Using a simple spacetime hosting a strong curvature naked singularity, we employ an analogue gravity model to study electromagnetic fields in this background. We find exact solutions to the full set of electrostatic and electrodynamic equations that remain regular even in the presence of the singularity. Moreover, certain solutions sustain a regular and bounded power flux across the singularity, suggesting that electromagnetic energy may be transmitted through it.

We study the mode dynamics of a generic quadratic fermionic Hamiltonian under a sudden quench protocol in momentum space. Modes with zero energy at any given time, $t$, are referred to as dynamical critical modes. Among all zero-energy modes, spin-flip symmetry is restored in the eigenvector corresponding to selected zero-energy modes. This symmetry restoration is used to define the dynamical quantum phase transition (DQPT). This shows that the occurrence of these dynamical critical modes is necessary but not sufficient for a DQPT. We show that the conditions on the quench protocol and time for such dynamical symmetry restoration are the same as the divergence of the rate function and integer jump in the dynamical topological order parameter, which have been the traditional identifiers of a DQPT. This perspective also naturally explains when one or both of DQPT and ground-state quantum phase transitions will occur.

Vacuum birefringence (VB), a fundamental prediction of nonlinear quantum electrodynamics (QED), has eluded direct laboratory detection due to its extreme weakness. We propose a compact, "self-probing" scheme where a GeV electron beam collides head-on with a petawatt laser pulse. Circularly polarized gamma-ray photons, generated via nonlinear Compton scattering in the same pulse, then probe the birefringent vacuum it induces. This integrated design bypasses the stringent synchronization and beam transport requirements of traditional pump-probe setups. Our nonperturbative strong-field QED simulations reveal a clear VB signature: conversion of circular to linear polarization, with the induced Stokes parameter $S_1$ reaching ~0.019 within the selected angular range. This corresponds to a refractive index difference $Δn = 1.829 \times 10^{-4}$ over micron-scale paths, directly measurable as a high-contrast "X-shape" asymmetry in $e^+e^-$ pair distributions. The scheme provides a feasible path to first laboratory VB detection with current laser and accelerator technologies.

We construct and classify asymptotically flat, static, spherically symmetric hairy black hole solutions in $U(1)$ gauge-invariant scalar-vector-tensor (SVT) theories carrying both electric and magnetic charges. Extending previous studies beyond the quadratic sector, we systematically incorporate cubic and quartic interaction terms in the presence of the magnetic charge. We derive a consistency condition for the quartic interaction that eliminates higher-order derivative terms induced by the magnetic charge, ensuring the theory remains second-order. We classify the obtained solutions based on their symmetry properties: shift-symmetric couplings yield secondary hair governed by the Noether current, whereas $ϕ$-dependent interactions generate primary hair. Crucially, our analysis reveals that the magnetic charge plays a key role in activating specific interaction sectors such as the cubic coupling $\tilde{f}_3$, which does not appear in the field equations in purely electric configurations. We identify solution branches that are intrinsic to the magnetic charge, as they cease to exist in the vanishing monopole limit ($P\to 0$). Furthermore, we demonstrate that the scalar hair exhibits distinct asymptotic decay rates depending on the interaction type, suggesting possible variations in observational signatures. Finally, we verify the global regularity of these solutions by connecting analytic expansions with numerical integration.

We consider deterministic particle dynamics with time evolving weights and their associated Kolmogorov equation and mean-field equation. We prove existence and unique- ness for the limit PDE alongside estimates on the growth of the logarithmic gradient as well as existence of weak solutions for the Kolmogorov equation satisfying an appropriate entropy inequality. We then apply these estimates and the relative entropy method as developed in [17], in order to derive the associated equation as a mean field limit. Our results cover both interactions and influence kernels with mild regularity assumptions.

