We propose a new method for computing the eigenvalue decomposition of a dense real normal matrix $A$ through the decomposition of its skew-symmetric part. The method relies on algorithms that are known to be efficiently implemented, such as the bidiagonal singular value decomposition and the symmetric eigenvalue decomposition. The advantages of this method stand for normal matrices with few real eigenvalues, such as random orthogonal matrices. We provide a stability and a complexity analysis of the method. The numerical performance is compared with existing algorithms. In most cases, the method has the same operation count as the Hessenberg factorization of a dense matrix. Finally, we provide experiments for the application of computing a Riemannian barycenter on the special orthogonal group.

In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation cases over a fixed time horizon [0, T] and propose novel contrast functions for parameter estimation. In the partial observation scenario, we tackle the challenge posed by unobserved velocities by introducing a surrogate process based on the increments of the observed positions. This requires a modified contrast function to account for the correlation between successive increments. Our analysis demonstrates that, despite the loss of Markovianity due to the velocity approximation in the partial observation case, the estimators converge to a Gaussian distribution (with a correction factor in the partial observation case). The proofs are based on Ito like bounds and an adaptation of the Euler scheme. Additionally, we provide insights into Hörmander's condition, which helps establish hypoellipticity in our model within the framework of stochastic calculus of variations.

Quadratic Gravity supplements the Einstein-Hilbert action by terms quadratic in the spacetime curvature. This leads to a rich phase space of static, compact gravitating objects including the Schwarzschild black hole, wormholes, and naked singularities. For the first time, we study the collapse of a spherically symmetric star with uniform dust density in this setting. We assume that the interior geometry respects the symmetries of the matter configuration, i.e., homogeneity and isotropy, thus it is insensitive to the Weyl-squared term and the interior dynamics is fully determined by $R$ and $R^2$. As our main result, we find that the collapse leads to the formation of a horizon, implying that the endpoint of a uniform dust collapse with a homogeneous and isotropic interior is not a horizonless spacetime. We also show that the curvature-squared contribution is responsible for making the collapse into a singularity faster than the standard Oppenheimer-Snyder scenario. Furthermore, the junction conditions connecting spacetime inside and outside the matter distribution are found to be significantly more constraining than their counterparts in General Relativity and we discuss key properties of any exterior solution matching to the spacetime inside the collapsing star. Finally, we comment on the potentially non-generic behavior entailed by our assumptions.

Entanglement plays a central role in the fundamental tests and practical applications of quantum mechanics. Because entanglement is a feature unique to quantum systems, its observations provide evidence of quantumness. Hence, if gravity can generate entanglement between quantum superpositions, this indicates that quantum amplitudes are field sources and that gravity is quantum. I study the dual spin-one-half Stern-Gerlach interferometers and show that the Pancharatnam phase is a tool that qualitatively distinguishes semiclassical from quantum gravity. The semiclassical evolution is equivalent to that of two independent interferometers in an external field. In this case, a phase jump was observed, as expected from the geodesic rule, which dictates the noncyclic evolution in the Bloch sphere. By contrast, in the quantum case, the quantum amplitudes are the sources of the gravitational field, inducing entanglement between the two interferometers, and the phase is continuous.

Dark matter with mass in the crossover range between wave dark matter and particle dark matter, around $(10^{-3},\, 10^3)\,$eV, remains relatively unexplored by terrestrial experiments. In this mass regime, dark matter scatters coherently with macroscopic objects. The effect of the coherent scattering greatly enhances the accelerations of the targets that the dark matter collisions cause by a factor of $\sim 10^{23}$. We propose a novel torsion balance experiment with test bodies of different geometric sizes to detect such dark matter-induced acceleration. This method provides the strongest constraints on the scattering cross-section between the dark matter and a nucleon in the mass range $(10^{-3}, 1)\,$eV.

