In this paper, we show that for all $k\geq 10^8$, every graph with minimum degree $k$ and girth at least $10^8$ contains an induced subdivision of a $K_{k+1}$. This answers a problem asked by Kühn and Osthus (originally attributed to Shi).

We develop a mechanism that enables supersymmetric Ward identities to be applied in non-supersymmetric theories. These identities are then used to streamline calculations in our target theories, potentially including phenomenological models. In these proceedings, we illustrate the method through operator renormalization in the Gross-Neveu-Yukawa model, where it leads to a significant optimization and a substantial reduction in computational effort. This serves as a toy example of the procedure that we ultimately aim to apply to Quantum Chromodynamics.

Studying the interaction between core-collapse supernova remnants (SNRs) and their surrounding environments is essential to understanding the mechanism for energy transfer to the interstellar medium (ISM) and the intrinsic physical properties of these remnants. In this paper, we focus on G309.8-2.6. Our new observations reveal that this object includes an SNR shell with a relic pulsar wind nebula (PWN) that extends well beyond the emission that has been previously observed in X-rays. We present new radio continuum and polarization images of G309.8-2.6 from the Evolutionary Map of the Universe (EMU) and Polarization Sky Survey of the Universe's Magnetism (POSSUM) surveys with the Australian Square Kilometre Array Pathfinder (ASKAP). The images reveal the complex and peculiar morphology of G309.8-2.6. The linear polarization displays an atypical S-shaped morphology and a highly ordered magnetic field. The rotation measure (RM) map shows a large-scale gradient or possible sign reversal, depending on the foreground RM. We reprocessed archival X-ray observations from Chandra and eROSITA, and retrieved archival H$α$ and infrared observations. We performed a joint analysis of the multiwavelength data and proposed scenarios to explain the unusual shape. Our results place new constraints on the magnetic field of G309.8-2.6, including its environment, and demonstrate the power of polarization observations in probing the properties of SNRs.

Recently, Rydberg atom has emerged as an attractive choice to realize quantum sensing of low-frequency electric field. The progress so far has mostly utilized the intensity and phase changes in probe laser and the corresponding detection mechanism still remains classical. Nevertheless, external field acting on the Rydberg state can induce the polarization variation of probe laser in the Rydberg electromagnetically induced transparency (EIT) system embedded in realistic multi-state atoms. We experimentally observe this phenomenon and realize signal extraction by appropriately utilizing the polarization degrees of freedom. Based on such a mechanism, we further design and implement a quantum weak measurement scheme, which clearly suppresses the technical noise and leads to considerable improvement of performance. Evaluation of the sensitivities across different post-selection angles demonstrates that the weak measurement results agree well with the theoretical model predictions. The advantages of our method are analyzed from multiple aspects, including characterizing the responses over different frequencies and comparing the responses of the weak measurement scheme and the traditional transmission-based method. After accounting for the screening effect of a measured ratio 17\% where the $^\text{87}$Rb atoms experience a substantially reduced field inside the glass cell, the performance reaches 33 $μ\text{V}~\text{cm}^\text{-1}~\text{Hz}^\text{-1/2}$ in sensitivity and 1.0 $μ\text{V/cm}$ in minimal detectable field for an integration time of 1000 s, as perceived by the atoms.

Based on the notion of vectors and linear subspaces for a matroid, we develop a theory of flats and hyperplane arrangements for T-matroids, where T is a tract. This leads to several cryptomorphic descriptions of T-matroids: in terms of its lattice of T-flats, as a hyperplane arrangement over T, as point-line arrangements in projective space over T and as a quiver representation over T. We examplify these notions in the case of tropical linear spaces, a.k.a. valuated matroids.

We discuss quantitative Calderón-Zygmund estimates in $W^{2,2}$ for 2D viscous Hamilton-Jacobi equations with natural growth in the gradient. We apply the result to obtain the existence of classical solutions for stationary second order Mean Field Games systems in 2D with (defocusing) coupling behaving like $m^α$ for any $α>0$. We also survey on the known results for the regularity of viscous Hamilton-Jacobi equations and second order Mean Field Games and list several open problems.

