To understand the nature of $X(2075)$ and $X(2085)$ observed by the BESIII collaboration in the $p\barΛ$ system, we systematically investigate the possibility that these states are compact hexaquark with triquark-antitriquark configurations for the first time. Within the framework of QCD sum rules, the mass spectrum and decay constants of such hexaquark states with quantum numbers $J^P=0^-, 0^+, 1^-, 1^+$ are studied. Consequently, six independent and nondegenerate hexaquark candidates are obtained, among which two $J^P = 1^-$ states exhibit masses consistent with $X(2075)$, while the two $J^P = 1^+$ states differ markedly from the mass of $X(2075)$ or $X(2085)$. The remaining two states with $J^P = 0^+$ and $0^-$ may serve as predictions for potential compact hexaquark configurations. Furthermore, the possible decay modes of these hexaquark states are analyzed, which could be the experimental signatures for their identification.

We theoretically investigate the impact of correlated hopping on thermoelectric transport through a quantum dot coupled to ferromagnetic leads. Using the accurate numerical renormalization group method, we analyze the transport characteristics, focusing on the interplay between electronic correlations, spin-dependent transport processes, and thermoelectric response. We calculate the electrical conductance and thermopower as functions of the dot energy level, lead polarization, and the amplitude of correlated hopping. Moreover, we analyze the effect of competing correlations on the Kondo resonance and discuss the asymmetry of conductance peaks under the influence of the exchange field. We demonstrate that the presence of correlated hopping is responsible for asymmetric spin-dependent transport characteristics. Our results provide valuable insight into how correlated hopping affects spin-dependent transport and thermoelectric efficiency in quantum dot systems with ferromagnetic contacts.

We report a random singlet ground state in the $S=\frac{1}{2}$ Heisenberg pyrochlore antiferromagnet NaCdCu$_2$F$_7$. Cationic Na$^+$/Cd$^{2+}$ disorder on the pyrochlore $A$ site generates a broad distribution of Cu$^{2+}$--F$^-$--Cu$^{2+}$ exchange couplings, introducing intrinsic magnetic bond disorder. Despite strong antiferromagnetic interactions ($θ_{\mathrm{CW}}=-72$~K), no magnetic order or global spin freezing is observed in DC and AC susceptibility, specific heat or $^{23}$Na nuclear magnetic resonance to 120 mK, with muon spin relaxation experiments confirming persistent spin dynamics to 58 mK. $T$-linear specific heat, a Curie-like susceptibility tail, and power-law scaling with data collapse in $χ(T)$, $M(H)$, $C_{\mathrm{mag}}/T$, $^{23}$Na $(1/T_1T)$ and the muon spin polarization $P(t)$ reveal a disorder-driven network of random singlets and orphan spins. Scaling across multiple bulk and local probes is consistent with a broad distribution of exchange energies, $P[\mathcal{J}] \sim \mathcal{J}^{-α}$. This behavior contrasts with previously-studied Na$A''B_2$F$_7$ pyrochlore fluorides, where magnetic bond disorder precipitates spin-glass freezing, underscoring the crucial role of strong $S=\frac{1}{2}$ quantum fluctuations in NaCdCu$_2$F$_7$.

We present a comprehensive evaluation of pretrained speech embedding systems for the detection of dysarthric speech using existing accessible data. Dysarthric speech datasets are often small and can suffer from recording biases as well as data imbalance. To address these we selected a range of datasets covering related conditions and adopt the use of several cross-validations runs to estimate the chance level. To certify that results are above chance, we compare the distribution of scores across these runs against the distribution of scores of a carefully crafted null hypothesis. In this manner, we evaluate 17 publicly available speech embedding systems across 6 different datasets, reporting the cross-validation performance on each. We also report cross-dataset results derived when training with one particular dataset and testing with another. We observed that within-dataset results vary considerably depending on the dataset, regardless of the embedding used, raising questions about which datasets should be used for benchmarking. We found that cross-dataset accuracy is, as expected, lower than within-dataset, highlighting challenges in the generalization of the systems. These findings have important implications for the clinical validity of systems trained and tested on the same dataset.

