We calculate the binding energies of the hypothetical mesonic atom, $K^+ K^-$ (kaonium), using the $K^+ K^- \to K^+ K^-$ elastic scattering amplitude. Our findings are in line with previously reported results, which involve solving an eigenvalue equation of the Kudryavtsev-Popov type. Using chiral perturbation theory, we show that kaonium manifests itself as a sharp resonance around 992 MeV accompanying $f_0 (980)$ or $a_0 (980)$ in cross-sections for processes $γγ\to π^0 π^0$ or $γγ\to π^0 η$. The latter process is particularly striking: the peak at the kaonium resonance energy is highly pronounced, with the ratio of the cross-sections $σ(γγ\to π^0 η) / σ(γγ\to π^0 π^0) \approx 9$. Due to the short lifetime of kaonium ($\sim 10^{-18}$ s) and its small decay width ($\sim 0.4$ keV), direct detection of this exotic atom poses a significant challenge and requires high experimental resolution. However, we show that once the formation of kaonium is considered in the cross-section, a better fit to the available experimental data is obtained.

Graphene is a promising platform for spin-based non-volatile memory, logic, and neuromorphic computing by combining long-distance spin transport with electrical tunability at room temperature. However, advancing beyond passive spin channels requires devices capable of generating large spin signals with efficient rectification capabilities, which are essential for active spintronic components. Here, we demonstrate a folded-bilayer graphene spin-valve device with giant non-local spin signals in the several mV range with pronounced spin-rectification effects. Efficient spin injection creates a significant spin accumulation of 20 meV and generates a spin diode effect with an asymmetry of over an order of magnitude between forward and reverse bias conditions. This spin-diode effect is expected to arise from nonlinear spin-charge interactions in the folded-bilayer graphene channel. These observed large spin signals and spin-diode effects in graphene systems offer a promising platform for developing active two-dimensional spintronic devices.

We study quantum quench dynamics in (1+1)-dimensional critical systems, starting from thermal pure states called crosscap states, and evolving them under spatially inhomogeneous Hamiltonians. The spatial inhomogeneity is introduced through a deformation of the Hamiltonian, expressed as linear combinations of the generators of the $SL^{(q)}(2,\mathbb{R})$ subalgebra of the Virasoro algebra. We analyze the free massless Dirac fermion theory and holographic conformal field theory as prototypical examples of integrable and non-integrable dynamics. Consistent with general expectations, "Möbius-type" deformations lead to thermalization in the non-integrable case, and to periodic revivals in the integrable one. In contrast, "sine-square-type" and "displacement-type" deformations prevent both thermalization and scrambling, instead producing late-time, graph-like entanglement patterns. These patterns emerge from the interplay between the deformed Hamiltonian and the crosscap initial state and appear to be universal: they are determined solely by the deformation profile while remaining largely insensitive to microscopic details. Finally, we perform a holographic calculation in three-dimensional gravity using AdS$_3$/CFT$_2$, which reproduces the main features of our (1+1)-dimensional study.

We consider the one dimensional 4th order, or bi-harmonic, nonlinear Schrödinger (NLS) equation, namely, $i u_t - Δ^2 u - 2a Δu + |u|^α u = 0, ~ x,a \in \R$, $α>0$, and investigate the dynamics of its solutions for various powers of $α$, including the ground state solutions and their perturbations, leading to scattering or blow-up dichotomy when $a \leq 0$, or to a trichotomy when $a>0$. Ground state solutions are numerically constructed, and their stability is studied, finding that the ground state solutions may form two branches, stable and unstable, which dictates the long-term behavior of solutions. Perturbations of the ground states on the unstable branch either lead to dispersion or the jump to a stable ground state. In the critical and supercritical cases, blow-up in finite time is also investigated, and it is conjectured that the blow-up happens with a scale-invariant profile (when $a=0$) regardless of the value of $a$ of the lower dispersion. The blow-up rate is also explored.

