Papers

We study a partial-participation variation of the Hotelling-Downs model. Voters each have a cost to vote, and only vote when the comparative gain from their preferred candidate exceeds the cost. Under this model the median voter theorem breaks, and we study the extent of polarization under equilibria in different voters and cost distributions. We find that the main predictor of polarization is the reverse-hazard-rate of the cost distribution, indicating that the driver of polarization under our model is the willingness of voters to respond to changes in positions of candidates. We then extend the model by adding parameters governing alienation and candidate competitiveness, showing that our results are robust even when taking into account other realistic factors.

As wireless systems evolve toward 6G and beyond, antenna apertures are increasingly expected to become more programmable, multifunctional, and responsive to diverse communication, sensing, and imaging requirements. Dynamic metasurface antennas (DMAs) offer a promising hardware pathway toward this vision by integrating electronically addressable metamaterial elements within microwave and millimeter-wave (mmWave) radiating apertures. Unlike conventional phased arrays relying on dedicated phase-shifting networks, DMAs manipulate guided waves in microwave structures through electronically controlled resonant elements. In this way, DMAs offer phase-shifter-less beam-steering, multibeam radiation, and programmable wavefront control. This article explores state-of-the-art DMA technology from a microwave-engineering perspective, spanning guided-wave excitation, reconfigurable resonant meta-elements, microwave tuning technologies, RF-digital integration, and FPGA-controlled beamforming. Closely related electronically steered metasurface antenna architectures are also discussed within a unified microwave-hardware framework. Recent advances illustrating how guided-wave DMA hardware and high-speed electronics facilitate programmable communication, sensing, imaging, and space-time functionalities are reviewed. Key microwave design challenges toward wideband, scalable, and highly integrated DMA apertures are highlighted. Finally, emerging opportunities in satellite communications, near-field connectivity, fixed wireless access, wave-domain computing, and integrated wireless functionalities are explored as future directions for DMA technology. This article provides a unified microwave engineering perspective on the design, practical implementation, and emerging capabilities of DMAs as programmable front-ends for next-generation wireless systems.

Deep learning-based speech enhancement is increasingly deployed on-device in hearing aids, headsets, and earbuds. Most of these devices, however, can only accelerate static int8 graphs, so a depth-varying network must be implemented as several graphs, orchestrated by a policy. In this paper, we supervise every intermediate depth of one causal model, then we fine-tune its output heads to guarantee that deeper outputs are never worse than shallower ones. Using this training protocol, we can derive a family of static models that are more Pareto-efficient than their equivalently-sized counterparts trained from scratch on the same budget. Specifically, we achieve up to 0.11 higher PESQ for equivalent compute, and match the best PESQ at 30% less compute. We then quantize the models to int8 and measure the latency-quality frontier on an STM32N6 microcontroller. On VoiceBank-DEMAND, the dynamic enhancer lies on the same frontier as the static models, rather than trading quality for dynamic execution. Running the policy on the companion Cortex-M55 takes only 26 $\mu$s per frame, while splitting the enhancer into separate NPU graphs adds 2.2% latency overhead. The cost of dynamic execution is therefore small.

Deploying real-time speech enhancement on resource-constrained devices requires meeting strict latency, memory, and energy constraints. Microcontroller NPUs can accelerate neural inference under these constraints, but only through a restricted set of operators in static, integer-quantized graphs. Recent speech-enhancement networks have reduced parameter counts and MACs to levels nominally suitable for microcontrollers, but their operators and execution patterns often remain incompatible with restricted NPUs. We address this gap by redesigning LiSenNet, a 37k parameter sub-band dual-path model, for the STM32N6570-DK Neural-ART accelerator. We replace its recurrent bottleneck with convolutional frequency and temporal mixers, reformulate unsupported operations as static int8-compatible primitives, and use bounded decoder activations to preserve quality after quantization. On VoiceBank-DEMAND, the final NPU-compatible model matches or exceeds the recurrent LiSenNet baseline, reaching PESQ 3.08 versus 3.01 in FP32 and 3.01 versus 2.93 in int8. Deployed on a microcontroller, it processes each 16 ms input hop in 4.83 ms, corresponding to a real-time factor of 0.30. Stateless receptive-field recomputation is an order of magnitude slower at the same frame rate despite higher accelerator utilization. These results show that parameter count and operator compatibility, quantization range, and persistent streaming state must be co-designed to achieve efficient real-time speech enhancement on restricted NPUs.

