An accurate determination of the dust attenuation within galaxies is essential to derive key physical properties such as the star formation rate (SFR). We present an analysis using the JWST/NIRISS data from the GLASS-JWST ERS programme to investigate and characterise the stellar and nebular reddening of galaxies at $1.0<z<2.4$, down to the sub-kpc scale. We use a multiregion fitting method to extract high-quality H$α$ and H$β$ emission line maps for 99 individual galaxies across a stellar mass range $7.0<\log_{10}(M_*/\mathrm{M}_{\odot})<10.5$. We find no evidence for ratios of the Balmer decrement (H$α$/H$β$) below the intrinsic limit for Case B recombination, beyond the expected variation from observational uncertainties. We reproduce the local correlation between the Balmer decrement and total stellar mass, and find no measurable difference when splitting the sample by redshift, with negligible attenuation below $\log_{10}(M_*/\mathrm{M}_{\odot})\lesssim8.5$. Similarly, the best-fit relation between the nebular and continuum reddening follows the same relation as in local starburst galaxies, $E(B-V)_{\mathrm{SED}} = (0.46\pm0.02)E(B-V)_{\mathrm{neb}}$, together indicating no significant evolution in the dust geometry within galaxies out to $z\lesssim2.4$. We derive best-fit linear relations between the differential nebular-stellar reddening and the SED-derived star formation rate (SFR) and stellar mass, finding statistically significant relations for both quantities. We use our spatially-resolved measurements to derive an empirical calibration between the resolved differential reddening, and the SFR surface density. These will enable crucial dust attenuation corrections for spatially-resolved science at higher redshifts where the Balmer lines are inaccessible, such as with future Roman grism observations.

In Online Learning to Rank (OLTR), ranking models are trained directly from live user interactions, but existing systems rely on a trusted central server to collect and process these interactions. This leaves operators free to introduce biases that conflict with user interests. Decentralized learning offers an attractive alternative, allowing users to collaboratively train a shared ranking model by exchanging model updates directly with one another, without any central authority. In such settings, however, malicious nodes can send poisoned model updates that degrade the ranking quality of honest nodes. We introduce RankGuard, a decentralized OLTR framework in which users collaboratively train ranking models and exchange model updates directly with other nodes. RankGuard defends against poisoning attacks by carefully evaluating incoming models against the user's own private click history, corrected for position bias. An incoming model is only aggregated if it better explains the user's past interactions than the current local model, making it fundamentally hard for malicious nodes to craft updates that pass this test without also genuinely helping the user. We derive a theoretical convergence guarantee of RankGuard. To the best of our knowledge, this is the first formal convergence analysis of a decentralized OLTR algorithm. We evaluate RankGuard against four poisoning attacks, including a powerful adaptive attack, using four standard benchmarks and three click models. RankGuard outperforms all baselines in most settings while being up to 62x more efficient than its closest competitors.

We describe $\texttt{stistools.barycentric_correction}$, a new Python utility for calculating barycentric timing corrections for HST/STIS observations. This tool replaces the deprecated $\texttt{stsdas.hst_calib.stis.odelaytime}$ IRAF function that was previously used for HST barycentric corrections. Our new utility uses $\texttt{astropy}$ for conversion between time formats and standards and introduces a new way to calculate HST's position through JPL Horizons, replacing the need to download separate HST orbital ephemeris files. Here, we describe the methods used in the new utility, the tests that were carried out to verify its accuracy, and explain some of the complexities involved in determining light travel times to accuracies down to a millisecond for HST. We also summarize the current understanding of the absolute accuracy of STIS time stamps.

The location of a star along the horizontal branch (HB) during core-helium burning is primarily determined by the amount of mass lost by its progenitor. We investigate the formation and properties of stripped core-helium-burning stars, focusing on how the residual hydrogen-envelope mass ($M_{\mathrm{env}}$) and the timing of envelope removal shape their properties. We used the MESA stellar evolution code to model stars that lose their hydrogen envelopes on the first giant branch. We explored two limiting cases for the timing of stripping, corresponding to the minimum and maximum core masses for helium ignition, for progenitors with initial masses below $\sim$6 $M_{\odot}$ at two metallicities ($Z=0.02$ and $Z=0.004$), while systematically varying $M_{\mathrm{env}}$. As expected, the effective temperature along the HB decreases as $M_{\mathrm{env}}$ increases. We determined the maximum $M_{\mathrm{env}}$ required to avoid subsequent evolution through the thermally pulsing asymptotic giant branch, which ranges from $\sim0.05$ $M_{\odot}$, for low-mass progenitors to $\sim0.30$ $M_{\odot}$ for intermediate-mass progenitors. In low-mass progenitors, early envelope removal triggers a late hot flash, naturally explaining the hottest blue hook stars. In intermediate-mass systems, partial envelope stripping can produce extended pre-HB configurations consistent with puffed-up stripped stars observed in binaries with Be companions. Our post-stripping evolutionary tracks are publicly available for use in binary evolution and population synthesis studies.

