Papers

Maritime moving-target observation scheduling with agile Earth observation satellites is a dynamic, sequence-dependent combinatorial optimization problem. Sea-surface targets move continuously, causing feasible observation windows to vary with target motion and satellite orbital geometry. The scheduler must jointly determine task selection, satellite assignment, observation-window selection, and observation ordering under time-window, attitude-maneuvering, and onboard-resource constraints. This paper proposes an implicit Q-learning-bootstrapped ant colony optimization method, termed IQACO, for multi-satellite maritime moving-target observation scheduling. Rather than directly learning a task-selection policy, IQACO embeds an offline implicit Q-learning module into constructive ant colony optimization to adaptively adjust the pheromone factor, heuristic factor, and evaporation rate. A compact search-state representation captures pheromone distribution, current and historical-best solution quality, and iteration progress. During online scheduling, ant colony optimization constructs feasible observation sequences, while the learned policy adjusts the search behavior according to the current search state. Experiments on 14 scenarios with different scales and satellite configurations show that IQACO consistently outperforms the compared algorithms, improving the mean objective value over conventional ant colony optimization by 2.86%-9.41%. Further comparative and supplementary experiments demonstrate its effectiveness and robustness across different scheduling conditions and problem settings. These results indicate that offline value learning provides an effective adaptive search-control mechanism for constrained maritime moving-target observation scheduling.

Heterogeneous agile Earth observation satellite (AEOS) scheduling requires task selection, satellite assignment, and observation sequencing under satellite-dependent visibility windows, attitude maneuvering requirements, energy consumption, and onboard storage constraints. Since satellites differ in orbital access, maneuvering capability, and payload resources, the same task may have different feasible windows, transition costs, and resource-consumption patterns on different platforms, which increases the difficulty of unified modeling and efficient optimization. To address this problem, this paper proposes an evolutionary policy optimization framework for heterogeneous AEOS scheduling with preference-adjustable weighted objectives. In the modeling layer, assignment-based indirect encoding is combined with decoder-based equivalent-cost evaluation to retain satellite-dependent constraints while integrating task gain, energy saving, and load balance into an interpretable scalar utility. In the optimization layer, schedule decoding, population-based search, and online actor-critic operator control are decoupled, so that reinforcement learning selects high-level search operators rather than constructing schedules directly. Based on this framework, a reinforcement-learning-assisted operator-selection memetic evolutionary algorithm (RLOSMEA) is developed to coordinate global exploration, feasibility recovery, and local refinement under a limited function-evaluation budget. Experiments on different heterogeneous AEOS scenarios show that RLOSMEA achieves higher overall weighted utility and more stable convergence than representative metaheuristic baselines. Sensitivity and learning-behavior analyses further confirm the robustness of the proposed method and the effectiveness of reinforcement-learning-guided operator selection.

Ternary transformers offer extreme memory and compute efficiency, but existing low-bit LoRA-based methods cannot directly fine-tune ternary weights. Current approaches either require dequantization, restoring low-bit base weights to higher precision to merge with adaptation weight, or update only quantization parameters, preventing a merged model that remains ternary. We propose ternary multiplicative adaptation, which represents discrete updates of ternary weights such as sign flips or zeroing through a low-rank Kronecker factorization into two small ternary matrices applied element-wise to ternary weights. This design is parameter-efficient and expressive, preserves the ternary domain, and supports direct merging without dequantization. Experiments on six models across language and vision, including ternarized LLaMA-3 1B and 3B and a ternary ViT-B/16, demonstrate that our method recovers much of the performance lost to quantization and outperforms strong low-bit and ternary baselines. Code is available at https://github.com/alexmanoo/ternary_adaptation.