We study a collapse process to construct the farthest Voronoi diagram of lines in three dimensions, given a spherical map of the diagram's unbounded features. The collapse process sweeps through the diagram in order of decreasing distance from the farthest lines. It follows the shrinking map, a cell complex on a topological sphere that encodes the locus of points with a fixed farthest distance. We show that, in three dimensions, the collapse process has exactly four non-terminal local event types that change the structure of the shrinking map: deletion, swap, local minimum, and local maximum events; plus one terminal event. This list is complete. We give intrinsic three-dimensional geometric descriptions of the four non-terminal events. First, we classify the two vertex-related events, deletion and swap events, by the spherical convex hull of the four tangent points from a vertex to its four defining lines. Then, we analyze the events related to the local extrema of the distance function along the trisector of three lines. We show that the distance function along a trisector has at most $4$ local maxima and $8$ local minima, and that both bounds are tight. The extrema can be found via a polynomial of degree $12$. As a byproduct, this gives a direct method for finding the smallest sphere tangent to three given lines. At each local extremum, the tangent sphere touches the three lines at points lying on a great circle. The collapse process and the completeness of the event list also apply, under similar general position assumptions, to the farthest Voronoi diagram of convex sites under strictly convex distance functions.

High-resolution digital elevation models (DEMs) support Earth observation applications, but paired training references are often available only at coarser output resolutions. Reconstructing finer terrain grids therefore requires both effective transfer beyond the supervised scale and control of dense-query computation. To address this problem, SCOPE learns a continuous terrain representation from coarser-resolution pairs. It predicts a latent coefficient field on the low-resolution grid and reuses local Fourier residual functions through basis evaluation and geometry-guided ensemble fusion. This separates high-dimensional coefficient prediction from output-grid construction. Experiments on geographically distributed land–ocean samples assess supervised reconstruction, unseen-scale inference, cross-domain generalization, and theoretical computation. SCOPE leads the compared methods across six metrics in the main supervised-scale evaluation. At an unseen factor three times the training factor, land reconstruction reduces RMSE and MAE by approximately 12% relative to bicubic interpolation, with errors close to target-scale fine-tuning. Ninefold output density increases counted multiply–accumulate operations by only about 2%. Frozen-model validation on held-out external marine regions reduces RMSE relative to the DEM-specific implicit baseline EBCF-CDEM by approximately 19% under self-downsampling and 2% with cross-product inputs, while also yielding lower RMSE than LIIF-MS in both settings. These results demonstrate the value of reusable coefficient fields for accurate reconstruction beyond the supervised resolution with low incremental arithmetic cost.

Event Vision Sensing (EVS) report threshold crossings of log-irradiance, so a static optical system imaging a static scene produces no output at all. The classical procedure for measuring a Point Spread Function (PSF), illuminating the system with a constant point source, therefore has no event-based equivalent: the probe must carry a temporal profile, and that profile becomes part of the measurement. A growing body of Computational Neuromorphic Imaging (CNI) work already exploits this, pairing engineered or modulated optics with event sensing, but each system adopts a particular excitation together with a particular reading of the event stream without the correspondence between the two being stated. We examine that correspondence directly within a analytical framework of an Linear Shift-Invariant (LSI) optical system with a specified Modulation Transfer Function (MTF), a first-order filter EVS pixel model, and three different temporal probes: a step function, a linear ramp and an exponential ramp. By analysing the inverse of the entire chain for different event-statistic, and comparing the results to the specified MTF, we identify the context where each probe is most relevant. We consider how photon-noise and cross-array threshold mismatch effects the analytical accuracy of the probe-inverse. Results show that the widely used step probe is highly susceptible to mismatch while resilient to photon shot-noise, while a linear rise probe and exponential rise probe retain their ability to infer signal levels even with high mismatch. We discuss the potential of dynamic-PSFs as components of a full forward operator from scene to events. In this, we use this analytical description to define dynamic-PSFs around EVS, and discuss the gaps toward a unified pixel model and a scene-composition framework required for CNI.

