The workings of the Maximum Entropy Principle in collective human behavior

We exhibit compelling evidence regarding how well does the MaxEnt principle describe the rank-distribution of city-populations via an exhaustive study of the 50 Spanish provinces (more than 8000 cities) in a time-window of 15 years (1996-2010). We show that the dynamics that governs the population-growth is the deciding factor that originates the observed distributions. The connection between dynamics and distributions is unravelled via MaxEnt.Comment: Additional material available at http://sthar.com/uploads/add.pd

Some inequalities on generalized entropies

We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young's inequality. We also give a generalized Han's inequality.Comment: 15 page

An exact expression to calculate the derivatives of position-dependent observables in molecular simulations with flexible constraints

In this work, we introduce an algorithm to compute the derivatives of physical observables along the constrained subspace when flexible constraints are imposed on the system (i.e., constraints in which the hard coordinates are fixed to configuration-dependent values). The presented scheme is exact, it does not contain any tunable parameter, and it only requires the calculation and inversion of a sub-block of the Hessian matrix of second derivatives of the function through which the constraints are defined. We also present a practical application to the case in which the sought observables are the Euclidean coordinates of complex molecular systems, and the function whose minimization defines the constraints is the potential energy. Finally, and in order to validate the method, which, as far as we are aware, is the first of its kind in the literature, we compare it to the natural and straightforward finite-differences approach in three molecules of biological relevance: methanol, N-methyl-acetamide and a tri-glycine peptideComment: 13 pages, 8 figures, published versio

Effective action of three-dimensional extended supersymmetric matter on gauge superfield background

We study the low-energy effective actions for gauge superfields induced by quantum N=2 and N=4 supersymmetric matter fields in three-dimensional Minkowski space. Analyzing the superconformal invariants in the N=2 superspace we propose a general form of the N=2 gauge invariant and superconformal effective action. The leading terms in this action are fixed by the symmetry up to the coefficients while the higher order terms with respect to the Maxwell field strength are found up to one arbitrary function of quasi-primary N=2 superfields constructed from the superfield strength and its covariant spinor derivatives. Then we find this function and the coefficients by direct quantum computations in the N=2 superspace. The effective action of N=4 gauge multiplet is obtained by generalizing the N=2 effective action.Comment: 1+27 pages; v2: minor corrections, references adde

Prediction of Optimal Folding Routes of Proteins That Satisfy the Principle of Lowest Entropy Loss: Dynamic Contact Maps and Optimal Control

An optimization model is introduced in which proteins try to evade high energy regions of the folding landscape, and prefer low entropy loss routes during folding. We make use of the framework of optimal control whose convenient solution provides practical and useful insight into the sequence of events during folding. We assume that the native state is available. As the protein folds, it makes different set of contacts at different folding steps. The dynamic contact map is constructed from these contacts. The topology of the dynamic contact map changes during the course of folding and this information is utilized in the dynamic optimization model. The solution is obtained using the optimal control theory. We show that the optimal solution can be cast into the form of a Gaussian Network that governs the optimal folding dynamics. Simulation results on three examples (CI2, Sso7d and Villin) show that folding starts by the formation of local clusters. Non-local clusters generally require the formation of several local clusters. Non-local clusters form cooperatively and not sequentially. We also observe that the optimal controller prefers “zipping” or small loop closure steps during folding. The folding routes predicted by the proposed method bear strong resemblance to the results in the literature

Rapid Analysis of Vessel Elements (RAVE): A Tool for Studying Physiologic, Pathologic and Tumor Angiogenesis

