Papers

Concept representations in diffusion models drift across network depth and denoising time, yet existing sparse autoencoders offer only per-block or per-timestep dictionaries, leaving no single feature dictionary for localization and intervention in the network. We present Shared Sparse Autoencoder (SharedSAE), which learns one sparse dictionary shared across four U-Net attention blocks and all 50 denoising steps of SDXL 1.0. A block-specific low-rank input adapter aligns the residual distribution of each block before the shared encoder, and a temporal conditioning module with a shared timestep branch and a block-timestep correction branch absorbs temporal non-stationarity. Despite spanning both axes, Shared SAE preserves a coherent dictionary structure. Built on the shared dictionary, localized feature suppression reduces the number of NudeNet-positive generations in the I2P detector-positive subset from 139 to 1. Tracing sparse features across the trajectory further reveals that concept representations are redistributed across U-Net blocks during generation, shifting from the earliest downsampling block toward intermediate and later blocks as denoising proceeds. SharedSAE thus provides a unified, interpretable, and intervention-ready representation space for diffusion models, enabling concept analysis and erasure at any covered block and denoising step.

We study codimension-one holomorphic foliations admitting invariant singular real-analytic Levi-flat varieties. Our main problem is to determine when the local meromorphic first integrals furnished by the Levi-flat geometry can be continued coherently and globalized. We introduce a pencil-singularity condition and a projective compatibility condition for local meromorphic parameters. In the projective plane these yield a characterization of foliations admitting a primitive rational first integral, while in higher-dimensional projective space they give a rational integrability criterion under a generic local-product hypothesis along the dicritical locus. We also obtain semi-global and Stein versions of these results. In a different direction, we study foliations admitting infinitely many invariant Levi-flat varieties and prove a Darboux-type alternative: either the foliation admits a rational first integral, or infinitely many Levi-flats contain a common invariant algebraic curve whose virtual holonomy is abelian. Under additional assumptions on the singularities, this leads to the existence of a closed rational, and in the absence of saddle-nodes a closed logarithmic, defining \(1\)-form.

We study a charged particle moving outside a spiral (screw) dislocation in a uniform magnetic field. Although the geometry is locally Euclidean, its global screw identification couples the conserved axial and azimuthal quantities through the combination \(\mathcal{J}=\ell-\beta k\) After eliminating the cyclic coordinates, the radial motion is governed by an inverse-square term determined by $\mathcal{J}$ and a harmonic confining term generated by the magnetic field. The corresponding reduced quantum problem is exactly solvable for $q\mathcal{B}_0\neq0$, yielding an equally spaced spectrum with an orientation-dependent energy shift. The radial probability density depends on $\mathcal{J}$, and opposite values of the screw-modified quantum number have identical spatial profiles but different energies for a fixed magnetic-field orientation. The radial size scales as \(\sqrt{\langle r^2\rangle_n}\propto |q\mathcal{B}_0|^{-1/2}\), with the magnetic length setting the localization scale. At $q\mathcal{B}_0=0$, the confining term vanishes, and the problem reduces to a scale-free inverse-square system. Thus, the screw parameter enters the dynamics through the global coupling of the conserved axial and azimuthal quantities, whereas the magnetic field provides radial confinement and its orientation determines the spectral asymmetry.

3D Gaussian Splatting has evolved from static reconstruction toward physics-integrated representations meant to predict how scenes change under interaction. This creates an evaluation problem: a rollout can look plausible while relying on incorrect internal mechanics, and visual agreement with observed motion does not establish a correct response to a new force, material edit, contact, or thermal intervention. We introduce GaussianBench, a physics-fidelity evaluation suite for physics-integrated Gaussian scene representations. It uses frozen file-based scenes, simulator-independent scorers, and analytical or measured references. The benchmark tests conservation, continuum response, heterogeneous-material coupling, Gaussian covariance transport and rendering, thermal phase change, and counterfactual response. Each reference declares its regime of validity, and outcomes distinguish PASS, FAIL, NA, and INVALID, separating physical failures from unsupported capabilities and invalid comparisons. We also provide GaussianFlesh, a thermomechanical reference entrant in which persistent 3D Gaussians act as both rendering primitives and continuum material points, advanced by a shared-grid MPM solver with per-particle constitutive dispatch and persistent thermal and phase state. We evaluate six released external systems: PhysGaussian, GaussianFluent, OmniPhysGS, PhysDreamer, Physics3D, and GASP. Testing every system the same way reveals failures that their original evaluations missed: a system can simulate a single material correctly but fail where two materials meet, or update its Gaussians correctly for a deformation it never produced. Matched faults and tolerance audits confirm these distinctions arise from the intended tests. Physics-integrated Gaussian systems must therefore be tested on their internal physical state, not just on whether their rollouts look plausible.

