With the rapid development of mobile computing technology, massive amounts of spatial data are continuously generated from various mobile terminals and sensing devices, such as smartphones, connected vehicles, and drones. Performing efficient distributed statistical analysis on this data is crucial for real-time mobile computing applications. However, the constrained and dynamic nature of mobile environments exacerbates the privacy challenge: centralizing sensitive data for analysis risks severe privacy leaks, while existing privacy-preserving techniques often introduce excessive overhead or inaccuracies. In this paper, we design, implement, and evaluate the first system that supports efficient and privacy-preserving distribution statistics analysis for mobile spatial data. First, we propose eSpat-B, which leverages two non-colluding servers and a newly designed improved distributed point functions (DPF) with octree partitioning. Furthermore, considering the frequent updates of spatial data, we propose another more efficient scheme, eSpat+. The core idea of this scheme is to utilize a K-Dimensional tree for spatial partitioning, combine it with incremental DPF for performing statistics analysis, and design an efficient update algorithm. Security analysis demonstrates that our schemes effectively protect data privacy throughout the statistical process. Extensive experiments on real-world trajectory datasets demonstrate that the proposed schemes significantly outperform existing approaches, reducing computation overhead by up to 1.2x and communication overhead by up to 20x while maintaining 100% statistical accuracy.

The minimal supersymmetric $SU(5)$ grand unified theory (GUT) provides a highly compelling framework for physics beyond the Standard Model (SM). However, it suffers from a severe phenomenological challenge: rapid proton decay mediated by colored-Higgsino exchange via dimension-five operators. Resolving this issue often requires adjustments to the Yukawa couplings and the potential sectors, generating a vast and complex parameter space where traditional brute-force numerical scans are rendered computationally intractable due to the curse of dimensionality. In this paper, we overcome this limitation by applying machine learning optimization techniques. We investigate a supersymmetric $SU(5)$ model extended with $\mathbf{45}$ and $\overline{\mathbf{45}}$ Higgs representations, defining a loss function based on the partial decay width of $p \to K^+ \barν$. Utilizing the Adam optimizer, we systematically explore the 33-dimensional parameter space to identify regions that suppress proton decay. Furthermore, we vary $\tan β$ to thoroughly investigate whether the optimized proton lifetime can consistently exceed the stringent experimental lower bound of $5.9 \times 10^{33}$ years established by the Super-Kamiokande collaboration.

We introduce the \emph{Morse ensemble polynomial} $\ME_K(z_0,\ldots,z_d)$ of a finite simplicial complex $K$, defined as the generating function $\ME_K = \sum_M \prod_i z_i^{c_i(M)}$ over all acyclic matchings $M$ on the face poset of $K$, where $c_i(M)$ counts critical $i$-simplices. This polynomial records the complete distribution of Morse vectors across all discrete Morse functions on $K$, and is an isomorphism invariant of simplicial complexes. Our main results are the following. \textbf{(I) The Laplacian Formula}: for any connected graph $G$, $\ME_G = z_1^{m-n}\det(z_0z_1\,I_n + L_G)$, identifying $\ME_G$ as a complete Laplacian spectral invariant and showing $\ME_G$ to be incomparable with the Tutte polynomial. \textbf{(II) The Top-Face Recursion}: adding a $d$-simplex $σ$ (with $\partialσ\subset K$) to a complex $K$ gives a recursion $\ME_{K\cup\{σ\}} = z_d\cdot\ME_K + \sum_{τ\precσ}(\ME_{P(K')\setminus\{σ,τ\}}-F(K,σ,τ))$. The correction term is controlled by the top incidence graph: an incidence-separation criterion detects exactly when $F=0$, and the incidence distance gives the leading obstruction term. As a topological application, this recursion gives exact coefficient recursions for perfect and optimal discrete Morse vectors. \textbf{(III) The independence ME polynomial} $Φ(G) := \ME_{\mathrm{Ind}(G)}$ is a fine graph invariant which strictly refines the graph-level Morse ensemble $\ME_G$, separates examples not distinguished by $T_G$ and $I(G;t)$, and records collapse-level information of $\mathrm{Ind}(G)$ through coefficients such as $[z_0]Φ(G)$.

