Papers

Let $\mathcal M$ be a diffuse semifinite von Neumann algebra endowed with a faithful normal semifinite trace $\tau$. We prove that, for every nonzero Banach space $Y$, the projective tensor product $L_1(\mathcal M,\tau)\widehat{\otimes}_{\pi}Y$ has the operator Daugavet property. Moreover, the witnessing operators may always be chosen contractive. This extends the operator Daugavet phenomenon from atomless vector-valued $L_1$-spaces to the semifinite noncommutative setting and yields further Daugavet-type consequences for projective symmetric tensor products, all without approximation assumptions.

We study $\widetilde{H}$-cobordisms of distinguished homology handles, introduced by Kawauchi in 1976 using infinite cyclic covers. Despite the extensive development of gauge-theoretic and Floer-theoretic invariants since Kawauchi's work, none were previously known to distinguish smooth and topological $\widetilde{H}$-cobordism. In this paper, we construct asymptotic invariants of distinguished homology handles by applying real Seiberg–Witten theory to finite cyclic covers. Using these invariants, we show that the kernel of the natural map from the smooth $\widetilde{H}$-cobordism group to its topological counterpart contains a subgroup isomorphic to $\mathbb{Z}$. We also define spin versions of these groups and show that the kernel of the corresponding natural map contains a subgroup isomorphic to $\mathbb{Z}^\infty$.

Voice assistants grounded in external knowledge typically use automatic speech recognition (ASR) to transcribe speech queries before retrieving evidence from textual knowledge bases. This cascade adds latency and propagates recognition errors, whereas direct speech retrieval is vulnerable to cross-modal misalignment. To address these limitations, we propose DUPAR, a conversational retrieval framework with complementary slow and fast paths. The fast path uses a task-adapted audio encoder aligned with frozen BGE-M3 text embeddings to search a cross-turn evidence cache. When cache confidence is insufficient, the slow path fuses full-index retrieval using audio and ASR-transcript embeddings, and the selected evidence refreshes the next-turn evidence cache through one-hop graph expansion. On a domain-specific knowledge base, our trained audio encoder approaches text-retrieval accuracy on clean speech with a 3.75$\times$ query-side speedup over ASR + Text Encoder. It raises average Recall@10 from 0.771 to 0.875 on the noise benchmark and improves overall Recall@1 by 4.2 percentage points across synthesized speaking styles. Compared with full-index audio retrieval, cross-turn evidence caching significantly reduces retrieval errors when the previous turn retrieves correct evidence and the follow-up targets a one-hop neighboring chunk.

Multi-encoder fusion extends Large Audio-Language Models (LALMs) beyond speech-centric recognition, but selecting encoders via intuition or exhaustive search often introduces redundant representations and inflates an already constrained compute budget. We propose CUES (Correlation-gUided Encoder Selection), a lightweight heuristic that estimates complementarity through task- and category-level Pearson correlations between encoders' performance profiles, scoring a candidate set from single-encoder evaluations alone–without fusion training during selection. Evaluated on the XARES-LLM benchmark with a frozen SmolLM2-135M backbone (LoRA-adapted) via five-fold cross-validation, CUES consistently identifies the same configuration per track from held-out development splits alone, without using test data for selection. For the broad Track~A suite, CUES selects a cross-family trio (Whisper-medium, mHuBERT-147, and Dasheng-base), achieving a 4.3% relative gain over Whisper-medium (0.771 vs. 0.739). For Track~B text generation, it re-anchors on a focused, speech-only pair (mHuBERT-147 and WavLM-base-plus) and actively abstains from adding a divergent encoder, outperforming mHuBERT-147 by 6.3% (0.589 vs. 0.554). Rather than a failure to scale, this divergence is consistent with a diversity–interference trade-off that CUES navigates per track from correlation signals alone: across the evaluated pool, added cross-family diversity tends toward an inverted-U on broad audio tasks but toward steady degradation on text generation, which favors a focused, speech-anchored set.