In the paper we describe some properties of function $$ y=r(x)=\lim_{n\to\infty}\frac{1}{n}\sum^{\infty}_{k=1}α_k(x), \text{ where } x=\sum^{\infty}_{k=1}α_k(x)4^{-k} $$ of $4$-adic digits asymptotic mean of fractional part of real number $x$, particularly properties of it's level sets $ S_θ=\left\{x: r(x)=θ,\: θ=const, \: 0\leqslantθ\leqslant 3\right\}, $ if all $4$-adic digits frequencies exist, i.e. $$ ν_i(x)=\lim_{n\to\infty}n^{-1}\#\{k: α_k(x)=i, i\leqslant n\}, \:\: i=0,1,2,3. $$ We provided an algorithm of constructing point from the set $S_θ$, and proved continuality and every where density of the set. We found conditions of zero and full Lebesgue measure and estimates of Hausdorff-Besicovitch fractal dimension.

We study topological, metric and fractal properties of set of numbers $[0;1]$ with given asymptotic mean of digits in their ternary representation. We investigate connection of these numbers and numbers with a given frequency of digits.

This is a survey article on the twisted dynamical zeta functions of Ruelle and Selberg and the Fried's conjecture. It is based on the mini-course: "Twisted Ruelle zeta function, complex-valued analytic torsion and the Fried's conjecture", given by the author during the thematic trimester programme: "Representation Theory and Noncommutative Geometry" at the Institut Henri Poincaré.

The DIarization and Speech Processing for LAnguage understanding in Conversational Environments - Medical (DISPLACE-M) challenge introduces a conversational AI benchmark for understanding goal-oriented, real-world medical dialogues. The challenge addresses multi-speaker interactions between frontline health workers and care seekers, characterized by spontaneous, noisy and overlapping speech. As part of the challenge, medical conversational dataset comprising 40 hours of development and 15 hours of blind evaluation recordings was released. We provided baseline systems across 4 tasks - speaker diarization, automatic speech recognition, topic identification and dialogue summarization - to enable consistent benchmarking. System performance is evaluated using diarization error rate (DER), time-constrained minimum-permutation word error rate (tcpWER) and ROUGE-L. This paper describes the Phase-I evaluation - data, tasks and baseline systems - along with the summary of the evaluation results.

We propose a protocol for implementing Barenco-type multi-qubit controlled gates using short driven spin chains. Starting from an Ising interaction with a transverse drive on the last spin, we construct an effective two-qubit Hamiltonian whose time evolution implements the Barenco gate $V_2(φ,ω,ϕ)$ and, in particular, a CNOT gate. We then embed this construction into a three-qubit $XXZ$ chain to realize the three-qubit Barenco gate $V_3(φ,ω,ϕ)$, which includes the Toffoli gate as a special case. The derivation is fully analytical: we perform a sequence of unitary transformations, identify decoupled subspaces, and apply a rotating-wave approximation to obtain simple effective Hamiltonians. We derive explicit conditions on the coupling strengths and driving parameters, provide closed-form expressions for the time-evolution operators in each relevant subspace, and characterize the quality of the implementation using the operator fidelity. Numerical simulations show that the protocol achieves high fidelities over broad parameter ranges, demonstrating its robustness and suitability for quantum information processing in spin-chain platforms.

Inspired by the work of Cossetti and D'Arca [CD25], we show that the general weighted $L^{p}$-Hardy type inequalities [CD25, Theorems 1.1 and 1.2] and the corresponding identities hold for all $1<p<\infty$, thus extending their results beyond the case $p\geq 2$. In addition, we present a general weighted $L^{p}$-Rellich type inequality with a sharp remainder term for quasilinear second order degenerate elliptic differential operators. In particular, even for the classical Laplacian, these identities appear to be new.