Although recent Multimodal Large Language Models (MLLMs) have advanced general product understanding, they implicitly encode product information into global embeddings, thereby limiting their ability to capture fine-grained attributes. This limitation hinders performance in tasks requiring precise attribute discrimination, such as distinguishing subtle material differences among visually similar products. To address this challenge, we propose HMGCLIP, a unified multimodal embedding framework. By constructing a heterogeneous hypergraph, we leverage hypergraph topology to mine structure-aware hard negatives and align multi-granular semantics at both relation and hyperedge levels. This design enables a dual-granularity inference mechanism that dynamically fuses attribute evidence for both fine-grained and coarse-grained downstream tasks. Furthermore, we release a comprehensive fine-grained e-commerce dataset to facilitate future benchmarking. Extensive experiments on this new dataset and the public MAVE benchmark show that HMGCLIP outperforms strong multimodal encoders, MLLMs, and e-commerce baselines, validating the superiority of HMGCLIP.

This paper describes the electricity markets and operational processes in the Irish power system and translates them into a Mixed Integer Linear Programming (MILP) model. The model is designed to estimate renewable generation Curtailment and Constraint. A full mathematical formulation is presented and tested on both a simple example and a realistic model of the Irish transmission network. The results show that the proposed formulation works as intended, capturing curtailment and constraint effects, while also highlighting model limitations and directions for future improvement.

In this paper, we propose Mahalanobis-Based Multi-Head Attention (MHA-CSP), a novel attention mechanism that replaces the standard dot-product with a Mahalanobis distance-based RBF kernel, which effectively computes attention in an infinite-dimensional feature space without increasing the parameter count. Crucially, the positive definiteness of the Mahalanobis distance enables a direct construction of Tree Attention: attention scores are built directly from accumulated distances, with a LogSumExp correction that rectifies the raw distance by subtracting the log-sum of edge exponentials. Moreover, the multi-head Mahalanobis distance matrices are themselves repurposed to construct an attention meshing mechanism, enabling cross-head kernel collaboration that simultaneously boosts accuracy and training efficiency. Extensive experiments demonstrate that MHA-CSP, with only 119K parameters and teacher forcing applied exclusively at the final hidden state, consistently outperforms Transformer and GCN baselines trained from scratch under identical conditions on long-sequence state tracking tasks. While these baselines rely on dense attention or graph propagation, MHA-CSP achieves robust structured reasoning via synthetic distance rectification—powered by Mahalanobis-based attention—and efficient information bypass inherited from the CSP backbone. This result highlights the effectiveness of complex-valued state propagation with collaborative multi-head rectification in capturing symbolic structures, establishing a new efficiency-performance trade-off for structured reasoning.

System prompts can be extracted from commercial LLMs with over 80% success and redeployed at zero cost, yet a prompt owner has no way to verify whether a suspected deployment is a clone. We propose Black-Box Behavioral Fingerprinting (BBF): the prompt owner registers a behavioral signature from model outputs and later tests whether a suspect deployment matches that signature more closely than an unrelated baseline. BBF requires only black-box API access. Through a large-scale study (4 model families, 8 benchmarks, 288{,}000 responses), we find that prompt choice explains 24.4% of output variance and same-model detection reaches AUC 0.876. Cross-model performance is bounded by detector identity, with off-diagonal AUC ranging from 0.845 (Claude as detector) down to 0.665 (Qwen) and overall mean 0.725. BBF resists non-adaptive prompt paraphrasing (AUC $\geq 0.889$) and is robust to imperfect extraction, but a single-sentence formal-tone prefix can collapse detection on short structured outputs (MNLI 0.978 $\to$ 0.547), isolating style-invariant detection as the key open problem. Diagnostic Query Optimization, a zero-cost query selection rule, adds $+0.120$ to cross-model AUC.

When a context asserts two values for one fact, a model commits to a cue – recency, repetition, position – but natural data rarely makes these disagree, so behavior cannot reveal which. We train 26M-parameter transformers on a synthetic language where recency and rarity are exactly coextensive, and separate them with a minimal causal edit that inverts one cue while holding the truth, token count and answer position fixed. All 75 runs reach accuracy >= 0.999, including where the trivial heuristic fails, so no held-in evaluation distinguishes them. Under intervention the per-cell readout does not replicate: 13 of 25 cells differ by more than 0.3 in sign fraction across three seeds, the largest by 0.879 against a standard error of 0.025. The construction predicts this – coextensive rules leave the objective indifferent between them – and the variance is ordered by how much of the optimization each comparison releases. What replicates is timing: escape from a positional shortcut with a closed-form ceiling, monotone in redundancy. Probed before that escape, attribution reverses sign in 32 of 75 runs at unchanged accuracy, and gating on circuit formation is necessary but not sufficient. The corpus fixes when a mechanism appears, not which one – a criterion for when mechanistic attribution to data is available at all, and our construction makes the unavailable case exact.