Jets and their reconstructions play a central role in precision measurements and searches for new physics at hadron colliders. Conventional jet clustering algorithms employ a fixed radius parameter, which may not optimally describe events containing jets of varying characteristic sizes. Building on the recently proposed dynamic radius jet clustering framework, we construct several substructure-inspired dynamic radius prescriptions based on jet angularities and energy correlation functions. A detailed study of these algorithms is performed, including detector effects within the Delphes framework and in the presence of high pileup corresponding to an average of 150 interactions per event, with pileup contamination mitigated using the PUPPI algorithm. The performance of the proposed algorithms is compared with that of the standard anti-$k_t$ algorithm in boosted $Vj$ ($V=W^\pm,Z$) and $tj$ events against dijet backgrounds. Using jet substructure observables and multivariate analysis based on boosted decision trees, we find that the dynamic radius algorithms lead to improved reconstruction of boosted heavy-particle jets and achieve better signal-background discrimination compared to the conventional fixed radius anti-$k_t$ clustering.

We investigate whether GPT-6-Astra, a general-purpose foundation model, can navigate unfamiliar environments using its own perception, reasoning, and decision-making capabilities. Our evaluation focuses on zero-shot vision-and-language navigation in continuous environments (VLN-CE) through a minimal interface in the Codex harness, aiming to unleash GPT-6-Astra's full potential for navigation. Using monocular RGB, GPT-6-Astra decides when to observe, how to move, and when to stop, without navigation-specific fine-tuning, a trained waypoint predictor, or a pre-built scene map. Our evaluation yields four key findings and implications. First, GPT-6-Astra achieves strong zero-shot navigation performance using only monocular RGB observations. On R2R-CE-100, GPT-6-Astra (ultra reasoning) achieves a success rate of 81.3%, exceeding the strongest reported zero-shot and even train-based success rates by 15.3 and 9.2 percentage points, respectively. Second, GPT-6-Astra exhibits promising capabilities in interpreting multi-stage instructions, understanding the environment, and adjusting routes. Third, execution and goal-verification failures persist even with ultra reasoning. Fourth, these results motivate combining general-purpose model capabilities with navigation-specific expertise. Based on these findings, future VLN research should investigate which aspects of instruction interpretation, spatial understanding, and navigation decision-making general-purpose models can handle directly, and where navigation-specific learning can extend their capabilities. This includes exploring how spatial representations, navigation experience, and learned control skills can improve progress tracking, error recovery, and goal verification while preserving the flexibility to adjust routes.

Standard point spread function (PSF) matching algorithms consider one image as the reference and aim to find a convolution kernel such that, when applied to the reference image, the PSFs of the reference and non-reference images are matched. This method works well if one image is a degraded version of the other. However, this is not always the case: if the PSFs of the two images have different orientations or shapes, a simple convolution of one of the images does not lead to a satisfactory match. While this can be trivially solved by convolving the first PSF with the second and vice-versa, this results in unnecessarily large PSFs. In this paper, we present a new algorithm, Dual Kernel Optimization (DKO), that simultaneously solves for two convolution kernels, one for each image, such that the PSFs match and the sizes of the kernels are minimized. This results in a minimally-degraded final set of PSFs. Since this problem is highly degenerate, we use Stochastic Gradient Langevin Dynamics (SGLD) which rigorously explores the parameter space and converges on the globally-optimal solution.We discuss the algorithmic challenges for this problem and the modifications to standard SGLD used to constrain it. Finally, we include a discussion on the application of this methodology to real-world images, including cases where the PSF varies over the field of view.

