Safe set computation is a fundamental challenge in safety-critical control systems, especially in direct data-driven settings where safety analysis is performed directly from noise-affected measurements, without explicit modeling. A recently proposed method, Data-Driven Hamiltonian (DDH), enables reachability analysis directly from measurements, without relying on prior knowledge of the underlying system dynamics. This paper extends the DDH framework to a robust setting that accounts for measurement noise, exogenous disturbances, and sampling-induced state-velocity estimation error. A Robust Data-Driven Hamiltonian (R-DDH) is derived from noisy measurements and shown to yield a certified lower bound on the exact Hamiltonian. This results in a provable under-approximation of the value function and an inner approximation of the associated safe set. The gap between the data-driven and exact Hamiltonians is quantified, and it is shown to converge to zero with more data in a noise-free setting with additive disturbances. The effectiveness of the approach is shown through two case studies: a constrained double integrator and an aircraft taxiing system with a nonlinear closed-loop controller operating under perceptual uncertainty.

This paper presents STORX: Shape and Topology Optimization for Research and Experimentation, an open-source MATLAB-based educational framework for learning and teaching computational design optimization. STORX provides a platform for parametric and level-set shape optimization, as well as topology optimization methods including density, level-set, and topological sensitivity approaches such as evolutionary and Pareto-tracing methods. All modules follow a consistent object-oriented structure and integrate visualization, sensitivity analysis, and finite element routines, enabling users to explore the continuum between shape and topology optimization in a transparent and reproducible manner. The code is designed to complement graduate-level coursework and independent research by emphasizing modularity and extensibility through a clear separation of intent. Core software interfaces are defined via abstract base classes, enabling new objective functionals and design/manufacturing constraints to be implemented by adding derived classes without modifying the core code. The paper also describes the software architecture and demonstrates how the framework maps mathematical formulations directly to executable code through a series of illustrative problems.

We start from a small open question, where Hetzl and Vierling asked whether two theories of induction, open induction and clause set cycles, are incomparable. They proved one direction and left the other open. Here we close it, and the proof is almost embarrassingly short, because the rules for addition can only fire when the first argument is $0$ or a successor, a Skolem constant is neither, so the terms $a{+}b$ and $b{+}a$ can never be touched, and a machine that can never touch them can never prove they are equal. The thing that separates the two theories is the order of two constants, and that order is a fact about numbers, not about symbols. We extract from this proof a small general principle, the Syntactic Invariance Principle, that names the shape of such arguments. We then close with a few speculative remarks on how this same shape appears, informally, in the known barriers to settling $\mathsf{P}$ versus $\mathsf{NP}$, where each barrier seems to point to a level of description that the techniques in the barrier cannot reach. We raise this as a suggestion rather than a theorem, since the analogy is real but we do not push it past the point where we can defend it. Along the way we raise an open question that the analogy suggests but does not settle, on whether a fast algorithm for $\SAT$, were it to exist, would always be exhibitable as a machine you can write down or whether it could be found, in some cases, only as a function on the numbers.

In the perpetual pursuit of performance, modern computing systems rely ever more on stateful mechanisms to accommodate the dynamics of workloads and physical environments, bolstering efficiency but confounding benchmarking and thereby the optimization of software. Indeed, by their nature, adaptive mechanisms introduce temporal dependencies between measurements and render naive estimators of individual program performance biased. Observing that rectifying such biases necessitates speculative assumptions about system dynamics, we call for prioritizing performance differentials over absolute measures and formalize software benchmarking as the decision problem of identifying the fastest program, for which relative knowledge suffices. To this end, we propose simple experiment designs admitting consistent estimators of contrasts, whereby program-specific biases cancel under tenable assumptions. These designs asymptotically yield the correct decision and afford a robust methodology for finite-budget benchmarking in stateful environments, bearing broad implications for the development of performance-sensitive software.

