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The spectral theory for operator pencils and operator differential-algebraic equations is studied. Special focus is laid on singular operator pencils and three different concepts of singularity of operator pencils are introduced. The…
This review article is the second part of the project ``Selected Topics of Social Physics". The first part has been devoted to equilibrium systems. The present part considers nonequilibrium systems. The style of the paper combines the…
This is the written version of a series of lectures reviewing the basics of duality as applied to p-forms and sigma-models. The ideas are introduced by way of worked examples, often quite detailed. Our approach is very pedestrian and the…
In this article we study exponential dichotomies for noninvertible linear difference equations in finite dimensions. After giving the definition, we study the extent to which the projection $P(k)$ in a dichotomy is unique. For equations on…
We introduce Deep Linear Discriminant Analysis (DeepLDA) which learns linearly separable latent representations in an end-to-end fashion. Classic LDA extracts features which preserve class separability and is used for dimensionality…
This paper presents new results concerning the observer design for wide classes of nonlinear systems with both sampled and delayed measurements. By using a small gain approach we provide sufficient conditions, which involve both the delay…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
Main purposes of the paper are followings: 1) To show examples of the calculations in domain of QFT via ``derivative rules'' of an expert system; 2) To consider advantages and disadvantage that technology of the calculations; 3) To reflect…
The aim of this paper is to give a new result of the differential Galois theory of linear ordinary differential equations. In particular, we compute differential Galois group for special type non-resonant Fuchsian system.
This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…
Nonlinear parametric systems have been widely used in modeling nonlinear dynamics in science and engineering. Bifurcation analysis of these nonlinear systems on the parameter space are usually used to study the solution structure such as…
This monograph, together with its accompanying first part Cattaneo, Idrobo and Titiunik (2020), collects and expands the instructional materials we prepared for more than $50$ short courses and workshops on Regression Discontinuity (RD)…
Synthetic biology is a recent area of biological engineering, whose aim is to provide cells with novel functionalities. A number of important results regarding the development of control circuits in synthetic biology have been achieved…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The…
The questions of global topological, smooth and holomorphic classifications of the differential systems, defined by covering foliations, are considered. The received results are applied to nonautonomous linear differential systems and…
This thesis is designed to be a self-contained exposition of the neurobiological and mathematical aspects of sensory perception, memory, and learning with a bias towards olfaction. The final chapters introduce a new approach to modeling…
The focus of this thesis is the construction and analysis of efficient representations in nonlinear signal processing, and the applications of these structures to inverse problems in a variety of fields. The work is composed of three major…