January 2026

arXiv:2601.10887v1 Announce Type: new Abstract: We propose a structure-preserving scheme for a hybrid model that couples the time-dependent Ginzburg-Landau (TDGL) equation of superconducting vortex dynamics and the nonlinear Bardeen-Cooper-Schrieffer (BCS) gap equation. This formulation is consistent with the classical TDGL equation in the near-critical temperature, while extending the applicability of the existing TDGL model to regimes beyond the critical temperature. The resulting system poses significant computational challenges due to its nonlinear and coupled structure. To achieve stable and […]

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arXiv:2601.10883v1 Announce Type: new Abstract: In antiquity, the seal embodied trust, secrecy, and integrity in safeguarding the exchange of letters and messages. The purpose of this work is to continue this tradition in the contemporary era, characterized by the presence of quantum computers, classical supercomputers, and increasingly sophisticated artificial intelligence. We introduce Z-Sigil, an asymmetric public-key cryptographic algorithm grounded in functional analysis, differential geometry, and algebraic topology, with the explicit goal of achieving resistance against both classical and […]

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arXiv:2601.10881v1 Announce Type: new Abstract: In the spanning-tree congestion problem ($mathsf{STC}$), we are given a graph $G$, and the objective is to compute a spanning tree of $G$ that minimizes the maximum edge congestion. While $mathsf{STC}$ is known to be $mathbb{NP}$-hard, even for some restricted graph classes, several key questions regarding its computational complexity remain open, and we address some of these in our paper. (i) For graphs of degree at most $d$, it is known that $mathsf{STC}$ […]

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arXiv:2601.10880v1 Announce Type: new Abstract: Promptable segmentation foundation models such as SAM3 have demonstrated strong generalization capabilities through interactive and concept-based prompting. However, their direct applicability to medical image segmentation remains limited by severe domain shifts, the absence of privileged spatial prompts, and the need to reason over complex anatomical and volumetric structures. Here we present Medical SAM3, a foundation model for universal prompt-driven medical image segmentation, obtained by fully fine-tuning SAM3 on large-scale, heterogeneous 2D and 3D […]

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arXiv:2601.10877v1 Announce Type: new Abstract: Open access to publication, software and hardware is central to robotics: it lowers barriers to entry, supports reproducible science and accelerates reliable system development. However, openness also exacerbates the inherent dual-use risks associated with research and innovation in robotics. It lowers barriers for states and non-state actors to develop and deploy robotics systems for military use and harmful purposes. Compared to other fields of engineering where dual-use risks are present – e.g., those […]

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arXiv:2601.10874v1 Announce Type: new Abstract: We study d-way balanced allocation, which assigns each incoming job to the lightest loaded among d randomly chosen servers. While prior work has extensively studied the performance of the basic scheme, there has been less published work on adapting this technique to many aspects of large-scale systems. Based on our experience in building and running planet-scale cloud applications, we extend the understanding of d-way balanced allocation along the following dimensions: (i) Bursts: Events […]

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arXiv:2601.10873v1 Announce Type: new Abstract: Deep neural networks constructed from linear maps and positively homogeneous nonlinearities (e.g., ReLU) possess a fundamental gauge symmetry: the network function is invariant to node-wise diagonal rescalings. However, standard gradient descent is not equivariant to this symmetry, causing optimization trajectories to depend heavily on arbitrary parameterizations. Prior work has proposed rescaling-invariant optimization schemes for positively homogeneous networks (e.g., path-based or path-space updates). Our contribution is complementary: we formulate the invariance requirement at the […]

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arXiv:2601.10869v1 Announce Type: new Abstract: This paper develops a generalized finite horizon recursive solution to the discrete time stage bound disturbance attenuation regulator (StDAR) for state feedback control. This problem addresses linear dynamical systems subject to stage bound disturbances, i.e., disturbance sequences constrained independently at each time step through stagewise squared two-norm bounds. The term generalized indicates that the results accommodate arbitrary initial states. By combining game theory and dynamic programming, this work derives a recursive solution for […]

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arXiv:2601.10868v1 Announce Type: new Abstract: This paper establishes convergence and steady-state properties for the signal bound disturbance attenuation regulator (SiDAR). Building on the finite horizon recursive solution developed in a companion paper, we introduce the steady-state SiDAR and derive its tractable linear matrix inequality (LMI) with $O(n^3)$ complexity. Systems are classified as degenerate or nondegenerate based on steady-state solution properties. For nondegenerate systems, the finite horizon solution converges to the steady-state solution for all states as the horizon […]

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arXiv:2601.10867v1 Announce Type: new Abstract: This paper develops a generalized finite horizon recursive solution to the discrete time signal bound disturbance attenuation regulator (SiDAR) for state feedback control. This problem addresses linear dynamical systems subject to signal bound disturbances, i.e., disturbance sequences whose squared signal two-norm is bounded by a fixed budget. The term generalized indicates that the results accommodate arbitrary initial states. By combining game theory and dynamic programming, we derive a recursive solution for the optimal […]

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