Related papers: Generalized Potential and Mathematical Principles …
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
Generative adversarial networks (GANs) are so complex that the existing learning theories do not provide a satisfactory explanation for why GANs have great success in practice. The same situation also remains largely open for deep neural…
In order to apply thermodynamics to systems in which entropy is not extensive, it has become customary to define generalized entropies. While this approach has been effective, it is not the only possible approach. We suggest that some…
The great innovation of the Generalized Theorem is that it gives us the philosophy to work out the knowledge that the number of roots of an equation depends on the subfields of the functional terms of the equation they generate. Thus, the…
In 1929 Heisenberg and Pauli laid the foundations of QFT by quantizing the fields (method of canonical quantization). This general theory of quantized fields has remained undisputed up to now. We show how the unmodified Heisenberg-Pauli…
Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…
Generalized uncertainty principles are effective changes to the Heisenberg uncertainty principle that emerge in several quantum gravity models. In the present letter, we study the consequences that two classes of these modifications yield…
Nonlinear field theories produce unstable but long-lived configurations known as oscillons. These structures have been studied with asymmetric and symmetric double-well potentials and extended to other forms of potentials. In the present…
We construct and investigate quantum fields induced on a d-dimensional dissipationless defect by bulk fields propagating in a (d+1)-dimensional space. All interactions are localized on the defect. We derive a unitary non-canonical quantum…
A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…
The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under…
This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…
A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very…
Following the seminal work of Zames, the input-output theory of the 70s acknowledged that incremental properties (e.g. incremental gain) are the relevant quantities to study in nonlinear feedback system analysis. Yet, non-incremental…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
Clapeyron's Theorem in classical linear elasticity provides a way to explicitly express the energy stored in an equilibrium configuration in terms of the work of the forces applied on the boundary. We derive several new integral relations…
The invariant distribution, which is characterized by the stationary Fokker-Planck equation, is an important object in the study of randomly perturbed dynamical systems. Traditional numerical methods for computing the invariant distribution…
Rich out of equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular or colloidal systems,…
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…