Boundary-condition (BC) handling is a major source of complexity in PDE solvers on structured and block-structured grids, especially for high-order methods and distributed-memory execution. We present Mat2Boundary, a DSL and compiler for boundary computations that models a broad class of boundary-conditions as affine sparse linear operators. This abstraction unifies halo copying, circular and symmetric mappings, zero padding, block-edge synchronization, and user-defined interpolation, while exposing a modular basic sub-matrix interface for declarative composition. To make this representation efficient, Mat2Boundary combines multi-stage programming and polyhedral analysis to generate matrix-free kernels for structured cases, support user-defined sparse matrices for irregular cases, eliminate redundant boundary work, and synthesize reusable communication schedules for distributed execution. Evaluated on two shallow-water equation solvers on cubed-sphere grids and HPCG, Mat2Boundary achieves up to 7.6$\times$ BC-kernel speedup, reduces BC code by over 70%, and scales to 1,344 CPU cores with 72%-88% efficiency.

Let $G$ be a compact Lie group that acts smoothly on a closed manifold $M$. Using a general Simonenko principle, we derive a novel criterion for the Fredholm property of $G$-pseudodifferential operators acting on Sobolev spaces of sections of vector bundles over $M$. In case the group is finite, we obtain a further characterization of the Fredholm property of $G$-pseudodifferential operators in terms of the invertibility of suitable symbols.

Spectrally multiplexed telecom quantum networks require quantum memories that combine efficient storage with programmable frequency addressing. An ideal integrated implementation should therefore unite a native telecom transition, efficient storage and fast on-chip spectral control. Here we demonstrate a cavity-enhanced quantum memory in an isotopically purified $^{167}\mathrm{Er}^{3+}$-doped thin-film lithium niobate microring resonator. Long-lived hyperfine shelving states support persistent, high-contrast atomic frequency comb preparation, with a single-component comb lifetime of $277.6 \pm 52.6$s. Together with cavity impedance matching, this yields an on-chip storage efficiency of $23.3 \pm 0.5\%$ for 100-ns storage. The intrinsic electro-optic response of lithium niobate enables frequency-selective storage and routing of retrieved photons at rates up to 20~MHz with inter-channel crosstalk below $10^{-4}$. We further store and retrieve time-energy-entangled telecom photons, violating an entanglement-witness bound by more than 11 standard deviations and thus verifying the quantum nature of the storage process. Our results establish erbium-doped thin-film lithium niobate as a programmable light--matter interface for spectrally multiplexed quantum networks.

Let $\mathcal{H}$ be the class of normalized complex valued harmonic functions $ f = h + \overline{g}$ defined on the unit disk $\mathbb{D}$, where $h$ and $g$ are analytic functions with the normalization conditions $h(0) = h'(0) - 1 = 0$ and $g(0) = 0$. For the class $R_H^{0}(γ, δ, λ)$ ( $0 \leq λ< γ\leq δ$) consisting of functions \( f = h+\bar{g} \in \mathcal{H}\) satisfying the condition $f_{\overline{z}}(0)=0$ and the inequality $ Re(γh'(z)+δz h''(z) +(\frac{δ- γ}{2})z^2 h'''(z)-λ)> |γg'(z)+δz g''(z) +(\frac{δ- γ}{2})z^2 g'''(z)|$, we obtain sharp improved Bohr Phenomenon, refined Bohr radius and the Bohr-Rogosinski inequality for the class $R_H^{0}(γ, δ, λ)$.

Let $Δ$ be a numerical semigroup and let $d\ge 2$ be an integer. We study the fiber of the quotient map \(S\mapsto S/d\) over $Δ$. We describe its elements as semigroups of the form $\langle X\rangle+dΔ$, for suitable finite sets $X\subseteqΔ$, and then analyze explicit and computable regions of this fiber. In particular, we introduce a family $Δ_d(a)$ of multiples with prescribed quotient and compute its generators, classical invariants, Apéry sets, and presentations. We also show that this construction preserves Wilf's inequality and controls the depth. Finally, we introduce the $\mathcal{M}_d(Δ)$-rank, determine its maximal value in the fiber, relate it to the ordinary embedding dimension, characterize the rank-one elements, and give closed formulas for their Frobenius-type invariants and pseudo-Frobenius numbers.