Large Language Models and vision-language models have shown remarkable success in the front-end design of Very Large-Scale Integrated Circuits, yet their capabilities for VLSI physical design remain significantly underexplored. The primary cause is the lack of standardized benchmarks for evaluating agentic physical design workflows that require high-dimensional, multi-stage optimization under strict design constraints, coordinated interaction with diverse Electronic Design Automation tools, and iterative refinement. This work introduces PDAGENT-BENCH, a comprehensive and multi-dimensional benchmark for evaluating LLM/VLM-based agents across the physical design stack. PDAGENT-BENCH integrates both task-level assessment and workflow-level execution. The benchmark suite contains 353 curated problems that combine conceptual questions with real-world industrial artifacts, with expert-validated references and executable solutions. These tasks cover five key capability dimensions: foundational knowledge, report comprehension, root-cause analysis, script generation, and full-flow implementation. In addition, the benchmark provides a unified, human-aligned agentic physical design workflow framework that enables closed-loop evaluation of holistic physical design in realistic EDA environments. Experiments on 11 state-of-the-art models reveal that while modern LLMs/VLMs perform competitively on conceptual tasks, they remain substantially limited in tool-centric execution (e.g., 42.2% on Innovus script generation) and long-horizon, multi-stage reasoning. Our studies further show that human-skill-enhanced agentic workflows significantly improve end-to-end physical design performance. PDAGENT-BENCH establishes a standardized, reproducible, and realistic evaluation framework for advancing LLM/VLM-driven holistic physical design automation. We will open source the benchmark and framework soon.

Internet blackouts, occurring due to technological mishaps or intentional governmental action, prevent citizens from accessing the internet. Citizens in regions where internet blackouts are common have utilized blackout-resistant technologies to maintain communication. Such technologies often rely on mobile mesh networks to provide limited messaging services. However, no technology currently exists which can provide continued access to knowledge sources on the web during a blackout. We present Cache to the Future (CttF): a system to cache and deliver static content hosted on the web during a blackout. CttF's distributed community ratings crowdsources caching at scale while cryptographic constructs (digital signatures, proofs-of-work) mitigate adversarial interference. Our realistic simulations demonstrate CttF delivering content at city-scale across a wide range of benign and adversarial scenarios.

This paper develops a compact collecting semantics for the residual behaviour left by nonterminating computation. For sequential time this is the tail-cluster set of the stream in the Stone-Cech compactification of the observation space. It gives a common semantics to ordinary recurrence, mixed recurrent behaviour, and escape through noncompact parts of the observation space. The basic theory establishes tail invariance, functoriality under continuous observations, and a temporal reading for clopen observations: containment in the corresponding clopen region of beta-X is eventual truth, while nonempty intersection is recurrence. Progress and fairness assumptions are represented by strengthening the time filter. Relational meanings are obtained by compactifying products, so correlations between observations made along the same asymptotic view of time are retained. The main application is to residual behaviour in CCS. Infinite executions are read as streams of residual processes modulo structural congruence. The resulting semantics distinguishes stable divergence, finite recurrent divergence, mixed recurrence with escape, and escape through unbounded residual growth. It validates residual-tail laws for prefixing, guarded unfolding, finite choice, and finite prefix-choice forms, while also identifying the boundary of those laws under parallel composition and synchronisation. Finite observational quotients provide the computational interface to the compact semantics: abstract meanings become recurrent states and strongly connected component calculations, and resource observations detect unbounded escape without requiring individual points of the Stone-Cech remainder to be inspected.

Neuro-symbolic AI (NeSy) pairs neural perception with symbolic reasoning, making it attractive for high-stakes domains where explainability and structured inference are required. However, this hybrid architecture introduces an enlarged attack surface spanning five layers: neural perception, symbolic knowledge bases, reasoning engines, agentic orchestration, and data stores -- each exploitable in ways absent from purely neural systems. This paper makes six contributions: (1) formal definitions of NeSy Attack Surface, Symbolic Integrity Violation (SIV), and Cross-Layer Amplification Ratio $\mathcal{X}$, decomposed into neural-caused and autonomous symbolic sensitivity components; (2) a unified threat model extending MITRE ATLAS with 11 NeSy-specific tactic extensions and a five-profile attacker taxonomy; (3) a symbolic-layer threat catalogue covering knowledge graph (KG) poisoning, ontology-merging, and inference-engine subversion; (4) analysis of cognitive risks -- automation bias, authority bias, and sycophantic reinforcement -- structurally amplified by NeSy's explicit logical explanations relative to black-box neural outputs; (5) interdisciplinary mitigations with measurable acceptance criteria aligned to NIST AI 600-1 and the EU AI Act; (6) three empirical benchmarks: (E1) targeted KG poisoning achieves break-even SIV at injection budget $B=5$ on a 205-entity medical KG, with a KG-specific stealth/SIV trade-off; (E2) PGD-10 at $\varepsilon=0.01$ yields $\mathcal{X}=5.884$ (95% CI $[4.64,\, 8.00]$, $p<0.0001$), confirmed adversarially specific by a matched-random baseline ($E^{R}_{\mathrm{rand}}=0$), on a DistilBERT+ProbLog pipeline; (E3) single-axiom OWL edits achieve 93.3% SIV success with 100% Pellet-consistency stealth, but held-out STIX detection fails at 50% (random-guessing level), an open problem.

