arXiv subjects

Moses Boudourides

Publications and source records attributed to Moses Boudourides.

13 recordsLinked to original sources

arXiv2026

Collective Hysteresis and Multistability in Threshold Networks

In a mechanistic model of the dawn chorus, Kaye showed that heterogeneous activation thresholds and a shared feedback signal determined by the population's active fraction can produce abrupt collective activation and hysteresis. We extend this mechanism to a network of interacting agents. Each node has a continuous activation level, and a nonnegative row-stochastic matrix determines how node activities contribute to individual feedback. We prove that sufficiently weak feedback yields a unique globally attracting equilibrium. For all feedback strengths, the homogeneous dynamics exactly reproduce Kaye's scalar equation; consequently, network topology does not alter the folds or cusp of the homogeneous branch, and no heterogeneous mode becomes unstable before the homogeneous mode. For equitable partitions, the network admits an exact quotient system in which nodes within a block receive the same aggregate input from every block. When blocks are uncoupled, the quotient reduces to independent copies of Kaye's scalar equation. We show that every assignment of stable scalar equilibria to blocks persists under sufficiently weak interblock coupling, producing a combinatorial family of stable quotient equilibria that lift to stable full-network equilibria and remain under small perturbations that break exact equitability. For two symmetrically coupled blocks, branches with unequal block activities terminate at a pair of symmetry-related cusp bifurcations. Near the onset of bistability, we derive scaling laws for the interblock coupling at which these bifurcations occur, the activity difference between the blocks at bifurcation, and the corresponding shift of the external stimulus from the scalar cusp. Numerical continuation confirms the scaling laws for gamma, logistic, and normal threshold distributions.

cs.SI↗

arXiv2026

Hodge Coercivity and Global Dynamics in Two-Field Edge-Cochain Systems with MHD-Type Cancellation

A finite-dimensional two-field system for divergence-free edge cochains is introduced. Its MHD-type designation refers only to a quadratic exchange pattern and exact total-energy cancellation; it is not a physical MHD discretization. A general cancellation class is separated from a corrected explicit realization: the anticommutator $D(a)J+JD(a)$ is skew-symmetric for diagonal $D(a)$ and skew-symmetric $J$, and its projected bilinear map has the required trilinear antisymmetry. The central result is a Hodge coercivity criterion: the full divergence-free space admits the Poincar\'e-type estimate needed for dissipativity if and only if its harmonic $1$-cochain space is trivial. Under this condition, global existence, an exact energy identity, an absorbing ball, and a compact global attractor follow. When harmonic modes are present, a harmonic-decoupled interaction class yields invariant harmonic affine fibres and fibre-wise attractors. Deterministic disk, annular, and two-hole examples illustrate the spectral criterion, energy law, and distinction between general harmonic exchange and harmonic-fibre invariance.

math.DS↗

arXiv2026

Consensus and Persistent Harmonic Edge Circulation in a Hodge-Theoretic Model of Networked Information Flow

We propose a finite-dimensional cochain model for information flow on an online communication complex. Node variables represent issue positions, while edge variables represent independently modelled signed information flow. The coupling is written in terms of the coboundary operator $d_0$ and the $1$-cochain Hodge Laplacian $\Delta_1=d_0d_0^*+d_1^*d_1$. We prove conservation of the mean opinion, a Lyapunov energy law, and convergence to an equilibrium determined by the initial harmonic projection of the edge flow. In particular, node opinions converge to consensus for every initial condition, whereas the edge flow converges to $P_{\mathcal H^1}u_0$. Thus, trivial first cohomology implies decay of the entire edge-flow variable, while nontrivial first cohomology provides capacity for a nonzero residual circulation only when the initial edge flow has a nonzero harmonic projection. The model therefore establishes that node consensus need not imply decay of an independently represented edge-flow variable; it does not model the formation, reinforcement, or amplification of behavioral echo chambers. We also consider linear damping and a bounded nonlinear saturation as modifications that remove persistent edge flow under the stated assumptions.

cs.SI↗

arXiv2026

LLMs for Qualitative and Mixed-Methods Social Network Analysis

This manuscript explores the integration of Large Language Models (LLMs) into the field of qualitative and mixed-methods social network analysis (SNA). We argue that the primary focus of this integration should be on enhancing the depth and rigor of qualitative SNA, rather than on replacing human researchers with automated systems. We begin by outlining the core principles of qualitative and mixed-methods SNA, emphasizing the importance of understanding the meaning of ties, the role of narratives, and the significance of relational identities. We then discuss how LLMs can be used as powerful tools to augment this work, from assisting with data collection and coding to supporting theory-building and abductive reasoning. We also address the limitations and ethical challenges of using LLMs in this context, including issues of bias, hallucination, and the need for reflexivity. We conclude with a series of research designs and practical recommendations for researchers who want to integrate LLMs into their work in a thoughtful and responsible way.

cs.SI↗

arXiv2026

Missing Links in Public Email and Covert Networks: A Comparative Evaluation of Link Prediction, Hyperlink Prediction, and ERGM Estimation