A functional digraph is a finite digraph in which each vertex has a unique out-neighbor. Considered up to isomorphism and endowed with the directed sum and product, functional digraphs form a semigroup that has recently attracted significant attention, particularly regarding its multiplicative structure. In this context, a functional digraph $X$ divides a functional digraph $A$ if there exists a functional digraph $Y$ such that $XY$ is isomorphic to $A$. The digraph $X$ is said to be prime if it is not the identity for the product, and if, for all functional digraphs $A$ and $B$, the fact that $X$ divides $AB$ implies that $X$ divides $A$ or $B$. In 2020, Antonio E. Porreca asked whether prime functional digraphs exist, and in 2023, his work led him to conjecture that they do not. However, in 2024, Barbora Hudcová discovered that this result had already been proved by Ralph Seifert in 1971, in a somewhat forgotten paper. The terminology in that work differs significantly from that used in recent studies, the framework is more general, and the non-existence of prime functional digraphs appears only as a part of broader results, relying on (overly) technical lemmas developed within this general setting. The aim of this note is to present a much more accessible version of Seifert's proof $-$ that no prime functional digraph exists $-$ by using the current language and simplifying each step as much as possible.

Chimeric antigen receptor (CAR) T cell therapy has shown remarkable success in hematological malignancies, yet patient responses remain highly variable and the roles of CD4+ and CD8+ subsets are not fully understood. We present an extended mathematical framework of CAR-T cell dynamics that explicitly models CD4+ helper and CD8+ cytotoxic lineages and their interactions with tumor antigen burden. Building on the Kirouac et al. (2023) model of antigen-regulated memory-effector-exhaustion transitions, our system of differential equations incorporates CD4-mediated modulation of CD8+ proliferation, cytotoxicity, and memory regeneration through biologically grounded, saturating interactions. Sensitivity analyses identify effector proliferation, antigen turnover, and CD8+ expansion rates as dominant drivers of treatment outcome. Virtual patient simulations recover reported qualitative trends in CAR-T composition, including enhanced expansion and tumor clearance for defined CD4:CD8 products relative to CD8-only formulations, while also revealing inter-patient variability and time-dependent effects. To assess the practical limits of patient-level prediction under parameter uncertainty, we introduce controlled noise into key parameters and show that direct mechanistic classification rapidly degrades. We then demonstrate that a simple feed-forward neural network can partially recover predictive signal from noisy inputs, outperforming a naive baseline while remaining consistent with mechanistic sensitivities. This work positions the extended model as a hypothesis generator, and illustrates how data-driven methods can complement mechanistic modeling when parameter uncertainty constrains predictive confidence.

We derive a vector generalization of the curvature-corrected Cramér--Rao bound (CRB) in the nonasymptotic regime using a Hilbert space square-root embedding. Building on previous scalar results, we establish a \emph{directional} curvature correction derived from the second fundamental form of the model manifold. To obtain matrix-valued refinements, we formulate sufficient conditions for a conservative matrix-level correction using a semidefinite program (SDP) based on sum-of-squares (SOS) relaxations. The framework is rigorously illustrated with two distinct geometries: (i) a curved Gaussian location model, which reveals a characteristic \textit{pinching effect} where directional bounds vanish along principal axes despite non-zero extrinsic curvature and classical subspace-based bounds using the second-order Bhattacharyya matrix provide overly optimistic variance predictions that fail to account for the manifold's directional topology, and (ii) a spherical multinomial model where the curvature is isotropic. Our results demonstrate that while classical second-order corrections using the Bhattacharyya matrix provide useful benchmarks derived from the local coordinate basis, the proposed directional and SOS-certified bounds offer a more faithful and geometry-consistent representation of the directional sensitivity and fundamental limits of estimation in curved statistical families.

This paper proposes a method for reconstructing three-dimensional turbulent flows from sparse measurements without the need for ground truth data during training. A weight-sharing network is developed to infer the full flow fields from measurements of velocity sampled at three planes and boundary pressure at one additional plane, inspired by experimental configurations. The weight-sharing network shares identical parameters along homogeneous directions, which results in efficient data utilization and reduced computational memory requirements. First, we compare the weight-sharing network to the PC-DualConvNet, adapted from prior work, by reconstructing a 3D Kolmogorov flow from noise-free measurements with a snapshot-enforced loss. Both networks accurately recover time-averaged 3D flow fields and the correct energy spectrum up to wavenumber 10. The weight-sharing network has the ability to infer flow structures distant from measurement planes. Second, we carry out reconstruction from measurements corrupted with white noise (SNR 15) using a mean-enforced loss. We show that, for the weight-sharing network, validation sensor loss on unseen data decreases with training sensor loss -- unlike PC-DualConvNet. This shows improved generalization and that training sensor loss estimates generalization error. The weight-sharing network offers good generalization, parameter efficiency, and hyperparameter robustness. The proposed method opens the possibility of three-dimensional flow reconstruction from experiments.

