursive and (iterative and semantic to stable In each case, the idea of a self-consistent fixed point of a recursive transformation provides and a on the of recursive fixed points and continuous processes. 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Bharat Bhasker, Patruni Muralidhara Rao, P. Vidhya Saraswathi, S. Gopal Krishna Patro · 8 authors
The Internet of Medical Things (IoMT) sector has advanced rapidly in recent years, and security and privacy are essential considerations in the IoMT due to the extensive scope and implementation of IoMT networks. Machine learning (ML) and blockchain (BC) technologies have dramatically improved the functionalities and services of Healthcare 5.0, giving rise to a new domain termed Smart Healthcare. A proactive healthcare system may prevent long-term harm by recognizing issues early. This would improve patients' quality of life while alleviating their worry and healthcare expenses. The IoMT facilitates several capabilities in information technology, including intelligent and interactive healthcare. Consolidating medical information into a singular repository to train a robust ML model engenders apprehensions around privacy, ownership, and adherence to regulatory standards due to increased concentration. Federated learning (FL) addresses previous challenges using a centralized aggregate server to distribute global learning models. The local participant controls patient data, ensuring data confidentiality and security. Hence, this study proposes the Federated Blockchain-IoT Framework for Sustainable Healthcare Systems (FBCI-SHS) for a secure health monitoring system. Additionally, this paper presents the Intrusion Detection System (IDS) as a tool for healthcare network intrusion detection, allowing doctors to track patients' vitals using medical sensors and anticipate when they could become sick so they can take preventative steps. The suggested system proves that the method is well-suited for medical monitoring. In contrast, the high prediction accuracy for intrusion detection and the high efficiency in disease detection achieved by the proposed FBI-SHS healthcare 5.0 system. The proposed method achieves data privacy and security by 98.73%, intrusion detection efficiency by 97.16%, disease detection accuracy by 96.425, proactive healthcare management by 98.37%, and interoperability by 96.74%.
Ethan Kinory, Kimberly Swanson Church, Sean Stein Smith
ABSTRACT Gartner lists blockchain and other distributed ledger technology as critical components of immersive experience technologies in the emerging tech hype cycle for 2022. Blockchain is a decentralized, distributed database linking records in secure information blocks available for network member review. This proposed learning strategy scaffolds students through blockchain concepts using in-class discussions, current events, short videos, collaborative research tasks, and experiential learning activities. The activities can be introduced in a single class period or a week of instruction to increase student awareness of this disruptive technology. Resources offered also benefit faculty by providing instructional materials for mastering introductory blockchain concepts before working with students. Addressing the growing need for increased awareness of emerging technologies, this learning strategy builds skillsets with blockchain fundamentals.
In order to attain Sustainable Development Goal (SDG) 7 - Access to affordable, reliable, and modern energy for all, and the energy-related SDGs (SDGs 9 and 13), innovative financing mechanisms are needed to attract a range of actors and sources of finance at scale. This paper examines the disruptive potential of fintech on the renewable energy investment model. In particular, it explores how fintechs underpinned by blockchain, crowdfunding, artificial intelligence/machine learning (AI/ML), and decentralized finance (DeFi) can unlock capital access, streamline transactions, and build transparency in clean energy financing ecosystems. Drawing on an integrative review approach and complemented by country case studies from Nigeria, Kenya, and India, the article highlights patterns of how fintech apps facilitate access to inclusive, distributed, and ESG-compliant renewable energy solutions. Key findings indicate that fintech significantly widens access to energy finance and fosters local stakeholders, but regulation, cybersecurity, and digital exclusion present scaling challenges. The paper is rooted in Financial Intermediation Theory and Sustainable Investment Theory, providing a conceptual model to explore how digital innovations and policy environments interact with sustainable energy outcomes. It concludes with policy suggestions for developing enabling regulatory frameworks, strengthening digital infrastructure, and promoting cross-sector collaboration to scale up fintech-facilitated energy transitions. This study contributes to the growing body of literature on digital sustainability and offers practical guidance for policymakers and other stakeholders on connecting financial innovation with global clean energy objectives.