A graph is perfectly divisible if for each of its induced subgraph $H$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and $ω(H[B]) < ω(H)$, and a graph $G$ is perfectly weight divisible if for every positive integral weight function on $V(G)$ and each of its induced subgraph $H$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and the maximum weight of a clique in $H[B]$ is smaller than the maximum weight of a clique in $H$. A clique $X$ of a connected graph $G$ is called a clique cutset if $G-X$ is disconnected. In this paper, we investigate the relationship between the perfect divisibility of a graph and its perfect weighted divisibility. We also show that $2P_3$-free or claw-free minimally nonperfectly divisible graphs contain no clique cutset, that conditionally answers a question of Hoàng [Discrete Math. \textbf{349} (2025) 114809].

Jets are produced in the earliest stages of heavy-ion collisions, where they can interact with a medium that is not yet close to local equilibrium. Motivated by this, we generalize the usual jet transport coefficient $\hat q$ to a Lorentz-covariant diffusion tensor $\hat q^{μν}$ within a leading-order elastic (Boltzmann/Fokker--Planck) description of jet--medium interactions. The tensor formulation organizes medium effects in a frame-covariant way and reveals additional information beyond the standard scalar definition, including energy diffusion and off-diagonal components that encode correlations between energy and momentum exchange which are absent (or redundant) in equilibrium. We illustrate the formalism in (tree-level) massless $λφ^4$ theory for isotropic but out-of-equilibrium states. For sufficiently large jet momentum, quantum statistical effects become subleading, so that the non-equilibrium evolution can be studied reliably in the classical (Boltzmann) limit. This allows us to solve the corresponding Boltzmann equation for the medium and determine the time dependence of $\hat q^{μν}$ as the system approaches equilibrium. We find that out-of-equilibrium corrections can either enhance or reduce jet momentum broadening, depending on the initial distribution function.

The shift from monolithic LLMs to distributed multi-agent architectures demands new frameworks for verifying and securing autonomous coordination. Unlike traditional multi-agent systems focused on cooperative state alignment, modern LLM patterns: multi-agent debate, constitutional oversight, helper-critic loops-rely on adversarial critique for error correction and reasoning refinement. Since LLMs are dynamical systems whose latent states are imperfectly observable from verbalized outputs, securing these networks requires understanding both macroscopic topology and microscopic agent observability. This paper establishes a rigorous graph-theoretic framework for analyzing consensus in signed, directed interaction networks, bridging graph theory and LLM reasoning by formally mapping Transformer cross-entropy log-odds to the signed Laplacian. We characterize agreement stability through structural balance theory, showing how unbalanced critique cycles produce logical frustration and persistent reasoning oscillations, and prove that unobservable latent states from hidden system prompts act as topological Trojan horses that destabilize cooperative consensus. To resolve unobservable deadlocks, we restrict interaction topologies to chordal graphs and apply matrix decomposition with Gram-Schmidt orthogonalization, proving that rank-one spectral edge perturbations deterministically break expertise symmetry by shifting eigenvalues into the stable left-half plane. Core contributions include consensus theorems, polynomial-time Perfect Elimination Ordering verification algorithms, and large-scale empirical validation on clustered ensembles of LLaMA-3, Mistral, and Gemma agents.

It is well established that dilute active dopants can melt an arrested amorphous solid by enhancing cage breaking and accelerating structural relaxation. Yet it remains unclear whether increasing persistence simply amplifies this effective melting or instead reorganizes the fluidization mechanism itself. Here we show that, in a minimal active-passive mixture, increasing persistence drives a crossover from homogeneous fluidization to a localized mechanical instability, demonstrating that sustained active forcing restructures relaxation in space rather than merely strengthening it. Persistent dopants accumulate stress and nucleate voids as their mechanically perturbed regions overlap. In this regime, rearrangements localize at void boundaries, and active and passive particles exhibit comparable mobility, producing dynamics reminiscent of crowd mosh pits. Persistence therefore reorganizes fluidization through stress accumulation and confinement, revealing a distinct nonequilibrium localization mechanism in disordered solids.