We investigate 3d de Sitter axion wormhole which contribute to the no-boundary density matrix. We identify "cosmological necklace" solutions: an infinite series of Euclidean saddles corresponding with repeated bounces. This results in an unbound gravitational entropy, and a divergent path integral. To remedy this, we study the gravitational path integral using a (mostly) Lorentzian lapse contour. Within a minisuperspace steepest-descent analysis, we find that a single necklace dominates, leading to a finite entropy. A crucial element is to take into account an $(a\to -a)$ redundancy in the FLRW path integral, where $a$ is the scale factor. Surprisingly, the dominant solution is not purely Euclidean. Its entropy turns out to be independent of the axion flux, and equals the empty de Sitter entropy. We also study higher-dimensional necklaces, sourced by either an axion flux or by Yang-Mills instantons, and argue for qualitatively similar results: the single necklace solution dominates along a Lorentzian lapse contour.

Avoided crossings in the correlated many-body spectrum play a central role in determining the conditions for adiabatic state preparation in interacting quantum systems. We investigate this connection in finite spin-boson systems by combining exact diagonalization of the many-body spectrum with time-dependent simulations of adiabatic switching protocols. By comparing the adiabatically prepared state with the exact ground state, we determine the switching times required for reliable preparation as a function of the spin-boson coupling strength and bosonic mode structure. We show that regions of small many-body level spacings, associated with avoided crossings, impose the strongest constraints on adiabatic preparation and explain the observed dependence of the required switching times on the interaction strength. Furthermore, while the ground-state energy follows the overall spectral trends, local observables such as Pauli matrix expectation values exhibit additional non-monotonic behavior arising from coherent oscillations in finite systems. These findings can provide concrete benchmarks for both the theoretical treatment of open quantum systems and practical implementations in quantum simulation and qubit control.

Magnetic tunnel junctions are foundational components of spintronic memory, sensing, and computing, and their performance depends critically on the magnetic metallic electrodes. This Perspective examines electrode materials through the lens of magnetic order and the distinct microscopic mechanisms that generate spin-selective tunneling. Conventional ferromagnets, including CoFeB and half-metallic Heusler alloys, support exchange-split electronic states and symmetry-filtered tunneling, whereas compensated collinear and noncollinear antiferromagnets exploit sublattice selectivity, spin-orbit anisotropy, vector spin textures, and magnetic multipoles. Altermagnets provide a collinear, zero-net-moment route based on symmetry-allowed momentum-dependent spin splitting. Across these material classes, we compare the origins of tunneling polarization, the roles of barrier evanescent states and interface termination, and strategies for electrically writing and reading the relevant magnetic order. This comparison reveals a broader design principle: effective electrode polarization is not a scalar bulk quantity, but a momentum-, orbital-, symmetry-, and interface-resolved transport property. Beyond the pursuit of ever larger tunneling magnetoresistance, future progress will depend on converting the unconventional spin polarization of emerging magnetic metals into electrically addressable, thermally robust, and reproducible tunneling functionality at realistic interfaces.