The interplay among superconductivity, magnetism, and nontrivial band topology represents one of the most compelling frontiers in condensed matter physics. The exploration of novel superconductivity in 3d transition-metal compounds, particularly the rare Cr-based systems containing strongly magnetic Cr ions, has long attracted attention owing to their unconventional pairing mechanisms that challenge conventional wisdom. Yet, Cr-based superconductors remain scarce, especially those possessing nontrivial topological character, underscoring the urgent need to uncover new members. Here we report the observation of superconductivity in pressure-amorphized Cr-based topological insulator CrP$_4$. Upon compression, CrP$_4$ undergoes an anomalous quantum phase transition from a metallic to a semiconducting-like state at around 15 GPa, driven by significant changes in the electronic structure. At approximately 70 GPa, re-metallization with superconductivity occurs alongside an irreversible amorphization. The superconducting transition temperature Tc increases monotonically with pressure, reaching 4.8 K at 141.3 GPa. Furthermore, theoretical calculations predict multiple topological phase transitions from a strong topological insulator to a trivial state and finally back to a strong topological state under pressure. Our study not only establishes CrP$_4$ as the first Cr-based amorphous superconductor but also opens a new paradigm for exploring superconducting and topological properties in amorphous materials.

We investigate the electronic structure, spin textures, and charge to spin/orbital transport in graphene encapsulated by 1T-TaS$_{2}$ monolayers in the charge density wave phase. Using first-principles calculations, tight-binding modeling, and the Kubo formalism, we show that the encapsulation stacking dictates fundamentally distinct transport regimes. In the asymmetrical (AA) stacking, proximity fields from both interfaces constructively interfere, yielding a cumulative Rashba phase of nearly $π/2$. This pure radial Rashba spin pattern leads to the unconventional Rashba-Edelstein effect, which robustly dominates over the conventional response by a factor of 35 across a wide energy range. Conversely, the symmetrical (AA') stacking preserves a horizontal mirror symmetry, establishing a stable, purely out-of-plane persistent spin texture. Furthermore, the computed orbital Hall effect is exceptionally efficient, surpassing the spin Hall effect by three orders of magnitude. Within the proximity-induced spectral gaps, the orbital Hall conductivity exhibits a finite plateau, whereas the spin Hall conductivity vanishes. Our findings establish graphene encapsulated heterostructures as a promising system for realizing distinct charge to spin and charge to orbital interconversion regimes determined by the choice of stacking order.

We propose a phase field model able to simulate hydrogen-assisted cracking in polycrystalline materials. Within a variational framework, the model simultaneously describes crack propagation and hydrogen segregation on crack surfaces and grain boundaries together with the associated reduction in interfacial energies. In the context of hydrogen-enhanced decohesion (HEDE) mechanisms, we demonstrate the ability of the model to capture the transition from transgranular cracking to hydrogen-assisted intergranular cracking.

In this paper, one constructs a nonlocal extension of the Rarita-Schwinger theory for spin-$3/2$ fermions. Two classes of analytic form factors are considered: scalar form factors $f(\Box)$ and Dirac-operator form factors $f(\slashed{\partial})$. The massless theory is treated together with a covariant nonlocal gauge fixing, which allows the propagator to be written directly in terms of the spin-$3/2$ projector. In the massive theory, we show that the free Rarita-Schwinger constraints remain intact for analytic form factors, so that the unphysical spin-$1/2$ sector does not become dynamical. For $f(\Box)$ the tensor-spinor structure of the propagator is the same as in the local theory, while the pole equation is deformed by the scalar form factor. For $f(\slashed{\partial})$ the physical modes obey a nonlocal Dirac-type equation, leading to modified dispersion relations that can be written explicitly for exponential form factors. We discuss the conditions under which the construction is ghost-free at the free level and identify the natural limitations that must be addressed before interactions are introduced.

