Related papers: On the spectral sequence associated to a multicomp…
Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of…
A composite symmetry of the nuclear structure, called multichannel dynamical symmetry is established. It can describe different cluster configurations (defined by different reaction channels) in a unified framework, thus it has a…
In this note, we investigate a mixture of combinatorial spectra and stratified simplicial sets, which would be thought of as a model of the spectrum objects of $(\infty, \infty)$-categories.
We introduce an intrinsic filtration to the magnitude chain complex of a metric space, and study basic properties of the associated spectral sequence of the magnitude homology. As an application, the third magnitude homology of the circle…
We compute explicitly (modulo solutions of certain algebraic equations) the spectra of infinite graphs obtained by attaching one or several infinite paths to some vertices of certain finite graphs. The main result concerns a canonical form…
This paper deals with the complexity of strings, which play an important role in biology (nucleotid sequences), information theory and computer science. The d-complexity of a string is defined as the number of its distinct d-substrings…
The common eigenfunctions of the twisted Cherednik operators can be first analyzed in the limit of $q\longrightarrow 1$. Then, the polynomial eigenfunctions form a simple set originating from the symmetric ground state of non-vanishing…
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane $\mathbb{P}^2$. They appear in the study of resonance and characteristic varieties of complex hyperplane arrangement complements…
Based upon the correlation matrix of the human promoter sequences, a complex network is constructed to capture the principal relationships between these promoters. It is a complex network has the properties of the right-skewed degree…
We give an exact formula for the number of distinct square patterns of a given size that occur in the Squiral tiling.
We completely determine the spectrum of an $I$-graph, that is, the eigenvalues of its adjacency matrix. We apply our result to prove known characterizations of connectedness and bipartiteness in $I$-graphs by using an spectral approach.…
The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex…
Fractals with different levels of self-similarity and magnification are defined as reduced fractals. It is shown that spectra of these reduced fractals can be constructed and used to describe levels of complexity of natural phenomena.…
In this note we classify sequences according to whether they are morphic, pure morphic, uniform morphic, pure uniform morphic, primitive morphic, or pure primitive morphic, and for each possibility we either give an example or prove that no…
We introduce tropical complexes, as an enrichment of the dual complex of a degeneration with additional data from non-transverse intersection numbers. We define cycles, divisors, and linear equivalence on tropical complexes, analogous both…
The paper introduces the concept of complex frequency. The imaginary part of the complex frequency is the variation with respect of a synchronous reference of the local bus frequency as commonly defined in power system studies. The real…
To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to $N$-multicomplexes. We present a family of model category structures on the…
We study homotopy theory of the category of spectral sequences with respect to the class of weak equivalences given by maps which are quasi-isomorphisms on a fixed page. We introduce the category of extended spectral sequences and show that…
We give a simple algebraic description of opetopes in terms of chain complexes, and we show how this description is related to combinatorial descriptions in terms of treelike structures. More generally, we show that the chain complexes…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…