3D Gaussian Splatting (3DGS) has recently emerged as a promising approach for 3D reconstruction, providing explicit, point-based representations and enabling high-quality real time rendering. However, when trained with sparse input views, 3DGS suffers from overfitting and structural degradation, leading to poor generalization on novel views. This limitation arises from its optimization relying solely on photometric loss without incorporating any 3D structure priors. To address this issue, we propose Coherent supergaussian Modeling with Spatial Priors (COSMOS). Inspired by the concept of superpoints from 3D segmentation, COSMOS introduces 3D structure priors by newly defining supergaussian groupings of Gaussians based on local geometric cues and appearance features. To this end, COSMOS applies inter group global self-attention across supergaussian groups and sparse local attention among individual Gaussians, enabling the integration of global and local spatial information. These structure-aware features are then used for predicting Gaussian attributes, facilitating more consistent 3D reconstructions. Furthermore, by leveraging supergaussian-based grouping, COSMOS enforces an intra-group positional regularization to maintain structural coherence and suppress floaters, thereby enhancing training stability under sparse-view conditions. Our experiments on Blender and DTU show that COSMOS surpasses state-of-the-art methods in sparse-view settings without any external depth supervision.

Large language models (LLMs) are increasingly used to assist developers with code, yet their implementations of cryptographic functionality often contain exploitable flaws. Minor design choices (e.g., static initialization vectors or missing authentication) can silently invalidate security guarantees. We introduce CIPHER(Cryptographic Insecurity Profiling via Hybrid Evaluation of Responses), a benchmark for measuring cryptographic vulnerability incidence in LLM-generated Python code under controlled security-guidance conditions. CIPHER uses insecure/neutral/secure prompt variants per task, a cryptography-specific vulnerability taxonomy, and line-level attribution via an automated scoring pipeline. Across a diverse set of widely used LLMs, we find that explicit secure prompting reduces some targeted issues but does not reliably eliminate cryptographic vulnerabilities overall. The benchmark and reproducible scoring pipeline will be publicly released upon publication.

Retrieving code functions, classes or files that are relevant in order to solve a given user query, bug report or feature request from large codebases is a fundamental challenge for Large Language Model (LLM)-based coding agents. Agentic approaches typically employ sparse retrieval methods like BM25 or dense embedding strategies to identify semantically relevant units. While embedding-based approaches can outperform BM25 by large margins, they often don't take into consideration the underlying graph-structured characteristics of the codebase. To address this, we propose SpIDER (Spatially Informed Dense Embedding Retrieval), an enhanced dense retrieval approach that integrates LLM-based reasoning along with auxiliary information obtained from graph-based exploration of the codebase. We further introduce SpIDER-Bench, a graph-structured evaluation benchmark curated from SWE-PolyBench, SWEBench-Verified and Multi-SWEBench, spanning codebases from Python, Java, JavaScript and TypeScript programming languages. Empirical results show that SpIDER consistently improves dense retrieval performance by at least 13% across programming languages and benchmarks in SpIDER-Bench.

Sequential recommendations (SR) predict users' future interactions based on their historical behavior. The rise of Large Language Models (LLMs) has brought powerful generative and reasoning capabilities, significantly enhancing SR performance, while Multimodal LLMs (MLLMs) further extend this by introducing data like images and interactive relationships. However, critical issues remain, i.e., (a) Suboptimal item representations caused by lengthy and redundant descriptions, leading to inefficiencies in both training and inference; (b) Modality-related cognitive bias, as LLMs are predominantly pretrained on textual data, limiting their ability to effectively integrate and utilize non-textual modalities; (c) Weakening sequential perception in long interaction sequences, where attention mechanisms struggle to capture earlier interactions, hindering the modeling of long-range dependencies. To address these issues, we propose Speeder, an efficient MLLM-based paradigm for SR featuring three key innovations: 1) Multimodal Representation Compression (MRC), which condenses item attributes into concise yet informative tokens, reducing redundancy and computational cost; 2) Modality-aware Progressive Optimization (MPO), enabling gradual learning of multimodal representations; 3) Sequential Position Awareness Enhancement (SPAE), improving the LLM's capability to capture both relative and absolute sequential dependencies in long interaction sequences. Extensive experiments on real-world datasets demonstrate the effectiveness and efficiency of Speeder. Speeder increases training speed to 250% of the original while reducing inference time to 25% on the Amazon dataset.