In this paper, we determine precise formulas for the diameters, the number of perfect matchings, and the Tutte polynomials for an infinite family of finite graphs, namely the Schreier graphs of tree automaton groups, also called tree graph automata. This enables us to easily find the number of spanning trees, spanning forests, and an explicit form for the chromatic polynomials. In the second part of the paper, we provide the precise values for the Wiener and Szeged index of any tree graph automaton.

This work is devoted to the analysis of the backward problem for a viscous Hamilton-Jacobi equation with degenerate diffusion and a general Hamiltonian that is not necessarily quadratic. First, we focus on linear degenerate parabolic equations in the nondivergence setting. We prove the conditional stability of the backward problem using Carleman estimates. Then, by a linearization technique, we prove similar results for the nonlinear viscous Hamilton-Jacobi equation. Regarding numerical identification, we first investigate the linear degenerate equation with noisy data using the adjoint state method, combined with a Conjugate Gradient algorithm, to solve the associated minimization problem. Finally, the numerical identification for the nonlinear viscous Hamilton-Jacobi equation is investigated by the Van Cittert iteration. Numerical tests are presented to show the performance of the proposed algorithms.

Diffusion Probabilistic Models (DPMs) are a well-established class of diffusion models for unconditional image generation, while SGMSE+ is a well-established conditional diffusion model for speech enhancement. One of the downsides of diffusion models is that solving the reverse process requires many evaluations of a large Neural Network. Although advanced fast sampling solvers have been developed for DPMs, they are not directly applicable to models such as SGMSE+ due to differences in their diffusion processes. Specifically, DPMs transform between the data distribution and a standard Gaussian distribution, whereas SGMSE+ interpolates between the target distribution and a noisy observation. This work first develops a formalism of interpolating Stochastic Differential Equations (iSDEs) that includes SGMSE+, and second proposes a solver for iSDEs. The proposed solver enables fast sampling with as few as 10 Neural Network evaluations across multiple speech restoration tasks.

The present study investigates a linear-quadratic Dirichlet control problem governed by a non-coercive elliptic equation posed on a possibly non-convex polygonal domain. Tikhonov regularization is carried out in an energy seminorm. The regularity of the solutions is established in appropriate weighted Sobolev spaces, and the finite element discretization of the problem is analyzed. In order to recover the optimal rate of convergence in polygonal non-convex domains, graded meshes are required. In addressing this particular problem, it is also necessary to introduce a discrete projection in the sense of $H^{1/2}(Γ)$ to deal with the non-homogeneous boundary condition. A thorough examination of the approximation properties of the discrete controls reveals that the discrete problems are strongly convex uniformly with respect to the discretization parameter. All these ingredients lead to optimal error estimates. Practical computational considerations and numerical examples are discussed at the end of the paper.

Keyword spotting (KWS) is crucial for many speech-driven applications, but robust KWS in noisy environments remains challenging. Conventional systems often rely on single-channel inputs and a cascaded pipeline separating front-end enhancement from KWS. This precludes joint optimization, inherently limiting performance. We present an end-to-end multi-channel KWS framework that exploits spatial cues to improve noise robustness. A spatial encoder learns inter-channel features, while a spatial embedding injects directional priors; the fused representation is processed by a streaming backbone. Experiments in simulated noisy conditions across multiple signal-to-noise ratios (SNRs) show that spatial modeling and directional priors each yield clear gains over baselines, with their combination achieving the best results. These findings validate end-to-end multi-channel spatial modeling, indicating strong potential for the target-speaker-aware detection in complex acoustic scenarios.

