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The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex basic non-commutative semi-algebraic set. The main theorem of this paper is a converse, a result which has implications for both semidefinite programming and…
In a recent paper Avis, Bremner, Tiwary and Watanabe gave a method for constructing linear programs (LPs) based on algorithms written in a simple programming language called Sparks. If an algorithm produces the solution $x$ to a problem in…
Mixed observable Markov decision processes (MOMDPs) are a modeling framework for autonomous systems described by both fully and partially observable states. In this work, we study the problem of synthesizing a control policy for MOMDPs that…
Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging…
In this paper, we provide an elementary, geometric, and unified framework to analyze conic programs that we call the strict complementarity approach. This framework allows us to establish error bounds and quantify the sensitivity of the…
Multi-core machines are ubiquitous. However, most inductive logic programming (ILP) approaches use only a single core, which severely limits their scalability. To address this limitation, we introduce parallel techniques based on…
Molecular computing promises massive parallelization to explore solution spaces, but so far practical implementations remain limited due to off-target binding and exponential proliferation of competing structures. Here, we investigate the…
Suppose we are given an $n$-dimensional order-3 symmetric tensor $T \in (\mathbb{R}^n)^{\otimes 3}$ that is the sum of $r$ random rank-1 terms. The problem of recovering the rank-1 components is possible in principle when $r \lesssim n^2$…
While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of…
A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under…
We study how much a linear program (LP) can be compressed when solved repeatedly, given prior knowledge about its objective function. Existing data-driven projection methods learn low-dimensional surrogate LPs with approximate…
The rapid growth of high-resolution scientific simulations and observation systems is generating massive spatiotemporal datasets, making efficient, error-bounded compression increasingly important. Meanwhile, decoder-only large language…
We study the Convex Set Disjointness (CSD) problem, where two players have input sets taken from an arbitrary fixed domain~$U\subseteq \mathbb{R}^d$ of size $\lvert U\rvert = n$. Their mutual goal is to decide using minimum communication…
Recent work has led to the development of an elegant theory of Linearly Solvable Markov Decision Processes (LMDPs) and related Path-Integral Control Problems. Traditionally, MDPs have been formulated using stochastic policies and a control…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…
The Survivable Network Design problem (SNDP) is a well-studied problem, motivated by the design of networks that are robust to faults under the assumption that any subset of edges up to a specific number can fail. We consider non-uniform…
In this paper we consider generalization of procedure of construction of potential systems for systems of partial differential equations with multidimensional spaces of conservation laws. More precisely, for construction of potential…
Differential positivity and K-cooperativity, a special case of differential positivity, extend differential approaches to control to nonlinear systems with multiple equilibria, such as switches or multi-agent consensus. To apply this…
Lazy search algorithms have been developed to efficiently solve planning problems in domains where the computational effort is dominated by the cost of edge evaluation. The existing algorithms operate by intelligently balancing…
The share-of-choice product design (SOCPD) problem is to find the product, as defined by its attributes, that maximizes market share arising from a collection of customer types or segments. When customers follow a logit model of choice, the…