We prove the continuity of asymptotic entropy as a function of the step distribution for non-degenerate probability measures with finite entropy on wreath products $ A \wr B = \bigoplus_B A \rtimes B $, where $A$ is any countable group and $B$ is a countable hyper-FC-central group that contains a finitely generated subgroup of at least cubic growth. As one step in proving the above, we show that on any countable group $G$ the probability that the $μ$-random walk on $G$ never returns to the identity is continuous in $μ$, for measures $μ$ such that the semigroup generated by the support of $μ$ contains a finitely generated subgroup of at least cubic growth. Finally, we show that among random walks on a group $G$ that admit a separable completely metrizable space $X$ as a model for their Poisson boundary, the weak continuity of the associated harmonic measures on $X$ implies the continuity of the asymptotic entropy. This result recovers the continuity of asymptotic entropy on known cases, such as Gromov hyperbolic groups and acylindrically hyperbolic groups, and extends it to new classes of groups, including linear groups and groups acting on $\mathrm{CAT}(0)$ spaces.

The rise of Generative AI (GAI) and Large Language Models (LLMs) has transformed industrial landscapes, offering unprecedented opportunities for efficiency and innovation while raising critical ethical, regulatory, and operational challenges. This study conducts a text-based analysis of 160 guidelines and policy statements across fourteen industrial sectors, utilizing systematic methods and text-mining techniques to evaluate the governance of these technologies. By examining global directives, industry practices, and sector-specific policies, the paper highlights the complexities of balancing innovation with ethical accountability and equitable access. The findings provide actionable insights and recommendations for fostering responsible, transparent, and safe integration of GAI and LLMs in diverse industry contexts.

We establish an $S$-duality converse to the one studied by the 1st, 2nd and 4th authors; this is also a case of a twisted version of the relative Langlands duality of Ben Zvi, Sakellaridis and Venkatesh.. Namely, we prove that the $S$-dual of $\text{SO}(2n+1)\times \text{Sp}(2n)$ acting on the tensor product of their tautological representations is the symplectic mirabolic space $\text{Sp}(2n)\times\text{Sp}(2n)$ acting on the product $T^* \text{Sp}(2n)$ and the tautological representations of $\text{Sp}(2n)$. (Note that due to the anomaly, the dual of the second factor $\text{Sp}(2n)$ is the metaplectic dual, i.e. $\text{Sp}(2n)$). We also formulate the corresponding global conjecture, which describes explicitly the categorical theta-correspondence on the Langlands dual side.

Let $Ω$ be an $n$-dimensional compact Riemannian manifold $(n \geq 3)$ with $C^\infty$ boundary, and consider $L^2$-normalized eigenfunctions $ - Δϕ_λ = λ^2 ϕ_λ$ with Dirichlet or Neumann boundary conditions . In this note, we extend well-known interior nonconcentration bounds up to the boundary. Specifically, in Theorem \ref{thm1}, using purely stationary local methods, we prove that for such $Ω$ it follows that for {\em any} $x_0 \in \overlineΩ$ (including boundary points) and for all $μ\geq C_Ω λ^{-1}$ with sufficiently large constant $C_Ω >0,$ \begin{equation} \label{nonconbdy} \| ϕ_λ\|_{B(x_0,μ)\cap Ω}^2 = O(μ). \end{equation} In Theorem \ref{thm2} we extend a result of Sogge \cite{So} to manifolds with smooth boundary and show that \begin{equation} \label{SUPBD} \| ϕ_λ\|_{L^\infty(Ω)} \leq C λ^{\frac{n}{2}} \cdot \Big( \sup_{x \in Ω} \| ϕ_λ \|_{L^2( B(x,λ^{-1}) \cap Ω)} \Big). \end{equation} The sharp sup bounds $\| ϕ_λ \|_{L^\infty(Ω)} = O(λ^{\frac{n-1}{2}})$ for Dirichlet or Neumann eigenfunctions proved by Grieser in \cite{Gr} are then an immediate consequence of Theorems \ref{thm1} and \ref{thm2}.