Sound event localization and detection (SELD) systems often rely on first-order Ambisonics (FOA) input, whereas obtaining useful FOA representations from irregular microphone arrays remains challenging. This paper proposes a two-stage SELD framework that learns a task-oriented, FOA-compatible representation from microphone-array signals. A neural residual encoder first refines conventional FOA encoding through a signal-dependent correction. A teacher–student scheme then transfers event and spatial knowledge from theoretical FOA representations through frame-level permutation-invariant knowledge distillation. Experiments on synthetic scenes with tetrahedral and 12-channel Benchmark arrays, together with real stationary-source recordings from the LOCATA dataset, show that teacher guidance consistently improves downstream SELD performance and substantially reduces localization error. Signal-level analysis further shows that lower FOA reconstruction error does not necessarily correspond to better SELD performance, indicating that the distilled representation is optimized primarily for task-relevant spatial information rather than strict FOA reconstruction.

We establish explicit sufficient conditions for multiplicity of positive solutions of the Hénon equation in the unit ball and for uniqueness in one dimension. In the Sobolev-subcritical range, a spherical harmonic function argument shows that the radial solution has Morse index greater than one and therefore differs from a ground state. In even dimensions, a degree-four perturbation in a symmetry and monotonicity cone yields a sufficient condition for nonradiality in the supercritical range. The one-dimensional uniqueness criterion follows from a comparison of weighted Dirichlet eigenvalues and a concavity estimate.

The world population is growing rapidly, and technology is improving in parallel. Meeting the huge demand for food for these 7 billion people not only depends on increasing food production but also on reducing food loss. Crop losses due to disease affect both the food supply and the financial and economic stability of a country. Tomatoes are among the top food-producing crops globally, and a significant portion of this production is lost due to disease. People have used Machine Learning techniques for feature extraction and early diagnosis of tomato diseases, and nowadays, Deep Learning-based models are widely used for disease recognition. However, most existing models are highly parameter-intensive, which increases the time required for training and inference. As a result, while lightweight models are more suitable for user-friendly applications, they often show a reduction in performance. To balance performance and model size, we propose CoAtNet-DeepMoE, a Convolution-Attention hybrid architecture for rich feature extraction, further enhanced with a DeepSeek Mixture of Experts to substantially reduce the number of parameters without sacrificing accuracy. We evaluate our model on both balanced and imbalanced datasets from Kaggle and PlantVillage, demonstrating robustness and achieving 99.80% accuracy, 99.80% precision, 99.80% recall, and 99.80% F1-score on Kaggle, and 99.83% accuracy, 99.85% precision, 99.76% recall, and 99.80% F1-score on PlantVillage, representing state-of-the-art performance with only 2.47M parameters. The source code will be available at https://github.com/nadimbrur/CoAt-MoE.

Segment Anything Models provide reusable priors, yet they require user prompts and cannot support fully automatic instrument segmentation. Automatic prompting is difficult for thin, articulated, reflective, and partly occluded tools, where several configurations can be valid. We formulate automatic prompting as lightweight point-set planning and isolate the point source under a frozen pathway. To this end, we present SetPlanner, a 1.52M-parameter plug-in point-set planner for frozen SAM. The plug-in preserves SAM's point-prompt interface and enables reuse across backbones. SetPlanner plans complete unordered K-point sets from geometry-aware targets with a permutation-aware conditional flow. SAM decodes eight candidates; their consensus readout yields a ground-truth-free prediction. Across three endoscopic datasets, SetPlanner wins all six transfer routes over a LoRA-adapted system. Under our frozen-pathway protocol, SetPlanner reaches 0.934 Dice on Kvasir-Instrument and recovers 96% of a 44.4-point localization gap, while candidate disagreement ranks low-Dice cases at AUROC 0.969.

We address a long-standing paradox in plate tectonics concerning the thermodynamics of its very origin: What supplies the thermal energy for the intense island-arc volcanism at the subduction zones, the supposedly cool end of the mantle convection? We surmise a first-principle physics model tracking the gravitational energy (Eg)-heat conversion within the mantle convection. The scenario points to a great amount of Eg release of ~10 TW induced by the thrust-faulting earthquakes that occur predominantly in the upper mantle at the subduction zones. Generally ~1000 times greater than the seismic energy release or nearly a quarter of the total terrestrial heat flow, this Eg release, upon conversion into heat in the irreversible convection process, supplies amply for the island-arc volcanism. Meanwhile similar but opposite and less vigorous Eg gains at ~2 TW occur at the diverging plate boundaries via the normal-faulting earthquakes. This model resolves the said paradox, and more importantly provides a new paradigm pointing to an active role of seismicity in the plate tectonic energetics and evolution of the convecting mantle.

