Related papers: Recent developments in finite Ramsey theory: found…
Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining amorphous…
This review summarizes the recent developments in topological string theory from the author's perspective, mostly focused on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects…
I report on a systematic derivation of the phenomenological ``adhesion approximation'' from gravitational instability together with a brief evaluation of the related status of analytical modeling of large-scale structure.
We investigate Tukey morphisms between binary relations, establishing several fundamental lemmas. We then specialize to finite binary relations, using computational methods to classify all binary relations with at most $6$ points in the…
Fundamental duality is a concept which refers to two irreducible, heterogeneous principles which are in opposite and complementary of each other. The complementary principle in quantum mechanics is also praised by Bohr. This important…
Building on earlier work, we discuss a general framework for exploring the cosmological dynamics of Higher Order Theories of Gravity. We show that once the theory of gravity has been specified, the cosmological equations can be written as a…
We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory…
Over the past 25 years, I have been involved in some intriguing developments in the foundations of physics, exploring the quantum reality problem, the relationship between quantum theory and gravity and the interplay between consciousness…
In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the…
The dynamical system approach has recently acquired great importance in the investigation on higher order theories of gravity. In this talk I review the main results and I give brief comments on the perspectives for further developments.
This report provides a brief review of recently developed extended framework for fundamental physics, designated as Quantum Field Mechanics and including causally complete and intrinsically unified theory of explicitly emerging elementary…
Using a Zariski topology associated to a finite field extensions, we give new proofs and generalize the primitive and normal basis theorems.
This note introduces a new notion of random dynamical system with inputs and outputs, and sketches a small-gain theorem for monotone systems which generalizes a similar theorem known for deterministic systems.
In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For…
We discuss the externally definable Ramsey property, a weakening of the Ramsey property for ultrahomogeneous structures, where the only colourings considered are those that are externally definable: that is, definable with parameters in an…
Some possible (re)sources of indeterminism and randomness encountered in physics are enumerated. These gaps in the physical laws, if they exist, could possibly be exploited for dualistic interfaces. We also speculate that physical laws and…
This thesis discusses various aspects of duality in quantum field theory and string theory. In the first part we consider duality in topological quantum field theories, concentrating on the Donaldson and Seiberg-Witten theories as (dual)…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
We review old and recent finite de Finetti theorems in total variation distance and in relative entropy, and we highlight their connections with bounds on the difference between sampling with and without replacement. We also establish two…
We acuminate the idea of a final theory of physics in order to analyze its logical implications and consequences. It is argued that the rationale of a final theory is the principle of sufficient reason. This implies that a final theory of…