We introduce and rigorously analyze a least-squares weak Galerkin (LS-WG) finite element method for the severely ill-posed Cauchy problem of convection--diffusion equations. The proposed framework utilizes weak derivatives defined on a class of discontinuous weak functions, enabling the natural treatment of complex boundary conditions and internal interfaces. A key advantage of the least-squares formulation is that it transforms the underlying non-self-adjoint operator into a discrete linear system that is inherently symmetric and positive definite (SPD). We demonstrate the geometric flexibility of the method on arbitrary polygonal and polyhedral partitions. Furthermore, we establish the uniqueness of the numerical solution and derive optimal-order error estimates in a carefully defined discrete energy norm. Extensive numerical tests are presented to confirm the theoretical convergence rates and highlight the algorithm's robustness and efficiency compared to standard Galerkin approaches.

This article introduces an algebraic framework for establishing eigenvalue bounds for symmetric positive definite tensors by leveraging intrinsic invariants, specifically the trace and determinant (resultant). We derive a hierarchy of inequalities via the Arithmetic Mean-Geometric Mean (AM-GM) inequality that yields progressively tighter upper and lower bounds for the tensor spectral radius and smallest eigenvalue. A comprehensive comparative analysis demonstrates that our invariant-based approach significantly outperforms classical coordinate-dependent methods such as the Gershgorin circle theorem. We explicitly show that our bounds remain robust and informative in scenarios where Gershgorin bounds fail, particularly for tensors with negative off-diagonal entries, where algebraic cancellations occur, and higher-order tensors, where combinatorial growth leads to loose estimates. Furthermore, we validate the practical utility of these bounds by applying them to certify the positive definiteness of Lyapunov functions in the stability analysis of nonlinear autonomous systems.

Exciton-polaritons provide a versatile platform for the study of a wide range of phenomena, including polariton lasers, topological polaritons, and bosonic condensation. Transition metal dichalcogenide monolayers host excitons with large oscillator strength and binding energies constituting a robust matter constituent that forms polaritons from cryogenic to room temperature when embedded in optical microcavities. Plasmonic nanoparticles arranged in lattice geometries offer strong field-confinement and high quality factors. However, the high sensitivity of monolayer excitons to strain and dielectric disorder necessitates encapsulation in atomically flat hBN to ensure a high optical quality, rendering plasmonics more challenging. Here, we employ our recently developed fabrication method for embedding gold nanodisk arrays into van der Waals heterostructures and compare two samples with opposite layer order. We observe that strain and etching-induced surface contamination can reduce the exciton quality and thus the light-matter interaction strength significantly. Our fabrication approach reduces interfacial irregularities and enables homogeneous large-area polariton lattices for a wide range of applications, such as polarization-control or topological polaritonics.

Let $X \subset ¶^5_{\C}$ be a smooth cubic fourfold.The Kuznetsov component $\sA_X$ is contained in the derived category $D^b(X)$ and the transcendental motive $t(X)$ is contained in the category of Chow motives $\sM_{rat}(\C))$. If $X$ and $Y$ are {\it Fourier -Mukai partners} and hence the categories $\sA_X$ and $\sA_Y$ are equivalent, then their transcendental motives $t(X)$ and $t(Y)$ are isomorphic. The aim of this note is to consider families of special cubic fourfolds $X$ with their FM-partners $Y$ and to give an explicit description of the isomorphism between the transcendental motives, in the case $X$ and $Y$ are rational and when they are conjecturally irrational. We also prove that ,for special cubic fourfolds $X $ in countably many Hassett divisors, with a symplectic automorphism of order 3, there exists another special cubic fourfold $Y$, an equivalence of categories $\sA^G_X \simeq \sA_{Y}$, where $\sA^G_X$ is the equivariant Kuznetsov component, and an isomorphism $t(X) \simeq t(Y)$.

We propose a novel and systematic differentially private (DP) inference framework for non-Euclidean data. First, we design two types of DP mechanisms for the Fréchet mean and variance with i.i.d. Riemannian manifold-valued data, tailored to different geometric structures and accompanied by analytic privacy budgets calibrated to the geometry of the underlying manifold. Second, we establish the consistency and central limit theorems (CLTs) of the proposed DP estimators, enabling a suite of statistical inference procedures under privacy protection. Furthermore, we provide comprehensive implementation guidelines and feasible procedures, including consistent DP estimators of the asymptotic variance in the CLTs. Extensive numerical experiments support the proposed methodologies. Finally, we demonstrate the effectiveness of our approach on real-world medical image and sociological datasets lying on two representative manifolds.