The paperfolding sequences form an uncountable class of infinite sequences over the alphabet $\{ -1, 1 \}$ that describe the sequence of folds arising from iterated folding of a piece of paper, followed by unfolding. In this note we observe that the sequence of run lengths in such a sequence, as well as the starting and ending positions of the $n$'th run, is $2$-synchronized and hence computable by a finite automaton. As a specific consequence, we obtain the recent results of Bunder, Bates, and Arnold, in much more generality, via a different approach. We also prove results about the critical exponent and subword complexity of these run-length sequences.

Multi-body dark matter annihilation is commonly expected to be suppressed by higher-order couplings and phase-space factors, therefore being ignored thus far. We show that, however, this does not hold for a class of nonthermal dark matter scenarios, where the dark matter particle becomes nonrelativistic at temperatures much higher than its mass. We exemplify such a multi-body process via ultralight pseudoscalar dark matter annihilation to diphotons, which leads to a novel photon proliferation effect in the early Universe. As a phenomenological application, we consider the photon temperature shift after neutrino decoupling, showing that the photon proliferation effect can render bounds on the ultralight dark matter couplings stronger than the existing constraints by several orders of magnitude. Our research can be extended to other interactions and dark matter candidates, highlighting the importance of multi-body processes in the early Universe.

We are motivated by studying a boundary-value problem for a class of semilinear degenerate elliptic equations \begin{align}\tag{P}\label{P} \begin{cases} - Δ_x u - |x|^{2α} \dfrac{\partial^2 u}{\partial y^2} = f(x,y,u) & \textrm{in } Ω, u = 0 & \textrm{on } \partial Ω, \end{cases} \end{align} where $x = (x_1, x_2) \in \mathbb{R}^2$, $Ω$ is a bounded smooth domain in $\mathbb{R}^3$, $(0,0,0) \in Ω$, and $α> 0$. In this paper, we will study this problem by establishing embedding theorems for weighted Sobolev spaces. To this end, we need a new Pólya-Szegö type inequality, which can be obtained by studying an isoperimetric problem for the corresponding weighted area. Our results then extend the existing ones in \cite{nga, Luyen2} to the three-dimensional context.

We consider a half-filled system of spin-1/2 fermions on a triangular ladder with spin-dependent hopping in the presence of spin-dependent flux. Using the Schrieffer-Wolff transformation, we derive an effective spin Hamiltonian describing the infrared properties of the system in the limit of strong on-site repulsion. The expansion is performed up to the third order in the hopping amplitude over on-site interaction energy. It is shown that the low-energy spin excitations are described by an anisotropic $XXZ$ Heisenberg model with Dzyaloshinskii-Moriya interaction and an unconventional three-spin (correlated exchange) term in the presence of an extended magnetic field. The latter couples not only to $z$-projection of the total spin on a triangular plaquette but also to the product of $z$-components of three spins located on vertices of the triangle. In the case of strong attractive interaction, the corresponding effective model is derived from the repulsive one using the one-spin-component particle-hole transformation. The effective Hamiltonian is given by the same $XXZ$ Heisenberg model, as in the repulsive case, but in terms of pseudospin (charge) operators.

In the present manuscript we address and solve for the first time a nonlocal discrete isoperimetric problem. We consider indeed a generalization of the classical perimeter, what we call a nonlocal bi-axial discrete perimeter, where, not only the external boundary of a polyomino $\mathcal{P}$ contributes to the perimeter, but all internal and external components of $\mathcal{P}$. Furthermore, we find and characterize its minimizers in the class of polyominoes with fixed area $n$. Moreover, we explain how the solution of the nonlocal discrete isoperimetric problem is related to the rigorous study of the metastable behavior of a long-range bi-axial Ising model.

Context: Logging is an important part of modern software projects; logs are used in several tasks such as debugging and testing. Due to the complex nature of logging, it remains a difficult task with several pitfalls that could have serious consequences. Several other domains of software engineering have mitigated such threats by identifying the early signs of more serious issues, i.e., 'smells'. However, this concept is not yet properly defined for logging. Objective: The goal of this study is to create a taxonomy of log smells that can help developers write better logging code. To further help the developers and to identify issues that need more attention from the research community, we also map the identified smells to existing tools repairing them. Methods: We conducted a survey of the scientific literature to identify logging issues and related tools. After extracting relevant data from 51 articles, we used open coding to define logging issues and applied card sorting to derive log smells from these issues. Finally, we classified the tools based on their reported output. Results: We present a taxonomy of nine log smells and describe several facets for each of them. We also review existing tools repairing/removing some of these facets, highlighting the lack of tools addressing some log smells and identifying future research opportunities to close this gap. Conclusions: Logging is vulnerable to log smells throughout all phases of its life cycle, and these issues can affect both logging implementation and the resulting log files. Understanding these smells - along with their causes and consequences - can help reduce their occurrence and lead to higher-quality logging.