We study the overshoot \(R_b=S_{τ(b)}-b\) of a random walk with independent identically distributed increments from a standardised one-parameter exponential family, with primary emphasis on the small-drift regime \(θ\downarrow0\). Unlike the classical renewal-process setting with nonnegative increments, we allow sign-changing increments and assume only a positive drift \(μ_θ>0\). For each \(k\in\mathbb N\) we obtain Lorden-type moment bounds, uniform in the barrier \(b\), for \(\E_θ[R_b^k]\) with an explicit remainder term decaying exponentially in \(b\). The proof reduces the problem to the renewal process of strict ascending ladder heights and combines a simple bound for the limiting overshoot moments with a uniform exponential estimate for the rate of convergence of the distribution functions of \(R_b\) to the limiting random variable \(R_\infty\) as \(b\to\infty\), uniformly in \(θ\in[0,θ^\ast]\). As a consequence, the classical constant \((k+2)/(k+1)\) arising in residual-life bounds improves to \(C_k=1\) for sufficiently large \(b\) at fixed \(θ\), and also uniformly over all \(b\ge0\) in the small-drift regime. Counterexamples are provided showing that the stronger inequality with \(kμ_θ\) in the denominator cannot hold uniformly in \((b,θ)\). Finally, the exponential CDF estimate is interpreted in terms of optimal transport: we obtain exponential convergence in the metric \(W_1\), a quantile coupling with \(\E|\widetilde R_b-\widetilde R_\infty|=O(e^{-rb})\), error bounds for Lipschitz functionals and a total-variation bound for smoothed distributions.

Word-level verification of arithmetic circuits with large operands typically relies on arbitrary-precision arithmetic, which can lead to significant computational overhead as word sizes grow. In this paper, we present a hybrid algebraic verification technique based on polynomial reasoning that combines linear and nonlinear rewriting. Our approach relies on multimodular reasoning using homomorphic images, where computations are performed in parallel modulo different primes, thereby avoiding any large-integer arithmetic. We implement the proposed method in the verification tool TalisMan2.0 and evaluate it on a suite of multiplier benchmarks. Our results show that hybrid multimodular reasoning significantly improves upon existing approaches.

As the Chinese Spallation Neutron Source enters Phase II, the increase in proton beam power will lead to a further boost in the intensity of pulsed neutron beams. To address the demand for higher event-rate readout electronics for energy-resolved neutron imaging detectors, we have developed a high-performance readout electronics system based on the Timepix4 chip. The prototype electronics system comprises a Timepix4 chip board and a high-performance digital board, which are interconnected through a custom FMC interface. The advantage of this system is its ability to achieve the full bandwidth readout of 160 Gbps for a single Timepix4 chip. The electronics system, based solely on a single ZYNQ-MPSOC chip, is capable of fully meeting the required performance specifications within a compact form factor of 8 cm x 30 cm. Furthermore, the system features a high-capacity external SODIMM memory interface (supporting up to 32 GB), which ensures stable data readout through a single 40 Gbps QSFP+ interface. As of the present moment, notable progress has been achieved, including the successful establishment of 16 data channels between Timepix4 and FPGA that operate error-free and stably at a speed of 5.12 Gbps, which is half of the maximum theoretical speed of 10.24 Gbps. The threshold standard deviation across all pixels is less than 50 e- after equalization. And the clear structural results obtained from X-ray experiments indicate that the functionality is essentially complete, allowing further testing.

We study the impact of an external magnetic field on the long-range electron transport in quasi-one-dimensional materials, such as polypeptides, (semi-) conducting polymers and macromolecules, taking into account the electron-lattice interaction. At relatively strong electron-lattice interaction extra electrons get self-trapped in the deformation potential well and form stable bound states, called large polarons which in the continuum approximation are known as solitons. Here we do not use the continuum approximation but solve the system of discrete nonlinear equations numerically. We show that the impact of a magnetic field on polaron dynamics depends not only on the field strength, but also on the parameter values of the system which define the properties of solitons such as their energy, amplitude and width of localisation. We also study the impact of a magnetic field on a polaron created by a donor complex on a chain.

Manual development of automatic tests for embedded C software is a strenuous and time-consuming task that does not scale well. With the accelerating pace of software release cycles, verification increasingly becomes the bottleneck in the embedded development workflow. This paper presents a Retrieval-Augmented Generation (RAG) pipeline as a solution for partial automation of the verification process. By grounding a large language model in project-specific artifacts, the approach reduces hallucinations and improves project alignment. An industrial evaluation showed that the generated tests are 100 % syntactically correct, with 85 % successfully passing runtime validation. The proposed solution has the potential to save up to 66 % of the testing time compared to manual test writing while generating 270 tests per hour.