Valley-layer coupling (VLC) two-dimensional (2D) materials define a distinct class of quantum systems in which valleys are related by crystal, rather than time-reversal ($\mathcal{T}$) symmetry, enabling gate-controlled valley-contrasted layer polarization. Here we extend this concept to excitons. Using TiSiCo as a prototype VLC material, we show that a perpendicular electric field $E_{\perp}$ controls exciton- dispersion anisotropy and thereby generates unconventional linear transverse exciton transport in both monolayer and twisted bilayer structures. In the monolayer, this response is characterized by anisotropy-induced transverse conductivities, arising from the antisymmetric combination of diagonal elements in the conductivity tensor and strongly tunable by $E_{\perp}$. In the twisted bilayer, symmetry additionally permits transverse responses from the symmetric part of the conductivity tensor. Since intralayer excitons in different layers are connected by the Förster coupling, these symmetric and antisymmetric responses coexist and compete with the recently proposed $\mathcal{T}$-even layer Hall and Nernst exciton counterflow. This interplay is highly tunable by twisted angle, temperature, and the direction of the in-plane driving force, providing a route to disentangle distinct transverse exciton transport signals experimentally. Our results establish $E_{\perp}$ as a powerful knob for controlling exciton transport via VLC and identify VLC 2D materials as a promising platform for engineered excitonic phenomena.

Novel view synthesis from unposed multi-view images remains challenging, as the model must jointly learn scene representations and camera parameters without pose supervision. Existing approaches largely fall into two extremes: implicit latent-space rendering is flexible and easy to optimize, but often yields weakly grounded camera estimation; explicit 3D representations provide stronger geometric grounding, but introduce heavier parameterization and more fragile optimization. In this paper, we present IRIS, a fully self-supervised framework that provides a practical middle ground between these two paradigms. Instead of decoding free latent tokens or reconstructing fully explicit 3D primitives, IRIS represents the scene as a latent neural field and renders novel views by querying this field under self-predicted cameras. Specifically, projected features from reference views are aggregated at sampled 3D points to form point-wise latent features, which are then composed along target rays for rendering. This design preserves the flexibility and optimization stability of implicit modeling, while introducing stronger geometric structure than unconstrained latent rendering. Extensive experiments show that IRIS achieves strong novel view synthesis quality with competitive pose accuracy under fully self-supervised learning. Our project page: https://leo-frank.github.io/IRIS

The brain needs an accurate internal model of the world to generate predictions and guide behavior. However, it must estimate the statistical structure of the environment from limited experience. This is particularly difficult for rare events, whose observed frequencies in a limited sample may substantially under- or overestimate their true frequencies. How the brain constructs an accurate internal model despite this sampling problem remains unclear. We address this problem using a Bayesian Confidence Propagation Neural Network (BCPNN) trained on event sequences from a Markov-chain random walk with controlled event frequencies. Treating the underlying Markov structure as the ground truth, we train the network on limited sample of event sequences and then allow it to generate autonomous replay based on the learned structure. We evaluate replay fidelity at the levels of both marginal event frequencies and conditional transition structure. We find that moderate neural noise, modeled as temporally correlated random fluctuations in unit activity during replay, is critical for faithful internal simulation. Without this variability, deterministic replay systematically under- or overrepresents rare events, whereas moderate noise restores both their marginal and conditional occurrence. Moderate noise also broadens the range of parameter values that produce accurate replay, making the model more robust to parameter variation. Together, these results support noise-assisted internal simulation as a potential mechanism for compensating for sampling errors arising from limited experience. Our model also provides a testable framework for investigating how altered neural variability may impair internal-model fidelity in disorders such as Parkinson's disease.