We prove convergence rates of linear sampling recovery of functions in abstract Bochner spaces satisfying weighted summability of their generalized polynomial chaos expansion coefficients. The underlying algorithm is a function-valued extension of the least squares method widely used and thoroughly studied in scalar-valued function recovery. We apply our theory to two core problems in Computational Uncertainty Quantification. First, we address non-intrusive approximations of solutions to parametric elliptic or parabolic PDEs with log-normal or affine inputs using a finite set of particular solvers. Second, we consider approximating infinite-dimensional holomorphic functions that arise as solutions to more general parametric PDEs with Gaussian random field inputs. Our framework allows a unified treatment of the log-normal and affine input models and yields substantial improvements in the state of the art of these problems. More specifically, we obtain convergence rates that improve known results by a polynomial factor in the log-normal case and by a logarithmic factor in the affine case.

In this paper, we consider polynomials and ideals obtained from the colored Jones polynomial in both commutative and noncommutative cases. In the commutative case, this ideal contains polynomials that can be regarded as the link version of the $A$-polynomial; in the noncommutative case, it consists of annihilating polynomials of the colored Jones polynomial and can be regarded as the link version of the $A_q$-polynomial. Moreover, we formulate the link version of the AJ conjecture.

In the low-altitude wireless networks, the simultaneous sensing data acquisition and sharing (SDAS) through an ISAC signaling strategy becomes a typical application scenario. In this paper, we mainly investigate three primary aspects of the SDAS system, namely, the information-theoretic framework, the optimal distribution of channel input, and the optimal waveform design for Gaussian signaling. First, we establish the information-theoretic framework and develop a modified source-channel separation theorem (MSST) tailored for the SDAS systems. The proposed MSST elucidates the relationship between achievable distortion, coding rate, and communication channel capacity in cases where the distortion metric is separable for sensing and communication (S\&C) processes. Second, we present an optimal channel input design for dual-functional signaling, which aims to minimize SDAS distortion under the constraints of the MSST and resource budget. We then conceive a two-step Blahut-Arimoto (BA)-based optimal search algorithm to numerically solve the functional optimization problem. Third, to provide practical design insights, we further propose an optimal waveform design for Gaussian signaling in multi-input multi-output (MIMO) SDAS systems. The associated covariance matrix optimization problem is addressed using a successive convex approximation (SCA)-based waveform design algorithm. Finally, we provide numerical simulation results to demonstrate the effectiveness of the proposed algorithms, which characterize the unique performance tradeoff between S&C processes.

Revisiting Kraśkiewicz and Pragacz's construction of Schubert modules, we provide a new proof that their characters are equal to Schubert polynomials. The main innovation is a representation-theoretic interpretation of a recurrence relation for Schubert polynomials recently discovered by Nadeau, Spink, and Tewari. Along the way, we review several related constructions, and show that the Nadeau-Spink-Tewari recursion determines the characters of flagged Schur modules coming from the broader classes of "transparent" and "translucent" diagrams. We conclude with a conjecture concerning the Schubert positivity of the characters of transparent diagrams.

We consider the free boundary problem for a 3-dimensional, incompressible, irrotational liquid drop of nearly spherical shape with capillarity. We study the problem from the beginning, extending some classical results from the flat case (capillary water waves) to the spherical geometry: the reduction to a problem on the boundary, its Hamiltonian structure, the analyticity and tame estimates for the Dirichlet-Neumann operator in Sobolev class, and a linearization formula for it, both with the method of the good unknown of Alinhac and by a differential geometry approach. Then we prove the bifurcation of traveling waves, which are nontrivial (i.e., nonspherical) fixed profiles rotating with constant angular velocity.