We define a sequence of integer-valued invariants $γ^k(L)$ for a $3$-component link $L$. We prove that the resulting $γ$-invariants are invariant under concordance, and more generally under weak cobordism, and that they lift certain Milnor invariants of 3-component links. To establish this, we introduce an invariant $h(L)$, a $3$-component analogue of the Kojima--Yamasaki $η$-invariant, and show that it recovers the $γ$-invariants. As applications, we obtain a weak-cobordism classification when the distinguished component has trivial Alexander polynomial and characterize knots that bound continuously embedded disks in $B^4$ whose complements have fundamental group $\mathbb{Z}$.

We identify a sharp interaction-degree threshold for the classical simulation of QAOA with $2$-local cost functions. At degree~$3$, classical sampling from depth-$1$ QAOA, even within multiplicative error $2^{n^{s}}$ for any fixed $s < 1$, would collapse the polynomial hierarchy to its third level. At degree $2$, exact classical sampling from depth-$p$ QAOA on $n$ qubits runs in time $n^{O(1)}$ whenever $p = O(\log n)$. The hard degree-$3$ instances have trivially optimizable cost functions, so sampling hardness does not by itself imply a quantum optimization advantage.

We develop a first and second fundamental theorem for $n$--tuples of bosonic and fermionic matrices, by developing graded analogues of the classical case.

A popular class of priors for symmetric positive-definite matrices assumes independent entries and adds a truncation to ensure positive-definiteness. While conceptually simple and often computationally convenient, unless done carefully this truncation can have unintended effects. If the truncated prior or its margins are significantly different from their untruncated counterpart, then its interpretability may suffer, its shrinkage properties become harder to characterise, and posterior inference may be affected in unanticipated ways. We investigate the effect of the truncation both for dense and sparse matrices, and show how to set prior parameters such as the variance of off-diagonal entries such that said effect is mitigated as the matrix dimension grows. We pay particular attention to sparse inference where, unless prior parameters are set carefully, the truncated prior and hence its corresponding posterior assign systematically higher mass to sparser structures than the untruncated prior.

The exodromy correspondence of Barwick, Glasman, and Haine computes constructible sheaves of spaces on a scheme $X$ as an $\infty$-category of continuous functors from the profinite category $\operatorname{Gal}(X)$. Viewing $\operatorname{Gal}(X)$ instead as a condensed category, this was extended by Wolf to an exodromy correspondence for pro-étale sheaves. Using the condensed perspective from the outset, we give a quick and self-contained proof of the pro-étale exodromy theorem. This is used to extract an exodromy theorem for (Postnikov complete) étale sheaves that does not yet appear in the literature, which is closely related to Lurie's work on ultracategories. Finally, we use this to give a new proof of the constructible étale exodromy correspondence of Barwick, Glasman, and Haine. Without additional effort, our method removes the qcqs hypotheses on the schemes, and gives versions for sheaves with coefficients in more general $\infty$-categories. Finally, we refine the methods to obtain a $κ$-condensed statement for any uncountable cardinal $κ$ such that $κ> \lvert \mathcal O_X(U) \rvert$ for every affine open $U \subseteq X$.

