The rapid growth of spatiotemporal data volumes needs to be handled by database systems capable of efficiently managing and querying such data. Existing systems such as PostGIS, SpaceTime, and MobilityDB offer partial solutions but differ widely in scope and performance. Also, first spatiotemporal benchmarks provide valuable insights but are limited in scope and, to our knowledge, no application-centric benchmarking suite exists. In this paper, we propose GeoBenchr, an open-source, application-centric benchmarking suite for spatiotemporal platforms. GeoBenchr enables comprehensive evaluation across diverse datasets, query types, and workload patterns, reflecting realistic use cases from domains such as cycling, aviation, and maritime tracking. We use our GeoBenchr prototype to evaluate several system aspects including scalability, configuration impact, and cross-platform performance comparison. Our results highlight the importance of application-centric benchmarking in selecting suitable spatiotemporal database systems for real-world scenarios.

We present guidelines for deriving new Nitsche Finite Element Methods to enforce equality and inequality constraints that act on the value of the unknown mechanical quantity. We first formulate the problem as a stabilized finite element method for the saddle point formulation where a Lagrange multiplier enforces the underlying constraint. The Nitsche method is then presented in a general minimization form, suitable for adding constraints to nonlinear finite element methods and allowing straightforward computational implementation with automatic differentation. This extends the method beyond classical boundary condition enforcement. To validate these ideas, we present Nitsche formulations for a range of problems in solid mechanics and give numerical evidence of the convergence rates of the Nitsche method.

Understanding the electrical double layer (EDL), i.e, the distribution of electrolyte at an electrified interface, in concentrated electrolytes is important for various technologies, such as supercapacitors, batteries and electrocatalysis. Atomistic approaches offer unprecedented detail, but are too computationally expensive to exhaustively investigate the EDL of concentrated electrolytes, motivating the development of continuum theories. In these concentrated electrolytes, correlations between ions and solvents are strong, through electrostatic and specific interactions, as well as significant excluded volume effects of the complicated molecular species, making the development of theories challenging. Thus far, there are mainly two distinct \textit{simple} theoretical approaches to understand the EDL of concentrated electrolytes, with account of these correlations beyond mean-field. One is a local-density approximation (LDA) based on treating electrostatic and specific interactions beyond mean-field through the ionic aggregation and solvation; where a simple conceptual understanding can be gained and reasonable agreement with experiments in terms of integrated quantities, but poor agreement for ion profiles and Debye capacitance. The other approach is to treat electrostatic correlations and excluded volume effects more rigorously with beyond LDA approaches, but at the cost of simplifying the chemical interactions between species; where excellent agreement can be obtained for ion profiles, differential capacitance, etc., but mainly for the simplified hard-sphere systems that the theories are based on. Here, we describe the merits and downfalls of these two approaches, how they have contributed to understanding anomalous underscreening, and outline future directions for these theoretical approaches.

Here we analyze ways to achieve deep subthreshold parametric squeezing or cooling of a single degree-of-freedom parametric resonator enhanced by a lock-in amplifier feedback loop. Due to the feedback, the dynamics of the parametric resonator becomes more complex and a Hopf bifurcation at the instability threshold can occur. Initially, we calculate the phase-dependent gain of parametric amplification with feedback of an added ac signal. In one approach, we obtain the amplification gain approximately using two independent approaches: the averaging method and the harmonic balance method. We also obtain this gain more exactly using Floquet theory and Green's functions methods. The Hopf bifurcation was predicted by the harmonic balance method and by Floquet theory, but not by the averaging method. In our analysis of fluctuations, we Fourier analyze the response of the parametric resonator with feedback to an added white noise. We were able to calculate, in addition to the noise spectral density, the squeezing of fluctuations in this resonator with feedback. Very strong squeezing or cooling can occur. Deamplification and cooling occur near the Hopf bifurcation, whereas squeezing occurs near a saddle-node bifurcation.

To ensure decidability and consistency of its type theory, a proof assistant should only accept terminating recursive functions and productive corecursive functions. Most proof assistants enforce this through syntactic conditions, which can be restrictive and non-modular. Sized types are a type-based alternative where (co)inductive types are annotated with additional size information. Well-founded induction on sizes can then be used to prove termination and productivity. An implementation of sized types exists in Agda, but it is currently inconsistent due to the addition of a largest size. We investigate an alternative approach, where intensional type theory is extended with a large type of sizes and parametric quantifiers over sizes. We show that inductive and coinductive types can be constructed in this theory, which improves on earlier work where this was only possible for the finitely-branching inductive types. The consistency of the theory is justified by an impredicative realisability model, which interprets the type of sizes as an uncountable ordinal.