Charged kaon--deuteron interactions offer a sensitive probe of the strangeness sector of QCD at low energy, particularly through their scattering parameters. Despite available theoretical predictions, experimental constraints remain absent, particularly for the $\rm K^{-}d$ system. The first measurement of femtoscopic correlation functions for $\rm K^{-}d \oplus K^{+}\overline{d}$ and $\rm K^{+}d \oplus K^{-}\overline{d}$ particle pairs in Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV recorded by ALICE at the LHC is presented. Correlation functions for both systems are analyzed in three centrality classes and fitted using the Lednický--Lyuboshitz model to extract the source size and strong interaction scattering lengths. The $\rm K^{-}d$ scattering length is found to be $\Re f_0 = -1.44 \pm 0.15\text{ (stat.)}^{+0.10}_{-0.10}$ (syst.) fm and $\Im f_0 = 1.34 \pm 0.33$ (stat.)$^{+0.21}_{-0.15}$ (syst.) fm, while for $\rm K^{+}d$ the value $\Re f_0 = -0.68 \pm 0.16$ (stat.)$^{+0.09}_{-0.09}$ (syst.) fm is obtained. These results provide the first constraints on the $\rm K^{\pm} d$ interaction modeling at low energy, delivering a long-awaited experimental benchmark for testing chiral QCD dynamics.

We study dualizing complexes on algebraic stacks. In particular, we show their existence for (tame) Deligne--Mumford stacks of equicharacteristic in great generality.

Let $M =\mathbb{H}^3/Γ$ be a finite-volume, noncompact hyperbolic 3-manifold. We show that the number of quasi-Fuchsian surface subgroups of $Γ$ (up to conjugacy and commensurability) of genus at most $g$ is bounded both above and below by functions of the form $(cg)^{2g}$. As a corollary, for all $h\geq 4$, the number of purely pseudo-Anosov closed surface subgroups of genus at most $g$ of the mapping class group $\mathrm{Mod}(S_{h,0})$ is bounded below by $(Cg)^{2g}$ for a universal constant $C$. In contrast, for some $g \geq 2$, we construct infinitely many conjugacy classes of genus-$g$ surface subgroups of $Γ$ with accidental parabolics.

Both in quantum theory and in general probabilistic theories, measurements with $n$ outcomes are modelled as $n$-tuples of \emph{effects} summing up to the unit effect. Why is this the case, and can this assumption be meaningfully relaxed? Here we develop \emph{generalized measurement theories (GMTs)} as a mathematical framework for physical theories that is complementary to general probabilistic theories, and where this kind of question can be made precise and answered. We then give a definition of \emph{probabilistic state} on a GMT, prove that measurements are made of effects in every GMT in which the probabilistic states separate the measurements, and also argue that this separation condition is physically well-motivated. Finally, we also discuss when a GMT should be considered classical and characterize GMTs corresponding to Boolean algebras as those that are strongly classical and projective.

Removing the CPU from the communication fast path is essential to efficient GPU-based ML and HPC application performance. However, existing GPU communication APIs either continue to rely on the CPU for communication or rely on APIs that place significant synchronization burdens on programmers. In this paper we describe the design, implementation, and evaluation of an MPI-based GPU communication API enabling easy-to-use, high-performance, CPU-free communication. This API builds on previously proposed MPI extensions and leverages HPE Slingshot 11 network card capabilities. We demonstrate the utility and performance of the API by showing how the API naturally enables CPU-free gather/scatter halo exchange communication primitives in the Cabana/Kokkos performance portability framework, and through a performance comparison with Cray MPICH on the Frontier and Tuolumne supercomputers. Results from this evaluation show up to a 50% reduction in medium message latency in simple GPU ping-pong exchanges and a 28% speedup improvement when strong scaling a halo-exchange benchmark to 8,192 GPUs of the Frontier supercomputer.