Already in $\bf{R}^4$, there are many minimal hypersurfaces, yet few structural results. We show that minimal submanifolds, of any dimension and codimension, that are confined in space are very restricted. It is well-known that the half-space theorem fails already for hypersurfaces in $\bf{R}^4$, where there are many examples contained in a slab. In $\bf{R}^3$ the height of the catenoid grows at a logarithmic rate, whereas in higher dimensions the height of the catenoid remains bounded. We will see that even in high dimensions, minimal submanifolds that are confined in space must satisfy strong structural restrictions. We show that any proper minimal immersion whose height grows sublinearly must have Euclidean volume growth. A consequence is an optimal Bernstein theorem in any dimension for stable hypersurfaces with sublinearly growing height that generalizes results of Moser, Bombieri-De Giorgi-Miranda, Trudinger, Caffarelli-Nirenberg-Spruck and Ecker-Huisken. Euclidean volume growth is a powerful property and there are many other consequences.

Let $P$ be a $d$-dimensional convex lattice polytope. In this article, we prove that the ratio of the volume of a normal-sized miniature of $P$ to that of $P$ is $1:\binom{2d+1}{d},$ which generalizes the known results for the unit hypercube and lattice simplices provided by the author. This theorem is proven by establishing that the number of horizontal miniatures of $P$ with resolution $t$ is a polynomial of degree $d+1$ in $t$ whose leading coefficient is $\mathrm{vol}\,P/(d+1),$ which is derived from Ehrhart theory.

Amorphous solids exhibit structural short-range order despite lacking long-range crystalline order, with this structural descriptor found to be important for determining mechanical properties. Nanobeam electron diffraction offers a potential route for experimental characterization of structural short-range order, yet efforts to date have been primarily qualitative in nature. In this work, machine learning approaches based on transfer learning are used to enable quantitative analysis of nanobeam electron diffraction data from amorphous solids. A ResNet-18 model is trained on simulated diffraction patterns taken from different locations within simulated metallic glasses and amorphous grain boundary complexions in the Cu-Zr alloy system that were created with hybrid molecular dynamics and Monte Carlo simulations. The disorder parameter is found to be a superior target structural descriptor compared to traditional Voronoi indices for this task. The model achieves a low validation mean absolute error across diffraction patterns corresponding to different interaction volumes, demonstrating excellent performance and potential transferability. Testing was performed using other simulated nanobeam electron diffraction data as well as experimental nanobeam electron diffraction patterns, showing that the model can reliably capture spatial variations in local structural state. As a whole, this framework is able to overcome the challenges in the quantitative experimental characterization of structural short-range order, enabling improved characterization of amorphous solids and the exploration of structure-property relationships.

We present PEPSKit$.$jl, a Julia package for simulating two-dimensional quantum many-body systems with infinite projected entangled-pair states (iPEPS). PEPSKit$.$jl builds on the TensorKit$.$jl package for tensor computations and provides high-level algorithms for iPEPS simulations that support both Abelian and non-Abelian symmetries, as well as fermionic systems. This work gives an overview of the main package features, which include support for ground-state, time-evolution, and finite-temperature simulations in systems with different physical symmetries and lattice geometries. These capabilities are illustrated through various examples and technical benchmarks.

We study Conditional Value-at-Risk (CVaR) variants of two canonical sequential decision problems: Pandora's box and the prophet inequality. For Pandora's box, the risk-aware problem retains an exact Weitzman-style index solution after a one-dimensional variational reduction. For the prophet inequality, the picture is different: for every CVaR level \(α\in(0,1)\), no positive constant approximation guarantee can hold without distributional structure, in sharp contrast with the risk-neutral case \(α=1\), and we characterize the tight instance-dependent guarantee. Already in two-item hard instances, the prophet's CVaR benchmark can be made arbitrarily large while every online policy's CVaR remains bounded. This impossibility is due to the nature of CVaR objective: it measures only the worst \(α\)-fraction of outcomes, so any compromise an online policy makes to preserve the chance of a large payoff in the upper \((1-α)\)-fraction does not help its CVaR. It turns out that additional distributional structure restores a uniform result: under continuous reward distributions satisfying a recentered increasing-failure-rate-average (IFRA) condition, a threshold policy achieves an explicit constant bound.

