Papers

We introduce a novel Bregman proximal algorithm for convex composite optimization by applying the standard Bregman proximal gradient (BPG) method to a mirror-coordinate reparameterization of the objective. In primal variables, the resulting algorithm alternates between a preconditioned gradient step followed by a right Bregman proximal update. Our analysis relies on relative smoothness holding in the mirror coordinates instead of primal coordinates. Under this condition, we prove monotonic decrease of the objective in the general convex setting. We then specialize the method to Poisson inverse problems using weighted negative entropy as the potential. The resulting scheme recovers the classical Richardson-Lucy multiplicative updates and extends them to general convex regularizers. Building on a recent convergence analysis of multiplicative updates, we establish a sublinear convergence rate in function values for the Poisson setting. Finally, we demonstrate the performance of the regularized algorithm on several imaging inverse problems with Poisson-distributed observations. The code is publicly available at https://github.com/Tmodrzyk/MU-Bregman.

While NorMuon has achieved strong empirical performance in pretraining, its underlying adaptive mechanism remains largely heuristic and poorly understood. In this work, we provide the first systematic theoretical analysis of NorMuon's adaptivity, revealing that it primarily arises from orthogonalization-induced geometry rather than genuine optimization dynamics, serving to offset the resulting geometric non-uniformity. Under exact orthogonalization, the adaptive scaling factors degenerate into a single global scalar for square and wide matrices, while for tall matrices their variation results from unevenly distributed row energy after orthogonalization. Under approximate orthogonalization, the orthogonality residuals introduce additional variation into the scaling, giving rise to a counterintuitive Orthogonalization–Adaptivity Paradox: more accurate orthogonalization weakens adaptivity. We further show that NorMuon's rigid row-wise scaling is geometrically misaligned with the one-sided orthogonal structure of tall matrices by distorting column orthogonality. Motivated by these limitations, we propose two core design principles that a desirable adaptive mechanism for Muon should satisfy. First, adaptive scaling should be decoupled from orthogonalization, with the scaling factors computed directly from raw gradients. Second, adaptive scaling should be aligned with the shape-dependent orthogonal structure of the polar factor, using row-wise scaling for wide matrices and column-wise scaling for tall matrices. We prove that this geometry-aligned scaling preserves the orthogonal structure of the update. By incorporating several other techniques, we obtain Decoupled Geometry-Aligned Muon (DGA-Muon). We establish convergence guarantees for DGA-Muon and empirically validate both our theoretical characterization of NorMuon's scaling degeneration and the superiority of DGA-Muon.

Geometry optimization is a major cost in many quantum-chemical workflows: each optimization step requires one force evaluation, and at the density-functional level that evaluation dominates the wall time. Research in this area has produced a broad range of optimization methods, and we ask whether a language model can improve on the best of them through autoresearch. An agent rewrites the optimizer itself to minimize force-call counts, restrained by two admission gates that reject premature stopping and improvements that do not generalize to unseen molecules. Starting from Sella, the fastest open-source optimizer available, the search produces AutoSella, a family of two optimizers. Both of them deliver consistent force-call reductions relative to Sella across held-out molecular benchmarks and potentials not used during the search. Most notably, at the r2SCAN-3c DFT level, the best variant requires only 40.2-77.2% of Sella's force calls while achieving the same energy reduction, even though agent used no DFT gradients.

Large language model (LLM)-based agents can exhibit deceptive behavior during task execution, including hiding failures, fabricating results, or falsely signaling task completion. Existing monitoring approaches mainly detect deception after it appears in observable actions or outputs. In this paper, we investigate whether deceptive behavior can be predicted from an agent's internal representations before it becomes externally visible. We frame deception monitoring as a trajectory-level representation analysis problem and align agent trajectories around key decision points. Using hidden states extracted before these points, we show that future honest and deceptive outcomes can be reliably distinguished, with predictive signals remaining detectable several model calls before the final decision. We further characterize the temporal evolution of these signals: deception-related representations are weak early in execution but become increasingly identifiable as trajectories progress, while transferable structure can emerge before the strongest decision-adjacent signals appear. Finally, we intervene on the identified honest-deceptive representation directions during inference and find that activation steering reduces downstream deceptive behavior, suggesting that these representations influence agent decisions. Our findings indicate that agent deception is an evolving internal process that can be detected and potentially mitigated before it is expressed externally.

