Related papers: On Robustness for the Skolem, Positivity and Ultim…

Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose…

A fundamental challenge in learning to control an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn…

The discreteness problem for finitely generated subgroups of $PSL(2,\mathbb{R})$ and $PSL(2,\mathbb{C})$ is a long-standing open problem. In this paper we consider whether or not this problem is decidable by an algorithm. Our main result is…

This paper reformulates and streamlines the core tools of robust stability and performance for LTI systems using now-standard methods in convex optimization. In particular, robustness analysis can be formulated directly as a primal convex…

Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations, such as the 3D Euler equations, develop infinite gradients from smooth initial…

Direct preference optimization methods have emerged as a computationally efficient alternative to Reinforcement Learning from Human Feedback (RLHF) for aligning Large Language Models (LLMs). Latest approaches have streamlined the alignment…

A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients becomes large. This paper introduces a procedure by which the discrete system obtained…

This work investigates robust monotonic convergent iterative learning control (ILC) for uncertain linear systems in both time and frequency domains, and the ILC algorithm optimizing the convergence speed in terms of $l_{2}$ norm of error…

Let gamma be a (not necessarily finite) structure with a finite relational signature. We prove that deciding whether a given existential positive sentence holds in gamma is in Logspace or complete for the class CSP(gamma)_NP under…

In stochastic control applications, typically only an ideal model (controlled transition kernel) is assumed and the control design is based on the given model, raising the problem of performance loss due to the mismatch between the assumed…

We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…

A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…

We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum…

Self-evolving reasoning frameworks let LLMs improve their reasoning capabilities by iteratively generating and solving problems without external supervision, using verifiable rewards. Ideally, such systems are expected to explore a diverse…

In this paper, we demonstrate that in many NP-complete variants of the stable matching problem, such as the Stable Hypergraph Matching problem, the Stable Multicommodity Flow problem, and the College Admission problem with common quotas, a…

A popular approach for addressing uncertainty in variational inequality problems is by solving the expected residual minimization (ERM) problem. This avenue necessitates distributional information associated with the uncertainty and…

In this paper, given a simple linear recurrence sequence of algebraic numbers, which has either a dominant characteristic root or exactly two characteristic roots of maximal modulus, we give some explicit lower bounds for the index beyond…

Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates…

Early-exiting neural networks enable adaptive inference by allowing inputs to exit at intermediate classifiers, reducing computation for easy samples while maintaining high accuracy. In practice, exits can be trained sequentially by…

We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…