We study missing-link inference in partially observed networks by systematically comparing dyadic link prediction (LP) with hyperlink prediction (HP) and an estimation-based ERGM comparator. LP serves as the primary baseline, using classical heuristics computed on the observed graph. HP extends this framework by scoring candidate higher-order structures (cliques) via lifted dyadic scores and via the CHEbyshev Spectral HyperlInk pREdictor (CHESHIRE). All methods are evaluated under a common masking protocol that removes dyadic evidence induced by held-out hyperlinks to ensure comparability. Across public email and covert-network datasets, LP remains strong for dyadic recovery, while HP -- particularly CHESHIRE -- provides gains when the inferential target is higher-order group structure. ERGMs offer an interpretable dependence-based complement through conditional tie probabilities. The contribution is a comparative, reproducible evaluation clarifying when LP, HP, and ERGM estimation are most appropriate under network missingness.

cs.SI↗

arXiv2026

A Multi-Source Framework for Relational Validation of Large Language Models Using Expert-Curated Encyclopedic Sources

This paper introduces a novel, multi-source framework for the relational validation of Large Language Models (LLMs). While existing benchmarks have demonstrated LLMs' proficiency at factual recall, their ability to understand and reproduce the intricate web of relationships that defines a domain's conceptual structure remains largely unexplored. Our three-layer analytical framework provides a scalable and robust methodology for assessing the depth of an LLM's knowledge across diverse academic domains. By comparing LLM-generated knowledge graphs to expert-curated encyclopedias, we reveal a consistent and significant ``relational deficit'': LLMs recognize domain-specific concepts but consistently fail to reproduce their relational structure. Our findings highlight the need for more sophisticated evaluation metrics that go beyond simple accuracy and assess the relational integrity of an LLM's knowledge. We demonstrate that this deficit is highly domain-dependent, with performance varying significantly across ten specialized encyclopedias spanning sociology, political science, philosophy, and other fields. The cases of complete relational failure in the most specialized domains are particularly revealing, suggesting that the LLM's internal knowledge representation is not aligned with the conceptual structures of these fields. This has significant implications for the deployment of LLMs in high-stakes applications that require a deep, nuanced understanding of domain-specific knowledge.

cs.SI↗

arXiv2026

Borda Aggregation Dynamics of Preference Orderings on Networks

We introduce and analyze a discrete-time network process in which each node holds a (weak) preference ordering over a finite set of alternatives and updates by local Borda aggregation. At each step, a node forms a weighted average (row-stochastic random-walk normalization) of its neighbors' Borda score vectors and projects the aggregated score back to a weak order. Updates are bounded: in each round, a node advances by at most one step along a shortest path in the fixed graph of preference orderings, following the direction prescribed by its neighbors' Borda-aggregated preferences. Our emphasis is dynamical: we develop sufficient conditions, stated directly in terms of graph topology, weights, and the bounded step rule, for (i) self-sustained oscillations in the absence of persistent sources, and (ii) forced oscillations under contrarian persistent camps. We also record robustness (structural stability) away from score-tie hyperplanes and contrast synchronous (Variant S) and asynchronous (Variant A) updating.

cs.SI↗

arXiv2026

Two-Path Operators, Triadic Decompositions, and Majorized Quotients for Ego-Centered Network Compression

Two-paths (wedges) are the elementary combinatorial objects behind clustering, triadic closure, redundancy, and brokerage. Motivated by a two-path formalism that links Burt's structural holes to node-centered ego networks, we develop an operator viewpoint in which wedge incidence induces a canonical ``two-walk'' matrix and a unique decomposition into an edge--supported (triadic) part and a nonedge-supported (open) part. We then study quotient/contraction constructions designed to compress collections of dominating ego networks together with selected ``traversing'' nodes, and we prove a two--walk transfer theorem under contraction, establishing an inequality with an explicit nonnegative error term and an equality characterization in terms of a wedge--equitable partition. Finally, we illustrate the theory on ten benchmark graphs and their ego-traversing contractions using table-driven diagnostics.

cs.SI↗

arXiv2026

The Algorithmic Blind Spot: Bias, Moral Status, and the Future of Robot Rights

Contemporary debates in AI ethics increasingly foreground the prospective moral status of artificial intelligence and the possibility of extending moral or legal rights to artificial agents. While such discussions raise substantive philosophical questions, they often proceed alongside a comparatively limited engagement with the empirically documented harms generated by algorithmic systems already embedded within social, legal, and economic institutions. We conceptualize this asymmetry as an algorithmic blind spot: a discursive-structural pattern in which disproportionate ethical investment in speculative future artificial agents marginalizes empirically documented and asymmetrically distributed harms affecting human populations. The paper analyzes prominent strands of the robot rights literature and juxtaposes them with empirical evidence of algorithmic bias and harm across domains including employment, criminal justice, surveillance, and facial recognition. It demonstrates how ethical preoccupation with hypothetical future entities can obscure existing injustices, diffuse responsibility, and impede mechanisms of accountability and redress. Without rejecting philosophical inquiry into the moral status of artificial systems, the paper instead emphasizes the importance of ethical prioritization and temporal ordering within AI ethics. Addressing the algorithmic blind spot, we argue, requires re-centering ethical evaluation on human impacts, institutional responsibility, and the governance of algorithmic systems currently in operation. In doing so, the paper introduces a conceptual framework for critically assessing ethical discourse in AI and underscores the need to align ethical reflection more closely with its immediate social consequences.