We construct the Conway-Wales lattice from a self-dual even code $C$ over $\mathbb{Z}_4$ whose binary layers interweave the Hamming codes $\mathcal{H}_7$ and $\mathcal{H}_8$. Explicit signed symmetries lift every automorphism of the binary residue, and the full signed code group is the coordinate-frame stabilizer of the Gaussian lattice. An integral reflection in an embedded scaled self-dual sublattice supplies an additional symmetry, from which the classical frame exchange is recovered. Counting intrinsically defined frames determines the full Gaussian isometry group, of order $583\,704\,576\,000$. Its quotient by the four Gaussian scalars is the Rudvalis simple group, and the derived subgroup of a cross stabilizer is the Tits simple group of order $17\,971\,200$. The construction, automorphism-group determination, and both simplicity proofs are carried out within the lattice, without assuming the known group orders or using a recognition or classification theorem.

An interesting question for discussion in university physics courses is whether gravity can conflict with the second law of thermodynamics. In this work, we address this question by comparing the behavior of an ideal gas in two conceptually different regimes: one in which gravitational effects can be neglected and another in which self-gravity becomes important. In the first case, free expansion provides the familiar example in which an increase in the volume accessible to the gas leads to an increase in entropy. Self-gravitating systems behave differently: gravitational contraction can reduce the volume occupied by matter while releasing energy and increasing the entropy of the surroundings. This illustrates why the usual intuition that increasing entropy necessarily corresponds to increasing spatial dispersion cannot be applied directly to self-gravitating systems. Using elementary thermodynamic arguments and a minimal amount of mathematics, we discuss this apparent tension and show how entropy must be considered for the complete system, including emitted radiation. The discussion is finally extended to black holes and Hawking radiation, where the appropriate framework is the generalized second law of thermodynamics. The analysis is intended to provide a pedagogical bridge between elementary thermodynamics and some of the distinctive thermodynamic properties of gravitating systems.

As the use of smart devices continues to increase, their potential to capture sensitive speech content raises growing privacy concerns. It is therefore critical to develop techniques that prevent information leakage while preserving the utility of the audio, and evaluation metrics that accurately quantify the level of privacy without overestimating it. In this work, we evaluate the effectiveness of two obfuscation techniques in protecting speech content, with particular emphasis on named entities, by adapting entity-aware privacy metrics from the Natural Language Processing field to the speech privacy domain. Further, we investigate several attack scenarios and show that fine-tuning on entity-rich data improves attack performance for some entity categories but not others. Finally, we provide guidance on metric selection based on whether the obfuscation method preserves temporal alignment.

Multimodal Large Language Models (MLLMs) have demonstrated remarkable reasoning capabilities across vision and language tasks. However, their massive computational and memory demands hinder real-world deployment. While recent efforts reduce costs by employing lightweight language backbones, existing paradigms remain computation-dense due to their static sparsity and depth allocation, which cannot adapt to the semantic complexity of each token. To this end, we propose MoR-MLLM, a computation-sparse MLLM based on the recent Mixture-of-Recursions (MoR) framework. MoR-MLLM introduces adaptive per-token recursion, allowing the model to dynamically adjust its recursive depth and allocate more computation to visually or linguistically challenging tokens while skipping redundant operations for simpler ones. To stabilize the training of recursive sparsity in multimodal settings, we further design a three-stage MoR-Tuning strategy and an entropy-regularized loss to encourage diverse routing distributions. Extensive experiments show that compared with recent advanced tiny MLLMs, our proposed MoR-MLLM can greatly reduce the training memory and computation complexity while retaining high performance on various vision-language tasks.