Graph Neural Networks (GNNs) represent a promising solution for Machine Learning (ML) based Network Intrusion Detection Systems (NIDS), thanks to their ability to leverage both network flow features and topological patterns. While GNN classifiers demonstrate superior robustness against feature-based adversarial attacks compared to other ML detectors, they remain vulnerable to structural adversarial attacks, where an attacker perturbs the underlying network graph topology by injecting edges or inserting nodes. Such attacks pose a realistic and severe threat, undermining the reliability of GNN-based NIDS in practical deployments. While countermeasures have been proposed in the literature, they often rely on assumptions that are unrealistic in real-world cybersecurity scenarios. In this paper, we propose a defense framework based on adversarial training to strengthen GNN-based NIDS against structural attacks. We generate adversarial samples by strategically replacing the source and destination nodes in benign network flows, thereby efficiently mimicking edge injection attacks. We evaluate our approach on two widely used datasets (CTU-13 and TON-IoT) using E-GraphSAGE as the base GNN classifier. Experimental results show that our approach produces hardened detectors with superior detection performance on clean graphs and enhanced robustness against structural adversarial attacks.

The transition to post-quantum cryptography is reshaping the Secure Shell (SSH) protocol for remote administration. Post-quantum key exchange has been deployed in OpenSSH and is being standardized, while SSH authentication largely remains a signature-replacement effort. This path preserves the familiar public-key credential model, but inherits the size and computation overhead of post-quantum signatures, which can increase latency, traffic, and server-side load. KEM-based authentication offers a natural alternative to this signature-centric path, and SSH makes this especially attractive at the user-authentication layer, which is method-extensible, separated from transport-layer key exchange and host-key authentication, and already protected by the established channel. We present a drop-in KEM-based user-authentication method for SSH that replaces client public-key signatures with a session-bound challenge-response proof. The method fits into SSH's existing user-authentication framework, preserving the public-key credential model and enabling incremental deployment alongside existing methods. We provide a reduction-based security argument in the post-quantum ACCE framework, implement the design in OpenSSH using liboqs, and evaluate it under representative RTTs, TCP initial-window settings, and post-quantum migration configurations. Our results show that KEM-based authentication is competitive with compact signature-based authentication under representative network settings, while reducing median handshake latency by up to about 10% against large-signature hybrid baselines. The advantages are clearer when post-quantum signatures stress transmission or computation: median latency under small TCP initial windows falls by up to 7.3% versus ML-DSA and 17.9% versus SLH-DSA, while server-side online cryptographic cost is 59.1% lower than that for ML-DSA in the same NIST category.

Electric vehicle (EV) charging loads exhibit strong behavioral heterogeneity and temporal variability, posing significant challenges for online probabilistic forecasting under evolving operating conditions. In particular, persistent charging patterns may differ substantially across stations, while recent behavioral changes can continuously alter the underlying load distributions. This paper proposes a behavior-guided online probabilistic forecasting framework that explicitly characterizes persistent station-specific patterns and recent behavioral changes. A dual-timescale behavior representation is constructed to distinguish long-term charging characteristics from recent behavioral states and quantify their deviations. These behavioral changes are further semantically encoded to guide drift-aware forecasting adaptation, while a delayed-feedback mechanism ensures temporally consistent online updates when observations become available across different forecasting horizons. Experiments on ten heterogeneous real-world charging stations demonstrate that the proposed method consistently outperforms conventional forecasting models and concept-drift-aware online baselines in forecasting accuracy and probabilistic reliability. For 1-h-ahead forecasting, the proposed method reduces MSE and Pinball loss by 15.3% and 17.8%, respectively, over the corresponding best baselines. For 4-h-ahead forecasting, the improvements further reach 16.8% and 22.6%, respectively, demonstrating consistent performance gains under evolving charging behaviors and extended forecasting horizons.