The main purpose of this paper is to compare the convergence properties of Padé approximants and rational Hermite-Padé approximants for some model class of multivalued analytic functions based of the inverse Zhoukovsky transform. We prove that in the class of analytic functions under consideration the rational Hermite-Padé approximants converge faster than the corresponding Padé approximants. In contrast to the classical vector potential-theoretic approach, which was introduced by A. A. Gonchar and E. A. Rakhmanov in 1981 and developed later by A. I. Aptekarev, V. N. Sorokin and others, the proofs here are based on some scalar mixed Green-logarithmic potential problems.

We study a generic quantum Markovian master equation for a linearly displaced or driven harmonic oscillator. It was known that the displacement dynamics of Gaussian mixed states depends on the unitary part of the Liouvillian, the decay rate of the system but not on the bath temperature. Here we further show that the fast-rotating modes do not affect the system's displacement dynamics under linear driving forces. Analytical solutions of the quantum master equation are obtained for displaced Gaussian mixed states. Because the non-driven and driven Liouvillians are related by a unitary displacement operator, they are expected to share the same exceptional points structure. At the exceptional points, the displacement of critically damped oscillator displays a characteristics polynomial-in-time prefactor multiplied by an exponential decay. We discuss how external time-dependent forces affect the displacement dynamics using impulsive force and harmonic force as examples. The results obtained for constant driving remain valid in the presence of time-dependent driving.

For an $r$-uniform hypergraph $G$, let $λ^{(p)}(G)$ denote its $p$-spectral radius, defined as the maximum of the polyform of $G$ over the unit sphere in the $\ell_p$-norm. Let $Q_k^r(n)$ be the complete $k$-chromatic $r$-graph on $n$ vertices with color classes as equal as possible. Kang--Nikiforov--Yuan conjectured that, for every $p\ge1$ and $n>(r-1)k$, the $r$-graph $Q_k^r(n)$ is the unique maximizer of $λ^{(p)}$ among all $k$-chromatic $r$-graphs of order $n$. They also conjectured the corresponding explicit bound \[ λ^{(p)}(G) \le r!\left(\tbinom nr-k\tbinom{n/k}{r}\right)n^{-r/p}, \] with equality only in the divisible extremal case. The case $r=3$ was established in their work. This paper resolves the remaining cases $r\ge4$, and hence settles both conjectures for all $r\ge3$. As a consequence, the same threshold gives an anti-Wilf-type spectral certificate: any $r$-graph of order $n$ whose $p$-spectral radius exceeds the displayed bound has chromatic number at least $k+1$.

We calculate the next-to-next-to-leading order (NNLO) QED corrections to the $C$-odd part of the differential cross section of the $e^+e^-\toμ^+μ^-$ process. This part contributes to the angular and forward-backward asymmetry. Together with our earlier paper [10.1007/JHEP08(2025)118], this work completes the analytical calculation of $e^+e^-\toμ^+μ^-$ differential cross section at NNLO.

We show that flying focus fields can be obtained from complex conformal transformation of plane waves, and that solutions of the massless wave equation in the so-obtained fields are, correspondingly, conformal transformations of the Volkov solutions. This leads to the result that photon emission amplitudes in a totally depleting flying focus beam may be computed directly from the corresponding plane wave amplitudes by taking a simple Gaussian average over certain momentum variables. In effect, this gives a way of introducing focussing effects into strong-field QED calculations `for free'. The extension of these results to scattering amplitudes including only partial depletion is discussed and some first results presented in the anti-self-dual limit.

