Papers

On a smooth Riemannian manifold, Aishwarya, Rotem and Shenfeld characterised nonnegative sectional curvature as the matrix displacement convexity of an entropy tensor, the Lagrangian, matrix-valued refinement of Shenfeld's entropy matrix. In order to extend the entropy tensor to a finite-dimensional Alexandrov space of curvature bounded below, we construct a parallel trivialisation satisfying both the cocycle property and the second variation formula. The construction is strongly inspired by Petrunin's synthetic parallel transport. The entropy tensor defined is taken in block-diagonal form; on smooth manifolds the resulting convexity property still characterises nonnegative sectional curvature exactly. We show that the smooth equivalence persists synthetically: an Alexandrov space has nonnegative curvature if and only if its entropy tensor is matrix displacement convex.

We study the zero-threshold lifting problem for polynomial multiple correlation sequences with respect to the measure-theoretic pro-nilfactor. The structure theory for polynomial multiple averages implies that, at every positive threshold, positivity on the pro-nilfactor lifts to positivity in the original system, except on a set of zero upper Banach density. We demonstrate that this lifting property does not hold at the zero threshold. Specifically, we construct an ergodic system and two sets of positive measure for which the pro-nilfactor correlation is positive along a set of times with positive upper density, while the corresponding exact correlation vanishes on this set. This provides a negative answer to a question posed by Glasscock, Koutsogiannis, Le, Moreira, Richter, and Robertson. %\cite{GKLMMRR}. Additionally, we prove a corresponding rigidity property. For any ergodic system, any essentially distinct family of integer polynomials vanishing at the origin, and any tuple of non-negative bounded functions, the zero-threshold discrepancy set is not piecewise syndetic.

There has been a growing body of work devoted to the study of effective cones of codimension-\(k\) cycles \(\text{Eff}^k(\overline{\rm{M}}_{g,n})\) on \(\overline{\rm{M}}_{g,n}\), the moduli space of \(n\) pointed stable curves of genus \(g\). In this paper, we remove the genus-dependence present in previous bounds on the number of marked points, and prove the following results: (1) \(\text{Eff}^k(\overline{\rm{M}}_{g,n})\) has infinitely many extremal rays for \(k\ge 2\), \(g\ge 3\) and \(n\ge 2k-2\), and (2) \(\text{Eff}^k(\overline{\rm{M}}_{g,n})\) is non-polyhedral for \(k\ge 2\), \(g\ge 1\) and \(n\ge k+5\). Moreover, we show that (3) every rational tails boundary stratum spans an extremal ray. Our method refines that of Chen and Coskun by extending arguments based on morphisms, or equivalently semiample divisors, to a setting that also allows for the use of nef divisors. Certain non-semiample nef divisors on \(\overline{\rm{M}}_{g,n}\), namely so-called semigroup kappa divisors of a particular kind, play a crucial role.

The emergence of the low-altitude economy (LAE) calls for highly integrated and reliable wireless systems that can simultaneously support communication and sensing (C&S) functions. Although integrated sensing and communication (ISAC) has been widely studied, most existing works focused on link-level or single-cell architectures in terrestrial environments, leaving the potential of network-level cooperative air-ground ISAC largely unexplored. To bridge this gap, a heterogeneous air-ground ISAC network architecture based on coordinated multipoint (CoMP) is proposed, which incorporates a cooperative hybrid mono/bi-static sensing scheme to enhance spatial diversity and sensing capability. In the proposed architecture, a two-tier base station (BS) deployment is adopted: master BSs are arranged in a hexagonal lattice, while slave BSs follow a Poisson point process distribution. This structure concurrently supports communication for terrestrial users and sensing for aerial targets. A holistic performance analysis framework for both C&S is further developed, accounting for key channel and network parameters. Simulation results reveal inherent trade-offs between C&S performance, especially under multi-BS cooperation and varying network density. These findings provide practical guidance for the deployment of scalable and efficient ISAC networks in LAE scenarios.

