Related papers: Algebraic Tools for the Analysis of State Space Mo…
State-space models are dynamical systems defined by a latent and an observed process. In ecology, stochastic state-space models in discrete time are most often used to describe the imperfectly observed dynamics of population sizes or animal…
In this work, we present a multiscale approach for the reliable coarse-scale approximation of spatial network models represented by a linear system of equations with respect to the nodes of a graph. The method is based on the ideas of the…
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…
In control theory, researchers need to understand a system's local and global behaviors in relation to its initial conditions. When discussing observability, the main focus is on the ability to analyze the system using an output space…
We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools. The project includes formal…
We consider structural equation models (SEMs), in which every variable is a function of a subset of the other variables and a stochastic error. Each such SEM is naturally associated with a directed graph describing the relationships between…
We establish conditions under which latent causal graphs are nonparametrically identifiable and can be reconstructed from unknown interventions in the latent space. Our primary focus is the identification of the latent structure in…
Features of the Jacobian matrix of the delay coordinates map are exploited for quantifying the robustness and reliability of state and parameter estimations for a given dynamical model using an observed time series. Relevant concepts of…
This article concerns the predictive modeling for spatio-temporal data as well as model interpretation using data information in space and time. We develop a novel approach based on supervised dimension reduction for such data in order to…
Binary classification is widely used in ML production systems. Monitoring classifiers in a constrained event space is well known. However, real world production systems often lack the ground truth these methods require. Privacy concerns may…
The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…
For associative algebras in many different categories, it is possible to develop the machinery of Gr\"obner bases. A Gr\"obner basis of defining relations for an algebra of such a category provides a "monomial replacement" of this algebra.…
Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We provide algorithmically verifiable necessary and sufficient conditions for fundamental system theoretic properties of discrete time linear systems subject to data losses. More precisely, the systems in our modeling framework are subject…
An adaptive state observer is proposed for a class of overparametrized uncertain linear time-invariant systems without restrictive requirement of their representation in the observer canonical form. It evolves the method of generalized…
This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We summarize recent progress on the theory and applications of structural identifiability of compartmental models. On the applications side, we review identifiability analyses undertaken recently for models arising in epidemiology,…
In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the…