Visual Language Models (VLMs) excel at describing visible scene content but struggle to reason about dynamic multi-agent interactions, where action semantics depend on coordinated roles and spatial-temporal dependencies. We formalize this capability as multi-agent tactical reasoning and introduce DoublesEval, a diagnostic evaluation framework that leverages professional doubles badminton as a structurally tractable testbed. DoublesEval employs a key-moment-based protocol that decomposes rallies into tactically salient instants and probes models across four interpretable dimensions: atomic recognition, intra-segment composite understanding, cross-segment causal reasoning, and high-level tactical abstraction. This design isolates where reasoning fails, rather than merely measuring answer correctness. To address observed failure modes, we propose TacticCheck, a lightweight constraint-guided test-time consistency checker that reranks candidate answers using the model's own lower-level tactical predictions, requiring no parameter updates or ground-truth labels at inference time. Evaluating four representative open-source VLMs on 60 curated rallies (yielding $\sim$9.6K structured instances) via a zero-shot protocol, we find that models remain weak across all diagnostic levels, with especially clear bottlenecks in spatial state, interaction binding, and terminal evidence. TacticCheck delivers consistent gains across all evaluated models, while still leaving a substantial gap to robust tactical reasoning. These results highlight the need for structured, interaction-aware evaluation paradigms for next-generation VLMs. The source code is available in \href{https://github.com/Chengjt1999/DoublesEval}{\textcolor{blue}{our GitHub repository}}.

Wearable device data enables continuous health monitoring, but suffers from structured missingness: features sharing a physical sensor drop out together. Deep imputation methods such as BRITS and SAITS have seen limited evaluation on multimodal physiological data under realistic missingness, and existing benchmarks use random-point holdout protocols that incorrectly assume missingness is independent across features and time. Using data from a person with epilepsy recorded on a Garmin smartwatch, we develop an evaluation protocol that mines contiguous missing-run templates from training data, stratifies them by per-feature gap-length quantiles, and injects them as block masks with preserved co-missingness structure. A matched training protocol exposing models to the same missingness distribution reduces BRITS's severe-gap MAE by 43%, demonstrating the potential benefit of the proposed evaluation and training protocol within this single-participant dataset. We further extend BRITS with time-of-day encoding and a circadian harmonic channel. No single model dominates: linear interpolation is optimal for slow-moving features over short gaps; extended BRITS achieves lower MAE on dynamic cardiac features in moderate and severe gaps; and SAITS better preserves the ground-truth distribution by Jensen-Shannon distance despite higher MAE. Ultimately, model rankings strongly depend on evaluation designs. By exposing how traditional evaluation methods obscure true model capabilities, our transferable protocol establishes critical steps towards developing better imputation strategies for future multi-sensor wearable datasets.

Responsible deployment of face verification systems requires more than accurate decisions: systems should also provide interpretable and auditable evidence that enables users to understand, assess, and challenge their decisions. Vision-language models (VLMs) provide a promising foundation for explainable face recognition by combining visual analysis with natural-language reasoning. However, relying on a single model may further limit the decision accuracy as well as provided explanations. This work therefore investigates whether multiple VLMs can be combined to improve recognition accuracy, and to enrich the explanations associated with those decisions. This work evaluates four VLMs as standalone face verification systems and subsequently proposes a fusion framework, where two source models provide similarity scores and textual justifications and a third VLM acts as a decider model. Four different fusion scenarios are considered, progressively providing the decider model with scores, justifications, face images, and combinations of these modalities. Overall, the findings suggest that the value of multi-VLM fusion extends beyond recognition performance. VLMs can provide complementary justifications and perspectives that enable richer explanations of face recognition decisions, supporting greater transparency, auditability, and error analysis. This is relevant to the development of responsible explainable face verification systems, where users and operators should be able to understand not only the final decision but also the evidence and potential sources underlying it. The proposed multimodal VLM, which combines decision scores, explanations, and face images, achieves higher recognition accuracy than state-of-the-art VLMs and domain-specific face recognition models, while also providing fused explanations that are expected to be more robust than those generated by individual VLMs.