This paper sets out a computational workflow that reconstructs the phylogeny of human Y-chromosome populations from a Variant Call Format (VCF) file of biallelic Single Nucleotide Polymorphisms (SNP). The two classical phylogenetic decisions - topology selection and root placement - are cast as Quadratic Unconstrained Binary Optimisation (QUBO) problems. The workflow combines two QUBO formulations with an Alternating Direction Method of Multipliers (ADMM) decomposition strategy and a plug-in Digitized Counter-Diabatic Quantum Optimization (DCQO) solver, enabling large phylogenetic optimization problems to be executed across multiple classical or quantum computing resources. The DCQO gate-based optimizer drives each ADMM-block QUBO with short-depth counter-diabatic circuits in the impulse regime, without the necessity for an outer variational loop. The combination of ADMM decomposition and the DCQO block solver facilitates problem sizes that surpass the qubit budget of any individual digital quantum processing unit call, while maintaining the integrity of the original objective. The workflow extracts genotype information from VCF files, reconstructs topology and rooting through two QUBO formulations, and annotates the resulting tree using PhyloTree. The resultant data set comprises a Nexus-annotated rooted tree, in addition to diagnostic figures. The workflow demonstrates the potential of modest-scale QUBO formulations combined with ADMM decomposition to serve as a scalable alternative to greedy heuristics in the domain of population genomics.

We address the challenge of syntactic parsing for Urdu, a morphologically rich language, and present state-of-the-art results for both constituency and dependency parsing. This paper offers four major contributions: 1) the conversion of the CLE-UTB phrase structure treebank into a dependency treebank by developing language-specific head-word and phrase-to-dependency label mapping rules; 2) a novel sequence labeling scheme that transforms the parsing task into a unified representation; 3) the training of contextualized word representations on a large 220 million tokens Urdu corpus collected from the web; and 4) development of parsing framework using two learning paradigms, single-task and multi-task learning. Several post-processing rules are applied to improve the quality of the automatically converted dependency structure treebank. The proposed sequence labeling scheme enables the use of a shared architecture that learns the syntactic structures from both grammatical structures simultaneously and hence improves generalization. Experiments show that the multi-task learning setup significantly enhances parsing performance, achieving an F1 score of 91.39 for constituency parsing (an improvement of 3.29 points) and a labeled attachment score of 85.69 for dependency parsing (an improvement of 1.49 points). These results demonstrate that learning cross-task representations provides measurable benefits and advances the state of syntactic parsing for Urdu.

This paper shows that one internal stabilization is enough to resolve all the self-referential tubes on an embedding. As an application, this paper gives a complete isotopy classification for embedded surfaces with a common geometric dual in orientable $S^2$-bundle over a surface, provided that the embedded surfaces have greater genus than the base surface of the bundle.

Let $H$ be a pointed Hopf algebra of square-free dimension over an algebraically closed field of characteristic $p>0$. We prove that either $H$ is a group algebra or $\dim H/|\G(H)|=p$, and that in the latter case $H$ belongs to exactly one of two explicit families of rank-one pointed Hopf algebras. We develop a truncated $q$-Weyl freeness principle for finite-dimensional Nichols algebras of quandle type. If $V=\bigoplus_{x\in X}\K e_x$, $X'\subsetneq X$ is a nonempty subquandle, $V'=\bigoplus_{x\in X'}\K e_x$, and $s\in X\setminus X'$, then $\mathcal B(V)\simeq\K[e_s]/(e_s^{m_s})\otimes C_{s,X'}\otimes\mathcal B(V')$ for some graded vector space $C_{s,X'}$, where $m_s$ is the nilpotency order of $e_s$; in particular, $(m_s)_z\,\mathcal H_{\mathcal B(V')}(z)\mid\mathcal H_{\mathcal B(V)}(z)$. In the non-group case, this yields a $p^2$-divisibility obstruction that rules out noncentral support for the infinitesimal braiding. Together with a graded-dual argument, the resulting rank-one reduction forces the diagram of $H$ to have dimension $p$.