P. Preethy Jemima, P. Privietha, Sylvia Grace J, Srideivanai Nagarajan · 5 authors
Smart contracts, which are implemented on decentralized blockchain systems to provide transparency, security, and immutability, are self-executing contracts with terms directly encoded into software. By removing middlemen and increasing efficiency and trust, these contracts automatically carry out predetermined activities once criteria are satisfied. Finance, supply chain management, real estate, and gaming are among the key uses. Notwithstanding their potential, smart contracts have some serious drawbacks, the most significant of which being security flaws. Incidents like the DAO hack on Ethereum provide as examples of how bugs, re-entrancy attacks, and unrestricted external calls have resulted in large financial losses. Widespread use requires addressing these issues. Developers should do thorough testing, including unit, integration, and edge case tests, and adhere to published recommendations such as Ethereum Smart Contract Security Best Practices in order to address security vulnerabilities in smart contracts. Thorough audits of both internal and external code are crucial, as are post-audit corrections. While proper management of external interactions, such as avoiding external calls and validating return values, lowers risks, security tools like Certora, MythX, and Slither can assist in identifying vulnerabilities. Security is further improved by employing multi-signature wallets for high-stakes transactions, using Checks-Effects-Interactions patterns and mutex locks to mitigate reentrancy attacks, and using Flashbots to stop transaction front-running. Additional protections include fallback procedures for recovering from unforeseen failures, monitoring solutions, and reusable contracts for emergency halts. When combined, these steps provide a strong foundation for risk reduction, enhanced security, and guaranteeing the dependability of smart contracts in practical implementations.
The metaverse is reshaping media industries by providing immersive 3D environments that challenge traditional communication models. This study investigates virtual spaces created by three major media outlets in Portugal: RFM (radio station), TVI (television channel), and Expresso (newspaper). Using virtual ethnographic methods, this study explores how these media brands represent themselves in the metaverse, identifying their differential attributes in terms of content variety, interactive features, and monetisation opportunities. While RFM primarily seeks platform expansion, TVI and Expresso utilise the metaverse as commemorative environments to mark their anniversaries, resulting in distinct experiential approaches. RFM reinforces its identity oriented towards entertainment and youth through gamification and avatar-based engagement mechanisms, including challenges, contests, and a points-based reward system. TVI diverges most from its traditional identity, emphasising innovation with a futuristic cosmic-themed space featuring non-fungible tokens (NFTs) of iconic broadcast pieces. Expresso adopts a more conservative approach, using the metaverse to support journalistic heritage through historical storytelling and new interactive formats. The findings indicate that, despite the participatory potential of the metaverse, Portuguese media outlets are choosing to maintain editorial control over content and user interactions. Ultimately, the research shows that the metaverse is not a one-size-fits-all solution, but a diverse and evolving environment where media brands promote different immersive experiences to position themselves as innovators and leaders in rapidly evolving digital ecosystems.
Zeyad Ghaleb Al-Mekhlaf, Murtaja Ali Saare, Jalal Mohammed Hachim Altmemi, Mahmood A. Al-Shareeda · 9 authors
The rapid adoption of Internet of Medical Things (IoMT) devices enables real-time patient monitoring and remote diagnostics and has revolutionized healthcare delivery. Traditional cryptographic schemes like RSA and ECC, which rely on meaningful mathematical challenges, are under great threat from quantum computing, threatening sensitive medical data confidentiality and integrity. This paper proposes a quantum-resistant healthcare security framework based on lattice-based cryptographic primitives such as Learning With Errors (LWE), Ring-LWE (RLWE), and Short Integer Solution (SIS). To this end, we design a five-phase IoMT-friendly framework—Initialization, Registration, Authentication, Data Exchange, and Treatment—where each phase is backed up by lightweight cryptography primitives that can be easily implemented on the low-resource IoMT devices. Relative to the state-of-the-art lattice- and hash-based constructions, our framework involves 50-75% smaller ciphertext sizes, up to a 50% reduction of the communication overhead, and nearly 60% less in computational cost. Furthermore, the solution relies on zero-knowledge proofs, homomorphic encryption as well and attribute-based access control to guarantee strong security and privacy. Using the AVISPA tool, the framework is formally verified, showing its resistance against classical and quantum adversaries. Focusing on tangible healthcare threats, including data tampering and unlicensed access to patient diagnostics, this research paves the way for scalable, efficient, and quantum-resistant medical data protection. Our results pave the way for future investigations into secure post-quantum healthcare and IoT applications.
