Related papers: Generalized Potential and Mathematical Principles …
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed…
Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…
With a scalar potential and a bivector potential, the vector field associated with the drift of a diffusion is decomposed into a generalized gradient field, a field perpendicular to the gradient, and a divergence-free field. We give such…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
A theory of dissipative generalized continuum mechanics is presented in the framework of weakly nonlocal non-equilibrium thermodynamics. The evolution equation of microdeformation is obtained by thermodynamic principles. Conditions of…
Quantum resource theory is perhaps the most revolutionary framework that quantum physics has ever experienced. It plays vigorous roles in unifying the quantification methods of a requisite quantum effect as wells as in identifying protocols…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
Recent studies of in vitro evolution of DNA via protein binding indicate that the evolution behavior is qualitatively different in different parameter regimes. I here present a general theory that is valid for a wide range of parameters,…
In this paper, we advance the network theory of aging and mortality by developing a causal mathematical model for the mortality rate. First, we show that in large networks, where health deficits accumulate at nodes representing health…
In the framework of the field theory it is shown that a time (viewed as a scalar temporal field) is an internal property of the physical system, which defines its causal structure and evolution. A new concept of internal time allows to…
We argue that the success of DFT can be understood in terms of a semiclassical expansion around a very specific limit. This limit was identified long ago by Lieb and Simon for the total electronic energy of a system. This is a universal…
The role of acceleration in particle physics can provide an alternative method for probing the properties of quantum gravity. To analyze acceleration-induced processes one utilizes the formalism of quantum field theory in curved spacetime.…
A generalization of Gy's theory for the variance of the fundamental sampling error is reviewed. Practical situations where the generalized model potentially leads to more accurate variance estimates are identified as: clustering of…
A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear…
We consider a general class of non-linear Bellman equations. These open up a design space of algorithms that have interesting properties, which has two potential advantages. First, we can perhaps better model natural phenomena. For…
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…
This paper describes perturbative framework, on the basis of closed-time-path formalism, for studying quasiuniform relativistic quantum field systems near equilibrium and nonequilibrium quasistationary systems. At the first part, starting…
The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $D$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the…