We report the discovery of J1351+0039, a new isolated dark galaxy candidate identified through a blind HI survey with the Five-hundred-meter Aperture Spherical radio Telescope (FAST), combined with deep optical imaging from the DESI Legacy Survey. The object displays a compact HI structure with a systemic velocity of V_{LSR} = 429.0 \kms and an inferred HI mass of 4.5*10^5 Msun at a distance of 3.6 Mpc. No optical counterpart is detected in the DESI images, with a g-band surface brightness limit of 28.1 mag arcsec^{-2}, corresponding to a stellar mass limit of M_{star} of 1.2*10^{5} Msun. The dynamical mass is estimated to be M_{dyn} of 1.3*10^{8} Msun, yielding a dark-to-baryonic mass ratio of 200, implying that J1351+0039 is overwhelmingly dominated by dark matter. While weak rotation is detected in J1351+0039, the kinematics are dominated by internal velocity dispersion, confirming pressure support and reminiscent of Reionization-Limited HI Clouds (RELHICs). J1351+0039 stands out as one of the most promising isolated RELHIC candidates, offering a unique laboratory for studying baryonic physics and dark matter in the absence of star formation.

Behavioural biometric templates are widely believed to degrade as the gap between enrolment and verification grows, but few studies measure this template ageing effect directly under controlled conditions. We collected a longitudinal dataset of 40 fixed passwords, each typed four times per weekly session over eight consecutive weeks. We compare a scaled-Manhattan matcher (M1), a gradient-boosted classifier (M2), a TypeNet-style recurrent embedding model (M3), and a TypeFormer-style Transformer (M4) under a 5-fold subject-disjoint protocol and a design that jointly varies mechanism and the enrolment-to-query gap, from 0 to 7 weeks. Template ageing proves large and systematic. Error increases monotonically with the gap for every mechanism, from an EER of 14.6-27.2% at a gap of zero to 25.5-37.1% at seven weeks, or 1.7% of decision error per week elapsed (p < 0.001). However, the choice of mechanism matters more than its rate of ageing. Baseline accuracy spans 12.6 percentage points across the four mechanisms, the degradation each accumulates over seven weeks spans only 2.3 points, and ageing never reorders them. A matcher can therefore be chosen on same-session accuracy, with ageing managed by re-enrolment scheduling rather than by matcher selection. The two properties are nonetheless distinct, as M3 is the least accurate mechanism yet ages significantly more slowly than M1 under every specification tested. Training randomness also matters differently by architecture, with 58% of the recurrent model's fold-to-fold variance attributable to seed noise against 19% for the Transformer. Because the smaller ageing-rate differences are sensitive to modelling choices, while the accuracy differences and the ageing effect are not, we recommend that comparative ageing-rate claims be supported by seed-level score fusion, independent replication, and an alternative outcome-model specification.

Learning executable motions from human videos offers a scalable solution for humanoid robots to acquire demonstration motions. However, existing pipelines typically first construct an explicit human motion representation and then convert it into robot motions via motion retargeting. Although such methods can effectively leverage large volumes of existing human data for training, the substantial differences between humans and humanoid robots in locomotion mechanisms and joint degree-of-freedom configurations make motions generated by this human-representation-centric approach difficult to execute on robots. Furthermore, errors introduced during human motion estimation inevitably propagate to the retargeting stage and cannot be eliminated via joint optimization. We propose BeyondRetarget, an end-to-end framework that directly maps monocular RGB videos to robot motions. Discarding the explicit human representation, this framework learns robot-oriented implicit representations directly from visual observations, enabling the model to capture cross-morphology motion structures. To generate motions more suitable for robot execution, we further design a contact-aware motion optimization mechanism to improve temporal consistency and physical plausibility. Experiments show that BeyondRetarget significantly improves the accuracy and robustness of generated robot motions, while achieving higher execution success rates and lower latency in both simulation environments and real humanoid robots.