This study examined the dynamic interconnectedness and portfolio implications within the cryptocurrency ecosystem, focusing on five representative digital assets across the core functional categories: Layer 1 cryptocurrencies (Bitcoin (BTC) and Ethereum (ETH)), decentralized finance (Uniswap (UNI)), stablecoins (Dai), and crypto infrastructure tokens (Maker (MKR)). Using the Extended Joint Connectedness Approach within a Time-Varying Parameter VAR framework, the analysis captured time-varying spillovers of return shocks and revealed a heterogeneous structure of systemic roles. Stablecoins consistently acted as net absorbers of shocks, reinforcing their defensive profile, while governance tokens, such as MKR, emerged as persistent net transmitters of systemic risk. Foundational assets like BTC and ETH predominantly absorbed shocks, contrary to their perceived dominance. These systemic roles were further translated into portfolio design, where connectedness-aware strategies, particularly the Minimum Connectedness Portfolio, demonstrated superior performance relative to traditional variance-based allocations, delivering enhanced risk-adjusted returns and resilience during stress periods. By linking return-based systemic interdependencies with practical asset allocation, the study offers a unified framework for understanding and managing crypto network risk. The findings carry practical relevance for portfolio managers, algorithmic strategy developers, and policymakers concerned with financial stability in digital asset markets.
Integrating blockchain into healthcare devices offers the potential for improved data control but faces significant usability and acceptance challenges. This study addresses this gap by evaluating CipherPal, an improved blockchain-enabled Smart Fidget Toy prototype, using a multi-framework approach to understand the interplay between technology, design, and user experience. We synthesized insights from three complementary frameworks: an expert review assessing adherence to Web3 Design Guidelines, a User Acceptance Toolkit assessment with professionals based on UTAUT2, and an extended three-day user testing study. The findings revealed that users valued CipherPal’s satisfying tactile interaction and perceived benefits for well-being, such as stress relief. However, significant usability barriers emerged, primarily related to challenging device–application connectivity and data synchronization. The multi-framework approach proved valuable in revealing these core tensions. While the device was conceptually accepted, the blockchain integration added significant interaction friction that overshadowed its potential benefits during the study. This research underscores the critical need for user-centered design in health-related blockchain applications, emphasizing that seamless usability and abstracting technical complexity are paramount for adoption.
Zero-Knowledge Proofs (ZKPs) are critical for privacy-preserving techniques and verifiable computation. Many ZKP protocols rely on key kernels such as the SumCheck protocol and Merkle Tree commitments to enable their key security properties. These kernels exhibit balanced binary tree computational patterns, which enable efficient hardware acceleration. Although prior work has investigated accelerating these kernels as part of an overarching ZKP protocol, exploiting this common tree pattern remains relatively underexplored. We conduct a systematic evaluation of these tree-based workloads under different traversal strategies, analyzing performance on multi-threaded CPUs and the Multifunction Tree Unit (MTU) hardware accelerator. We introduce a hardware-friendly Hybrid Traversal for binary tree that improves parallelism and scalability while significantly reducing memory traffic on hardware. Our results show that MTU achieves up to $1478\times$ speedup over CPU at DDR-level bandwidth and that our hybrid traversal outperforms breadth-first search by up to $3\times$. These findings offer practical guidance for designing efficient hardware accelerators for ZKP workloads with binary tree structures.