The modulo-sum problem, proposed by Körner and Marton (KM), is a representative problem in the field of distributed source coding. In the modulo-sum problem, two correlated sources are encoded separately, and the decoder decodes the modulo-sum of the sources. It is clear that the Slepian-Wolf (SW) coding rate region is achievable for the modulo-sum problem. Körner and Marton proved that the SW coding rate region can be improved by structured coding based on linear codes. Ahlswede and Han (AH) proposed AH coding, which combines structured coding and random coding, and expressed its rate using auxiliary random variables. However, it was conjectured that the minimum sum rate of AH coding cannot be smaller than the minimum of the sum rates achievable by KM coding or SW coding. Subsequently, Kakishima and Watanabe considered a multi-letter extension of AH coding, and designed the auxiliary random variables by taking the XOR of adjacent bits of the source sequences. Through numerical computation, they demonstrated the existence of source parameters for which multi-letter AH coding improves upon SW coding. However, this confirmation remained numerical, and the conditions under which multi-letter extended AH coding improves upon SW coding have not been analytically characterized. In this study, we analytically characterize the conditions under which multi-letter extended AH coding improves upon SW coding. Our condition is tight in the sense that it coincides with the complement of the known SW optimal sufficient condition. To obtain the conditions, we apply the method of types to reduce the evaluation of the multi-letter expression to a comparison of single-letter divergences, which might be of independent interest.

In this work we provide theoretical and practical results of the Safeguarded Augmented Lagrangian Method (SALM) for constrained composite optimization problems whose objective is the sum of a smooth and a nonsmooth function. We obtain global convergence results to an M-stationary point for SALM under the Polyak-Lojasiewicz constraint qualification (PLCQ). For this result the boundedness of the Lagrange multipliers is crucial, and this is shown under the assumption that the nonsmooth part of the objective function is locally Lipschitz continuous. A counterexample shows that one cannot expect to get bounded multipliers without such an assumption. The performance of the algorithm is evaluated numerically on a set of sparse portfolio optimization problems with two different regularization terms, one being Lipschitz and the other one being non-Lipschitz. The results are significantly better for the Lipschitz sparsity term, whereas the underlying method generates seemingly unbounded multipliers in many instances when using the non-Lipschitz sparsity function.

This letter studies energy optimization of short-packet transmission for event-triggered remote monitoring over finite-blocklength wireless links. A wireless sensor node generates updates only when the source state changes, and freshness is measured by the Version Age of Information (VAoI). We model the VAoI evolution as a Markov chain and show its coupling with the packet error rate, characterized by decoding error probability, and average delay. Then, we formulate a transmit-power allocation problem that minimizes the long-term average energy consumption under a VAoI constraint and solve it using a low-complexity search method. Numerical results show that the update arrival probability and blocklength strongly affect the energy–VAoI tradeoff, and that optimizing long-term energy consumption can substantially reduce energy compared with minimizing the energy per transmission.

A topological space $X$ is continuously homogeneous if for any $x,y\in X$ there exists a continuous surjection $f:X\to X$ with $f(x)=y$. We show that continuously homogeneous hereditarily indecomposable continua are tree-like, therefore, extending results of Bing and Rogers for homeomorphism and a result of Sturm for the pseudo-circle and pseudo-solenoids. This also provides a partial answer to the question of Lewis whether all continuously homogeneous hereditarily indecomposable continua are homogeneous.

We study the equivariant lifting of cleft extensions of abelian categories and its impact on singularity categories. Specifically, we establish the necessary framework for lifting a cleft extension to a G-equivariant cleft extension. Furthermore, we prove that a restriction functor associated to a cleft extension induces a singular equivalence if and only if its equivariant counterpart does. As a concrete application, we demonstrate that the skew group ring of a $G$-equivariant $\theta$-extension is isomorphic to a $\widehat{\theta}$-extension of the base skew group ring, allowing us to lift singular equivalences for these structures.