We prove that the Scott topology commutes with arbitrary products of countably presented frames and that every such product has a sober Scott space. In particular, this holds for arbitrary products of countable complete Heyting algebras. For a family of consonant spaces, Scott-product compatibility of their open-set lattices is equivalent to consonance of their topological sum. Countable generation does not suffice: a countably generated spatial frame can have a non-sober Scott space and fail the product identity for its square. We also show that the cardinal spectra of Scott non-sober frames and spatial frames are upward closed and, under the Continuum Hypothesis, consist of all uncountable cardinals. Finally, every Artinian $T_0$ web space is a $B$-space; if it is also a $d$-space, it carries the Scott topology of an algebraic dcpo. Consequently, every Artinian meet-continuous dcpo is algebraic. This yields a dichotomy theorem: a dcpo with a non-sober Scott space must fail meet continuity or Artinianity.

Contact-rich physical human–robot interaction (pHRI) imposes time-varying demands associated with physical interaction, motor regulation, and physiological response, motivating continuous assessment of interaction workload. This paper presents an online multimodal assessment framework that integrates interaction wrench, planar tool-center-point (TCP) kinematics, and skin conductance level (SCL) into four interpretable workload-related factors. Their relative contributions are adjusted using path curvature to reflect changes in motion demand and task progression to account for gradual physiological variation over time. The framework was evaluated with 24 participants across 18 controlled combinations of temperature, acoustic noise, and illuminance under two admittance-control modes. Strict leave-one-subject-out (LOSO) evaluation used standardized pupil diameter ($\mathrm{PD}_z$) as an independent physiological reference and included comparisons with static variants and representative state-of-the-art learning-based baselines. The proposed framework achieves a cohort-mean $30\,\mathrm{s}$ block-wise Spearman correlation of $\rho_{30}=0.308$ with the physiological reference, with positive subject-level correspondence in 23 of 24 participants. Its overall performance is comparable to the state-of-the-art learning-based baseline. At the same time, our framework keeps the assessment process transparent through explicit workload-related factors and defined weighting rules, while outperforming the corresponding fixed-weight formulation. The framework also maintains consistent performance across the two tested admittance-control modes. These results support a transparent and interpretable approach to continuous interaction workload assessment in contact-rich pHRI.

We study an optimal control problem for a two-equations Keller-Segel system on a bounded domain with Neumann boundary conditions, where the chemotactic sensitivity is modulated by a control $f(x,t)$ acting on the taxis flux $\nabla\!\cdot(f\,u\,\nabla v)$. We prove the well-posedness of the state equation under low regularity assumptions. The analysis is based on the study of an $\varepsilon$-regularized problem, the application of Schauder's fixed point theorem, $\varepsilon$-independent, positivity and a priori estimates, the passage to the limit as $\varepsilon \to 0$, and a uniqueness argument. For a cost functional combining trajectory tracking, taxis penalization, control regularization, and terminal objectives, we establish the existence of optimal controls and derive the first-order optimality conditions through a Lagrange multiplier framework, leading to an adjoint system and a variational inequality for the optimal control. A numerical scheme based on spline collocation in space and Runge-Kutta time-stepping is set and implemented. Numerical experiments are performed to simulate the free and controlled dynamics in conservative and non-conservative cases.

AI is increasingly used to support decarbonization decisions across the built environment, yet the development, training, and use of AI consume energy and induce CO2e emissions. However, existing assessments often report physical-system savings while omitting AI-side emissions. Moreover, they rarely account for the mismatch between when AI costs occur and when decarbonization benefits materialize, which may be substantial for infrastructure-scale projects. To address these issues, we present a time-aware assessment framework that models avoided emissions and AI-induced emissions as discrete-time streams over a finite time horizon. In demonstrating this process, we seek to show that time-aware assessment can support temporal decision-making, identify cases in which accounting for time value of carbon can change preferred rankings relative to time-invariant totals, and explore how decisions may vary with slightly different governance priorities. Using four representative interventions with intentionally different temporal profiles (multi-project low-carbon concrete design support, AI-assisted construction logistics, agentic HVAC control, and predictive maintenance), we demonstrate how discounting can change preferred rankings relative to time-invariant totals and supports ranking sensitivity analysis, discounted payback screening, and break-even discount-rate analysis. We also provide decision guidelines that support go/no-go screening, timing decisions, and minimum "bang-for-your-buck" thresholds. Ultimately, this work contributes a lightweight framework for deciding whether and when to deploy AI-enabled interventions for decarbonization under explicit time preference.

