Related papers: Complex structures as critical points
Geometric structures on $\mathbb N Q$-manifolds, i.e.~non-negatively graded manifolds with an homological vector field, encode non-graded geometric data on Lie algebroids and their higher analogues. A particularly relevant class of…
We consider detection and localization of an abrupt break in the covariance structure of high-dimensional random data. The paper proposes a novel testing procedure for this problem. Due to its nature, the approach requires a properly chosen…
The principle of virtual work for dissipative systems is stated. Partially controlled systems are discussed and the concept of a generating families of forms is introduced. The notion of a critical point of a family of convex forms is…
We study complex Dirac structures, that is, Dirac structures in the complexified generalized tangent bundle. These include presymplectic foliations, transverse holomorphic structures, CR-related geometries and generalized complex…
The geometrical structure is among the most fundamental ingredients in understanding complex systems. Is there any systematic approach in defining structures quantitatively, rather than illustratively? If yes, what are the basic principles…
We study possibilities for semantic and syntactic rigidity, i.e., the rigidity with respect to automorphism group and with respect to definable closure. Variations of rigidity and their degrees are studied in general case, for special…
Let a cluster be a term with a number of patterns occurring in it. We give two accounts of clusters, a geometric one as sets of (node and edge) positions, and an inductive one as pairs of terms with gaps (2nd order variables) and…
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
We revisit finite racks and quandles using a perspective based on permutations which can aid in the understanding of the structure. As a consequence we recover old results and prove new ones. We also present and analyze several examples.
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…
We studied the formation of complex patterns using a variational principle and a standard energy functional. These patterns evolve by letting the system to search for the optimal configuration of a high conductivity channel, that in one…
We analyze different data of the variation of the fine structure constant obtained with different methods to check their consistency.We test consistency using the modified Student test and confidence intervals. We split the data sets in…
Formal Concept Analysis (FCA) is a mathematical framework for knowledge representation and discovery. It performs a hierarchical clustering over a set of objects described by attributes, resulting in conceptual structures in which objects…
The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
The aim of this paper is to construct horizontal Chern forms of a holomorphic vector bundle using complex Finsler structures. Also, some properties of these forms are studied.
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…
Recent key observational results on the variation of fine structure constant, the proton to electron mass ratio and the gravitational constant are reviewed. The necessity to substantiate the dark sector of cosmology and to test gravity on…