Papers

Continual pre-training and fine-tuning in Large Language Models (LLMs) inevitably induce catastrophic forgetting, typically mitigated by replay using often-inaccessible original data. In this data-free regime, we analyze where forgetting occurs and why. Systematic parameter freezing across five settings up to 1.4B reveals that forgetting concentrates selectively in the output embeddings of tokens rarely seen in the new corpus, whereas the same sqrt(v-hat) band of the body is inert and new learning resides elsewhere. This localization is governed by the vocabulary deficiency of the corpus rather than the training mode, allowing pre-retraining risk ranking from token counts alone within a fixed base model. Mechanistically, absent tokens receive persistent one-sided softmax gradients that Adam's second-moment (sqrt(v-hat)) normalization amplifies into full-sized updates. We therefore propose an intervention: raising Adam's epsilon exclusively for the output projection during training. Across eight settings spanning 160M to 12B parameters and four model families, this removes 39.4% to 67.9% of forgetting across all seven stable configurations without degrading target learning or requiring per-model tuning. The defense combines additively or better with replay (79.8% on Qwen/Korean) and rescues released-head LoRA from a 23-fold forgetting surge. Because post-hoc editing of the drifted rows recovers under 5% of forgetting, the intervention must operate during training. Our findings indicate that a single-line optimizer adjustment may serve as the primary defense against catastrophic forgetting where the corpus starves the vocabulary.

Binary black holes formed dynamically in star clusters are often associated with nearly equal-mass pairing. We show that this expectation is incomplete. The more general prediction of dynamical assembly is an ordered-pairing relation in which the two black holes are drawn independently from a common one–body mass spectrum and then ordered by mass. Once the primary-mass distribution is known, this relation fixes the conditional companion distribution $p(m_2\mid m_1)$. We validate this picture with cluster simulations. In these models, the ordered-draw relation reproduces the morphology of the mass-pairing distribution, including fixed-$m_2$ ridges that are inherited from the one–body mass spectrum: features at nearly constant secondary mass that extend over a range of primary masses and therefore correspond to decreasing $q=m_2/m_1$ as $m_1$ increases. Thus, the geometry of the mass distribution itself becomes a formation-channel diagnostic. Dynamical pairing maps peaks of the primary-mass spectrum into fixed-$m_2$ ridges with predictable amplitude, whereas isolated binary evolution more naturally produces structures at fixed $q$. Applying this test to a non-parametric reconstruction of the gravitational-wave population, we find a tentative enhancement at $m_2\simeq 30~ M_\odot$ for $m_1\gtrsim 40~ M_\odot$ that is broadly compatible with ordered pairing. Finally, we show that dynamical formation naturally explains the rapid decline of the secondary-mass distribution above $\sim30~M_\odot$ recently reported by the LIGO–Virgo–KAGRA Collaboration.

We prove the Hassanzadeh-Nasrollah Nejad-Simis conjecture: if $f\in (x_1,\ldots,x_n)^2\subsetneq k[[x_1,\ldots,x_n]]$ has an isolated critical point and $\operatorname{char}k=0$, then its Euler conductor $J_f:f$ is not contained in the Tjurina ideal $(J_f,f)$. More generally, if $A=R/I$ is a nonzero Noetherian $k$-algebra and $a=[f]\in A$ is nilpotent with $d_{A/k}a=0$, then $I:f\nsubseteq(I,f)$. For a local ring $(R,\mathfrak n)$ we obtain the stronger noncontainment $I:f\nsubseteq(I,f)+\mathfrak n(I:f)$. The proof reduces a hypothetical containment to a self-exact square-zero element and detects its differential by the trace of a regular representation over the dual numbers. Finally, an explicit five-variable isolated singularity satisfies $J_f:f\subseteq\overline{J_f}$, disproving the integral-closure strengthening proposed by Ma and Zuo.

