Papers

Tree-encoded partitionings of graphs are fundamental tools for the decomposition and approximation of graph signals. For the efficient approximation of such graph signals, we develop strategies based on $hp$-refinement by combining domain decomposition with an improved local approximation using polynomials of higher degree. In this way, from a given graph partitioning tree, a more efficient subtree is extracted in which the cost of the signal approximation is considerably reduced by still maintaining the same total error. To this end, we interpret the refinement process as a binary knapsack problem to determine an enhanced partitioning tree. We further study an a-posteriori strategy which prunes the partitioning tree by optimizing the polynomial degrees over the subdomains. To make polynomial basis systems accessible for general graphs or high-dimensional data, we propose local embeddings of graphs into low dimensional Euclidean spaces. We underpin the efficiency of our algorithms with extensive numerical tests which carefully assess the impact of the applied refinements and optimization strategies.

We address the challenge of cross-link interference in dynamic time-division duplexing (TDD) systems. Specifically, we focus on mitigating the interference caused by access points (APs) operating in downlink to APs operating in uplink. To this end, we exploit that channels between APs typically vary much more slowly over time than channels between users and APs. This observation allows us to jointly estimate the uplink user data and the AP-AP channels using a least-squares formulation over multiple coherence intervals, during which the AP-AP channels stay constant. We derive conditions for unique solvability of this least-squares problem by analyzing the rank of the regression matrix. For cases where a unique solution does not exist, we propose to transform the problem into a uniquely solvable one by sacrificing a subset of the uplink data samples. Numerical results demonstrate that our proposed methods achieve substantial gains over baseline algorithms. Further, we observe that one of our proposed algorithms achieves almost perfect AP-AP interference mitigation when the AP-AP channels vary very slowly over time.

Electrocardiogram (ECG) artifact contamination frequently occurs in surface electromyography (sEMG) when muscles are recorded near the heart. Existing neural network (NN)-based approaches typically perform waveform-level end-to-end denoising with pointwise losses, but often fail to preserve the spectral structures of sEMG. In addition, these models do not exploit the prior knowledge that ECG mainly distorts the low-frequency band of sEMG. We propose SSEMG-Net, a spectrogram-domain model that explicitly captures sEMG-ECG interactions using a bidirectional Mamba backbone and a dual-head decoder for magnitude masking and wrapped-phase estimation. The magnitude masking module is physiologically aware, restricting denoising to the low-frequency sub-band where ECG activity predominates. Experimental results demonstrate that SSEMG-Net achieves superior signal quality and lower feature-extraction error compared to prior methods, underscoring its potential for clinical applications where preserving sEMG spectral features is essential.

We prove, with the aid of AI, that for every real symmetric forcing matrix $Q\succeq0$, the unique solution of a continuous-time Lyapunov equation is entrywise nonnegative whenever the state matrix is a real Hurwitz companion matrix. This proves an earlier conjecture. The proof makes no assumption on the spectrum of the state matrix, and is made possible by means of using Horner polynomial matrices. We also show that discrete-time counterpart of the conjecture is false: Counterexamples can be readily constructed to show that Schur companion matrices, including one generated by a polynomial with all positive coefficients, yield solutions with negative off-diagonal entries even with identity forcing.

The rapid growth of artificial intelligence (AI) computing is transforming data centers into large, dynamic electrical loads. Their deployment is primarily constrained by energy availability and grid-connection capacity, which is further aggravated by the ability of power-delivery architectures, control systems, and computing workloads to operate reliably during fast grid disturbances. This article presents a technological perspective on AI data centers as grid-interactive computing systems. First, it reviews grid-integration bottlenecks, evolving connection policies, grid-code requirements, which has fostered new technological trends via spatio-temporal flexibility available through workload orchestration, cooling systems, on-site resources, and energy storage. Second, it maps the evolution of power-delivery architectures from medium-voltage grid interfaces to chip-level, discussing higher-voltage DC distribution, solid-state transformers, wide-bandgap devices, advanced chip-level power delivery, and liquid cooling. Third, it establishes a three-level stability framework spanning rack-level DC-bus dynamics, facility-level converter interactions, and system-level grid-coupled behavior. The framework connects dominant instability mechanisms, including constant power load effects, impedance interactions, forced oscillations, and operating-mode transitions, with suitable modeling, assessment, and mitigation approaches. Synthesizing these topics, this article highlights grid-to-chip co-design as a central requirement for scalable AI infrastructure, linking computing workloads, power-delivery systems, energy buffers, and grid operation.

