State-space Correlations and Stabilities

The state-space pair correlation functions and notion of stability of extremal and non-extremal black holes in string theory and M-theory are considered from the viewpoints of thermodynamic Ruppeiner geometry. From the perspective of intrinsic Riemannian geometry, the stability properties of these black branes are divulged from the positivity of principle minors of the space-state metric tensor. We have explicitly analyzed the state-space configurations for (i) the two and three charge extremal black holes, (ii) the four and six charge non-extremal black branes, which both arise from the string theory solutions. An extension is considered for the $D_6$-$D_4$-$D_2$-$D_0$ multi-centered black branes, fractional small black branes and two charge rotating fuzzy rings in the setup of Mathur's fuzzball configurations. The state-space pair correlations and nature of stabilities have been investigated for three charged bubbling black brane foams, and thereby the M-theory solutions are brought into the present consideration. In the case of extremal black brane configurations, we have pointed out that the ratio of diagonal space-state correlations varies as inverse square of the chosen parameters, while the off diagonal components vary as inverse of the chosen parameters. We discuss the significance of this observation for the non-extremal black brane configurations, and find similar conclusion that the state-space correlations extenuate as the chosen parameters are increased.Comment: 35 pages, Keywords: Black Hole Physics, Higher-dimensional Black Branes, State-space Correlations and Statistical Configurations. PACS numbers: 04.70.-s Physics of black holes; 04.70.Bw Classical black holes; 04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics; 04.50.Gh Higher-dimensional black holes, black strings, and related object

Automatic Detection of Critical Dermoscopy Features for Malignant Melanoma Diagnosis

Improved methods for computer-aided analysis of identifying features of skin lesions from digital images of the lesions are provided. Improved preprocessing of the image that 1) eliminates artifacts that occlude or distort skin lesion features and 2) identifies groups of pixels within the skin lesion that represent features and/or facilitate the quantification of features are provided including improved digital hair removal algorithms. Improved methods for analyzing lesion features are also provided

Application of Adaptive Filters in Processing of Solar Corona Images

Fotografování sluneční koróny patří mezi nejobtížnější úlohy astrofotografie a zároveň je jednou z klíčových metod pro studium koróny. Tato práce přináší ucelený souhrn metod pro pozorování sluneční koróny pomocí snímků. Práce obsahuje nutnou matematickou teorii, postup pro zpracování snímků a souhrn adaptivních filtrů pro vizualizaci koronálních struktur v digitálních obrazech. Dále přináší návrh nových metod určených především pro obrazy s vyšším obsahem šumu, než je běžné u obrazů bílé koróny pořízených během úplných zatmění Slunce, např. pro obrazy pořízené pomocí úzkopásmových filtrů. Fourier normalizing-radial-graded filter, který byl navržen v rámci této práce, je založen na aproximaci hodnot pixelů a jejich variability pomocí trigonometrických polynomů s využitím dalších vlastností obrazu.Solar corona photography counts among the most complicated tasks in astrophotography. It also plays a key role for research of the solar corona. This thesis brings an a complete overview of methods for imaging the solar corona. The thesis contains necessary methematical background, the sequence of steps for image processing, an overview of adaptive filters used for visualization of corona structures in digital images, and new methods are proposed, especially for images which contain more noise than it is typical for images of the white corona taken during total solar eclipses, e.g. images taken with narrow-band filters. The Fourier normalizing-radial-graded filter method that I proposed during my PhD study are based on approximation of pixel values and their variability with trigonometric polynomials using other properties of the image.

Algebraic Topology for Data Scientists

This book gives a thorough introduction to topological data analysis (TDA), the application of algebraic topology to data science. Algebraic topology is traditionally a very specialized field of math, and most mathematicians have never been exposed to it, let alone data scientists, computer scientists, and analysts. I have three goals in writing this book. The first is to bring people up to speed who are missing a lot of the necessary background. I will describe the topics in point-set topology, abstract algebra, and homology theory needed for a good understanding of TDA. The second is to explain TDA and some current applications and techniques. Finally, I would like to answer some questions about more advanced topics such as cohomology, homotopy, obstruction theory, and Steenrod squares, and what they can tell us about data. It is hoped that readers will acquire the tools to start to think about these topics and where they might fit in.Comment: 322 pages, 69 figures, 5 table

Mapping the distribution of packing topologies within protein interiors shows predominant preference for specific packing motifs

<p>Abstract</p> <p>Background</p> <p>Mapping protein primary sequences to their three dimensional folds referred to as the 'second genetic code' remains an unsolved scientific problem. A crucial part of the problem concerns the geometrical specificity in side chain association leading to densely packed protein cores, a hallmark of correctly folded native structures. Thus, any model of packing within proteins should constitute an indispensable component of protein folding and design.</p> <p>Results</p> <p>In this study an attempt has been made to find, characterize and classify recurring patterns in the packing of side chain atoms within a protein which sustains its native fold. The interaction of side chain atoms within the protein core has been represented as a contact network based on the surface complementarity and overlap between associating side chain surfaces. Some network topologies definitely appear to be preferred and they have been termed 'packing motifs', analogous to super secondary structures in proteins. Study of the distribution of these motifs reveals the ubiquitous presence of typical smaller graphs, which appear to get linked or coalesce to give larger graphs, reminiscent of the nucleation-condensation model in protein folding. One such frequently occurring motif, also envisaged as the unit of clustering, the three residue clique was invariably found in regions of dense packing. Finally, topological measures based on surface contact networks appeared to be effective in discriminating sequences native to a specific fold amongst a set of decoys.</p> <p>Conclusions</p> <p>Out of innumerable topological possibilities, only a finite number of specific packing motifs are actually realized in proteins. This small number of motifs could serve as a basis set in the construction of larger networks. Of these, the triplet clique exhibits distinct preference both in terms of composition and geometry.</p