Auditory attention and selective phase-locking are central to human speech understanding in complex acoustic scenes and cocktail party settings, yet these capabilities in multilingual subjects remain poorly understood. While machine understanding of natural speech has advanced in recent years, questions persist about comprehension of overlapped and mixed-channel speech. We propose a systematic paradigm for studying humans and machines in speech question-answering tasks in multilingual settings with clean and mixed-channel speech. For human listeners, selective attention to a target speaker was significantly better in their native language (L1) than in their second language (L2). For machine listening, speech-based large language models (LLMs) match or exceed human performance in clean, single-speaker conditions but often struggle to selectively attend in two-speaker settings. These results reveal a key divergence: humans rely on attentional cues that are more streamlined in their native language, whereas LLMs default to parallel information extraction which exceed human skills.

This work presents a geometric refinement of the classical Cramér--Rao bound (CRB) in the non-asymptotic regime by incorporating curvature-aware corrections based on the second fundamental form associated with the statistical model manifold. That is, our formulation shows that relying on the extrinsic geometry of the square root embedding of the manifold in the ambient Hilbert space comprising square integrable functions with respect to a fixed base measure offers a rigorous (and intuitive) way to improve upon the CRB and some of its variants, such as the Bhattacharyya-type bounds, that use higher-order derivatives of the log-likelihood. Precisely, the improved bounds in the latter case make explicit use of the elegant framework offered by employing the Faà di Bruno formula and exponential Bell polynomials in expressing the jets associated with the square root embedding in terms of the raw scores. The interplay between the geometry of the statistical embedding and the behavior of the estimator variance is quantitatively analyzed in concrete examples, showing that our corrections can meaningfully tighten the lower bound, suggesting further exploration into connections with estimator efficiency in more general situations.

AI technologies are increasingly deployed in high-stakes domains such as education, healthcare, law, and agriculture to address complex challenges in non-Western contexts. This paper examines eight real-world deployments spanning seven countries and 18 languages, combining 17 interviews with AI developers and domain experts with secondary research. Our findings identify six cross-cutting factors - Language, Institution, Safety, Task, End-User Demography, and Domain - that structured how systems were designed and deployed. These factors were shaped by Sociocultural (diversity, practices), Institutional (resources, policies), and Technological (capabilities, limits) influences. We find that building effective AI systems required extensive collaboration between AI developers and domain experts, with human resources proving more critical to achieving safe and effective outcomes in high-stakes domains than technological expertise alone. Additionally, we present 12 guidelines synthesizing these dynamics for designing AI for social good systems that are culturally grounded, equitable, and responsive to the needs of non-Western contexts.

Projective geodesic extensions are reparametrizations of the trajectories of a nonholonomic mechanical system (with only a kinetic energy Lagrangian), in such a way that they can be interpreted as part of the geodesics of a Riemannian metric. We derive necessary and sufficient conditions for the existence of these extensions, in the case where the constrained Lagrangian remains preserved up to a conformal transformation. When the nonholonomic system has a symmetry group (a Chaplygin system), we clarify the relation between projective geodesic extensions and closely related concepts, such as $ϕ$-simplicity, invariant measures and Hamiltonization. Throughout the paper, new and relevant examples illustrate the key differences between all these concepts.