The energy transition is reshaping residential electricity consumption through the increasing adoption of distributed generation, electrified appliances, and demand-response programs. Understanding these evolving behaviors requires access to granular smart-meter data for applications such as load forecasting, appliance detection, and demand-side flexibility analysis. However, such data are subject to strict access restrictions and data-protection regulations. Thus, realistic synthetic alternatives are necessary. In this paper, we introduce LoaDiff, a diffusion-based generative model for year-long, sub-hourly smart-meter load curves. LoaDiff supports flexible conditioning on static household attributes, such as appliance ownership, and dynamic contextual variables, including calendar information and outdoor temperature. We evaluate the model against multiple generative baselines on three residential electricity-consumption datasets. Our experiments assess four complementary dimensions: fidelity and diversity, training-record memorization risk, downstream utility for load forecasting and appliance detection, and conditional controllability under alternative temperature conditions. The results show that LoaDiff generates realistic and diverse load profiles, achieves a favorable trade-off between generation quality and limited evidence of memorization, preserves information useful for downstream energy applications, and responds coherently to changes in conditioning variables.

This paper presents a novel approach for data-driven self-learning control of highly flexible, modular manufacturing systems. Specifically, we employ a novel framework for model-based reinforcement learning which introduces approximate inverse process models within the training of reinforcement policies. This approach disentangles the learning of actuation dynamics and the dynamics in state space, resulting in RL-based training solely within the task space. We propose a lightweight feedforward architecture for approximate inverse models and integrate them within the policy network of standard RL algorithms. We apply the approach to a laboratory modular production testbed with heterogeneous production modules. The results underline the efficiency improvements for modular manufacturing units in terms of both performance and training speed, particularly for off-policy algorithms.

Multi-threshold (MT) sampling records crossing times at selected thresholds for parameter estimation and waveform reconstruction. We develop a mathematical framework that defines the signal space and sampling operators and maps the signal distribution to the distribution of recorded crossings. The framework distinguishes model mismatch, signal noise, threshold mismatch, and threshold noise. Finite point measures accommodate variable crossing counts and preserve multiplicity after time quantization. Stochastic crossing, timing, and selection operators and their associated Markov kernels describe the sampling process. For nonhomogeneous Poisson photon arrivals and deterministic MT sampling, we derive the exact cumulative distribution function (CDF) of the first recorded crossing time at a specified threshold within a recorded-time interval. Under additional regularity and local monotonicity conditions, this CDF admits a one-dimensional Fourier representation. For a scintillation pulse model, numerical CDFs and standard deviations of the first recorded crossing time agree with independent Monte Carlo simulations, providing a quantitative basis for comparing threshold settings. The framework provides a foundation for MT performance evaluation, parameter estimation, waveform reconstruction, and sampler design.

This paper develops a critic-free policy iteration (PI) method for continuous-time linear zero-sum games. The central idea is to characterize the saddle-point policies directly in the joint policy space, rather than treating the quadratic value matrix as an iterative variable. A policy game Riccati equation (PGRE) is introduced whose unknowns are policy gains only. Its solutions are shown to be in one-to-one correspondence with the symmetric solutions of the game algebraic Riccati equation. Based on a stabilizing anchor, PI is performed directly in the actor space. The actor-space Jacobian is nonsingular at every stabilizing policy, and the resulting policy sequence coincides with that of simultaneous PI. For unknown dynamics, a data-driven algorithm uses a single batch of data and nullspace projection of endpoint increments to eliminate the value matrix, yielding an actor-only regression. A necessary and sufficient rank condition for unique policy recovery is established and shown to be iteration-invariant, demonstrating that critic identifiability is unnecessary. A power systems frequency-regulation example verifies convergence and policy recovery, while scalability tests demonstrate substantial reductions in computational and memory requirements.