When solids melt while sliding down heated inclines, their motion is governed by a complex coupling between heat transfer, phase change, gravity and viscous dissipation. Despite relevance across a variety of domains, like kitchen physics, geophysics, tribology, and manufacturing, this coupled problem lacks understanding and quantitative experimental validation. Here we report experiments with ice and paraffin wax on a temperature-controlled ramp that achieve terminal velocities from 0.01 m/s to 2 m/s across wide parameter ranges. We develop a theoretical model that captures the self-regulating feedback between melt-layer thickness, sliding velocity, and heat transfer. Without any adjustable parameters, our model collapses all measurements, validating the fundamental mechanism and enabling predictions for analogous systems.

Processing regulations and resulting requirements to achieve regulatory compliance in software engineering (SE) is a developing challenge due to the continuously growing amount, complexity, and expanding scope of regulations. Despite the growing amount of newly suggested regulatory requirements engineering (RE) approaches by the research community, industry remains under pressure to assure their integration into their RE and overall software development life cycle (SDLC) practices to facilitate a seamless and legally valid compliance by design. As of today, we still have limited empirical understanding of how this can be achieved. Such integration should avoid additional burdens and address the demands of legal knowledge intensity, cross-functional communication and consistency between different involved viewpoints. Intermediary results of this doctoral study showed that regulatory RE has peculiarities distinguishing it from the engineering of other requirements. Oftentimes, organizations establish standalone regulatory RE processes on the organizational level. However, software development teams usually approach compliance by design in an ad-hoc manner, rather than in a systematic way. Among other, because of the complexity of the coordination between the involved viewpoints. The goal of this paper is to report and get feedback about the synthesis and future evaluation of our Artefact Model for Regulatory Requirements Engineering (AM4RRE) for a integrated compliance by design. We hope this paper will spark discussions about regulatory RE and help us refine plans for the final stage of the doctoral study.

We present the first on-sky demonstration of dual-field interferometry at the CHARA Array and the first direct resolution of the inner Ba--Bb subsystem in the bright hierarchical triple $α$ Piscium. Using $H$-band fringe tracking on component A with MIRC-X to stabilize $K$-band science fringes on component B with MYSTIC, we detected a companion at a projected separation of 7 mas, confirming a long-suspected but previously unresolved short-period subsystem within the B component. The nearly equal $H/K$-band flux ratio indicates that Ba and Bb are near-twin F-type stars, consistent with the two narrow-lined components seen in optical spectra of B. By combining CHARA interferometry with archival VLTI/GRAVITY astrometry and radial velocities from archival and new spectroscopy (NARVAL and ARCES), we derive a well-constrained orbit with a period of $P = 25$ d, eccentricity $e \simeq 0.6$, and inclination $i \simeq 65^\circ$, yielding precise dynamical masses of $1.668\pm0.033\,M_\odot$ and $1.646\pm0.029\,M_\odot$. No additional companion is detected down to $ΔH \approx 5$ at separations of 0.2--2 AU. We also obtained dual-field differential astrometry of the wide A--B pair with a precision of ~0.234 mas at a separation of $1.85''$, with an error budget dominated by internal delay-line actuators, fringe-tracking performance and chromatic dispersion. While the long-period outer orbit is not refined by these measurements, their agreement with the published astrometric orbit provides an on-sky validation of the CHARA dual-field mode. These results establish $α$ Psc as a well-characterized hierarchical system suitable for future benchmark studies and demonstrate CHARA's new capability for off-axis interferometry and sub-mas astrometry on arcsecond-scale binaries.

Random matrices acting on structured sets play a fundamental role in high-dimensional geometry, compressed sensing, and randomized algorithms. Existing results primarily focus on subgaussian models, when random matrices act as near-isometries on sets with optimal tail behavior. Nevertheless, very often in applications we deal with distributions with heavy tails that are not subgaussian but have at least exponential-type tails. In this work, we study random matrices A whose rows (or columns) have $α$-subexponential tail distributions with $α\in (0,2]$. So subgaussian and sub-exponential models are included in as special cases. We establish concentration type inequality for $Ax$, where x belongs to the bounded subsets of $\mathbb{R}^n$, showing that their geometric distortion is governed by Talagrand's functional of the set and depends on the tail parameter $α$. Our results extend the known optimal inequalities in the subgaussian regime ($α=2$), and provide new guarantees for heavier-tailed, yet exponentially integrable, random matrices. These findings extend the theory of random matrices beyond the subgaussian framework. Moreover, they yield near-isometric embedding results applicable to dimension reduction and allow us to make robust high-dimensional inference under non-Gaussian measurements.