We develop and analyze iterative methods for computing the principal square root of third-order tensors under the T-product framework. Tensor extensions of the Newton iteration (quadratic convergence) and the Denman--Beavers iteration (geometric convergence with simultaneous computation of the inverse square root) are proposed, with rigorous convergence guarantees established via the Fourier-domain block-diagonalization of the T-product. We apply these methods to image processing, introducing Tensor Decorrelated Grayscale conversion, T-Whitening, and optimal color transfer under the T-product geometry. We also formulate the Tensor Bures--Wasserstein distance and prove it defines a valid metric on the space of T-positive definite tensors. Numerical experiments confirm rapid convergence and demonstrate that the proposed tensor-based techniques offer improved structural preservation and cross-channel decorrelation compared to classical methods.

We introduce a systematic analysis of density functional approximation errors in solids by separating functional-driven from density-driven contributions using quantum Monte Carlo densities of silicon, sodium chloride, and copper as reference. Typically, functional errors dominate, but we identify important exceptions where density-driven errors exceed functional errors by factors of 2-3, notably for SOGGA11 and τ-HCTH in the semiconductor and the insulator. Material dependence is striking: 63% of functionals show error cancellation in silicon versus 18% in copper, and only five functionals surpass LDA accuracy for metallic copper even with exact densities. For silicon and sodium chloride, GILL or BECKE exchange combined with PBE, PW91, or P86 correlation achieves near-exact xc energies on QMC densities, while copper requires specialized functionals like PBEsol or PBELYP. High-quality densities consistently reduce density-driven errors across all systems. Historical analysis reveals that 1990s GGA functionals outperform many modern meta-GGAs, contradicting expectations of systematic improvement along Jacob's ladder. These results provide practical guidance for functional selection and highlight implications for machine learning potential development, where material-dependent error cancellation may compromise transferability.

We prove a Mostow rigidity theorem for foliated bundles over closed hyperbolic manifolds of dimension $n \geq 3$ endowed with a completely invariant measure of full support. These include solenoidal manifolds obtained as inverse limits of directed systems of finite coverings of closed hyperbolic manifolds. This theorem then extends to skew solenoidal manifolds for which the action of the holonomy group is twisted by means of a cocycle.

Let $X$ be a real normed vector space with a cone $K\subseteq X$ satisfying either (i) $K$ is closed with non-empty interior or (ii) $K$ has non-zero extremals or (iii) $K$ is closed and $X$ is a Banach space. In this short note, we provide a method to construct an invertible linear map $T\colon X\to X$ such that $T[K]\subseteq K$ but $T^{-1}[K]\not\subseteq~K$. In particular, we show that, for every cone automorphism $S\colon X\to X$, there exists a rank one perturbation of $S$ which is positive and invertible, but does not have a positive inverse. We provide examples from four diverse situations.

The NA61/SHINE experiment at the CERN SPS is a multipurpose fixed-target spectrometer for charged and neutral hadron measurements. Its research program includes studies of strong interactions as well as reference measurements for neutrino and cosmic-ray physics. One major goal of its strong interaction program is to determine the existence and pinpoint the location of the QCD critical point, an object of both experimental and theoretical studies. This contribution will summarize the current status of NA61/SHINE critical point searches in nucleus-nucleus collisions, in the collision energy range $\sqrt{s_{NN}} = 5-17$~GeV. The review includes studies of fluctuations of net-electric charge, femtoscopy analysis of $π-π$ pairs, as well as intermittency of protons and negatively charged hadrons. No clear indication of the critical point has been observed so far. Finally, we report on the development of novel methods aimed at solving the long-standing problem of bin-by-bin correlations in experimental intermittency analysis, and for a more accurate handling of systematics and uncertainties.

Altermagnets have attracted intense interest because they have the advantages of both ferromagnets and antiferromagnets. However, their experimental identification remains challenging, in particular for the A-type altermagnets that account for a large group of material candidates. Here, we discover a kind of anisotropic surface spin waves in A-type altermagnets, which is absent in ferromagnets and conventional antiferromagnets. The anisotropic surface spin waves arise directly from the nature of altermagnets, i.e., the spin-opposite sublattices cannot be related by translation or inversion, which breaks the combined spatial-inversion and time-reversal symmetry, leading to the anisotropic surface spin waves with two properties, the chirality-dependent top-bottom positions and chiral split constant frequency contours. We further show that these two properties can be measured experimentally from the stray field and by resonance absorption spectrum, respectively. Our results provide a signature for detecting altermagnets and will inspire spin-based logic and information-storage devices.