We investigate CP-violating effects in electroweak interactions at future high-energy muon colliders within the Standard Model Effective Field Theory (SMEFT) framework. Focusing on four dimension-six CP-odd operators -- $ \mathcal{O}_{\widetilde{W}}, \mathcal{O}_{H\widetilde{W}}, \mathcal{O}_{H\widetilde{W}B}, \mathcal{O}_{H\widetilde{B}}$ -- we analyze vector boson fusion production of $W$ and Higgs bosons using CP-odd observables and their asymmetries. With detailed simulations including parton showering, hadronization, and detector effects, we derive exclusion sensitivities through a binned likelihood analysis. For example, at $\sqrt{s} = 3$ TeV with 2 ab$^{-1}$, the coefficient $C_{\widetilde{W}}$ can be constrained at the $\mathcal{O}(0.02)$ level, improving to $\mathcal{O}(0.008)$ at 10 TeV with 2 ab$^{-1}$, and $\mathcal{O}(0.003)$ with 10 ab$^{-1}$. These results significantly surpass current LHC and projected ILC sensitivities, demonstrating the unique potential of high-energy muon colliders to provide direct and model-independent probes of CP violation in the electroweak sector.

This work is concerned with relaxation models arising from numerical schemes for hyperbolic-parabolic systems. Such models are a hyperbolic system with both the hyperbolic part and the stiff source term involving a small positive parameter, and thus are endowed with complicated multiscale properties. Relaxation models are the basis of constructing corresponding numerical schemes and a critical issue is the convergence of their solutions to those of the given target systems, the justification of which is still lacking. In this work, we employ the recently proposed theory for general hyperbolic relaxation systems to validate relaxation models in numerical schemes of hyperbolic-parabolic systems. By verifying the convergence criteria, we demonstrate the convergence, and thereby the approximation validity, of five representative relaxation models, providing a solid basis for the effectiveness of the corresponding numerical schemes. Moreover, we propose a new relaxation model for the general multi-dimensional hyperbolic-parabolic system. With some mild assumptions on the system, we show that the proposed model satisfies the convergence criteria. We remark that the existing relaxation models are constructed only for a special case of hyperbolic-parabolic system, while our new relaxation model is valid for general systems.

Metal hydrides MHx with low hydrogen content are not expected to show high-Tc superconductivity owing to the low hydrogen-derived electronic density of states at Fermi level and the limited hydrogen contribution to electron-phonon coupling strength. In this work, we report on the successful synthesis of a novel bismuth dihydride superconductor, Cmcm-BiH$_2$, at approximately 150 GPa, and the discovery of superconductivity with Tc about 62 K at 163 GPa, marking the first instance of superconductor among the MH$_2$-type metal dihydrides. Cmcm-BiH$_2$ adopts a unique host-guest type structure, in which the Bi atoms via weak Bi-Bi covalent bonds form a three-dimensional open-channel framework that encapsulates H$_2$-like molecules as guests, thereby broadening the structural diversity of hydrides under high pressures. The occurrence of superconductivity is evidenced by a sharp drop of resistivity to zero and the characteristic downward shift of Tc under applied magnetic fields. Notably, Cmcm-BiH$_2$ remains stable down to at least 97 GPa during decompression, with the calculated lowest pressure for dynamic stability of 10 GPa. In-depth analysis reveals that the covalent bismuth open-channel structure forms metallic conduction channels, dominates the electronic states near the Fermi level, and contributes approximately 51% of the total $lambda$ in Cmcm-BiH$_2$, distinguishing it from known high-pressure hydride superconductors. These findings highlight the critical role of non-hydrogen elements in producing superconductivity and open new avenues for the design and optimization of high-Tc hydride superconductors.

We consider the discrimination of quantum sequences under maximum-confidence measurements and show that the optimal discrimination of a quantum sequence ensemble can always be factorized into that of each individual ensemble. In other words, the optimal quantum sequence discrimination under maximum-confidence measurements can be achieved just by performing a maximum-confidence discrimination independently at each step of the quantum sequence. We also show that the maximum confidence of identifying a quantum sequence is to achieve the maximum confidence of identifying each state comprising the quantum sequence. We further provide a necessary and sufficient condition for the optimal quantum state discrimination under maximum-confidence measurements.