Simulations and observations of the low-latitude magnetosphere-magnetosheath boundary layer indicate that the Kelvin-Helmholtz instability (KHI) drives vortex structures that enhance plasma mixing and magnetic reconnection, influencing transport and particle acceleration. We investigate the spatial localization, species dependence, and physical mechanisms of plasma mixing driven by the nonlinear evolution of the KHI. We perform high-resolution two-dimensional Particle-In-Cell simulations using a finite-Larmor-radius shear-flow initial configuration. Plasma mixing is quantified using particle labeling, a complementary density-based mixing tracer, and diagnostics of magnetic reconnection. Mixing across the shear layer is present but localized, occurring mainly in narrow interface regions and plasma structures. Ions mix more effectively than electrons, which remain largely frozen to field lines. Enhanced mixing spatially and temporally correlates with localized magnetic reconnection within and between KH vortices. Cross-boundary transport driven by the kinetic KHI remains intrinsically localized and is mediated by vortex advection and magnetic reconnection. Electron mixing is strongly constrained, indicating that kinetic-scale transport across collisionless shear layers remains limited.

Electric dipole and polarizability surfaces are developed for the methanol (CH$_3$OH) molecule using ab initio electronic structure data, computed at the CCSD/aug-cc-pVTZ level of theory, and equivariant neural networks. These property surfaces are used to compute vibrational infrared and Raman intensities with variational vibrational energies and wave functions. The energies and wave functions, fully accounting for the large-amplitude motion and tunneling splitting states, are from continued variational vibrational computations, based on earlier work [Sunaga et al., J. Chem. Phys., 2025, 163, 064101], up to 3700 cm$^{-1}$ beyond the zero-point vibration, now reaching the O-H stretching fundamental. All vibrational fundamentals, combination and overtone bands are in excellent agreement with available (gas-phase) experimental data, with a 2.2 cm$^{-1}$ root-mean-squared deviation of the fundamentals from experiment. These developments constitute an important step towards a quantitative and comprehensive exact quantum dynamics model of the methanol molecule, and a linelist for astrophysical applications.

The stochastic dynamics of flagellar beating for micro-swimmers, such as flagellated cells, sperms and microalgae, is widely thought to include a feedback mechanism between flagellar shape and the rate of activation/de-activation of the $N \gg 1$ driving molecular motors. In the context of the so-called rigid filament models, where the axoneme is described by a single degree of freedom $X(t)$, we investigate the effect of direct coupling between the activity dynamics of adjacent motors, parametrized by $K \ge 0$. A functional Fokker-Planck equation for $X$ and the state of the $N$ motors is obtained. In the limit of small coupling $K \ll 1$, we derive a system of equations governing the dynamics of the Fourier modes of the active motor density, obtaining estimates for several observables and the fluctuations' quality factor $Q$. For larger $K$ we resort to numerical simulations. The effect of introducing the coupling $K>0$ is to increase characteristic times and the beating period. Moreover for large $K$s the limit cycle becomes bi-stable, with abrupt avalanches of the motor dynamics. Increasing $K$ is similar to what observed in the case $K=0$ when the confining elastic force is strongly reduced. The quality factor of fluctuations has a non-monotonic behavior: it first increases with $K$, then decreases. This is accompanied by the reduction and eventual disappearance of regions where the fraction of activated motor is nor $0$ neither $1$.

I argue that if a special science satisfies certain key assumptions that are familiar from physicalist accounts of the special sciences and from physics, then its causal regularities have an associated notion of entropy, and that this causal entropy cannot decrease from a robust cause to its effect. Due to its analogy with the second laws of thermodynamics and statistical physics, I call the latter conclusion the causal second law. In this paper, I clarify the key assumptions, prove the causal second law, give sufficient conditions for causal entropy increase, relate the causal second law to statistical mechanics and thermodynamics, and argue that the reversibility objection does not threaten it. In addition, I claim that the causal second law is compatible with a non-metaphysical understanding of supervenience and the open systems view, argue that it does not imply a causal time arrow, reflect on relaxing the robustness condition, question whether it is necessary to invoke thermodynamics to show that special sciences' time arrows exist, and discuss a transition-relative-frequency-based, special-science-internal characterization of causal regularities.