The Burning Number Problem (BNP) models the spread of information or contagion in a network through a discrete-time process on a graph. At each step, one new vertex is selected as a burning source, while fire simultaneously spreads from previously burned vertices to their neighbors. The burning number of a graph is the minimum number of steps required to burn all vertices. The decision version asks whether the burning number is at most a given integer $k$. BNP is known to be NP-complete even on restricted graph classes such as path forests. We study BNP on connected regular graphs, a natural and previously unexplored graph class. We prove that BNP is NP-complete on connected cubic graphs, and moreover APX-hard under this restriction. We further show that BNP remains APX-hard on connected $d$-regular graphs for every fixed $d \geq 4$.

We study the regularized vacuum stress tensor of scalar fields in maximally symmetric spacetime and assess the feasibility of driving primordial inflation or current cosmic acceleration by analyzing the existence of solutions to the Friedmann equation. We find that a conformally coupled scalar field with mass of order $10$ $M_{\text{pl}}$ can be a candidate for both the inflaton and dark energy, suggesting that these two components may have the same quantum origin. In contrast, a minimally coupled scalar field cannot serve as either the inflaton or dark energy regardless of its mass.

We provide a comprehensive overview of the current status of higher-codimension defect systems. We review the holographic description and field theoretic properties of codimension-2 defects within the framework of defect Conformal Field Theories (dCFTs). Starting from the well-established classification of $1/2$-BPS supersymmetric defects, we examine their realisation through probe branes and bubbling supergravity geometries. Special emphasis is placed on recent developments involving non-supersymmetric D3/D5 configurations and their holographic interpolations. We discuss the calculation of important physical observables, such as one-point functions of the stress-energy tensor and chiral primary operators, across both weak and strong coupling regimes. The agreement of the results in the two regimes exhibits the full power of the holographic principle. This is a proceedings contribution to the Athens Workshop in Theoretical Physics: 10th Anniversary, held at the National and Kapodistrian University of Athens on December 17-19 2025.

Motivated by the increasing precision of neutrino oscillation data, we study the corrections to the TM$_2$ neutrino mixing framework, emanating from $(1,2)$ sector of the charged lepton, for both the standard LMA and dark-LMA solutions. We employ the Wolfenstein parameterization of the charged-lepton mixing matrix, characterized by two additional parameters $(λ,δ)$, which effectively reconciles the TM$_2$ neutrino-mixing predictions with current oscillation data. For the LMA solution, the allowed ranges are $0.1 \lesssim λ\lesssim 0.33$ and $δ\in (20^\circ\!-\!90^\circ)\oplus(270^\circ\!-\!340^\circ)$, while the dark-LMA case requires $λ>0.24$ and $125^\circ<δ<235^\circ$. Interestingly, for LMA case, the upper bound $λ\le 0.33$ is found to be dictated by the atmospheric mixing angle $θ_{23}$. The model predicts sizeable CP violation, with $|J_{CP}|$ reaching values as large as $0.13$. We, also, analyze the effective Majorana mass parameter $m_{ee}$ relevant for neutrinoless double beta decay. The inverted hierarchy region lies within the sensitivity of future experiments for both solutions, whereas only part of the normal hierarchy region can be tested.

Modern researchers engage in diverse activities, assume multiple contribution roles, and produce a variety of outputs beyond traditional publications. This broader view of research contributions is increasingly recognised by responsible research assessment initiatives. However, existing researcher profiling platforms remain largely focused on publications and publication-centric indicators, offering limited support for contextualised and multi-dimensional representations of research careers. This paper presents BIP! Scholar, a platform that supports flexible researcher profiling through a template-driven approach. Researchers can create profiles tailored to different presentation or assessment contexts using track-based, narrative-style, or hybrid templates which support the representation of diverse outputs, contribution roles, and broader research activities. The platform also supports research assessment experts who wish to design and evaluate experimental profile templates.