We study matrix and tensor denoising when the underlying signal is \textbf{not} necessarily low-rank. In the tensor setting, we observe \[ Y = X^\ast + Z \in \mathbb{R}^{p_1 \times p_2 \times p_3}, \] where $X^\ast$ is an unknown signal tensor and $Z$ is a noise tensor. We propose a one-step variant of the higher-order SVD (HOSVD) estimator, denoted $\widetilde X$, and show that, uniformly over any user-specified Tucker ranks $(r_1,r_2,r_3)$, with high probability, \[ \|\widetilde X - X^\ast\|_{\mathrm F}^2 = O\Big( κ^2\Big\{r_1r_2r_3 + \sum_{k=1}^3 p_k r_k\Big\} + ξ_{(r_1,r_2,r_3)}^2 \Big). \] Here, $ξ_{(r_1,r_2,r_3)}$ is the best achievable Tucker rank-$(r_1,r_2,r_3)$ approximation error of $X^\ast$ (bias), $κ^2$ quantifies the noise level, and $κ^2\{r_1r_2r_3+\sum_{k=1}^3 p_k r_k\}$ is the variance term scaling with the effective degrees of freedom of $\widetilde X$. This yields a rank-adaptive bias-variance tradeoff: increasing $(r_1,r_2,r_3)$ decreases the bias $ξ_{(r_1,r_2,r_3)}$ while increasing variance. In the matrix setting, we show that truncated SVD achieves an analogous bias-variance tradeoff for arbitrary signal matrices. Notably, our matrix result requires \textbf{no} assumptions on the signal matrix, such as finite rank or spectral gaps. Finally, we complement our upper bounds with matching information-theoretic lower bounds, showing that the resulting bias-variance tradeoff is minimax optimal up to universal constants in both the matrix and tensor settings.

Kleinberg and Mullainathan (2024) recently proposed a formal framework called language generation in the limit and showed that given a sequence of example strings from an unknown target language drawn from any countable collection, an algorithm can correctly generate unseen strings from the target language within finite time. This notion was further refined by Li, Raman, and Tewari (2024), who defined stricter categories of non-uniform and uniform generation. They showed that a finite union of uniformly generatable collections is generatable in the limit, and asked if the same is true for non-uniform generation. We begin by resolving the question in the negative: we give a uniformly generatable collection and a non-uniformly generatable collection whose union is not generatable in the limit. We then use facets of this construction to further our understanding of several variants of language generation. The first two, generation with noise and without samples, were introduced by Raman and Raman (2025) and Li, Raman, and Tewari (2024) respectively. We show the equivalence of these models for uniform and non-uniform generation, and provide a characterization of non-uniform noisy generation. The former paper asked if there is any separation between noisy and non-noisy generation in the limit -- we show that such a separation exists even with a single noisy string. Finally, we study the framework of generation with feedback, introduced by Charikar and Pabbaraju (2025), where the algorithm is strengthened by allowing it to ask membership queries. We show finite queries add no power, but infinite queries yield a strictly more powerful model. In summary, the results in this paper resolve the union-closedness of language generation in the limit, and leverage those techniques (and others) to give precise characterizations for natural variants that incorporate noise, loss, and feedback.

In recent years, artificial intelligence has significantly advanced medical image segmentation. Nonetheless, challenges remain, including efficient 3D medical image processing across diverse modalities and handling data variability. In this work, we introduce Hierarchical Soft Mixture-of-Experts (HoME), a two-level token-routing layer for efficient long-context modeling, specifically designed for 3D medical image segmentation. Built on the Mamba Selective State Space Model (SSM) backbone, HoME enhances sequential modeling through adaptive expert routing. In the first level, a Soft Mixture-of-Experts (SMoE) layer partitions input sequences into local groups, routing tokens to specialized per-group experts for localized feature extraction. The second level aggregates these outputs through a global SMoE layer, enabling cross-group information fusion and global context refinement. This hierarchical design, combining local expert routing with global expert refinement, enhances generalizability and segmentation performance, surpassing state-of-the-art results across datasets from the three most widely used 3D medical imaging modalities and varying data qualities. The code is publicly available at https://github.com/gmum/MambaHoME.