Jev offers an alternative interface for language understanding: given an input and predefined questions, it returns probabilistic decisions rather than free-form responses. Whether this interface can support effective reasoning for text classification against leading LLMs remains an open questions. We introduce Emo-Jev, a training-free framework with two complementary implementations. Emo-Jev-D decomposes classification into task-specific atomic judgments and composes their probabilities into a final prediction. Emo-Jev-SC constructs multiple judgment paths from complementary perspectives and aggregates their predictions into a consensus decision. We evaluate Emo-Jev on eight datasets spanning sentiment analysis, emotion recognition, sarcasm detection and humor detection, comparing against direct Jev classification and five SoTA LLMs under input/output and chain-of-thought reasoning. Standard Jev achieves 62.93% average macro-F1 versus 67.28% for the strongest LLM baseline, with lower observed latency and generally lower cost.

This paper investigates static, spherically symmetric traversable wormholes supported by Casimir energy within de Rham-Gabadadze-Tolley (dRGT) massive gravity. By deriving the exact shape function $b(r) = r_0 + \frac{\pi^3(-r + r_0)}{90 r r_0} - \frac{1}{2} C m_g^2 (r - r_0)[2C c_2 + c_1(r + r_0)]$, we verify that the geometry satisfies the local Morris–Thorne throat and traversability conditions, including $b(r_0)=r_0$ and $b'(r_0)<1$. For the nonzero massive-gravity parameters considered here, the resulting spacetime is not asymptotically flat, and its large-$r$ behavior is governed by the massive-gravity contributions to the shape function. The Casimir energy density $\rho = -\pi^2/(720 r^4)$ ensures the Null Energy Condition is violated throughout the throat region, as demonstrated by the negative behavior of $(\rho + p_r)$ and $(\rho - |p_r|)$ across all parameter values. Analysis of the volume integral quantifier reveals that the massive gravity parameter $m_g^2 c_2$ directly regulates the exotic matter requirement, with the integrated NEC violation becoming more negative as $m_g^2 c_2$ increases from $0.1$ to $0.5$. The mechanical equilibrium is rigorously established via the generalized Tolman-Oppenheimer-Volkoff equation, where the anisotropic force precisely balances the gravitational and hydrostatic forces. The quasinormal mode spectrum for scalar perturbations is extracted using both the analytical Mashhoon method and direct numerical integration. The effective potential forms a symmetric barrier at the throat, with the peak height increasing with the multipole number $\ell$. The damping rate $|\omega_I|$ grows systematically with increasing massive gravity parameter. These distinct spectral signatures provide robust theoretical markers for distinguishing Casimir wormholes from black holes in future gravitational wave observations.

The information-theoretic construct of synergy refers to the statistical structure that is contained in three or more variables, but not in any subset of them. Here we leverage recent advances in multivariate information theory to show that synergy is far more prevalent in complex systems than previously thought. In particular, we show that many-body systems tend to become strongly dominated by synergy as the number of subcomponents grows. At the same time, our results also reveal that commonly used tools for statistical modelling severely underestimate synergistic structures. These findings imply that synergy constitutes a prevalent, yet often invisible, informational component of complex systems. With a certain poetic licence, we interpret these results as suggesting that synergy is the dark matter of statistics - interdependencies that we know exist, but standard instruments fail to detect.

Let $G=\langle a,b\rangle$ be a finite group with distinct nonidentity generators, and suppose that $H=\langle ba^{-1}\rangle$ is normal. We determine exactly which complementary generator choices on the nonterminal cosets of $H$ extend to two arc-disjoint Hamiltonian paths with both terminal vertices in $H$. The associated return residue must avoid an explicit set of at most six residues. When $[G:H]\ge3$, any two nonterminal cosets may be left free while all other choices are prescribed; two is best possible. Every such Cayley digraph has two arc-disjoint Hamiltonian paths; this includes all two-generator Cayley digraphs of finite abelian groups. The criterion follows from a complete distance formula for the Hamiltonian cut spectra of $\mathrm{Cay}(\mathbb{Z}_q;\{D,D+1\})$. Their unique nondegenerate exception comes from the odd central coefficient $(q-1)/2$. The geometric ingredient is a confinement theorem: two sector-filled integer sequences satisfying a length inequality, with overlapping ranges and distance at least two, have one sequence contained in a single gap of the other. Sector filling bounds alternation, and the length inequality excludes interlacing. A self-contained proof of the primitive-ray cycle profile follows the intersection geometry of Curran and Witte.