Three-dimensional ultrasound (US) is a safe, radiation-free complementary modality to CT and X-rays for longitudinal monitoring, yet its segmentation-derived partial point clouds are extremely artifact-laden. Consequently, it is challenging to recover a clean and complete anatomical structure from such US point clouds. In this paper, we present UBone3D, a novel framework based on physics-rectified conditional flow matching (CFM) that performs point cloud completion directly from partial US observations. UBone3D models deterministic physics artifacts (e.g., surface thickening, streaking, dropouts) via a simulated physics proxy, and introduces test-time physics rectification to steer the shape completion. At inference, the completion is jointly steered by two decoupled forces: (1) anatomical plausibility enforced by a CT-trained generative shape prior, BoneFM, and (2) physics consistency enforced by USimNet in the ultrasound formation space. Extensive experiments on simulated and in-vivo data demonstrate significant improvements in reconstruction accuracy and anatomical fidelity over existing baselines.

This work investigates a number of approaches to prevent catastrophic forgetting in class incremental learning scenarios for sound event classification tasks. We analyze the problem using architectural and regularization approaches, using FSD50K and AudioSet datasets. We design incremental stages and solutions that selectively protect the kernels of the network from weight updates to prevent catastrophic forgetting, and a dynamic head solution that expands itself each time a new task is learned. The findings show that catastrophic forgetting mainly happens in deeper layers, in particular in the classifier head. For the studied in-domain sound classification problem, the solution that seems to alleviate catastrophic forgetting and is the most efficient is a full freezing of the feature extractor with a fine-tuning of the dynamic head classifier, showing little to no forgetting and great training stability, and a good balance between memory-stability and learning plasticity.

Accurate estimation of aboveground biomass density is essential for quantifying forest carbon stocks. NASA's GEDI mission provides valuable canopy structure data, but its sparse sampling necessitates the use of simulators to calibrate biomass models at field inventory locations. The widely used simulator of Hancock et al. (2019) emulates GEDI waveforms from airborne LiDAR point clouds, yet it has never been validated over European temperate forests. Here, we compare approximately 9,500 pairs of observed and simulated GEDI relative height (RH) profiles across French forests using the national airborne LiDAR program as input. We separate two sources of error: waveform modeling differences, assessed by referencing both simulated and real RH metrics to a common ALS-derived ground elevation, and ground detection bias, evaluated by comparing each GEDI L2A processing algorithm against the ALS reference. Under the baseline configuration, the mean absolute bias across the full RH profile reaches 0.69 m in leaf-on and 1.28 m in leaf-off conditions. Switching to intensity-based return weighting and selecting the a3 L2A algorithm reduces these biases to 0.44 m and 0.40 m respectively. The a3 algorithm also achieves near-unbiased ground detection (-0.03 m versus -0.88 m for the default), directly reducing a previously overlooked source of error. We also show that leaf-off acquisitions and low-sensitivity shots, both typically excluded from standard biomass products, are simulated as reliably as their counterparts, substantially expanding the potential calibration and inference datasets.

In modern power systems with high penetration of Inverter-Based Resources (IBR), most converters operate in Grid-Following (GFL) mode. Some buses exhibit inherently low Short-Circuit Ratios (SCRs), a property majorly shaped by network topology. The integration of GFL-IBR onto such weak buses thus demands attention to static voltage stability. To address this issue, market mechanisms have been proposed to incentivize generators to provide voltage stability services, such as commitment of synchronous generators for reducing the equivalent impedance at low SCR buses and adaptive reactive power support from GFL-IBR. To compute shadow prices for these services, previously proposed methods such as the `restricted' and `dispatchable' approaches may fail to guarantee operating cost recovery for voltage-stability service providers. As the resulting prices are determined purely from a social surplus maximization objective, the profitability of units is entirely overlooked. This suggests that new pricing methodologies are needed to satisfy cost-recovery requirements. Therefore, this paper proposes a pricing method based on a primal-dual formulation. Case studies demonstrate that the proposed method can consistently produce revenue-adequate shadow prices, enabling all participating units to recover their costs without supplementary uplift payments.