The proper design and architecture of testing machine learning models, especially in their application to quantitative finance problems, is crucial. The most important aspect of this process is selecting an adequate loss function for training, validation, estimation purposes, and hyperparameter tuning. Therefore, in this research, through empirical experiments on equity and cryptocurrency assets, we apply the Mean Absolute Directional Loss (MADL) function, which is more adequate for optimizing forecast-generating models used in algorithmic investment strategies. The MADL function results are compared between Transformer and LSTM models, and we show that in almost every case, Transformer results are significantly better than those obtained with LSTM.
Blockchain systems have been a part of mainstream academic research, and a hot topic at that. It has spread to almost every subfield in the computer science literature, as well as economics and finance. Especially in a world where digital trust is much sought for, blockchains offer a rich variety of desired properties, such as immutability, public auditing, decentralised record keeping, among others. Not only has it been a research topic of its own, the integration of blockchains into other systems has been proposed as solutions in many areas, ranging from grid computing, cloud and fog computing, to internet of things, self driving vehicles , and smart cities. In many cases the primary function attributed to blockchains in these contexts is resource management. Although much attention is paid to this topic, the focus is on single resource allocation scenarios. Even the cases where multiple resource types are to be allocated, are treated as single resource type scenarios, and problems are formulated as allocating standardised bundles consisting of a fixed amount of each of them, such as virtual machines. The present study addresses the problem of allocating multiple resource types among tasks with heterogeneous resource demands with a smart contract adaptation of Precomputed Dominant Resource Fairness; an algorithm that approximates Dominant Resource Fairness, without loop iterations, which makes it preferable in the blockchain context because of the block gas limit. We present the resulting algorithm, Autonomous Dominant Resource Fairness, along with the empirical data collected from the tests run on the algorithm. The results show that Autonomous Dominant Resource Fairness is a gas-cost efficient algorithm, which can be used to manage hundreds of resource types for unlimited number of users.
The rise of decentralized finance (DeFi) has created a growing demand for accurate yield and performance forecasting to guide liquidity allocation strategies. In this study, we benchmark six models, XGBoost, Random Forest, LSTM, Transformer, quantum neural networks (QNN), and quantum support vector machines with quantum feature maps (QSVM-QNN), on one year of historical data from 28 Curve Finance pools. We evaluate model performance on test MAE, RMSE, and directional accuracy. Our results show that classical ensemble models, particularly XGBoost and Random Forest, consistently outperform both deep learning and quantum models. XGBoost achieves the highest directional accuracy (71.57%) with a test MAE of 1.80, while Random Forest attains the lowest test MAE of 1.77 and 71.36% accuracy. In contrast, quantum models underperform with directional accuracy below 50% and higher errors, highlighting current limitations in applying quantum machine learning to real-world DeFi time series data. This work offers a reproducible benchmark and practical insights into model suitability for DeFi applications, emphasizing the robustness of classical methods over emerging quantum approaches in this domain.
Privacy-Preserving Federated Learning (PPFL) has emerged as a secure distributed Machine Learning (ML) paradigm that aggregates locally trained gradients without exposing raw data. To defend against model poisoning threats, several robustness-enhanced PPFL schemes have been proposed by integrating anomaly detection. Nevertheless, they still face two major challenges: (1) the reliance on heavyweight encryption techniques results in substantial communication and computation overhead; and (2) single-strategy defense mechanisms often fail to provide sufficient robustness against adaptive adversaries. To overcome these challenges, we propose DP2Guard, a lightweight PPFL framework that enhances both privacy and robustness. DP2Guard leverages a lightweight gradient masking mechanism to replace costly cryptographic operations while ensuring the privacy of local gradients. A hybrid defense strategy is proposed, which extracts gradient features using singular value decomposition and cosine similarity, and applies a clustering algorithm to effectively identify malicious gradients. Additionally, DP2Guard adopts a trust score-based adaptive aggregation scheme that adjusts client weights according to historical behavior, while blockchain records aggregated results and trust scores to ensure tamper-proof and auditable training. Extensive experiments conducted on two public datasets demonstrate that DP2Guard effectively defends against four advanced poisoning attacks while ensuring privacy with reduced communication and computation costs.