The geometric shadow of a black hole cannot observationally distinguish horizonless exotic compact objects. We break this degeneracy by mapping the fundamental quantum decoherence of the horizon (the Danielson-Satishchandran-Wald mechanism) into a macroscopic effective reflectivity $\mathcal{R}$. Utilizing Kerr ray tracing, we show that a partially reflective boundary ($\mathcal{R}>0$) generates delayed electromagnetic echoes under both specular and diffuse (Lambertian) conditions. In the spatial domain, these echoes illuminate the inner shadow and alter low-frequency visibilities, while leaving metric-governed photon subrings unchanged. The signal strength scales with the membrane compactness $\epsilon$ as $\epsilon^{\Gamma}$, where $\Gamma=0$ for specular reflection and $\Gamma\to1$ for diffuse re-emission due to escape-cone collapse. This brings specular reflectivities down to $\mathcal{R}\simeq0.12$ (ngEHT) and $0.04$ (BHEX) within reach of static imaging. For Sagittarius A$^\ast$, we translate these echoes into a robust time-domain signature. Using an Autocorrelation Function (ACF) pipeline, we demonstrate that single-flare echoes can be cleanly extracted from severe accretion red noise, achieving a $3\sigma$ detection for amplitudes $\mathcal{A}\gtrsim0.3$ within 15 to 33 hours of continuous monitoring. This framework provides a directly deployable pathway to test black hole unitarity.

We formulate a generally covariant extension of London electrodynamics in four-dimensional curved spacetime and investigate the propagation of electromagnetic perturbations in a superconducting medium surrounding a black hole. The ordinary London relation is promoted to a gauge-invariant four-dimensional constitutive equation involving the electromagnetic four-potential and the phase of the superconducting condensate. When combined with the covariant Maxwell equations, the resulting system is equivalent, in the London (unitary) gauge, to a Proca theory with an effective photon mass set by the inverse London penetration depth. We derive the corresponding Schrödinger-like wave equations for electromagnetic perturbations in the axial and polar sectors of the Schwarzschild spacetime in the presence of the superconducting plasma. The axial sector is governed by a single Regge–Wheeler-type equation whose effective potential contains the London mass term, whereas the polar sector contains two coupled physical degrees of freedom. Quasinormal-mode boundary conditions are formulated for the Schwarzschild geometry. The London penetration depth shifts the oscillation frequencies, modifies the damping rates, and can generate long-lived quasibound configurations when the effective field mass is sufficiently large. This formalism provides a framework for studying electromagnetic relaxation in curved superconducting media, compact objects containing superconducting phases, and effective massive-vector fields around black holes.

The quaternary Preparata codes of Hammons, Kumar, Calderbank, Sloane and Solé are $\mathbb{Z}_4$-linear codes of length $2^m$ with $4^{2^m-m-1}$ codewords. They are usually studied through their binary Gray images, that is, in the Lee metric. We consider them instead as codes over a 4-letter alphabet with the Hamming metric. We show that for odd $m$ they have covering radius 2 and minimum distance 4, so they are quasi-perfect. For even $m$ the same construction has covering radius 3. The proof is a short computation with Teichmüller representatives in the Galois ring $\mathrm{GR}(4,m)$, and it also gives the coset weight distribution. The covering density of these codes tends to $9/8$. The best previously known infinite families of quaternary codes with covering radius 2 have covering density about 1.5. Consequently $K_4(n,2)\le 4^{n-m-1}$ for all $n\ge 2^m$ and odd $m$, which improves the best available bounds for a range of lengths above each $2^m$. For $m=3$ the code is the octacode, and it gives $K_4(8,2)\le 256$; the previous bound was 352, from 2005, and the best lower bound is 251. We also give a quaternary code showing $K_4(6,2)\le 48$, where the previous bound was 52, together with consequences for larger alphabets.