This paper develops and analyses the Fair Play Automatic Market Maker (FP-AMM), a programmable electricity allocation mechanism in which scarcity allocation is treated as a controlled, stateful, and auditable cyber-physical process. Existing mechanisms such as locational marginal pricing are memoryless and cannot account for historical service outcomes, preventing guarantees of equitable treatment across market intervals. The FP-AMM employs a two-stage stochastic clearing rule comprising service-priority sampling and inverse-fairness weighting, coupled with a DC-OPF feasibility set and bounded shortage memory updated through a saturated integrator. Four main results are established. First, the shortage-memory state is invariant in $[0,1]^N$ and the update map is a contraction with rate $1-β$. Second, the intra-interval clearing operator converges linearly to a unique fixed point with contraction factor $q\in(0,1)$. Third, under the Fair Play priority rule, the per-node delivery ratio converges almost surely to the contracted target $F^\star$, with a finite-time $O(1/\sqrt{T})$ bound obtained via Lyapunov analysis of the deficit recursion. Fourth, event-triggered execution guarantees practical ultimate boundedness of the allocation tracking error and quantifies the computation-fidelity trade-off. The mechanism is validated on the IEEE 14-, 57-, and 118-bus systems over $T=5000$ market intervals. Fairness convergence to $F^\star$ is achieved on all benchmarks, peak weak-bus fairness error is reduced by 54% on the IEEE-57 network and by up to 55% relative to an equal-weight baseline during scarcity periods, and DC feasibility is maintained throughout.

Dynamic Gaussian compression is normally optimized for complete files or complete progressive prefixes, but interactive rendering encounters partial representations: some spatiotemporal regions are present, others missing, and late refinements cannot affect the displayed frame. We study dynamic Gaussian representations whose incomplete delivery states remain directly renderable and whose degradation is optimized in image space. Gaussian primitives are organized into independently addressable spatiotemporal clusters with a base level and three refinements; training samples partial dependency graphs, renders many counterfactual states in one GPU batch, and minimizes expected distortion, tail distortion, temporal inconsistency, rate, and prefix regressions. A counterfactual utility layer measures the marginal render contribution of each completion group across valid receiver contexts. The same graph admits a concrete delivery realization with MTU-bounded entropy-coded chunks, deadline-aware scheduling, and receiver-side dependency closure. On held-out views, the finest refinement has negative mean marginal utility in 3/32 D-NeRF bouncingballs, 49/64 HyperNeRF broom2, and 28/64 HyperNeRF chicken clusters; its lower-tail utility is negative in 21/32, 61/64, and 42/64 clusters, respectively. On broom2, render-utility ordering removes both PSNR regressions produced by nominal layer order at matched byte budgets; on chicken, utilities measured on disjoint training cameras improve held-out PSNR by 3.03 dB at the lowest matched budget. These scoped results show why nominal refinement order cannot substitute for render-conditioned utility: the formulation treats network delivery as a distribution over renderable scene states rather than as an external wrapper around a graphics codec.