FrontVeg V2 is an open-source, training-free software framework for foregroundaware zero-shot segmentation of plant traits in high-resolution images of trellised crops. The pipeline combines monocular depth estimation, automatic foreground extraction using Valley-Aware Depth Thresholding, tiled zero-shot segmentation, Graph-Based Mask Assembly, and geometry-aware fusion. This design enables plant organs and disease symptoms to be segmented while reducing detections arising from neighboring vegetation rows. The current implementation integrates Depth Anything V2 (DAV2) and SAM3 and can be used through both command-line batch processing and a Napari graphical interface. FrontVeg V2 provides a reusable framework for multi-crop, multi-trait digital phenotyping without task-specific model retraining.

We introduce contraction tree boundary matrix product states (CT-bMPS), a scalable approximate contraction method for general closed tensor networks. CT-bMPS represents the boundary tensor and its complementary environment at each edge of a contraction tree as matrix product states. This representation allows local compression based on a reduced transition matrix to incorporate environment information along arbitrary contraction trees, while keeping the time and memory costs polynomial in the network size and bond dimension. We benchmark the method on a variety of models and applications, including Ising partition functions, random tensor networks, kicked Ising dynamics, and quantum error correction decoding. These benchmarks demonstrate improved accuracy and computational efficiency over existing general-purpose approximate contraction methods, together with the ability to handle larger and more complex networks. Optimized contraction trees and environment updates substantially improve accuracy without increasing the bond dimension. These results establish CT-bMPS as a general and scalable approximation framework with flexible contraction orders and environment-based compression for a wide range of applications.

Let $(M^n,g_0)$ be a closed connected Einstein manifold with positive scalar curvature, where $n\ge6$. Using an Obata-type identity, we prove that every smooth metric conformal to $g_0$ with constant sixth-order $Q$-curvature is Einstein.

This paper investigates the non-emptiness of the fuzzy core and introduces the notion of the TU-fuzzy core for pure exchange economies with discontinuous utility functions. We propose two stability conditions: local fuzzy-coalition stability and local TU-fuzzy-coalition stability. We also introduce an independent-$\pi$-balanced family of subsets of the agent set to construct two payoff-dependent NTU games. These constructions serve as bridges linking the fuzzy core, the TU-fuzzy core, and NTU games. Under the proposed stability conditions, we establish the non-emptiness of the fuzzy core for economies with quasi-concave utility functions and the non-emptiness of the TU-fuzzy core for economies with concave utility functions.

Brain MRI interpretation is a longitudinal clinical reasoning problem: radiologists compare serial studies, integrate information across MRI sequences, localize findings within volumetric anatomy, and translate this evidence into report-grounded assessments. Existing medical VQA and 3D imaging benchmarks capture important parts of this workflow, but often evaluate brain MRI through isolated images, static volumes, or ungrounded report-style answers, thereby obscuring failures in the evidence chain that support clinical validity. We introduce BrainTRACE, a report-grounded benchmark for evaluating whether vision-language models can trace the evidence structure required for longitudinal brain MRI interpretation. BrainTRACE contains 7,273 scored VQA instances derived from 1,778 longitudinal patients, 7,299 MRI studies, and approximately 29k co-registered 3D MRI sequence volumes. The benchmark is organized by five levels of clinical reasoning, from acquisition recognition to case-level synthesis, and by evidence demands covering longitudinal comparison, report-grounded references, multi-sequence integration, and volumetric spatial evidence. BrainTRACE supports rendered inputs compatible with standard VLM interfaces, a 3D-evidence condition, and a decomposed case-reasoning track that audits six steps in a longitudinal evidence chain. Evaluation of 20 VLM configurations shows that current systems can identify isolated visual cues but rarely compose them into grounded longitudinal interpretations. We release the benchmark specification, evaluation lists, scoring implementation, scoring rubrics, and audit-record format to support reproducible progress in brain MRI VLM evaluation.