We respond to the critique by Watters et al. (2026) of the statistical analyses in Villarroel et al. (2025) and Bruehl & Villarroel (2025). We argue that the critique conflates object-level validation with ensemble-level statistical inference and relies on a reduced, heterogeneously filtered subset originally constructed for a different scientific purpose. We further question whether the aggressively filtered subset used in Watters et al. (2026) demonstrates a meaningful improvement in sample purity, given the twenty-fold reduction in sample size. Our simple, visual check does not suggest that it does. The subset further lacks complete temporal information and is seriously statistically underpowered for testing the reported Earth-shadow deficit. We emphasise that the horizontal separation metric used for plate assignment and time reconstruction as in Watters et al. (2026) depends on the inclusion of the cos(Dec) factor to ensure geometric consistency. Any omission would alter plate assignment and inferred observation times. Moreover, the analyses presented in Watters et al. (2026) do not include uncertainty estimates or error propagation, limiting the interpretability of the claimed null results. We conclude that the principal findings reported in Villarroel et al. (2025) and Bruehl & Villarroel (2025) are not invalidated by the analyses presented in Watters et al. (2026).

Hardware-secured remote attestation is essential to establishing trust in the integrity of confidential virtual machines (cVMs), but is difficult to use in practice because verifying attestation evidence requires the use of hardware-specific cryptographic logic. This increases both maintenance costs and the verifiers' trusted computing base. We introduce the concept of self-verifying remote attestation evidence. Each attestation bundle identifies its verification logic in the form of a WebAssembly component that is downloaded by the verifier and executed. This approach transforms evidence verification into a platform-agnostic functionality that is implemented once for all platforms: the verifier measures the verification logic and then executes it to validate the evidence. As a result, verifiers can validate attestation evidence without any platform-specific code; the verification logic is just another measurement whose reference value can be checked with existing mechanisms. We implement this concept as TrustMee, a platform-agnostic verification driver for the Trustee framework. We demonstrate its functionality with self-verifying evidence for AMD SEV-SNP, Intel TDX, and Intel SGX attestations, producing attestation claims in the standard Entity Attestation Token (EAT) format.

Correlation functions and correlation lengths are frequently used to describe phase transitions in quantum systems, but they require an explicit choice of observables. The recently introduced information lattice instead provides an observable-independent way to identify where and at which scale information is contained in quantum lattice models. Here, we use it to study the difference between the metallic and insulating regime of one-dimensional noninteracting tight-binding chains. We find that the information per scale follows a power law in metals at low temperature and that Friedel-like oscillations are visible in the information lattice. At high temperature or in insulators at low temperature, the information per scale decays exponentially. Thus, the information lattice is a useful tool for analyzing the metal-insulator transition.

Recent concurrent work by Dupré la Tour and Fujii and by Hollender, Manurangsi, Meka, and Suksompong [ITCS'26] introduced a generalization of classical discrepancy theory to non-additive functions, motivated by applications in fair division. As many classical techniques from discrepancy theory seem to fail in this setting, including linear algebraic methods like the Beck-Fiala Theorem [Discrete Appl. Math '81], it remains widely open whether comparable non-additive bounds can be achieved. Towards a better understanding of non-additive discrepancy, we study coverage functions in a sparse setting comparable to the classical Beck-Fiala Theorem. Our setting generalizes the additive Beck-Fiala setting, rank functions of partition matroids, and edge coverage in graphs. More precisely, assuming each of the $n$ items covers only $t$ elements across all functions, we prove a constructive discrepancy bound that is polynomial in $t$, the number of colors $k$, and $\log n$.