Because of their ability to enable new forms of cryptanalysis, quantum computers pose a threat to the cryptographic algorithms that are widely used to secure contemporary computer systems. A practical quantum computer may emerge within the next ten years or so, but due to theorised "harvest now, decrypt later" style attacker behaviour, mitigations are necessary today. Recent advances in cryptography and security architecture show promise in supporting the design of systems that exhibit resilience against quantum-enabled cryptanalysis, however there is a key gap in the literature around the subject of deriving tolerances for such systems. In this paper, we introduce the concept of rotation time as a measure of crypto agility, and derive an approximation that links rotation time tolerance to security risk tolerance. Historical CVE data is used to calculate illustrative values for rotation time tolerance, which is found to be of the order of hours to days. This demonstrates that using crypto agility in conjunction with hybrid encryption is an effective approach for designing quantum-resilient systems, but may necessitate challenging technical and operational tolerances in order to meet organisational risk tolerances.

Modern blockchain state management faces a critical scalability bottleneck: maintaining cryptographic commitments over hundreds of millions of entries becomes computationally prohibitive. Ethereum's transition to Verkle Trees: polynomial commitment accumulators reducing proof sizes from O(width * depth) to O(depth) via constant-size IPA vector commitments, is a critical step toward stateless operation. Yet, current implementations exhibit pathological characteristics that burden home validators. We identify four inefficiencies in the reference go-verkle implementation \cite{kaur2025goverkle, kaur2025goethereum}: (1) phantom node creation during non-existent account deletion; (2) 64-byte database keys triggering excessive LSM-tree compaction; (3) redundant memory copying in proof deserialization; (4) a Proof of Absence wire format incompatibility causing non-deterministic serialization. We present Fractional Verkle Trees (FVT), a hypertree decomposition partitioning global state into N independent sub-accumulators coordinated by a Merkle commitment tree, achieving improved cache locality, zero-lock-contention goroutine-parallel commitment computation, and faster root recomputation (91 $μ$s vs $\sim$500 ms). We address each inefficiency via existence checks, 32-byte SHA256 node references, zero-copy reference-counted buffers, and HashMap-based lexicographic deduplication. Benchmarks on Apple M1 Pro show 57\% heap allocation reduction (566,760 to 242,004 bytes per 10K proofs), parallel insertion at 2,433 ns/op, and network-wide elimination of 4.85 PB/year across 6,000 full nodes, advancing the Ethereum stateless roadmap.

This position paper examines a paradox encountered in UX research practice: a situation where real human participants delivered less authentic insights than AI personas might have, due to context-induced biases. We share our experience developing research-based AI personas using OpenAI's custom GPT builder and conducting a design thinking workshop with high-net-worth banking clients. The workshop setting, including a luxury hotel, present portfolio managers, and hospitality dynamics, introduced biases that compromised the feedback. We propose that AI personas offer an underexplored opportunity to mitigate certain human limitations in user research, and call for frameworks that help teams recognize when traditional research contexts introduce biases that AI personas might help avoid.

Logs record the runtime behavior of software and are widely used in various tasks such as debugging, testing, and fault diagnosis. With the increase in system size and complexity, log analysis has gradually become a challenging task. Current industrial systems typically use log aggregation systems such as Grafana Loki and ELK to simplify the log collection and analysis process. Engineers write queries using the DSL query language provided by these systems can complete a variety of log analysis tasks. However, writing these queries is often time-consuming and labor-intensive, as it requires engineers to have a thorough understanding of the DSL syntax and the detailed information contained in the logs. To address these challenges, this paper proposes LogCopilot, an automated log aggregation analysis framework based on large language models (LLMs). LogCopilot accepts natural language log analysis instructions and accomplishes automated log analysis through knowledge retrieval and tool calling. LogCopilot constructs a hierarchical knowledge base to represent and provide key knowledge in logs. And it achieves automated log aggregation analysis by generating and executing LogQL queries. The evaluation based on four log datasets confirm the effectiveness of LogCopilot, which achieves an average accuracy of 76.8% and outperforms baseline approaches. Moreover, experiment results shows that LogCopilot is effective in LogQL query generation.