Fuzzy sphere models conjecturally realize 3d CFTs in small systems of spinful fermions, but why they work so well is still not fully understood. Their Hamiltonians are built from electron density operators projected to the lowest Landau level. We analyze the algebra of the density modes and verify that it satisfies the Jacobi identity. The fuzzy sphere geometry admits two thermodynamic limits: a local planar limit yielding the fuzzy plane, and a commutative limit yielding an ordinary sphere. In the planar limit, high-angular-momentum modes recover the Girvin-MacDonald-Platzman algebra, whereas in the commutative limit, the low-angular-momentum modes become semiclassical. Upon further restricting to a subspace with few spin flips above the paramagnetic reference state, they behave approximately as harmonic oscillators. We also find an explicit representation of the conformal algebra $so(3,2)$ in the minimal two-electron system and extend it to larger systems via an $so(3)$ equivariant coproduct. Because the coproduct splits one $so(3)$ representation into a tensor product, it is structurally mismatched with the thermodynamic limit of critical fuzzy sphere models.

We construct the Weil restriction map for l-adic cohomology and, more generally, for mixed Weil cohomology theories. We study its compatibility with the motivic cycle class map and show that these constructions admit a natural interpretation in the triangulated categories of motives. Using Grothendieck's six-functor formalism, we prove that the Weil restriction map arises intrinsically from the functorial structures of these categories. This provides a conceptual framework for understanding the interaction between Weil restriction, motivic cohomology, and realization functors.

We prove a generic flatness result for the cohomology of thickenings of a projective scheme that is smooth over a Noetherian domain containing a field of characteristic zero. Our study is motivated, in part, by a classical question in algebraic geometry: Given a set of $m$ distinct points in projective space over a field, and $t$ a positive integer, determine the least degree of a hypersurface that passes through each point with multiplicity at least $t$. Related to this, it remains unresolved whether there exists a dense open set of $m$-tuples of points for which this least degree is constant for each $t\ge 1$. Investigating this connection in the case of nine points in projective plane, we construct a local cohomology module that is not generically free; moreover, we show that it has infinitely many associated prime ideals.

We establish that every set of $k=10$ natural numbers determines at least $30$ distinct pairwise sums or at least $30$ distinct pairwise products, as well as the analogous result for $k=11$ and at least $34$ sums/products, with sharpness uniquely (up to scaling) exhibited by $\{1, 2, 3, 4, 6, 8, 9, 12, 16, 18\}$ and $\{1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24\}$, respectively. This extends previous work of the fifth author with Clevenger, Havard, Heard, Lott, and Wilson, which established the corresponding thresholds for $k\leq 9$. Included is a classification result for sets of $10$ real numbers (resp. positive real numbers) determining at most $29$ pairwise sums (resp. pairwise products) that do not contain $8$ elements of any single arithmetic progression (resp. geometric progression), as well as some observations controlling additive quadruples in small subsets of two-dimensional generalized geometric progressions.

We develop a general canonical quantization scheme for $k$-essence cosmology in scalar-tensor theory. Utilizing the Dirac-Bergmann algorithm, we construct the Hamiltonian associated with the cosmological field equations and identify the first- and second-class constraints. The introduction of appropriate canonically conjugate variables with respect to Dirac brackets, allows for the canonical quantization of the model. In these new variables, the Hamiltonian constraint reduces to a quadratic function with no potential term. Its quantum realization leads to a Wheeler-DeWitt equation reminiscent of the massless Klein-Gordon case. As an illustrative example, we consider the action of a tachyonic field and investigate the conditions under which a phantom crossing can occur as a quantum tunneling effect. For the simplified constant potential case, we investigate the consequences of different boundary conditions on the singularity avoidance and to the mean expansion rate.