Continuous long-term monitoring and diagnosis of biomedical signals, such as electrocardiograms (ECGs), can help mitigate an increasing threat to public health. Artificial Intelligence (AI) models, such as Convolutional Neural Networks (CNNs), provide accurate monitoring and classification for relevant diseases; however, they require more computational resources than conventional AI hardware can typically afford, especially for a resource-constrained environment on the edge. In this work, we present BenDi, an energy-efficient quasi-stochastic systolic architecture for bioelectronic systems on the edge. BenDi leverages multiple levels of energy and power optimization, ranging from circuits to software quantization, including low supply voltage, the \underline{Ben}t-Pyramid data format for quasi-stochastic multiplication, the \underline{Di}P systolic dataflow, and hardware-aware quantization, to handle CNNs with high accuracy on the edge within limited hardware budgets. The hardware implementation results, using a commercial 22nm technology, show that BenDi architecture, at 0.5 Voltage and 100 MHz, offers 3.35x smaller area and 5x higher energy efficiency, compared to state-of-the-art binary-based weight-stationary systolic architectures. Regarding Bioelectronic edge systems, BenDi achieves an order-of-magnitude improvement in energy efficiency and another order-of-magnitude improvement in area efficiency, compared to its counterparts. This significant improvement comes at the cost of 1\% to 3.3\% accuracy loss on the MIT-BIH and Apnea-ECG benchmarks, respectively, compared with conventional computing using the 32-bit floating-point format.

The Stokes parameters are three real parameters that completely characterize partially coherent optical fields spanned by two modes -- whether a pair of polarization or spatial modes -- and their use is thus ubiquitous in optics. Because the Stokes parameters are defined through an expansion of the $2\times2$ coherence matrix in terms of the Pauli matrices, they cannot be applied to optical fields comprising three modes, which are described by a $3\times3$ coherence matrix. Examples of such fields include the polarization of non-paraxial fields (spanned by three orthogonal polarization modes), and fields comprising three spatial or temporal modes. It has long been theorized that the $3\times3$ Gell-Mann matrices -- developed in high-energy particle physics -- can serve as a basis for $3\times3$ optical coherence matrices, with 8~expansion coefficients known as the Stokes-Gell-Mann (SGM) parameters, but the measurement procedure is daunting, and the SGM parameters have not been measured directly to date in optics. Here we present the first measurements of the SGM parameters for partially coherent three-mode light in a photonic integrated platform comprising a hexagonal mesh of Mach-Zehnder interferometers. Measuring the SGM parameters on chip, from which we reconstruct the $3\times3$ coherence matrix facilitates exploring the full space of iso-entropy fields that can be inter-converted into each other unitarily, and those that share the same value of entropy and yet cannot be inter-converted unitarily. These results pave the way to utilizing multimode partially coherent light in applications involving optical communications, sensing, and information processing.

We prove a prescribed-leftover-chord theorem for Hamiltonian Berge cycles of odd order. Let $C$ be a Hamiltonian Berge cycle on $n=2r+1$ vertices, and let $\mathcal G$ be a set of hyperedges, all of size at least $r$, containing the hyperedges of $C$. If $D\subseteq\{2,\ldots,r\}$ and $|\mathcal G|\ge n+|D|$, then the hyperedges can be reassigned to the adjacent pairs of the same cyclic order so that, for each $d\in D$, a distinct unused hyperedge realizes cyclic distance $d$. Consequently, the odd-order case of the one-extra-edge question of Bailey, Hollars, Li and Luo has an affirmative answer for all $n=2r+1\ge7$, in the convention including Berge cycles of length $2$. The proof combines an additive lemma in $\mathbb Z_{2r+1}$ with an alternating matching exchange.

We study general properties of the perfectoidization of finite algebras over a perfectoid ring, which helps to understand some precise and explicit descriptions. For example, we prove that if $A=R[t]/(m(t))$ where $m(t)$ is monic, $R$ is perfectoid and the discriminant $d$ of $m(t)$ is a non-zero divisor of $R$ satisfying a bounded torsion condition, then $dA_{\mathrm{pfd}}\subset A$. We also prove a density criterion reducing the construction of the perfectoidization to adjoining suitable $p$-power roots modulo $p$. In the second part of the paper, we compute perfectoidizations in several families of examples, including Kummer-type extensions and split finite algebras.