Given a topological space $Z$, let $PM(Z)$ be the space of bounded continuous pseudometrics on $Z$, which is endowed with the sup-norm, and let $SPM(Z)$ be the unit sphere of $PM(Z)$. In this paper, we shall prove that for all non-degenerate compact metrizable spaces $X$ and $Y$, and for any surjective isometry $T : SPM(X) \to SPM(Y)$, there exists a homeomorphism $\phi : Y \to X$ such that for any metric $d \in SPM(X)$ and for any pair of points $(x,y) \in Y^2$, $T(d)(x,y) = d(\phi(x),\phi(y))$. As a corollary, we can solve a variant of Tingley's problem on spaces of metics.

Let $S$ be a minimal surface of general type with $K_S^2=1$ and $p_g(S)=2$, called a $(1,2)$-surface. We give a geometric recovery and refinement of D. Wen's bound $|\mathrm{Aut}(S)|\leq 200$ using the canonical genus-two fibration and the double-cover model over the Hirzebruch surface $\Sigma_2$. Computing $\mathrm{Aut}(\Sigma_2)$ from its Cox ring separates the action on the base $\mathbb{P}^1$ from the vertical kernel. If $\overline K_0$ denotes the vertical image on $\Sigma_2$, then $\overline K_0$ is cyclic of order $5$, $4$, $2$, or $1$, and we prove the respective sharp bounds $|\mathrm{Aut}(S)|\leq 200, 192, 48, 80$. The proof combines singularity indices of genus-two fibrations with invariant divisors arising from the branch equation. We also construct admissible branch divisors attaining all four bounds and show that their full automorphism groups are, respectively, $(C_{10}\times C_{10})\rtimes C_2$, $(BO_{48}\times C_8)/\langle(-I,J^4)\rangle$, $(BT_{24}\times C_4)/\langle(-I,J^2)\rangle$, and $C_{40}\times C_2$. Here $BO_{48}$ and $BT_{24}$ denote the binary octahedral and binary tetrahedral groups, respectively, and $J$ denotes a generator of the corresponding cyclic factor.

In this paper, we investigate weighted composition operators $W_{f,g}$ commuting with complex symmetric weighted composition operators $W_{\psi, \varphi}$ on the classical Fock space $\mathcal{F}^{2}(\mathbb{C})$. In particular, we investigate the symbols $f$ and $g$ give rise to $W_{f,g}$ commuting with a complex symmetric weighted composition operator on $\mathcal{F}^{2}$. We further characterize when the commuting weighted composition operators are self-adjoint and normal.

Multi-resource allocation in network-congested, multi-tenant systems in which demand exceeds available capacity is challenging, as there is no straightforward way to determine how much of each resource to assign, especially when resources are interdependent. Classical approaches such as Dominant Resource Fairness (DRF), which generalizes Max-Min Fairness (MMF) to multiple resources, assume linear proportional dependencies across resources, requiring allocations to follow fixed proportions implied by tenants demands. However, this assumption may lead to inefficient allocations and resource waste, with allocated resources that go unused in practice. In this paper, we consider a multi-resource orchestrator and propose the Dependency-aware Dominant Resource Fairness (DDRF) policy, a centralized generalization of DRF that considers inter-resource dependencies: it equalizes active dominant shares of congested resources, preserving DRFs desirable properties, while avoiding its inefficiency with low-demand tenants. We prove that DDRF always saturates at least one congested resource, ensuring Pareto efficiency and eliminating resource waste. We evaluate DDRF using Amazon EC2 traces and a virtualized radio access network (vRAN) use case while considering real resource dependencies. The results show that DDRF improves effective user satisfaction by up to 80% and reduces resource waste by up to 60% compared to dependency-agnostic baselines, while improving Jain's fairness index by more than 15% compared to the utilitarian policy.