Reliable correction of nonaxisymmetric error fields (EFs) is essential to the safety and performance of tokamak operation. Although resonant error field correction (EFC) is well established, supported by an improved understanding of 3D plasma response, the residual fields left after resonant EFC remain an open question: they are expected to be predominantly nonresonant, yet can still degrade both confinement and stability. Here we introduce a systematic EFC scheme that minimizes resonant and nonresonant EF effects simultaneously, based on neoclassical torque response computed from self-consistent perturbed equilibria. The scheme extends the method developed for designing quasi-symmetric magnetic perturbations to the case where actual error fields are present. Application to standard ITER target plasmas with a range of intrinsic EF scenarios demonstrates the advantages of this quasi-symmetric (QS) EFC scheme for controlling residual EFs. QS EFC consistently yields low-torque solutions while strongly suppressing resonant response, outperforming single-mode resonant overlap EFC in most cases and approaching the performance of multimodal resonant EFC. We also show that the QS EFC solution varies only tolerably between half- and full-$I_p$ ITER scenarios, despite the greater sensitivity expected from its higher-order nature.

A language model can fail a syntactic test in two distinct ways: by not encoding the relevant structure, or by encoding it but failing to use it at the output. Behavioral evaluation alone cannot tell these apart. We propose a three-level evaluation framework (behavioral deployment, LM-head readout, and probe recoverability) measured on the same items under the same binary decision. Using a compact trilingual (English, Chinese, German) control-dependency benchmark, we find that probe recoverability exceeds or equals LM-head readout, which in turn exceeds or equals behavioral deployment, across seven models and all three languages in the aggregate. The recoverability surplus is never negative across all 14 (model, task) conditions. The disconnect concentrates in subject-control, where a nearest-noun heuristic gives the wrong answer. The single largest gap (0.653) appears on Qwen3-0.6B Instruct in question answering. The gap persists at Qwen3-14B Instruct. Instruction tuning degrades deployment more than encoding in percentage terms. We rule out option-position bias, late-layer erasure, output-formatting artifacts, and probe-training variance. The pattern is consistent with decoding that favors surface shortcuts, and the behavior-probe gap measures the strength of that preference. Activation patching shows the gap is layer-localized. Under instruction tuning, the LM-head-decoded layer shifts approximately ten layers later than the probe-decoded layer. These findings argue that behavioral evaluation understates what models encode, while probing alone overstates what they deploy.

The Brinkman penalisation method embeds boundary-value problems on complex domains into a simple computational box by modeling the solid region as a strongly dissipative medium, avoiding body-fitted mesh generation. We show that multi-symplectic Hamiltonian PDEs regularised by Brinkman-type penalisation retain a multi-conformal symplectic structure under a compatibility condition linking the symplectic matrix and the penalisation projection. This yields an exact local conservation law, under which the multi-symplectic two-form is conserved in the fluid region and decays exponentially inside the solid. The linear wave equation with Brinkman friction and Maxwell's equations with artificial Ohmic conductivity satisfy this condition, with explicit modified Hamiltonian densities. Building on this, we propose (i) structure-preserving numerical integrators via Strang splitting that satisfy a discrete conformal conservation law, and (ii) conformal symplectic neural operators that interleave exact dissipative flows with learnable multi-symplectic evolution operators, allowing geometry-dependent operator learning. Numerical experiments on wave and electromagnetic scattering demonstrate that our methods reproduce correct local energy budgets and avoid unphysical energy drift, providing a principled framework for physics-consistent scientific machine learning on complex domains.

Network-controlled repeaters (NCRs) are emerg- ing as low-cost, band-selective active scatterers that can re- shape the wireless propagation environment without backhaul or tight phase synchronization. We study physical-layer design for repeater-assisted multiple-input multiple-output (RA-MIMO) networks, such as hardware impairments, gain and activation control, duplexing, channel-state information acquisition, and wideband delay effects. We then discuss integrated sensing and communication (ISAC), where repeaters can extend non- line-of-sight (NLoS) visibility, improve target observability, and enhance weak-echo detection. These gains, however, are limited by amplified noise, clutter, feedback, and calibration errors, motivating joint optimization and gain control frameworks for swarm repeater deployments within ISAC.

