7189 papers
This paper introduces the double Zarankiewicz number , defined via bipartite graphs allowing "double edges" corresponding to squared bilinear forms, to establish improved lower bounds for the maximum SOS rank of biquadratic forms and resolve the previously noted gap in the case.
This paper introduces U-OBCA, an uncertainty-aware optimization-based collision avoidance framework that utilizes Wasserstein distributionally robust chance constraints to handle polygon-shaped robots and obstacles without geometric simplification, thereby significantly reducing conservatism and improving navigation efficiency in narrow, cluttered environments compared to existing methods.
This paper establishes the regularizing properties of quantum relative entropy for solving the inverse problem of quantum state tomography in high or infinite dimensions, providing the necessary theoretical foundations and computational tools to apply iterative convex optimization algorithms to practical examples like PINEM and optical homodyne tomography.
This paper extends the theory of compatible Poisson brackets and Poisson-commutative subalgebras to reductive Lie algebras decomposed into two complementary solvable horospherical subalgebras, while also deriving results related to the Adler-Kostant-Symes theory.
This article provides a comprehensive survey of multi-species Keller--Segel systems, synthesizing classical and recent results on their analytical well-posedness, blow-up mechanisms, and pattern formation dynamics to clarify the structural principles governing complex chemotactic interactions in biological and ecological contexts.
This paper reviews the classification of finite distance-transitive graphs, demonstrating that those with large diameters are predominantly geodesic-transitive with structured geodesics, while also providing counterexamples and extending the analysis to polar Grassmann graphs.
This paper proposes the NSGDA-M algorithm, a stochastic first-order method with momentum and normalization, to solve nonconvex-strongly concave minimax problems under generalized smoothness conditions, achieving an stochastic gradient complexity for finding an -stationary point.
This paper introduces WaterSIC, a novel linear layer quantization algorithm that achieves information-theoretically near-optimal performance by allocating different quantization rates to weight columns via a waterfilling strategy, thereby significantly outperforming existing methods like GPTQ and establishing new state-of-the-art results for LLMs across 1 to 4-bit quantization rates.
This paper establishes quadratic form representations and explicit eigenvalue bounds for the Hessian matrices of resistance distance and Kirchhoff index in positive-weighted graphs using generalized matrix inverses, while also proving the strong convexity of the Kirchhoff index with respect to edge weights.
The paper proves that any -pseudoconcave subset of the graph of a continuous function (or of locally representable as such a graph) can be decomposed into a disjoint union of -dimensional complex manifolds.
This paper establishes that the moduli of -valued constructible sheaves and perverse sheaves on a compact oriented manifold with a conically smooth stratification are -shifted Lagrangian, a result derived from constructing a relative left -Calabi--Yau structure via lax gluing of categorical cubes and identifying symplectic leaves for perverse sheaves with prescribed monodromy.
This paper proves the -convergence of the time-splitting scheme to the unique global strong solution of the nonlinear Dirac equation in 1+1 dimensions by establishing pointwise estimates, constructing a modified Glimm-type functional for stability, and demonstrating the precompactness of the approximate solutions.
This paper investigates how mismatched log-likelihood ratios (LLRs) impact belief propagation decoding of overcomplete quantum LDPC codes, revealing that while performance is sensitive to initialization in low noise, the optimal FER is robust across a wide range of LLR values, suggesting that LLR mismatch can be effectively utilized as a regularization control parameter rather than a quantity requiring precise channel matching.
This paper introduces a computationally tractable framework for stochastic optimal control in partially observable, nonlinear systems that explicitly integrates feedforward planning with feedback uncertainties, demonstrating how muscle co-contraction in human neuromechanics emerges as an optimal adaptation to sensorimotor constraints.
This paper extends the Edge of Stability phenomenon to non-Euclidean gradient descent by introducing a generalized sharpness measure based on directional smoothness, demonstrating that diverse optimizers exhibit similar stability thresholds and oscillatory behaviors across arbitrary geometric norms.
This paper introduces a general framework for "s-of-k" positional games where players score points by claiming at least elements of a winning set, and comprehensively analyzes the resulting scores under both optimal play and pairing-restricted strategies across various regular grid structures.
This paper presents a general framework for deriving Nitsche Finite Element Methods to enforce equality and inequality constraints in solid mechanics by reformulating stabilized saddle point problems into a minimization form suitable for nonlinear applications and automatic differentiation, while validating the approach through numerical convergence studies.
This paper establishes the Limiting Absorption Principle for time-harmonic acoustic and electromagnetic scattering from bi-periodic inhomogeneous layers supporting Bound States in the Continuum, thereby deriving a sharp radiation condition that ensures solution uniqueness by combining the classical Rayleigh expansion with a newly proven orthogonal identity.
This paper presents a formal control synthesis framework for continuous-state stochastic systems that minimizes a linear combination of system entropy (measured by KL divergence to uniform) and cumulative cost by deriving novel bounds on the entropy difference between continuous distributions and their finite-state abstractions, thereby enabling entropy-aware controllers with rigorous performance guarantees.
This paper extends the homogeneous second-order descent method (HSODM) to bound-constrained nonlinear optimization by proposing the SOBASIP algorithm, which utilizes affine scaling and homogenization techniques to achieve a global iteration complexity of for finding -approximate second-order stationary points and exhibits local superlinear convergence.