Ocean wave forecasting is essential for maritime safety, offshore operations, and coastal resilience, yet remains challenging due to systematic biases in physics-based models. Physical models, while widely used, rely on approximations and parameterizations that limit their accuracy under complex ocean-atmosphere conditions. To enhance ocean wave forecasting, we propose BridgeCast, within a physics-AI hybrid framework for bias correction. BridgeCast is a probabilistic model based on conditional flow matching (CFM) that learns to transform physical model forecasts into reanalysis-like fields. It treats physical forecasts as corrupted observations and employs a continuous-time generative process to bridge their distribution toward that of reanalysis data. BridgeCast is parameterized by a Transformer-based architecture that enables spatiotemporal modeling, incorporation of exogenous atmospheric variables, and flexible inference via both ordinary and stochastic differential equation formulations. Extensive experiments on real-world datasets demonstrate that BridgeCast consistently outperforms state-of-the-art baselines across regions and forecast lead times.

A charge-$r$ coupling vortex can remain as one fused order-$r$ zero or split into $r$ nearby unit-charge zeros after weak symmetry breaking. The two configurations have the same total winding and the same number of dark states in the lowest-Landau-level projection, so neither the imposed orbital angular momentum nor the total winding number distinguishes their local geometry. We study this distinction in a two-component Haldane-sphere model coupled by a Raman field. For monopole flux $N$, the detuning $\tau_{\rm c}$ at which a defect branch crosses zero energy scales as $|\tau_{\rm c}|\sim N^{-(r+1)}$ for a fused zero and $N^{-2}$ for resolved unit zeros. A Feshbach reduction establishes these asymptotic laws for the full multiband Hamiltonian, and numerical calculations in a monopole-harmonic basis confirm the fused-vortex scaling for $r=1,2,3$. For a partially split cluster of diameter $d$, the scaling crosses over when $d$ is comparable to the magnetic length $\ell_B$, allowing $d$ to be inferred spectroscopically even below the spatial resolution of direct imaging.

Cross-context KV-cache reuse predicts a shared segment's keys and values under a new prefix instead of recomputing them, and has been reported to do so without quality loss. We find otherwise, and identify two problems. (1) A hidden cost: on MMLU and GSM8K, reuse costs substantial accuracy. (2) A decision at the wrong unit: no rule for deciding whether to reuse a cache removes that cost. What does help is choosing which parts of the cache to recompute, and the value of choosing well falls as the unit of choice grows: informed selection removes 49.5% of the cache error beyond chance at single rows (one token's keys and values), 10.6% at 64-token chunks, and nothing at the level of whole calls. Budgeted Cache Repair (BCR) acts at the unit where selection still pays. It drafts two tokens from the assembled cache, ranks cache rows by the attention those tokens pay them, and recomputes a fixed budget of rows exactly, in one of three layouts. The cost is paid rather than predicted away, and the draft that fails as a gate succeeds as a selector. BCR restores GSM8K to dense-prefill accuracy while still serving most calls from cache, and its best layout outperforms every reuse baseline's mean in the reference grid. The draft also beats a coin-flip selector at the same budget - a control prior evaluations lack.

Predicting phenotypic and transcriptional responses to perturbations at single-cell resolution provides a powerful tool for probing biological systems. However, existing methods typically rely on fixed mappings learned during training, making it challenging to calibrate distribution shifts or adapt to novel perturbation conditions during inference. Here, we present scEGFlow, an energy-guided flow matching framework that dynamically bridges control and perturbed cellular states. scEGFlow models continuous transitions from control cell populations to perturbed states using conditional flow matching. It then applies condition-specific energy gradients to correct and steer these predictions, enabling flexible adjustments without retraining the flow model. Evaluations across benchmarks spanning imaging phenotypes and transcriptomic profiles show that scEGFlow outperforms existing methods in reconstructing response distributions under both seen and unseen perturbation conditions, faithfully preserving cellular manifold geometry and population heterogeneity. This advantage is notable when adapting to new conditions with only a few measured cells, consistently improving prediction accuracy. Furthermore, scEGFlow accurately recapitulates perturbation-induced up- and down-regulation patterns across consensus gene expression signatures, where energy guidance improves the agreement between predicted and observed regulatory directions. Ultimately, these findings demonstrate that scEGFlow provides a modular, generalizable, and steerable solution for single-cell perturbation modeling. By grounding generative flows in learned biological landscapes, this architecture establishes a new computational paradigm for navigating and manipulating cellular behavior in silico.