We define the Carrollian black holes corresponding to the limit of Schwarzschild-(A)dS spacetime and its higher-derivative counterpart known as Schwarzschild-Bach-(A)dS spacetime, which is also a static spherically symmetric vacuum solution of quadratic gravity. By analyzing motion of massive particles in these geometries, we found that: In the case of Schwarzschild-(A)dS, a (nearly) tangential particle from infinity will wind around the extremal surface with a finite number of windings depending on the impact parameter and the cosmological constant. In Schwarzschild-Bach-(A)dS, a particle passing close enough to the extremal surface will have an infinite number of windings; hence, it will not escape to asymptotic infinity as in Schwarzschild-(A)dS. We also calculate the thermodynamical quantities for such black holes and argue that it is analogous to an incompressible thermodynamical system with divergent entropy when the temperature goes to zero (in the strict Carroll limit). We then define a divergent specific heat that can be positive, negative, or zero.

We consider the electromagnetic form factors ratio in the Rosenbluth and polarization methods. We explore the impact of adding new particles as the mediators in the electron-proton scattering on these ratios. Consequently, we find some bound on the scalar coupling as $α_{sc}\sim 10^{-5}$ for $m_{sc}\sim 5 MeV-2 GeV$ and $α_{sc}\sim 10^{-4}-10^{-3}$ for $m_{sc}\sim 2-10 GeV$. Meanwhile, the vector coupling is bounded as $α_v\sim 10^{-5}$ for $m_v\sim 5 MeV-1.1 GeV$ and $α_v\sim 10^{-4}-10^{-3}$ for $m_v\sim 1.2-10 GeV$. These constraints are in complete agreement with those which is found from other independent experiments.

The rapid growth of the Internet of Things (IoT) introduces challenges in secure authentication and delegation due to the limited computational capabilities of devices. Proxy signature schemes offer an effective solution by enabling controlled delegation of signing rights to more capable entities, such as gateway nodes. However, most existing schemes rely on classical assumptions that are likely to be broken by quantum adversaries. In this work, we address these challenges by proposing an isogeny-based post-quantum proxy signature scheme, \textit{CSI-PS}. The scheme leverages the hardness of the Group Action Inverse Problem (GAIP) to ensure quantum-resistant security while maintaining efficiency suitable for resource-constrained environments. We further demonstrate its applicability in IoT architectures through a gateway-based delegation model. Our analysis shows that the proposed scheme strikes an effective balance between security and efficiency in terms of computation and communication overhead, along with provable security under the EUF-CMA notion.

We study the decay of a thermally excited metastable vacuum in classical field theory using real-time numerical simulations. We find a significantly lower decay rate than predicted by standard thermal theory at moderate temperatures, $E_b/T\sim 10$, where $E_b$ is the critical bubble energy. The discrepancy is due to the violation of thermal equilibrium during the critical bubble nucleation and is reduced if thermalization is enhanced by introduction of dissipation and thermal noise. We formulate a condition for the system to remain in equilibrium during the nucleation process and show that it is generally violated in weakly coupled field theories. Nevertheless, we argue that the violation of thermal equilibrium becomes irrelevant for the false vacuum decay rate at sufficiently low temperatures and the standard thermal rate is recovered.

This paper develops and discusses a residual-based a posteriori error estimator for parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and the backward Euler method in time. The proposed error indicator bounds the error quantities globally in space from above and below, and globally in time from above and locally from below. Based on the derived error indicator, a space-time adaptive algorithm is proposed. Numerical experiments illustrate and complement the theory.