Robert Bruner \cite[Questions 6.1 and 6.2]{Bruner2026} asked whether the secondary cohomology of the fibers $F_n$, $F_{n\mathbb{Z}}$, and $F$ can be computed to determine the $E_3$-terms of their Adams spectral sequences, and whether the Bruner-Rognes two-extension formula for the ordinary Adams $d_2$ is intrinsic to secondary cohomology. In this work, we give an unconditional affirmative answer to both questions. Working in the Baues-Nassau secondary Steenrod algebra, we construct explicit secondary mapping-fiber resolutions for these fibers using a tracked Adem reduction algorithm and the Baues-Jibladze recursive completion. We determine the secondary Ext groups, independently recovering Bruner's $E_3$-terms: \[ \operatorname{Ext}_{\mathcal{B}}^{*,*}(H_{\mathcal{B}}^* F_n, \mathbb{F}_2) \cong \mathbb{F}_2 \oplus Σ^{1,n}\mathbb{F}_2, \] \[ \operatorname{Ext}_{\mathcal{B}}^{*,*}(H_{\mathcal{B}}^* F_{n\mathbb{Z}}, \mathbb{F}_2) \cong \mathbb{F}_2[h_0] \oplus Σ^{1,n}\mathbb{F}_2, \] \[ \operatorname{Ext}_{\mathcal{B}}^{*,*}(H_{\mathcal{B}}^* F, \mathbb{F}_2) \cong \mathbb{F}_2[h_0] \oplus \bigoplus_{j>0} Σ^{1,2^j}\mathbb{F}_2 \oplus \bigoplus_{\substack{i>0 \\ i \text{ not a power of } 2}} Σ^{0,2i-1}\mathbb{F}_2. \] This direct calculation answers Question 6.1. Finally, we prove that the primary shadow of the first secondary differential in our construction is identically the Bruner-Rognes Yoneda composite associated with the corresponding two-extension, thereby answering Question 6.2.

In social dilemmas self-interested learning agents face the choice between the societal benefit of cooperation and the immediate reward of defection. Significant evidence exists on the benefits of assortment mechanisms such as partner selection for the emergence of cooperation, but this is largely available through agent-based simulations. In this paper, we provide an analytical solution to the problem, studying the policy-gradient dynamics in a multi-agent environment with partner selection. We show how partner selection changes the opponent distribution and hence the reward landscape, and prove this promotes cooperation under simple rules known from the literature. In particular, we find that population variance is a necessary condition for cooperation to emerge. Using a two-dimensional Wiener process, we extend the dynamics to capture the stochastic effects of partner selection and the resulting opponent distribution. We derive a sufficient condition for the population to be cooperation-promoting and prove the existence of a stationary distribution. Simulations confirm that the stochastic model accurately captures the policy-gradient dynamics and clarifies how the learning rate affects the emergence of cooperation.

Orthogonal frequency division multiplexing (OFDM) is a key waveform for integrated sensing and communication (ISAC) due to its spectral efficiency and compatibility with modern wireless standards. In multi-target and clutter-rich environments, however, payload-based OFDM-ISAC can suffer from data-dependent sidelobes induced by non-constant-modulus modulation symbols. To overcome these limitations, this paper proposes a region-of-interest mismatched filter (ROI-MMF) that suppresses sidelobes within a prescribed delay region while preserving the mainlobe response. By leveraging the Woodbury identity, the proposed design admits an efficient closed-form implementation whose complexity scales with the ROI size rather than the number of subcarriers. We theoretically provide the ranging mean-square error (MSE) of the designed ROI-MMF, which shows the superior performance compared to conventional matched filtering (MF) and reciprocal filtering (RF) sensing receivers. Simulations across various constellations show that the proposed sensing receiver achieves a ranging MSE approaching the Cramér-Rao bound (CRB), which notably confirms that our design preserves the target ranging performance even under the non-constant-modulus constellation. Finally, the framework is experimentally validated with our over-the-air OFDM-ISAC testbed.