Magnetic Ap stars that have a strong enough field and a sufficiently low v sin i show spectral lines resolved into their magnetically split components. This allows their mean magnetic field modulus <B> to be determined. We complement the existing knowledge of the rotational magnetic variability and of the binarity of a sample of 34 Ap stars with resolved magnetically split lines by analysing observations obtained between 1999 and 2004 that had not been exploited before and, when available, observatory archive data. We determine the values of <B> and of the radial velocity by measuring the magnetic splitting and the wavelength shift of the Fe lambda 6149.2 Å line in high-resolution spectra recorded in natural light. Combining our measurements with published ones, we characterise the variability of both quantities. We derived for the first time the accurate, unambiguous values of the rotation periods of HD 29578 and HD 165474. We set lower limits of years to decades to the rotation periods of six stars and identified four more that have not shown any significant <B> variations over timescales of 13 to 33 years. We established that HD 47103 is the first Ap star with a rotation period of years known to have a magnetic field significantly exceeding 7.5 kG. We achieved the first determination of the orbital elements of HD 116114, HD 142070, and HD 144897, and we refined the orbital elements of six other binaries.

Objective audio quality metrics typically provide point estimates, whereas listening tests yield score distributions from which mean opinion scores (MOS), confidence intervals (CIs), and significance decisions are derived. We propose a lightweight intrusive metric that combines a PEAQ-style perceptual front-end (ITU-R BS.1387) with a bagging ensemble of regressors. Calibration with subjective data aligns ensemble outputs with listener scores. The resulting item-dependent score distributions enable uncertainty assessment, panel-size-matched CIs, and identification of less conclusive predictions. Calibration improves agreement with subjective distributions and CI coverage across all evaluated datasets while preserving MOS accuracy. Using only 11 fixed PEAQ features, low-capacity regressors, and public training data, the method performs comparably to more data-intensive end-to-end approaches. Its output can support uncertainty-aware assessment and target listening tests towards uncertain conditions. The distributions also enable approximate pairwise comparisons, but not yet reliable significance inference.

The magnetic properties of Sm-based intermetallics are governed by a delicate interplay between localized $4f$ states, exchange interactions, and valence fluctuations, yet the role of dynamical $4f$ correlations remains poorly understood. Here we investigate the electronic structure and magnetic anisotropy of SmCo$_5$ and SmCu$_5$ using self-consistent DFT+$U$(ED), which explicitly treats dynamical fluctuations of the Sm $4f$ shell. We find that SmCo$_5$ exhibits pronounced Sm$^{2+}$–Sm$^{3+}$ valence fluctuations, with the $4f$ ground state dominated by $f^5$ and $f^6$ configurations. The resulting dynamical $4f$ correlations yield near compensation of the Sm spin and orbital moments and provide a quantitative description of the electronic structure, magnetic moments, and large uniaxial magnetic anisotropy of SmCo$_5$. Upon replacing Co with Cu, the balance shifts toward the $f^6$ configuration, with substantial changes in the Sm spin and orbital moments. In SmCu$_5$, this evolution of the $4f$ configuration is accompanied by a pronounced reduction of both the total magnetic moment and magnetic anisotropy. These results demonstrate that dynamical $4f$ valence fluctuations are essential for understanding the contrasting magnetic properties of SmCo$_5$ and SmCu$_5$ and provide a microscopic framework for describing magnetic anisotropy upon Co to Cu substitution in Sm(Co,Cu)$_5$.

