We study the AJ conjecture for $(r,2)$-cables of a knot, where $r$ is an odd integer. Using skein theory, we show that the AJ conjecture holds true for most $(r,2)$-cables of some classes of two-bridge knots and pretzel knots....
Atmospheric heat redistribution shapes the remote appearance of rocky exoplanets but there is currently no easy way to predict a planet's heat redistribution from its physical properties. This paper proposes an analytical scaling theory for the heat...
We review the prototype model of a grand unified theory on the orbifold $S^1/Z_2$ and discuss topics related to the choice of boundary conditions; the dynamical rearrangement of gauge symmetry and the equivalence classes of BCs. We explore a family...
The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac operators...
In this paper we analyze and discuss the historical and philosophical development of the notion of logical possibility focusing on its specific meaning in classical and quantum mechanics. Taking into account the logical structure of quantum theory we...
Recently Dzhafarov and Kon published the paper advertising the possibility to use the coupling technique of classical probability theory to model incompatible observables in quantum physics and quantum-like models of psychology. Here I present commen...
In 1966, the Brazilian physicist Klaus Tausk circulated a preprint from the International Centre for Theoretical Physics, in Trieste, criticizing the theory put forward by Daneri, Loinger & Prosperi on the measurement problem in quantum mechanics....
We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category. Moreover, the fu...
Large-scale systems with inherent heterogeneity often exhibit complex dynamics that are crucial for their functional properties. However, understanding how such heterogeneity shapes these dynamics remains a significant challenge, particularly in syst...
We revisit the exact solution of the two space-time dimensional quantum field theory of a free massless boson with a periodic boundary interaction and self-dual period. We analyze the model by using a mapping to free fermions with a boundary mass t...
This review presents a brief discussion of the theory of Cold Dark Matter of structure formation in the universe, describing the main processes determining the power spectrum, the non-linear gravitational collapse, the formation of galaxies and the...
We present a survey of results concerning the use of inductive constructions to study the rigidity of frameworks. By inductive constructions we mean simple graph moves which can be shown to preserve the rigidity of the corresponding framework. We des...
This paper presents a novel approach to machine learning algorithm design based on information theory, specifically mutual information (MI). We propose a framework for learning and representing functional relationships in data using MI-based features...
A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint frameworks in a...
Graphical models for finite-dimensional spin glasses and real-world combinatorial optimization and satisfaction problems usually have an abundant number of short loops. The cluster variation method and its extension, the region graph method, are theo...
Within the framework of the previously proposed formulation of the quantum theory of gravity in terms of world histories, it was suggested that the universe has its own mass. This quantity is analogous to the mass of a particle in relativistic mechan...
The meaning of CLINICIAN is a person qualified in the clinical practice of medicine, psychiatry, or psychology as distinguished from one specializing in laboratory or research techniques or in theory.
The statistical concept of Gambler's Ruin suggests that gambling has a large amount of risk. Nevertheless, gambling at casinos and gambling on the Internet are both hugely popular activities. In recent years, both prospect theory and lab-controlled e...
Simpson and the second author asked whether there exists a characterization of the natural numbers by a second-order sentence which is provably categorical in the theory RCA$^*_0$. We answer in the negative, showing that for any characterization of t...
The major assumption of the Lorentz-Lorenz theory about uniformity of local fields and atomic polarization in dense material does not hold in finite groups of atoms, as we reported earlier [A. E. Kaplan and S. N. Volkov, Phys. Rev. Lett., v. 101, 1...