In this paper, we investigate thermodynamical aspects of a novel static non-extremal black hole solution in the five-dimensional anti-de Sitter (AdS) space carrying four independent electric charge parameters and with a negative cosmological constant, within the framework of $D=5$, $\mathcal{N} = 2$ gauged supergravity coupled to three vector multiplets specified by the pre-potential $\mathcal{V} = STU -W^2U \equiv 1$. A central outcome of our work is the demonstration that the thermodynamics of this solution consistently satisfies both the differential and integral forms of the mass formulae of black hole thermodynamics. When the fourth charge is set to zero, our configuration reduces to the known three-charge static non-extremal AdS$_5$ black hole within the gauged $STU$ model, and its thermodynamic behavior connects smoothly to that limit. Finally, we also provide a brief discussion about topological classifications of its thermodynamics.

The degree of freedom of the scalar field in scalar-tensor gravity is employed as "time" to deparametrize the Hamiltonian constraint of the theory. The deparametrized system is then nonperturbatively quantized by the approach of loop quantum gravity. This results in a discrete time evolution of the physical states with respect to the gravitational degree of freedom in the quantum theory. In the corresponding Brans-Dicke cosmological model, the physical solutions to the quantum Hamiltonian constraint are obtained in the light of the deparametrization. The quantum dynamics indicates that the classical big bang singularity is replaced by a quantum bounce.

Suppose $F$ is an infinite field and let $f \in F\{X_1, \dots,X_m\}$ be a noncommutative polynomial. Partially answering a query of Makar-Limanov, we show that there are numbers $d$ and $m'$ such that, if $F$ is closed under taking $d$th roots, for any $n \ge m'$ there are matrices $A_1,\dots,A_m$ in~$M_n(F)$ such that $f(A_1,\dots,A_m)$ is upper triangular with $n-m'$ prescribed diagonal entries. When f is homogeneous, $f(A_1,\dots,A_m)$ is diagonal with $n-m'$ prescribed diagonal entries. When f is multilinear, we can take $d=1$ and $m' = [\frac{m-1}{2}]$, and the upper left $(n-m')\times (n-m')$ piece of $f(A_1,\dots,A_m)$ can be taken to be $diag(β_1,\dots, β_{n-m'})$, for indeterminates $β_i$. Furthermore, if $f$ is not a polynomial identity of $ k \times k $ matrices, then at least $ n - k $ characteristic values of $ f(A_1,\dots,A_m) $ may be taken to be algebraically independent.

This paper studies nonparametric local (over-)identification and the semiparametric efficiency in modern causal frameworks. We develop a unified approach that begins by translating structural models with latent variables into their induced statistical models of observables and then analyzes local overidentification through conditional moment restrictions. We apply this approach to three popular classes of causal models: (1) the general treatment model under unconfoundedness; (2) the negative control model, and (3) the long-term causal inference model under unobserved confounding. The first model yields a locally just-identified statistical model, implying that all regular asymptotically linear estimators of the treatment effect have the same asymptotic variance, which equals the (trivial) semiparametric efficient variance bound. In contrast, the latter two models involve nonparametric endogeneity and are naturally locally overidentified; consequently, some doubly robust orthogonal moment estimators of the average treatment effect are inefficient. Whereas existing work typically imposes strong conditions to restore local just-identification to justify the efficiency of their doubly robust orthogonal moment estimators, we characterize the semiparametric efficient variance bounds, along with efficient estimators, for the (locally) overidentified models (2) and (3). A small real data application, along with a simulation study, illustrates the semiparametric efficiency gains in model (3).

Dark-matter-dominated dwarf galaxies provide an excellent laboratory for testing dark matter models at small scale and, in particular, the ultralight dark matter (ULDM) class of models. Within the framework of self-interacting bosonic dark matter, we use the observed velocity-dispersion profiles of seven dwarf spheroidal galaxies to constrain the parameters of ULDM. In our modeling, we account for the impact of the baryonic component on the velocity dispersion and ULDM halo structure. We find that the repulsive self-interaction of ULDM, which fits the observations, is almost negligible, consistent with non-interacting ULDM with a boson mass of approximately $1.6 \times 10^{-22}\,\mathrm{eV}$. In contrast, for attractively interacting ULDM, the best fit corresponds to a smaller boson mass of about $1.3 \times 10^{-22}\,\mathrm{eV}$, with self-interaction playing a significant role in shaping the dark-matter halo and thereby influencing the interpretation of observations.