The Bekenstein-Hawking entropy, proportional to one quarter of the horizon area, is fundamental in black hole thermodynamics and can also be understood via the AdS/CFT correspondence, such as the 3D BTZ black hole and 2D CFT. In this work, we adopt the Kerr/CFT approach to analyze the central charge and black hole entropy for regular extremal black-bounce spacetimes, including the counterparts of the Kerr, Kerr-Newman, and Reissner-Nordström black holes. These spacetimes are free of curvature singularities at $r=0$. We derive the near horizon geometries of these spacetimes and find that they exhibit enhanced symmetry, namely SL$(2,\mathbb{R})\times \mathrm{U}(1)$ or SL$(2,\mathbb{R}) \times \mathrm{SO}(3)$. By imposing appropriate boundary conditions, we analyze their asymptotic symmetry groups, which contain diffeomorphisms as well as the $\mathrm{U}(1)_{\rm gauge}$ symmetry arising from the electromagnetic field. We then extract the central charge from the charge algebra and evaluate the left-moving temperature of the Frolov-Thorne vacuum. It is worth emphasizing that in the black-bounce Kerr-Newman case, the central charge from the electromagnetic contribution vanishes. Furthermore, in the black-bounce Reissner-Nordström case, we uplift the 4D geometry to a 5D configuration by incorporating a $\mathrm{U}(1)$ gauge fiber. Our results show that the microscopic entropy calculated from the Cardy formula is consistent with the Bekenstein-Hawking entropy. This agreement suggests that the Kerr/CFT approach remains valid for certain regular spacetimes without curvature singularities, thereby providing a microscopic statistical understanding of black hole entropy.

An agentic framework is proposed for autonomous site-specific base station (BS) deployment in wireless network planning. In contrast to conventional approaches that rely on manual site surveys or extensive ray-tracing (RT) simulations with significant human intervention, the proposed framework autonomously explores and optimizes BS deployment under a limited RT evaluation budget, enabling resource-efficient network planning. To this end, a continuous, geometry-grounded deployment action space is first constructed from three-dimensional (3D) wireless digital twins. Within this action space, an agent team operates through a stateful perception–reasoning–reflection loop. Specifically, a Placement Agent first generates candidate BS deployments in two complementary modes: an experience-guided mode that refines promising solutions, and an exploration mode that avoids getting stuck in local optima. After the candidate deployments are evaluated through RT, a Reflection Agent interprets the RT results together with the scene geometry, identifies performance-limiting factors such as blockage, overlapping coverage, and uncovered areas, and converts these diagnoses into guidance for subsequent deployment. Through this iterative process, site-specific experience is accumulated and deployment plans are optimized without human intervention. Numerical results in two realistic urban scenarios show that: 1) the proposed approach substantially outperforms heuristic, learning-based, and large language model (LLM)-assisted methods; 2) it achieves highly competitive coverage against the optimal solution while requiring substantially fewer transmitter-level RT evaluations; 3) site-specific reflection effectively turns raw RT feedback into refinement guidance, whereas the dual-mode mechanism preserves diversity and facilitates escape from local optima.

MLegS is an open-source Modern Fortran code package for solving linear and nonlinear time-dependent partial differential equations on radially unbounded domains. It builds on an earlier in-house prototype, recasting it as a modular solver with a unified interface for fields, transforms, and spectral operators. Within this framework, the numerical formulation maps $0\leq r<\infty$ onto a finite interval, where associated Legendre functions provide the radial basis, while Fourier series represent the periodic azimuthal and axial directions. The mapped radial basis represents radial infinity without imposing an artificial boundary condition at finite radius while incorporating the regularity required at $r=0$ according to azimuthal order. The implementation distributes the corresponding field layouts using the Message-Passing Interface (MPI), with strong- and weak-scaling measurements extending to 512 cores across four compute nodes. Beyond parallel performance, three examples assess the solver across diffusion, reaction-diffusion, and vortex dynamics: closed-form diffusion solutions establish spectral spatial convergence and the design orders of both semi-implicit integrators; a Fisher-Kolmogorov-Petrovsky-Piskunov front matches the linearized solution and propagates at the classical speed within its logarithmic correction; and vortex-pair simulations based on toroidal-poloidal decomposition yield a measured Crow growth rate $2.7\%$ above the theoretical prediction and demonstrate the reconnection of the vortex pair.