Unsupervised domain adaptation (UDA) has been widely concerned in the fields of machine learning, pattern recognition, and computer vision. Traditional UDA learning usually assumes that the label spaces of the source and target domains are exactly the same and only needs to solve the problem of sample distribution drift existing between two domains. However, in real world applications, the label spaces between two domains may be different. In this case, there are both sample distribution drift and class spatial difference between domains, namely Universal Domain Adaptation (UniDA) learning scenario. At present, existing works rarely offer theoretical analysis for universal domain adaptation. In this paper, we provide an upper bound of the generalization error for universal domain adaptation. According to the proposed generalization error bound, we propose a novel UniDA algorithm called Joint Distribution Alignment for Universal Domain Adaptation (JAUA), which aligns the joint distributions by minimizing the distribution discrepancy calculated by Chi-Square divergence. Furthermore, we propose a progressive pseudo-labeling method to assign the pseudo labels to unlabeled target samples. The experiment results on six public image datasets demonstrate the superiority of JAUA in handling the UniDA problem.

Using monthly Niño-3.4 anomalies through July 2026, we investigate how much predictive information is contained in delayed observations of the index. Ridge regression identifies informative delays, while multilayer perceptron and sparse identification of nonlinear dynamics (SINDy) models test whether nonlinear complexity provides additional direct forecast skill; gated recurrent unit (GRU) and long short-term memory (LSTM) networks provide a complementary test in which the temporal representation is learned internally. Delayed observations substantially improve forecasts over persistence and climatology at leads of up to six months, but increasing model complexity provides no systematic improvement. Historical recursive experiments favor a simple explicit SINDy recurrence and select shallow recurrent architectures, with no appreciable gain from learning the temporal representation internally. These results support a compact predictive representation of Niño-3.4 evolution in which the representation of past information is more consequential than model complexity. As a prospective application, the selected models are used to forecast the developing 2026 event beyond the last available observation and to compare its predicted evolution with completed historical El Niño events.

Non-parametric (partial) identification of counterfactual queries typically relies on a fully specified causal graph. Motivated by settings with incomplete domain knowledge, we challenge this requirement by leveraging structural assumptions that are inherently implied by the query itself. We show that any counterfactual inquiry induces a, mostly partial, topological ordering over relevant variables, which, in turn, enables an explicit query parametrisation reducing the identification task to a linear program. This allows bounding arbitrary counterfactual and nested counterfactual queries. Our work can be viewed as a generalisation of the classical bounding framework of Tian and Pearl (2000), originally developed for probabilities of causation. We also prove the tightness of our bounds by constructing structural causal models that attain the bounds whilst being compatible with both the observed data and the query-implied order. To assess both the generality and practical utility of the proposed bounding procedure, we revisit several case studies from the literature, demonstrating how the derived bounds can be used to yield informative insights even in the absence of an input causal graph.

Learning operators from sequentially collected data arises in adaptive experimental design, Bayesian optimization, and dynamical-system modelling, where observations may be dependent, and future inputs or sensing operators may depend on preceding data. We derive time-uniform self-normalized concentration bounds for stochastic processes in Hilbert spaces with vector-valued noise. We use these bounds to obtain regression-error guarantees for linear operators, including targets outside the Hilbert estimation space, and for nonlinear parametric operators trained with strongly convex losses and regularizers. Our results allow possibly infinite-dimensional inputs and outputs without independence or mixing assumptions, providing a major step towards convergence guarantees for adaptive operator learning and learning from stochastic dynamical data.

