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Treating the two-dimensional Minkowski space as a Wick rotated version of the complex plane, we characterize the causal automorphisms in two-dimensional Minkowski space as the M\"{a}rzke-Wheeler maps of a certain class of observers. We also…
We argue that purely local experiments can distinguish a stationary charged particle in a static gravitational field from an accelerated particle in (gravity-free) Minkowski space. Some common arguments to the contrary are analyzed and…
We investigate the kinematics of the motion of an observer with constant proper acceleration (relativistic hyperbolic motion) in 1+1 and 1+3 dimensional Minkowski spacetimes. We provide explicit formulas for all the kinematic quantities up…
A generalization of the standard model of Dirac particle in external electromagnetic field is proposed. In the generalization we take into account interactions of this particle with environment, which is described by the memory function.…
Non-Markovian processes may arise in physics due to memory effects of environmental degrees of freedom. For quantum non-Markovianity, it is an ongoing debate to clarify whether such memory effects have a verifiable quantum origin, or…
In Minkowski space, an accelerated reference frame may be defined as one that is related to an inertial frame by a sequence of instantaneous Lorentz transformations. Such an accelerated observer sees a causal horizon, and the quantum vacuum…
The nonlocal theory of accelerated systems is extended to the propagation of Dirac particles. The implications of nonlocality for the phenomenon of spin-rotation coupling are discussed. The Lorentz-invariant nonlocal Dirac equation is…
Moving average models, linear or nonlinear, are characterized by their short memory. This paper shows that, in the presence of feedback in the dynamics, the above characteristic can disappear.
Experiments often probe observables that correspond to low-dimensional projections of highdimensional dynamics. In such situations distinct microscopic configurations become lumped into the same observable state. It is well known that…
In nonlocal general relativity, linearized gravitational waves are damped as they propagate from the source to the receiver in the Minkowski vacuum. Nonlocal gravity is a generalization of Einstein's theory of gravitation in which…
Collective motion in active matter is usually modelled through instantaneous local alignment, where each agent updates its heading from the current configuration of its neighbours. Many biological and engineered agents, however, possess…
Multi-modality is an important feature of sensor based activity recognition. In this work, we consider two inherent characteristics of human activities, the spatially-temporally varying salience of features and the relations between…
Memory effects play a fundamental role in the study of the dynamics of open quantum systems. There exist two conceptually distinct notions of memory discussed for quantum channels in the literature. In quantum information theory quantum…
It is proved by means of the dynamical effects of special relativity that velocity caused by accelerating process is not a relative concept. The influence of accelerating process should be considered in space-time theory. Besides the…
The characterisation of information processing is an important task in complex systems science. Information dynamics is a quantitative methodology for modelling the intrinsic information processing conducted by a process represented as a…
In medical imaging, technical progress or changes in diagnostic procedures lead to a continuous change in image appearance. Scanner manufacturer, reconstruction kernel, dose, other protocol specific settings or administering of contrast…
In model-based reinforcement learning, generative and temporal models of environments can be leveraged to boost agent performance, either by tuning the agent's representations during training or via use as part of an explicit planning…
The relativistic jerk, snap and all higher-order kinematical D-vectors are defined for the motion of a massive particle in a D-dimensional Minkowski spacetime. We illustrate the formalism with stationary motions, for which we provide a new,…
Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…
We study the role of acceleration in the twin paradox. From the coordinate transformation that relates an accelerated and an inertial observer we find that, from the point of view of the accelerated observer, the rate of the differential…