Origami-inspired metamaterials exploit the interplay between geometry and elasticity to achieve programmable mechanical responses. Yet the origin and tunability of snap-through instabilities in non-rigidly foldable patterns remain poorly understood. Here we show that the Mars tessellation, a degree-4 vertex origami pattern composed of alternating square and rhombic faces, is not rigidly foldable because the folding-speed ratios required for vertex compatibility cannot be propagated consistently across neighboring units. This geometric incompatibility forces the facets to bend during folding, giving rise to a reproducible snap-through discontinuity in the force-displacement curve with a mean force drop of about 92.6 +/- 5.5 %, marking a transition between metastable states. Laser scoring of additional diagonal creases, guided by strain-field simulations, enables continuous tuning of the snap magnitude. These results reveal a general mechanism by which geometric frustration can be harnessed to program multistability in thin-sheet metamaterials.

In this paper, we prove the asymptotic stability of the critical constant steady state for a simplified parabolic--elliptic Keller--Segel system in $\mathbb{R}^N$ ($N \ge 3$), which admits a one-parameter family of constant steady states. Although the stability threshold for constant steady states is known, the critical case has remained open. We also show that the convergence rate in the critical case differs from the rates obtained for previously studied subcritical constant steady states.

Smart cities rely on interconnected cyber-physical systems that integrate sensors, IoT devices, cloud platforms, and AI-driven services and decision-making. While these systems enhance city services, they also introduce complex cybersecurity challenges due to their large attack surfaces, heterogeneous data flows, and evolving threat vectors. Developing and validating cybersecurity tools for smart cities requires high-quality datasets that accurately represent real operational conditions. However, real-world datasets are often incomplete, contain privacy-sensitive data, are difficult to access, or lack sufficient malicious activity to support tool development. This research addresses this critical gap by proposing an AI-based synthetic data generation (SDG) framework designed specifically for smart city cybersecurity research. The proposed framework leverages generative artificial intelligence models to produce high-fidelity synthetic cybersecurity datasets that replicate realistic device behaviors, network interactions, and cyber-attack scenarios. The synthetic datasets are evaluated for conformity to protocol standards, statistical similarity to original datasets, and utility in common security tools. The resulting synthetic data generation framework and evaluation metrics are expected to advance smart city cybersecurity by enabling researchers to model threats more effectively and evaluate defensive techniques more comprehensively to better protect critical smart city infrastructures.

We investigate the localization properties of cavity-coupled electronic states in disordered systems, motivated by recent proposals of cavity-mediated hopping in quantum Hall systems. We first introduce a minimal two-band model in which localized states in a disordered one-dimensional band are coupled, through a homogeneous cavity mode, to an excited band of delocalized states. Combining perturbation theory with a transfer-matrix approach, we show that cavity-assisted hopping between localized states decays exponentially with distance, implying that the eigenstates remain localized even beyond the perturbative regime. Nevertheless, the corresponding localization length increases with the light-matter coupling strength and can extend over several lattice sites in the single-electron ultrastrong-coupling regime. We then study a disordered Landau band coupled to a cavity mode within the framework developed in Refs.[1,2]. We find that the effective cavity-mediated coupling between edge states also decays exponentially with distance, but with a localization length that can reach micrometer scales for experimentally realistic parameters. By analyzing the inverse participation ratio, we show that this enhanced coupling is predominantly mediated by the most extended states of the upper Landau band. Our results demonstrate that, while cavity-induced hopping in disordered quantum Hall systems remains exponentially localized, the associated localization length can become sufficiently large for the corresponding states to exhibit effectively delocalized behavior on mesoscopic length scales.