cs.CY↗

arXiv2026

From Line Knowledge Digraphs to Sheaf Semantics: A Categorical Framework for Knowledge Graphs

This paper proposes a categorical framework for knowledge graphs linking combinatorial graph structure with topos-theoretic semantics. Knowledge graphs are represented as labelled directed multigraphs and analysed through incidence matrices and line knowledge digraph constructions. The graph induces a free category whose morphisms correspond to relational paths. To model context-dependent meaning, a Grothendieck topology is defined on the free category generated by the graph leading to a topos of sheaves that supports local-to-global semantic reasoning. The framework connects graph-theoretic structure, categorical composition, and sheaf semantics in a unified mathematical model for contextual relational reasoning.

cs.SI↗

arXiv2026

Structural Hallucination in Large Language Models: A Network-Based Evaluation of Knowledge Organization and Citation Integrity

Large Language Models (LLMs) increasingly mediate access to scholarly information, yet their outputs are typically evaluated at the level of individual statements rather than knowledge structure. This paper introduces structural hallucination: systematic distortion of conceptual organization, relational architecture, and bibliographic grounding that remains invisible to sentence-level accuracy metrics. To detect such distortions, we develop a network-based hallucination stress test grounded in knowledge graph extraction, graph similarity analysis, centrality comparison, and citation integrity verification. The protocol is applied to three structured domains representing core forms of scholarly knowledge: Roget's Thesaurus (1911) as a historical knowledge organization system; Wikidata philosophers as a biographical knowledge graph; and bibliographic citation records retrieved from the Dimensions.ai database. Across all domains, substantial structural divergence is observed. In the lexical benchmark, macro-averaged F1 scores fall below 0.05; in the biographical benchmark, hallucination rates exceed 93%; and in the bibliometric benchmark, citation omission reaches 91.9%. Network-level comparison in the Roget reconstruction further reveals node-set Jaccard similarity of 0.028 and source-mismatch rates above 94%. These findings show that structural fidelity cannot be inferred from local fluency alone. The proposed stress test provides a reproducible instrument for evaluating the structural integrity of LLM-generated knowledge representations within knowledge organization and information quality research.

cs.SI↗

arXiv2026

Boundary-Value Friedkin-Johnsen Dynamics and Influence-Based Centralities on Networks

Understanding which nodes are most able to transmit or receive influence is a central problem in networked opinion dynamics, yet topology-only centrality measures do not account for heterogeneous susceptibility to social influence. We study source-specific, susceptibility-dependent influence in the Friedkin-Johnsen model on directed weighted networks. By treating fully stubborn agents as boundary nodes and the remaining agents as interior nodes, we formulate the dynamics as a discrete boundary-value problem. This formulation yields a Green operator and an all-source steady-state response matrix that quantify how a fixed opinion at each source propagates to every target. Building on this response matrix, we define influence-based broadcasting and reception measures that distinguish structural position from model-implied influence. We establish conditions for existence and uniqueness of the steady state, derive transient and steady-state representations, and characterize sensitivity to susceptibility parameters and perturbations of the influence network. For the undirected homogeneous-susceptibility specialization, we also provide a corresponding spectral analysis. Computational experiments on benchmark networks illustrate how heterogeneous susceptibility profiles shape response-based rankings and how these rankings differ from topology-only centralities. The framework provides a basis for studying influence propagation, source selection, and susceptibility-aware network intervention.

cs.SI↗

arXiv2026

Interior--Boundary Assortativity Profiles on Networks and Applications to SIS Epidemic Dynamics

We introduce interior-boundary assortativity profiles as a structural refinement of Newman's assortativity coefficient and show that they arise naturally from epidemic dynamics on networks. Given a fixed partition of the node set, edges are stratified according to whether their endpoints are interior or boundary nodes relative to the partition, yielding type-restricted assortativity components. We prove an exact decomposition theorem showing how classical scalar assortativity collapses heterogeneous interior-boundary interactions into a single number. We then study a SIS epidemic model and consider equilibrium infection probabilities as node attributes. Under mild connectivity and positivity assumptions, we show that boundary dominance (a dynamical concentration of infection mass on interface nodes) implies a strictly negative boundary-to-interior assortativity component. This establishes a rigorous link between directed conductance, equilibrium flow geometry, and the sign structure of assortative mixing induced by the dynamics. Our results demonstrate that assortativity profiles encode dynamical information invisible to scalar summaries and provide a mathematically grounded bridge between network partition geometry and nonlinear dynamics on graphs.

cs.SI↗