In this article we prove a derived version of the Marsden-Weinstein-Meyer symplectic reduction theorem. We model the symplectic quotient as a dg-groupoid. We then construct the reduced symplectic form inside the Bott-Shulman complex of the groupoid. Finally, we show that the reduced form satisfies a derived analogue of the non-degeneracy condition.

We introduce the notions of $rgs$ and $irgs$ for Keisler measures, motivated by the study of generically stable random types and their associated Morley sequences. We obtain characterizations of these notions in terms of averages of classical first-order formulas over suitable probabilistic partitions (Theorems 3.2 and 3.3). We compare these notions with $fim$, $fam$, and self-averaging, and show that for types the notions $fim$, $irgs$, and $rgs$ coincide. We prove that every $irgs$ measure is dependent (Theorem 4.5); consequently, such measures are symmetric (Corollary 4.8). Furthermore, we show that for $irgs$ measures the model-theoretic instability events $\mathbf{O}^φ$, $\mathbf{I}^φ$, and $\mathbf{L}^φ$ have $\mathbb{P}_μ$-measure zero (Theorem 5.4), extending results from [8] beyond the $fim$ case.

We formulate a landscape theory for the long-time wave packet spreading of free and harmonically trapped particles with quantum fluctuations and its related dissipation. We show that the diffusion, localization, and collapse of wave packets arise from symmetry structures of an underlying landscape in covariance space. The geometry of this landscape determines the asymptotic fate of the wave packet. In the quantum landscape description, the trapping potential and bath fluctuation break the landscape symmetry in distinct ways: the former lifts the valley-like landscape of a fluctuation-free free particle into a bowl-like landscape, leading to collapse, whereas the latter tilts the valley and turns localization into diffusion. The resulting landscape symmetry breaking accounts for the noncommuting long-time limits and abrupt changes in the asymptotic wave-packet width. This establishes landscape symmetry breaking as a unified geometric origin of wave-packet diffusion, localization, and collapse in quantum Brownian motion.

We report the detailed jet properties of eROSITA Final Equatorial Depth Survey (eFEDS) J084222.9+001000 (hereafter ID830), a radio-loud super-Eddington quasar at $z=3.4351$, revealed by Very Long Baseline Array (VLBA) observations at 1.6 GHz, 4.9 GHz, and 8.2 GHz. Thanks to the high spatial resolution of the VLBA, we successfully resolve a parsec-scale core-jet structure of ID830, and find a well-collimated jet extending over $\approx 745$ pc, making it the most distant and one of the very few currently known radio-loud quasars with a resolved jet associated with super-Eddington accretion. The physical scale and evolutionary track of ID830 differs markedly from the low-$z$ analogues, such as nearby radio-luminous high-Eddington narrow-line Seyfert 1 galaxies, suggesting that this source represents a distinct high-$z$ population compared to previously known samples, with important implications for AGN feedback in early galaxy evolution. We also find that the jet has a relativistic speed of $v \gtrsim 0.19c$ and a modest viewing angle of $ϕ\lesssim 79^\circ$ to the line of sight, although its emission is not significantly Doppler-boosted ($δ\sim 1$). This provides the first evidence that such a relativistic and collimated jet can be produced over several hundred parsecs in the super-Eddington phase, lasting for at least $10^{3\text{-}4}$ yr. Our results call for further theoretical and numerical studies to understand the physical processes required to sustain such large-scale collimation in super-Eddington accretion, which remains a missing piece.

