Papers

Effective evaluation of zero-day jamming detectors requires robust adversarial models. However, existing attack models often assume prior knowledge of the target receiver, limiting their utility as evaluation benchmarks. On the detection side, existing detectors fail to capture the global temporal-spectral structure of jamming behavior and cannot differentiate zero-day strategies as they emerge. This paper addresses these limitations through a two-pronged framework. First, an online detection framework is introduced that combines a graph attention network (GAT) for temporal-spectral representation learning with Dirichlet process (DP)-means clustering. This framework jointly classifies known and discovers zero-day strategies within a unified learning objective. Second, an inference-driven reinforcement learning (RL) jammer is proposed as an adversarial benchmark. The jammer treats the target receiver as a black-box, infers the detector state via hypothesis testing, and optimizes the trade-off between attack impact and stealth. Simulation results show that the proposed RL jammer outperforms benchmarks, achieving 33% higher attack efficacy and 67% higher stealth. The proposed detection framework against the proposed RL jammer is shown to achieve 20% higher detection accuracy than the benchmarks.

We consider variable-density Cahn–Hilliard–Navier–Stokes (CHNS) discretizations on finite element meshes that may change between accepted time levels through fixed-topology motion or topology-changing remeshing. When the discrete spaces vary in time, the phase, kinetic, and pressure histories entering a multistep scheme are measured in different discrete structures and cannot, in general, be transferred by a single operator. We develop decoupled backward Euler (BE) and second-order backward differentiation formula (BDF2) schemes by combining exact physical cross-mesh pairings with history representations compatible with the corresponding phase-energy, kinetic-energy, and pressure-gradient storages. The phase update also determines an Abels–Garcke–Grün-consistent mass flux used in the momentum transport. A scalar capillary-exchange equation separates the phase and fluid solves while retaining the discrete energy exchange. The resulting field subproblems are linear, the scalar equation has a unique positive solution, and the schemes satisfy modified energy balances without a time-step restriction under the stated admissibility assumptions. Numerical experiments confirm second-order temporal convergence under both mesh updates, phase-mass conservation, modified-energy decay in the unforced tests, and comparable Rayleigh–Taylor and rising-bubble dynamics.

Quantile-based reinforcement learning provides an interpretable approach to risk-sensitive decision-making by optimizing a prescribed quantile of the cumulative-return distribution. Despite this appeal, learning under a point quantile objective is challenging: quantiles can change abruptly under small perturbations of the return distribution, and exact quantile-sensitive planning requires computationally demanding distributional optimization. Lower-buffered quantiles alleviate the former difficulty by averaging neighboring quantiles immediately below the target level, providing a smoother surrogate while preserving the underlying point-quantile objective. Existing methods based on this principle, however, remain model-based and rely on explicit return-law planning, limiting their applicability beyond small tabular problems. We develop Deep-BQRL, a model-free distributional reinforcement-learning framework that extends buffered-quantile learning to neural function approximation. The method learns conditional return quantiles directly from sampled transitions, constructs buffered action scores from the relevant region of the learned quantile function, and uses ensemble disagreement to guide exploration. An augmented input representation allows the learned policy to respond to trajectory information without explicitly reproducing the quantile-state recursion required by exact planning. Experiments on an asset-selling optimal-stopping problem and slippery FrozenLake compare Deep-BQRL with model-based UCB-BQRL and tabular PPO and TRPO implementations. In asset selling, Deep-BQRL attains smaller mean cumulative point-quantile policy gaps than PPO and TRPO at the reported target levels, while UCB-BQRL retains the smallest gaps. The learned stopping decisions also vary with the target quantile, providing an interpretable illustration of the method's risk-sensitive behavior.

This article is concerned with mixed Steklov–Robin eigenvalues on bounded domains in $\mathbb{R}^{n}, n \geq 2$, with Lipschitz boundary. Specifically, we consider domains with symmetry of order $4$ containing a spherical hole. We obtain isoperimetric inequalities for the $k$-th Steklov-Robin eigenvalues for each $k \in \{2, 3, \dots, n+1\}$. We provide examples to emphasize the fact that the symmetry assumptions, on the family of domains considered, are crucial.