Large language models (LLMs) are being used in many applications and prompts for these models are integrated into software applications as code-like artifacts. These prompts behave much like traditional software in that they take inputs, generate outputs, and perform some specific function. However, prompts differ from traditional code in many ways and require new approaches to ensure that they are robust. For example, unlike traditional software the output of a prompt depends on the AI model that interprets it. Also, while natural language prompts are easy to modify, the impact of updates is harder to predict. New approaches to testing, debugging, and modifying prompts with respect to the model running them are required. To address some of these issues, we developed PromptPex, an LLM-based tool to automatically generate and evaluate unit tests for a given prompt. PromptPex extracts input and output specifications from a prompt and uses them to generate diverse, targeted, and valid unit tests. These tests are instrumental in identifying regressions when a prompt is changed and also serve as a tool to understand how prompts are interpreted by different models. We use PromptPex to generate tests for eight benchmark prompts and evaluate the quality of the generated tests by seeing if they can cause each of four diverse models to produce invalid output. PromptPex consistently creates tests that result in more invalid model outputs than a carefully constructed baseline LLM-based test generator. Furthermore, by extracting concrete specifications from the input prompt, PromptPex allows prompt writers to clearly understand and test specific aspects of their prompts. The source code of PromptPex is available at https://github.com/microsoft/promptpex.

Recent work has shown that front-end code generated by Large Language Models (LLMs) can embed deceptive designs. To assess the magnitude of this problem, identify the factors that influence deceptive design production, and test strategies for reducing deceptive designs, we carried out two studies which generated and analyzed 1,296 LLM-generated web components, along with a design rationale for each. The first study tested four LLMs for 15 common ecommerce components. Overall 55.8% of components contained at least one deceptive design, and 30.6% contained two or more. Occurence varied significantly across models, with DeepSeek-V3 producing the fewest. Interface interference emerged as the dominant strategy, using color psychology to influence actions and hiding essential information. The first study found that prompts emphasizing business interests (e.g., increasing sales) significantly increased deceptive designs, so a second study tested a variety of prompting strategies to reduce their frequency, finding a values-centered approach the most effective. Our findings highlight risks in using LLMs for coding and offer recommendations for LLM developers and providers.

Directed acyclic graph (DAG) learning is a central task in structure discovery and causal inference. Although the field has witnessed remarkable advances over the past few years, it remains statistically and computationally challenging to learn a single (point estimate) DAG from data, let alone provide uncertainty quantification. We address the difficult task of quantifying graph uncertainty by developing a Bayesian variational inference framework based on novel, provably valid distributions that have support directly on the space of sparse DAGs. These distributions, which we use to define our prior and variational posterior, are induced by a projection operation that maps an arbitrary continuous distribution onto the space of sparse weighted acyclic adjacency matrices. While this projection is combinatorial, it can be solved efficiently using recent continuous reformulations of acyclicity constraints. We empirically demonstrate that our method, ProDAG, can outperform state-of-the-art alternatives in both accuracy and uncertainty quantification.

To construct the high-temperature effective field theory of gauge-Higgs models up to $\mathcal{O}(g^6)$ in the gauge coupling, we integrate out hard modes to three-loop level and use the next-to-next-to-leading order effective potential. For the Abelian Higgs model, we quantify the impact of both higher-dimensional operators and higher-loop corrections on thermodynamic parameters relevant for gravitational-wave observables, finding that one-loop dimension-six effects typically dominate over two- and three-loop corrections to super-renormalizable parameters for the strongest transitions. We derive the three-loop scalar and Debye masses for the ${\rm U(1)}$ and ${\rm SU}(N)$ gauge-Higgs models, as well as the two-loop quartic couplings for the Abelian case, show gauge independence of physical parameters, and demonstrate that no new master integrals are required for the matching, while consistency of 4d and 3d renormalizability points to previously missing contributions in these master integrals.