Obesity is widely recognized as a serious and pervasive health concern. We study obesity through body mass index (BMI), which is known to be highly heritable, and identify important genetic risk factors for BMI from hundreds of thousands of single nucleotide polymorphisms (SNPs) in the Framingham Study data. Several challenges arise when using traditional genome-wide association studies (GWAS): (1) They suffer from a low power due to a combination of a limited number of participants and the stringent genome-wide significance threshold; (2) existing prior knowledge from large meta-analyses may provide valuable guidance but is often underutilized; (3) the one-at-a-time univariate marginal regression framework ignores the joint and conditional nature of genetic effects; (4) GWAS focus solely on mean outcomes, whereas obesity inherently concerns abnormally high BMI levels. To address these challenges, we conduct the analysis by proposing and applying a novel Knowledge Integration Quantile Regression (KIQR) approach via simultaneous variable selection and estimation, focusing on the conditional high quantiles of BMI, which are most relevant to obesity risk, while integrating prior information from large-scale studies such as the GIANT consortium and UK Biobank. Notably, we identified promising novel associations: rs3798696 in \textit{TFAP2A}, rs7070523 in \textit{ITIH5}, and rs178260 in \textit{AIFM3}, which have not previously been reported in the GWAS literature. These findings provide new insights into the genetic architecture of obesity and demonstrate that quantile-based modeling with integrated prior knowledge can potentially uncover novel genes missed by traditional GWAS approaches. An R implementation and simulation scripts are available at: https://github.com/KIQR-submission/KIQR

Determining the limiting behaviour of the Jacobian as the underlying curve degenerates has been the subject of much interest. For nodal singularities, there are beautiful constructions of Caporaso as well as Pandharipande of compactified universal Jacobians over the moduli space of stable curves. Alexeev later obtained a canonical such compactification by extending the Torelli map out of the Deligne-Mumford compactification of $\mathcal{M}_{g,n}$. In contrast, Alexeev and Brunyate proved that the Torelli map does not extend over the cuspidal locus in Schubert's alternative compactification of pseudostable curves. In this paper, we consider curves with singularities that locally look like the axes in $m$-space, which we call axis-like singularities. We construct an alternative compactification of $\mathcal{M}_{g,n}$ consisting of curves with such singularities and prove that the Torelli map extends out of this compactification. Furthermore, for every alternative compactification in the sense of Smyth, we identify an axis-like locus over which the Torelli map extends.

This paper contributes to the study of optimal experimental design for Bayesian inverse problems governed by partial differential equations (PDEs). We derive estimates for the parametric regularity of multivariate double integration problems over high-dimensional parameter and data domains arising in Bayesian optimal design problems. We provide a detailed analysis for these double integration problems using two approaches: a full tensor product and a sparse tensor product combination of quasi-Monte Carlo (QMC) cubature rules over the parameter and data domains. Specifically, we show that the latter approach significantly improves the convergence rate, exhibiting performance comparable to that of QMC integration of a single high-dimensional integral. Furthermore, we numerically verify the predicted convergence rates for an elliptic PDE problem with an unknown diffusion coefficient in two spatial dimensions, offering empirical evidence supporting the theoretical results and highlighting practical applicability.

This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed method combines components from consensus-based optimization algorithm with a newly introduced forcing term directed at the constraint set. A rigorous mean-field limit of the particle system is derived, and the convergence of the mean-field limit to the constrained minimizer is established. Additionally, we introduce a stable discretized algorithm and conduct various numerical experiments to demonstrate the performance of the proposed method.

A Service Level Agreement (SLA) is a formal contract between a service provider and a consumer, representing a crucial instrument to define, manage, and maintain relationships between these two parties. The SLA's ability to define the Quality of Service (QoS) expectations, standards, and accountability helps to deliver high-quality services and increase client confidence in disparate application domains, such as Cloud computing and the Internet of Things. An open research direction in this context is related to the possible integration of new metrics to address the security and privacy aspects of services, thus providing protection of sensitive information, mitigating risks, and building trust. This survey paper identifies state of the art covering concepts, approaches, and open problems of SLA management with a distinctive and original focus on the recent development of Security SLA (SecSLA). It contributes by carrying out a comprehensive review and covering the gap between the analyses proposed in existing surveys and the most recent literature on this topic, spanning from 2017 to 2023. Moreover, it proposes a novel classification criterium to organize the analysis based on SLA life cycle phases. This original point of view can help both academics and industrial practitioners to understand and properly locate existing contributions in the advancement of the different aspects of SLA technology. The present work highlights the importance of the covered topics and the need for new research improvements to tackle present and demanding challenges.