We study the distance set problem for pairs of compact sets $A, B\subset \mathbb{R}^n$, $n\geq 2$. We show that if $B$ is contained in a hyperplane and \begin{align*} \dim_{H} A+\dim_{H} B>n, \end{align*} then the distance set $ Δ(A,B):=\left\{ \vert x-y\vert: x\in A, y\in B\right\}$ has positive Lebesgue measure, and the dimensional threshold is sharp. This yields new positive results for Falconer's distance problem in certain regimes, particularly where the best known bounds fail to apply. We further establish Falconer's distance conjecture for certain classes of product sets under additional structural assumptions. Specifically, if $A=A_1\times A_2\subset \mathbb{R}^{m}\times \mathbb{R}^{n-m}$ for some $0\leq m\leq n-1$, where $A_2$ is a Salem set, and \[ \dim_HA>\frac{n}{2}, \] then the distance set $Δ(A):=\left\{|x-y|: x,y\in A\right\} $ has positive Lebesgue measure. A key feature of our argument is the interpretation of the original map as a suitable projection. We extend the analysis to a broad class of smooth functions, recovering the sharp result of Koh, Pham, and Shen (J. Funct. Anal. 286 (2024)) for quadratic polynomials in three variables.

We introduce the PenduMAV, an exactly actuated (6-input) omnidirectional multirotor that structurally eliminates internal forces at equilibria. The vehicle features one actively-tilting propeller and three propellers mounted on passive pendulum links via universal joints. This architecture achieves full 6D wrench generation while avoiding the structural and energetic costs of input redundancy and internal forces. After deriving the full multibody dynamics, we demonstrate that a forced equilibrium exists for every main platform pose. To asymptotically stabilize the closed-loop system, we design a coordinate-invariant nonlinear controller based on dynamic feedback linearization and backstepping, utilizing the left-trivialized error on SE(3). System stability is formally guaranteed through Lyapunov analysis of the zero dynamics. Finally, Gazebo simulations (videos available at https://www.youtube.com/playlist?list=PL4N8pJgvqASQX6AWEpg3NCZ6QdGBPfbXq) validate the approach, showcasing fully decoupled attitude and translational tracking under parametric uncertainty and actuator noise.

We apply the automatic stellar stream detection algorithm StarStream to Gaia Data Release 3 and identify 87 stellar streams associated with Galactic globular clusters (GCs), including 34 high-quality cases with median completeness and purity both exceeding 50%, as estimated from modeling mock streams. These detections double the number of known GC streams, and increase the fraction of GCs with tidal streams at high Galactic latitudes (|b| > 30 degree) to 75%. In contrast to visual expectations, many new streams are wide or short, or misaligned with their progenitors' orbits. Taking advantage of the unbiased density measurements enabled by our method, we also estimate the mass loss rate for the progenitor GCs. We find that several low-mass, large-size clusters have enhanced mass loss rates, indicating that they are approaching complete tidal disruption.

We study strong fractional maximal operator and fractional integral operator associated with Zygmund dilation defined on Heisenberg group. Characterizations are established for the L^p to L^q regularity of these two operators.

Hadronic vacuum polarization at low virtualities limits the precision of experimental tests of the standard model via important physical observables. Here we compute that effect in two-flavor chiral perturbation theory to three loops. Among the master integrals that describe the amplitude, six are elliptic functions of the momentum. Of these five are new to this work, although all can be related to the three-loop sunset integral. The renormalizability of the amplitude hinges on relations between the master integrals that were not previously known and that are not consequences of the integration-by-parts reduction. Our result is intended to serve as a starting point for phenomenological calculations, as well as the computation of finite-volume corrections in lattice QCD.

In quantum censorship, an agency oversees quantum communication in a public-domain network. The agency restricts the users communication to the free states of a quantum resource theory (QRT). Despite quantum correlations being fragile, any realistic censorship leaves behind some quantumness, raising concerns that censorship may be overcome through revival or distillation of quantum resources. Here, we introduce censorship protocols that do not require a perfect erasure of a quantum resource, but rather deem censorship successful if users are unable to restore the original quantum state using free operations. We investigate under which conditions censorship is secure, and when it might fail. Moreover, we address the issue of account sharing in quantum networks, wherein independent parties assist in transmitting quantum resources to censored users. This connects resource censorship to timely topics such as quantum catalysis and resource-assisted communication. Censorship protocols offer a novel perspective on quantum network security, that differs fundamentally from existing approaches such as quantum and post-quantum cryptography.