Memory-augmented reinforcement learning strengthens LLM agents' ability to solve complex long-horizon tasks. Skills are one such form of memory, pairing instructions with an applicability condition over task types. However, retaining every skill indiscriminately as the policy improves lets obsolete or harmful entries accumulate and mislead the agent. We propose SkillForge, an agentic RL method that compiles and evolves the skill library through a fitness-driven skill lifecycle of trial, active, stable, and retired states, so that the skills and the model co-evolve throughout training. A pre-RL evaluation phase first uses the base model's own rollouts to pre-retire low-fitness skills, yielding a filtered library that then seeds supervised fine-tuning. Reinforcement learning takes over from this checkpoint, and at each iteration selective retirement, stabilization, and LLM-guided mutation continue to forge the skill library alongside policy optimization. Across multiple interactive agent benchmarks, SkillForge achieves the highest aggregate success rate, delivering up to 7.8% relative improvement over the strongest baseline while keeping the skill library compact throughout training. We introduce SkillFurnace, a dataset of 5k+ annotated records bundling retirement-filtered SFT trajectories, evolved skill libraries with fitness annotations, and retirement events with human-annotated failure categories to support research on skill quality and lifecycle management.

Instruction text-to-speech (ITTS) systems systematically encode acoustic gender skews from descriptive style prompts, such as occupations or personas, even when demographic attributes are left unspecified. Calibrating the implicit gender distribution of the synthesized voices, across heterogeneous architectures and without model retraining or overriding explicit user prompts, is an open problem. In this work, we propose model-adaptive steering, a training-free bias calibration method that steers post-encoder conditioning representations using a group deviation vector paired with a coarse-to-fine strength search on a development set. A deterministic lexical gate bypasses intervention whenever explicit gender keywords are detected, preserving intended prompt semantics. Evaluated on a 12,800-prompt held-out benchmark across four ITTS models (three architectures), the proposed method reduces aggregate calibration error from 11.5–28.1 to 0.8–5.9 percentage points (e.g., shifting Parler-TTS Mini from 78.1% and PromptTTS++ from 27.3% female to 50.8–52.4%). Output rates stay within 0.9 pp across anchor set sizes at fixed operating points, while UTMOS decreases by at most 0.08 and WER degrades by at most 3.3 pp.

Video deepfakes targeting a specific individual, the Person-of-Interest (POI), are the most harmful ones, and, since a public figure is abundantly recorded, a detector can be built from genuine footage of that individual. Such detectors commonly describe a subject through a 3D Morphable Model (3DMM) and adopt its coefficients as a whole, so which part of that description carries the signal has never been measured. We dissect it, holding the encoder, the training corpus and the enrollment protocol fixed and varying only what the encoder observes. The groups of coefficients prove largely redundant, since the shape block alone recovers almost all the accuracy of the full vector, and their temporal evolution contributes a real but bounded amount. We further show that the dense surface the same fit returns, which these detectors discard, carries identity information that the coefficients do not, and that it helps precisely where they are weakest. We assemble the best configuration into MOTIF, a visual-only detector trained on real videos only, with no manipulated video and no POI-specific data. It improves on both state-of-the-art POI detectors in every dataset and manipulation of our benchmark and at two quality levels. Our experimental code will be released at https://github.com/polimi-ispl/MOTIF.

Bentert, Fomin, Golovach, Korhonen, Lochet, Panolan, Ramanujan, Saurabh, and Simonov (SODA 2025) initiated the parameterized study of Edge-Disjoint Shortest Cycle Packing: given a weighted graph $G$ and an integer $k$, decide whether $G$ contains $k$ edge-disjoint cycles of minimum weight. They showed that the problem admits an algorithm running in time $n^{O(k^6)}$ and asked whether it is fixed-parameter tractable or $W[1]$-hard parameterized by $k$. We resolve this question by proving that Edge-Disjoint Shortest Cycle Packing is $W[1]$-hard parameterized by $k$, even on unweighted subcubic graphs. The same lower bound also applies to the vertex-disjoint variant. For planar graphs, they provides a construction of a kernel with $O(k^2)$ vertices and an algorithm running in time $k^{O(k)} \cdot n^{O(1)}$, and explicitly asked whether the problem admits a single-exponential algorithm of running time $2^{O(k)} \cdot n^{O(1)}$. Rather than addressing this question in isolation, we introduce a more general framework, Diverse Shortest Cycle Coverage, which asks for $k$ shortest cycles that may overlap in a controlled way while maximizing the total weight of covered edges. This framework simultaneously captures edge-disjoint shortest cycle packing, the problem of finding diverse shortest cycles, and the problem of maximizing edge coverage by shortest cycles. Our main algorithmic result shows that Diverse Shortest Cycle Coverage can be solved on planar graphs in time $2^{O(k)} \cdot n^{O(1)}$, thereby giving a single-exponential algorithm for Edge-Disjoint Shortest Cycle Packing as a special case. The key idea of our algorithm is a structural analysis of the Laminar Shortest Cycles Tree, a tree-like decomposition that reveals a laminar interaction pattern among shortest cycles in planar graphs and enables an efficient dynamic programming algorithm.

