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Let $\Theta$ be a finite alphabet. We consider a bundle of measure preserving transformations $(T_{\theta})_{\theta \in \Theta}$ acting on a probability space $(X,\mu)$, which are chosen randomly according to an ergodic stochastic process…
Modern machine learning algorithms, especially deep learning based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear…
The workflow satisfiability problem is concerned with determining whether it is possible to find an allocation of authorized users to the steps in a workflow in such a way that all constraints are satisfied. The problem is NP-hard in…
Reconfigurable multi-robot cells offer a promising approach to meet fluctuating assembly demands. However, the recurrent planning of their configurations introduces new challenges, particularly in generating optimized, coordinated…
In this manuscript, we introduce a family of parametrized non-homogeneous linear complex differential equations on $[1,\infty)$, depending on a complex parameter. We identify a "Rotation number hypothesis" on the non-homogeneous term, which…
We study the topology of a random cubical complex associated to Bernoulli site percolation on a cubical grid. We begin by establishing a limit law for homotopy types. More precisely, looking within an expanding window, we define a sequence…
This chapter compiles a number of results that apply the theory of parameterized algorithmics to the running-time analysis of randomized search heuristics such as evolutionary algorithms. The parameterized approach articulates the running…
A venerable problem in combinatorics and geometry asks whether a given incidence relation may be realized by a configuration of points and lines. The classic version of this would ask for algebraic lines over some field or possibly real…
We study Farber's topological complexity for monotone symplectic manifolds. More precisely, we estimate the topological complexity of 4-dimensional spherically monotone manifolds whose Kodaira dimension is not $-\infty$.
In the present work, a new computational framework for structural topology optimization based on the concept of moving deformable components is proposed. Compared with the traditional pixel or node point-based solution framework, the…
We study the parameterized complexity of a generalization of the coordinated motion planning problem on graphs, where the goal is to route a specified subset of a given set of $k$ robots to their destinations with the aim of minimizing the…
We study the synthesis problem for distributed architectures with a parametric number of finite-state components. Parameterized specifications arise naturally in a synthesis setting, but thus far it was unclear how to detect realizability…
This paper explores topological complexity in the finite equivariant setting. We first define and study an equivariant version of Tanaka's combinatorial complexity for finite topological spaces. We explore the relationships between this…
We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…
A crucial challenge arising in the design of large-scale logistical networks is to optimize parcel sortation for routing. We study this problem under the recent graph-theoretic formalization of Van Dyk, Klause, Koenemann and Megow (IPCO…
We investigate the parameterized computational complexity of the satisfiability problem for modal logic and attempt to pinpoint relevant structural parameters which cause the problem's combinatorial explosion, beyond the number of…
A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter…
The unordered configuration space of $n$ points on a graph $\Gamma,$ denoted here by $UC^n(\Gamma),$ can be viewed as the space of all configurations of $n$ unlabeled robots on a system of one-dimensional tracks, which is interpreted as a…