While Large Language Models (LLMs) rely on highly non-linear components, in this work we demonstrate that they exhibit fundamental linearity: when inputs from distinct text streams are linearly combined, the model outputs a superposition of the individual next-token distributions. We term this the Superposition Linearity Hypothesis. We provide evidence that superposition is an intrinsic property of the Transformer architecture rather than an emergent consequence of training; in fact, we observe that it tends to diminish as pretraining progresses. However, we demonstrate that linearity can be substantially restored through lightweight fine-tuning, significantly reducing the divergence between the predicted next-token distribution and the average of the individual next-token distributions. Finally, we introduce a guided decoding procedure that disentangles superposed outputs, enabling the simultaneous generation of two coherent continuations from a single forward pass.

Consider an optimal dynamic treatment regime, $g^{\textbf{opt}}$ correctly identified from a large, perfectly executed sequentially randomized experiment. Even when the experimental results are generalizable to a future target population, there is no guarantee that $g^{\textbf{opt}}$ outperforms human decision-makers; human experts can do better than $g^{\textbf{opt}}$ whenever they have access to relevant information beyond the covariates recorded in the experiment. Motivated by this observation, we derive results on a new class of regimes called initiation regimes, which generalize existing results on superoptimal regimes. These regimes follow human decision-makers up to the point where it becomes more beneficial to initiate a sequential optimal regime, and are guaranteed to outperform both purely human and purely algorithmic decision rules, e.g., based on reinforcement learning algorithms. Furthermore, we present modified experimental designs that identify the best initiation regimes, show how the best initiation regime can be identified from classical observational data under explicit assumptions, and give estimation and statistical inference methodology for these regimes. To illustrate the practical utility of the methods, we consider initiation regimes in a case study on treatment of lower back pain.

In the present work, we study the properties of the sparse entropic quadrature method, a recently proposed method for the closure of systems of moment equations in rarefied gas dynamics. We prove the properties of the method regarding its well-posedness, hyperbolicity, and stability for first-order spatial convection schemes. We apply the method to two model rarefied gas dynamics problems and compare the results with those given by a discrete velocity method and show that it is capable of reproducing rarefied gas effects whilst having significantly fewer degrees of freedom than the discrete velocity method.

The two-component Becker-Döring model is a two-dimensional coagulation-fragmentation equation that describes the dynamics of clusters built from two different types of monomers growing and shrinking through monomer interaction. We show the existence and mass conservation of solutions and give a partial result regarding uniqueness. Furthermore, we prove under the assumption of detailed balance the entropy equation, followed by a detailed study of the equilibrium states and relative entropies. We can determine the minimum of all relative entropies under sequences of fixed Type I and Type II masses and fully describe the minimising sequences in the weak* topology.

The Vera C. Rubin Observatory will enable large-scale characterization of minor bodies through high-cadence, multi-band photometry. Early Science Validation (SV) observations from 2025-2026 provide one of the first extensive datasets for Solar System studies, but typically with sparser and more heterogeneous coverage than the Rubin First Look data, where hundreds of observations were available for well-characterized objects. In this work, we build on the methodology developed for the Rubin First Look data to extract asteroid rotation periods, amplitudes, colors, and taxonomic classifications from early Rubin SV data using multi-band (griz) photometry. Rotation periods are determined through a combination of high-order Fourier light-curve fitting and multi-band Lomb-Scargle analysis. A unified light-curve model is then used to derive rotation-corrected colors, which are converted into taxonomic classes using calibrated color indices and spectral slopes. We validate the method on objects with sufficient observational coverage and show that preliminary physical properties can be estimated from sparse and irregular datasets, while robust determinations require improved temporal coverage. By simulating sparsely observed data, we identify the observational conditions required for period determinations. The inclusion of z-band photometry extends traditional color-based taxonomy and improves compositional discrimination relative to gri-only analyses.

In this paper, we prove global well-posedness and scattering below the energy space for the defocusing nonlinear Schrödinger equation with intercritical power nonlinearities in spatial dimensions $d\geq3$, improving the regularity threshold of Vişan and Zhang [Differ. Integr. Equations, 22(2009), 99-124].