Existing procedural terrain generation methods produce coherent, downhill-flowing river networks only on fixed domains, whereas approaches that extend to infinite worlds typically sacrifice network coherence or downhill-flow guarantees. This work presents a deterministic, terrain-aware, downhill-flowing river algorithm for infinite procedural worlds. Tectonic plate seeds define both continuous terrain fields and corresponding bounded Voronoi-like plate domains, so localized river preprocessing can operate directly on the geometric domain without sampling terrain fields for the purpose of locating plate boundaries. Within each plate, the terrain field is sampled on a low-resolution grid, and rivers are traced downhill from highland source nodes to coastlines, local minima, or existing confluences. River heights are then monotonically adjusted along each path so that every stored segment descends. The resulting river network is generated and cached lazily per plate, so each plate is processed independently of its neighbors. During full-resolution terrain sampling, the distance to the cached river network is computed exactly, and river height is interpolated along nearby segments and blended with the locally evaluated terrain on demand, without caching the blended result itself. Because the warp of the plate borders is bounded below the river border margin, this guarantees downhill flow along every river channel of the final terrain. Together, these design choices make terrain-aware river generation practical for interactive procedural worlds by supporting efficient on-demand evaluation, as demonstrated by the performance analysis presented in this work.

Retrieval-augmented generation (RAG) can ground large language models in external evidence, but retrieved context does not guarantee that generated claims are factually supported. This problem is especially relevant in multi-hop RAG, where retrieval and reasoning proceed through multiple dependent stages. We study whether claim-level conformal factuality control, previously developed for RAG, remains effective in this setting. We apply split-conformal claim filtering to multi-hop RAG and evaluate it on HotpotQA, Natural Questions, and TriviaQA using Llama 3.1 8B and GPT-4o-mini, together with a single-hop reference experiment. Across all six multi-hop model-dataset configurations, increasingly stringent conformal targets consistently increase the fraction of responses whose retained claims are fully supported. At the 95% target, this rate ranges from 95.80% to 97.20%, compared with 55.60%-76.03% without filtering. However, the improvement is strongly selective: only 4.41%-31.09% of generated claims are retained and 9.70%-51.40% of responses remain non-empty at the 95% target. These results show that conformal factuality extends to multi-hop RAG, while demonstrating that nominal reliability must be interpreted jointly with claim retention and abstention.

We develop a finite-band method for the reduction of families of indefinite integrals. The starting point is the case in which the logarithmic derivative $K'(x)/K(x)$ is a rational function. This leads to adapted polynomial and Laurent-type bases and to upper triangular band matrices. The framework includes generalized real Schwarz–Christoffel integrals and more general hyperexponential weights. We then extend the construction to the case in which the logarithmic derivative $K'(x)/K(x)$ is algebraic over the field of real rational functions. The associated finite-dimensional differential module gives rise naturally to block-band systems. Finally, we show that functions satisfying linear differential equations with real polynomial coefficients give rise to finite recurrences for their moments. The resulting reduction is effective: for a prescribed target integral it is enough to solve a finite triangular band system, and only the reduction data associated with the target are required. We also discuss arithmetic complexity and give explicit examples illustrating the scalar and block reductions. The algorithms are implemented in the accompanying Mathematica package BandedReduction.