Brane tilings are bipartite periodic graphs on the 2-torus and realize a large family of 4d N=1 supersymmetric gauge theories corresponding to toric Calabi-Yau 3-folds. We present a complete classification of dimer integrable systems corresponding to the 30 brane tilings whose toric Calabi-Yau 3-folds are given by the 16 reflexive polygons in 2 dimensions. For each dimer integrable system associated to a reflexive polygon, we present the Casimirs, the single Hamiltonian built from 1-loops, the spectral curve, and the Poisson commutation relations. We also identify all birational equivalences between dimer integrable systems in this classification by presenting the birational transformations that match the Casimirs and the Hamiltonians as well as the spectral curves and Poisson structures between equivalent dimer integrable systems. In total, we identify 16 pairs of birationally equivalent dimer integrable systems which combined with Seiberg duality between the corresponding brane tilings form 5 distinct equivalence classes. Echoing phenomena observed for brane brick models realizing a family of 2d (0,2) supersymmetric gauge theories corresponding to toric Calabi-Yau 4-folds, we illustrate that deformations of brane tilings, including mass deformations, correspond to the birational transformations we discover in this work, and leave invariant the number of generators of the mesonic moduli space as well as the corresponding U(1)R-refined Hilbert series.

Constant-time (CT) verification tools are commonly used for detecting potential side-channel vulnerabilities in cryptographic libraries. Recently, a new class of tools, called speculative constant-time (SCT) tools, has also been used for detecting potential Spectre vulnerabilities. In many cases, these SCT tools have emerged as liftings of CT tools. However, these liftings are seldom defined precisely and are almost never analyzed formally. The goal of this paper is to address this gap, by developing formal foundations for these liftings, and to demonstrate that these foundations can yield practical benefits. Concretely, we introduce a program transformation, coined Speculation-Passing Style (SPS), for reducing SCT verification to CT verification. Essentially, the transformation instruments the program with a new input that corresponds to attacker-controlled predictions and modifies the program to follow them. This approach is sound and complete, in the sense that a program is SCT if and only if its SPS transform is CT. Thus, we can leverage existing CT verification tools to prove SCT; we illustrate this by combining SPS with three standard methodologies for CT verification, namely reducing it to non-interference, assertion safety and dynamic taint analysis. We realize these combinations with three existing tools, EasyCrypt, BINSEC, and ctgrind, and we evaluate them on Kocher's benchmarks for Spectre-v1. Our results focus on Spectre-v1 in the standard CT leakage model; however, we also discuss applications of our method to other variants of Spectre and other leakage models.

A fundamental question in the field of quantum reference frames concerns what global properties of a system can be determined by observers operating entirely from within that system. We investigate this question by extending both the perspectival and perspective-neutral approaches beyond the commonly studied zero total momentum case to arbitrary fixed charge sectors. When the entire system, including the reference frames, moves at a fixed total momentum $P$ relative to an external frame, this global charge becomes encoded in the quantum states and transformations between reference frames. Our extension leads to modified relative states and observables with QRF transformations that induce an additional $P$-dependent phase, treating all charge sectors as equally fundamental. By granting the internal observers successively more access and resources, we identify under which conditions they can infer the total momentum. These results clarify the relationship between major QRF approaches -- perspectival, perspective-neutral, operational, and extra-particle -- showing how their differing conclusions stem from different assumptions about which observables are deemed accessible from within. Our findings cast light on the relation between local and global perspectives and raise fundamental questions about scenarios where no global perspective exists, contributing to a deeper understanding of relationality and the role of perspectives in quantum theory.

Dopants can tune the performance of MoS2 in various applications, but use of molecular dynamics simulations for doped MoS2 materials discovery is limited by the lack of multi-dopant interatomic potentials. Universal machine learning interatomic potentials (MLIPs) could be a solution, but the accuracy of these potentials must first be evaluated. Here, we evaluate the accuracy of a recently developed MLIP, META's Universal Model for Atoms (UMA), for 25 different MoS2 dopants spanning metals, non-metals, and transition metals in Mo substitution, S substitution, and intercalated positions by benchmarking the MLIP-predicted formation energy and the dopant-induced structural change against density functional theory calculations. The computational framework for MLIP validation and simulations are described in detail and the source code is made open source. The MLIP is then demonstrated by performing heating-cooling simulations of MoS2 supercells with all 25 dopants. These simulations capture complex phenomena including dopant clustering, MoS2 layer fracturing, interlayer diffusion, and chemical compound formation at orders-of-magnitude reduced computational cost compared to density functional theory. This work provides a computational workflow for application-oriented design of doped-MoS2, enabling high-throughput screening of dopant candidates and optimization of compositions for targeted tribological, electronic, and optoelectronic performance. Github Repo Link: https://github.com/AbrarFaiyad/Machine-Learning-Interatomic-Potential-UMA-Enables-MD-Simulations-of-MoS2-Doped

