Related papers: The Variant-Rule, Another Logically Universal Rule
The random flights are (continuous time) random walkswith finite velocity. Often, these models describe the stochastic motions arising in biology. In this paper we study the large time asymptotic behavior of random flights. We prove the…
We propose a minimal off-lattice model of living organisms where just a very few dynamical rules of growth are assumed. The stable coexistence of many clusters is detected when we replace the global restriction rule by a locally applied…
There may be structural principles pertaining to the general behavior of systems that lead to similarities in a variety of different contexts. Classic examples include the descriptive power of fractals, the importance of surface area to…
A general organizing principle is proposed that can be used to derive the equations of motion describing the near-equilibrium dynamics of causal and thermodynamically stable relativistic systems. The latter are found to display some new…
In the {\em Many Worlds Interpretation} of quantum mechanics, the range of possible worlds (or histories) provides variation, and the Anthropic Principle is a selective principle analogous to natural selection. When looked on in this way,…
We consider all possible dynamical theories which evolve two transverse vector fields out of a three-dimensional Euclidean hyperplane, subject to only two assumptions: (i) the evolution is local in space, and (ii) the theory is invariant…
Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations - those that can be caused to happen and those that cannot. This is a departure from…
We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the…
Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…
We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…
Based on the doubly special relativity we find a new type of generalized uncertainty principle (GUP) where the coordinate remain unaltered at the high energy while the momentum is deformed at the high energy so that it may be bounded from…
This paper is aimed at a (mostly) pedagogical exposition of the derivation of the motion equations of certain modifications of general relativity. Here we derive in all detail the motion equations in the Brans-Dicke theory with the cubic…
We demonstrate the emergence of scaling laws in the benchmark top versus QCD jet classification problem in collider physics. Six distinct physically-motivated classifiers exhibit power-law scaling of the binary cross-entropy test loss as a…
The dynamics of some non-conservative and dissipative systems can be derived by calculating the first variation of an action-dependent action, according to the variational principle of Herglotz. This is directly analogous to the variational…
This paper evaluates the capabilities of 28 large language models (LLMs) to reason with 20 defeasible reasoning patterns involving generic generalizations (e.g., 'Birds fly', 'Ravens are black') central to non-monotonic logic. Generics are…
We shall show that the abstract and formal rules which govern the quantum kinematic and dynamics can be derived from a law of change of the information content or the degree of uncertainty that the system has a certain configuration in a…
Optimization of unitary transformations in Variational Quantum Algorithms benefits highly from efficient evaluation of cost function gradients with respect to amplitudes of unitary generators. We propose several extensions of the…
We derive the relativistic velocity addition law, the transformations of electromagnetic fields and space-time intervals by examining the drift velocities in a crossed electromagnetic field configuration. The postulate of the light velocity…
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…
In the rotational sandpile model, either the clockwise or the anti-clockwise toppling rule is assigned to all the lattice sites. It has all the features of a stochastic sandpile model but belongs to a different universality class than the…