As a foundation for optimization, convexity is useful beyond the classical settings of Euclidean and Hilbert space. The broader arena of nonpositively curved metric spaces, which includes manifolds like hyperbolic space, as well as metric trees and more general CAT(0) cubical complexes, supports primal tools like proximal operations for geodesically convex functions. However, the lack of linear structure in such spaces complicates dual constructions like subgradients. To address this hurdle, we introduce a new type of subgradient for functions on Hadamard spaces, based on Busemann functions. Our notion supports generalizations of classical stochastic and incremental subgradient methods, with guaranteed complexity bounds. We illustrate with subgradient algorithms for $p$-mean problems in general Hadamard spaces, in particular computing medians in BHV tree space.

Many traditional robust control approaches assume linearity of the system and independence between the system state-input and the parameters of its approximant (possibly lower-order) model. This assumption implies that the application of robust control design to the underlying system introduces no distributional shifts in the parameters of its approximant model. This is generally not true when the underlying system is nonlinear, which may require different approximant models with different parameter distributions when operated at different regions of the state-input space. Therefore, a robust controller has to be robust under the approximant model with parameter distribution that will be experienced in the future data, after applying this control, not the parameter distribution seen in the learning data or assumed in the design. In this paper, we seek a solution to this problem by restricting the newly designed closed-loop system to be consistent with the learning data and slowing down any distributional shifts in the state-input space of the underlying system, and therefore, in the parameter space of its approximant model. In computational terms, the objective of dampening the shifts in the parameter distribution is formulated as a convex semi-definite program that can be solved efficiently by standard software packages. We evaluate the proposed approach on a simple yet telling gain-scheduling problem, which can be equivalently posed as a robust control problem.

Witt group of real algebraic curves has been studied since Knebusch in 1970s. But few results are known if the base field is non-Archimedean except the hyperelliptic case by works of Parimala, Arason et al.. In this paper, we compute the derived Witt groups of smooth proper curves over nondyadic local fields with $char\neq2$ by reduction, with a general study of the existence of Theta characteristics.

We investigate the analytic properties of a Dirichlet series involving the Fourier-Jacobi coefficients of two cusp forms for orthogonal groups of signature $(2,n+2)$. Using an orthogonal Eisenstein series of Klingen type, we obtain an integral representation for this Dirichlet series. In the case when the corresponding lattice has only one $1$-dimensional cusp, we rewrite this Eisenstein series in the form of an Epstein zeta function. If additionally $4 \mid n$, we deduce a theta correspondence between this Eisenstein series and a Siegel Eisenstein series for the symplectic group of degree $2$. We obtain, in this way, the meromorphic continuation of the Dirichlet series to $\mathbb{C}$ as a corollary. In the case of the $E_8$ lattice, we are able to further deduce a precise functional equation for the Dirichlet series.

We study internal diffusion limited aggregation on $\mathbb{Z}$, where a cluster is grown incrementally by adding, for each random walk dispatched from the origin, the first site it reaches outside the cluster. We assume that the increment distribution $X$ of the driving random walks has $\mathbb{E} X =0$, but need neither be simple nor symmetric, and can have $\mathbb{E} (X^2) = \infty$, for example. For the case where $\mathbb{E} (X^2) < \infty$, we prove that after $m$ of the random walks have been dispatched, all but $o(m)$ sites in the cluster form an approximately symmetric contiguous block around the origin. This strengthens a result of Blachère, for centred random walks whose increments have finite $3$rd moments, to the optimal moments condition. On the other hand, if $X$ is in the domain of attraction of a symmetric $α$-stable law, $1 < α<2$, we prove that the cluster contains a contiguous block of $δm +o(m)$ sites, where $0 < δ< 1$, but, unlike the finite-variance case, one may not take $δ=1$.