To date, the second-order post-Newtonian (2PN) Hamiltonian has been known in closed analytic form only for systems of up to three point masses. In this paper, we present an analytic expression for the general $N$-body 2PN Hamiltonian in the ADM gauge up to a single integral term that, to our knowledge, has no known closed-form analytic solution. We show that the integrals appearing in the 2PN Hamiltonian can be evaluated numerically to machine precision, allowing for cross-validation against analytical results and enabling the full numerical computation of the $N$-body 2PN Hamiltonian. Furthermore, we demonstrate the practical feasibility of the numerical integration of the equations of motion for $N$ bodies at 2PN order using different methods and discuss several strategies for improving computational efficiency.

We study the projected sensitivity of direct electroweakino production $pp \to \tildeχ_1^{\pm} \tildeχ_2^0$ at the HL-LHC in a simplified framework with wino-like, mass degenerate $\tildeχ_1^{\pm}$ and $\tildeχ_2^0$, and a bino-like lightest neutralino $\tildeχ_1^0$, assuming R-parity violating~(RPV) through the baryon number violating $λ^{\prime \prime}_{112}u^c d^c d^c$ and $λ^{\prime \prime}_{113}u^c d^c b^c$ operators. We consider three channels with the $λ^{\prime \prime}_{112}u^c d^c d^c$ RPV operator: $Wh$ mediated $1\,\ell + 2\,b + \rm E{\!\!\!/}_T$, $Wh$ mediated $1\,\ell + (\geq 2\,j) + 2\, γ+ \rm E{\!\!\!/}_T$, and $WZ$ mediated $3\ell + (\geq 2 j) + \rm E{\!\!\!/}_T$. In each channel, we train benchmark-specific multi-layer perceptrons (MLPs), analogous to signal-region classifiers, on the four-momenta of the final state particles along with a small set of higher-level observables to distinguish the signal from the dominant SM backgrounds. We find that the HL-LHC will be able to probe winos up to $\sim 900~$GeV, $\sim 780~$GeV, and $\sim 880~$GeV in the $Wh$ mediated $1\,\ell + 2\,b + \rm E{\!\!\!/}_T$, $Wh$ mediated $1\,\ell + (\geq 2\,j) + 2\, γ+ \rm E{\!\!\!/}_T$, and $WZ$ mediated $3\ell + (\geq 2 j) + \rm E{\!\!\!/}_T$ channels, respectively, for $m_{\tildeχ_1^0} \sim 50~$GeV, in the presence of $λ^{\prime \prime}_{112}u^c d^c d^c$ couplings, at $2σ$ sensitivity. In case the $λ^{\prime \prime}_{113}u^c d^c b^c$ operator is solely switched on, the projected sensitivity for winos reach up to $\sim 700~$GeV for $Wh$ mediated $1\,\ell + (\geq 1\,b)\, + (\geq 1j)\, + 2\, γ+ \rm E{\!\!\!/}_T$ and $\sim 850~$GeV for the $WZ$ mediated $3\ell + (\geq 1 b) + \rm E{\!\!\!/}_T$ channel.

Towards the Lang--Vojta conjecture, we prove results on finiteness and Zariski degeneracy of $S$-integral points of varieties over number fields $k$, including many cases with geometrically irreducible boundary divisors. Our approach builds on the study of arithmetic and geometric properties of moduli spaces of curves with extra structure. As an application, we provide families of explicit examples of geometrically irreducible divisors on the projective plane (such as the dual of any smooth curve of degree at least $3$), with respect to which the sets of $S$-integral points are finite. Answering a question of Achenjang and Morrow, we show that, other than the case of curves, every normal projective variety admits a geometrically irreducible divisor $D$ for which finiteness of $(D,S)$-integral points holds over every finite extension of $k$.