In this paper, we rigorously justify the low Mach number limit of the full compressible Navier-Stokes equations in a three-dimensional smooth bounded domain, subject to the no-slip boundary condition for the velocity and well-prepared initial data. In the presence of heat conduction and large temperature variations, we establish the uniform estimates for strong solutions on a time interval independent of the Mach number by constructing an energy functional in a Sobolev framework. The no-slip boundary condition cannot provide the vorticity boundary relation used in the slip-boundary setting. To overcome this difficulty, a divergence-free Stokes lifting of the boundary trace for the time derivative of the modified velocity is employed to define a test function vanishing on the boundary, which enables the transfer of a priori estimates from the velocity to the temperature.

Full-field Fourier-domain optical coherence tomography (FF-FD-OCT) enables rapid volumetric imaging but lacks the confocal gating inherent to point-scanning OCT. By acquiring volumes under multiple oblique illuminations, a digital confocal volume can be synthesized in post-processing, a technique originally developed within the framework of reflection matrix imaging (RMI). Existing implementations, however, are often time-domain, off-axis, or use a Michelson interferometer, which reduces sensitivity, speed and the usable space-bandwidth product (SBP). Here, we present an oblique-illumination FF-FD-OCT system in a Mach-Zehnder configuration. This setup enables optimal use of SBP, providing up to a fourfold increase in effective acquisition throughput. In addition, we pose the scattering and aberrations as an overdetermined system, allowing a closed-form solution of an alternating least squares problem. The resulting iterative optimization is equivalent to the state-of-the-art closed-loop accumulation of single scattering (CLASS) algorithm. We demonstrate the setup and reconstruction method in lens tissue, a PSF phantom, a USAF target, and a model eye. The resulting digital confocal volumes provide locally optimized focusing and detection quality, and show improved resolution and signal-to-noise ratio (SNR) compared to conventional FF-FD-OCT. The technique combines the advantages of FF-FD-OCT and confocal OCT while mitigating the limitations of both approaches.

The beamforming problem of intelligent reflecting surface (IRS) has been extensively considered from an optimization perspective assuming that channel state information (CSI) is available. However, the reality is that the existing prototypes seldom follow this model-based approach because channel estimation is technically difficult and costly for the network protocols and hardware to date. A recent trend is to perform beamforming blindly without channel knowledge. This work looks at blind beamforming from a reinforcement learning point of view. We first show that the existing blind beamforming method boils down to a special case of the greedy algorithm in the reinforcement learning context. We analyze the resulting cumulative regret, and further propose an upper approximation to facilitate the optimization of the exploration probability. Moreover, we show that a gradient sampling scheme can improve the efficiency of reinforcement learning as compared to the uniform sampling scheme adopted in the existing blind beamforming method. We further verify the convergence of the proposed gradient sampling scheme by showing that it is a stochastic approximation to gradient ascent. Finally, we physically implement the proposed method in a real-world prototype system. Our field test results show that, as compared to the existing blind beamforming method, the proposed gradient sampling boosts the average signal-to-noise ratio (SNR) by more than 5 dB with 1000 samples.

We examine, in the Landau background gauge, the effective action of a quantum theory of gravitational and matter fields. We analyse the BRST invariance of this theory and study the Ward identities which implement the symmetry of the background effective action. The off-shell and on-shell counterterm Lagrangians are explicitly calculated in this gauge at one-loop order. We argue that the matter self-energy in the Landau background gauge, which is finite to this order, may be finite also at higher loops.