Silicon carbide (SiC) is the leading wide-bandgap semiconductor material, providing mature doping and device fabrication. Additionally, SiC hosts a multitude of optically active point defects (color centers) and is relevant for many applications in quantum technologies. A crucial step towards harnessing the full potential of the SiC platform includes technologies to create color centers with defined localization and density, e.g. to facilitate their coupling to nano-photonic structures and to observe cooperative effects. Here, silicon vacancy centers and divacancies stand out as no impurity atom is needed and high-thermal budget annealing steps can be avoided. We characterize the effect of localized, femtosecond laser irradiation of SiC, investigating surface modifications and photoluminescence including Raman spectroscopy and optical lifetime measurements. We employ commercial high-purity, semi-insulating substrates and an industrial grade laser system to explore broader applicability of the method. As a novel approach, we apply femtosecond laser irradiation to SiC substrates with an epitaxial graphene layer and find that the threshold for photoluminescence due to laser treatment is lowered.

Recently it was shown that essentially all regular black hole models constructed so far can be obtained as solutions of vacuum gravity equations, upon considering an infinite series of quasi-topological higher curvature corrections. Here we show that such a construction can be upgraded to yield regular black holes with vanishing inner horizon surface gravity. In four dimensions, such a condition is necessary for the absence of classical instabilities associated with mass inflation on the inner horizon.

Path integral Monte Carlo (PIMC) and path integral molecular dynamics (PIMD) provide the golden standard for the ab initio simulations of identical particles. In this work, we achieved significant GPU acceleration based on PIMD, which is equivalent to PIMC in the ab initio simulations, and developed an open-source PIMD code repository that does not rely on any other third party library. Numerical experiments show that for a system of 1600 interacting identical bosons in a harmonic trap, using a single GPU and a single CPU, it only takes two hours to achieve satisfactory simulation accuracy. With the increase of the number of identical particles, the advantage of GPU acceleration over CPU becomes more obvious, making it possible to simulate tens of thousands of identical particles from first principles using a single GPU. For example, for a system of 10000 non-interacting bosons, numerical experiments show that it takes 23 hours to obtain a simulation that is highly consistent with the exact results. Our study shows that GPU acceleration can lay a solid foundation for the wide application of PIMD simulations for extremely large-scale identical particle quantum systems with more than 10,000 particles. Numerical experiments show that a 24GB GPU can simulate up to 40000 identical particles from first principles, and the GPU acceleration leads to a roughly linear relationship between the computation time and the number of identical particles. In addition, we have also successfully implemented simulations for fictitious identical particle thermodynamics using GPU to overcome the Fermion sign problem, which makes it promising to efficiently and accurately simulate tens of thousands of fermions based on GPU.

Algebraic theories, sometimes called equational theories, are syntactic notions given by finitary operations and equations, such as monoids, groups, and rings. There is a well-known category-theoretic treatment of them that algebraic theories are equivalent to finitary monads on $\mathbf{Set}$. In this paper, using partial Horn theories, we syntactically generalize such an equivalence to arbitrary locally presentable categories from $\mathbf{Set}$; the corresponding algebraic concepts relative to locally presentable categories are called relative algebraic theories. Finally, we give a framework for universal algebra relative to locally presentable categories by generalizing Birkhoff's variety theorem.

Irredundance has been studied in the context of dominating sets, via the concept of private neighbor. Here irredundance of zero forcing sets is introduced via the concept of a private fort and the upper and lower zero forcing irrdedundance numbers $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are defined. Bounds on $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are established and graphs having extreme values of $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are characterized. The effect of the join and corona operations is studied. As the concept of a zero forcing irrdedundant set is new, there are many questions for future research.