For all positive integers $\ell$ and $r$, we prove that a finite simple rank-$r$ gammoid with no $U_{2,\ell+2}$-minor has at most $\ell(r-1)+1$ elements. This gives an affirmative answer to Problem~7.2 of Boretsky and Walsh [European J. Combin.\ 137 (2026), 104419], for both gammoids and transversal matroids. The bound is sharp for every $\ell$ and $r$. The key estimate is that, for every finite simple gammoid $M$, the sum of $|L|-2$ over its long lines is at most $|E(M)|-r(M)$.

We prove that every solution of the classical rational Calogero-Moser system can be approximated, after subtracting a common linear drift from the particle positions, by rational multisoliton solutions of the focusing continuum Calogero-Moser equation, uniformly for all time. The construction identifies the multisoliton inverse spectral matrix as a rank-one dissipative perturbation of Moser's time-dependent Hermitian position matrix. A uniform lower bound on the particle separation then yields quantitative control of the multisoliton poles. Their real parts and real velocities approximate the shifted particle positions and velocities with errors of order $\varepsilon^2$, while the pole heights are positive and sum exactly to $\varepsilon$. Using the exact Poisson-kernel representation of the multisoliton density, we obtain convergence to the atomic particle measure in bounded-Lipschitz distance at rate $O(\varepsilon(1+|\log\varepsilon|))$, uniformly in time. We also derive the large-time distribution of pole height at fixed $\varepsilon$, with one distinguished branch retaining the limiting height and the remaining heights decaying quadratically in time. Explicit two-particle formulas illustrate the approximation and show that the real-position error estimate is sharp.

We study the unforced viscous Katz–Pavlović dyadic model with non-negative smooth initial data for two shell settings. For super-exponential scales $N_n=N_0^{b^n}$, with $N_0>1$ and $1<b<2$, we prove that $\alpha=1/(b+2)$ is the sharp dissipation threshold: every such datum produces a globally smooth solution at and above this value, whereas suitable compactly supported data lose regularity in finite time below it. For geometric scales $N_n=N_0\Lambda^n$, global regularity holds when $\alpha\geq1/3$ and $4\alpha-1>(\log2)/(2\log\Lambda)$. In particular, for $\Lambda>2^{3/2}$, the result reaches $\alpha=1/3$ and, together with the known classical blow-up theorem, identifies the sharp threshold in classical shell ratios.

We study what noisy data can justify before a manifold and its intrinsic dimension are assumed. For repeated observations with independent isotropic Gaussian errors of unknown variance, we compose a support confidence event with a sound geometric verifier to certify a nearby smooth witness of arbitrary compact latent support. Whole-support inference requires an external lower mass condition; independent validation instead certifies proximity of probability mass. Separate all-scale hypotheses yield true-support structure and dimension recovery: a credited Reifenberg–Dini criterion and positive continuous density give local $C^1$ structure and consistent dimension estimation, while two-sided Ahlfors regularity and positive reach give quantitative covariance separation under the stated sampling and observation-transfer conditions. An exact-arithmetic implementation verifies restricted witness families. A further matrix check certifies linear coordinates on a geometrically verified affine span containing the witness and propagates approximation and decoding errors. This restricted construction neither implements the general minimal-dimension Whitney theorem nor infers exact manifold support from finite approximation. Executed torus and Julia-set experiments test the observation-to-witness-to-coordinate route, including singular-support controls. Dynamical systems and chaos are the primary application context; state-identification and finite-horizon prediction results are conditional on observation embeddings and transition validation. Takens reconstruction is an optional scalar-delay application requiring additional smoothness, dynamics and observable conditions. Image comparisons are auxiliary reconstruction diagnostics. The finite-data verifier establishes neither those dynamical conditions nor the all-scale geometric premises for true-dimension recovery.

We give a proof, that does not rely on analytic determinacy, of the existence of an idealistic analytic equivalence relation with Borel classes that is not classwise Borel isomorphic to an orbit equivalence relation. This result answers a question of Becker, and Calderoni and Motto Ros. Our proof proceeds through an analysis of Borel complexity of certain sets of countable rooted trees defined via the notion of the Lusin derivative.