Mapping the physical conditions of the shocked plasma of young supernova remnants (SNR) is crucial for understanding their explosion mechanisms, ejecta structure, and large-scale asymmetries. Using $>350$ ks of XRISM/Resolve high spectral resolution observations of Cassiopeia A (Cas A), the youngest known Galactic core-collapse SNR, we present the first microcalorimeter-based plasma parameter maps of any SNR. We tessellate Cas A into $1'\times1'$ regions and fit the broadband spectra as thermal emission from two pure-metal ejecta components -- corresponding to intermediate-mass elements (IMEs) and iron-group elements (IGEs) -- plus nonthermal synchrotron radiation. For robust inference, we introduce UltraSPEX, a Bayesian framework that couples the SPEX plasma code with the UltraNest nested-sampling algorithm, yielding full posterior distributions and exploration of parameter degeneracies. Key findings include enhanced Ar/Si and Ca/Si abundance ratios near the base of the Si-rich jets, and a high Ni/Fe mass ratio ($0.08\pm0.015$) in the base of NE jet. IGEs ejecta exhibit systematically higher Doppler velocities and broadenings than IMEs ejecta in most regions, with maximum differences of $\sim800$ km/s and $\sim1200$ km/s, respectively; Ca shows distinct (faster) kinematics from other IMEs in several SE regions. The ionization timescale and electron temperature show a robust anti-correlation, particularly for IGEs. This relation and measured parameter values could be explained by semi-analytical models with significant ejecta clumping (overdensities of $\sim10$ for IGEs and up to $\sim100$ for IMEs) and reduced historical reverse-shock velocities. Nonthermal emission accounts for a substantial fraction, with at least 47% of the 4--6 keV continuum and dominates in the western regions, where the spectrum hardens.

We present a framework for systematic computations of scattering amplitudes for gravitational Raman scattering, -- the inelastic scattering of massless fields off compact relativistic objects. We focus on the small-frequency (post-Minkowskian, PM) regime relevant for the study of tidal effects, which can be mapped onto gravitational wave observables during the inspiraling phase of a merger. We demonstrate that this setup is ideal for systematic studies of tidal effects, in a way that is free from coordinate, gauge, and field redefinition ambiguities. We use a combination of worldline effective field theory, the background field method, and advanced scattering amplitude techniques to derive phase shifts for scattering of spin-$0,1,2$ fields off generic compact objects at third PM order. We demonstrate that the inclusion of the recoil of the object is crucial for consistency of this calculation. Focusing on a particular case of black holes, we extract the leading static and dynamical Love numbers of the spin-0 field and the static Love number of the spin-1 field in four dimensions by matching our EFT amplitudes and calculations in General Relativity. We show, fully on-shell, that the leading static Love numbers vanish identically, while the dynamical Love numbers are not zero and run logarithmically. The latter resolves the ambiguities of previous off-shell matching calculations. We also extend our results to seven dimensions, where spin-2 Love numbers undergo a renormalization group running at 2PM, which we compute explicitly. In addition, we extract the leading static Love numbers of spin-0 and spin-1 fields in five dimensions, which also run.

Say you and some friends decide to make brackets for March Madness and are told how each of your brackets scored. The question we ask is: when can you determine how the actual tournament went given your scores? We determine the exact minimum number of brackets needed to do this for any March Madness-style tournament regardless of the scoring system used, and more generally we prove effective bounds for the problem for arbitrary single-elimination tournaments.