Building automation and control systems integrate heating, ventilation, air conditioning, lighting, sensing, and management functions through specialized communication protocols. While this integration enables flexible building operation, it also creates complex cyber-physical environments that are difficult to inspect, secure, and explain to new analysts. This paper presents a practical security and human-centered case study of a BACnet/IP building automation testbed with DALI lighting infrastructure, investigated during a domotics-oriented cybersecurity hackathon in Thun, Switzerland in April 2026. The study combines network-oriented enumeration, object-level inspection, physical rack analysis, and reflective HCI analysis of tool-supported learning. Using Yabe and BACteria, the work documents observable BACnet services, reconstructs structured object hierarchies, identifies room-level lighting-control paths, and maps BACnet objects to DALI group-level infrastructure. The analysis emphasizes that BACS assessment is not only a technical protocol task: it also requires usable tool interfaces, physical observability, interpretable naming conventions, and safe mental models for command priorities. The paper contributes a compact case study of BACnet/DALI exploration in an educational testbed and discusses implications for cybersecurity education, human-centered security tooling, and responsible experimentation in cyber-physical building environments.

Large language model (LLM) coding agents are increasingly applied to code translation and optimization, yet their effectiveness in performance-critical high-performance computing (HPC) settings remains poorly characterized. This paper evaluates LLM-based coding workflows on SZ-family error-bounded lossy compression kernels, which combine numerical constraints with memory-intensive and control-flow-heavy implementations. We study two representative CUDA workloads (SZp and SZx) and target two heterogeneous execution platforms: NVIDIA GPUs and Cerebras wafer-scale accelerators. Focusing on single-agent iterative generation, we analyze not only final throughput but also agent runtime behavior, including iteration patterns, sensitivity to prompt specification, and characteristic failure modes. Our results reveal a pronounced cross-architecture divergence. On GPUs, stronger models can achieve substantially higher throughput but exhibit increased sensitivity to prompt precision and optimization guidance, whereas on Cerebras the dominant challenge lies in producing runnable programs under a PE-centric spatial execution model. We further observe that LLM agents are more effective on modular kernels (SZx) than on tightly coupled bit-level pipelines (SZp), where structural dependencies hinder optimization progress. These findings suggest that evaluating LLM coding agents for HPC requires accounting for both performance outcomes and architecture-specific robustness, and that success on thread-based platforms does not directly transfer to spatial accelerators.

We introduce Ergodic Deviation-Robust Equilibrium (EDRE), a dynamics-relative equilibrium concept for repeated finite games in which agents learn via entropic mirror descent (EMD). EDRE requires three properties to hold simultaneously for the same profile and learning run: (E1) the limit profile is an $\varepsilon$-Nash equilibrium at a product distribution; (E2) along the entire learning trajectory, every fixed coalition's cumulative aggregate (summed-unilateral) deviation gain is $\tilde{\mathcal{O}}(\sqrt{T})$ with high probability; and (E3) the limit profile is a fixed point of the EMD map, so that it is selected by the dynamics rather than merely certified as an equilibrium. We prove that the $\sqrt{T}$ deviation-regret rate is order-tight, establish existence in exact-potential games (via Nash's theorem, with a constructive proximal route under concavity) together with Lyapunov monotonicity of EMD (and pointwise convergence when the fixed-point set is a singleton), and extend the selection property to monotone polymatrix games through variational inequalities. Although a static EDRE coincides with an $\varepsilon$-Nash equilibrium, its content is dynamic: robust (positive-measure) selection under EMD excludes linearly unstable equilibria, so EDRE acts as a Nash equilibrium equipped with a dynamic certificate rather than a static refinement. On the complexity side, we show that computing EDRE is PPAD-hard in general polymatrix games and belongs to promise-PPAD for potential games. A worked $2\times 2$ coordination-game example illustrates all components of the framework. Additional results, including a bandit-feedback extension, a period-doubling route to Li-Yorke chaos for the two-strategy EMD map at large step size, a linear-program formulation for minimum-cost steering, and supporting simulations, appear in the appendices.

Channel charting (CC) in real-world coordinates is a recently proposed self-supervised machine learning method that maps high-dimensional channel state information (CSI) to user equipment (UE) position. In this paper, we extend CC to also estimate UE orientation, which can further assist tasks such as beamfinding, precoding, and beam- and cell-assignment. To this end, we propose a novel orientation triplet loss that accounts for angle periodicity and an alignment loss that embeds estimated orientations in real-world coordinates in a self-supervised fashion. Using real-world CSI measurements from a standard-compliant 5G NR system, we demonstrate that the proposed method achieves position and orientation estimation accuracy close to that of supervised approaches trained with ground-truth labels.