Compact mobile robots must recover scene geometry under changing lighting and surface texture while working within tight payload and cost limits. We present a compact mobile robot that uses origami-inspired wheels for locomotion and active control of its sensing geometry. As the wheels move between terrain-adaptive configurations, the changing chassis pitch sweeps a 2D LiDAR through intermediate elevations; held wheel positions provide a chosen viewing angle. An IMU accounts for chassis attitude, and a fusion node projects LiDAR returns into the RGB-D depth stream supplied to RTAB-Map. The arrangement uses the wheel actuation already present on a sub-300 USD, sub-2 kg prototype to extend the scanner's viewing geometry. We assess depth fusion in a textureless indoor corridor and an outdoor sunlit area, with three runs per sensor configuration in each setting. Mean full-frame invalid-depth fractions fell from 21% to 11% indoors and from 48% to 18% outdoors. The prototype combines improved depth coverage with a continuously adjustable LiDAR viewpoint using the same actuation that reconfigures its wheels.

Long inputs and extended generation increase the storage and access costs of the key-value (KV) cache. Low-bit quantization reduces storage and memory traffic, while query-channel pruning can further reduce key-cache reads. Rotation-based quantization redistributes the energy of key outliers across channels. To maintain computational invariance, the same orthogonal transform must be applied to queries, preserving query-key dot products. However, this rotation can disperse query energy, weakening the separation between a few large components to retain and many small ones to prune. We introduce Dual-QK, which uses paired non-orthogonal query and key transforms to address this conflict. Using calibrated query and key statistics, Dual-QK combines partial key whitening with a query-aligned basis to balance key scales for INT2 quantization and concentrate query energy for dynamic channel pruning. Channel-0 protection and bucket-relative RoPE support low-bit accuracy over long contexts. Experiments on four models across five generative benchmarks and long-context retrieval tasks show improved accuracy over OSCAR on most tasks at 40% query-channel sparsity. At a 128K context, Dual-QK provides $6.8\times$ KV-cache compression and an estimated $8.3\times$ reduction in KV read volume relative to unpruned BF16. Under the evaluated configurations, our SGLang implementation achieves up to $3.75\times$ the decoding throughput of unpruned BF16.

A collection of $m \geq 2$ lines through the origin in $\mathbb{R}^2$ is balanced if the sum of the orthogonal projections onto these lines equals $m/2$ times the identity. A line arrangement in $\mathbb{RP}^2$, endowed with the round metric of curvature $1$, is point-balanced if the tangent lines at every vertex form a balanced collection. A line arrangement $\mathcal{A}$ in $\mathbb{RP}^2$ has the Hirzebruch property if it consists of $3k$ lines and every line contains exactly $k+1$ vertices. Using a Kempf–Ness convexity argument, we show that an irreducible arrangement $\mathcal{A}$ has the Hirzebruch property if and only if its projective equivalence class contains a point-balanced representative, unique up to orthogonal transformations. We then combine elementary properties of balanced collections of lines in $\mathbb{R}^2$ with spherical geometry to prove that every irreducible point-balanced arrangement is a reflection arrangement. This gives a new proof of Panov's classification of real Hirzebruch arrangements.

Security monitoring of edge-IoT fleets faces three structural challenges. (i) A per-node monitor is cheap but cannot see attacks that coordinate across devices. (ii) A cloud monitor sees the full fleet but pays for that view in bandwidth. (iii) Even at the cloud, a monitor built on a single RV engine can be fooled by an attacker who compromises a device, raises one malicious request, and then goes silent: once the events stop, an event-triggered monitor has nothing left to evaluate. We propose a three-layer hierarchical runtime-verification framework that addresses all three. The edge layer classifies events as they happen, the gateway layer aggregates short windows of per-device behaviour, and the cloud layer runs two complementary RV engines. MonPoly handles first-order temporal correlation over the merged alert stream: coordinated overflow (which genuinely quantifies across devices) plus per-device multi-vector APT, escalation, and persistent-campaign patterns. RTLola handles a time-triggered silent-node property that an event-triggered engine cannot detect within a bounded delay under fleet silence. We evaluate the framework on a 15-actor Docker testbed covering eight attack profiles plus a silent-bypass scenario. In the controlled labelled testbed, every device-attributable incident the framework raises names an attacker-labelled device, and the RTLola tier catches silent-bypass attempts the event-triggered tier misses. Per-event monitoring stays in the microsecond range at the edge and gateway, with low end-to-end alert-to-incident latency at the cloud.