The usual semantics of multi-agent epistemic logic is based on Kripke models, defined in terms of binary relations on a set of possible worlds. Recently, there has been a growing interest in using simplicial complexes rather than graphs, as models for multi-agent epistemic logic. This approach uses agents' views as the fundamental object instead of worlds. A set of views by different agents about a world forms a simplex, and a set of simplexes defines a simplicial complex, that can serve as a model for multi-agent epistemic logic. This new approach reveals topological information that is implicit in Kripke models, because the binary indistinguishability relations are more clearly seen as n-ary relations in the simplicial complex. This paper, written for an economics audience, introduces simplicial models to non-experts and connects distributed computing, epistemic logic and topology. Our focus is on distributed knowledge and its fixed point, common distributed knowledge. These concepts arise when considering the knowledge that a group of agents would acquire, if they could communicate their local knowledge perfectly. While common knowledge has been shown to be related to consensus, we illustrate how distributed knowledge is related to a task weaker to consensus, called majority consensus. We describe three models of communication, some well-known (immediate snapshot), and others less studied (related to broadcast and test-and-set). When majority consensus is solvable, we describe the distributed knowledge that is used to solve it. When it is not solvable, we present a logical obstruction, a formula that should always be known according to the task specification, but which the players cannot know.

When do two irreducible polynomials with integer coefficients define the same number field? One can define an action of $\mathrm{GL}_2 \times \mathrm{GL}_1$ on the space of polynomials of degree $n$ so that for any two polynomials $f$ and $g$ in the same orbit, the roots of $f$ may be expressed as rational linear transformations of the roots of $g$; thus, they generate the same field. In this article, we show that almost all polynomials of degree $n$ with size at most $X$ can only define the same number field as another polynomial of degree $n$ with size at most $X$ if they lie in the same orbit for this group action. (Here we measure the size of polynomials by the greatest absolute value of their coefficients.) This improves on work of Bhargava, Shankar, and Wang, who proved a similar statement for a positive proportion of polynomials. Using this result, we prove that the number of degree $n$ fields such that the smallest polynomial defining the field has size at most $X$ is asymptotic to a constant times $X^{n+1}$ as long as $n\geq 3$. For $n = 2$, we obtain a precise asymptotic of the form $\frac{27}{π^2} X^2$.

We show that all filtrable bundles on a Hopf surface $X$ must have jumps and we prove the existence of filtrable stable bundles on $X$ with any value of $c_2>0$. On a somewhat opposite direction, for each integer $r\ge 2$ we prove the existence of irreducible rank $r$ vector bundles on $X$ with trivial determinant, $c_2=1$, and no jumps. We then apply elementary operations in codimension $2$ to points of the moduli space $\mathcal M_{r,n}$ of rank $r$ stable vector bundles on $X$ with $c_2=n$ to obtain torsion free sheaves with $c_2=n+1$. Namely, starting with a surjection $v\colon E \rightarrow \mathbb C_p$ from a vector bundle $E \in \mathcal M_{r,n}$ to a skyscraper sheaf supported at a point $p\in X$, we prove that if $E'$ is any torsion free sheaf fitting into a short exact sequence of the form $0 \longrightarrow E'\longrightarrow E\stackrel{v}{\longrightarrow}\mathbb C_p \longrightarrow 0,$ then $E'$ is in the closure of $\mathcal M_{r,n+1}$. We discuss various properties of vector bundles and torsion free sheaves and introduce the concept of very irreducible bundles to describe bundles whose symmetric powers $S^n(E)$ are irreducible for all $n> 0$. We then show that any rank $2$ bundle on $X$ whose graph contains a component corresponding to a surjective morphism $\mathbb P^1\to \mathbb P^1$ is very irreducible.

Sequential recommendation (SR) models predict a user's next interaction by modeling their historical behaviors. Transformer-based SR methods, notably BERT4Rec, effectively capture these patterns but incur significant computational overhead due to extensive intermediate computations associated with Softmax-based attention. We propose Cotten4Rec, a novel SR model utilizing linear-time cosine similarity attention, implemented through a single optimized compute unified device architecture (CUDA) kernel. By minimizing intermediate buffers and kernel-launch overhead, Cotten4Rec substantially reduces resource usage compared to BERT4Rec and the linear-attention baseline, LinRec, especially for datasets with moderate sequence lengths and vocabulary sizes. Evaluations across three benchmark datasets confirm that Cotten4Rec achieves considerable reductions in memory and runtime with minimal compromise in recommendation accuracy, demonstrating Cotten4Rec's viability as an efficient alternative for practical, large-scale sequential recommendation scenarios where computational resources are critical.