In this paper, we design two chapters to discuss trade dynamics with heterogeneous fluctuations, contributing new insights to macroeconomic issues related to international trade. In the first chapter, we model general exchange rate fluctuations through stochastic processes and analyze the impact of heterogeneous price shocks on export competitiveness. We find that monetary policy and innovation both show positive effects on export trade, while monetary policy stabilizes exchange rate fluctuations to comprehensively boost provincial export competitiveness, innovation reduces its reliance on exchange rate mechanisms. The optimal policy according to exchange rate fluctuations aims to solve the wealth distribution of exporters, and it suggests that optimal policy should promote dynamic transitions in trade patterns rather than maintain existing comparative advantages in heterogeneous trade structures. In the second chapter, we model labor market fluctuations and the ability to utilize production factors through stochastic processes, and we analyze the impact of heterogeneous aggregate production shocks on general international trade. We find that labor market fluctuations only benefit international trade under the cooperation policy. Moreover, for both sanction and cooperation policy scenarios, positive shocks (i.e., shocks where average wage growth in the labor market exceeds unemployment) strengthen their impact on import trade while weakening their impact on export trade, and vice versa. Regarding the theories proposed in these two chapters, we prove them through empirical analyses using the provincial data of China.

Meta-black-box optimization has been significantly advanced through the use of large language models (LLMs), yet in fancy on constrained evolutionary optimization. In this work, AwesomeDE is proposed that leverages LLMs as the strategy of meta-optimizer to generate update rules for constrained evolutionary algorithm without human intervention. On the meanwhile, $RTO^2H$ framework is introduced for standardize prompt design of LLMs. The meta-optimizer is trained on a diverse set of constrained optimization problems. Key components, including prompt design and iterative refinement, are systematically analyzed to determine their impact on design quality. Experimental results demonstrate that the proposed approach outperforms existing methods in terms of computational efficiency and solution accuracy. Furthermore, AwesomeDE is shown to generalize well across distinct problem domains, suggesting its potential for broad applicability. This research contributes to the field by providing a scalable and data-driven methodology for automated constrained algorithm design, while also highlighting limitations and directions for future work.

The notorious sign problem severely limits the applicability of quantum Monte Carlo (QMC) simulations, as statistical errors grow exponentially with system size and inverse temperature. A recent proposal of a quantum-computing stochastic series expansion (qc-SSE) method suggested that the problem could be avoided by introducing constant energy shifts into the Hamiltonian. Here we critically examine this framework and show that it does not strictly resolve the sign problem for Hamiltonians with non-commuting terms. Instead, it provides a practical mitigation strategy that suppresses the occurrence of negative weights. Using the antiferromagnetic anisotropic XY chain as a test case, we analyze the dependence of the average sign on system size, temperature, anisotropy, and shift parameters. An operator contraction method is introduced to improve efficiency. Our results demonstrate that moderate shifts optimally balance sign mitigation and statistical accuracy, while large shifts amplify errors, leaving the sign problem unresolved but alleviated.

We develop, simulate and extend an initial proposition by Chaves et al. concerning a random incompressible vector field able to reproduce key ingredients of three-dimensional turbulence in both space and time. In this article, we focus on the important underlying Gaussian framework. Presently, the statistical spatial structure of this velocity field is consistent with a divergence-free fractional Gaussian vector field that encodes all known properties of homogeneous and isotropic fluid turbulence at a given finite Reynolds number, up to second-order statistics. The temporal structure of the velocity field is introduced through a stochastic evolution of the respective Fourier modes. In the simplest picture, Fourier modes evolve according to an Ornstein-Uhlenbeck process, where the characteristic time scale depends on the wave-vector amplitude. For consistency with direct numerical simulations (DNSs) of the Navier-Stokes equations, this time scale is inversely proportional to the wave vector amplitude. As a consequence, the characteristic velocity that governs the eddies is independent of their size and is related to the velocity standard deviation, which is consistent with some features of the so-called sweeping effect. To ensure differentiability in time while respecting the Markovian nature of the evolution, we use the methodology developed by Viggiano et al. to propose a fully consistent stochastic picture. We finally derive analytically all statistical quantities in a continuous setup and develop precise and efficient numerical schemes of the corresponding periodic framework. Both exact predictions and numerical estimations of the model are compared to DNSs provided by the Johns Hopkins database.

We prove that every functor from the category of Hilbert spaces and linear isometric embeddings to the category of sets which preserves directed colimits must be essentially constant on all infinite-dimensional spaces. In other words, every finitary set-valued imaginary over the theory of Hilbert spaces, in a broad signature-independent sense, must be essentially trivial. This extends a result and answers a question by Lieberman--Rosický--Vasey, who showed that no such functor on the supercategory of Hilbert spaces and injective linear contractions can be faithful.