Strong chromospheric absorption lines such as H$\alpha$ 6562.8 A and Ca II 8542.1 A provide vital diagnostics of plasma dynamics and thermal structure in the solar chromosphere. Multilayer spectral inversion (MLSI) offers a physically interpretable framework for modeling these lines using a finite number of radiative-transfer layers, but conventional MLSI relies on pixel-by-pixel nonlinear least-squares fitting, making it computationally expensive for large imaging spectroscopic data sets. Here, we introduce a physics-informed neural-network (PINN) framework to accelerate MLSI while preserving its analytic radiative-transfer formulation. The network predicts MLSI parameters directly from observed line profiles and passes them through a differentiable MLSI forward model to synthesize spectra. Training follows a two-stage approach: an initial stage optimized solely via spectral reconstruction loss, followed by fine-tuning that combines spectral consistency with parameter-space supervision from conventional MLSI results on a single reference image. This strategy eliminates the need for large precomputed training sets while maintaining physical interpretability. Applied to Fast Imaging Solar Spectrograph (FISS) observations from the Goode Solar Telescope (GST) targeting both quiet-Sun and active-region regions, MLSI-PINN parameter maps reproduce the primary spatial structures of direct inversions, achieving an arithmetic mean pixel-wise Pearson correlation coefficient of 0.933 across all evaluated parameters. The reconstructed spectra closely match both observed profiles and conventional MLSI fits. Post-training, MLSI-PINN processes a raster in approximately 5-15 seconds compared to 3-5 minutes for conventional MLSI, delivering an inference speedup of about 12-60 times without substantial loss in reconstruction quality, enabling efficient MLSI analysis on large chromospheric data sets.

We study data structure lower bounds for the Approximate Matrix Powering (AMP) problem. Given a substochastic, symmetric matrix $\mathbf{M}\in\mathbb{R}^{n\times n}$ and parameters $k$ and $\alpha$, the goal is to preprocess $\mathbf{M}$ so as to answer entry queries $(u,v)\mapsto \mathbf{M}^{k}[u,v]$ up to additive error $1/n^{\alpha}$. We focus on AMP in the succinct and systematic regime, in which the data structure stores $\mathbf{M}$ verbatim, uses an additional $r$ bits of redundancy, and must answer queries by probing only a small number of entries of $\mathbf{M}$. Our main conceptual contribution is a general framework for proving probe–redundancy trade-offs for systematic data structures. We introduce the query-with-sketch model and develop a min-entropy-based approach that lifts conditional min-entropy bounds in the absence of redundancy to probe lower bounds in the presence of redundancy. We then establish these min-entropy bounds using problem-specific analytic and algebraic tools, for the downstream applications to AMP and its variants. As a consequence, our results provide new unconditional evidence toward a conjecture of Patrascu and Roditty (2010) on the space required for constant-time set-disjointness queries.

Chatterjee and Sloman proved that a bounded measurable similarity function with sufficiently small average Gromov hyperbolicity admits a tree representation with small mean approximation error. Their argument uses a weighted version of Szemerédi's regularity lemma and does not yield explicit quantitative bounds. Here, we establish a tighter relation between average hyperbolicity and mean tree approximation error. For a similarity function $s:S\times S\to[0,b]$, we prove that $$\operatorname{Tree}(s) \leq (63/e)^{1/3} \sqrt[3]{b^2 \operatorname{Hyp}(s)} \leq 2.8512 \sqrt[3]{b^2 \operatorname{Hyp}(s)}.$$ The proof uses a simple pivoting construction inspired by \KwikCluster. We also discuss the optimal dependence on average hyperbolicity, including a square-root lower bound, and connections with ultrametric fitting.