Anomaly detection in communication networks remains a challenge, particularly in time-sensitive environments where stale information can affect system reliability. In this work, we propose an anomaly detection framework that leverages Age of Information (AoI) as a temporal indicator for identifying abnormal network behaviors. The AoI has been studied for network performance optimization, however, its applicability to anomaly detection remains unexplored. The proposed framework integrates a feature selection technique based on the estimated Peak Age of Information (ePAoI) with multiple machine learning models for communication networks as a complementary indicator. The evaluation results demonstrate that ePAoI-based feature selection enhances the performance of the anomaly detection framework while significantly reducing the computational complexity.

We study asynchronous continuation replanning in a two-population linear–quadratic mean field game with deterministic open-loop controls and heterogeneous, possibly erroneous initial information. At exogenous opportunities, one population recomputes its continuation response from the physical aggregate state reached, with the opponent's active plan frozen. The state–plan target needed to initialize replanning is recoverable from local aggregate observations if and only if a kernel-inclusion condition holds; full recovery of the hidden initial input is unnecessary. For revisions accumulating before the terminal time, spectral stability of the limiting two-response cycle yields bounded physical execution and a finite state left limit. The zero-extended continuation plans then converge strongly to the mean field equilibrium restarted from that state. A scalar counterexample shows that well-posed continuation problems and a convergent physical state can coexist with divergent remaining plans. We also construct an exact causal implementation from local aggregate observations and establish finite-population robustness on every fixed finite opportunity prefix. Revision records match with probability tending to one, and the mean-square implementation error truncated to the matching event is \(O(N_*^{-1})\), where \(N_*\) is the smaller population size.

The growing share of Inverter-Based Resources (IBRs) is changing the operation of modern Active Distribution Networks (ADNs), raising concerns for grid stability, protection, and reliability. In this paper, we investigate the dynamic behavior of a Medium-Voltage (MV) portion of an ADN during the transition from grid-connected to islanded operation. The study considers a Grid-Following (GFL) converter and Synchronous Generators (SGs) operated under two distinct regulation modes: a fixed-setpoint, non-regulating condition representative of present-day distribution networks, and an active frequency/voltage-regulating condition representative of SGs equipped with governor and AVR control. Detailed electromagnetic transient (EMT) models of both technologies have been developed in DIgSILENT PowerFactory that quantifies the sensitivity of island persistence to SG regulation mode and inertia. The results show that when DERs operate at a fixed power setpoint, the risk of forming a sustained, undetected electrical island is limited, since the isolated network drifts out of the protection thresholds within tens of seconds. Conversely, enabling frequency and voltage regulation on the SGs is sufficient to sustain an unintentional island indefinitely without triggering conventional protection, regardless of system inertia.

Reconfigurable robots can change their contact geometry when a fixed body cannot negotiate an obstacle. A variable-geometry truss (VGT) distributes this shape change through a load-bearing structure, but coupling it to a mobile base creates a high-dimensional coordination problem. GeoTrussRover combines an electrically actuated VGT, a wheeled base, and contact-semantic morphology planning and control. We solve one source traversal and extract four contact-semantic primitives that describe coordination among 21 members. Physics-constrained projection adapts them to unseen step heights with the same contact topology. When every phase remains feasible, adaptation does not recompute the complete motion. If one phase violates the new physical constraints, only that phase is recomputed. A full-space QP then tracks the adapted motion and corrects member and wheel errors. For transfer from 0.10m to 0.075m, the method reduces objective-function evaluations by 63.7% relative to full recomputation. Contact-phase feasibility analysis covers step heights from 0.10 to 0.46m, or 1.08 to 4.97 wheel radii, with the upper value near the theoretical feasible boundary. The electric prototype traverses 2.11 wheel radii. The resulting low-dimensional representation stores task coordination in a hyper-redundant, load-bearing morphology and reuses it during locomotion.