Artificial intelligence (AI) has become a key enabler for next-generation wireless communication systems, offering powerful tools to cope with the increasing complexity, dynamics, and heterogeneity of modern wireless environments. To illustrate the role and impact of AI in wireless communications, this paper takes collaborative spectrum sensing (CSS) in cognitive and intelligent wireless networks as a representative application and surveys recent advances from an AI perspective. We first introduce the fundamentals of CSS, including the general framework, classical detector design, fusion strategies and evaluation metrics. Then, we present an overview of the state-of-the-art research on AI-driven CSS, classified into three categories according to learning paradigms: discriminative deep learning (DL), generative DL models, and deep reinforcement learning (DRL). Building on this, we explore AI-empowered semantic communication (SemCom) as a paradigm-shifting solution for CSS. By extracting and transmitting task-relevant features, SemCom upgrades CSS from a computation-centric approach to a highly efficient joint communication and computation framework. Both single-user and multi-user SemCom scenarios are elaborated in detail. Finally, we discuss limitations, open challenges, and future research directions at the intersection of AI and wireless communication.

Consider a community of scientists whose labs are each capable of conducting a different set of experiments. The scientists want to work together to confirm a new hypothesis, but to ensure blindness, their labs generally prohibit the scientists from communicating with each other. Further, each scientist can only make so many retractions to their lab before having to cease inquiry and suspend judgement forever. How might the scientists coordinate whether to affirm or suspend judgement on this hypothesis in light of their private experiments so that their labs are guaranteed to converge to the same conclusion and that this conclusion will not be a false positive? Call this problem 'inductive coordinated attack.' In this paper, we develop a logic for solving inductive coordinated attack by determining when and how a hypothesis can become what we call 'common inductive knowledge.' We begin by precisifying Lewis' account of common knowledge in Convention which describes the generation of higher-order expectations between agents as hinging upon agents' inductive standards and a shared witness. Our language has a rather rich syntax in order to capture equally rich notions central to Lewis' account; for instance, we speak of an agent 'having inductive reason to believe' a proposition and one proposition 'indicating' to an agent that another proposition holds. This syntax affords a novel topological semantics which, following Kelly 1996's approach in The Logic of Reliable Inquiry, takes as primitives agents' information bases. In particular, we endow each agent with a 'switching tolerance' meant to represent their personal inductive standards for learning. After establishing soundness of our proof system with respect to this semantics, we conclude by showing how our logic can be used to solve inductive coordinated attack.

We present a statistical mechanics framework for modeling equilibrium friction coefficients using the Generalized Langevin Equation (GLE). We show that the kernel, obtained via the Fluctuation-Dissipation Theorem (FDT) from the stochastic force autocorrelation measured in a thermal equilibrium state, is sufficient to model the dynamics of the system in a Non-Equilibrium Steady State (NESS). This approach provides a computationally efficient path to modeling complex equilibrium friction problems. We apply this framework to the canonical problem of test particle drag in a uniform plasma. The GLE formalism is shown to naturally capture non-Markovian phenomena through the moments of the kernel, including an effective mass renormalization and oscillatory relaxation. We demonstrate that the standard Chandrasekhar stopping power formula arises naturally as the Markovian limit of this equilibrium memory kernel. These theoretical predictions are quantitatively validated by direct Particle-in-Cell simulations, which confirm the predicted oscillatory structure of the memory kernel. This work thus establishes a practical method for predicting equilibrium friction properties from first-principles equilibrium simulations.

We study the thermodynamic performance of a periodic quantum Otto cycle operating on the single-impurity Anderson model. Using a decomposition of the time-evolution generator based on the principle of minimal dissipation, combined with the numerically exact hierarchical equations of motion (HEOM) method, we analyze the operating regimes of the quantum thermal machine and investigate effects of Coulomb interactions, strong system-reservoir coupling, and energy level alignments. Our results show that Coulomb interaction can change the operating regimes and may lead to an enhancement of the efficiency.

Objectives. Major research and implementation efforts have been devoted to indexing articles according to the major topics discussed, but much less effort to indexing their publication types and study designs (collectively, PTs). In this Perspective, we discuss how indexing PTs differs from topical MeSH indexing and requires a different approach. Materials and Methods. Rather than focus on the technical aspects of machine learning-based indexing models, we emphasize the goals and purposes for which biomedical articles are indexed, and the surprisingly thorny question of how indexing systems should be evaluated. Results. Topical Medical Subject Heading (MeSH) terms are assigned to articles that cover the major topics discussed; when more than one term is applicable, only the most specific term is assigned. In contrast, PTs are assigned to articles that have a given structure or use a particular design. To meet the needs of end-users, particularly groups involved in evidence syntheses, PT indexing needs to be comprehensive and employ probabilistic goodness-of-fit prediction scores. Whereas existing NLM hierarchies place publication types and study design-related terms on separate trees from each other, we have created a unified hierarchy that permits more appropriate retrieval via automatic expansion. Discussion. Automated PT indexing systems should allow users to input article records or full-text PDFs and receive scores in real time. This will offer consistent indexing across bibliographic databases, as well as preprints and unpublished manuscripts. Conclusions. Automated PT indexing systems, properly designed and implemented, hold the promise of greatly improving the retrieval of biomedical articles, saving substantial effort when writing evidence syntheses and benefiting other users as well.

