Related papers: A Real-Analytic Approach to Differential-Algebraic…
Almost all problems in applied mathematics, including the analysis of dynamical systems, deal with spaces of real-valued functions on Euclidean domains in their formulation and solution. In this paper, we describe the the tool Ariadne,…
Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a…
Trace slicing is a widely used technique for execution trace analysis that is effectively used in program debugging, analysis and comprehension. In this paper, we present a backward trace slicing technique that can be used for the analysis…
We give a proposal to generalize the concept of the differential equations on time scales, such that they can be more appropriate for the analysis of real world problems, and give more opportunities to increase the theoretical depth of…
A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in…
The complexity of modern software systems entails the need for reconfiguration mechanisms gov- erning the dynamic evolution of their execution configurations in response to both external stimulus or internal performance measures. Formally,…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean…
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
Ensuring the safe and reliable operation of integrated electricity and gas systems (IEGS) requires dynamic energy flow (DEF) simulation tools that achieve high accuracy and computational efficiency. However, the inherent strong nonlinearity…
The partitioned approach for the numerical integration of power system differential algebraic equations faces inherent numerical stability challenges due to delays between the computation of state and algebraic variables. Such delays can…
Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of…
In probabilistic reasoning, the traditionally discrete domain has been elevated to the hybrid domain encompassing additionally continuous random variables. Inference in the hybrid domain, however, usually necessitates to condone trade-offs…
The purpose of this article is to construct a toolbox, in Dynamical Systems, to support the idea that ``whenever we can prove a limit theorem in the classical sense for a dynamical system, we can prove a suitable almost-sure version based…
We propose the concept of adaptable processes as a way of overcoming the limitations that process calculi have for describing patterns of dynamic process evolution. Such patterns rely on direct ways of controlling the behavior and location…
Differential graded (DG) commutative algebra provides powerful techniques for proving theorems about modules over commutative rings. These notes are a somewhat colloquial introduction to these techniques. In order to provide some motivation…
Some approaches to solving challenging dynamic programming problems, such as Q-learning, begin by transforming the Bellman equation into an alternative functional equation, in order to open up a new line of attack. Our paper studies this…
Electrical circuits are present in a variety of technologies, making their design an important part of computer aided engineering. The growing number of parameters that affect the final design leads to a need for new approaches to quantify…
We offer a lattice-theoretic account of dynamic slicing for {\pi}-calculus, building on prior work in the sequential setting. For any run of a concurrent program, we exhibit a Galois connection relating forward slices of the start…