Large language model (LLM) agents are increasingly capable of acting in complex tool-use environments, yet they often fail to recognize when tasks are infeasible and no valid solution exists. Recent work has formalized this reliability gap as the problem of agentic abstention, and existing approaches typically optimize a model or agent harness against a fixed set of tasks, leading to limited generalization to unseen failure modes. We introduce HERA, a framework for harness-environment co-evolution for agentic abstention. HERA consists of (i) a pipeline to automatically construct verifiable pairs of feasible and infeasible tasks by applying controlled environment mutations that transform solvable tasks into cases requiring abstention, and (ii) a co-evolution procedure in which performance failures on previous tasks are used to drive harness adaptation and generate new execution environments and tasks geared towards previous weaknesses. On held-out evaluation tasks, an evolved harness from HERA improves abstention accuracy from 61.7% to 83.3% while improving feasible-task completion from 68.3% to 76.7%, achieving the highest abstention and feasible-task completion among the compared methods. The resulting best harness transfers across 19 other LLMs, improving abstention accuracy by 15.3 percentage points on average without any model-specific optimization, and enabling smaller models to match the performance of more powerful models at an estimated 85% lower cost.

Population prompts are widely used to generate synthetic survey responses, but they combine information supplied at inference with associations already encoded during pretraining. We introduce an alternative construction that maps declared aggregate preference anchors into group-indexed choice policies. For each population, the signs of six Global Preferences Survey (GPS) coordinates deterministically label a shared bank of paired synthetic responses, and Direct Preference Optimization fits a parameter-efficient adapter to those comparisons. We evaluate the adapters on candidate World Values Survey (WVS) items using prompts that omit country names and distinguish four questions: recovery of the imposed labels, transfer of the anchor signal to new text, coherence between the GPS anchors and human WVS responses, and agreement between adapter and human scores. The adapters recover the imposed pairwise labels. On a purposively selected sixteen-country development panel, adapter trust scores completely separate the two GPS-sign groups and have a rank correlation of (0.74) with continuous GPS trust scores. Human-GPS and adapter-human associations remain unresolved on the same panel, and results for the other preference dimensions are heterogeneous. These findings show that an anchored policy can retain a declared aggregate signal without thereby reproducing human response patterns. The contribution is therefore both an inspectable construction and an evaluation framework that separates anchor transfer from human criterion agreement.

A classical well-quasi-ordering result guarantees the existence of non-uniform linear-time algorithms for all problems in Strict NP on relational structures of bounded treedepth; however, this provides neither a procedure for constructing these algorithms nor computable bounds on their parameter dependence. We turn this existential result into a uniform algorithmic metatheorem. Given a Strict NP sentence $\varphi$ and a relational structure $\mathcal{R}$, our algorithm decides whether $\mathcal{R}\models\varphi$ in time $f(|\varphi|, td(\mathcal{R})) \cdot |\mathcal{R}|$ for a computable function $f$, where the treedepth of $\mathcal{R}$ is measured on the Gaifman graph. The algorithm also constructs witness relations, with the polynomial exponent depending on their arity, and provides a unified framework for settling hereditary graph problems parameterized by treedepth. We also present several applications - among others, our result resolves open questions on the fixed-parameter tractability of computing the stack number, queue number, track number and twin-width parameterized by treedepth.

A perfect isometry $I$ (introduced by Broué) between two blocks $b$ and $c$ is a frequent phenomenon in the block theory of finite groups. It maps an irreducible character $\psi$ of $c$ to $\pm$ an irreducible character of $b$. Broué proved that the ratio of the codegrees of $\psi$ and $I(\psi)$ is a rational number with $p$-value zero and that its class in $\mathbb{F}_p$ is independent of $\psi$. This element is called the Broué invariant of $I$ by Boltje. The goal of this paper is to show that if $I$ comes from a Morita equivalence with an endopermutation source $V$, then, up to a sign, the Broué invariant of $I$ is determined by local data of $b$ and $c$. Therefore, up to a sign, it is independent of the endopermutation-source Morita equivalence. Moreover, we show that the sign factor is given by the reduction of the rank of $V$ modulo $p$. As a corollary, we obtain that the Isaacs–Navarro refinement of the Alperin–McKay conjecture holds for inertial blocks.