This paper introduces the Exact Ensemble Kalman Filter (ExEnKF), a novel algorithm for state estimation in discrete-time nonlinear filtering problems with linear observations. Unlike traditional Ensemble Kalman Filters (EnKFs), which approximate the filtering distribution using ensembles of Dirac measures, the ExEnKF employs Gaussian measures, enabling more efficient exploration of the state space and potentially alleviating the curse of dimensionality. We prove the algorithm's asymptotic consistency with the optimal filter (Theorem 3.1), establishing a convergence rate of order 1/ $\sqrt$ N for N particles. Numerical experiments on the Lorenz-96 multiscale model demonstrate that the ExEnKF outperforms the standard EnKF under model misspecification and poor initialization, particularly in highly stochastic regimes. The algorithm's robustness is further highlighted by its ability to track hidden components of the true signal, even when observations are generated from a different model (e.g., multiscale vs. single-scale). This work advances the theoretical understanding of ensemble methods in nonlinear filtering and provides a practical alternative to sequential Monte Carlo methods for high-dimensional systems

We prove the global-in-time existence of weak solutions to the isothermal Maxwell–Stefan system on the whole space $\mathbb R^3$. The main difficulty is that, unlike in bounded domains, the concentrations generally have infinite mass and the standard mixing entropy is not finite. We therefore work with the relative entropy with respect to a strictly positive constant equilibrium state. The proof proceeds by solving the problem on balls $B_R$ with no-flux boundary conditions, using the bounded-domain entropy theory, and deriving estimates independent of $R$. These estimates yield uniform control of the relative entropy, the gradients $\nabla\sqrt{c_i}$, and the fluxes $J_i$. Passing to the limit $R\to\infty$ is achieved by local compactness and a diagonal argument. The resulting weak solution satisfies the Maxwell–Stefan system in the sense of distributions and obeys a global relative entropy inequality.

We study subhomogeneity for finite-dimensional operator systems, and collect and extend characterizations in terms of the $C^*$-envelope, $d$-maximality, complete positivity, dual $d$-minimality, and non-commutative boundary conditions. We then show that the dual of a subhomogeneous operator system, while not necessarily subhomogeneous itself, is always a quotient of a subhomogeneous system. We complement these characterizations with examples and counterexamples, including minimal and maximal systems over certain polyhedral cones.

A theoretical analysis of CRC-aided successive cancellation list (CA-SCL) decoding for polar codes remains an open problem, despite its widespread practical adoption. While low-density parity-check (LDPC) codes benefit from mature analytical tools, such as density evolution (DE), for predicting the performance of belief-propagation (BP) decoding, similar techniques are not directly applicable to CA-SCL decoding. This limitation stems from the complex path-pruning mechanism inherent in CA-SCL decoding. In this paper, we propose an analytical framework based on a novel path-survival model that captures the evolution of the correct path's rank during decoding. The proposed framework enables efficient prediction of CA-SCL decoding performance without requiring exhaustive list-specific Monte Carlo simulations. Extensive numerical evaluations demonstrate its effectiveness across a wide range of code lengths, code rates, list sizes, and channel models.

In this article, we propose a two-sample test based on the Wasserstein 2-distance between two 1D samples, where the first sample is assumed to be Gaussian based on an approximation of the underlying distribution by a log-normal distribution. A two-sample test is performed to decide whether two samples are drawn from the same distribution or not. We evaluate the proposed method on synthetic data and extend it to the multivariate case. We also show that this test is closely related to the Shapiro-Wilk normality test.

In this work, we consider a two-dimensional time-space fractional diffusion equation with a variable coefficient and investigate the inverse source problem of reconstructing the source term f(x,y) , after regularizing the problem using the quasi-boundary value method to mitigate ill-posedness. A finite difference discretization results in a large-scale linear system with a multilevel Toeplitz-like block structure. We perform a spectral analysis of the associated matrix sequences, employing tools from Generalized Locally Toeplitz (GLT) theory, and construct efficient preconditioners based on the GLT analysis. The proposed preconditioners preserve the multilevel structure of the discretization matrices and leads to a general eigenvalue clustering around one for the preconditioned sequence. Numerical experiments validate the theoretical findings and demonstrate that the proposed approach significantly accelerates the convergence of the GMRES method in reconstructing the source term in the two-dimensional space-time fractional diffusion equation.

