Related papers: A linear time algorithm to verify strong structura…
In this paper, we study the statistical difficulty of learning to control linear systems. We focus on two standard benchmarks, the sample complexity of stabilization, and the regret of the online learning of the Linear Quadratic Regulator…
Many algorithms use data structures that maintain properties of matrices undergoing some changes. The applications are wide-ranging and include for example matchings, shortest paths, linear programming, semi-definite programming, convex…
This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…
Mechanized verification of liveness properties for infinite programs with effects and nondeterminism is challenging. Existing temporal reasoning frameworks operate at the level of models such as traces and automata. Reasoning happens at a…
Strong mixing property holds for a broad class of linear and nonlinear time series models such as ARMA and GARCH models. In this article we study correlation structure of strong mixing sequences, and some asymptotic properties are…
For a large class of random matrices $A$ and vectors $b$, we show that linear systems formed from the pair $(A,b)$ are controllable with high probability. Despite the fact that minimal controllability problems are, in general, NP-hard, we…
We present a new algorithm for the statistical model checking of Markov chains with respect to unbounded temporal properties, such as reachability and full linear temporal logic. The main idea is that we monitor each simulation run on the…
This article studies two problems related to observability and efficient constrained sensor placement in linear time-invariant discrete-time systems with partial state observations. (i) We impose the condition that both the set of outputs…
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
This methodology paper addresses high-performance high-productivity programming on spatial architectures. Spatial architectures are efficient for executing dataflow algorithms, yet for high-performance programming, the productivity is low…
Many autonomous systems, such as robots and self-driving cars, involve real-time decision making in complex environments, and require prediction of future outcomes from limited data. Moreover, their decisions are increasingly required to be…
A block graph is a graph in which every block is a complete graph. Let $G$ be a block graph and let $A(G)$ be its (0,1)-adjacency matrix. Graph $G$ is called nonsingular (singular) if $A(G)$ is nonsingular (singular). Characterizing…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
In this paper, the controllability and observability of linear multi-agent systems over matrix-weighted signed networks are analyzed. Firstly, the definition of equitable partition of matrix-weighted signed multi-agent system is given, and…
Recent technological advancements have led to the rapid generation of high-throughput biological data, which can be used to address novel scientific questions in broad areas of research. These data can be thought of as a large matrix with…
Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…
In this article, a new notion of modal strong structural controllability is introduced and examined for a family of LTI networks. These networks include structured LTI subsystems, whose system matrices have the same zero/nonzero/arbitrary…
We propose a new efficient algorithm for detecting if a cycle in a timed automaton can be iterated infinitely often. Existing methods for this problem have a complexity which is exponential in the number of clocks. Our method is polynomial:…