Related papers: Time Reparametrization and Chaotic Dynamics in Con…

We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…

We give a simple characterization of chaos for weighted composition $C_0$-semigroups on $L^p_\rho(\Omega)$ for an open interval $\Omega\subseteq\mathbb{R}$. Moreover, we characterize chaos for these classes of $C_0$-semigroups on the closed…

The Thermal Time Hypotheis (TTH) has been proposed as a general method for identifying a time variable from within background-free theories which do not come equipped with a pre-defined clock variable. Here, we explore some implications of…

Constructal Law states that a finite-size flow system that persists in time evolves its configuration so as to provide progressively easier access to the currents that flow through it. Classical Constructal theory derives hierarchical flow…

We consider the class of conditional graph patterns (\emph{CGPs}) that allow user to query data graphs with complex patterns that contain negation and predicates. To overcome the prohibitive cost of subgraph isomorphism, we consider…

When we are interested in the long-term behaviour of solutions to linear evolution equations, a large variety of techniques from the theory of $C_0$-semigroups is at our disposal. However, if we consider for instance parabolic equations…

Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. While existing approaches analyze these phenomena in…

We investigate the temporal dynamics of the PT-Symmetric nonlinear oscillators in the presence of Duffing nonlinearity for two forms of oscillator configuration. In the former, we consider two oscillator coupled to each other. One…

We study geometry of two-dimensional models of conformal space-time based on the group of Moebius transformation. The natural geometric invariants, called cycles, are used to linearise Moebius action. Conformal completion of the space-time…

The process of identifying a time variable in time reparameterization invariant theories results in great ambiguities about the actual laws of physics described by a given theory. A theory set up to describe one set of physical laws can…

Collapse models possibly suggest the need for a better understanding of the structure of space-time. We argue that physical space, and space-time, are emergent features of the Universe, which arise as a result of dynamical collapse of the…

Here we present an strategy for the derivation of a time-dependent Dyson map which ensures simultaneously the unitarity of the time evolution and the observability of a quasi-Hermitian Hamiltonian. The time-dependent Dyson map is derived…

A new class of conformal field theories is presented, where the background gravitational field is conformally flat. Conformally flat (CF) spacetimes enjoy conformal properties quite similar to the ones of flat spacetime. The conformal…

This paper presents a more complete version than hitherto published of our explanation of a transition from regular to irregular motions and more generally of the nature of a certain kind of deterministic chaos. To this end we introduced a…

A world-volume model of non-critical 3-brane is quantized in a strong coupling phase where fluctuations of the conformal mode become dominant. This phase, called the conformal-mode dominant phase, is realized at the very high energy far…

Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an {\it arrow of time} that follows from the fact that…

The conception of the conformal phase transiton (CPT), which is relevant for the description of non-perturbative dynamics in gauge theories, is introduced and elaborated. The main features of such a phase transition are established. In…

Conformal prediction is a distribution-free and model-agnostic uncertainty-quantification method that provides finite-sample prediction intervals with guaranteed coverage. In this work, for the first time, we apply conformal-prediction to…

Consider the following class of conformable time-fractional stochastic equation $$T_{\alpha,t}^a u(x,t)=\lambda\sigma(u(x,t))\dot{W}_t,\,\,\,\,x\in\mathbb{R},\,t\in[a,\infty), \,\,0<\alpha<1,$$ with a non-random initial condition…

Discrete time crystals (DTCs) are new phases of matter characterized by the presence of an observable evolving with $nT$ periodicity under a $T$-periodic Hamiltonian, where $n>1$ is an integer insensitive to small parameter variations. In…