RTL source-level debugging research requires benchmark artifacts that provide faulty designs together with precise change locations, executable test stimuli, and reproducible configurations. Available Verilog resources usually provide only a subset of these elements. We present VeriBugBench, a framework for constructing Verilog RTL debugging benchmarks through empirically grounded fault construction, LLM-based testbench enhancement, and execution-based retention. The mutation library maps recurring, multi-granularity repair patterns observed in RTL bug-fix histories to 19 executable inverse operators. For each project, an LLM generates a design-specific stimulus phase from the clean DUT and original testbench; the phase is composed with the original testbench for candidate execution. Applying the framework to 45 open-source projects yields VeriBugBench-v1.0, with 2,608 executable single-fault instances whose effects are observable at design outputs. Across the 45 projects, the assembled testbenches increase mean project-level fault observability from 36.01% to 39.54% and improve line coverage and execution-trace diversity on average. VeriBugBench provides versioned RTL variants, source-level ground truth, testbenches, and execution artifacts for evaluating RTL debugging methods.

We consider composite optimization with a smooth, possibly nonconvex function and a separable convex polyhedral term. Such problems have a simple nonsmooth structure but arise widely in applications. Existing Newton-type methods may fail to identify nonsmooth coordinates during direction computation, move coordinates away from those reached by the full step during line search, or rely on separate first-order steps for identification. In this work, we propose a unified inexact proximal Newton method that couples structure identification with second-order acceleration through a proximal line search designed to retain the nonsmooth structure revealed at the local model. In particular, on a predicted working set, we solve a quadratic model inexactly but enforce its constraints exactly, allowing coordinates to reach new kinks without leaving the selected affine intervals. This set also includes small-margin kink coordinates to exploit the Hessian coupling effect. To globalize the direction, we construct a proximal line search using an isotropic proximal model whose linear term is chosen so that the initial trial exactly recovers the full step. Backtracking increases the proximal curvature until sufficient decrease holds, allowing coordinates to remain at kinks reached by the full step while damping other components. Generating each trial point requires only proximal operator evaluations. We prove finite backtracking and finite active-set identification under strict complementarity and a non-singular reduced Hessian, together with local Q-superlinear convergence under a directional Dennis-More condition and vanishing relative inexactness. Numerical results verify the effectiveness of the proposed method.

A decomposable randomized encoding (DRE) for a function $f$ allows $n$ parties, using shared randomness, to encode their individual inputs locally so that the collection of encodings reveals $f(x_1,\ldots,x_n)$ and nothing else. DREs are widely used in efficient multiparty computation. Their main complexity measure is size, the total bit length of the local encodings. Yet the optimal DRE size remains poorly understood even for the $n$-bit OR function. We prove the first superlinear lower bound for OR and, more generally, for every non-periodic symmetric function. Under an additional symmetry assumption, we prove a sharp $\Omega(n\log n)$ lower bound for OR, matching the classic construction of Feige, Kilian, and Naor (STOC 1994). We also prove the first $\Omega(n^2)$ lower bound on DRE size for non-explicit Boolean functions.

Automated execution algorithms are organized into schedule-based and liquidity-seeking families. This paper concerns the first, whose members – Time-Weighted Average Price (TWAP), Volume-Weighted Average Price (VWAP), Percentage of Volume (POV) and Implementation Shortfall – are all model-based: each derives its decisions from an explicit model, forecast, schedule or control rule. We introduce Shadow-PPOV, a passive POV whose order-placement rate is set from observed order flow rather than from traded volume. Placing a passive order to fill efficiently conventionally involves an order-book model and a fill prediction. Shadow-PPOV replaces that prediction with tracking: on observing a third-party add, it may transmit its own limit order at the same price on the same venue, recording a single association between the observed order's exchange identifier and its own. Cancellation is then identifier-driven – the shadow is withdrawn when the order it follows ends, at once on a cancel and after a brief grace window on a trade. The placement decision is thus model-free: price and venue are read off the observed order. Model-free is not information-free. Shadow-PPOV reads every order-book message and places only where a participant has just committed capital, while computing nothing from what it reads. Information is inherited from the flow rather than derived from a model. We evaluate Shadow-PPOV on a full calendar year of replayed Chicago Mercantile Exchange (CME) ES futures in a deterministic market-replay simulator, reporting its slippage and latency sensitivity and comparing it against the aggressive equivalent POV. We propose it as a model-free benchmark for passive-order placement, against which a predictive placement model can be scored. The algorithm and the order-book simulator are implemented in the open-source kaspar-hft project.