Modern online platforms commonly rank ads and organic content separately before blending them into a feed displayed to the user, overlooking externalities: an item's click-through rate depends on its surrounding content, not only on its own position. Recent learning-based feed generation mechanisms model some of these cross-type interactions to globally optimize for the whole feed's welfare. However, these approaches either fix the ordering of organic content, or lack exact strategyproofness guarantees for bidders. To combat these shortfalls, we introduce the Maximal-in-Range Transformer (MIRT) mechanism class, which uses a transformer to generate a range of candidate feeds that jointly order ads and organic content, and selects the welfare-maximizing feed in the range. However, there is a tension: strategyproofness requires the generated range to be bid-independent, even though a candidate feed's welfare depends linearly on the bids. Our key technical contribution is a reinforcement learning approach that incorporates both candidate generation and bid-aware selection into training, enabling a bid-independent transformer to learn to generate high-welfare ranges by accounting for both individual feed quality and the collective quality of the range. Additionally, we bound the pseudo-dimension of the MIRT class under hard attention, showing that near-optimal expected welfare is learnable with sample complexity polynomial in the transformer size and only logarithmic in the range size. Empirically, MIRT outperforms the previous non-strategyproof state-of-the-art feed models while remaining exactly strategyproof. Our results show that transformer-based auctions can deliver externality-aware whole-feed optimization without sacrificing exact incentive compatibility, removing a major obstacle to their practical deployment.

The classical Murnaghan-Nakayama rule is a recursive formula for computing the values of complex irreducible characters of the symmetric group $S_n$. Alun Morris proved a recursive formula for evaluating the values of irreducible spin characters of $\widetilde{S}_n$, where $\widetilde{S}_n$ is one of the Schur covers of $S_n$ defined by $\widetilde{S}_n:=\langle t_1,t_2,\cdots,t_{n-1},z\ |\ z^2=1,\ t_i^2=z,\ (t_it_{i+1})^3=z, \ t_it_j=zt_jt_i\ \text{if}\ |i-j|>1\rangle$. A recursive formula for evaluating the values of complex irreducible characters of the wreath product $G\wr S_n$, where $G$ is a finite group, was proved by J. Stembridge. In this article, we state and prove a recursive formula to compute the values of the irreducible spin characters of the wreath product $G\wr \widetilde{S}_n$. For the convenience of implementing these recursive formulas, we extend the notion of 0-1 boundary sequence of a Young diagram to shifted Young diagrams.

We combine CaCuTe with sequential subspace optimization (SESOP) for smooth convex minimization under Lipschitz continuity of the Hessian. The resulting method, CaCuSESOP, achieves the global rate $O(k^{-2})$ with a fixed number of Hessian–vector products per iteration, while removing key limitations of classical SESOP. In particular, exact minimization of the original objective is replaced by minimization of a low-dimensional cubic upper model, which needs only be solved to a computable accuracy. The cubic regularization parameter is selected by backtracking. If the Hessian at the minimizer is positive definite, CaCuSESOP automatically attains an accelerated local linear rate with complexity $O(\sqrt{\kappa_\star}\log(1/\varepsilon))$. Neither the local strong-convexity parameter, the condition number $\kappa_\star$, nor the optimal value is supplied to the algorithm. We give finite bounds for entering this regime and adapting the restart schedule. Finally, we prove that the global $O(k^{-2})$ rate is optimal for the considered fixed-budget gradient/Hessian–vector-product linear-span oracle class, even with momentum and unrestricted memory.