We investigate majority-vote opinion dynamics on Geometric Inhomogeneous Random Graphs (GIRGs), a powerful model for spatial complex networks. In contrast to classic coarsening dynamics where a single opinion typically achieves global consensus, our simulations reveal that sufficiently large, localized opinion domains do not disappear. Instead, they stabilize, leading to a persistent coexistence of competing opinions. To understand the mechanism behind this arrested coarsening, we develop and analyze a tractable mean-field model of the interface between two opinion domains. Our main theoretical result rigorously establishes the existence of a stable, non-trivial limiting distribution for the interface profile in a mean-field analysis. This demonstrates that the boundary between opinions is stationary, providing a mathematical explanation for how complex network geometry can support robust opinion diversity in social systems.

Quantum token protocols enable unforgeable quantum tokens promising unconditional security beyond classical cryptographic assumptions. We show here that the three stages of the Quantum token protocols involving the preparation, storage and verification can be made more secure when involving spin-photon interfaces that leverage high fidelity hybrid tripartite (spin-photon-spin) entanglement, Bell state measurements and highly coherent spin quantum memories. Further we describe the physical implementation of various stages of the protocol using the hybrid electron and nuclear spins in diamond interfaced with time-bin photons.

Multimodal Object-Entity Relation Extraction (MORE) is a challenging task in information extraction research. It aims to identify relations between visual objects and textual entities, requiring complex multimodal understanding and cross-modal reasoning abilities. Existing methods, mainly classification-based or generation-based without reasoning, struggle to handle complex extraction scenarios in the MORE task and suffer from limited scalability and intermediate reasoning transparency. To address these challenges, we propose MORE-R1, a novel model that introduces explicit stepwise reasoning with Reinforcement Learning (RL) to enable Large Vision-Language Model (LVLM) to address the MORE task effectively. MORE-R1 integrates a two-stage training process, including an initial cold-start training stage with Supervised Fine-Tuning (SFT) and a subsequent RL stage for reasoning ability optimization. In the initial stage, we design an efficient way to automatically construct a high-quality SFT dataset containing fine-grained stepwise reasoning tailored to the MORE task, enabling the model to learn an effective reasoning paradigm. In the subsequent stage, we employ the Group Relative Policy Optimization (GRPO) RL algorithm with a Progressive Sample-Mixing Strategy to stabilize training and further enhance model's reasoning ability on hard samples. Comprehensive experiments on the MORE benchmark demonstrate that MORE-R1 achieves state-of-the-art performance with significant improvement over baselines.

Inspired by Mukai's work on K3 surfaces, we introduce and study a notion of semi-rigidity for stable sheaves on smooth polarised varieties, designed to capture the existence of stable deformations of direct sums. We show that semi-rigidity is detected by the absence of decomposable elements in the kernel of the Yoneda pairing. We apply the resulting criterion to line bundles on smooth projective varieties and to line bundles supported on smooth Lagrangian subvarieties of hyper-Kähler manifolds.

We study the problem of finding an acyclic orientation of an undirected graph with constrained in-degree parities specified by a subset T of vertices. An orientation is called T -odd if a vertex v has odd in-degree if and only if v P T . While the unconstrained parity orientation problem is polynomial (Chevalier et al. (1983)), imposing acyclicity makes it more challenging, and its complexity remains an open question. Szegedy and Szegedy ( 2006) proposed a randomized polynomial-time algorithm for this problem, but it is not known whether it belongs to co-NP. Furthermore, Gravier et al. (2025) showed the problem becomes NP-complete on partially directed graphs, even when restricted to planar cubic graphs. We identify three necessary conditions for the existence of acyclic T -odd orientation: a global parity condition P, and two conditions S and S ensuring the existence of potential sources and sinks. Following the work of Frank and Kiraly (2002), we define graph classes containing the graphs for which a given subset of the necessary conditions P, S and S is also sufficient for the existence of an acyclic T -odd orientation. We establish the inclusion relationships between these classes. We complete the study of these classes by a characterization of the solvable instances for Cartesian products of paths and cycles. The proofs of these results are all constructive, so that acyclic T -odd orientations can be built in polynomial time whenever they exist. We use these families, along with cliques, to demonstrate the strictness of the class inclusions in our hierarchy.