Channel state information (CSI)-based neural positioning learns a mapping from CSI measurements to user equipment (UE) positions using neural networks. However, most existing performance evaluations utilize randomly partitioned train/test CSI-dataset splits, which fail to reflect the generalization requirements of practical deployments and present optimistic results. In this paper, we study the spatial and temporal generalization of neural positioning with standard-compliant Wi-Fi and 5G NR systems for three real-world CSI datasets acquired in indoor and outdoor environments. We assess generalization with two different architectures, a conventional multilayer perceptron (MLP) and a novel transformer architecture, to unseen spatial regions, unseen UE trajectories, and CSI measurement campaigns separated by one week. Our experiments show that both architectures generalize well in space and time, and the proposed transformer consistently outperforms the MLP in positioning accuracy while requiring fewer model parameters.

Modern AI systems increasingly solve a task not with a single model call but with several imperfect agents working together: some propose pieces of a solution, others verify them, and the results are combined. These systems often outperform any single model, yet it is rarely clear why they succeed or when they will fail. We model such a system as message passing on a sparse graph, the structure that underlies low-density parity-check (LDPC) codes, and extend the density-evolution machinery of coding theory to this richer setting. In our model a task is a set of coupled binary subclaims, and an agent architecture is a sparse, role-typed factor graph whose check nodes are noisy Boolean verifier nodes, each computing a local Boolean function of the subclaims it touches. Three distinct failure modes, all modeled as erasures (an agent abstaining, a verifier returning no usable output, and a message lost between two agents), propagate as the agents exchange set-valued messages. The check agents combine these messages by a single logical-forcing rule that specializes to XOR, AND, OR, implication, and Horn constraints. This is more than a relabeling of LDPC theory: the verifier functions are nonlinear and value-asymmetric, and the three failure modes do not reduce to a single effective channel, so they require new threshold, finite-length, and converse results rather than a direct reuse of parity-check density evolution. We prove a density-evolution theorem that predicts the asymptotic fraction of unresolved subclaims on random role-typed architectures, with an extension to deterministic, locally tree-like graph sequences. The XOR case recovers the classical LDPC recursion on the binary erasure channel (BEC); the AND case exposes an asymmetry between positive and negative verifier certificates.

Equalization-enhanced phase noise is avoided by applying phase noise compensation (PNC) before chromatic dispersion compensation. Feedforward and iterative PNC algorithms based on expectation propagation are proposed. Both achieve information rates close to channels without phase noise for 100 GBaud 64-QAM and 10,000 km of fiber.

In 1965, Wegner conjectured that every finite family \(\mathcal R\) of axis-parallel rectangles in the plane satisfies \(τ(\mathcal R) \le 2ν(\mathcal R)-1\), where \(τ(\mathcal R)\) denotes the minimum number of points needed to pierce all rectangles in \(\mathcal R\), and \(ν(\mathcal R)\) denotes the maximum size of a pairwise disjoint subfamily. Over the last six decades, the conjecture has motivated a long line of work: it has been verified for several special classes of rectangle families, and the best known general upper bounds have been progressively improved, but the conjecture itself had remained open. We give an explicit counterexample. More precisely, we construct a triangle-free rectangle-intersection graph on \(n\) vertices whose independence number is at most \(n/4\). Since the graph is triangle-free, no point of the plane can lie in three rectangles; hence every piercing point hits at most two rectangles. Consequently, \(τ(\mathcal R) \ge n/2 \ge 2ν(\mathcal R)\), contradicting Wegner's conjectured bound. We also give a slightly more general construction for which \(τ(\mathcal R) \ge 2.21ν(\mathcal R)\). This shows that the standard point relaxation, equivalently the clique relaxation, for the Maximum Independent Set of Rectangles problem has integrality gap at least \(2.21\).