Recovering the full 3D spine anatomy from intraoperative ultrasound is an ill-posed inverse problem, as the complete structure must be inferred from incomplete and noisy observations. Acoustic occlusions and limited field of view create large unobserved regions, while view-dependent artifacts lead to variability in expert annotations of the visible anatomy. Current supervised ultrasound shape completion methods rely on synthetically generated incomplete-complete paired data to learn conditional mappings under a predefined distribution of simulated occlusions. However, real intraoperative occlusions do not necessarily follow this distribution, which can limit generalization to patient data. As a result, accurate and robust completion from noisy partial observations remains an unsolved problem. We propose a zero-shot shape completion framework that reconstructs the entire lumbar spine from partial ultrasound observations without relying on simulated training data. To accommodate unseen and irregular patterns of missing structures, we introduce blended completion, a mechanism that integrates the learned anatomical prior with incoming partial geometry at inference time. The method learns a generative diffusion prior over full anatomical shapes represented in an adaptive octree structure, enabling efficient modeling of the complete spine in a single forward pass. Validation on phantom and volunteer data shows that decoupling completion from a predefined corruption distribution improves generalisation under real occlusions, outperforming a fully supervised variant by 22% on HD95 completion error. Code and data are available at https://github.com/miruna20/ZODIAC.

LLM-as-a-judge evaluation is usually assessed by agreement and robustness to surface perturbations, but reliability does not establish construct validity. We formalize construct validity for an evaluator as a two-dimensional profile: invariance S, the probability that a verdict is unchanged under construct-preserving edits, and construct sensitivity R, the probability that it changes under minimal construct-changing edits. We show that S and R are independent and that no scalar summary preserves all relevant comparisons. We measure the profile across 7 judges and 4 domains using 7 construct-changing intervention types and 5 register-only controls, with intervention direction determined by human annotators and generation, verification, and judging assigned to disjoint model families. At matched invariance S >= 0.90, judges average S = 0.945 but R = 0.319. Sensitivity also differs between scope and strength edits: R_scope = 0.383 versus R_strength = 0.262, a +0.121 gap with the same sign for all 7 judges. We further audit five public label sets and find that surface-only predictors reproduce 55%-67% of labels in paired mode, including 67.4% of MT-Bench human votes. These results show that high judge agreement can coexist with weak sensitivity to changes in the construct being evaluated, motivating joint reporting of invariance and sensitivity and auditing the validation set itself.

Quantitative assessment of muscle MRI is crucial for monitoring neuromuscular disorders (NMD). This study introduces an automated radiomic phenotyping framework based on original features engineered across five main architectural domains: quantitative morphometry, spatial distribution, geometric shape, interactions between progressive fat replacement stages, and graph-based topology. Utilizing 1184 MRI scans from the CoMPaSS-NMD project, we map the complex 3D architecture of heterogeneous intramuscular lipodegeneration into objective, morphologically interpretable biomarkers. We introduce a graph-based skeletonization of fat infiltrates to quantify muscle architectural changes, establishing a multi-dimensional extension of traditional, spatially-agnostic volume metrics by mapping topological networks across the entire 3D muscle volume. Statistical screening via non-parametric Kruskal-Wallis analysis confirmed the discriminative power of these novel descriptors across the genetic hierarchy. Notably, topological network metrics (e.g., SF1_Skel_Nodes, $\epsilon^2$ = 0.2656) and interface dynamics metrics (e.g., SF2_To_SF1_Dist_Min, $\epsilon^2$ = 0.2092) demonstrated substantial effect sizes, providing deeper structural insights than classical volumetric assessments. Post-hoc pairwise evaluations and UMAP projections further indicated the capability of these topological and 3D geometric invariants to capture disease-specific macroscopic infiltration patterns. These results demonstrate that global architectural features represent a highly promising class of biomarkers for differential diagnosis, offering new avenues for tracking longitudinal disease dynamics in neuromuscular diagnostics. The developed automated feature extraction pipeline is integrated and available within the MUSCAT (MUSCle fAt Topology) library.

Against the background of the widespread use of Artificial Intelligence (AI) tools in the field of justice, this paper aims to explore how an AI solution designed to draft initial reports for reporting image-based sexual abuses (IBSA) could help, support, or assist in facilitating access to justice. In our approach, access to justice is facilitated not only by easing the path to denounce IBSA (which currently has the lowest reporting rate), but also by offering an early, and thus more accurate, report draft to law enforcement authorities, providing later support also for judges. Building upon earlier approaches, we designed an improved version and tested it with three experts. In this sense, the paper advocates for AI solutions offering effective and efficient support in early reporting of IBSA.

