Related papers: On the spectral sequence associated to a multicomp…
We explain how to set up the homotopy spectral sequence of a (co)simplicial object in an $\infty$-category, with an emphasis on how to construct the differentials in a model-invariant manner.
We consider the spectrum of birth and death chains on a $n$-path. An iterative scheme is proposed to compute any eigenvalue with exponential convergence rate independent of $n$. This allows one to determine the whole spectrum in order $n^2$…
Biological systems, from a cell to the human brain, are inherently complex. A powerful representation of such systems, described by an intricate web of relationships across multiple scales, is provided by complex networks. Recently, several…
Complex unit gain graphs may exhibit various kinds of symmetry. In this work, we explore structural symmetry, spectral symmetry and sign-symmetry in such graphs, and their respective relations to one-another. Our main result is a…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…
Complex network formalism allows to explain the behavior of systems composed by interacting units. Several prototypical network models have been proposed thus far. The small-world model has been introduced to mimic two important features…
We say that a semigroup of matrices has a submultiplicative spectrum if the spectrum of the product of any two elements of the semigroup is contained in the product of the two spectra in question (as sets). In this note we explore an…
We introduce the notion of strip complex. A strip complex is a special type of complex obtained by gluing "strips" along their natural boundaries according to a given graph structure. The most familiar example is the one dimensional complex…
We consider a variety of connections between threshold graphs, shifted complexes, and simplicial complexes naturally formed from a graph. These graphical complexes include the independent set, neighborhood, and dominance complexes. We…
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.
We give a formalism of mixed sheaves on varieties over a subfield of the complex number field.
Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…
For a scheme X, we construct a sheaf C of complexes on X such that for every quasi-compact open subset U of X, C(U) is quasi-isomorphic to the Hochschild complex of the scheme U. Since C is moreover acyclic for taking sections on…
Connections on a trivial bundle MxG can be identified with their holonomy maps, i.e. with homomorphisms of a groupoid of paths in M into the gauge group G. For a connected compact G, various algebras depending on the set of the smooth…
A mechanism for the inheritance of properties of spectra by differential spectra is developed and applied to prove geometric properties of morphisms of differential algebraic varieties.
Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit…
We introduce the abstract notion of a chain, which is a sequence of $n$ points in the plane, ordered by $x$-coordinates, so that the edge between any two consecutive points is unavoidable as far as triangulations are concerned. A general…
Speckle patterns are a powerful tool for high-precision metrology, as they allow remarkable performance in relatively simple setups. Nonetheless, researchers in this field follow rather distinct paths due to underappreciated general…
This article focuses on the dynamics of the different tridimensional principal slices of the multicomplex Multibrot sets. First, we define an equivalence relation between those slices. Then, we characterize them in order to establish…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…