Related papers: The Variant-Rule, Another Logically Universal Rule
This is a study of the one-dimensional elementary cellular automaton rule 54 in the new formalism of "flexible time". We derive algebraic expressions for groups of several cells and their evolution in time. With them we can describe the…
Evolution and learning are two of the fundamental mechanisms by which life adapts in order to survive and to transcend limitations. These biological phenomena inspired successful computational methods such as evolutionary algorithms and…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
In this paper we construct higher-order variational integrators for a class of degenerate systems described by Lagrangians that are linear in velocities. We analyze the geometry underlying such systems and develop the appropriate theory for…
In quantum experiments the acquisition and representation of basic experimental information is governed by the multinomial probability distribution. There exist unique random variables, whose standard deviation becomes asymptotically…
We propose a variational alternative to the Trotter-Suzuki decomposition that provides greater control over errors while preserving the unitary structure of time evolution. The variational parameters in our ansatz are derived from a global…
The model of the homogenous and isotropic universe is considered in which the coordinate system of reference is not defined by the matter but is a priori specified. The scale factor of the universe changes following the linear law. The…
Data taken from observations of the natural world or laboratory measurements often depend on parameters which can vary in unexpected ways. In this paper we demonstrate how machine learning can be leveraged to detect changes in global…
In this paper the variation principles from theoretical physics is considered that would describe the process of routing in computer networks. The total traffic which is currently served on all hops of the route has been chosen as the…
The variational principle for the special and general relativistic hydrodynamics are discussed in view of its application to obtain approximate solutions to these problems. We show that effective Lagrangians can be obtained for suitable…
We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original…
Selfdual variational principles are introduced in order to construct solutions for Hamiltonian and other dynamical systems which satisfy a variety of linear and nonlinear boundary conditions including many of the standard ones. These…
We establish the general conditions under which evolution in the laws of physics and matter creation or destruction are closely intertwined. They make use of global time variables canonically dual to the constants of Nature. Such times flow…
We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…
We generalize the classical Lie results on a basis of differential invariants for a one-parameter group of local transformations to the case of arbitrary number of independent and dependent variables. It is proved that if universal…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
A new derivation of the Bernoulli equation for water waves in three-dimensional rotating and translating coordinate systems is given. An alternative view on the Bateman-Luke variational principle is presented. The variational principle…
Similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth, formation of a network of lakes and rivers, magnetization of type-II superconductors, and…
The paper studies defeasible reasoning in rule-based systems, in particular about legal norms and contracts. We identify rule modifiers that specify how rules interact and how they can be overridden. We then define rule transformations that…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…