Multi-agent systems (MAS) leverage interactions between agents to perform complex tasks. Despite their success, we show that these interactions can also lead to homogenization, i.e., agents converging to similar behaviors. Homogenization in MAS can reduce agent diversity and reinforce shared failures. In this paper, we operationalize homogenization using three metrics: conformity to the majority, polarization towards extremes, and growing inertia against changes over subsequent interactions. We evaluate homogenization in MAS for code generation, hiring, and scientific peer review. Across these tasks, we show that homogenization translates to concrete downstream risks: in code generation, it hides and amplifies correlated errors which can create systemic vulnerabilities; in hiring, it allows the influence of biased agents to persist long after their removal; and in peer review, it creates uneven evaluation standards across research areas. Our results establish homogenization as a failure mode of MAS, demonstrating that MAS evaluations must move beyond aggregate performance to carefully analyze interaction dynamics. Finally, we show that simple approaches to increase diversity—leveraging sampling stochasticity and mixed-models MAS—fail to reduce homogenization risks, highlighting the need for strategies to effectively leverage agent diversity.

Dense visual text requires image generators to reproduce long strings across multiple regions with correct placement and legibility. As short-string rendering improves, evaluation must test sustained performance across more demanding scenes. We introduce UltraText Bench, a bilingual benchmark for prompt-only generation of dense visual text. It contains 432 prompts spanning 24 real-world scene categories and three difficulty levels, split equally between English and Chinese. Each human-reviewed prompt supplies exact strings for four to twelve text regions, paired with structured references for their content, placement, and visual attributes. We use the Q-Judger vision-language model to assess each image against the complete reference, reporting text fidelity, text clarity, spatial quality, and scene quality. Across 24 model configurations, these dimensions reveal different strengths: Z-Image-Turbo gains 3.81 clarity points over Z-Image-Base while losing 14.76 fidelity points under the reported settings. Performance also varies with workload; Qwen-Image-2512's English composite falls from 86.50 at L1 to 42.86 at L3. Ten participants took part in human evaluation of the automatic scores. Repository: https://github.com/LINs-lab/UltraText_Bench.

Physics simulation is a cornerstone of many computer graphics applications, ranging from video games and virtual reality to visual effects and computational design. The number of techniques for physically-based modeling and animation has thus skyrocketed over the past few decades, facilitating the simulation of a wide variety of materials and physical phenomena. These course notes provide an in-depth introduction to multiphysics simulation methods for computer graphics, covering the mathematical foundations, key algorithms, and practical considerations behind the most widely used approaches. We focus on methods developed by the computer graphics community for simulating various physical phenomena and materials – including rigid and deformable bodies, fluids, and granular materials – as well as the interactions between them. For each method, we present the underlying mathematical framework with detailed derivations and discuss how different materials and coupling strategies fit into the formulation. A selection of software frameworks that offer out-of-the-box multiphysics modeling capabilities is also presented. Finally, we touch on emerging trends in physics-based animation, including machine learning-based methods which have become increasingly popular in recent years.

Generative 3D Gaussian head avatars provide high-quality, efficient rendering, but synthesising the Gaussian representation remains computationally expensive, limiting deployment on resource-constrained and edge devices. We introduce an efficient generator architecture for unconditional 3D Gaussian head synthesis, based on a parameter-efficient synthesis block and depth-wise separable convolutions while retaining style-based conditioning. Our architecture reduces generator complexity without requiring model compression or quantisation. Compared with the baseline model, our approach reduces FLOPs by 94%, parameter count by 70%, and model size by 81%, while maintaining competitive generation quality. We further demonstrate practical CPU inference and browser-based execution on mobile devices using ONNX Runtime, enabling 3D Gaussian avatar synthesis without dedicated GPU hardware or application-specific software. In addition to conventional image-quality metrics, we evaluate multi-view consistency, training cost, and deployment performance. Code, trained models, and evaluation tools will be released publicly.