The efficiency of Large Language Model (LLM) serving is fundamentally limited by the sequential nature of autoregressive decoding. Speculative Decoding (SD) mitigates this by using a lightweight draft model to speculate future tokens, which are then validated by the LLM in a single parallel forward pass. To further boost efficiency, multi-candidate schemes propose diverse candidate sets to increase the likelihood of token acceptance. However, we show that these schemes are bottlenecked by Residual Drift: a phenomenon where the rejection of initial candidates causes the residual target distribution to diverge from the draft model's predictions. This shift renders subsequent candidates ineffective and forces the system into expensive resampling. To resolve this, we propose ResiSpec, a framework that strategically reforms the proposal distribution during verification to anchor the residual target mass within the draft model's high-confidence regions. By mathematically re-aligning the verification process without compromising output exactness, ResiSpec prevents candidate obsolescence and achieves up to 1.92$\times$ speedup over state-of-the-art multi-candidate methods. Code is available at https://github.com/Czzzk/Resispec.

For multiplicatively independent natural numbers $\alpha$ and $\beta$, Villemaire showed in 1992 that the first-order theory of Presburger arithmetic expanded with both Büchi predicates $V_\alpha$ and $V_\beta$ is undecidable, as it encodes multiplication. In recent years, Hieronymi and Schulz showed that Presburger arithmetic expanded with the weaker power predicates $\alpha^\mathbb{N} = \{\alpha^n: n \in \mathbb{N}\}$ and $\beta^\mathbb{N}$ is also undecidable, while Karimov et al. showed that the existential fragment of this theory is decidable. These results left open the natural problem of determining the decidability of the existential fragment of Villemaire's original expansion. We settle this question for coprime $\alpha$ and $\beta$. Specifically, we give a quantifier-elimination argument that proves the decidability of the existential fragment of $\mathsf{FO}(\mathbb{Z};<,+, V_\alpha, V_\beta)$.

We prove the rank-one Lyapunov spectral identity recorded as Problem 9.1 in the 2004 collection of unsolved problems in mathematical systems and control theory. Let $P,Q,R$ solve the coupled discrete Lyapunov and Sylvester equations associated with $A$ and its rank-one update $A_2=A+vw^\top$. When the displayed inverses exist, we show that $P^{-1}RQ^{-1}R^\top$ and $(I+PQ)^{-1}$ have the same characteristic polynomial. A rank-one determinant factorization of the equation for $Q$ produces a scalar bilinear kernel. Evaluating it at the eigenvalues of $A$ and at their reciprocals gives $RQ^{-1}R^\top=BQ^{-1}B=P-BPB$, after which the two target matrices are the same two factors in opposite order. Polynomial continuation extends the identity from a nonempty open set of admissible systems to the full admissible domain and yields a determinant corollary without stability assumptions; when the spectra of $A$ and $A_2$ are disjoint, $Z=b(A)^{-1}P$ gives an explicit similarity. In the Schur-stable realization setting, the result recovers the associated principal-angle and past/future canonical-correlation spectra.

We study distributed hypothesis testing and establish the exact error exponent in single-letter form for new testing problems. In distributed hypothesis testing, a receiver decides between $\mathcal{H}_0:P_{XY}$ and $\mathcal{H}_1:Q_{XY}$ based on $Y^n$ and a rate-limited description of $X^n$. So far, such single-letter forms are known only for testing against independence, studied by Ahlswede and Csiszár, and testing against conditional independence, studied by Rahman and Wagner. In this paper, we study testing against dependence, where $P_{XY}=P_XP_Y$, and show that its error exponent is given by Han's exponent, which is established by single-letterizing a multi-letter version of Han's exponent. We also disprove a previous conjecture of Han claiming that the error exponent is given by the lautum information, as we show that Han's exponent can strictly exceed the latter. We then consider the Cartesian product of testing against dependence and testing against independence, and derive a single-letter characterization of its error exponent. We next study testing against conditional dependence, which is the dependence-testing counterpart of the setting studied by Rahman and Wagner. We derive a single-letter converse bound for the error exponent by introducing and solving a related setting where the side information is also available to the transmitter. We show that our converse bound is tight in some cases by using a conditional-coding version of the quantization scheme. Finally, we extend our converse method for testing against dependence to the general setting, and recover a recently established single-letter converse bound.