In this work, we develop new pulse designs and embedding strategies to improve the analog quantum subroutines of hybrid column generation (CG) algorithms based on neutral-atoms quantum computers (NAQCs). These strategies are designed to improve the quality and diversity of the samples generated. We apply these to an important combinatorial optimization (CO) problem in logistics, namely the fleet assignment. Depending on the instance tested, our quantum protocol has a performance that is either comparable or worse than the best classical method tested, both in terms of the number of iterations and final objective value. We identify the cause of these suboptimal solutions as a result of our quantum protocol often generating high-quality but degenerate samples. We address this limitation by introducing a greedy post-processing technique, Make\_Diff, which applies bit-wise modifications to degenerate samples in order to return a non-degenerate set. With this modification, our quantum protocol becomes competitive with an exact solver for the subproblem, all the while being resilient to state preparation and measurements (SPAM) errors. We also compare our CG scheme with a Gurobi solver and find that it performs better on over 50\% of our synthetic instances and that, despite Gurobi having a more extensive runtime. These improvements and benchmarks herald the potential of deploying hybrid CG schemes on NISQ devices for industrially relevant CO problems.

The CCAT Observatory's primary science instrument, Prime-Cam, is nearing readiness for deployment to the Fred Young Submillimeter Telescope (FYST) in the Atacama Desert in northern Chile. When fully deployed, Prime-Cam will field approximately 100,000 kinetic inductance detectors (KIDs) across seven instrument modules making both broadband and polarimetric measurements. Meanwhile, in-lab characterization of the first CCAT instrument module, a 280 GHz broadband camera fielding over 10,000 KIDs, is currently underway in the testbed instrument Mod-Cam. Both Mod-Cam and Prime-Cam will employ 46 cm long low-thermal-conductivity flexible circuits ("stripline") between 4 K and 300 K to connect large-format arrays of multiplexed KIDs in each instrument module to readout electronics. The 280 GHz camera currently installed in Mod-Cam uses six of these striplines to read out its over 10,000 detectors. We have examined the thermal and electrical performance of the stripline installed in Mod-Cam. We begin by characterizing the OFHC copper in the stripline traces, allowing for the estimation of thermal loading through these flexible circuits in their configurations in both Mod-Cam and Prime-Cam. We then directly measure the thermal conductivity of the stripline, finding it is best described by $kA = 22\pm6~T^{0.84\pm0.09}~\mathrm{μ~W~m~K^{-1}}$ for temperature ranges of 6 K < T < 20 K and $kA~=~0.6\pm0.3~T^{-0.4\pm0.1}~\mathrm{mW~m~K^{-1}}$ for ranges from 20 K < T < 80 K. Following our thermal characterizations, we report on the transmission and crosstalk properties of the Mod-Cam readout chain, isolating elevated crosstalk to SMP-SMA transition printed circuit boards (PCBs) that interface with the stripline. This finding validates the stripline circuit as a viable high-density cabling option for large-format array readout.

Security verification of communication protocols in industrial and safety-critical systems is challenging because implementations are often proprietary, accessible only as black boxes, and too complex for manual modeling. As a result, existing security testing approaches usually depend on incomplete test suites and/or require labor-intensive modeling, limiting coverage, scalability, and trust. This paper addresses the problem of systematically verifying protocol security-properties without access to internal system models. We propose a flexible and scalable method for formal verification of communication protocols that combines active automata learning with model checking to enable rigorous security analysis of black-box protocol implementations. The key contributions include: (i) a method for augmenting learned protocol models with security-relevant propositions, (ii) a fully automated transformation pipeline from learned models to model-checking artifacts, (iii) reusable, generic security property templates that are instantiated in protocol-specific models, and (iv) empirical validation through case studies demonstrating applicability in different protocols and domains. The results show that the approach enables scalable and systematic discovery of security vulnerabilities in black-box systems while reducing modeling effort and improving automation compared with traditional verification workflows.

