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Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…
Although quintessence cosmologies seem to explain the amount of cosmological constant today, the required conditions are severe. For example, an extremely slowly varying and light scalar field that rolls toward the vanishing vacuum energy…
Motivated by the fact that information is encoded and processed by physical systems, the P versus NP problem is examined in terms of physical processes. In particular, we consider P as a class of deterministic, and NP as nondeterministic,…
One of the most stimulating recent ideas in particle physics involves a possibility that our universe has additional compactified spatial dimensions, perhaps as large as 1 mm. In this review, we discuss the results of recent experimental…
Many water-based optimization metaheuristics have been introduced during the last decade, both for combinatorial and for continuous optimization. Despite the strong similarities of these methods in terms of their underlying natural…
Shepard's Universal Law of Generalization offered a compelling case for the first physics-like law in cognitive science that should hold for all intelligent agents in the universe. Shepard's account is based on a rational Bayesian model of…
The classical gravitational two-body problem is generalized in order to be applicable also to weak gravitational fields. The equation of motion holds both for terrestrial and large cosmic scales, the Newtonian gravitational law represents a…
In this paper we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists' sense vanishes for any p > 1. Our…
It is demonstrated that under the hypothesis of boundedness, the semantics appears as a property of spontaneous physical processes. It turns that both semantic structure and semantic meaning have their own physical agents each of which is…
The first part of this article summarizes the evidence for Dark Energy and Dark Matter, as well as the naturalness issues which plague current theories of Dark Energy. The main point of this part is to argue why these naturalness issues…
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…
A geometric approach to derive the Nambu brackets for ideal two-dimensional (2D) hydrodynamics is suggested. The derivation is based on two-forms with vanishing integrals in a periodic domain, and with resulting dynamics constrained by an…
High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…
We discuss a systematic way to dimensionally regularize divergent sums arising in field theories with an arbitrary number of physical compact dimensions or finite temperature. The method preserves the same symmetries of the action as the…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
General relativity poses serious problems for counterfactual propositions peculiar to it as a physical theory. Because these problems arise solely from the dynamical nature of spacetime geometry, they are shared by all schools of thought on…
Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the…
Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…
Nonuniformity is a central concept in computational complexity with powerful connections to circuit complexity and randomness. Nonuniform reductions have been used to study the isomorphism conjecture for NP and completeness for larger…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…