This work presents the application of parametric Operator Inference (OpInf) -- a nonintrusive reduced-order modeling (ROM) technique that learns a low-dimensional representation of a high-fidelity model -- to the numerical model of the purging process in semiconductor manufacturing. Leveraging the data-driven nature of the OpInf framework, we aim to forecast the flow field within a plasma-enhanced chemical vapor deposition (PECVD) chamber using computational fluid dynamics (CFD) simulation data. Our model simplifies the system by excluding plasma dynamics and chemical reactions, while still capturing the key features of the purging flow behavior. The parametric OpInf framework learns nine ROMs based on varying argon mass flow rates at the inlet and different outlet pressures. It then interpolates these ROMs to predict the system's behavior for 25 parameter combinations, including 16 scenarios that are not seen in training. The parametric OpInf ROMs, trained on 36\% of the data and tested on 64\%, demonstrate accuracy across the entire parameter domain, with a maximum error of 9.32\%. Furthermore, the ROM achieves an approximate 142-fold speedup in online computations compared to the full-order model CFD simulation. These OpInf ROMs may be used for fast and accurate predictions of the purging flow in the PECVD chamber, which could facilitate effective particle contamination control in semiconductor manufacturing.

Word-representable graphs, characterized by the existence of a semi-transitive orientation, form a well-studied class of graphs. Comparability graphs form another well-studied class and constitute a subclass of word-representable graphs. Both classes are hereditary and admit characterizations in terms of minimal forbidden induced subgraphs. While the minimal forbidden induced subgraphs for comparability graphs are completely characterized, the corresponding characterization for word-representable graphs remains open. In this paper, we precisely determine which minimal non-comparability graphs are also minimal non-word-representable graphs by classifying minimal non-comparability graphs according to whether they are word-representable. As a consequence, we provide a complete description of minimal non-word-representable graphs containing an all-adjacent vertex. We also address an open problem posed by Kenkireth et al.\ concerning the cover number of word-representable graphs by comparability graphs. We demonstrate the existence of word-representable graphs on $n$ vertices whose cover number by comparability graphs is $Ω(\log n)$, which establishes that the universal $O(\log n)$ upper bound is asymptotically tight for the class of word-representable graphs. For triangle-free circle graphs, we establish that the cover number by comparability graphs is at most $3$ and demonstrate that this bound is tight. More generally, we show that for any circle graph $G$ with clique number $ω(G)$, the cover number by comparability graphs is bounded by $O(\log ω(G))$. Finally, we identify four subclasses of word-representable graphs for which the cover number by comparability graphs of every graph in these classes is at most $2$.

A regularized Boussinesq equation is studied as a dispersive, long-wave (quasicontinuum) approximation of the Fermi-Pasta-Ulam lattice with a general cubic interaction force. Explicit periodic traveling wave solutions in terms of Jacobi elliptic functions are classified, and their solitary-wave, kink, and trigonometric limits are obtained. The Whitham modulation equations describing slow modulations of periodic traveling wave solutions are derived using an averaged variational principle. The convexity (strict hyperbolicity, genuine nonlinearity) of the resulting hydrodynamic-type equations is examined numerically in general and analytically in the solitary-wave and harmonic limits. In particular, the loss of hyperbolicity and the formation of complex conjugate characteristic speeds is shown to lead to modulational instability of periodic traveling waves. The onset of modulational instability is verified by numerical computations of linearized spectra for periodic traveling waves and initial value problems that also reveal additional short-wave instabilities.