LLMs are evolving rapidly, with newer models offering stronger capabilities. This suggests that in LLM-based relevance judging, more capable models will achieve higher agreement with human judgements under the same prompt. We challenge this understanding by investigating the behavior of LLM-based relevance judges under backbone evolution. Keeping the prompts fixed, we evaluate a representative single-prompt (UMBRELA) and a rubric-based prompt (EXAM) across sequential model versions of commercial (Gemini, GPT) and open-weight (Qwen, Llama) models. Overall, we find no consistent evidence that newer versions lead to better relevance judges. Crucially, similar or improved aggregate performance does not imply judgment stability: correct judgements made by an earlier version of an LLM backbone are not necessarily preserved by later versions. We investigate the potential drivers of these regressions. Our findings caution against the assumption that judging prompts designed and validated for one backbone version will perform equivalently or better when the model is updated, even within the same family.

Acoustic foundation models (AFMs) have democratized acoustic applications, enabling powerful models for tasks ranging from speech recognition to speaker verification with minimal resources. However, the security of applications based on AFMs remains largely underexplored. Our work addresses this gap by proposing the Foundation Acoustic model Backdoor (FAB) attack, demonstrating that state-of-the-art AFMs are susceptible to backdooring under practical settings. Despite making minimal assumptions about adversary capabilities (e.g., no access to pre-training data), we show that FAB preserves benign performance while inducing backdoors that survive fine-tuning and cause significant degradation across diverse downstream tasks when activated. Notably, FAB utilizes task-agnostic, physically realizable, inconspicuous, and sync-free triggers (e.g., a background siren). We evaluate FAB using two leading AFMs, nine downstream tasks, and four different triggers. We further demonstrate its effectiveness against established defenses and across both digital and physical domains. While extensive end-to-end fine-tuning can mitigate FAB, such a defense is resource-intensive and task-specific. Our work highlights critical risks to AFMs and calls for advanced defenses.

Smoking cessation remains a complex self-regulatory challenge, often undermined by cue-triggered cravings arising from habitual, emotional, and social contexts. Existing wearable cessation systems are largely reactive, detecting smoking events only after lapses occur and thus missing the critical window for timely intervention. Guided by cue-reactivity theory and Self-Determination Theory (SDT), we argue that future digital health systems should shift from retrospective feedback toward proactive craving management that supports user autonomy and competence. To inform the design of such systems, we present a formative pilot qualitative study involving semi-structured interviews with 10 smokers and ex-smokers from a multi-ethnic Asian population, a demographic underrepresented in current wearable AI and smoking cessation research. Through an iterative co-design interview process, we examine (1) the barriers and facilitators to smoking cessation and (2) the desired design features of wearable systems targeting cravings before lapses occur. Our findings identify key craving predictors across habitual, emotional, and social dimensions, alongside user-preferred intervention strategies such as social accountability, personalized support, rewards, and just-in-time distraction techniques. Participants also emphasized the importance of trust, privacy, personalization, and non-judgmental interaction styles. These insights directly inform the design of AURA, a novel smartwatch-smartphone ecosystem for proactive craving detection and intervention using commercially available wearable devices.

Cyber resiliency in edge-IoT deployments is fundamentally an economic problem: detection must keep critical processes operating under attack, but defender resources (compute, bandwidth, operator attention) are bounded. Centralised cloud monitoring offers expressive cross-device detection at prohibitive bandwidth cost; purely edge-local monitoring is cheap but blind to coordinated multi-device attacks where the asymmetric balance favours the attacker. We propose a lightweight hierarchical security-monitoring framework, built on formal runtime-verification methods, that occupies the practical middle ground at quantified cost. Each edge device runs a lightweight TeSSLa stream specification (size, payload validity, rate, and timestamp-drift predicates) that emits a four-valued verdict per aggregation window at sub-microsecond per-event cost; the gateway runs a parametric first-order MonPoly monitor over the per-device verdict streams at microsecond-scale per-verdict cost. The edge-to-gateway uplink carries roughly one Boolean per aggregation window per node, orders of magnitude smaller than the raw packet stream. The gateway tier detects coordinated attack patterns that no single-node monitor can see, shifting the asymmetric cost balance toward the defender. Every alert carries a witness set naming the device, the monitor tier, and the predicate that fired, providing an auditable record of the decision. We evaluate the framework on a container-host testbed spanning nominal and attacker nodes across four attack classes (buffer overflow, time spoofing, denial-of-service, and mixed advanced-persistent-threat patterns), and describe the edge- and gateway-tier specifications together with the cost-versus-coverage trade-off as monitor levels are added.

