Related papers: Lorentzian threads and generalized complexities
We develop a classification of general Carrollian structures, permitting affine connections with both torsion and non-metricity. We compare with a recent classification of general Galilean structures in order to present a unified…
We provide a characterization of complex tori using holomorphic symmetric differentials. With the same method we show that compact complex manifolds of Kodaira dimension 0 having some symmetric power of the cotangent bundle globally…
Dimensional reduction of the M5 brane on a Lorentzian manifold along a lightlike direction results in a five-dimensional gauge theory, which can be reformulated covariantly in six dimensions, where one puts the Lie derivatives along the…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
In this chapter we describe a selection of mathematical techniques and results that suggest interesting links between the theory of gratings and the theory of homogenization, including a brief introduction to the latter. By no means do we…
This paper initiates a discrete Hodge theory for cellular sheaves taking values in a category of lattices and Galois connections. The key development is the Tarski Laplacian, an endomorphism on the cochain complex whose fixed points yield a…
Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…
We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of…
We address the observability problem for ensembles that are described by probability distributions. The problem is to reconstruct a probability distribution of the initial state from the time-evolution of the probability distribution of the…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
We present a method to compute high-order derivatives of the total energy which can be used in the framework of density functional theory. We provide a proof of the $2n+1$ theorem for a general class of energy functionals in which the…
We introduce a general deterministic model for Apollonian Networks in an iterative fashion. The networks have small-world effect and scale-free topology. We calculate the exact results for the degree exponent, the clustering coefficient and…
We show that in any symmetric monoidal category, if a weight for colimits is absolute, then the resulting colimit of any diagram of dualizable objects is again dualizable. Moreover, in this case, if an endomorphism of the colimit is induced…
In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…
the program of Langlands is studied here on the basis of: a)new concepts of global class field theory related to the explicit construction of global class fields and of reciprocity laws; b)the representations of the reductive algebraic…
For the algebra L= K <x, d/dx, \int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an…
We investigate the formation of an infinite cluster of entangled threads in a (2+1)-dimensional system. We demonstrate that topological percolation belongs to the universality class of the standard 2D bond percolation. We compute the…
It is shown that gravitational lensing by point masses arranged in an infinitely extended regular lattice can be studied analytically using the Weierstrass functions. In particular, we draw the critical curves and the caustic networks for…
Gravitational lensing allows us to probe the structure of matter on a broad range of astronomical scales, and as light from a distant source traverses an intervening galaxy, compact matter such as planets, stars, and black holes act as…
A finite subgroup of $GL(n,\mathbb C)$ is involutory if the sum of the dimensions of its irreducible complex representations is given by the number of absolute involutions in the group. A uniform combinatorial model is constructed for all…