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This attempt to "derive" space is part of the Random Dynamics project. The Random Dynamics philosophy is that what we observe at our low energy level can be interpreted as some Taylor tail of the physics taking place at a higher energy…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
In this paper, we show that the difficulties of interpretation of the principle of least action concerning "final causes" or "efficient causes" are due to the existence of two different actions, the "Euler-Lagrange action" (or classical…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this…
The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Since a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need…
Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum random walk on the line: the use of multiple…
By and large the process of learning concepts that are embedded in time is regarded as quite a mature research topic. Hidden Markov models, recurrent neural networks are, amongst others, successful approaches to learning from temporal data.…
A ridge function is a function of several variables that is constant along certain directions in its domain. Using classical dimensional analysis, we show that many physical laws are ridge functions; this fact yields insight into the…
In this article, we consider vibrational systems with semi-active damping that are described by a second-order model. In order to minimize the influence of external inputs to the system response, we are optimizing some damping values. As…
The least action principle is exploited as a simulation tool to find the optimal dynamic path for spatially extended systems driven by a small noise. Applications are presented for thermally activated switching of a spatially-extended…
Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given…
This paper proposes a variational approach to describe the evolution of organization of complex systems from first principles, as increased efficiency of physical action. Most simply stated, physical action is the product of the energy and…
Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…
Physics-based reinforcement learning tasks can benefit from simplified physics simulators as they potentially allow near-optimal policies to be learned in simulation. However, such simulators require the latent factors (e.g. mass, friction…
Two well-known conceptual conundrums of quantum mechanics referred to as instantaneous action-at-a-distance and inseparable wave-particle character are tackled using the principle of least action. Since any measurement is an action, it is…