SSpeech imagery is attractive as a brain-computer interface paradigm for communication because it is endogenous and intrinsically linguistic. Yet despite growing interest, its dominant scalp-EEG spatiotemporal characteristics remain poorly characterized. Here, we asked how speech imagery appears in scalp EEG and compared it against finger motor imagery. Using a within-subject dataset containing speech imagery, finger motor imagery, and no-task trials recorded under the same trial structure, we analyzed band-power dynamics across channels and time. Finger motor imagery showed the expected contralateral mu/alpha and low-beta desynchronization over sensorimotor areas, whereas speech imagery showed a weaker, more distributed alpha-dominant increase. After normalization to each condition's own post-trial interval, the speech-related alpha increase changed only modestly after cue onset, indicating that much of the speech-versus-no-task difference was already present during the instruction period. A classifier discriminating imagery from no-task reached mean balanced accuracies of 0.563 $\pm$ 0.072 for speech imagery and 0.718 $\pm$ 0.127 for motor imagery, with a stronger alpha/beta dependence for motor imagery than for speech imagery. Together, these results provide a clearer group-level characterization of speech imagery in scalp EEG and indicate that its dominant spatiotemporal pattern differs from that of finger motor imagery and is more consistent with substantial non-articulatory task-related contributions than with a clear articulatory-motor analogue.

CeSiI is a van der Waals heavy-fermion metal recently found to exhibit unconventional superconductivity near a pressure-induced antiferromagnetic quantum critical point (QCP) at Pc =6 GPa. Here, we report a comprehensive single-crystal X-ray diffraction study of CeSiI under high pressures up to 8.3 GPa at room temperature, revealing subtle structural responses that precede pressure-driven QCP. We find that the unit-cell volume decreases smoothly upon compression without showing any structural phase transition in the investigated pressure range. Intriguingly, we observe abrupt and concurrent anisotropic responses of the lattice parameters around Pc =6 GPa, i.e., the a-axis contracts while the c-axis enlongated suddenly, with the unit-cell volume smoothily varies with pressure. Structural refinements further show that these lattice anomalies primarily originate from changes of Ce-Ce and Ce-Si bond lengths, as well as a flattening of the inner honeycomb Si layer within the CeSiI monolayer around Pc. Our findings establish an interesting case linking pressure-driven electronic transition of QCP at low temperatures to incipient structural responses at room temperature, thereby providing fresh insight into the pressure-temperature phase diagram of CeSiI.

We construct a five-state model for photoexcitation in Y6 (BTP-4F) dimers, and then solve the non-adiabtic dynamics using the Hierarchical Equations of Motion (HEOM) method. We find that triplets are populated mainly via a transiently excited \textit{intermolecular} charge-transfer singlet to triplet Frenkel exciton route; this route is not available to the monomer. Analysis of one-particle transition density matrices suggests that the charge-transfer states are spatially distinct to the Frenkel exciton states, indicating that the large spin-orbit-coupling for this transition is due to it being permitted by an associated change in orbital character. Aggregation in Y6 therefore directly enables fast and high-yield intersystem crossing. We selenise our model dimers, significantly enhancing spin-orbit-coupling, which then accelerates this charge-transfer mediated route. Looking forwards to simulations on larger aggregates, we show that, though Marcus theory gives qualitatively correct dynamics, the long-time yields are incorrect due to it missing quantum recurrences. Instead, we show that the recently developed memory-kernel projector\cite{Gestsson2025-ez} method can produce semi-classical rates directly from the HEOM equations which lead to quantitatively correct dynamics and yields.

In this article, we relate any Farey triangle in the extended upper half-plane to a variant of Colmez--Fontaine's fundamental lemma in $p$-adic Hodge theory. In particular, their original fundamental lemma corresponds to the fundamental Farey triangle $(\frac{1}{0},\frac{1}{1},\frac{0}{1})$.

N6-methyladenosine (m6A) is the most abundant internal modification in eukaryotic mRNA. However, most existing predictors use adenosine-centered formulations that are computationally inefficient and prone to false positives. Here we present m6A-FORM, a transformer-based foundation model for RNA methylation that uses MeRIP-seq peaks as methylation-enriched priors and is pretrained on approximately 22 million peak-derived sequences from 143 human MeRIP-seq studies. After fine-tuning with high-confidence single-nucleotide m6A annotations from m6A-Atlas v2.0 and GLORI, m6A-FORM-sites achieves state-of-the-art m6A site prediction performance, with a PR-AUC of 0.635 and ROC-AUC of 0.988, improving PR-AUC by at least 0.14 over existing methods while enabling substantially faster inference. Task-specific adaptation further supports prediction of binding sites for 19 m6A-associated regulators and identification of YTHDF2-bound m6A sites associated with mRNA degradation. Applying m6A-FORM across 67 datasets from 24 human tissues identifies 19,631 tissue-conserved sites with distinct localization, clustering, methylation, expression, RBP-interaction, and decay-associated signatures.