Background: The OpenSSF Scorecard is widely used to assess the security posture of open-source software repositories, with the Maintained metric serving as a key indicator of recent maintenance activities, helping users identify actively maintained projects and potentially abandoned dependencies. However, the metric is inherently retrospective, providing only a short-term snapshot based on the past 90 days of repository activity and offering no insight into the future. This limitation complicates risk assessment for developers and organizations that rely on open-source dependencies. Aims: In this paper, we investigate the feasibility of forecasting future maintenance activities as captured by the OpenSSF Maintained score. Method: Focusing on 3,220 GitHub repositories linked to one of the top 1% most central PyPI libraries, as ranked by PageRank, we reconstruct historical Maintained scores over a three-year period and frame the problem as a multivariate time series forecasting task. We study four target representations: the raw Maintained score (0-10), a bucketed score capturing low (0-2), moderate (3-7), and high (8-10) maintenance levels, the numerical trend slope between consecutive scores, and categorical trend types (downward, stable, upward). We compare a machine learning model (Random Forest) and a deep learning model (LSTM) using training windows of 3-12 months and forecasting horizons of 1-6 months. Results: Our results show that future maintenance activity can be forecasted with meaningful accuracy, particularly when using aggregated representations such as bucketed scores and trend types leading to accuracies above 0.95 and 0.79. Notably, simpler machine learning models perform at least on par with deep learning approaches, suggesting that effective forecasting does not require complex architectures.

The Deep Underground Neutrino Experiment (DUNE) Phase-II Far Detector is considering an approximately 2000\,m$^2$ photon detection system to achieve a target mean light yield of 180\,PE/MeV. Meeting this requirement demands scalable, cost-effective, and high-quality wavelength-shifter (WLS) coatings capable of converting 127\,nm liquid-argon scintillation light into visible photons with controlled and reproducible optical performance. We report on the successful realization of an industrial physical vapor deposition (PVD) process for \textit{p}-terphenyl (pTP) coatings, adapted from vacuum deposition techniques developed for OLED display manufacturing, to produce uniform WLS layers on large-area inorganic substrates, a task traditionally challenged by adhesion and uniformity issues at organic--inorganic interfaces. Surface characterization by profilometry and spectroscopic measurements demonstrates edge-region thickness variation below 10\% and emission spectra consistent with high-quality pTP reference samples. The industrial process demonstrates reproducibility, scalability, and significantly reduced production time compared to laboratory-based methods, while maintaining optical characteristics consistent with established pTP reference samples. These results establish a viable pathway for mass production of high-performance pTP coatings for DUNE FD3 and future neutrino experiments, from a coating manufacturing and process standpoint. Detector-level performance validation, including quantitative VUV conversion efficiency measurements at 127\,nm, is identified as future work.

Machine learning property attestations allow provers (e.g., model providers or owners) to attest properties of their models/datasets to verifiers (e.g., regulators, customers), enabling accountability towards regulations and policies. But, current approaches do not support generative models or large datasets. We present PAL*M, a property attestation framework for large generative models, illustrated using large language models. PAL*M defines properties across training and inference, leverages confidential virtual machines with security-aware GPUs for coverage of CPU-GPU operations, and proposes using incremental multiset hashing over memory-mapped datasets to efficiently track their integrity. We implement PAL*M on Intel TDX+NVIDIA H100 and evaluate it using state-of-the-art models and datasets, showing PAL*M is efficient, incurring < 11% overhead for common operations. Finally, we use the Tamarin Prover symbolic verification tool to formally model PAL*M's property attestation protocol, confirming that its security guarantees are upheld under the defined threat model.