We propose a result of global stability for the equations of homogeneous, incompressible magnetohydrodynamics (MHD) on a torus of any dimension $d \in \{2,3,...\}$, with positive viscosity and resistivity. This result applies to the $C^\infty$ global solutions, with a conveniently defined decay property for large times; it is expressed by fully explicit estimates, formulated via $H^p$-type Sobolev norms of arbitrarily high order $p$. The present stability result is similar to that proposed by one of us for the Navier-Stokes (NS) equation \cite{glosta}; it is derived from a suitable formulation of the MHD equations proposed in our previous work \cite{MHD}, emphasizing strong structural analogies with the NS case. A basic tool in the proof of the present stability result is a general theory of approximate solutions of the MHD Cauchy problem, that we developed in \cite{MHD} on the grounds of previous results on the NS equation \cite{smooth} and of the above structural similarities. We also introduce a class of Beltrami-type initial data for the MHD equations; although being arbitrarily large, these data produce global and decaying MHD solutions, fitting the framework of the present stability result. Comparisons with the previous literature on these subjects are performed.

We investigate the existence and severity of local modes in posterior distributions from Bayesian analyses. These are known to occur in posterior tails resulting from heavy-tailed error models such as those used in robust regression. To understand this phenomenon clearly, we consider in detail location models with Student-$t$ errors in dimension $d$ with sample size $n$. For sufficiently heavy-tailed data-generating distributions, extreme observations become increasingly isolated as $n \to \infty$. We show that each such observation induces a unique local posterior mode with probability tending to $1$. We refer to such a local mode as a micromode. These micromodes are typically small in height but their domains of attraction are large and grow polynomially with $n$. We then connect this posterior geometry to computation. We establish an Arrhenius law for the time taken by one-dimensional piecewise deterministic Monte Carlo algorithms to exit these micromodes. Our analysis identifies a phase transition where a misspecified and overly underdispersed model causes exit times to increase sharply, leading to a pronounced deterioration in sampling performance.

Baym and Farrar (arXiv:2601.02300v1) have recently pointed out a puzzle in understanding the role of the hyperfine interaction in the ground state of a hydrogen atom. If one uses a variational wave function in which the Bohr radius, $a_0$ is replaced by a variational radius parameter, $R$, first-order perturbation theory can give a contribution to the energy proportional to $-1/R^3$. This raises the question of why the hyperfine interaction does not lead to collapse of hydrogen. I show that including the effects of the non-zero size of the proton leads to a resolution of the puzzle such that the variational procedure yields a value of $R$ that is indistinguishable from $a_0$.

We demonstrate that dark matter axion production is enhanced through a natural and unavoidable mechanism: primordial temperature fluctuations periodically modulate the axion mass during the QCD phase transition, thereby triggering parametric resonance in axion field evolution. This interplay between parametric resonance and the misalignment mechanism shifts the predicted axion mass window for the observed dark matter abundance to $10^{-4}-10^{-3} \, \text{eV}$, displacing the canonical axion mass window to previously unexplored higher ranges.

The quasar OP 313 was discovered in December 2023 in very-high-energy $γ$ rays above 100 GeV, enabling for the first time a complete characterization of its emission. However, the lack of updated measurements of its accretion disk, broad line region and dusty torus hampers a detailed interpretation of the role of accretion in the observed $γ$-ray production. We intend to characterize, during high-activity states, the external photon fields contributing to the IR-to-UV emission$-$namely dusty torus, broad line region and accretion disk$-$and investigate potential variability and blurring effects on the broad emission lines. We present new spectroscopic observations of OP 313 with the NOT and TNG telescopes to characterize its optical spectrum and variability with respect to archival observations from SDSS. We measure the luminosity of different broad emission lines, characterizing the broad line region, accretion disk and dusty torus. We measure the Mg II emission line, with an average flux of $F_{\mathrm{Mg \ II}} = (0.85 \pm 0.11)\times 10^{-14}$ erg cm$^{-2}$ s$^{-1}$. Its equivalent width and luminosity are consistent with a constant line with a variable non-thermal continuum. From the stable Mg II line we derive a constant luminosity of the thermal components, $\log(L_{\mathrm{BLR}} \ \mathrm{[erg \ s^{-1}]}) = 44.91 \pm 0.19$, $\log(L_{\mathrm{disk}} \ \mathrm{[erg \ s^{-1}]}) = 45.91 \pm 0.19$ and $\log(L_{\mathrm{torus}} \ \mathrm{[erg \ s^{-1}]}) = 44.70 \pm 0.16$, and estimated a BH mass of $\log(M_{BH}/M_{\odot})=8.36 \pm 0.18$, in line with with that derived from the C III] line. These characteristics and the indicator of the accretion rate from the disk/Eddington luminosity ratio $λ=L_{AD}/L_{Edd} = 0.23 \pm 0.10$, along with a high Compton dominance, favour a FSRQ-like nature, contrary to the argued changing-look nature.