We develop the method of central extensions (the Skjelbred–Sund method) for nilpotent right alternative algebras over the field of complex numbers and apply it to obtain the algebraic classification of five-dimensional nilpotent right alternative algebras. More precisely, we classify, up to isomorphism, all complex five-dimensional nilpotent right alternative algebras that have no annihilator component (that is, which are not a direct sum of a smaller algebra and a one-dimensional algebra with zero product) and which are not $2$-step nilpotent. Every such algebra is a non-split central extension of a nontrivial nilpotent right alternative algebra of dimension three (by a two-dimensional space) or of dimension four (by a one-dimensional space). For each of the relevant three- and four-dimensional algebras we compute the second cohomology space, the automorphism group and its action on the second cohomology, and we determine all orbits that give non-split extensions. The resulting list consists of $124$ algebras and families of algebras; it contains $29$ algebras with two-dimensional annihilator and $95$ algebras with one-dimensional annihilator.

We study the singlet sector of large-$N$, $O(N)$ vector model on $S^1_\beta\times S^2_r$ in presence of an angular potential $\Omega$. We compute the free energy of the model both at the free fixed point as well as the non-trivial fixed point. The model undergoes a phase transition when the temperature $T$ and angular potential attain the relation $T^2r^2\sim N (1-\omega^2)$, where $\omega=r\Omega$ and $r$ is the radius of $S^2$, with $Tr\gg1$, at both the fixed points, with different numerical coefficients. The transition was studied earlier at zero angular potential at $Tr\sim \sqrt{N}$. The holonomy eigenvalue distribution, having support on the full circle below the transition, develops a gap above it, called the Gross-Witten-Wadia transition. The angular potential introduces an additional parameter to such a transition, tuning it, the transition can occur even at a fixed temperature. We show that for the free model transition can occur as $1-\omega^2\sim 1/N$ while $Tr\sim O(1)$. For the interacting model the computation is performed at a limit $Tr\gg1$, thus we show the same at a large but fixed temperature which does not scale as $\sqrt{N}$. In the ungapped phase, the free energy exhibits a double pole near $\omega^2=1$ for both the fixed points. This is possibly due to the fact that the theory projected onto the singlets is non-local and therefore need not obey the leading simple pole scaling of a local thermal effective action.

Third-order dispersion turns the soliton of the nonlinear Schrödinger equation, which underlies optical analogues of event horizons in fibers, into a weakly radiating solitary wave. We compute three of its properties without assuming a thermal emission law. First, the linearized (Bogoliubov-de Gennes) problem must be posed about the stationary state of the dispersive equation: linearizing about the integrable profile produces a complex quartet that is converged in grid and box, grows as the square root of the dispersion strength and is spurious. About the stationary state, on a periodic grid, the zero-mode sector consists of two Jordan blocks of size two and the spectrum is real at the operating point, including negative-energy box modes of the resonant branch. Second, we measure the steady Cherenkov emission of adiabatically prepared solitons from the flux of the radiation behind them, over eight decades. The radiation is phase-matched in the frame of the drifting soliton, and the first-order rate falls short of the measured one by factors of 29 to 45. Expressed through a scaled dispersion coefficient of the local soliton, the measured rate describes launched solitons of three amplitudes; with norm and momentum balance, and no further fitted parameter, it reproduces their recoil and the slow decay of their loss rate; at weak dispersion the loss of a launched soliton is the shedding of its launch mismatch. Third, a census of the asymptotic channels shows that long-wavelength upstream emission requires the chemical potential of the soliton, lowered by the comoving-frame Doppler shift of a drifting soliton, to lie inside the analysis band, which bounds the soliton amplitude. In a kinematic model of the flow the surface gravity has a closed form; the thermal relation and the entanglement built on it are imposed inputs of that model. The construction applies to Raman-free Kerr media.

We develop a non-asymptotic theory for nonparametric drift estimation in discretely observed multi-dimensional Lévy-driven stochastic differential equations using sparse ReLU neural networks. Under exponential \(\beta\)-mixing and an exponential-tail condition on the Lévy measure, we establish an oracle inequality for the least-squares estimator. The jump component changes both the martingale structure and the concentration regime relative to diffusion models: continuous martingales are replaced by discontinuous martingales, while the relevant empirical-process fluctuations are sub-exponential rather than sub-Gaussian. We handle these difficulties without truncating the observed increments, using an exponential-supermartingale argument for compensated Poisson integrals and \(\psi_1\)-chaining. Despite the weaker concentration, the resulting statistical bound is, up to constants, of the same order as the corresponding diffusion bound. For drift functions with hierarchical compositional structure, this yields intrinsic-dimensional convergence rates. The framework allows infinite jump activity and, in some cases, infinite variation. Finally, we establish a minimax lower bound on a fixed non-trivial compound-Poisson submodel. Together with the upper bound, this shows that the estimator is minimax optimal up to logarithmic factors.

