Related papers: Generalised Kauffman Clock Theorems
Kempe equivalence is a classical and fundamental notion in graph coloring theory. In the present paper we establish a connection between Kempe equivalence and quadratic stable set ring, which are toric rings associated to graphs. In fact,…
We develop a scattering theory for time-periodic Hamiltonians on discrete graphs, including long-range potentials with zero average for the period, and show the existence and completeness of wave operators.
Using the recently proposed covariant framework of general relativistic stochastic mechanics and stochastic thermodynamics, we proved the detailed and integral fluctuation theorems in curved spacetime. The time-reversal transformation is…
To any two-dimensional rational plane in four-dimensional space one can naturally attach a point in the Grassmannian Gr(2,4) and four lattices of rank two. Here, the first two lattices originate from the plane and its orthogonal complement…
We develop a theory of umkehr maps for twisted generalized homology theories. In this theory, interesting umkehr maps, including generalizations of important classical ones, are induced by cartesian morphisms of a certain category opfibred…
The central arguments for a generalised form of proper time as the basis for a unified theory, accounting for the Standard Model of particle physics and encompassing all four forces of nature including a consistent `quantum gravity', are…
Two natural generalizations of knot theory are the study of spatially embedded graphs, and Kauffman's theory of virtual knots. In this paper we combine these approaches to begin the study of virtual spatial graphs.
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…
We present the lattice structure of Feynman diagram renormalization in physical QFTs from the viewpoint of Dyson-Schwinger-Equations and the core Hopf algebra of Feynman diagrams. The lattice structure encapsules the nestedness of diagrams.…
Feynman perturbation theory for nonabelian gauge theory in light-like gauge is investigated. A lattice along two space-like directions is used as a gauge invariant ultraviolet regularization. For preservation of the polinomiality of action…
We study the non-unitary relation between quantum gravitational models defined using different internal times. We show that despite the non-unitarity, it is possible to provide a prescription for making unambiguous, though restricted,…
In this paper we propose the PCP-like theorem for sub-linear time inapproximability. Abboud et al. have devised the distributed PCP framework for sub-quadratic time inapproximability. We show that the distributed PCP theorem can be…
We provide a characterization of upper locally distributive lattices (ULD-lattices) in terms of edge colorings of their cover graphs. In many instances where a set of combinatorial objects carries the order structure of a lattice this…
Warped time-frequency systems have recently been introduced as a class of structured continuous frames for functions on the real line. Herein, we generalize this framework to the setting of functions of arbitrary dimensionality. After…
A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special…
By extending the framework of the gravitational clock compass we show how a suitably prepared set of clocks can be used to extract information about the gravitational field in the context of General Relativity. Conceptual differences…
Assuming the Generalized Riemann Hypothesis, we design a deterministic algorithm that, given a prime p and positive integer m=o(sqrt(p)/(log p)^4), outputs an elliptic curve E over the finite field F_p for which the cardinality of E(F_p) is…
For the first time it is shown that the logic of quantum mechanics can be derived from Classical Physics. An orthomodular lattice of propositions, characteristic of quantum logic, is constructed for manifolds in Einstein's theory of general…
We present an elementary proof of a generalization of Kirchoff's matrix tree theorem to directed, weighted graphs. The proof is based on a specific factorization of the Laplacian matrices associated to the graphs, which only involves the…
The notion of $L^p$-distributions is introduced on Riemannian symmetric spaces of noncompact type and their main properties are established. We use a geometric description for the topology of the space of test functions in terms of the…