In this note, we investigate iterations of consistency, local and uniform reflection over $\mathbf{HA}$ (Heyting Arithmetic). In the case of uniform reflection, we give a new proof of Dragalin's extension of Feferman's completeness theorem to $\mathbf{HA}$, drawing on Rathjen's proof of Feferman's classical result.

We investigate the shear flow of a sludge mimicking slurries produced by the nuclear industry and constituted of a dispersion of non-Brownian particles into an attractive colloidal dispersion at a total solid volume fraction of about 10%. Combining rheometry and ultrasound flow imaging, we show that, upon decreasing the shear rate, the flow transitions from a homogeneous shear profile in the bulk to a fully arrested plug-like state with total wall slip, through an oscillatory regime where strong fluctuations of the slip velocity propagate along the vorticity direction. When the shear stress is imposed close to the yield stress, the shear rate presents large, quasi-periodic peaks, associated with the propagation of local stick-and-slip events along the vorticity direction. Such complex dynamics, reminiscent of similar phenomena reported in much denser suspensions, highlight the importance of local flow characterization to fully understand sludge rheology.

This study conceptualizes electronic dose to water, which is the radiation energy imparted to a unit mass of water by electronic interactions. The new dosimetry framework excludes nuclear interactions and consequently associated corrections and uncertainties from conventional dosimetry. Based on the international code of practice for dosimetry in radiotherapy, the procedures to determine electronic doses were formulated for high-energy photon, electron, proton, and ion beams. Nitrogen-based water-equivalent gas (WEG) mixtures were designed for use in gas-sealed ionization chambers for proton and ion beams. The proposed procedures were tested in a thought experiment and demonstrated compatibility with conventional absorbed dose for photon and electron beams and improved accuracy for proton and ion beams. The dosimetric uncertainty will be reduced from \SI{1.4}{\%} to \SI{1.3}{\%} for proton beams and from \SI{2.4}{\%} to \SI{1.9}{\%} for ion beams. With WEG ionization chambers, it will be further reduced to \SI{0.7}{\%} for proton beams and \SI{1.0}{\%} for ion beams. The new dose concept, electronic dose to water, can be readily used in radiotherapy practice and it will be medically more relevant than absorbed dose.

We consider the orbital motion of a test particle in the gravitational field of a massive body (that might be a black hole) with mass $m$ placed on the expanding cosmological manifold described by the McVittie metric. We introduce the local coordinates attached to the massive body to eliminate nonphysical, coordinates-dependent effects associated with Hubble expansion. The resultant equation of motion of the test particle are analyzed by the method of osculating elements with application of time-averaging technique. We demonstrate that the orbit of the test particle is not subject to the cosmological expansion up to the terms of the second order in the Hubble parameter. However, the cosmological expansion causes the precession of the orbit of the test particle with time and changes the frequency of the mean orbital motion. We show that the direction of motion of the orbital precession depends on the Hubble parameter as well as the deceleration parameter of the universe. We give numeric estimates for the rate of the orbital precession with respect to time due to the cosmological expansion in case of several astrophysical systems.

In light of the increase in frequency of extreme heat events, there is a critical need to develop tools to identify geographic locations that are at risk of heat-related mortality. This paper aims to identify locations by assessing holes in cooling-center coverage using persistent homology (PH), a method from topological data analysis (TDA). Persistent homology has shown promising results in identifying holes in coverage of specific resources. We adapt these methods using a witness complex construction to study the coverage of cooling centers. We test our approach on four locations (central Boston, MA; central Austin, TX; Portland, OR; and Miami, FL) and use death times, a measurement of the size and scale of the gap in coverage, to identify most at risk regions. For comparison, we implement a standard technique for studying the risk of heat-related mortality called a heat vulnerability index (HVI). The HVI is a numerical score calculated for a geographic area based on demographic information. PH and the HVI identify different locations as vulnerable, thus indicating a potential value of assessing vulnerability from multiple perspectives. By using the regions identified by both persistent homology and the HVI, we provide a more holistic understanding of coverage.