This paper investigates the effect of oscillator phase noise in orthogonal time frequency space (OTFS) systems. The paper provides in-depth analysis of the interference due to phase noise in the delay-Doppler domain and derives expressions for SINR for three different oscillator types, namely free-running oscillators, continuous-time phase locked loops (PLLs) and discrete-time PLLs. The analysis demonstrates the OTFS is sensitive to phase noise and requires appropriate estimation and compensation. In particular, the analysis shows phase noise imposed inter-Doppler-interference (IDI) is severe and that existing phase noise estimation techniques which only consider the common-phase-error (CPE) can not compensate this IDI effectively. Additionally, the existing methods in the OTFS literature on phase noise assume the channel to be a known single tap channel. Hence, in this paper, we propose a method for joint channel and phase noise estimation using a Wiener filtering approach. Our proposed method exploits the statistical nature of both the phase noise and the Doppler spread channel. Our numerical results demonstrate the superior performance of our proposed technique, with gains of up to 8~dB in terms of bit error rate (BER) over existing methods in the literature.

The application of quantum computing to data management has attracted growing interest, yet remains constrained by a limited understanding of how the physical behaviour of quantum devices relates to the structure and difficulty of database problems. In particular, evaluating quantum annealing approaches for combinatorial optimisation, which is central to many data management tasks, poses significant challenges beyond the scope of conventional empirical and complexity-theoretic methods. We present a computational toolbox for the systematic numerical analysis of quantum annealing processes derived from data management problem formulations. Adopting a physics-informed perspective, the toolbox enables the study of spectral and dynamical properties -- such as energy gaps and eigenstate structure -- that are inaccessible through direct hardware measurements, yet essential for understanding computational hardness and scaling behaviour. Our approach further provides derived quantities and visualisation techniques that support the interpretation of optimisation dynamics, the identification of structural similarities to canonical physical models, and the construction of reduced effective descriptions. By bridging methodological gaps between quantum computing and database systems research, this work establishes a principled foundation for evaluating quantum approaches and guiding future co-design efforts.

The deployment of Fully Homomorphic Encryption (FHE) at scale is hindered due to its heavy computational overhead. While specialized hardware accelerators like Google Tensor Processing Units (TPUs) can help, mapping complex cryptographic kernels onto such architectures remains a challenge. Efficient execution requires co-optimization between the systolic array-based Matrix Multiplication Unit (MXU) and Vector Processing Units (VPUs), as well as the orchestration of data movement across the vector register files. Existing compiler stacks often abstract low-level hardware utilization, requiring developers to adopt a manual trial-and-error process that often results in fragmented execution and underutilized resources. To accelerate this development process, we use AlphaEvolve to automate the exploration of hardware-aware cryptographic-kernel optimizations. We frame optimization as an evolutionary search problem, utilizing the closed-loop system provided by AlphaEvolve, that leverages LLM-driven code generation. We use real-world feedback from hardware execution and rigorous correctness testing to guide the evolution process. We evaluate AlphaEvolve optimization on primitives for both the TFHE (Jaxite) and CKKS (CROSS) FHE schemes on Google Cloud TPUv5e, a contemporary TPU architecture. Within 24 hours of automated exploration, AlphaEvolve discovered implementation-level optimizations that improve TFHE bootstrap latency by 2.5x and CKKS rotation and multiplication latency by 1.31x and 1.18x, respectively, relative to human-engineered state of the art. These results demonstrate that AlphaEvolve can be used to enable researchers to navigate the optimization trade-offs between cryptography, compilers, and hardware accelerators.

In this article we consider a $\mathbb{Z}_2$-odd $SU(2)$ quartet with hypercharge $Y = +\frac{1}{2}$ as an extension of the Standard Model whose scalar potential which introduces three additional Higgs portal and two self-couplings. We first investigate the possibility of having Landau poles (LPs) in one-loop and Fixed Points (FPs) in two-loop $β$-functions of the Higgs quartic couplings. The role of portal and self-couplings with and without residual phases is extensively investigated in obtaining the Fixed Point at two-loop. The model also can provide us with $\mathbb{Z}_2$-odd neutral scalar as the possible dark matter. However not always the lightest state corresponds to the neutral states, and we look into one-loop mass correction for an enhanced dark matter parameter space. This also gives rise to interesting phenomenology of the next-to-lightest particle which can be singly charged, doubly charged or neutral scalar. We performed a detailed study of dark matter relic calculation with one-loop masses and with direct detection bounds, and found out that, unlike the minimal inert extensions of $SU(2)$ multiplets, here the dark matter mass can go beyond 15 TeV without crossing the observed relic. Finally, we summarized with a few benchmark points for future studies.