Magnetic winding: what is it and what is it good for?

Magnetic winding is a fundamental topological quantity that underpins magnetic helicity and measures the entanglement of magnetic field lines. Like magnetic helicity, magnetic winding is also an invariant of ideal magnetohydrodynamics. In this article, we give a detailed description of what magnetic winding describes, how to calculate it and how to interpret it in relation to helicity. We show how magnetic winding provides a clear topological description of magnetic fields (open or closed) and we give examples to show how magnetic winding and helicity can behave differently, thus revealing different and important information about the underlying magnetic field.

Hand contour classification using evolutionary algorithm

A biometric identification of persons wchich utilize contour of a human hand belogs to still very interesting and still not totally explored areas and its accuracy and effectiveness depends on technical capabilities to some extent. Presented paper solves given problem using combination of different algorithms. A hand contour is used, topological description of the hand, evolutionary algorithm, algorithm linear regression to estimate the knuckles positions and for contours comparison is used an algorithm Iterative Closest Point (ICP) in its genuine shape. All 5 fingers is at computer classification fully moveable, thumb has 2 knuckles. Modern evolutionary optimizers enable markedly to cut down computational demands of the algorithm ICP. Experimental verification of proposed recipes were performed with use of two different databases named THID and GPDS with persons of both gender and different age (cca 20-65let) with total number of oeprons in individual database 104 and 94. Experimental results checked succesfuly suitability of use combination of methods ICP and evolutionary optimizer which is named as EPSDE for solving of the given task with algorithmic complexity O(N) and success rate give by coefficient THID:EER=0.38% and GPDS:EER=0.35% on real images.

The attractor of piecewise expanding maps of the interval

We consider piecewise expanding maps of the interval with finitely many branches of monotonicity and show that they are generically combinatorially stable, i.e. the number of ergodic attractors and their corresponding mixing components do not change under small perturbations of the map. Our methods provide a topological description of the attractor and give an elementary proof of the density of periodic orbits.

On Certain Counting Polynomial of Titanium Dioxide Nanotubes

Background: In 1936, Polya introduced the concept of a counting polynomial in chemistry. However, the subject established little attention from chemists for some decades even though the spectra of the characteristic polynomial of graphs were considered extensively by numerical means in order to obtain the molecular orbitals of unsaturated hydrocarbons. Counting polynomial is a sequence representation of a topological stuff so that the exponents precise the magnitude of its partitions while the coefficients are correlated to the occurrence of these partitions. Counting polynomials play a vital role in topological description of bipartite structures as well as counts of equidistant and non-equidistant edges in graphs. Omega, Sadhana, PI polynomials are wide examples of counting polynomials. Methods: Mathematical chemistry is a division of abstract chemistry in which we debate and forecast the chemical structure by using mathematical models. Chemical graph theory is a subdivision of mathematical chemistry in which the structure of a chemical compound can be embodied by a labelled graph whose vertices are atoms and edges are covalent bonds between the atoms. We use graph theoretic technique in finding the counting polynomials of TiO2 nanotubes. : Let ! be the molecular graph of TiO2. Then (!, !) = !!10!!+8!−2!−2 + (2! +1) !10!!+8!−2! + 2(! + 1)10!!+8!−2 Results: In this paper, the omega, Sadhana and PI counting polynomials are studied. These polynomials are useful in determining the omega, Sadhana and PI topological indices which play an important role in studies of Quantitative structure-activity relationship (QSAR) and Quantitative structure-property relationship (QSPR) which are used to predict the biological activities and properties of chemical compounds. Conclusion: These counting polynomials play an important role in topological description of bipartite structures as well as counts equidistance and non-equidistance edges in graphs. Computing distancecounting polynomial is under investigation.

Topological descriptions of protein folding

How knotted proteins fold has remained controversial since the identification of deeply knotted proteins nearly two decades ago. Both computational and experimental approaches have been used to investigate protein knot formation. Motivated by the computer simulations of Bölinger et al. [Bölinger D, et al. (2010) PLoS Comput Biol 6:e1000731] for the folding of the 61-knotted α-haloacid dehalogenase (DehI) protein, we introduce a topological description of knot folding that could describe pathways for the formation of all currently known protein knot types and predicts knot types that might be identified in the future. We analyze fingerprint data from crystal structures of protein knots as evidence that particular protein knots may fold according to specific pathways from our theory. Our results confirm Taylor’s twisted hairpin theory of knot folding for the 31-knotted proteins and the 41-knotted ketol-acid reductoisomerases and present alternative folding mechanisms for the 41-knotted phytochromes and the 52- and 61-knotted proteins.