In this paper, we obtain a complete list of stationary and axisymmetric spacetimes, generated from a Minkowski spacetime using the Ernst technique. We do so by operating on the associated seed potentials with a composition of Ehlers and Harrison transformations. In particular, assigning an additional ``electric'' or ``magnetic'' tag to the transformations, we investigate the new spacetimes obtained either via a composition of magnetic Ehlers and Harrison transformations (first part) or via a magnetic-electric combination (second part). In the first part, the resulting type D spacetime, dubbed electromagnetic swirling universe, features key properties, separately found in swirling and (Bonnor--)Melvin spacetimes, the latter recovered in appropriate limits. A detailed analysis of the geometry is included, and subtle issues are addressed. A detailed proof that the spacetime belongs to the Kundt family, is included, and a notable relation to the planar-Reissner-Nordström-NUT black hole is also meticulously worked out. This relation is further exploited to reverse-engineer the form of the solution in the presence of a nontrivial cosmological constant. A Schwarzschild black hole embedded into the new background is also discussed. In the second part, we present four novel stationary and axisymmetric asymptotically nonflat type I spacetimes, which are naively expected to be extensions of the Melvin or swirling solution including a NUT parameter or electromagnetic charges. We actually find that they are, under conditions, free of curvature and topological singularities, with the physical meaning of the electric transformation parameters in these backgrounds requiring further investigation.

Atomic dark matter is usually considered to be produced asymmetrically in the early Universe. In this work, we first propose that the symmetric atomic dark matter can be thermally produced through the freeze-out mechanism. The dominant atom anti-atom annihilation channel is the atomic rearrangement. It has a geometrical cross section much larger than that of elementary fermions. After the atomic formation, this annihilation process further depletes dark matter particles and finally freezes out. To give the observed dark matter relic, the dark atoms are naturally ultraheavy, ranging from $10^6$ to $10^{10} \,\mathrm{GeV}$.

We give a model-independent definition of limits for diagrams valued in an $(\infty,n)$-category. We show that this definition is compatible with the existing notion of homotopy 2-limits for 2-categories, with the existing notion of $(\infty,1)$-limits for $(\infty,1)$-categories, and with itself across different values of $n$.

In this study, we conduct experimental investigations on the behavior of confined self-propelled particles within a circular arena, employing small commercial robots capable of locomotion, communication, and information processing. These robots execute circular trajectories, which can be clockwise or counterclockwise, based on two internal states. Using a majority-based stochastic decision algorithm, each robot can reverse its direction based on the states of two neighboring robots. By manipulating a control parameter governing the interaction, the system exhibits a transition-from a state where all robots rotate randomly to one where they rotate uniformly in the same direction. Moreover, this transition significantly impacts the trajectories of the robots. To extend our findings to larger systems, we introduce a mathematical model enabling characterization of the order transition type and the resulting trajectories. Our results reveal a second-order transition from active Brownian to chiral motion. Lastly, we analyze the particle density within the arena, examining how it varies concerning system size and the control parameter.

A singular foliation $\mathcal{F}$ on a complete Riemannian manifold $M$ is called Singular Riemannian foliation (SRF for short) if its leaves are locally equidistant, e.g., the partition of $M$ into the orbits of a Lie group action by isometries. In this paper, we investigate variational problems in compact Riemannian manifolds equipped with SRFs with special properties, which we name as AVP. Examples of such SRFs being considered include isoparametric foliations, SRFs on Euclidean fiber bundles, and the partition of $M$ into the orbits of a Lie group acting by isometries. More precisely, we prove an analog to Palais' Principle of Symmetric Criticality for $\mathcal{F}$-symmetric integral operators on the Banach spaces $W^{1,p}(M)$. This result together with a version of the Rellich--Kondrachov--Hebey--Vaugon Embedding Theorem for $\mathcal{F}$-basic Sobolev functions allows us to circumvent difficulties with Sobolev's critical exponents when considering applications of techniques from Calculus of Variations to find solutions to PDEs. To exemplify this, we prove the existence of countably infinite many weak solutions to a class of variational problems, which includes $p$-Kirchhoff problems for manifolds equipped with AVP.