The rapid evolution of telemedicine has enhanced healthcare accessibility, yet significant challenges persist, particularly in data security, patient engagement, latency, and scalability. Existing telemedicine solutions rely on centralized architectures, making Electronic Health Records (EHRs) susceptible to data breaches and unauthorized access. This research proposes a novel system which integrates the metaverse and blockchain into telemedicine which can be a transformative approach to solve problems in remote healthcare. By combining immersive virtual environments with decentralized data management, the proposed solution described in this paper aims to give users more ways to interact with each other, enhanced data security, increased efficiency, and higher scalability. The Metaverse serves as the foundation for the implementation of 3D consultation rooms, virtual training spaces, and individual care. Blockchain offers safe, transparent, and immutable data exchange that will create patient-empowered medical records for them. Real-time devices and analysis of real-time physiological data from wearables, sensors, Internet of Things (IoT) devices, and Artificial Intelligence (AI) analytics complete the system. The proposed solution extensively uses Virtual Reality (VR)/Augmented Reality (AR) devices, IoT sensors, Ethereum, and the Unity 3D platform, among others. Assessments indicate that system receives a significantly high level of satisfaction from its users, better secured data, increased automation of processes, and compliance with global standards such as General Data Protection Regulation (GDPR). Compliance with such global standards is achieved through smart contract-based access management, smart contract-based consent management, and immutable audit trails in the blockchain. Moreover, this research demonstrates that incorporating high-tech tools like AI and VR into telemedicine is currently feasible. This paves the way for the creation of even more secure and user-friendly telemedicine platforms that employ neural networks. This research sets a foundation for next-generation telemedicine ecosystems.
The proliferation of autonomous systems, from collaborative AI agents to decentralized decision-making units, has introduced a new dimension of machine-to-machine interaction. However, the communication between intelligent agents, especially in critical domains such as cybersecurity, defense, and finance, remains vulnerable to interception, spoofing, impersonation, and logic poisoning. This paper proposes a novel security-first communication framework designed specifically for AI-to-AI interaction. We explore foundational agent communication models, identify key security challenges in inter-agent exchange, and develop a comprehensive architecture embedding authentication, message integrity, encryption, trust verification, and agent self-defense mechanisms. A prototype implementation demonstrates how secure session establishment, encrypted payload exchange, and identity attestation can be achieved using modern cryptographic methods in a distributed agent swarm. Evaluations highlight both the threat landscape and performance implications of adding secure layers to agent dialogues. This work provides a blueprint for designing resilient AI systems that can securely reason, coordinate, and act in untrusted environments.
Type of the article: Research ArticleAbstractThis paper investigates the determinants of local public investment in Morocco, a country undergoing decentralization and facing persistent regional disparities. The study aims to identify the key factors driving capital expenditure across Morocco’s 12 regions and their local governments, including regional, provincial, and municipal councils, from 2017 to 2024. A dynamic panel of 96 observations is constructed, and a generalized method of moments (GMM) estimator is applied to address endogeneity, control for regional fixed effects, and account for the temporal persistence of investment. The choice of GMM is supported by prior descriptive analysis and the absence of spatial autocorrelation, confirmed by Moran’s I test. The results show that financial resources play a central role in shaping regional investment levels. Specifically, both own-source revenues and central government transfers have a positive and statistically significant effect on investment, with elasticities of 0.43 and 1.35, respectively. Public debt also contributes positively (0.21%), suggesting its potential as a complementary financing tool. In contrast, personnel expenditure exerts a crowding-out effect (−0.48%), reducing the fiscal space available for investment. Other operating expenditures and regional population show no significant impact. The model is robust (R² = 0.757) and satisfies the Hansen test (p = 0.095). Overall, the findings highlight the decisive role of financial autonomy and the effectiveness of intergovernmental transfers in enhancing the investment capacity of local governments. The results also call for better management of operating expenses to avoid limiting capital investment potential.