A unified kernel-free boundary integral (KFBI) framework is proposed for the Allen-Cahn and Cahn Hilliard equations with homogeneous no-flux boundary conditions on two- and three-dimensional irregular domains. With a stabilized first-order implici-explicit (IMEX) discretization, the Allen-Cahn update reduces to a Neumann modified Helmholtz problem. An auxiliary-variable reformulation reduces the Cahn-Hilliard update to subproblems of the same type without evaluating the Laplacian of the nonlinear source. The Cahn-Hilliard update requires two sequential solves for real shifts, while complex-conjugate shifts allow the real-valued solution to be reconstructed from a single complex solve. All subproblems are handled by the same KFBI solver that indirectly evaluates potentials through equivalent interface problems. To correct discrete mass defects in the Cahn-Hilliard update, a geometry-weighted discrete $L\v{s}$ mass projection is constructed tailored to the KFBI treatment of irregular boundaries. Exterior overlap weights are redistributed to physical nodes, excluding auxiliary KFBI extension values from the mass calculation. Numerical experiments demonstrate second-order spatial convergence, first order convergence of paired temporal-error indicators, and preservation of the prescribed discrete mass. The reported source-free simulations exhibit energy decay, with cumulative projection-induced energy perturbations remaining small relative to the observed dissipation.

We derive a thermodynamically-consistent model of fluid flow through a poroelastic medium. Starting from elastic and fluid free-energy densities, an energy-dissipation rate, and a kinematic constraint, the force-balance equations are derived using variational principles, with the pressure–density constitutive relation emerging as a direct consequence of the variational structure; the same kinematic constraint also supplies the total-flux transport structure. In the ideal-gas limit, the model linearization recovers the classical linear Biot equations. For power-law fluid energies, it yields isentropic pressure–density relations. A key advantage of the variational formulation is that extensions to richer physics, such as thermal effects, chemical reactions, or multi-component fluids, can be incorporated systematically by augmenting the energy and dissipation functionals without redesigning the force-balance or transport closure. We support the model with an energy-compatible two-field discretization and study consolidation under a surface load with three lateral-boundary treatments and three fluid-compressibility exponents.

For a vector bundle $E$ on a smooth projective curve $C$, one defines the Quot scheme $Q:=Q_d(E,C)$ parametrizing subsheaves of $E$ having length $d$ torsion quotients. We describe the indecomposable components of the tangent bundle $T_Q$ of $Q$, thus characterizing when $T_Q$ is indecomposable. We also characterize when $T_Q$ is simple; in fact, we completely describe the endomorphism rings of the indecomposable components of $T_Q$. As an application, we determine when two products of such Quot schemes can be isomorphic.

Let $G$ be a Borel digraph with maximum out-degree $d \in \mathbb{N}$. We show that $G$ admits a random Borel $(2d+1)$-coloring for which every edge is almost surely not monochromatic. This gives a simpler proof of a recent result of Pelayo-Gómez: such a graph $G$ admits a measurable proper $(2d+1)$-coloring with respect to any Borel probability measure on $V(G)$. Our proof is an adaptation of Pelayo-Gómez's proof to the randomized Borel setting.

Let $X_{\mathsf{KW}}$ be the Kadets–Werner modification of a closed subspace of $L_1$ constructed by Bourgain and Rosenthal in 1980. In this short note, it is shown that $X_{\mathsf{KW}}$ is asymptotically midpoint uniformly convex. Since $X_{\mathsf{KW}}$ has the Daugavet Property, it fails the Point of Continuity Property and thus does not admit an equivalent norm that is asymptotically uniformly convex. Therefore, the previously known properties of $X_{\mathsf{KW}}$ and the new geometric observation answer, in the negative, the question of Dilworth, Kutzarova, Randrianarivony, Revalski and Zhivkov whether asymptotic midpoint uniform convexity and asymptotic uniform convexity are isomorphically equivalent and a question of Perreau whether asymptotic midpoint uniform convexity implies the Point of Continuity Property.