We study the Ising spin glass with independent, identically distributed couplings on the diamond hierarchical lattice with $n$ branches, of effective dimension $1+\log_2 n$; $n=4$ is the Migdal-Kadanoff lattice of $\mathbb{Z}^3$. For $n\ge4$ and every coupling law with a bounded density we prove that at sufficiently low temperature $T>0$, uniformly in the level of the lattice, the poles are ordered, every spin has Edwards-Anderson parameter $1-O(T)$ when the poles are fixed, and the overlap of two free-boundary replicas has second moment $1-O(T)$. For standard Gaussian couplings, $n=3,4,5,7,8$ and every $T\le T^*(n)=4/15,\,6/7,\,6/5,\,7/4,\,2$ ($0.89$ to $0.98$ times numerical estimates of $T_c$), a computer-assisted proof gives pole order and, as the level tends to infinity, site-overlap order and the blue-cluster statements below; likewise for every larger $n$ at these temperatures. Previously, spin-glass order on these lattices with frustrated independent couplings had been proved only for more than $10^{18}$ branches (Collet and Eckmann, 1984). The key step is growth of the effective coupling under the exact renormalization map: for $n\ge4$, by a one-step contraction, via Rogozin's inequality, of a density bound on an event of high probability; near $T_c$, by interval-arithmetic bounds in the peakedness order. A transfer theorem following the ancestor-chain argument of Collet and Eckmann turns this growth into bulk statements. In the Chayes-Machta-Redner representation the same input gives a blue cluster that contains both poles with probability tending to one and whose expected density is bounded away from zero, while the largest other blue cluster has density tending to zero in probability and in $L^1$; hence blue-cluster density imbalance. To our knowledge this is the first proof of such an imbalance for a spin glass on a graph other than the complete graph.

Tamazight (Amazigh) is, together with Arabic, one of the two official languages of Morocco, yet it remains severely under-resourced for speech technology: pub licly available labelled audio is scarce, generally lacks information on the regional variety spoken, and is often of uneven transcription quality. This article describes the TutlAit dataset, a corpus of Moroccan Tamazight speech paired with Modern Standard Arabic text and explicit regional accent labels. The data were collected with TutlAit, a purpose-built crowdsourcing web application (React 18 front end, Django 5 / Django REST Framework back-end, PostgreSQL database). Native speakers recruited through targeted LinkedIn and Instagram campaigns created an account, declared their regional variety (Atlas, Souss, Rif or other) and demographic information, and then contributed through two workflows: Text-to Audio, in which an Arabic sentence is displayed and the volunteer records its oral Tamazight rendering in the browser, and Audio-to-Text, in which a Tamazight excerpt is played and the volunteer types its Arabic transcription. A complemen tary set of segments was obtained from freely accessible Tamazight audiovisual media, segmented and annotated with ELAN and imported through a bulk CSV/ZIP pipeline. Every upload is converted server-side to 16kHz mono WAV, hashed with SHA-256 for duplicate rejection, checked for duration bounds and validated by an administrator. The dataset contains 13,384 audio files totalling 75,231 seconds (approximately 20.9 hours, about 3.01GB). The Atlas variety accounts for 9,956 files (14.08h) and the Souss variety for 3,378 files (6.75h); small Rif (22 files) and Kabyle (28 files) subsets are also included. The corpus can be reused for speech recognition, speech translation and accent identification for Moroccan Tamazight.

Genetic design automation maps Boolean specifications to regulatory networks and DNA sequences, but a successful mapping does not establish the probability that every output remains correct over time. This paper presents Proof-Carrying Synthetic Biology (PCS-Bio), a formal architecture for acyclic genetic logic circuits operated under fixed inputs. An ideal checker connects Boolean equivalence, sequence and model provenance, local stochastic contracts, and any surrogate-to-target discrepancy bounds. Under explicit semantic and checker assumptions, these obligations imply a joint temporal refinement guarantee without assuming independence among molecular events. Assignment-specific sufficient cubes select the branches needed to prove each output value. This can reduce risk and delay accounting provided that the retained local contracts remain uniform over the physically present but logically masked inputs. The reported evaluation exercises three separate interfaces: an archived Cello execution with sequence reconstruction, a restricted exact rational checker for a synthetic finite-state instance, and diagnostic IEEE~754 binary64 replay. Across 60 deterministic Boolean formula graphs, slicing reduced the worst-assignment risk-charge sum in 55 cases and the maximum accounting delay in 54. These results concern proof accounting and selected implementation components. They do not establish an integrated sequence-bound temporal certificate or physical validation.

