Between the Barrio and the City: Pathways of Work among Scavenging Families

In this article, I will reconstruct, through brief stories, some of the traits that characterize the way of life of families in the El Salvador neighborhood, in Buenos Aires, Argentina, go scavenging everyday in Buenos Aires city. These stories will not only tell us who they are and how they arrived at the El Salvador neighborhood, from where, and in what manner they began to salir con la carreta, but will also permit us to move closer to the day-to-day existence of these families in relationship to their life in the barrio and the activities they engage in, thereby giving us a fuller understanding of family dynamics. In the research that originated this paper, I followed an ethnographical perspective to study and analyze the way of life of those families living from the recyclable waste they recollect in Buenos Aires city.Fil: Gorban, Debora. Universidad Nacional de San Martín. Instituto de Altos Estudios Sociales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Inference of analytical thermodynamic models for biological networks

We present an automated algorithm for inferring analytical models of closed reactive biochemical mixtures, on the basis of standard approaches borrowed from thermodynamics and kinetic theory of gases. As an input, the method requires a number of steady states (i.e. an equilibria cloud in the phase-space), and at least one time series of measurements for each species. Validations are discussed for both the Michaelis-Menten mechanism (four species, two conservation laws) and the mitogen-activated protein kinase - MAPK - mechanism (eleven species, three conservation laws

Systems with inheritance: dynamics of distributions with conservation of support, natural selection and finite-dimensional asymptotics

If we find a representation of an infinite-dimensional dynamical system as a nonlinear kinetic system with {\it conservation of supports} of distributions, then (after some additional technical steps) we can state that the asymptotics is finite-dimensional. This conservation of support has a {\it quasi-biological interpretation, inheritance} (if a gene was not presented initially in a isolated population without mutations, then it cannot appear at later time). These quasi-biological models can describe various physical, chemical, and, of course, biological systems. The finite-dimensional asymptotic demonstrates effects of {\it ``natural" selection}. The estimations of asymptotic dimension are presented. The support of an individual limit distribution is almost always small. But the union of such supports can be the whole space even for one solution. Possible are such situations: a solution is a finite set of narrow peaks getting in time more and more narrow, moving slower and slower. It is possible that these peaks do not tend to fixed positions, rather they continue moving, and the path covered tends to infinity at $t \rightarrow \infty$. The {\it drift equations} for peaks motion are obtained. Various types of stability are studied. In example, models of cell division self-synchronization are studied. The appropriate construction of notion of typicalness in infinite-dimensional spaces is discussed, and the ``completely thin" sets are introduced

Entropy: The Markov Ordering Approach

The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii) existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i) and (ii) are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the {\em Markov order}). The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally "most random" distributions.Comment: 50 pages, 4 figures, Postprint version. More detailed discussion of the various entropy additivity properties and separation of variables for independent subsystems in MaxEnt problem is added in Section 4.2. Bibliography is extende

Maxallent: Maximizers of all Entropies and Uncertainty of Uncertainty

The entropy maximum approach (Maxent) was developed as a minimization of the subjective uncertainty measured by the Boltzmann--Gibbs--Shannon entropy. Many new entropies have been invented in the second half of the 20th century. Now there exists a rich choice of entropies for fitting needs. This diversity of entropies gave rise to a Maxent "anarchism". Maxent approach is now the conditional maximization of an appropriate entropy for the evaluation of the probability distribution when our information is partial and incomplete. The rich choice of non-classical entropies causes a new problem: which entropy is better for a given class of applications? We understand entropy as a measure of uncertainty which increases in Markov processes. In this work, we describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the Markov order). For inference, this approach results in a set of conditionally "most random" distributions. Each distribution from this set is a maximizer of its own entropy. This "uncertainty of uncertainty" is unavoidable in analysis of non-equilibrium systems. Surprisingly, the constructive description of this set of maximizers is possible. Two decomposition theorems for Markov processes provide a tool for this description.Comment: 23 pages, 4 figures, Correction in Conclusion (postprint

Monotonically equivalent entropies and solution of additivity equation

Generalized entropies are studied as Lyapunov functions for the Master equation (Markov chains). Three basic properties of these Lyapunov functions are taken into consideration: universality (independence of the kinetic coefficients), trace-form (the form of sum over the states), and additivity (for composition of independent subsystems). All the entropies, which have all three properties simultaneously and are defined for positive probabilities, are found. They form a one-parametric family. We consider also pairs of entropies $S_{1}$, $S_{2}$, which are connected by the monotonous transformation $S_{2}=F(S_{1})$ (equivalent entropies). All classes of pairs of universal equivalent entropies, one of which has a trace-form, and another is additive (these entropies can be different one from another), were found. These classes consist of two one-parametric families: the family of entropies, which are equivalent to the additive trace-form entropies, and the family of Renyi-Tsallis entropies.Comment: elsart-LaTeX2e, 11 page

Kinetic Path Summation, Multi--Sheeted Extension of Master Equation, and Evaluation of Ergodicity Coefficient

We study the Master equation with time--dependent coefficients, a linear kinetic equation for the Markov chains or for the monomolecular chemical kinetics. For the solution of this equation a path summation formula is proved. This formula represents the solution as a sum of solutions for simple kinetic schemes (kinetic paths), which are available in explicit analytical form. The relaxation rate is studied and a family of estimates for the relaxation time and the ergodicity coefficient is developed. To calculate the estimates we introduce the multi--sheeted extensions of the initial kinetics. This approach allows us to exploit the internal ("micro")structure of the extended kinetics without perturbation of the base kinetics.Comment: The final journal versio

PCA and K-Means decipher genome

In this paper, we aim to give a tutorial for undergraduate students studying statistical methods and/or bioinformatics. The students will learn how data visualization can help in genomic sequence analysis. Students start with a fragment of genetic text of a bacterial genome and analyze its structure. By means of principal component analysis they ``discover'' that the information in the genome is encoded by non-overlapping triplets. Next, they learn how to find gene positions. This exercise on PCA and K-Means clustering enables active study of the basic bioinformatics notions. Appendix 1 contains program listings that go along with this exercise. Appendix 2 includes 2D PCA plots of triplet usage in moving frame for a series of bacterial genomes from GC-poor to GC-rich ones. Animated 3D PCA plots are attached as separate gif files. Topology (cluster structure) and geometry (mutual positions of clusters) of these plots depends clearly on GC-content.Comment: 18 pages, with program listings for MatLab, PCA analysis of genomes and additional animated 3D PCA plot