We develop a decision-theoretic framework for distributed Bayesian experimental design in which local agents evaluate candidate experiments using expected information gain and transmit their local design decisions to a fusion center. Unlike centralized Bayesian design, where all likelihood components and information-gain values are available to a single planner, the fusion center in the distributed setting chooses a global experiment from compressed local recommendations. We derive the Bayes-optimal fusion rule, which selects the experiment with largest conditional expected centralized information gain given the observed local design decisions. This rule is analogous in spirit to optimal fusion rules in distributed detection, but differs fundamentally because the underlying utility is expected information gain and the resulting loss is information-gain regret rather than classification error. We also establish information-loss bounds and identify conditions under which the decision-only fusion rule is asymptotically equivalent to the centralized design. Numerical experiments show that Bayes-optimal fusion closely approximates the centralized oracle, whereas majority voting can be highly suboptimal when a minority of sites carry disproportionate information.

Response-adaptive randomization (RAR) in clinical trials aims to improve ethical and statistical efficiency by dynamically allocating patients to treatments based on observed outcomes. While RAR based on a target optimal allocation have been extensively studied for two-arms settings, their extension to multi-treatment experiments ($K \geq 2$) remains theoretically fragmented, with most existing methods focusing on specific algorithms or restricted target allocations. In this paper, we introduce a unified framework for response-adaptive targeting, the $α$-Rebalancing Targeting Strategies ($α$RTS), which generalize the ERADE two-armed strategy of Hu et al. [2009]. We prove that all designs in this family share fundamental asymptotic properties: strong consistency, asymptotic normality of allocation proportions and treatment effect estimators, and asymptotic efficiency. To address sparse target regimes (where some treatments are asymptotically eliminated), we further propose $α$RTS with Forced Exploration, a variant that guarantees infinite sampling for all treatments while preserving the asymptotic guarantees. Extensive simulations illustrate the finite-sample behavior of $α$RTS variants in a 3-armed context, highlighting in particular the critical role of forced exploration in sparse settings.

Given a simple graph on $n$ vertices and a parameter $k$, the triangle-densest-$k$-subgraph problem is known to be computationally hard in the worst case. To circumvent the computational hardness, we study an average-case model where a triangle-dense subgraph on $k$ vertices is planted in an Erdős-Rényi random graph on $n$ vertices. For the recovery of the planted subgraph, we propose a simple spectral algorithm and a semidefinite program, both of which use a graph matrix whose entries are local signed triangle counts. Theoretical guarantees for these algorithms are established through spectral analysis of the graph matrix. Finally, we provide evidence showing a statistical-to-computational gap analogous to that for the planted clique problem. The computational threshold in terms of the subgraph size $k$ is at least $\sqrt{n}$ in the framework of low-degree polynomial algorithms, while the information-theoretic threshold is at most logarithmic in $n$.

Mediation analysis is essential for decomposing the causal effect of a treatment into direct and indirect pathways. However, many practical settings rely on the stringent assumption that recanting witnesses, defined as treatment-induced mediator-outcome confounders, are either absent or fully known a priori. Such a requirement is often untenable, especially when these variables remain unobservable due to measurement difficulties or privacy constraints. In this paper, we leverage proximal causal inference to develop three novel identification strategies to address the challenge of identifying path-specific effects in the presence of unknown recanting witnesses. Building on this, we develop a semiparametric inference framework that derives the efficient influence function and proposes a proximal multiply robust estimator, which remains consistent if at least one set of nuisance models is correctly specified. When all nuisance models are correctly specified and converge at appropriate rates, the estimator is asymptotically normal and achieves the semiparametric efficiency bound. We provide a minimax optimization-based debiased machine learning procedure for point estimation and constructing valid confidence intervals. The performance of the proposed methods is demonstrated by simulation studies and a real data application.

This paper considers the problem of a low-thrust spacecraft pursuit-evasion differential game with an arbitrary terminal relative speed constraint. It addresses the terminal phase of the engagement for two relatively close spacecraft near a circular orbit. The problem is formulated as a linear-quadratic zero-sum differential game, with soft constraints on the terminal relative position and velocity, and running costs on the players' control efforts. An analytical, closed-loop, minimum-fuel-consumption optimal guidance law is derived for each player, forming a saddle-point solution. It is proven that any terminal speed can be achieved by properly choosing the weighting parameters of the cost function. To verify the optimality of the solution, a conjugate point analysis is performed when the cost function velocity weighting matrix is either positive or negative definite. The negative-definite case arises at high terminal speeds and is seldom seen in the literature. The performance of the derived guidance law is evaluated in simulations for different target maneuvers and compared to a state-of-the-art optimal-control-based guidance law. The simulations show that the derived guidance law satisfies the constraints and offers a substantial advantage over the optimal-control-based guidance law when the target is optimally evading.