Discrete-time non-symmetric algebraic Riccati equations (DTNAREs) arise in game-theoretic computations of Nash equilibria. Solving such equations at large scale is often computationally prohibitive. This paper develops a numerical approach for large-scale DTNAREs whose solutions are low rank. A low-rank alternating direction implicit (ADI) method is introduced that recursively constructs a low-rank stabilizing solution without explicitly solving any projected DTNARE. Through the pole-placement property of the low-rank ADI iteration, the method ensures that the implicitly solved projected DTNARE always admits a stabilizing solution. An automatic shift-generation strategy is also developed for the ADI iterations. Once an initial shift is provided, the algorithm computes the low-rank solution without further user intervention. Numerical experiments on DTNAREs with dimensions between \(10^6\) and \(10^7\) demonstrate the accuracy and efficiency of the method. The results confirm that the proposed low-rank ADI algorithm is an effective solver for large-scale DTNAREs that would otherwise be computationally prohibitive.

We study Scott products and sobriety of countable meet-continuous domains, meaning meet-continuous dcpos without any additional continuity or least-element assumption. Using the complete-lattice test-family theorem of Xu and Ji, we prove finite-product equality for those domains that are $L$-dcpos, and for the weaker class whose principal ideals have suprema of all nonempty subsets. For an arbitrary family of nonempty countable meet-continuous $L$-dcpos, we prove that the Scott topology on the order product equals the product of the factor Scott topologies if and only if only finitely many factors lack a least element. We also establish sobriety under bounded completeness and under additional common-upper-bound conditions. Assuming square-product equality, sobriety is characterized by Scott closedness of common-upper-bound sections associated with irreducible Scott-closed sets, with an equivalent sequential formulation in the countable case. Two extraction lemmas extend to meet-semilattice dcpos. The finite-product and sobriety questions for general countable meet-continuous domains remain unresolved here.

Nested clustered optimization allocates within each cluster from the cluster's own covariance block and then across the resulting cluster portfolios. Block inversion says the unconstrained minimum-variance portfolio has the same two-tier shape, with each block replaced by its Schur complement against every other asset. Conditioning instead on one knot from each other cluster truncates the conditioning set in the manner of a Vecchia approximation, and we give the rank-one model of cross-cluster dependence under which it is exact. Damping the complement by $\gamma\in[0,1]$ then gives a bridge with nested clustered optimization at $\gamma=0$ and the global optimum at $\gamma=1$, with no linear solve larger than a cluster or the number of clusters. Under estimation error the optimal $\gamma$ can be strictly interior and full coupling can remain optimal, and we give the local theorem at the minimum-variance end with exact examples of both, including a symmetric family in which the optimum is a closed form.

In this paper, we realize volumes of representations as real-valued Chern-Simons invariants in Nil, Sol, and Euclidean geometries. To this end, we formulate a Chern-Simons invariant of a pair of connections on a principal bundle that need not be trivial. For a connected closed oriented 3-manifold $M$ and a representation $\rho\colon\pi_1(M)\to G$ into the identity component $G$ of the isometry group of one of these geometries, we construct an auxiliary connection on the associated flat $G$-bundle. We show that, for a suitably normalized invariant polynomial, the Chern-Simons invariant of the auxiliary and flat connections equals the volume of the representation. For the holonomy representation of a geometric structure, this invariant recovers the Riemannian volume. We also compute the Chern-Simons invariant of the Levi-Civita connection for representative closed manifolds in each of these geometries.

The cloud radio access network (C-RAN) mitigates inter-cell interference by jointly processing the observations of distributed remote units (RUs) at a centralized unit (CU), but limited fronthaul capacity forces each RU to compress its received signal. Under transform-compress-forward, an RU transforms its signal and quantizes the resulting coefficients, with bit allocation distributing a finite bit budget across them. Classical reverse waterfilling assumes Gaussian sources, yet practical finite-alphabet symbols carry mutual information that saturates at $\log_2 M$, leaving bit allocation for such inputs unresolved. We address this by formulating bit allocation as maximizing the finite-alphabet generalized mutual information (GMI) achieved after linear MMSE (LMMSE) detection at the CU. Via the I-MMSE relation, this yields a fixed-point update whose converged solution decomposes into a vessel height, a shared water level, and a finite-alphabet mercury level; we term it {reverse mercury/waterfilling} (RMWF). Numerical results show that RMWF sustains end-to-end rate under tight fronthaul budgets and remains robust under antenna scaling, which is increasingly consequential as antenna counts outpace fronthaul capacity in modern C-RAN.