A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three distinct empirical examples are presented: (1) examine the differences between group means of correlated (repeated) or independent samples, (2) examine if a mean vector equals to a specific fixed vector, and (3) investigate if samples come from a specific population distribution. The simulation examples indicate that the new test has similar statistical power as uniformly the most powerful (unbiased) tests. Moreover, these examples demonstrate that the new test is a powerful goodness-of-fit test.

In this article, we analyze semi-discrete finite element approximation and full discretization of a fourth-order stochastic pseudo-parabolic equation in a bounded convex polygonal domain driven by additive Wiener noise. We use the finite element method for spatial discretization and the semi-implicit method for temporal discretization, and obtain strong convergence rates with respect to both the spatial and temporal mesh sizes. Numerical experiments are presented to support the theoretical convergence rates.

Wavelength division multiplexers are fundamental to the functioning and performance of integrated photonic circuits, with applications ranging from optical interconnects to sensing and quantum technologies. Current solutions are limited by trade-offs between channel spacing, crosstalk, insertion loss, and device footprint. Here, we develop a novel design approach that co-optimizes inverse-designed wavelength division multiplexers and distributed Bragg gratings to achieve ultra-low crosstalk without compromising insertion loss. We experimentally demonstrate less than -40 dB crosstalk for wavelength channel spacing of 15 nm in foundry-compatible silicon and silicon nitride devices across the telecommunications C- and L-bands. Our design process is highly adaptable, allowing for seamless scaling to a greater number of output channels, different spectral windows, and easy translation across various material platforms.

The stellar haloes and intra-cluster light around galaxies are crucial test beds for dark matter (DM) physics and galaxy formation models. We consider the role that the numerical resolution plays in the modelling of these systems by studying the stripping of satellites in the IllustrisTNG cosmological simulations. We focus on host haloes of total halo mass $M_{\mathrm 200c}=10^{12-15}M_{\odot}$ and satellites of stellar mass $>10^{7}$$M_{\odot}$, and compare stellar halo / satellite properties across 9 IllustrisTNG runs with baryonic particle mass resolution between $8.5\times10^4M_{\odot}$ and $7\times10^8$$M_{\odot}$, using a Lagrangian-region technique to identify counterpart satellites across different resolution simulations of the same volume. We publish the corresponding catalogues alongside this paper. We demonstrate that the stripping of DM from satellites that orbit in group- and cluster-mass hosts is largely independent of resolution at least until 90 per cent of their initial mass at infall has been stripped. We do not find evidence for spurious disruption of galaxies due to insufficient resolution for the satellite masses we consider. By contrast, the stripping of stellar mass is strongly resolution-dependent: each factor of 8 improvement in particle stellar mass typically adds 2Gyr to the stripping time. Improved numerical resolution within the IllustrisTNG model generally results in more compact satellites with larger stellar masses, which in turn generate more centrally concentrated stellar haloes and intra-cluster mass profiles. However, the concomitant increase in stellar mass with increased resolution of both satellites and hosts may still be the cause for the overprediction of the stellar halo mass at large host radii relative to observations seen in some previous studies.

Galactic diffuse emissions in gamma rays and neutrinos arise from interactions of cosmic rays with the interstellar medium and probe the cosmic-ray intensity away from the Solar system. Model predictions for those are influenced by the properties of cosmic-ray sources, and understanding the impact of cosmic-ray sources on Galactic diffuse emissions is key for interpreting measurements by LHAASO, Tibet AS-gamma, IceCube, and the upcoming SWGO. We consider supernova remnants as prototypical cosmic-ray sources and study the impact of their discreteness on the Galactic diffuse emissions in different source injection and near-source transport models in a stochastic Monte Carlo study. Three lessons exemplify the results of our simulations: First, the distributions of Galactic diffuse emission intensities can be described by a mixture model of stable laws and Gaussian distributions. Second, the maximal deviations caused by discrete sources across the sky depend on energy, reaching typically tens of percent in burst-like and energy-dependent escape scenarios but order unity or larger in a time-dependent diffusion scenario. Third, the additional model uncertainty from source stochasticity is subdominant in burst-like and energy-dependent escape scenarios, but becomes sizeable above some tens of TeV in the time-dependent diffusion scenario, where it can help reconcile model predictions with LHAASO measurements. With increased spatial resolution, especially at energies beyond tens of TeV, measurements of Galactic diffuse emissions can be expected to constrain source models and locate cosmic ray sources.

