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We explore nonlocally modified models of gravity, inspired by quantum loop corrections, as a mechanism for explaining current cosmic acceleration. These theories enjoy two major advantages: they allow a delayed response to cosmic events,…
There are analyzed two classical systems defined on twist-deformed acceleration-enlarged Newton-Hooke space-times - nonrelativistic particle moving in constant field force $\vec{F}$ and harmonic oscillator model. It is demonstrated that…
{This paper is a comparison of the Minkowski, Einstein and Einstein dual theories of relativity. The dual is based on an identity relating the observer time and the proper time as a contact transformation on configuration space, which…
Online action recognition is an important task for human centered intelligent services, which is still difficult to achieve due to the varieties and uncertainties of spatial and temporal scales of human actions. In this paper, we propose…
A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with…
We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied…
We introduce a sensitive test of memory effects in successive events. The test consists of a combination K of binary correlations at successive times. K decays monotonically from K = 1 for uncorrelated events as a Markov process; whereas…
Human movement has been studied for decades and dynamic laws of motion that are common to all humans have been derived. Yet, every individual moves differently from everyone else (faster/slower, harder/smoother etc). We propose here an…
We investigate associative-memory behavior in a reconfigurable particle packing programmed by purely local cyclic driving. The system is a two-dimensional bidisperse Lennard--Jones particle assembly with periodic boundaries evolved under…
We investigate the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to their separation. The two-atom system is treated as an open system coupled with fluctuating electromagnetic fields in…
The concept of rigid reference frame and of constricted spatial metric, given in the previous work [\emph{Class. Quantum Grav.} {\bf 21}, 3067,(2004)] are here applied to some specific space-times: In particular, the rigid rotating disc…
The properties of the equation of Dirac type in three-dimensional and five-dimensional Minkowski space-time with respect to time reflection (in sense of Pauli and Wigner) as well as to the operation of charge conjugation are investigated.…
We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator…
1. Spatial memory plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in…
We study a simple nonlocal-in-time dynamic system proposed for the effective modeling of complex diffusive regimes in heterogeneous media. We present its solutions and their commonly studied statistics such as the mean square distance. This…
We present a phase-based formulation of special relativity in which the kinematical structure of the theory is reconstructed from the requirement of phase coherence of localized wave states. Starting from the assumption that physical…
It was previously shown that models with deformations of special relativity that have an energy-dependent yet observer-independent speed of light suffer from nonlocal effects that are in conflict with observation to very high precision. In…
Doubly special relativity has been studied for the last twenty years as a way to go beyond the special relativistic kinematics, trying to capture residual effects of a quantum gravity theory. In particular, in doubly special relativity the…
We report the experimental observation of memory effects in a vertically vibrated thin granular layer. Following a quench in the input acceleration, the granular temperature exhibits an anomalous Kovacs memory effect confined to the initial…
We study the implications of time-varying wave mechanics, and show how the standard wave equation is modified if the speed of a wave is not constant in time. In particular, waves which experience longitudinal acceleration are shown to have…