We study online control of a scalar storage system with adversarial nonnegative arrivals, known retention coefficient, and convex costs depending on both state and action. Each action must respect current resource availability and is chosen before the current arrival and cost function are revealed. For the existing simplex disturbance-action policy class, we give an exact reparameterization by cumulative allocation fractions and a decay-weighted projected subgradient update. The resulting regret bound is independent of policy memory length. For fixed retention coefficient and cost constants, the controller achieves $O(\sqrt T)$ regret against the best fixed infinite-memory policy in this class, using $O(\log T)$ memory and arithmetic operations per round and one cost-subgradient query. A storage-specific block construction gives a matching lower bound against every causal feasible controller, including randomized controllers. Writing $\tau=(1-\alpha)^{-1}$, the minimax expected regret is $\Theta(\sqrt T\min\{T,\tau\}^{3/2})$ for every finite-memory simplex policy class and its infinite-memory extension, when $\alpha\in[1/2,1)$, $T\ge4$, and the positive cost constants are fixed. This identifies the joint horizon and retention-time dependence for these policy benchmarks.

We prove Korn's first inequalities with and without boundary conditions in $GSBD^p$ ($1<p<\infty$) in $C^{1,1}$-regular thin domains with Lipschitz thickness boundaries with a constant $C h^{-p},$ that is optimal if the domain mid-surface contains a flat region, e.g., if the domain contains a piece of plate. For the one with boundary condition, we impose zero Dirichlet boundary conditions on the thin lateral faces of the shell, where we prove that the same estimate holds with no subtracted rigid motion like in the classical case for Sobolev vector fields.

In this article, we study the spatial fluctuations of the solution to the stochastic wave equation with a nonlinear drift and multiplicative Gaussian noise in dimensions one and two. The noise is white in time, and its spatial covariance is either integrable or given by a Riesz kernel; space-time white noise in dimension one is also included. We establish spatial ergodicity, convergence of the rescaled covariance, and prove a quantitative central limit theorem for the spatial fluctuations. We also obtain the corresponding functional central limit theorem. Our approach exploits the compact support of the wave kernel to obtain an estimate for the spatially integrated second Malliavin derivative which is compatible with a bound for the total variation. Further arguments based on the Clark-Ocone formula are used to control the drift contributions.

We study a strongly damped viscoelastic wave equation with a logarithmic source whose measurable exponent satisfies $2<p_-\le p(x) \le p_+<2^*$. An optimal pointwise correction to the source–potential inequality defines a shifted energy. Under suitable kernel conditions, we prove finite-time blow-up for negative shifted energy and for a class of nonnegative shifted energies with no fixed upper energy threshold. Explicit upper lifespan bounds follow from an estimate for reaching negative shifted energy and a concavity argument. We also construct smooth blow-up data at every prescribed real energy level and show that our lifespan estimate covers additional data in the constant-exponent case. Explicit examples are given to illustrate the blow-up results.

We prove that random groups in the Gromov density model (under a certain divisibility condition) have property (T) asymptotically almost surely for any density $d > \frac{1}{4}$. This established $\frac{1}{4}$ as the threshold for property (T), since it was shown by Ashcroft that they do not have property (T) for $d < \frac{1}{4}$.

For $N\ge2$, $0<\beta<N$ and $q>1$, we study maximizers of the critical singular anisotropic Moser–Trudinger integral \[ \int_{\mathbb{R}^N} \frac{\Phi_{N,q,\beta} (\lambda_N(1-\beta/N)|u|^{N/(N-1)})} {F^o(x)^\beta}\,\mathrm{d}x, \qquad \|F(\nabla u)\|_N^a+\|u\|_q^b\le 1. \] where $a>0$, $0<b\le N$ and $\Phi_{N,q,\beta}$ is the integrable Taylor remainder. The supremum is attained for every $a>0$ when $b<N$. For $b=N$ and $1<q<q_+$, the first retained Taylor term separates two regimes, with \[ q_-:=\frac{N^2(N-2)}{(N-1)(N-\beta)},\qquad q_+:=\frac{N^2}{N-\beta}. \] Attainment holds for every $a>0$ if $1<q<q_-$, while for $q>1$, $q_-\le q<q_+$, there is a finite threshold $a_c>N$ and attainment holds if and only if $0<a\le a_c$. An exact Euclidean reduction shows that the threshold is independent of the anisotropy. The proof combines critical–subcritical scaling with a nonlinear Green-function concentration bound. Radial flux and Pohozaev identities determine the first correction to the subcritical supremum, and refined Green tests give the strict comparison needed for attainment at the finite threshold, including in dimension two.

