background: no data is available on morphology and genetic characteristics of echinococcus granulosus derived from donkeys of iran, despite of its existence in donkeys.in the present study morphometric variations of the rostellar hooks of protoscoleces and genotype characteristics of hydatid cyst of donkey from iran were determined. methods: protoscoleces prepared from hydatid cyst of donkey of...

A new approach to algorithmic computation of the homology of spaces and maps is presented. The key point of the approach is a change in the representation of sets. The proposed representation is based on a combinatorial variant of the Čech homology and the Nerve Theorem. In many situations this change of the representation of the input may help in bypassing the problems with the complexity of t...

In this article we study the digital homology groups of digital images which are based on the singular homology groups of topological spaces in algebraic topology. Specifically, we define a digitally standard n-simplex, a digitally singular nsimplex, and the digital homology groups of digital images with k -adjacency relations. We then construct a covariant functor from a category of digital im...

we investigate the relative cohomology and relative homology theories of $f$-gorenstein modules, consider the relations between classical and $f$-gorenstein (co)homology theories.

Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computational pipeline, since standard constructions lead large inputs, and tasks this area tend be expensive. We propose two methods for chain complexes free 2-parameter persistence modules. The first method extends multi-ch...

This paper generalizes the Max-Flow Min-Cut (MFMC) theorem from the setting of numerical capacities to cellular sheaves of semimodules on directed graphs. Motivating examples of semimodules include probability distributions, multicommodity capacity constraints, and logical propositions. Directed algebraic topology provides the tools necessary for capturing the salient information in such a gene...

A. In general, Lagrangian Floer homology HF∗(L, φH(L)) – if well-defined – is not isomorphic to the singular homology of the Lagrangian submanifold L. For arbitrary closed Lagrangian submanifolds a local version of Floer homology HF ∗ (L, φH(L)) is defined in [Flo89, Oh96] which is isomorphic to singular homology. This construction assumes that the Hamiltonian function H is sufficiently ...

While standard persistent homology has been successful in extracting information from metric datasets, its applicability to more general data, e.g. directed networks, is hindered by its natural insensitivity to asymmetry. We extend a construction of homology of digraphs due to Grigoryan, Lin, Muranov and Yau to the persistent framework. The result, which we call persistent path homology or PPH,...

Using derived categories of equivariant coherent sheaves, we construct a categorification of the tangle calculus associated to sl(2) and its standard representation. Our construction is related to that of Seidel-Smith by homological mirror symmetry. We show that the resulting doubly graded knot homology agrees with Khovanov homology.

In this paper, using Waldhausen’s standard degree 1-maps between handlebodies, we show that the Casson invariant of oriented integral homology 3-spheres is a homotopy invariant. This provides a map from homotopy classes of oriented integral homology 3-spheres to the integers. It also gives an obstruction to finding orientationreversing self homotopy equivalences of such 3-manifolds.