Prey aggregation is widely regarded as a defense against predation, yet we show that in disease-structured populations subject to predator-induced fear and demographic Allee thresholds, aggregation can paradoxically accelerate ecosystem collapse. We develop and analyze a susceptible-infectious-predator model incorporating dual fear responses -- together with a sublinear aggregation-based predation term and an Allee effect. Critically, we derive an explicit upper bound on the extinction time that decreases as predator pressure increases or aggregation strengthens, quantifying for the first time how behavioral and demographic parameters jointly determine the speed of ecological collapse. This finite-time extinction subsequently triggers a cascade collapse of the infected prey and predator populations, driving the entire ecological community to extinction. Bifurcation analysis reveals transcritical, saddle-node, and Hopf bifurcations as fear intensity, aggregation strength, and Allee threshold vary. Two-parameter continuation further identifies the precise regions of the fear--Allee parameter plane in which stable coexistence, oscillatory coexistence, predator exclusion, and finite-time extinction occur, demonstrating that stronger aggregation monotonically enlarges the finite-time extinction region while weaker aggregation supports a richer landscape of coexistence dynamics. These results demonstrate that behavioral defenses operating at the population level can generate abrupt ecological tipping points when they interact with disease dynamics and demographic vulnerability.

Movable antennas (MAs) are a promising technology to improve wireless data rates by dynamically adjusting their positions to avoid deep fading. However, finding the optimal MA positions requires full channel state information (CSI) for all possible locations within the movement region, creating massive channel estimation overhead. This paper proposes a deep neural network (DNN)-based learning framework to predict the optimal positions of multiple transmit MAs in a multi-user multiple-input single-output (MISO) system, entirely bypassing explicit channel estimation.First, we analyze a single-user MISO case, revealing a complex, highly nonlinear mapping between the optimal MA positions and the channel power gains from a specific subset of locations in the transmit region to the user. Because this mapping cannot be mathematically characterized for practical channel models, we train a DNN via supervised learning to capture it. The pre-trained DNN can then determine optimized MA positions in real-time relying only on partial power measurements from the transmit region.Extending this to multi-user scenarios is challenging due to complex rate expressions and the lack of globally optimal position solutions to use as training labels. To overcome this, we develop an unsupervised training framework that directly maximizes the multi-user sum-rate. This framework utilizes an attention-based architecture to extract latent features from the partial channel measurements and effectively manage inter-user interference. Simulation results show that our proposed approach achieves near-optimal performance in single-user systems and surpasses conventional CSI-based alternating optimization algorithms in multi-user environments.

Dense Gaussian networks are degree-four algebraic interconnection networks with compact diameter and simple modular routing. This paper studies non-redundant one-to-all broadcast repair in the dense Gaussian network generated by $α=k+(k+1)i$. We propose multi-orientation edge-minimum repair (MOEM), which evaluates a constant-size family of Gaussian broadcast-tree orientations, selects a fault-aware orientation, contracts the fault-pruned tree into healthy components, and reconnects those components using external component-crossing repair edges. The resulting structure is a rooted spanning tree of the healthy subgraph, so each healthy node receives the message exactly once and no faulty node is used. We prove that, for a chosen orientation with $c$ fault-pruned components and a connected healthy component graph, the repair step is non-redundant and uses the minimum possible number $c-1$ of external component-repair edges. We also prove that, for every one- or two-fault placement, the MOEM orientation family contains a repair with depth at most $k+2$. The depth proof combines a certificate framework, an explicit four-case off-axis analysis, and a five-component orthogonal-axis certificate. Exhaustive validation for $k=5,\ldots,10$ and large-scale validation through $k=200$ confirm the implementation and show that random two-fault repairs use approximately two external repair edges.