This paper considers an $N$-server distributed computing setting with $K$ users requesting functions that are arbitrary multivariable polynomial evaluations of $L$ real (potentially non-linear) basis subfunctions, where each function output is raised to a bounded power. Our aim is to seek efficient task allocation and data communication techniques that reduce computation and communication costs. To this end, we take a tensor-theoretic approach, in which we represent the requested non-linearly decomposable functions using a properly designed tensor $\bar{\mathcal{F}}$, whose sparse decomposition into a tensor $\bar{\mathcal{E}}$ and a matrix $\mathbf{D}$ directly defines the task assignment, connectivity, and communication patterns. We design a lossless achievable scheme that integrates fixed-support SVD-based tensor factorization with multi-dimensional tiling of $\bar{\mathcal{E}}$ and $\mathbf{D}$, followed by a bipartite graph matching-based recursive assignment of tiles. This step transforms an overlapping decomposition into a disjoint one and reduces the resulting sum rank of the tiles, thereby decreasing the number of required servers. Under mild dimensionality conditions, we derive an explicit zero-error characterization of the achievable system rate $K/N$. Numerical simulations demonstrate the computational and communication savings over existing state-of-the-art matrix factorization approaches across a wide range of system parameters.

Integrating Sensing and Communications (ISAC) has emerged as a promising paradigm for Sixth Generation (6G) and Wi-Fi 7 networks, with the communication-centric approach being particularly attractive due to its compatibility with current standards. Typical communication signals comprise both deterministic known pilot signals and random unknown data payloads. Most existing approaches either rely solely on pilots for positioning, thereby ignoring the radar information present in the received data symbols that constitute the majority of each frame, or rely on data decisions, which bounds positioning performance to that of the communication system. To overcome these limitations, we propose a novel method that extracts positioning information from data payloads without decoding them. We consider an opportunistic scenario in which communication signals from a user are captured by a passive radar equipped with a uniform linear array of antennas. We show that, in this setting, the estimation can be efficiently implemented using Fast Fourier Transforms. Finally, we demonstrate superior localization performance compared to existing methods in the literature through numerical simulations.

Let $k$ be a perfect field with $\mathrm{char}(k)\neq 2,3$, set $K=k(t)$, and let $\mathcal{W}_n^{\min}$ be the moduli stack of minimal elliptic curves over $K$ of Faltings height $n$, constructed via the height-moduli framework of Bejleri-Park-Satriano applied to $\overline{\mathcal{M}}_{1,1}\simeq\mathcal{P}(4,6)$. The Shioda-Tate formula $ρ(S)=T(S)+\mathrm{rk}(E/K)$ decomposes the Picard rank of the associated elliptic surface into the trivial lattice rank, which is local (determined by Kodaira fiber types), and the Mordell-Weil rank, which is global. The motivic height zeta function weighted by the trivial lattice rank is rational in $s=t^{1/12}$ in the dimensionally completed Grothendieck ring, via a combination of exact Euler products on the isotrivial loci $j\equiv 0, 1728$ and a motivic discriminant stabilization adapting Vakil-Wood to $Δ=4a_4^3+27a_6^2$; over $k=\mathbb{C}$, this yields bidegree-wise Hodge number stabilization. The Kudla-Millson theta correspondence shows that the distribution of new Mordell-Weil sections by canonical height is governed by a modular form of weight $6n-2$ for $\mathrm{SL}_2(\mathbb{Z})$. Combining Shepherd-Barron's diagonalization of the Gauss-Manin connection with Kodaira-Spencer transversality, we establish unconditionally that at every Faltings height $n\ge 3$ and for every $1 \le r \le \lfloor(10n-2)/(n-1)\rfloor$, there exist infinitely many stable elliptic surfaces with Mordell-Weil rank $\mathrm{rk}(E/K) \ge r$, and that infinitely many canonical heights $\hat{h}(P)=d$ are realized by Mordell-Weil sections.

Recently, sharp matrix concentration inequalities~\cite{BBvH23,BvH24} were developed using the theory of free probability. In this work, we design polynomial time deterministic algorithms to construct outcomes that satisfy the guarantees of these inequalities. As direct consequences, we obtain polynomial time deterministic algorithms for the matrix Spencer problem~\cite{BJM23} and for constructing near-Ramanujan graphs. Our proofs show that the concepts and techniques in free probability are useful not only for mathematical analyses but also for efficient computations.

