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The "theory of open sub-functorial dynamics" is a new theory that defines interacting generalized dynamical systems. The interactions between these dynamics produce new dynamics which, of course, can then enter into other interactions. A…

A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to…

Classical machine learning approaches are sensitive to non-stationarity. Transfer learning can address non-stationarity by sharing knowledge from one system to another, however, in areas like machine prognostics and defense, data is…

We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of…

Consistent Recalibration models (CRC) have been introduced to capture in necessary generality the dynamic features of term structures of derivatives' prices. Several approaches have been suggested to tackle this problem, but all of them,…

In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…

Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…

The description of an open quantum system's decay almost always requires several approximations as to remain tractable. Here, we first revisit the meaning, domain and seeming contradictions of a few of the most widely used of such…

Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However,…

Structure-preserving approaches to dynamics discovery have demonstrated great potential for modeling physical systems due to their use of strong inductive biases, which enforce key features such as conservation laws and dissipative…

The concept of sequential choice functions is introduced and studied. This concept applies to the reduction of the problem of stable matchings with sequential workers to a situation where the workers are linear.

This note presents an extension to the neural artistic style transfer algorithm (Gatys et al.). The original algorithm transforms an image to have the style of another given image. For example, a photograph can be transformed to have the…

The conformable derivative has been promoted in numerous publications as a new fractional derivative operator. This article provides a critical reassessment of this claim. We demonstrate that the conformable derivative is not a fractional…

Projects are finite terminating endeavors with distinctive outcomes, usually, occurring under transient conditions. Nevertheless, most estimation, planning, and scheduling approaches overlook the dynamics of project-based systems in…

Learning behavioral patterns from observational data has been a de-facto approach to motion forecasting. Yet, the current paradigm suffers from two shortcomings: brittle under distribution shifts and inefficient for knowledge transfer. In…

The present article is devoted to one class of generalizations of the Salem functions. To construct such functions by systems of functional equations, the generalized shift operator is used.

A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…

A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…

A clear definition of system dynamics modeling can provide shared understanding and clarify the impact of the field. We introduce a set of characteristics that define quantitative system dynamics, selected to capture core philosophy,…

Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…