Cyber-Physical Systems (CPS) are commonly represented through multiple interconnected models. During development, CPS consistency requires that shared model elements remain compatible across these models. Uncertainty, for example, due to sensor noise or model abstraction, changes the admissible values of model elements and can introduce inconsistencies, i.e., situations in which models can no longer be jointly satisfied. While existing approaches can determine consistency for a given uncertainty configuration, they provide limited support for systematically exploring, analyzing, and explaining inconsistency across large uncertainty spaces. We address this challenge by reformulating inconsistency as an intervention response modeling problem. Using Saltelli sampling and multi-fidelity Monte Carlo estimation, we generate intervention-response datasets and train a surrogate model that directly predicts inconsistency from the propagated uncertainty geometry. Experiments on 48 scenarios and 10 CPS domains show that the surrogate matches Monte Carlo estimates while reducing evaluation time from milliseconds to microseconds, enabling orders-of-magnitude more response-surface evaluations within fixed computational budgets. Building on the learned response surfaces, we perform sensitivity analysis to identify dominant uncertainty drivers and introduce a gradient-based consistency recourse method to determine minimal uncertainty interventions that restore consistency. The results show that inconsistency under uncertainty can be effectively learned, analyzed, and repaired through response-surface modeling, providing a scalable foundation for uncertainty-aware consistency management in CPS development.

We address few-shot object detection with vision-language models (VLMs) in out-of-domain settings such as aerial, industrial, and medical imagery, using only ten annotated images for supervision. Existing adaptation methods are discrete prompt optimization and LoRA fine-tuning. We revisit a third option: soft prompting, where a small number of continuous prompt tokens are optimized while the pretrained backbone remains frozen. We identify two key design choices. First, placing prompt tokens at the cross-modal boundary between visual and text tokens outperforms other placements (10.0 vs. 8.4 mAP). Second, initializing prompts from the empty space token outperforms semantic and random initialization. With these choices, one to three learned tokens (7,168 parameters on average) match the best LoRA configuration on Roboflow20-VL (14.2 mAP, 10-shot) while training over 20,000x fewer parameters. Soft prompting remains harder to optimize, exhibiting higher variance across random seeds. Unlike LoRA, however, it causes no forgetting: the LoRA rank matching our accuracy reduces NaturalBench VQA accuracy by 35% relative, rising to 56% at the largest rank, whereas soft prompting leaves pretrained performance unchanged. The learned tokens behave like prompts rather than weights. They transfer to a newer model without retraining (+0.8 mAP on Qwen3.5-9B) and can be verbalized into readable prompts competitive with prompt-search methods (matching DetPO and outperforming GEPA). The approach also extends beyond detection. On RoboCasa manipulation tasks, the frozen $\pi_{0.5}$ vision-language-action policy benefits from soft prompting, matching the LoRA baseline on two of three tasks when tokens are placed at the gradient bottleneck. These results suggest modern VLMs already encode much of what is needed for specialized domains; the challenge is learning how to ask.

Modulo-folding analog-to-digital converters (MF-ADCs) enable low-dynamic-range quantizers to sample high-amplitude signals without clipping. However, downstream processing traditionally relies on waveform unfolding algorithms, which require high oversampling rates and are highly sensitive to noise. For communication receivers, where the goal is symbol detection rather than signal reconstruction, unfolding is a redundant intermediate step. In this paper, we propose an unfolding-free maximum-likelihood symbol-detection framework for oversampled MF-ADCs in the presence of joint channel and quantization noise. By leveraging modulo wrap cancellation, we derive an exact, single-term Mahalanobis-distance metric that operates directly on folded observations. To handle long sequences, we introduce a parallelized block search algorithm that reduces computational complexity to scale linearly with sequence length. Simulations show our detector significantly outperforms existing unfolding baselines and approaches unclipped conventional ADC performance.

Existing single-channel co-frequency signal blind separation (SCSBS) algorithms struggle to balance separation accuracy, computational complexity, and robustness, while current channel state information (CSI) estimation methods lack precision. To address these limitations, we propose a sequential detection (SD)-based iterative separation (SDIS) algorithm. SDIS incorporates a delayed unscented Kalman filter (DUKF) into an iterative decision feedback framework, jointly enhancing signal separation and CSI estimation. Simulation results show that SDIS outperforms benchmarks in separation accuracy, CSI estimation accuracy, computational efficiency, and robustness. Notably, when the mean bit error rate (MBER) drops below $10^{-4}$, SDIS can tolerate at least $0.8$ dB more noise than the benchmarks.