In this paper, we investigate several subsets of $n$-copulas and $n$-quasi-copulas from the perspective of convex-lineability and the recently introduced concept of convex-spaceability. Our purpose is to determine when such families contain extremely large algebraic structures, namely linearly independent sets of cardinality of the continuum whose convex hull, and in some cases a closed convex linearly independent subset, remain entirely inside the class under study. These include the families of asymmetric copulas, copulas with maximal asymmetric measure, and proper $n$-quasi-copulas, among others. In contrast, for several other natural classes of copulas we show that (maximal) convex lineability holds while convex spaceability remains an open problem.

Healthcare professionals (HCPs) face increasing occupational stress and burnout. Supporting HCPs need for relatedness is fundamental to their psychological wellbeing and resilience. However, how technologies could support HCPs relatedness in the workplace remains less explored. This study incorporated semi-structured interviews (n = 15) and co-design workshops (n = 21) with HCPs working in the UK National Health Service (NHS), to explore their current practices and preferences for workplace relatedness support, and how technology could be utilized to benefit relatedness. Qualitative analysis yielded a four-layer model of HCPs relatedness need, which includes Informal Interactions, Camaraderie and Bond, Community and Organizational Care, and Shared Identity. Workshops generated eight design concepts (e.g., Playful Encounter, Collocated Action, and Memories and Stories) that operationalize the four relatedness need layers. We conclude by highlighting the theoretical relevance, practical design implications, and the necessity to strengthen relatedness support for HCPs in the era of digitalization and artificial intelligence.

As AI systems increasingly become embedded in interactive and im-mersive artistic environments, artists and technologists are discovering new opportunities to engage with their interpretive and autonomous capacities as creative collaborators in live performance. The focus of this work-in-progress is on outlining conceptual and technical foundations under which performance-makers and interactive architecture can collaborate within rehearsal settings. It introduces a rehearsal-oriented prototype system for shaping and testing AI-mediated environments within creative practice. This approach treats interactive architecture as a performative agent that senses spatial behaviour and speech, interprets these signals through a large language model, and generates real-time environmental adaptations. Designed for deployment in physical performance spaces, the system employs virtual blueprints to support iterative experimentation and creative dialogue between artists and AI agents, using reasoning traces to inform architectural interaction design grounded in dramaturgical principles.

Exhaustive subgroup treatment effect plots are constructed by displaying all subgroup treatment effects of interest against subgroup sample size, providing a useful overview of the observed treatment effect heterogeneity in a clinical trial. As in any exploratory subgroup analysis, however, the observed estimates suffer from small sample sizes and multiplicity issues. To facilitate more interpretable exploratory assessments, this paper introduces a computationally efficient method to generate homogeneity regions within exhaustive subgroup treatment effect plots. Using the Doubly Robust (DR) learner, pseudo-outcomes are used to estimate subgroup effects and derive reference distributions, quantifying how surprising observed heterogeneity is under a homogeneous effects model. Explicit formulas are derived for the homogeneity region and different methods for calculation of the critical values are compared. The method is illustrated with a cardiovascular trial and evaluated via simulation, showing well-calibrated inference and improved performance over standard approaches using simple differences of observed group means.