In this paper, we introduce the notions of parabolic representation pair variety and relative representation variety of a given parabolic type. We investigate the local behavior of these varieties. The Zariski tangent space and the tangent quadratic cones are described. By the Riemann--Hilbert--Deligne correspondence, we pro-represent the analytic germs of these varieties by functors related to certain groupoids of parabolic logarithmic flat bundles. Under suitable assumptions, we prove that the differential graded Lie algebra (DGLA) controlling the deformation of parabolic logarithmic flat bundle is mixedly formal. Finally, we construct the moduli space of weighted parabolic representation pairs, and, by means of quiver representation theory, we establish the Kobayashi--Hitchin-type theorem for polystable parabolic representation pairs.

Federated Recommendation (FR) is a new learning paradigm to tackle the learn-to-rank problem in a privacy-preservation manner. How to integrate multi-modality features into federated recommendation is still an open challenge in terms of efficiency, distribution heterogeneity, and fine-grained alignment. To address these challenges, we propose a novel multimodal fusion mechanism in federated recommendation settings (GFMFR). Specifically, it offloads multimodal representation learning to the server, which stores item content and employs a high-capacity encoder to generate expressive representations, alleviating client-side overhead. Moreover, a group-aware item representation fusion approach enables fine-grained knowledge sharing among similar users while retaining individual preferences. The proposed fusion loss could be simply plugged into any existing federated recommender systems empowering their capability by adding multi-modality features. Extensive experiments on five public benchmark datasets demonstrate that GFMFR consistently outperforms state-of-the-art multimodal FR baselines.

Given an Abelian groups $G$, denote $μ(G)$ the size of its largest sum-free subset and $f_{\max}(G)$ the number of maximal sum-free sets in $G$. Confirming a prediction by Liu and Sharifzadeh, we prove that all even-order $G\ne \mathbb{Z}_2^k$ have exponentially fewer maximal sum-free sets than $\mathbb{Z}_2^k$, i.e. $f_{\max}(G) \leq 2^{(1/2-c)μ(G)}$, where $c > 10^{-64}$. We construct an infinite family of Abelian groups $G$ with intermediate growth in the number of maximal sum-free sets, i.e., with $ 2^{(\frac{1}{2}+c)μ(G)}\leq f_{\max}(G) \leq 3^{(\frac{1}{3}-c)μ(G)} $, where $c=10^{-4}$. This disproves a conjecture of Liu and Sharifzadeh and also answers a question of Hassler and Treglown in the negative. Furthermore, we determine for every even-order group $G$, the number of maximal distinct sum-free sets (where a distinct sum is $a+b= c$ with distinct $a,b,c$): it is $ 2^{(1/2+o(1))μ(G)}$ with the only exception being $G=\mathbb{Z}_2^k \oplus \mathbb{Z}_3$, when this function is $3^{(1/3+o(1))μ(G)}$, refuting a conjecture of Hassler and Treglown. Our proofs rely on a container theorem due to Green and Ruzsa. Another key ingredient is a sharp upper bound we establish on the number of maximal independent sets in graphs with given matching number, which interpolates between the classical results of Moon and Moser, and Hujter and Tuza. A special case of our bound implies that every $n$-vertex graph with a perfect matching has at most $2^{n/2}$ maximal independent sets, resolving another conjecture of Hassler and Treglown.

In this paper, we theoretically and experimentally analyze sequential processors with limited communication between parts. We compare the expressivity of sequential quantum and classical processors under the same constraints. They consist of three or four modules, each of which processes local data. The modules of the quantum processor are linked through one-qubit or one-qutrit communication, while those of the classical processor communicate through one bit or one trit. For the classical processor, we prove bounds on its performance in terms of inequalities on correlations of the output with a target function. We theoretically show that the quantum processor violates these inequalities. We show this violation experimentally on a silicon photonics setup. We describe how to find the classical bound on correlations with arbitrary target function by reducing the problem to the minimization of an Ising-type spin-glass Hamiltonian. Our theory is applicable in general problems, such as the low-rank binary matrix approximation.