Recently, large language model (LLM) based ASR models have achieved significant progress, yet they generally lack support for multi-speaker scenarios, where the cocktail party problem remains a critical bottleneck for further advancing ASR. Existing TS-ASR methods, including end-to-end architectures with speaker embeddings and latest LLM-based explorations suffer from degraded single-speaker performance and the inability to reject when the target speaker is absent. In this paper, we propose Xiaomi-CocktailASR-1, an LLM-based end-to-end TS-ASR architecture. By utilizing reference speech as voiceprint prompts, it directly transcribes the target speaker's speech without requiring speech separation. Xiaomi-CocktailASR-1 maintains competitive performance in single-speaker scenarios, comparable to mainstream ASR models. It also features a negative sample rejection capability, outputting empty text when the target speaker is absent from the mixed speech. Additionally, Xiaomi-CocktailASR-1 supports a Chain-of-Thought (CoT) reasoning mode to provide explicit reasoning steps. Extensive experiments on various synthetic and real-world multispeaker benchmarks demonstrate that Xiaomi-CocktailASR-1 achieves state-of-the-art performance, effectively addressing the cocktail party problem through a unified architecture that balances multispeaker and single-speaker recognition accuracy, along with rejection capability.

Tracking the temporal evolution of network topologies is a fundamental challenge in social networks, epidemiology, and sensor systems, among others. This paper develops an exact Bayesian tracker for unweighted, directed graphs using nodal signal observations. This framework yields the full posterior probability distribution over network states at each time step, naturally enabling uncertainty quantification, prediction, and principled decision-making. We model the network dynamics as a Markov process on the Boolean hypercube, where edges transition independently according to a flip probability. For efficient computation, we cast the prediction step as a dyadic convolution, and leverage the Fast Walsh-Hadamard Transform to reduce the computational cost from $\mathcal{O} (4^k)$ to $\mathcal{O} (k 2^k)$, where $k$ is the maximum node degree. When the network transition probabilities are unknown, we develop an Expectation-Maximization framework to learn them from the observed signals. Comprehensive experiments on synthetic and six real-world datasets validate the proposed method and demonstrate its superior tracking accuracy, faster recovery from topological changes, and meaningful uncertainty estimates compared to state-of-the-art and classical baselines.

We propose a preference optimization framework with Large Audio-Language Model (LALM) feedback for controllable non-verbal vocalization (NVV) generation in continuous autoregressive speech models. To construct preference data without human preference annotation, we build a bilingual prompt corpus by combining NVV-injected real transcripts with LLM-generated semantically aligned prompts, perform stochastic model rollouts, and use a LALM to rank candidate utterances and form same-prompt chosen–rejected pairs. We then adopt a two-stage optimization strategy: Rejection Sampling Fine-Tuning (RSFT) first adapts the model to LALM-selected high-scoring samples, followed by Anchored Flow-DPO, which formulates pairwise preference optimization using utterance-level flow-matching loss and retains the chosen-sample flow-matching objective as an SFT anchor. This design enables DPO-style preference learning without explicit sequence likelihoods while preserving direct supervision on preferred realizations. On the official 1,600-utterance NVVSpeech Challenge Track~2 test set, our method achieves a Final Track2Score of 75.80 (79.39 ZH / 72.21 EN), outperforming the VoxCPM2 baseline by +1.84. The improvements are mainly driven by higher NVV Accuracy and NVV Perceptual Effect, while Overall Quality remains stable.

Radiomap blind prediction infers radiomaps from observable representations of the propagation environment and base station (BS) configuration without field measurements. These representations are inherently incomplete and cannot uniquely determine the target radiomap. Under squared loss, we identify the conditional-mean radiomap as the population-optimal deterministic target and decompose domain risk into target-approximation error and irreducible uncertainty. The train-test risk gap motivates propagation priors as cross-domain guidance, although their partial or simplified forms may bias the attainable predictor. We therefore propose RadioDecomp, which treats a prior-guided predictor as a correctable base and uses deterministic residual refinement to learn its remaining predictable discrepancy. We instantiate RadioDecomp as RadioLSR (LoS-Shadow-Residual). Experiments under cross-configuration and cross-environment settings show that RadioLSR is especially effective for cross-configuration generalization and provides overall gains over a controlled monolithic counterpart under cross-environment generalization.