Despite decades of research, cardinality estimation remains the optimizer's Achilles heel, with industrial-strength systems exhibiting a systemic tendency toward underestimation. At cloud scale, this is a severe production vulnerability: in Microsoft's Fabric Data Warehouse (DW), a mere 0.05% of extreme underestimates account for 95% of all CPU under-allocation, causing preventable slowdowns for thousands of queries daily. Yet recent theoretical work on provable upper bounds only corrects overestimation, leaving the more harmful problem of underestimation unaddressed. We argue that closing this gap is an urgent priority for the database community. As a vital step toward this goal, we introduce xBound, the first theoretical framework for computing provable join size lower bounds. By clipping the optimizer's estimates from below, xBound offers strict mathematical safety nets demanded by production systems - using only a handful of lightweight base table statistics. We demonstrate xBound's practical impact on Fabric DW: on the StackOverflow-CEB benchmark, it corrects 23.6% of Fabric DW's underestimates, yielding end-to-end query speedups of up to 20.1x, demonstrating that even a first step toward provable lower bounds can deliver meaningful production gains and motivating the community to further pursue this critical, open direction.

The \emph{Tree Augmentation Problem (TAP)} is given a tree $T=(V,E_T)$ and additional set of {\em links} $E$ on $V\times V$, find $F \subseteq E$ such that $T \cup F$ is $2$-edge-connected, and $|F|$ is minimum. The problem is APX-hard \cite{r} even in if links are only between leaves \cite{r}. The best known approximation ratio for TAP is $1.393$, due to Traub and Zenklusen~\cite{tr1} J.~ACM,~2025 using the {\em relative greedy} technique \cite{zel}. \noindent We introduce a new technique called the {\em deferred local ratio technique}. In this technique, the disjointness of the local-ratio primal-dual type does not hold. The technique applies Set Cover problem under certain conditions (see Section \ref{lr}). We use it provide a We use it to provide a $4/3$ approximation algorithm for TAP. It is possible this technique will find future applications. The running time is The running time is $O(m\cdot\sqrt{n})$ time \cite{vaz}, \cite{vaz1}. Faster than \cite{tr1} \cite{LS} and LP based algorithms as we do not enumeratestructures of size $exp(Θ(f(1/ε)\cdot \log n)).$ Nor do we scale and round. \noindent \cite{ed} has an implementation \cite{kol} that is extensively used in the industry.

We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove information-theoretic lower bounds together with matching or near-matching upper bounds, covering both fixed and random designs under Hilbert-valued Gaussian noise and Gaussian white noise errors. The rates are controlled by the spectrum of the covariance operator of the measure that defines the error metric. Our setup is very general and allows for measures with unbounded support. A key implication is a curse of sample complexity, which shows that the minimax risk for generic Lipschitz operators cannot decay at any algebraic rate in the sample size. We obtain sharp characterizations when the covariance spectrum decays exponentially and provide general upper and lower bounds in slower-decay regimes. Finally, we show that assuming higher regularity, i.e., Hölder smoothness, does not improve minimax rates over the Lipschitz case, up to potential constants. Thus, we show that learning operators of any finite regularity necessarily suffers a curse of sample complexity.

Mauve is a low-cost small satellite developed and operated by Blue Skies Space Ltd. The payload features a 13 cm telescope connected with a fibre that feeds into a UV-Vis spectrometer. The detector covers the 200-700 nm range in a single shot, obtaining low resolution spectra at R~20-65. Mauve has launched on 28th November 2025, reaching a 510 km Low-Earth Sun-synchronous orbit. The satellite will enable UV and visible observations of a variety of stellar objects in our Galaxy, filling the gaps in the ultraviolet space-based data. The researchers that have already joined the mission have defined the science themes, observational strategy and targets that Mauve will observe in the first year of operations. To date 10 science themes have been developed by the Mauve science collaboration for year 1, with observational strategies that include both long duration monitoring and short cadence snapshots. Here, we describe these themes and the science that Mauve will undertake in its first year of operations.

We show that various categories of trees can be modeled by Grothendieck constructions on categories of trees with a fixed set of leaves. We prove this result for the dendroidal category $Ω$, the category $Ω^G$ of trees with a $G$-action for a finite group $G$, and finally for the category of genuine equivariant trees $Ω_G$ that has played an important role in recent work on genuine equivariant operads.