We define a notion of total positivity for the symmetric space $G/K$ by taking the Hausdorff closure of the image of Lusztig's totally positive part $G_{>0}$ in $G/K$. We introduce double Bruhat cells for the symmetric space and define their totally positive pieces. We prove a cell decomposition of the totally nonnegative symmetric space, give explicit positive parametrizations of all cells, establish closure relations, and show that the transition maps between the two natural families of parametrizations are subtraction-free.

This paper investigates transfer principles for generalized convexity of spectral functions on Euclidean Jordan algebras. A spectral function is induced by the eigenvalue map and an underlying symmetric function on a symmetric subset of $\mathbb{R}^n$. We establish transfer principles for several generalized convexity notions, such as (strict/semistrict) quasiconvexity and (strict) pseudoconvexity, together with their strong variants, by showing that these properties are preserved in both directions between a spectral function and its associated symmetric function. These results extend the transfer principles for (strict) convexity and provide a unified framework for generalized convexity in the setting of Euclidean Jordan algebras.

We present the ”Power Spiral Map”, a continuous angular evolution of the linear coordinate grid established in our previous work. While that previous Power Map utilized a seed value translating along a horizontal axis, this work builds upon a seed angle ($\theta$) projected onto a unit diameter circle. This operation controls two coupled geometric behaviors: an internal area-preserving partition of unity within a reference square (cos 2 $\theta$ + sin 2 $\theta$ = 1) and an external recursive scaling mechanism (sec $\theta$ and cos $\theta$) that dictates the expansion or contraction of successive generations of squares unfolding as a spiral in the 2D plane. We demonstrate that continuous variation of this angular parameter generates discrete geometric alignments that yield polynomial identities, with examples of the Golden Ratio ($\Phi$) and the Plastic Ratio ($\psi$) defined through purely planar intersections.

We present a novel methodology for studying large deviations principles (LDPs) of random matrices. By utilizing a partially lifted variant of random duality theory (RDT), we develop a generic LDP framework that completely circumvents traditional random matrix theory (RMT) methods. To demonstrate the framework's simplicity and accuracy, we apply it to the Wishart and Wigner GOE classical statistical ensembles. In both cases, we obtain elegant LDP characterizations of the upper and lower spectral edges that fully match the results achieved through traditional Coulomb gas methodologies in [85,95].

We construct a discrete realization of two-dimensional Carroll dilaton gravity based on a BF-type gauge structure with holonomy variables on lattice links. The bulk theory remains topological, while the physical dynamics is encoded in boundary degrees of freedom. Imposing admissible boundary conditions, we derive the asymptotic symmetry structure directly at the lattice level. The least restrictive conditions yield an affine extension of the Carroll algebra, while additional constraints reduce the symmetry to a conformal sector governed by a discrete Virasoro-type algebra. In the continuum limit, the lattice symmetry structure reproduces the expected affine Carroll algebra together with its conformal reduction. The construction therefore provides the ultra-relativistic counterpart of discrete Jackiw-Teitelboim(JT) gravity.

Building on the large-sample analysis of infinitesimal gradient boosting (Dombry and Duchamps, 2024), we study the fluctuations of the process around its deterministic limit and establish a functional central limit theorem: the rescaled deviations converge in distribution to a Gaussian process. The analysis is carried out in a reproducing kernel Hilbert space (RKHS) naturally associated with the softmax gradient tree base learner, in which the boosting process is characterized as the solution of an autonomous ordinary differential equation (ODE). The proof rests on a general stochastic perturbation analysis of ODEs in Banach spaces, which is of independent interest: whenever a sequence of vector fields converges and satisfies a central limit theorem, so does the associated ODE solution. We first illustrate this perturbation approach in the simpler setting of kernel gradient flow, where the Gaussian limit admits an explicit characterization, and then consider the more complicated tree-based gradient boosting setting.