Text-to-visualization (text-to-vis) models for tabular data have become essential tools in the era of big data, enabling users to generate visualizations and make data-driven decisions through natural language queries (NLQs). Despite their growing adoption, the security vulnerabilities of these models remain largely unexplored. To address this gap, we propose VisPoison, a backdoor attack framework that realistically simulates three types of attacks on text-to-vis models via data poisoning: data exposure, misleading visualizations, and denial-of-service (DoS). Specifically, VisPoison introduces two types of stealthy triggers to enable both proactive and passive backdoor activations. Proactive triggers are deliberately inserted by attackers using rare-word patterns to extract sensitive information, whereas passive triggers are unintentionally activated by users through first-word prompts, resulting in visualization errors or DoS failures. To support these triggers, we craft specialized payloads for visualization queries that allow compromised models to function normally on benign inputs while producing malicious outputs in the presence of triggers. Extensive evaluations on both trainable and in-context learning (ICL)-based text-to-vis models show that VisPoison achieves attack success rates exceeding 90\%, exposing serious vulnerabilities. Additionally, existing defense strategies reveal limited effectiveness against VisPoison, underscoring the urgent need for more robust and security-aware text-to-vis systems to safeguard human-data interaction.

Forecasting risk (as measured by quantiles) and systemic risk (as measured by Adrian and Brunnermeiers's (2016) CoVaR) is important in economics and finance. However, past research has shown that predictive relationships may be unstable over time. Therefore, this paper develops structural break tests in predictive quantile and CoVaR regressions. These tests can detect changes in the forecasting power of covariates, and are based on the principle of self-normalization. We show that our tests are valid irrespective of whether the predictors are stationary or near-stationary, rendering the tests suitable for a range of practical applications. Simulations illustrate the good finite-sample properties of our tests. Two empirical applications concerning equity premium and systemic risk forecasting models show the usefulness of the tests.

We decompose the counting statistics of many-body interference experiments into contributions associated with distinct irreducible exchange symmetries. To do so, we perform a Fourier transform over the symmetric group $S_N$ on the collection of $N!$ many-body transition amplitudes connecting two states of a system of $N$ particles. We apply our formalism to the interference of partially distinguishable bosons and fermions and describe mechanisms responsible for completely destructive interference in many-body systems obeying specific exchange symmetries, including, but not limited to, bosons and fermions.

High-quality element distribution maps enable precise analysis of the material composition and condition of Old Master paintings. These maps are typically produced from data acquired through Macro X-ray fluorescence (MA-XRF) scanning, a non-invasive technique that collects spectral information. However, MA-XRF is often limited by a trade-off between acquisition time and resolution. Achieving higher resolution requires longer scanning times, which can be impractical for detailed analysis of large artworks. Super-resolution MA-XRF provides an alternative solution by enhancing the quality of MA-XRF scans while reducing the need for extended scanning sessions. This paper introduces a tailored super-resolution approach to improve MA-XRF analysis of Old Master paintings. Our method proposes a novel adversarial neural network architecture for MA-XRF, inspired by the Learned Iterative Shrinkage-Thresholding Algorithm. It is specifically designed to work in an unsupervised manner, making efficient use of the limited available data. This design avoids the need for extensive datasets or pre-trained networks, allowing it to be trained using just a single high-resolution RGB image alongside low-resolution MA-XRF data. Numerical results demonstrate that our method outperforms existing state-of-the-art super-resolution techniques for MA-XRF scans of Old Master paintings.

We present the phenomenology of the charged Higgs boson $H^\pm$ appearing in a fermionic dark matter model mediated by an additional scalar doublet. In order to couple the dark matter fermion to the scalar doublet, we introduce a U(1)$_X$ gauge symmetry, which is spontaneously broken at electroweak symmetry breaking, resulting in a massive $Z'$ gauge boson. Since $Z'$ is generically light, the model is subject to strong constraints from electroweak precision observables. As a result, the charged Higgs boson mass allowed by current experimental bounds is typically light in this model, 110 GeV $<m_{H^\pm}<$ 170 GeV. Such a light charged Higgs boson will be produced mainly through top-quark decays at the LHC. Additionally, depending on the mass of the additional neutral Higgs boson $h$ and the dark gauge boson $Z'$, the direct production channels $pp \to H^\pm Z'$ and $pp \to H^\pm h$ can become sizable. We investigate the corresponding signal processes at the LHC to assess the discovery potential for $H^\pm$. Current ATLAS and CMS searches for light charged Higgs bosons already impose further constraints on the model. We also discuss the implications of dark matter in relation to the charged Higgs boson phenomenology.