In-context learning (ICL) promises training-free adaptation for audio, where labeling every new condition is costly. Yet existing audio ICL studies largely measure Task Recognition, where demonstrations merely cue pre-trained capabilities, rather than Task Learning, where a genuinely new input-label mapping must be inferred from demonstrations alone. We introduce AudioICL-Bench, a diagnostic benchmark whose per-episode rules are resampled so that no correct answer is recoverable from prior knowledge. Its nine tasks are organized along two axes that separate what must be learned from demonstrations from what must be perceived in the signal, enabling failures to be attributed to either source. Across five Large Audio Language Models, the strongest models readily bind arbitrary sounds to new labels when perception is easy, but collapse on temporal measurement and composing multiple induced rules, revealing two primary capability boundaries: temporal perception and multi-rule composition.

We consider the problem of finding sparse solutions of an underdetermined linear system $Ax=b$. In contrast to conventional approaches based on greedy algorithms or convex relaxation, we reformulate sparse approximation as a structured system of polynomial equations and connect with the literature on tensor methods. We develop an eigenvalue decomposition based method that formally guarantees recovery of all sparse solutions if there is more than one. We also develop two optimization-based methods achieving favorable computational complexity. The new methods allow explicit control of the target sparsity. Numerical experiments illustrate the performance and compare to basis pursuit (denoising) and orthogonal matching pursuit.

Optimal scheduling of combined chemo-immunotherapy is often formulated as a control-affine optimal control problem, which generically yields boundary-selected (bang-bang-type) protocols unless singular arcs occur. This structure, while convenient, neglects saturating pharmacodynamics at high dose rates. We incorporate Michaelis-Menten saturation directly into the therapy channels, making the dynamics non-control-affine and the Hamiltonian nonlinear in each control. With strictly positive exposure penalties, the Hamiltonian admits an explicit three-regime pointwise minimization law: each input is chosen at the lower bound, the upper bound, or as a unique interior minimizer. On interior intervals the strict Legendre condition holds, so continuously modulated dosing arises as a regular interior extremal rather than a singular-arc or smoothing artifact. The resulting transcription is nonconvex; we therefore use a hybrid Quantum Particle Swarm Optimization (QPSO)-Sequential Quadratic Programming (SQP) pipeline, where QPSO provides a constraint-aware warm start and SQP enforces feasibility and Karush-Kuhn-Tucker (KKT) optimality on a collocation grid. Costate reconstruction corroborates the Pontryagin Minimum Principle (PMP) structure and the predicted boundary/interior regime transitions.

Deep learning models, notably Long Short-Term Memory (LSTM), have demonstrated promising performance in channel estimation for high-mobility vehicular environments. However, their black-box nature and architectural overhead limit trustworthiness and efficiency. Classical explainable AI (XAI) methods rely on costly iterative processes, offering only input-level filtering without addressing architectural fine-tuning. To overcome these limitations, this paper proposes the XAI-assisted Recurrent neural network Attribution for Channel Estimation (X-RACE) framework. X-RACE uses a low-complexity, one-shot dual-optimization strategy to simultaneously evaluate and prune irrelevant input subcarriers and internal hidden units. Furthermore, we propose novel temporal XAI metrics: Saturation Time, Importance Drift, and Relevance Contrast to characterize the LSTM's learning dynamics and memory convergence. Extensive simulations demonstrate that X-RACE reduces inference complexity by at least 44.1% while improving or preserving Bit Error Rate (BER) performance, outperforming classical XAI schemes.

Optimal control in cancer chemotherapy is challenged by tumor heterogeneity and mutations, which complicate treatment effectiveness. Traditional methods, such as Pontryagin's maximum principle (PMP), are often hindered by their reliance on an initial guess for the costate equation, affecting accuracy and convergence. To address these limitations, this work introduces a hybrid quantum particle swarm optimization (QPSO) method based on regularization. QPSO is employed for global exploration to approximate the optimal control trajectory, followed by a regularization-based refinement to ensure smoothness and consistency with optimality conditions. The Hamiltonian function is used for first- and second-order optimality checks, verifying solution quality. Numerical case studies explore various drug effectiveness functions, demonstrating the role of periodic and localized drug delivery in achieving robust tumor suppression and providing insights into the impact of different drug combinations on optimal chemotherapy strategies.