Let $G$ be a finite and simple graph without isolated vertices. We investigate the projective dimension of the closed neighborhood hypergraph $\mathcal{N}[G]$ and its relationship with the Castelnuovo-Mumford regularity of the extended bipartite double cover $\mathfrak{B}_e(G)$ of $G$. We establish the general upper bound $\operatorname{prod-dim} (\mathcal{N}[G]) \leq \operatorname{reg}(\mathfrak{B}_e(G))$ for all graphs. Furthermore, we prove that the exact equalities $\operatorname{prod-dim} (\mathcal{N}[G]) = \operatorname{reg}(\mathfrak{B}_e(G)) =\alpha(G)$ hold when $G$ belongs to several prominent graph classes, including König-Egerváry (contains all bipartite graphs), cographs, co-chordal, chordal and comparability graphs, where $\alpha(G)$ denotes the independence number. Our method of proofs relies on connecting algebraic invariants to the underlying combinatorial structure of graphs through covering, domination and matching parameters, together with the use of homology tools.

This work presents a digitally controlled adaptive power conversion framework that dynamically co-optimizes inductor configuration and switching frequency to achieve high efficiency across a wide range of load conditions. Conventional buck converters are typically optimized for a single operating point, leading to efficiency degradation under dynamic loads due to mismatches between inductance, switching frequency, and load current. To address this limitation, a reconfigurable inductor architecture is proposed. With this approach, the effective inductance and switching frequency are adjusted at runtime with on-chip digital controller. An end-to-end design methodology is developed, integrating physics-based analytical modeling, finite element method (FEM) simulations, and an optimization framework to determine preferred operating points across the load range. The resulting configurations are stored in a lookup table and implemented in real time through a low-overhead control scheme. The system explicitly accounts for both inductor and switching device losses, enabling co-optimization of conduction and switching losses within current ripple and continuous conduction mode (CCM) constraints. To ensure robust operation under fast load transients, a hysteresis-based control strategy is introduced to mitigate temporary CCM violations caused by sensing latency. An entry-margin condition is derived under which continuous conduction is guaranteed for a bounded load slew rate. Simulation results demonstrate a 4.5 percentage-point improvement in average efficiency and up to a 32% reduction in average power loss relative to fixed configurations, highlighting the effectiveness of adaptive inductance-frequency management in integrated power delivery systems with dynamic load profiles.

This paper considers prediction-error identification of a subnetwork embedded in a dynamic network. Measured boundary signals entering the subnetwork are appended to the exogenous inputs. Consistency requires that the part of these boundary signals generated by the subnetwork be reconstructible from the measured history; the subnetwork may be enlarged to obtain a simple structural sufficient condition. Under the stated model, stability, delay, disturbance-separation, informativity, and identifiability assumptions, the resulting criterion yields consistent estimates of the subnetwork transfer functions. The predictor may depend nonlinearly on the open-loop transfer functions, allowing consistent estimation with fewer measured internal signals than methods based on predictors that are linear in those transfer functions.

Human activity recognition (HAR) relies on transforming sensor signals into informative representations for classification. Although deep learning and handcrafted features are widely used, the role of representation itself is often not systematically isolated. Signature transforms provide a mathematically grounded way to encode temporal order and cross-channel interactions, but their value for HAR under a fully reproducible and leakage-aware framework remains unclear. To evaluate whether signature-based feature learning improves HAR performance compared with raw-signal baselines, and to assess the effects of embedding strategy, truncation depth, model choice, and sensor configuration. Experiments were conducted on the UCI HAR dataset using a fully reproducible pipeline with the original train–test split preserved and subject-disjoint validation to prevent leakage. Three representations were compared: raw flattened signals, time-augmented paths, and lead–lag transformed paths. Signature features were computed at multiple truncation depths and evaluated using multilayer perceptron (MLP) and Random Forest (RF) classifiers under identical preprocessing and validation procedures. A prior K-means-based feature reduction study was also reproduced for comparison. Signature-based representations improved performance when paired with RF models, the best configuration was time-augmented six-channel signatures at depth 6 using entropy-based RF achieving 0.858 accuracy and 0.859 macro F1, outperforming the strongest raw baseline (0.816 accuracy). Lead–lag representations were competitive at moderate depths but did not surpass the best time-augmented models. MLP models did not exceed raw baselines. Signature-based feature learning can improve HAR, but its benefit depends on alignment between representation design and classifier choice.