Extreme solar particle events reveal that the Sun can occasionally produce eruptions significantly more energetic than those observed in the modern era. These events are thought to originate from powerful coronal mass ejections, typically associated with large solar flares triggered by magnetic field reconnection in complex active regions. Stellar observations indicate that Sun-like stars can host superflares exceeding 10^34 erg roughly once per century, yet it remains uncertain whether the Sun can reach such flare energies. We empirically estimate the upper limit of solar flare energies using statistical relations between flare - ribbon areas and released energy derived from modern observations. By extrapolating these upper-envelope relations to the largest sunspot group recorded since 1859 - the Great Sunspot of 8 April 1947 - we find that exceptionally large and complex solar active regions could, in principle, produce flares with bolometric energies of a few 10^34 erg.

We determine the finite-temperature phase diagram and critical behavior of the classical square-lattice Heisenberg-compass model using large-scale Monte Carlo simulations and finite-size scaling. Six symmetry distinct ordered phases are identified. The four phases that simultaneously break the spin-lattice $C_4$ and in-plane spin-inversion symmetries undergo continuous transitions in the Ashkin-Teller universality class, with the associated critical lines terminating at four-state Potts points, beyond which the transitions become first order. In contrast, the two $z$-polarized phases display conventional two-dimensional Ising criticality. Our results reveal how the interplay between Heisenberg exchange and compass anisotropy organizes these distinct critical regimes, thereby completing the characterization of the model's thermal phase transitions.

There is a growing demand for software engineering education (SEE) for professionals because of the increasing demand, active evolution of the technological landscape, and changes in the skills required by the practice. Integrating requirements engineering (RE) courses into SEE curricula for professionals systematically and effectively is challenging. In particular, curricula for professionals have different demands, are more dynamic, and modular in nature. In this study, we report on our experience in the development of three SEE curricula for professionals and the integration of RE courses into such curricula. We suggest basic principles for such integration and describe the systematic approach focused on course content mapping that we have developed.

Power company operators make power generation plans one day in advance, in what is known as the Unit Commitment (UC) problem. UC is exposed to uncertainties, such as unknown electricity load and disturbances caused by renewable energy sources, especially PVs. In previous research, we proposed the Renewable Energy Robust Optimization Problem (RE-RP), which solves these uncertainties by considering suppression. In this paper, we propose a new model called RE-RP with fairness (RE-RPfair), which aims to achieve fair allocation among PVs allocation. This model is an expansion of the original RE-RP, and we prove its effectiveness through simulation. To measure the degree of fairness, we use the Gini Index, which is well-known in social science.

We introduce mollified Christoffel-Darboux (CD) kernels on varieties, a systematic regularization of the classical CD kernel associated with a probability measure on a compact domain. The main motivations are twofold: first, to sharpen the classical on/off-support dichotomy of the CD polynomial by replacing linear growth on the support by a uniform bound; second, to obtain consistent and quantitatively controlled recovery of densities from moment data, without the need to know the equilibrium measure of the underlying domain. Our contributions are the following: (i) We introduce families of mollifiers on algebraic varieties. For each measure and degree on such a variety we define a mollified CD kernel, which can be computed from the moments of the underlying measure by linear algebra. (ii) We prove, by elementary arguments, that an improved dichotomy property holds: on the interior of the support the mollified CD polynomial is uniformly bounded in the degree, while outside the support it grows exponentially with the degree. (iii) Assuming Sobolev regularity of the density with respect to a reference measure, we derive explicit convergence rates for density recovery for measures in Euclidean space via mollified CD kernel. (iv) On the unit sphere, we show that suitably chosen algebraic mollifiers, constructed from zonal polynomials, lead to kernels with improved rates, building on classical constructive approximation results.