Quantification of microvascular network structure is important in a myriad of emerging research fields including microvessel remodeling in response to ischemia and drug therapy, tumor angiogenesis, and retinopathy. To mitigate analyst-specific variation in measurements and to ensure that measurements represent actual changes in vessel network structure and morphology, a reliable and automatic tool for quantifying microvascular network architecture is needed. Moreover, an analysis tool capable of acquiring and processing large data sets will facilitate advanced computational analysis and simulation of microvascular growth and remodeling processes and enable more high throughput discovery. To this end, we have produced an automatic and rapid vessel detection and quantification system using a MATLAB graphical user interface (GUI) that vastly reduces time spent on analysis and greatly increases repeatability. Analysis yields numerical measures of vessel volume fraction, vessel length density, fractal dimension (a measure of tortuosity), and radii of murine vascular networks. Because our GUI is open sourced to all, it can be easily modified to measure parameters such as percent coverage of non-endothelial cells, number of loops in a vascular bed, amount of perfusion and two-dimensional branch angle. Importantly, the GUI is compatible with standard fluorescent staining and imaging protocols, but also has utility analyzing brightfield vascular images, obtained, for example, in dorsal skinfold chambers. A manually measured image can be typically completed in 20 minutes to 1 hour. In stark comparison, using our GUI, image analysis time is reduced to around 1 minute. This drastic reduction in analysis time coupled with increased repeatability makes this tool valuable for all vessel research especially those requiring rapid and reproducible results, such as anti-angiogenic drug screening

Genome-Wide Analysis of Human Disease Alleles Reveals That Their Locations Are Correlated in Paralogous Proteins

The millions of mutations and polymorphisms that occur in human populations are potential predictors of disease, of our reactions to drugs, of predisposition to microbial infections, and of age-related conditions such as impaired brain and cardiovascular functions. However, predicting the phenotypic consequences and eventual clinical significance of a sequence variant is not an easy task. Computational approaches have found perturbation of conserved amino acids to be a useful criterion for identifying variants likely to have phenotypic consequences. To our knowledge, however, no study to date has explored the potential of variants that occur at homologous positions within paralogous human proteins as a means of identifying polymorphisms with likely phenotypic consequences. In order to investigate the potential of this approach, we have assembled a unique collection of known disease-causing variants from OMIM and the Human Genome Mutation Database (HGMD) and used them to identify and characterize pairs of sequence variants that occur at homologous positions within paralogous human proteins. Our analyses demonstrate that the locations of variants are correlated in paralogous proteins. Moreover, if one member of a variant-pair is disease-causing, its partner is likely to be disease-causing as well. Thus, information about variant-pairs can be used to identify potentially disease-causing variants, extend existing procedures for polymorphism prioritization, and provide a suite of candidates for further diagnostic and therapeutic purposes

Three Dimensional Visualization and Fractal Analysis of Mosaic Patches in Rat Chimeras: Cell Assortment in Liver, Adrenal Cortex and Cornea

The production of organ parenchyma in a rapid and reproducible manner is critical to normal development. In chimeras produced by the combination of genetically distinguishable tissues, mosaic patterns of cells derived from the combined genotypes can be visualized. These patterns comprise patches of contiguously similar genotypes and are different in different organs but similar in a given organ from individual to individual. Thus, the processes that produce the patterns are regulated and conserved. We have previously established that mosaic patches in multiple tissues are fractal, consistent with an iterative, recursive growth model with simple stereotypical division rules. Fractal dimensions of various tissues are consistent with algorithmic models in which changing a single variable (e.g. daughter cell placement after division) switches the mosaic pattern from islands to stripes of cells. Here we show that the spiral pattern previously observed in mouse cornea can also be visualized in rat chimeras. While it is generally held that the pattern is induced by stem cell division dynamics, there is an unexplained discrepancy in the speed of cellular migration and the emergence of the pattern. We demonstrate in chimeric rat corneas both island and striped patterns exist depending on the age of the animal. The patches that comprise the pattern are fractal, and the fractal dimension changes with the age of the animal and indicates the constraint in patch complexity as the spiral pattern emerges. The spiral patterns are consistent with a loxodrome. Such data are likely to be relevant to growth and cell division in organ systems and will help in understanding how organ parenchyma are generated and maintained from multipotent stem cell populations located in specific topographical locations within the organ. Ultimately, understanding algorithmic growth is likely to be essential in achieving organ regeneration in vivo or in vitro from stem cell populations