Recent progress in ultrafast x-ray sources helped establish x-rays as an important tool for probing lattice and magnetic dynamics initiated by femtosecond optical pulses. Here, we explore the potential of ultrashort hard x-ray pulses for driving magnetic dynamics. We use a transient grating technique in which a spatially periodic x-ray excitation pattern gives rise to material excitations at a well-defined wave vector, whose dynamics are monitored via diffraction of an optical probe pulse. The excitation of a ferrimagnetic gadolinium bismuth iron garnet film placed in an external tilted magnetic field by x-rays at the Gd L3 edge results in both magnetic and non-magnetic transient gratings whose contributions to the diffracted signal are separated by polarization analysis. We observe the magnetization precession at both longitudinal acoustic and spin wave frequencies. An analysis with the Landau-Lifshitz-Gilbert equation indicates that the magnetization precession is driven by strain resulting from thermal expansion induced by absorbed x-rays. The results establish x-ray transient gratings as a tool for driving coherent phonons and magnons, with the potential of accessing wave vectors across the entire Brillouin zone.

For a compact and connected Lie group $G$, we present an explicit construction of an $\mathbb{S}^1$-gerbe over the differentiable stack $[G/G]$ in the framework of $\mathbb{S}^1$-central extensions of Lie groupoids. This gives a complete proof of the construction outlined earlier by Behrend--Xu--Zhang, together with an explicit proof of the differential-form identity stated there without proof. In particular, when $G$ is compact, simple, and simply connected, the Dixmier--Douady class of the resulting gerbe is the canonical generator of ${\rm H}^3_G(G,\mathbb Z)$.

This article investigates the well-posedness of weak solutions to non-linear parabolic PDEs driven by rough coefficients with rough initial data in critical homogeneous Besov spaces. Well-posedness is understood in the sense of existence and uniqueness of maximal weak solutions in suitable weighted $Z$-spaces in the absence of smallness conditions. We showcase our theory with an application to rough reaction--diffusion equations. Subsequent articles will treat further classes of equations, including equations of Burgers-type and quasi-linear problems, using the same approach. Our toolkit includes a novel theory of hypercontractive singular integral operators (SIOs) on weighted $Z$-spaces and a self-improving property for super-linear reverse Hölder inequalities.

Let $λ$, $μ$, $λ'$, $μ'$ be partitions. The conjecture of Lam, Postnikov and Pylyavskyy states that, if $λ+μ= λ' + μ'$, and $\min(λ_i-λ_j, μ_i-μ_j) \leq λ'_i - λ'_j \leq \max(λ_i-λ_j, μ_i-μ_j)$ for all $1 \leq i<j \leq n$, then $s_{λ'} s_{μ'} - s_λ s_μ$ is Schur nonnegative. We prove this conjecture. Our proof is based on two key ideas. First, we introduce a new combinatorial model for Littlewood-Richardson coefficients which we name ``skeps", which are similar to but distinct from Knutson and Tao's hives. Second, we use tools from Murota's theory of L-convexity to prove an L-log-concavity theorem for skeps.

The first search for the $B_s^0\rightarrow K^-π^+γ$ decay in the range $796<m(K^-π^+)<1800\,\text{MeV/}c^2$ is performed using data from proton-proton collisions collected by the LHCb experiment at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9 fb$^{-1}$. The photons are reconstructed through their conversion into an electron-positron pair, which significantly improves the mass resolution of the reconstructed decays with respect to decays with an unconverted photon. A signal excess with a significance of 3.5 standard deviations is measured, constituting the first experimental evidence for this decay. In the range $796<m(K^-π^+)<996\,\text{MeV/}c^2$, the ratio ${\cal R}$ between the branching fractions of the signal decay and the favoured $\kern 0.18em\overline{\kern -0.18em B}{}^0\rightarrow K^- π^+γ$ decay is measured to be ${\cal R} = (3.7\pm1.2\pm0.4)\times10^{-2}$ where the first uncertainty is statistical and the second is systematic. This measurement is consistent with the value predicted in the Standard Model. In the range $996<m(K^-π^+)<1800\,\text{MeV/}c^2$, the ratio ${\cal R} = (0.2\pm2.7\pm1.3)\times10^{-2}$ is measured.