We introduce a secondary index map from relative K-homology to the K-theory of a relative structure algebra. We prove an algebraic Mayer-Vietoris sequence for the relative structure algebra, and prove compatibility of the secondary index map with the Mayer-Vietoris boundary map. As an application, we compute the secondary index of the Dirac operator on an even-dimensional spin manifold with collared metric having uniformly positive scalar curvature on the boundary. This computation leads to a refinement of the delocalized APS-index theorem.

We consider the interaction of a viscous incompressible fluid with a flexible elastic shell occupying the boundary of the fluid's domain in two space dimensions. The shell is modelled by a perfectly elastic linearised beam equation. It is an open problem in fluid-structure interaction, even for the idealised case of a perfectly elastic plate, if a self-intersection of the structure can be excluded in the long run. We show that by adding a physically well-motived and sufficiently strong transport noise in the structure equation, the self-intersection does not occur before any given end-time with any prescribed probability smaller than 1.

In this paper we are going to discuss compactness in combinatorial Banach spaces. After discussing the definition and structure of these spaces, we proceed to propose compactness criteria for them and for their extensions. Finally, we demonstrate their connection with theory of hypergraphs.

In this paper, we prove that every separable unital AT algebra of real rank zero has complexity rank at most one. In particular, every irrational rotation algebra has complexity rank one. This answers a question of Jaime and Willett.

The properties of high-spin band structures in $^{74}$Br nucleus are investigated using the triaxial projected shell model (TPSM) and particle triaxial rotor (PTR) approaches. It has already been demonstrated that lowest three bands observed in $^{74}$Br have a characteristic feature of a chiral-wobbler. The first excited band is the chiral partner of the yrast band and the second excited band is the wobbling band based on the yrast state. We have analyzed the third excited band using the TPSM and PTR calculated quantities, and a unique character of this band is revealed. It is predicted that this band is the chiral partner of the second excited band, and is also a wobbling mode based on the first excited band.

Camouflaged object detection requires pixel-accurate masks, but obtaining such annotations is slow and costly, making synthetic training images an attractive alternative. Under a fixed generation budget, however, it remains unclear which real-image regions to target for synthetic data generation. We study an uncertainty-guided generation strategy that clusters the unlabelled real images, identifies clusters on which the model is least certain, allocates synthetic generation toward those clusters, and iteratively retrains the model. Across 103 training runs, uncertainty-based targeting does not outperform random allocation. Five independent controls further show that this null result is not an artifact: targeted training sets are measurably different from random sets, but the difference is explained by concentrating the generation budget rather than by where uncertainty is concentrated, as every concentration rule we test reproduces the effect and, on boundary accuracy, so does aiming at the clusters the model was most certain about. Separately, we find substantial data contamination in CHAMELEON, with 50 of its 76 images duplicated from training data despite the standard overlap check reporting zero overlap. Together, these results show that, under a fixed synthetic-data budget, budget concentration, not uncertainty-based targeting, accounts for the observed training-set effects.

A gate voltage can suppress the critical current of a superconducting nanowire, and various scenarios have been proposed to describe these observations. The key difficulty is that these scenarios, including both leakage-driven and field-driven mechanisms, are impossible to disentangle in standard experiments. Here, we resolve this issue by studying a fully suspended superconducting nanowire of amorphous MoGe, separated from the gate by vacuum, eliminating all leakage-driven channels. We measure the phase slip escape rate $\Gamma$ and find a large gate-induced enhancement of $\Gamma$, exponential over six orders of magnitude. Fitting various escape-rate models reveals a strong deviation from simple phase slip models, hinting at a complex interaction between the electrostatic field and the phase slip centers. Surprisingly, $\Gamma$ is not invariant under reversal of the gate-voltage polarity. Our work establishes a clear and nontrivial connection between gate voltage and $\Gamma$, guiding future research into the origins of the effect.