Reasoning about floating-point arithmetic is notoriously hard. While static and dynamic analysis techniques or program repair have made significant progress, more work is still needed to make them relevant to real-world code. On the critical path to that goal is understanding what real-world floating-point code looks like. To close that knowledge gap, this paper presents the first large-scale empirical study of floating-point arithmetic usage across public GitHub repositories. We focus on statically typed languages to allow our study to scale to millions of repositories. We follow state-of the art mining practices including random sampling and filtering based on only intrinsic properties to avoid bias, and identify floating-point usage by searching for keywords in the source code, and programming language constructs (e.g., loops) by parsing the code. Our evaluation supports the claim often made in papers that floating-point arithmetic is widely used. Comparing statistics such as size and usage of certain constructs and functions, we find that benchmarks used in literature to evaluate automated reasoning techniques for floating-point arithmetic are in certain aspects representative of 'real-world' code, but not in all. We publish a dataset of 10 million real-world floating-point functions extracted from our study. We demonstrate in a case study how it may be used to identify new floating-point benchmarks and help future techniques for floating-point arithmetic to be designed and evaluated to match actual users' expectations.

For $α>0$ and $σ> 0$, we consider the following probability distribution on $α\mathbb N_0$: $π_{α,σ} = \exp \big(- \fracσ{α^2}\big) \sum_{n=0}^{\infty} \frac{1}{n!} \big(\fracσ{α^2}\big)^n δ_{αn}$, where $δ_y$ denotes the Dirac measure with mass at $y$. For $α=1$, $π_{1,σ}$ is the Poisson distribution with parameter $σ$. Furthermore, the centered probability distribution $\tilde π_{α,σ} = \exp \big(- \fracσ{α^2}\big) \sum_{n=0}^{\infty} \frac{1}{n!} \big(\fracσ{α^2}\big)^n δ_{αn-σ/α}$ weakly converges to $μ_σ$ as $α\to0$. Here $μ_σ$ is the Gaussian distribution with mean zero and variance $σ$. Let $(c_n)_{n=0}^\infty$ be the monic polynomial sequence that is orthogonal with respect to the measure $μ_{α,σ}$. In particular, for $α=1$, $(c_n)_{n=0}^\infty$ is a sequence of Charlier polynomials. Let $\mathbb F_σ(\mathbb C)$ denote the Bargmann space of all entire functions $f(z)=\sum_{n=0}^\infty f_nz^n$ with $f_n \in \mathbb C$ satisfying $ \sum_{n=0}^{\infty} {| f_n |}^2 \, n! \, σ^n < \infty$. The generalized Segal--Bargmann transform associated with the measure $π_{α,σ}$ is a unitary operator $\mathcal S:L^2(α\mathbb N_0,π_{α,σ})\to \mathbb F_σ(\mathbb C)$ that satisfies $(\mathcal Sc_n)(z)=z^n$ for $n\in\mathbb N_0$. We present some new results related to the operator $\mathcal S$. In particular, we observe how the study of $\mathcal S$ naturally leads to the normal ordering in the Weyl algebra.

In Navier--Stokes (NS) turbulence, large-scale turbulent flows inevitably determine small-scale flows. Previous studies using data assimilation with the three-dimensional NS equations indicate that employing observational data resolved down to a specific length scale, $\ell^{3D}_{\ast}$, enables the successful reconstruction of small-scale flows. Such a length scale of `essential resolution of observation' for reconstruction $\ell^{3D}_{\ast}$ is close to the dissipation scale in three-dimensional NS turbulence. % Here we study the equivalent length scale in {\it two}-dimensional NS turbulence, $\ell^{2D}_{\ast}$, and compare with the three-dimensional case. Our numerical studies using data assimilation and conditional Lyapunov exponents reveal that, for Kolmogorov flows with Ekman drag, the length scale $\ell^{2D}_{\ast}$ is actually close to the forcing scale, substantially larger than the dissipation scale. Furthermore, we discuss the origin of the significant relative difference between the length scales, $\ell^{2D}_{\ast}$ and $\ell^{3D}_{\ast}$, based on inter-scale interactions, `cascades' and orbital instabilities in turbulence dynamics.

