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``Weak'', ``protective'', and ``delayed observation'' measurements are analyzed in the framework of the Bohm interpretation of quantum theory. It is argued that the above varieties of measurements manifest some difficulties of the Bohm…
We analyse biased ensembles of trajectories for diffusive systems. In trajectories biased either by the total activity or the total current, we use fluctuating hydrodynamics to show that these systems exhibit phase transtions into…
The problem of belief tracking in the presence of stochastic actions and observations is pervasive and yet computationally intractable. In this work we show however that probabilistic beliefs can be maintained in factored form exactly and…
This work addresses the problem of predicting the motion trajectories of dynamic objects in the environment. Recent advances in predicting motion patterns often rely on machine learning techniques to extrapolate motion patterns from…
The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
Pilot wave theory endows particles with definite positions at all times governed by deterministic dynamics. However, individual particle trajectories are generically undetectable by experiment. This idea might seem to be contested in light…
This paper studies conditions for invariance of dynamical systems on stratified do- mains as originally introduced by Bressan and Hong. We establish Hamiltonian conditions for both weak and strong invariance of trajectories on systems with…
From "surreal" trajectories to which-way measurements, Basil Hiley had a lesson: claims of falsifying the Bohmian model do not withstand scrutiny provided the model is applied correctly. In this work we compute de Broglie-Bohm trajectories…
We derive continuity equation and exact expression for flow probability density in a space with arbitrary deformed algebra leading to minimal length. In coordinate representation the flow probability density is presented as infinite series…
Bohmian mechanics, also referred to as the de Broglie-Bohm pilot-wave theory, represents a deterministic and nonlocal interpretation of quantum mechanics. Since its origination in 1927, despite many attempts, reconciling it with…
Oscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian within classically narrow energy ranges have been shown to depend on closed compound orbits. These are formed by a pair of orbit…
A logconcave likelihood is as important to proper statistical inference as a convex cost function is important to variational optimization. Quantization is often disregarded when writing likelihood models, ignoring the limitations of the…
Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem. Existing approaches retrain the model with auxiliary variance heads, maintain costly ensembles, or…
Usually tunneling is established after imposing some matching conditions on the (time-independent) wave function and its first derivative at the boundaries of a barrier. Here an alternative scheme is proposed to determine tunneling and…
It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes…
Topological properties of physical systems play a crucial role in our understanding of nature, yet their experimental determination remains elusive. We show that the mean helicity, a dynamical invariant in ideal flows, quantitatively…
Although intensively studied in recent years, the optimization of the transient (time-dependent) control of large real-world gas networks is still out of reach for current state-of-the-art approaches. For this reason, we present further…
The Boris algorithm for integrating charged particle trajectories in electric and magnetic fields is popular due to its simple implementation, rapid iteration, and observed long-term numerical fidelity. The underlying cause of this…
Complex trajectories for Hamiltonians of the form H=p^n+V(x) are studied. For n=2 time-reversal symmetry prevents trajectories from crossing. However, for n>2 trajectories may indeed cross, and as a result, the complex trajectories for such…