In this paper we present the full details of construction a Morse–Floer type homology related to superquadratic perturbation Dirac-geodesic model. This is computed explicitly using Leray–Serre spectral sequence and computation leads us several existence results Dirac-geodesics.

Given a 3D binary voxel-based digital object V , an algorithm for computing homological information for V via a polyhedral cell complex is designed. By homological information we understand not only Betti numbers, representative cycles of homology classes and homological classification of cycles but also the computation of homology numbers related additional algebraic structures defined on homo...

Abstract We introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of singular subanalytic germs. The main novelty our approach is allow “moderately discontinuous” chains, are specially advantageous for capturing the subtleties outer phenomena. Our invariant finitely generated graded abelian group any and homomorphisms ....

Recently, Ozsváth and Szabó introduced some algebraic constructions computing knot Floer homology in the spirit of bordered homology, including a family algebras $\mathcal B (n)$ and, for generator braid group on $n$ strands, certain t

Although functionally related proteins can be reliably predicted from phylogenetic profiles, many functional modules do not seem to evolve cohesively according to case studies and systematic analyses in prokaryotes. In this study we quantify the extent of evolutionary cohesiveness of functional modules in eukaryotes and probe the biological and methodological factors influencing our estimates. ...

Although insertions and deletions (indels) are a common type of evolutionary sequence variation, their origins and their functional consequences have not been comprehensively understood. There is evidence that, on one hand, classical alignment procedures only roughly reflect the evolutionary processes and, on the other hand, that they cause structural changes in the proteins’ surfaces. We first...

Identification of homologous chromosomal regions is important for understanding evolutionary processes that shape genome evolution, such as genome rearrangements and large scale duplication events. If these chromosomal regions have diverged significantly, statistical tests to determine whether observed similarities in gene content are due to history or chance are imperative. Currently available...

Background: LuxI is a component of the quorum sensing signaling pathway in Vibrio fischeri responsible for the inducer synthesis that is essential for bioluminescence. Methods: Homology modeling of LuxI was carried out using Phyre2 and refined with the GalaxyWEB server. Five models were generated and evaluated by ERRAT, ANOLEA, QMEAN6, and Procheck. Results: Five refined models were gener...

Sequence alignment underpins common tasks in molecular biology, including genome annotation, molecular phylogenetics, and homology modeling. Fundamental to sequence alignment is the placement of gaps, which represent character insertions or deletions. We assessed the ability of a generalized affine gap cost model to reliably detect remote protein homology and to produce high-quality alignments....

This paper focuses on developing an efficient algorithm for analyzing a directed network (graph) from topological viewpoint. A prevalent technique such analysis involves computation of homology groups and their persistence. These concepts are well suited spaces that not directed. As result, one needs concept accommodates orientations in input space. Path-homology developed graphs by Grigoryan e...