Fluctuation theorems establish that thermodynamic processes at the microscale can occasionally result in negative entropy production. At the microscale, another distinct possibility becomes more likely: processes in which no entropy is produced overall. In this work, we explore the constraints imposed by such null-entropy events on the fluctuations of thermodynamic currents. By incorporating the probability of null-entropy events, we obtain tighter bounds on finite-time thermodynamic uncertainty relations derived from fluctuation theorems. We validate this framework using an example of a qudit SWAP engine.

In this paper we investigate analytically the formation of finite time singularities in the three dimensional incompressible Euler equations under the model of Gibbon, Fokas, and Doering for vorticity stretching within a bounded cylindrical domain and under axisymmetric conditions. We derive explicit Lagrangian solutions for the vorticity, its stretching rate, fluid pathlines, and velocity components by exploiting constants of motion associated with the field dependent infinitesimal symmetries of the system. The central finding is that the existence and nature of a finite time singularity are determined exclusively by the local geometric structure of the initial vortex stretching rate near its global minimum. Whether a singularity forms depends on how flat this profile is at the minimum. Flatter profiles delay the blowup and sufficient flatness can suppress it entirely. For power law behavior near the minimum, critical thresholds for the exponent are identified which separate regular solutions from those that develop a finite time singularity. These thresholds differ depending on whether the singularity occurs at the centre of the cylinder or on a ring away from the centre, with minima at the centre requiring higher flatness to avoid blowup. This work provides a rigorous analytical framework that elucidates how the local geometric structure of the initial conditions governs the potential for singularity formation in 3D fluid flows, offering fundamental insights into the interplay between symmetry, initial data, and the development of extreme events in idealised turbulence.

We present a proof of the reverse isoperimetric inequality - a central conjecture in extended black hole thermodynamics - for black holes in Einstein gravity with $D \geq 4$, employing a two-pronged geometric-analytic method. Our analysis shows that the reversal of the usual isoperimetric inequality originates from the structure of curved backgrounds governed by Einstein's equations, thereby underscoring the fundamental role of gravity in the reverse isoperimetric property of AdS black hole horizons.

This paper will provide several classes of strictly stationary, countable-state, irreducible, aperiodic Markov chains that are reversible and have finite second moments, such that the central limit theorem fails to hold. The main purpose is to examine the extent to which, for the development of central limit theory for strictly stationary Markov chains (and functions of them) under the strong mixing and absolute regularity conditions, the property of reversibility (if it holds) can provide extra leverage. It is known, partly as a by-product of research done by Roberts, Rosenthal, and Tweedie in two papers in 1997 and 2001, that for the case of exponential mixing rates, reversibility provides notable extra leverage of that kind. In contrast, a class of counterexamples in a paper of Doukhan, Massart, and Rio in 1994 showed (implicitly) that for the case of power-type mixing rates, reversibility apparently provides almost no such extra leverage. Further perspective on that latter fact will be provided by some counterexamples in this paper. Other counterexamples here will (indirectly) provide some tentative, uncertain evidence for the possibility that for mixing rates that are ``between'' power-type and exponential (for example, sub-exponential), reversibility may in fact provide some small but nontrivial extra leverage.

In this paper, we introduce discrete approximate circle bundles, a class of objects designed to serve as the data science analog of circle bundles from algebraic topology. We show that, under appropriate conditions, one can meaningfully and stably identify a discrete approximate circle bundle with an isomorphism class of true circle bundles. We also describe two cohomology invariants which uniquely determine the isomorphism class of a circle bundle, and provide algorithms to compute them given a discrete approximate representative. Finally, we propose a novel methodology for coordinatization and dimensionality reduction of circle bundle data. To illustrate the practical utility and viability of our algorithms, we present applications to both real and synthetic datasets from computer vision (e.g., modeling optical flow). The paper is accompanied by an open-source software package, with full documentation and tutorials, enabling reproducible implementation of the proposed algorithms and experiments, including those used to generate the figures in this paper.