We study multilevel fair resource allocation with tree-structured hierarchical relations among agents. At each level, the problem can be viewed locally as allocating an agent's bundle to its children, the overall allocation being a trace of this process iterated down to the leaves. Assuming that internal nodes' utilities are the utilitarian welfare of their children, and the leaves have classical additive utilities over items, we first propose multilevel adaptations of usual envy-based fairness notions (e.g., WEF1). We present three adaptations and show that the choice among them is not neutral. We prove that, under identical preferences, the three adapted envy-based notions coincide, and that the Multilevel extension of Weighted Round Robin (Chakraborty et al., 2021) (MWRR) guarantees them. We then show that under general preferences, MWRR may guarantee some notions while failing others. Finally, through experiments, we show that MWRR may still perform well even for adaptations it does not formally guarantee.

Profitability metrics, such as the single-product gross profit margin, constitute the standard toolbox to prioritize products in sales and operations planning (S&OP). These metrics leverage the premise that production lines can be committed independently, which endows them with a simple per-ton ranking that a planner can compute and use easily in practice. However, coupled plants, especially polymer plants whose parallel lines draw simultaneously on a single bulk feed, can fundamentally undermine this premise and mislead to value-destroying production plans. We propose a framework built on what we call the Augmented Gross Profit for Product Clusters (AGPPC), which converts the per-ton ranking metric into a per-coupled-hour ranking that carries a per-instance optimality certificate. We present the theory of AGPPC, which combines the co-production column concept with a fluid relaxation of the planning problem, alongside an integrated bilinear mixed integer program of the plant and a McCormick-linearized baseline that provides certified bounds for it, and we demonstrate its effectiveness on real operational data from an Indonesian polymer producer, where the coupling-aware metric alone raises operating profit by 7.6% and the full optimization by 28% over current practice.

Integrated sensing and communication (ISAC) is a rising technology in the next wireless communication networks, enabling the simultaneous execution of communication and sensing tasks by fully utilizing limited spectrum resources. In this work, we investigate the secrecy performance of a dual-uncrewed aerial vehicle (UAV)-assisted secure ISAC system. Specifically, a base station UAV communicates with users and transmits radar signals to locate potential eavesdroppers, while simultaneously providing information to a jammer UAV to perform jamming tasks. Considering constraints such as maximum UAV velocity, transmit power, propulsion energy, and sensing thresholds, we maximize the average secrecy rate by optimizing user scheduling strategies, time allocation, transmit power, and UAV trajectories. The presence of a non-convex problem, originating from tightly coupled variables, is tackled by an efficient iterative algorithm. In particular, the original optimization problem is decomposed into six subproblems, and non-convex subproblems are transformed into approximately convex forms via successive convex approximation. Then, block coordinate descent techniques are employed to solve all subproblems sequentially. Numerical results demonstrate the convergence and effectiveness of the proposed algorithm.

The rapidly expanding scale of electric vehicle (EV) fleets and continuously decreasing battery costs are making vehicle-to-grid services a reality. In this paper, we study the interaction between the problems of an EV aggregator's bidding in the regulation market and power allocation (i.e., determining the (dis)charging powers of the EVs in regulation deployment). Although the two problems are coupled, they are often regarded as decoupled and optimized separately for complexity issues. However, failing to consider the coupling of bidding and power allocation can lead to a decline in the profit of the EV aggregator (EVA). In this paper, we propose a framework for co-optimizing EVA bidding and power allocation in the regulation market. The bidding model is formulated as a stochastic programming problem with embedded power allocation in discretized regulation signal scenarios. To meet the solution time requirement for regulation deployment, we further propose a power allocation model that can be solved online. It utilizes the Lagrange multipliers from the bidding problem to ensure that the allocation results correspond to the optimal solution of the bidding problem. The effect of the proposed framework on improving EVA profits and reducing degradation costs is verified in the case study.