Related papers: A Constraint Solving Approach to Tropical Equilibr…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of Ordinary Differential Equations. Alternative approaches based on formal calculi, often derived from process algebras or term…
We present two effective tools for computing the positive tropicalization of algebraic varieties. First, we outline conditions under which the initial ideal can be used to compute the positive tropicalization, offering a real analogue to…
Tropical ideals, introduced in arXiv:1609.03838, define subschemes of tropical toric varieties. We prove that the top-dimensional parts of their varieties are balanced polyhedral complexes of the same dimension as the ideal. This means that…
Inverse problems are ubiquitous in science and engineering. Many of these are naturally formulated as a PDE-constrained optimization problem. These non-linear, large-scale, constrained optimization problems know many challenges, of which…
Perturbation theory alone fails to describe thermodynamics of the electroweak phase transition. We review a technique combining perturbative and non-perturbative methods to overcome this challenge. Accordingly, the principal theme is a…
In the recent years, considerable attention has been paid to preserving structures and invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced system. In the context of Hamiltonian systems,…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Equilibrating proteins and other biomacromolecules is cardinal for molecular dynamics simulation of such biological systems in which they perform free dynamics without any externally-applied mechanical constraint, until thermodynamic…
An arrangement of finitely many tropical hyperplanes in the tropical torus leads to a notion of `type' data for points, with the underlying unlabeled arrangement giving rise to `coarse type'. It is shown that the decomposition of the…
This paper presents a nonlinear model predictive control strategy for stochastic systems with general (state and input dependent) disturbances subject to chance constraints. Our approach uses an online computed stochastic tube to ensure…
In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic…
This work presents a new sufficient condition for synthesizing nonlinear controllers that yield bounded closed-loop tracking error transients despite the presence of unmatched uncertainties that are concurrently being learned online. The…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
The aim of this paper is twofold: first, to extend the area of applications of tropical optimization by solving new constrained location problems, and second, to offer new closed-form solutions to general problems that are of interest to…
In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…
Linear mixed-effects models are a central analytical tool for modeling hierarchical and longitudinal data, as they allow simultaneous representation of fixed and random sources of variation. In practice, inference for such models is most…