Characterization of time-frequency (TF) quantum states requires reliable reconstruction of their TF distributions. However, imperfect transmission or measurement channels can distort reconstructed joint spectral intensities (JSIs), especially when the underlying perturbation mechanism is unknown. Here, we experimentally demonstrate a reconstruction and correction framework that uses a TF grid state as an intrinsic frequency-domain reference. By analyzing the displacement of the grid points, a Gaussian process regression model is employed to reconstruct a correction mapping for the nonlinear coordinate deformation without assuming a prior physical model of the distortion. The learned mapping reduces the residual coordinate deviation of the TF grid state by approximately a factor of 11 and, when applied to an independent frequency-entangled test state, improves the Gaussian-shape fidelity from 76.2\% to 90.0\%. These results establish TF grid states as practical metrological resources for diagnosing and correcting distortions in TF quantum systems, providing a pathway toward distortion-resilient quantum communication and high-dimensional quantum information processing.

Virtual reality (VR) and head-mounted displays are constantly gaining popularity in various fields such as education, military, entertainment, and health. Although such technologies provide a high sense of immersion, they can also trigger symptoms of discomfort. This condition is called cybersickness (CS) and is quite popular in recent virtual reality publications. This work proposes a novel experimental analysis using symbolic machine learning to rank potential causes of CS in VR games. We estimate CS causes and rank them according to their impact using classical machine learning. Experiments are performed using two virtual reality games and 6 experimental protocols along with 37 valid samples from a total of 88 volunteers. Our results show that rotation and acceleration triggered cybersickness more frequently in a flight game in contrast to a race game. We could also observe that subjects that are less experienced with VR are more prone to feel discomfort. Former experience plays a more important role on the race game, as this game provides more liberty to the user in terms of controllers, more displacement alternatives and a more user-controlled acceleration. Furthermore, different causes that trigger discomfort arise based on short or long term VR exposures. We suggest strategies for mitigating CS for these two scenarios: short and long term exposure experiences and compare the two highlighted scenarios (race and flight).

The rapid integration of large language models (LLMs) into mobile applications has introduced a new class of credential security risk: leaked credentials that grant unauthorized access to LLM inference services, causing financial damage to developers. Prior work on credential leakage has focused primarily on Android apps; to date, no empirical study has systematically investigated LLM API key leakage in iOS applications. We present the first in-depth empirical study of API key leakage in LLM-integrated apps. We construct a high-quality dataset of 444 iOS applications, filtered from 1092 candidates through a standardized process, and develop LLMKeyLens, a dynamic analysis framework that detects LLM API key leakage via traffic interception, provider-specific key extraction, and active validity confirmation, requiring neither source code access nor binary decryption. Our analysis reveals that 282 applications expose exploitable LLM API credentials in network traffic, spanning at least ten providers. We identify three leakage patterns: JWT-based token leakage (48%), unauthenticated backend proxy access (33%), and plaintext API key transmission (19%). To assess remediation, we re-analyzed the same 282 vulnerable applications three months after responsible disclosure; only 28% had remediated the reported vulnerability, while 72% remained exploitable, with persistent issues stemming from unauthenticated backends and broken JWT implementations. Our findings show that LLM API key leakage is both prevalent and persistent in the iOS ecosystem, exposing a systemic gap between developer practice and secure integration principles, and suggest that secure LLM integration requires not only developer awareness but also explicit security guidance from providers and platform-level enforcement.