The effect of competitive pressure on ESG may diverge. On the one hand, when competitive pressure increases, firms have incentives to increase moral capital by fulfilling ESG to hedge against risks, on the other hand, the decline in firm performance due to competition may weaken firms' ability to fulfill ESG. Research on this issue has important theoretical and practical significance. Based on data from Chinese listed companies from 2010 to 2022, we used business similarity as a proxy for competitive pressure and find it significantly improves corporate ESG performance, i.e., the risk hedging effect of ESG dominates. Corporate financing constraints negatively moderate this effect. The ability of firms to transfer risk increases as their business becomes more decentralized, which in turn weakens this effect. Conversely, when firms have more concentrated sales, their ability to transfer risk diminishes, amplifying this effect. Our study explores the measure of competitive pressure and business similarity, also expands the research on the impact of business characteristics on the non-economic consequences of firms and ESG motivations.
Amid the growing debate over how cryptocurrencies are reshaping global finance, this study explores the nexus between Bitcoin, Brent Crude Oil, Gold and the U.S. Dollar Index. We used a time-varying vector autoregressive (tvVAR) model to examine the connection among these four assets during the Trump (2017–2020) and Biden (2021–2024) governments. The 48-week return forecast of the Bitcoin–Gold correlation was also conducted by using the Bayesian Structural Time Series (BSTS) model. Results indicate that Bitcoin was the most volatile asset, while the U.S. Dollar remained the least volatile under both regimes. Under Trump, U.S. Dollar significantly influenced Oil and Bitcoin while Bitcoin and Gold were negatively linked to Oil and positively associated with U.S. Dollar. An inverse relationship between Bitcoin and Gold also emerged. Under Biden, Bitcoin, Gold, and U.S. Dollar all significantly affected Oil with Bitcoin showing a positive impact. Bitcoin and Gold remained negatively correlated though not significantly, and the Dollar maintained positive ties with both. Forecasts show a positive link between Bitcoin and Gold in the coming year. However, Bitcoin does not exhibit consistent characteristics of a safe-haven asset during the U.S. presidential transitions examined, largely due to its high volatility and unstable correlations with a traditional safe-haven asset, Gold. This study contributes to the understanding of shifting relationships between digital and traditional assets across political regimes.
Brittany Hagedorn, Jeremy Cooper, Oluwole Odutolu, Ojukwu Mark Ojukwu · 5 authors
Abstract Background The availability of essential medicines and supplies remains a serious impediment to effective primary health care (PHC) in many lower and lower middle-income countries. Most of these countries rely on centralized procurement, centralized stores, and a “push” distribution system. We describe here the impacts of a large-scale randomized trial in Nigeria, which provided modest funding directly to facilities to spend, on supply availability. Methods Districts in three states were randomly allocated to either direct facility financing (DFF) or performance-based financing (PBF) and matched to a control group. Both DFF and PBF transferred funds to facility bank accounts and allowed the facility management committee to spend on operational costs, including essential drugs. Facilities could procure medicines on the government’s essential drug list from pre-approved suppliers if they were certified by the national drug regulator. We conducted a difference-in-difference (DiD) analysis using facility survey data to assess the impact on availability of essential drugs and supplies. Results Drug availability was initially similar for the three arms of the trial (9 of 29 essential medicines). After three years, DFF and PBF facilities had significantly higher product availability than control (p<0.05). This amounted to an increase of 28/ 34 percentage points in DFF/PBF facilities (an additional 8/10 products, respectively), and only 10% in control (3 additional products). We did note that there was little difference between control and intervention arms in the availability of medicines for donor-supported vertical programs like immunization, family planning, and malaria. However, there were very large improvements for products like antibiotics, obstetrical drugs, diagnostics, and TB medications. Conclusion Providing funds directly to health facilities improved drug availability. It was superior to the typical centralized procurement and “push” distribution system that is widespread in lower-income settings. This approach is already spreading and should be adopted more widely.