For a real symmetric matrix $H$ and distinct vertices $a,b$, we classify exponents $k$ for which $H^k$ has perfect state transfer (PST) from $a$ to $b$. If their supported eigenvalues are integer multiples of a common positive number, every odd exponent reduces to $H$ and every positive even exponent reduces to $H^2$. We determine the minimum transfer times using a greatest common divisor of supported spectral differences. For rational symmetric matrices, symmetry of the source vertex support about zero implies the odd-power equivalence without a commensurability assumption; this includes all bipartite graphs. If the source vertex supports zero, PST under one positive even power implies PST under every positive even power. For a symmetric three-point quadratic spectrum whose outer projection signs agree and differ from the central sign, a nonzero rational shift leaves exactly one PST exponent. We classify all adjacency powers of hypercubes, cycles, and Johnson graphs, and all adjacency squares of paths. In particular, the adjacency matrix of $P_7$ has PST from vertex $2$ to vertex $6$ only at exponent $2$.

Chaos emerges when stretching is repeatedly recycled by reinjection. We uncover a new route to chaos in which the decisive variable is the temporal order of non-normal tangent maps: periodic and chaotic states can share essentially the same one-step stretching statistics while their ordered products acquire opposite Lyapunov growth. We introduce the ordered-product growth rate $h_L$ over $L$ successive tangent maps, which reveals how states indistinguishable at one step separate under geometric composition and identifies the finite composition scale at which chaos emerges. We use this mechanism to establish a new form of global chaos control: minute phase actions reorient the successive non-normal amplification directions so that their geometric composition becomes contracting, suppressing chaos at fixed dissipation without reducing local amplification or targeting a preselected orbit.

World-action models (WAMs) have emerged as a promising paradigm for robot manipulation by jointly modeling future visual dynamics and robot actions. However, existing WAMs are trained predominantly on successful trajectories, making them prone to failure when real-world execution diverges from the learned dynamics. This issue is amplified in autoregressive WAMs, where execution errors become part of the causal history and continue to influence subsequent predictions. To this end, we introduce \method{}, a training-free framework that reformulates failure recovery as test-time scaling over causal histories. This formulation decomposes recovery into three coupled decisions: when to revise the causal history, where to recover a reliable history prefix, and which history configuration best supports subsequent execution. Specifically, \method{} realizes these decisions through three stages: 1) Progress-Aware Recovery Trigger detects persistent non-progress and triggers recovery only when the current execution state permits intervention; 2) History-Prefix Recovery identifies the unreliable history suffix, retrieves a historical anchor matching the current physical state, and reconstructs the causal KV state from the retained prefix while conditioning on the latest real observation; and 3) Hypothesis Verification compares the future continuations induced by complete-history, recovered-prefix, and full-reset hypotheses, and commits the best-supported hypothesis. Experiments in both simulated and real-world manipulation settings demonstrate consistent improvements in task success, while ablations confirm the contribution of each recovery stage.

Large-amplitude entrywise corruption can distort flow-field data and contaminate extracted modes. Robust principal component analysis (RPCA) separates low-rank flow content from a sparse corruption component, but recovery deteriorates when corruption occupies a large fraction of measurements. We introduce library-learning-assisted robust principal component analysis (LLA-RPCA), which restricts the recovered spatial basis to combinations of functions from a fixed candidate library and prescribes the available modal capacity. Here, the library contains standard trigonometric functions and graph-Laplacian eigenfunctions. The decomposition is solved via augmented-Lagrangian alternating minimization. The method is evaluated on a post-stall NACA0012 wake, oscillating-cylinder wake video data, and particle image velocimetry (PIV) measurements of a flat plate undergoing a transverse gust encounter. For the first two cases, synthetic large-amplitude entrywise corruption is imposed over fractions from 0% to 90%. LLA-RPCA retains coherent wake structures and recovers dominant linear modes at corruption levels where standard RPCA retains residual corruption, attenuates the reconstructed field, or collapses to a one-dimensional reconstruction. For the experimental gust-encounter case, standard RPCA exhibits a trade-off between attenuating coherent flow content and retaining naturally occurring PIV artifacts as its tuning factor increases. Conversely, LLA-RPCA suppresses artifacts while consistently preserving coherent velocity and derived-vorticity structures. These results indicate that a library-constrained reconstruction with prescribed modal capacity improves denoising and modal recovery when the prescribed representation adequately captures the relevant spatial content.