Microbial genomes and metagenomes contain millions of proteins whose enzymatic functions remain unknown, the enzyme dark matter. While deep learning has improved protein function prediction, most methods are black boxes relying on sequence or structural similarity, limiting discovery of novel catalytic activities. The ESMC-6B protein language model and its sparse autoencoder with a 16,384-dimensional codebook of interpretable biological concepts, each annotated by GPT-5, creates a new opportunity: using these features directly as semantic signatures for enzyme function. Here, we show that ESMC-SAE features enable accurate and interpretable enzyme commission (EC) number prediction without task-specific training or GPU-intensive computation. On a balanced benchmark of 4,868 microbial SwissProt enzymes across 161 EC3 subclasses, ESMC-SAE binary features achieve 78.9% top-1 and 88.5% top-5 accuracy, 37.6% higher than 3-mer baselines (57.3%). In leave-one-EC3-class-out evaluation simulating discovery of novel enzyme classes, SAE features recover the EC1 superclass in 47.7% of cases (3.3x random, 14.3%), versus 26.6% for sequence methods. Discriminative features correspond to mechanistically interpretable concepts: catalytic triad geometry for hydrolases, NAD(P)H-binding Rossmann folds for oxidoreductases, phosphate-binding P-loops for transferases. We also survey the ESM Atlas of 7.7 million clusters and identify 169,859 dark enzyme-like candidates across all major microbial phyla. Our results establish a paradigm for enzyme function discovery in microbial dark matter: interpretable by design, scalable without GPU clusters, and applicable to the billions of proteins in the ESM Atlas.

Based on the canonical description of a non-interacting Bose gas, we work out how both thermodynamic and statistical properties change perturbatively with respect to weak two-particle interactions. Up to first order, we obtain a recursion formula for the canonical partition function, which consists of the same Feynman diagrams as the grand-canonical description but with different Feynman rules. Resumming this recursion formula for the canonical partition function allows one to characterize the statistics of the ground-state occupancy by its respective cumulants. We demonstrate the applicability of this approach by analyzing a dilute Bose gas with contact interaction in a box trap. To this end, we used Dirichlet boundary conditions in view of their relevance for current experiments with atomic gases, where the box trap is implemented, for instance, with digital mirror devices.

We compute the stable homology of complex braid groups of types $B(e,e,n)$ and $B(2e,e,n)$ for fixed $e\ge2$ and increasing $n$. This accounts for the stable homology of all infinite families of complex braid groups. We achieve this by explicitly computing a quillenization of their stable classifying spaces. In particular, we provide a proof of an identification of the stable homology of Artin groups of type $D$ claimed by Fuchs in the '70s.

The distribution of the effective inspiral spin ($χ_\mathrm{eff}$) of the binary black holes detected by LIGO-Virgo-KAGRA can shed light on their formation pathways. We analyze the GWTC-5.0 dataset with two models-one flexible, one fully parametric-that jointly describe $χ_\mathrm{eff}$ and primary mass. We clarify that the previously-reported skewness in the $χ_\mathrm{eff}$ distribution is better understood as additional structure beyond a non-skewed Gaussian bulk centered at small $χ_\mathrm{eff}$. This additional structure extends to larger $|χ_\mathrm{eff}|$, a result previously reported using GWTC-4.0 data. We measure the asymmetry of the distribution of $χ_\mathrm{eff}$ outside the Gaussian bulk from the data. With both the parametric and the flexible analyses, we find tentative evidence for a mass-dependent excess of positive $χ_\mathrm{eff}$ over negative ones outside the Gaussian bulk. Only at $m_1 \in [46,65]\,M_\odot$ do the data require a negative $χ_\mathrm{eff}$ component outside the Gaussian bulk, with $23\text{:}1$ odds. If $χ_\mathrm{eff}$ outside the Gaussian bulk are produced by hierarchical mergers-as it has been suggested-then a fraction of those mergers may be produced in environments that can generate a surplus of binaries with positive $χ_\mathrm{eff}$, such as the disks of active galactic nuclei.

To gain deeper insight into the role of hole kinetics in determining magnetism in highly frustrated doped Mott insulators, we consider the single-hole counter-Nagaoka problem on the kagome lattice, using magnetization as a tuning parameter. Near full polarization, a doped hole delocalizes upon binding reversed spins in a pattern of singlet bonds which we term resonating-valence-bond (RVB) polaron. These RVB polarons can have extremely small effective bandwidths, and hence exhibit self-trapping. By tuning the spin polarization, we track the evolution of these states toward the unpolarized sector, where we observe the emergence of $\sqrt{3}\times\sqrt{3}$ antiferromagnetic correlation reminiscent of the classical Potts and Heisenberg models on the kagome lattice. These results provide a framework to understand how RVB physics at short scales evolves into conventional magnetic correlations at long scales.

We study metric spaces that in some sense thin out at infinity. We define and investigate a measure of sparsity that is a quasi-isometry invariant, and introduce an analogue of topological ends for sparse spaces that is also invariant under quasi-isometries. We study some 51F30examples arising in various contexts.