Related papers: On the serial connection of the regular asynchrono…
We present the notion of asymptotically non-terminating initial variable values for linear loop programs. Those values are directly associated to initial variable values for which the corresponding program does not terminate. Our…
Synchronization of network-coupled dynamical units is important to a variety of natural and engineered processes including circadian rhythms, cardiac function, neural processing, and power grids. Despite this ubiquity, it remains poorly…
Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…
An RGD system $\mathcal{D}$ is called \emph{linear w.r.t. a root basis $\mathcal{B}$} if the commutation relations between the root groups of $\mathcal{D}$ are `linear' in a certain sense. Moreover, $\mathcal{D}$ is called…
Taking an interaction network oriented perspective in informatics raises the challenge to describe deterministic finite systems which take part in networks of nondeterministic interactions. The traditional approach to describe processes as…
Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Most generally, dynamic functional connectivity (FC) refers to the non-instantaneous couplings across timeseries from a set of brain areas, here as measured by fMRI. This is in contrast to static FC, which is defined as purely instantaneous…
We define and analyze the operations of addition and intersection of linear time-invariant systems in the behavioral setting, where systems are viewed as sets of trajectories rather than input-output maps. The classical definition of…
The Theory of Functional Connections (TFC) is a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The functionals derived from this method, called \emph{constrained expressions},…
Network systems and their control are highly important and appear in a variety of applications, including vehicle platooning and formation con- trol. Especially vehicle platoons are highly investigated and an interesting problem that arises…
Measures generated by Iterated Function Systems composed of uncountably many one--dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or…
Binary machines are a generalization of Feedback Shift Registers (FSRs) in which both, feedback and feedforward, connections are allowed and no chain connection between the register stages is required. In this paper, we present an algorithm…
Given a synchronous system, we study the question whether the behaviour of that system can be exhibited by a (non-trivially) distributed and hence asynchronous implementation. In this paper we show, by counterexample, that synchronous…
Synchronization is essential for the operation of AC power systems: All generators in the power grid must rotate with fixed relative phases to enable a steady flow of electric power. Understanding the conditions for and the limitations of…
Motivated by the successful application of the theory of regular languages to formal verification of finite-state systems, there is a renewed interest in developing a theory of analyzable functions from strings to numerical values that can…
In the setting of nonstandard analysis we introduce the notion of flexible sequence. The terms of flexible sequences are external numbers. These are a sort of analogue for the classical \emph{O$ (\cdot ) $} and \emph{o$ (\cdot ) $} notation…
Linearising the dynamics of nonlinear mechanical systems is an important and open research area. A common approach is feedback linearisation, which is a nonlinear control method that transforms the input-output response of a nonlinear…
This paper shows that the concept of complex frequency, originally introduced to characterize the dynamics of signals with complex values, constitutes a generalization of eigenvalues when applied to the states of linear time-invariant (LTI)…
A syntactic model is presented for the specification of finite-state synchronous digital logic systems with complex input/output interfaces, which control the flow of data between opaque computational elements, and for the composition of…