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In this paper, we introduce an extension of rectangular metric spaces called controlled rectangular metric spaces, by changing the rectangular inequality as follows: \begin{equation*} d(x, y)\leq\alpha(x, u)d(x, u)+\alpha(u, v)d(u,…
We study an intermittent map which has exactly two ergodic invariant densities. The densities are supported on two subintervals with a common boundary point. Due to certain perturbations, leakage of mass through subsets, called holes, of…
We expand the time reversal symmetry arguments of quantum mechanics, originally proposed by Wigner in the context of unitary dynamics, to contain situations including generalized measurements for monitored quantum systems. We propose a…
We prove existence of (at most denumerable many) absolutely continuous invariant probability measures for random one-dimensional dynamical systems with asymptotic expansion. If the rate of expansion (Lyapunov exponents) is bounded away from…
The long-time existence and umbilicity estimates for compact, graphical solutions to expanding curvature flows are deduced in Riemannian warped products of a real interval with a compact fibre. Notably we do not assume the ambient manifold…
We propose a novel chaos indicator -- time-reversed Shannon entropy (TRSE) -- that leverages the interplay between time-reversal symmetry breaking and information entropy in curved spacetimes. By quantifying statistical discrepancies…
After a discussion on the state of local equilibrium with temperature inhomogeneity, comparing mixture state reprsentation in statistical mechanics and pure state representation in thermo field dynamics, a simple model is solved to show…
We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider…
A simple model of an irreversible process is introduced. The equation of iterations in the model includes a noise generation term. We study the properties of the system when the noise generation term is a stochastic process (e.g. a random…
Motivated by entropic optimal transport, time reversal of diffusion processes is revisited. An integration by parts formula is derived for the carr\'e du champ of a Markov process in an abstract space. It leads to a time reversal formula…
The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a new set of statistical tests for time series irreversibility based on standard and horizontal visibility graphs. Specifically,…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
We introduce a general framework for testing temporal symmetries in time series based on the distribution of ordinal patterns. While previous approaches have focused on specific forms of asymmetry, such as time reversal, our method provides…
We investigate ergodic properties of a one-dimensional intermittent map that has not only an indifferent fixed point but also a singular structure such that a uniform measure is invariant under mapping. The most striking aspect of our model…
We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…
A relevant problem in dynamics is to characterize how deterministic systems may exhibit features typically associated to stochastic processes. A widely studied example is the study of (normal or anomalous) transport properties for…
For piecewise $C^1$ interval maps possibly containing critical points and discontinuities with negative Schwarzian derivative, under two summability conditions on the growth of the derivative and recurrence along critical orbits, we prove…
From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to itself. Interesting dynamics arise on the invariant diagonal,…
We show that the Wheeler-DeWitt equation with a consistent boundary condition is only compatible with an arrow of time that formally reverses in a recollapsing universe. Consistency of these opposite arrows is facilitated by quantum effects…
In measurement design, it is common to engineer anti-contrast readouts -- two measurements that respond as differently as possible to the same inputs so that contributions that affect both readouts in the same way are suppressed. To assess…