Recently, we notice that a pressure-based lattice Boltzmann (LB) method was established to recover the volume-averaged Navier-Stokes equations (VANSE), which serve as the cornerstone of various fluid-solid multiphase models. It decouples the pressure from density and exhibits excellent numerical performance, however, the widely adopted density-based LB scheme still suffers from significant spurious velocities and inconsistency with VANSE. To remedy this issue, a multiple-relaxation-time LB method is devised in this work, which incorporates a provisional equation of state in an adjusted density equilibrium distribution to decouple the void fraction from density. The Galilean invariance of the recovered VANSE is guaranteed by introducing a penalty source term in moment space, effectively eliminating unwanted numerical errors. Through the Chapman-Enskog analysis and detailed numerical validations, this novel method is proved to be capable of recovering VANSE with second-order accuracy consistently, and well-suited for handling void fraction fields with large gradients and spatiotemporal distributions.

The data collected by autonomous vehicle (AV) sensors such as LiDAR and cameras is crucial for creating high-definition (HD) maps to provide higher accuracy and enable a higher level of automation. Nevertheless, offloading this large volume of raw data to edge servers leads to increased latency due to network congestion in highly dense environments such as Vehicular Adhoc networks (VANET). To address this challenge, researchers have focused on the dynamic allocation of minimum contention window (CWmin) value. While this approach could be sufficient for fairness, it might not be adequate for prioritizing different services, as it also involves other parameters such as maximum contention window (CWmax) and infer-frame space number (IFSn). In response to this, we extend the scope of previous solutions to include the control of not only CWmin but also the adjustment of two other parameters in the standard IEEE802.11: CWmax and IFSn, alongside waiting transmission time. To achieve this, we introduced a methodology involving a cross-layer solution between the application and MAC layers. Additionally, we utilised multi-agent techniques, emphasising a hierarchical structure and independent learning (IL) to improve latency to efficiently handle map updates while interacting with multiple services. This approach demonstrated an improvement in latency against the standard IEEE802.11p EDCA by $31\%$, $49\%$, $87.3\%$, and $64\%$ for Voice, Video, HD Map, and Best-effort, respectively.

In this paper, we study characteristics of horofunction boundaries of Carnot groups. In particular, we show that for Carnot groups, i.e., stratified nilpotent Lie groups equipped with certain left-invariant homogeneous metrics, all horofunctions are piecewise-defined using Pansu derivatives. For higher Heisenberg groups and filiform Lie groups, two families which generalize the standard 3-dimensional real Heisenberg group, we study the dimensions and topologies of their horofunction boundaries. In doing so, we find that filiform Lie groups of dimension $n\geq 8$ provide the first-known examples of Carnot groups $G$ whose horofunction boundaries are not of dimension $\dim(G) - 1$.

There are many similarities between the theories of matroids and $q$-matroids. However, when dealing with the direct sum of $q$-matroids many differences arise. Most notably, it has recently been shown that the direct sum of representable $q$-matroids is not necessarily representable. In this work, we focus on the direct sum of uniform $q$-matroids. Using algebraic and geometric tools, together with the notion of cyclic flats of $q$-matroids, we show that this is always representable, by providing a representation over a sufficiently large field.

Determining the best attainable threshold for qudit magic state distillation is directly related to the question of whether or not contextuality is sufficient for universal quantum computation. We show that the performance of a qudit correcting code for magic state distillation is captured by its complete weight enumerator. For the qutrit strange state -- a maximally magic non-stabilizer state -- the performance of a code is captured by its simple weight enumerator. This result allows us to carry out an extensive search for high-threshold magic state distillation routines for the strange state. Our search covers all $[[n,1]]_3$ qutrit stabilizer codes with a complete set of transversal Clifford gates for $n\leq 23$, and all $[[n,1]]_3$ stabilizer codes with a transversal $H^2$ gate with $n \leq 9$ qudits. For $n=23$, we find over 600 CSS codes that can distill the qutrit strange state with cubic noise suppression. While none of these codes surpass the threshold of the 11-qutrit Golay code, their existence suggests that, for large codes, the ability to distill the qutrit strange state is somewhat generic.