We construct locally compact non-unital spectral triples for a noncommutative planar system determined by a fixed nondegenerate irreducible unitary sector of the kinematical symmetry group \(G_{\mathrm{NC}}\). The sector is labelled by central parameters \((\hbar_0,\vartheta_0,B_0)\), with \(\hbar_0,\vartheta_0,B_0\neq0\) and \(\hbar_0-\vartheta_0B_0\neq0\). For this sector, the triples \((\mathcal S_{\hbar_0,\vartheta_0,B_0},\mathcal H, D^{r,s}_{\hbar_0,\vartheta_0,B_0})\) form an even two-parameter family indexed by \((r,s)\), and different choices of \((r,s)\) give unitarily equivalent realizations. The unperturbed Dirac operators have Landau-type spectral levels of infinite multiplicity; hence local compactness, rather than compact resolvent, is the relevant analytic condition. We then identify the represented algebra \(π(\mathcal S_{\hbar_0,\vartheta_0,B_0})\) with the effective Moyal Fréchet \(\ast\)-algebra with deformation parameter \(\vartheta_{\mathrm{eff}} =\frac{\vartheta_0}{1-\vartheta_0B_0/\hbar_0}.\) For each star-product realization parameter \(\varrho\), this yields spectral triples over the involutive Moyal algebra \(\mathcal A_{\vartheta_{\mathrm{eff}},\varrho}\). External \(U(1)_{\star_{\vartheta_{\mathrm{eff}},\varrho}}\)-gauge potentials are incorporated by localizing the affine gauge potentials with smooth cutoffs. The resulting bounded self-adjoint perturbations \(B_R^{(\varrho)}\) define Dirac operators \(D_R^{\varrho,r,s}=D^{\prime\,r,s}+B_R^{(\varrho)}.\) Finally, as \(R\to\infty\), these operators converge in the strong resolvent sense to a self-adjoint limiting operator \(D_\infty\), the closure of the formal minimally coupled operator. Thus the finite-cutoff triples rigorously approximate the limiting minimally coupled Dirac operator associated with the fixed nondegenerate \(G_{\mathrm{NC}}\)-sector.

Galaxy clusters are the largest virialized structures in the Universe and are predominantly dominated by dark matter. The hydrostatic mass and the mass obtained from gravitational lensing measurements generally differ, a discrepancy known as the hydrostatic mass bias. In this work, we derive the hydrostatic mass of galaxy clusters within the framework of Rastall gravity. We consider two scenarios: (i) the absence of dark matter and (ii) the presence of dark matter. In both cases, we constrain the Rastall parameter in the cluster-scale using observational data. In the first scenario, Rastall gravity effectively reduces the hydrostatic mass, bringing it closer to the observed baryonic mass. The best linear fit yields a slope $\mathbf{M}=1.07\pm0.11$, indicating a near one-to-one correspondence between the two masses. In the second scenario, Rastall gravity helps to alleviate the hydrostatic mass bias. The linear fit between the Rastall hydrostatic mass and the observed lensing mass results in a best-fit slope $\mathbf{M}=0.99\pm0.26$, which is very close to unity. We also calculate the goodness-of-fit for every fit. The statistical evaluations indicate that Rastall gravity provides a viable phenomenological framework that can improve certain aspects of the mass discrepancy problem at the level of scaling relations. However, it does not universally outperform other modified gravity model, when evaluated using standard goodness-of-fit criteria.

Evaluating visualization systems in niche domains such as genomics is challenging due to scarcity of domain experts and difficulty recruiting a representative user base. While LLM-based synthetic personas are increasingly used to ease evaluation bottlenecks, they face well-founded skepticism. Rather than weighing synthetic personas as substitutes for real users, we ask a fundamental open question: when synthetic personas evaluate a real visualization system, what do they actually produce, and how does that output change when grounded in documented human contexts? We present Sycamore, an exploratory three-condition probe design using Geranium, a search engine for multimodal genomics visualization, as a case study. Sycamore evaluates Geranium using: (1) ungrounded synthetic personas from generic LLM priors; (2) grounded synthetic personas constrained by voice-of-customer artifacts from a prior interview study; and (3) a published baseline study of real domain experts. We observe that grounding shifts synthetic feedback toward the language and concerns of documented users, while ungrounded evaluators drift toward operational specifics that real participants did not raise; both synthetic conditions, however, converge on a find-and-adapt frame and miss the image-modality preference observed in the expert study. We discuss what these observations imply for where synthetic personas might fit alongside expert studies in domain-specific visualization evaluation. All supplemental materials are available at https://osf.io/kdfr3/.