We consider the initial value problem for the Euler–Korteweg equations in the class of irrotational flows. In every space dimension $d \geqslant 2$, we establish a quantitative lower bound for the lifespan of solutions that explicitly exhibits its dependence on the Weber number, the Mach number, and the Sobolev norm of the initial perturbation. In particular, this lower bound can be taken arbitrarily large in a low-Weber-number regime under a suitable algebraic relation between the Mach and Weber numbers.

The outage probability in a network of cooperative unmanned airborne vehicles (UAVs) over generalized fading channels is studied analytically using finite mixture with expectation maximization technique. A relay-based topology with one ground control unit (GCU) is considered, where the cooperative UAVs can communicate with the GCU directly or through relay. The application the UAV assigned for specifies the minimum required transmission rate the UAV should achieve. The outage probability of the system is defined as the probability that either the transmission rate over any of the links drops below a predefined minimum threshold for that link or the Relay-GCU link is not able to transmit the aggregate data from all relayed UAVs and the minimum rate required by the relay UAV itself. Throughout the paper, expressions for the outage probability and the average achievable bit rate of a cooperative multi-carrier system are derived over generalized fading channels. Finite Mixture with Expectation-Maximization algorithm is utilized to derive a simple approximate expression for the probability density function (pdf) of the achievable bit rate assuming adaptive M-ary quadrature amplitude modulation (M-QAM). This pdf is used to derive closed-form expressions for the outage probability and the average bit rate.

Seasonal succession and human intervention profoundly influence dengue fever transmission, and both humans and mosquito vectors can disperse over long distances. This paper proposes a nonlocal reaction-diffusion dengue model with moving boundaries that incorporates dry-wet seasonality and impulsive intervention. We first present the existence and uniqueness of the global solution to the model, then introduce the definition of the generalized principal eigenvalue, prove its uniqueness when the kernel functions coincide via the method of separation of variables, and further discuss its associated properties. Using this eigenvalue as an index, we obtain a spreading-vanishing dichotomy and derive two criteria that characterize the spreading and vanishing states, respectively. Our results extend both the nonlocal diffusion model without impulsive intervention and the model with impulsive intervention but without seasonal succession. Finally, we validate our theoretical findings and investigate how various factors affect dengue transmission through numerical simulations. The numerical results indicate that a shorter dry season makes disease containment more difficult, whereas more intensive impulsive intervention enhances control efficacy.

We establish a complete characterization of local $C^1$ linearizability for planar diffeomorphisms. For every prescribed hyperbolic real Jordan form, we obtain necessary and sufficient integrability conditions on the modulus of continuity of the derivative for local $C^1$ linearizability. These criteria reduce to three canonical thresholds: the classical, polynomially weighted, and squared-logarithmically weighted Dini conditions. Each threshold is optimal: whenever the corresponding condition fails, we construct a diffeomorphism with the identical linear part that is not locally $C^1$ linearizable. For every non-hyperbolic linear part, explicit polynomial counterexamples show that smoothness alone cannot guarantee even local topological linearization. Beyond $C^1$ existence, we determine the optimal regularity for the derivative of the linearizing conjugacy in every hyperbolic case, with the optimality established by counterexamples.

We give new conditions on allowable powers of a prime $p$ dividing an integer group determinant for the group $\mathbb{Z}_p^n$, and show these conditions are sharp for $n\leq 5$. The values coprime to $p$ for these groups are already known; determining which multiples of allowable powers of $p$ occur is much more complicated. We show that all multiples of sufficiently large powers of $p$ occur as integer group determinants of $\mathbb{Z}_p^n$. We also provide a complete characterization for the group $\mathbb{Z}_3^3$, where particular arithmetic conditions are required for multiples of certain powers of $3$.