The $k$-distance graph $G^k$ of a graph $G$ has the same vertex set as $G$ and two vertices are adjacent if and only if their distance is $k$ in $G$. These graphs have been extensively studied for their connection properties. In this paper, we study various properties of these graphs, including clique number and periodicity. For all $k$, we show that there exists a $k$-distance graph that is weakly periodic for any size period. Our main result is a proof that if $k > 2$ then there exists a $k$-distance graph of any size (strong) period. Finally, we provide evidence that there exists an upper bound on the periodicity of a connected $2$-distance graph as a function of $|V|$.

The Donsker–Varadhan formula characterizes the ordinary Bayesian posterior as the solution of an unrestricted $\mathsf{KL}$-regularized variational problem. Generalized variational inference replaces this regularizer by other divergences, but the resulting measure-valued optimization problem is often studied only after restriction to a parametric variational family. This paper studies the unrestricted measure-level problem. Given a measurable space $(\mathcal{Z},\mathfrak{Z})$, a prior probability measure $P$, a measurable loss $\ell:\mathcal{Z}\to(-\infty,\infty]$, a regularization strength $\alpha>0$, and a divergence $\mathsf{D}(Q\Vert P)$, we seek probability measures in \[ \underset{Q\in\mathcal{P}(\mathcal{Z})}{\mathrm{arg\,min}}\left\{\int_{\mathcal{Z}} \ell\,\mathrm{d}Q+\alpha\mathsf{D}(Q\Vert P)\right\}. \] For $f$-divergence penalties we derive a scalar inverse-gradient density formula and a one-dimensional dual identity; the Kullback–Leibler, Cressie–Read, and squared-Hellinger problems are treated as examples. Reverse $f$-divergences and mixed forward/reverse Kullback–Leibler penalties follow from the same separable integral principle. For Bregman divergences between densities we obtain a density-space solution with a scalar mass multiplier, including least-squares, density-power, and Burg/Itakura–Saito examples. For Rényi penalties of order $r>1$ we derive a normalized truncated-power characterization and a threshold equation for every global optimizer. Finite model-weight formulas and simple conjugate Bayesian model illustrations show how these closed forms are realized in practice and differ from the traditional solutions.

Let F be a totally real field, and let p be prime. Under standard Taylor–Wiles hypotheses, we show that an irreducible, 2-dimensional, totally odd mod p representation of the absolute Galois group of F admits lifts lying on arbitrary prescribed components of local deformation rings, allowing potentially semistable conditions with arbitrary regular Hodge–Tate weights.

Defeaturing is routinely employed in numerical simulations of medium- and high-voltage equipment, not only to reduce computational costs but also to make meshing possible. But the errors that this practice introduces in the predicted breakdown/inception voltages are currently neglected. This work presents a goal-oriented a posteriori error estimation framework that aims at assessing such defeaturing errors in inception voltage computations. The methodology combines a first-order approximation of the inception voltage error with dual-weighted residual estimators, providing an error bound that quantifies the impact of defeaturing on the simulation results. The approach builds upon the streamer integral model for inception voltage prediction and uses the recently proposed certified goal-oriented analysis-aware defeaturing estimator of~[1] for elliptic PDEs. The first-order approximation of the inception voltage is a linear functional J of the background electric field whose definition involves a line integral along the critical field line, and is therefore only of low regularity. To meet the abstract regularity assumption of the goal-oriented theory, we introduce a Gaussian mollification of J. The methodology is illustrated on a pin-plate benchmark with a small protrusion of varying size and shape, using a single shared adaptive mesh and an adaptive coupling of the mollification width to the local mesh size in order to ensure that the defeaturing error dominates over the discretization and the regularization errors.

We primarily study several combinatorial properties of Ramsey-type ideals on countably infinite sets. Specifically, we show new combinatorial characterizations of Ramsey ideals through various partition and convergence properties. Furthermore, we analyze ideal versions of some relevant high-dimensional Ramsey-type theorems, in order to research ideals related to finite colorings of barriers on the natural numbers as well as ideals associated with finite partitions of any family of finite subsets of the natural numbers. In particular, Galvin ideals are introduced as an intermediate combinatorial concept between Ramsey ideals and semiselective ideals.