Acoustic echo and background noise pose challenges on speech enhancement in hands-free systems and speakerphones. Discriminatively trained end-to-end methods represent a powerful solution for joint acoustic echo control (AEC) and denoising. However, with the advent of generative methods, diffusion-based approaches have seen remarkable performance in speech enhancement tasks. In this work, to the best of our knowledge, we provide the first (still non-causal) diffusion-based AEC model (DiffVQE) that is reproducible in terms of topology, training data, and training framework. So far, without employing diffusion, Microsoft's discriminative DeepVQE model has been shown to excel any of the ICASSP 2023 AEC Challenge entries achieving remarkable performance. Using data from the Interspeech 2025 URGENT Challenge for a diverse, high-quality training dataset, our DiffVQE excels DeepVQE both in echo and noise control performance, as well as in computational complexity and model size.

As computational thinking (CT) becomes increasingly important to physics education, the need for authentic, project-based assessments has grown. While open-ended multimodal assignments, such as Computational Physics Essays (CPEs), help capture student reasoning and encourage active learning, they introduce a significant evaluation bottleneck. Manually grading these complex notebooks across a complex taxonomy of computational practices is resource-intensive and limits scalability in large-enrollment courses. In this study, we investigated the viability of using a multimodal Large Language Model (LLM) to automate the evaluation of 100 student-generated CPEs. Using a human-coded baseline, we systematically evaluated the model's capacity to detect student engagement across 20 distinct CT sub-practices and a holistic overall quality score. The results showed that the LLM performs very well on clearly defined tasks, achieving an 84% exact agreement with human raters on the binary sub-practices. However, more subjective constructs proved challenging, with the model reaching only a 71% agreement for the holistic quality analysis. Our findings demonstrated that while LLMs can reliably automate the detection of specific computational practices, subjective evaluation remains a hurdle.

Quantum fluctuations are often suppressed in ferromagnetic materials because they admit a simple unfrustrated ground state, greatly limiting the scope of the phenomena that can be observed. In this work, we show how naturally occurring magnetization-non-conserving couplings fundamentally alter this paradigm by demonstrating the existence of a chiral ferromagnet that is stabilized by quantum fluctuations. More specifically, we show how these spin-orbit interactions modify the classical phase diagram; whereas a classical analysis predicts only achiral collinear states, we observe fluctuation-stabilized phases, including a ferromagnet with large orbital chirality and a chiral stripe. We elucidate how such couplings generate a scalar orbital chirality spontaneously, in contrast to conventional mechanisms which rely upon a field-induced canting of vector chiral order. The resultant chiral states exhibit distinct transport signatures, namely an enhanced thermal Hall effect, and are of direct relevance to moiré heterostructures, Rydberg-atom arrays, and solid-state materials featuring non-Kramers spins

We consider the equal sum partition problem, motivated by distance magic graph labeling: Given $n,k \in \N$ such that $k\, | \sum_{i=1}^ni$ and a partition $p_1+\cdots+p_k=n$, when is it possible to find a partition of the set $\{1,2,\ldots,n\}$ into $k$ subsets of sizes $p_1,\dots,p_k$, such that the element sum in each subset is the same? A known necessary condition is the \emph{slack condition}, requiring that for all $j$, placing the largest possible elements in the $j$ smallest sets yields a total sum that is at least what is needed. However, this condition is not sufficient, and known counterexamples exist. This work clarifies the boundary between solvable and unsolvable instances of the problem. We extend the list of unsolvable problem instances satisfying the slack condition by exhibiting infinite families where the $n/k$ ratio is any rational number in the interval $(2,\frac{24}{7})$, and a new criterion for unsolvability. Furthermore, we show that the slack condition is natural, as it is both necessary and sufficient for the fractional relaxation of the problem. Based on this result, we prove that the problem is solvable for the class of linear partitions, where $k$ is fixed, $p_1,\ldots,p_k$ grow linearly with $n$, and where the slack condition holds in a strong sense. We do this by applying a randomized rounding algorithm to a solution of the fractional relaxation of the problem and proving that the algorithm has an exponentially small failure probability.