In this work, we analyze a two-parameter $(\mu, b)$ asymmetric family of traversable wormhole solutions generated by a massless conformally coupled scalar field. We show that, for a suitable range of parameters, the spacetime is everywhere regular and has two asymptotically flat regions. We then define the wormhole throat and verify the flare-out condition, which leads to violations of the classical energy conditions in GR, thereby requiring exotic matter to hold the throat open. We further analyze the motion of photons governed by null geodesics through an effective potential. The resulting trajectories are computed numerically and visualized using embedding diagrams. Following this route, we investigate scalar perturbations governed by the massless Klein-Gordon equation and find the QNM spectrum semianalytically and numerically. Interestingly enough, we show that such perturbations are governed by only one parameter $\mu$. Therefore, in $D = 4$, we find an isospectrality between the wormhole and the BBMB/Extremal Reissner-Nordström black hole. In the spirit of the seminal work of Morris and Thorne, we derive the conditions for traversability and compute the proper time for a traveler to traverse the wormhole. Finally, we discuss possible extensions and future directions for our work.

Existing benchmarks evaluate tabletop manipulation, flat-floor household activity, or humanoid locomotion and manipulation as separate task groups; none scores vertical mobility and dexterous work on a fragile payload in one long-horizon episode. We present Fiatlux, a light-bulb replacement benchmark built on NVIDIA Isaac Lab. In one episode, a Unitree G1 humanoid positions a step ladder under a ceiling or wall fixture, climbs it, exchanges a spent bulb in a socket for a fresh one, and leaves the spent one in a disposal crate. We decompose the episode into twelve subtask environments scored on difficulty-weighted gates. The goal is a successful replacement, with the fresh bulb seated, the spent one disposed of, neither dropped, and a fragility bound not crossed. Runs that fall short can earn partial credit. Observations are split into a standard mode (signals a physical robot could sense or estimate) and a privileged mode (exact simulator state). We specify the evaluation protocol and provide reference baseline implementations spanning RSL-RL PPO, zero-shot NVIDIA GR00T N1.7 Vision-Language-Action (VLA) models, and whole-body controllers. Additionally, we provide the teleoperated recordings used to specify and check the success gates. The benchmark code and the teleoperated recordings are available at fiatlux-bench.github.io.

Power systems are often represented by high-dimensional dynamic models, making nonlinear control design computationally expensive and limiting its practical application. Oscillation analysis and damping control therefore commonly rely on linearized models, which do not capture the nonlinear oscillatory behavior induced by large disturbances. This paper proposes an isostable-based model reduction method for nonlinear modal analysis of power systems. The method constructs an invariant manifold associated with a selected oscillatory mode and uses isostable coordinates to describe the mode with only two real state variables. The isostable formulation gives linear autonomous modal dynamics, with nonlinear state reconstruction and input response computed on the modal manifold. An optimal damping control problem is then formulated directly in the reduced coordinates. Case studies on the IEEE 39-bus system demonstrate the accuracy of the proposed model in describing nonlinear oscillations and show improved damping compared with control designed using a linear reduced model.

Nonlinear sustained oscillations involving inverter-based resources can happen when device and network interactions produce an attracting limit cycle around an unstable equilibrium. A damping controller must then describe nonlinear dynamics over the region between the two invariant sets, where a local equilibrium linearization can be insufficient. In this paper, a controlled phase–isostable model is first developed on a two-dimensional invariant manifold connecting the equilibrium and the limit cycle. Dynamics on this surface are represented by phase and isostable coordinates, while physical states and control inputs are related to these coordinates through nonlinear reconstruction and response functions. The required functions are computed from connecting trajectories and periodic-orbit data. A control strategy is then designed to provide extra damping while limiting phase distortion. Case studies on a two-area system and an IEEE 39-bus system demonstrate more effective oscillation damping than the compared equilibrium-linearized designs under the same conditions.

We investigate the von Neumann–Jordan constant of Banach tensor products equipped with the injective and projective tensor norms. We first establish lower estimates in terms of the geometric properties of the factor spaces and show that, whenever both factors are infinite-dimensional, the von Neumann–Jordan constants of both canonical tensor products attain the maximal value \(2\). For finite-dimensional factors, we obtain explicit results for classical sequence spaces and characterize the extremal case through operator-space and orthogonal-contact conditions. We further derive dimension-sensitive estimates based on Euclidean sections. Finally, we study the constant under equivalent renormings and determine its exact renorming envelope for injective and projective tensor products. As consequences, we characterize when these tensor products are superreflexive and when they are weak Hilbert spaces. These results clarify the influence of tensor norms, dimension, and renorming on the von Neumann–Jordan geometry of Banach tensor products.