We study the surface Stokes-Cahn-Hilliard system governing tangential flow and phase separation in viscous fluid membranes. The equations are posed on a closed, stationary $C^2$ hypersurface $\Gamma\subset\mathbb{R}^{d+1}$, $d=2,3$. For constant viscosity and mobility and a class of regular double-well potentials, we prove global existence and uniqueness of weak solutions for initial phase fields in $H^1(\Gamma)$, with the velocity chosen orthogonal to the Killing fields. These solutions satisfy an energy equality and conserve mass. We establish Lipschitz continuous dependence in energy norms on every finite time interval, including for initial data with different means, and derive higher regularity results for $d=2$ under additional smoothness assumptions on the surface, potential, and initial data. We also develop a fully discrete unfitted finite element method that conserves the total phase and satisfies an exact discrete energy identity. The method combines a penalty on approximate Killing fields with projections in the transport and capillary terms to control these modes while preserving the energy balance. Numerical experiments examine the identification of Killing fields and illustrate phase separation on a torus and a liposome with experimentally informed material parameters.

Mid-circuit measurements with feedforward reduce the optimal worst-case quantum depth for exact $n$-qubit unitary synthesis from $\Theta(n)$ to $O(1)$, using arbitrary one- and two-qubit gates and unrestricted ancillary space. Measurements and resets without feedforward remain subject to the circuit causal-cone bound. Our deterministic construction uses single-qubit measurements, $O(1)$ rounds of parity feedforward, and $O(n4^n\log(n+2))$ total qubits, with all ancillas starting and ending in $|0\rangle$. Classical processing is not counted in quantum depth. We teleport only the matrix error of an approximation by Nehoran and Yuen. An exactly prepared ancillary state encodes this error, whose action is added back by coherent interference. At operator-norm error $2^{-n}$, one step of amplitude amplification suffices. Coherent fanout circuits achieve the same constant-depth bound, while circuits using only one- and two-qubit gates attain depth $\Theta(n)$ with $O(4^n\log^2(n+2))$ gates. Generic targets require $\Omega(4^n/(h+1))$ qubits at depth $h$, even under unrestricted classical control. Our depth-width trade-offs meet this bound within a factor $O(n^2)$ for $1\le h\le2^n$.

As the nearest radio galaxy, Centaurus A (Cen A) has been observed across multiple wavelengths and over a broad range of angular scales, providing valuable insights into the functioning of radio galaxies. However, despite being a known source of gamma rays, the physical mechanisms responsible for these high energy emissions remain unclear. In this study, we explore the capabilities of the Cherenkov Telescope Array Observatory (CTAO) to provide insights into the origin of the gamma-ray emission from Cen A. Using simulated observations based on the CTAO Instrument Response Functions (IRF) for the Alpha Configuration of telescopes, we investigate both the spectral and morphological domains to assess the observatory's potential to constrain competing models of particle acceleration in the kiloparsec-scale jet and the Southern Giant Lobe. For the jet, we explore CTAO observations with t=50 and 200h for different leptonic and hadronic origin scenarios for the very-high-energy gamma-ray emission. We show that longer observation campaigns (t=200h) would probe the presence of hard spectral components extending to tens of TeV. Morphological simulations demonstrate that CTAO can resolve the extended gamma-ray emission along the jet, discriminating between point-like and Gaussian spatial models within t=50h, assuming a known background model and an optimistic zenith angle $\vartheta=$20{\deg}. Under similar hypotheses, we studied the Giant Lobes evaluating both diffuse and filamentary emission templates for the S1 region detected by Fermi-LAT. We found that CTAO-South can be sensitive to hadronic scenarios with proton energies extending beyond 10 TeV, for the Alpha Configuration and $\vartheta=$20{\deg}. Overall, our results indicate that CTAO observations of Cen A can provide a decisive step toward unveiling the mechanisms driving the high-energy emission and particle acceleration in radio galaxies