Compressed Text Indexes:From Theory to Practice!

A compressed full-text self-index represents a text in a compressed form and still answers queries efficiently. This technology represents a breakthrough over the text indexing techniques of the previous decade, whose indexes required several times the size of the text. Although it is relatively new, this technology has matured up to a point where theoretical research is giving way to practical developments. Nonetheless this requires significant programming skills, a deep engineering effort, and a strong algorithmic background to dig into the research results. To date only isolated implementations and focused comparisons of compressed indexes have been reported, and they missed a common API, which prevented their re-use or deployment within other applications. The goal of this paper is to fill this gap. First, we present the existing implementations of compressed indexes from a practitioner's point of view. Second, we introduce the Pizza&Chili site, which offers tuned implementations and a standardized API for the most successful compressed full-text self-indexes, together with effective testbeds and scripts for their automatic validation and test. Third, we show the results of our extensive experiments on these codes with the aim of demonstrating the practical relevance of this novel and exciting technology

Entropy involved in fidelity of DNA replication

Information has an entropic character which can be analyzed within the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is performed sufficiently slowly. Structural and recent single-molecule assays have provided dynamic details of polymerase machinery with insight into information processing. We introduce a rigorous characterization of Shannon Information in biomolecular systems and apply it to DNA replication in the limit of no dissipation. Specifically, we devise an equilibrium pathway in DNA replication to determine the entropy generated in copying the information from a DNA template in the absence of friction. Both the initial state, the free nucleotides randomly distributed in certain concentrations, and the final state, a polymerized strand, are mesoscopic equilibrium states for the nucleotide distribution. We use empirical stacking free energies to calculate the probabilities of incorporation of the nucleotides. The copied strand is, to first order of approximation, a state of independent and non-indentically distributed random variables for which the nucleotide that is incorporated by the polymerase at each step is dictated by the template strand, and to second order of approximation, a state of non-uniformly distributed random variables with nearest-neighbor interactions for which the recognition of secondary structure by the polymerase in the resultant double-stranded polymer determines the entropy of the replicated strand. Two incorporation mechanisms arise naturally and their biological meanings are explained. It is known that replication occurs far from equilibrium and therefore the Shannon entropy here derived represents an upper bound for replication to take place. Likewise, this entropy sets a universal lower bound for the copying fidelity in replication.Comment: 25 pages, 5 figure

Leadership and management in second generation medium-size family businesses: a comparative study

A research study was conducted among 10 second generation owners of medium-size family businesses in Mexico to gain a better understanding of how their firms were founded and of how these business owners have succeeded in growing their companies and keeping their business alive for more than 40 years. Literature from leadership, management, and family business was reviewed to analyze the existing research on the topic. The literature review revealed that many authors have addressed similar issues, but from different perspectives. This study presents the experiences of a group of second generation business owners in great detail, focusing on their role as leaders and managers of their organizations. A comparative case study was conducted. A detailed description of each study case is presented to familiarize the readers with the participants and their companies. The study found that the companies researched were started in the 1950s and 1960s, a time when there was little competition and little government regulation in Mexico. At the time, several entrepreneurs were able to take advantage of this situation and positioned themselves as first entrants in their respective industries. However, in the 1970s and 1980s, Mexico experienced several devaluations, resulting in great deals of uncertainty for the business community. Most recently, in the 1990s and 2000s, it has been difficult for medium-size family firms to stay alive due to intense global competition. The business owners who participated in this study think that the most important factors for the survival of their firms have been: adopting new technologies; implementing modern business management practices; offering excellent customer service; projecting confidence as leaders; and gaining long-term commitment from key employees. The findings of this study are consistent with the literature review. However, this research provides a more detailed description of certain events and presents a closer look at the reality of the day to day experiences of medium-size family business owners

Effect of electro discharge machining (EDM) on the AISI316L SS white layer microstructure and corrosion resistance

The localised corrosion resistance of austenitic stainless steels is strongly influenced by the quality of finished surface. EDM machining induces substantial changes by the high thermal gradients generated by electric sparks. Experimental techniques such as roughness measurement, scanning electron microscopy (SEM), energy dispersive microanalysis (EDX) and X-ray diffraction technique, reveal microgeometrical, microstructural, chemical and mechanical changes. These changes lead to white and heat-affected layers with a depth less than 100 μm. The white layer is a melted material characterised by dendritic structure and constituted by austenite, chromium carbide and ε-carbide. The heat-affected layer is characterised by very large grain size comparatively to the bulk material. Electrochemical test coupled with metallographic examinations using SEM reveals a weakening of the resistance to pitting and intergranular corrosion comparatively to diamond polished surface. This weakening is correlated to differences in structure and chemical composition of white layer. Susceptibility to stress corrosion cracking has been attributed to the field of tensile residual stresses resulting from thermal effects. The removal of the white layer material by polishing or wire brushing restores the corrosion resistance of the AISI316L SS

Viscous contact problems in glaciology

Viscous contact problems describe the time evolution of fluid flows in contact with a surface from which they can detach and reattach. They can be modelled by coupling the Stokes equations with contact boundary conditions and a free boundary equation that evolves the geometry of the domain occupied by the fluid. These problems are of particular importance in glaciology, where they arise in the study of grounding lines and subglacial cavities. This work investigates the numerical approximation of viscous contact problems with applications to these two examples in glaciology. We commence by formulating the viscous contact problems that model subglacial cavitation and marine ice sheets in Chapter 1. We state the different variational inequalities that arise in these problems and are equivalent to the Stokes equations with contact boundary conditions. We then propose a novel framework for building numerical schemes for these problems in Chapter 2. This framework considers a family of discrete variational inequalities and establishes certain conditions that should be satisfied when approximating the free boundary equations. We then describe the numerical scheme that is used for the remainder of this work and compare it with different schemes that fit the framework introduced beforehand. Chapter 3 is dedicated to the numerical analysis of one of the Stokes variational inequalities formulated in this work. We give rigorous proofs on the conditions under which it is well-posed and its finite element approximation converges. By developing theoretical tools based on existing work in the numerical analysis of variational inequalities and p-Stokes systems, our analysis deals with three substantial difficulties arising in this system: the presence of rigid modes in the space of admissible velocity fields, the nonlinear rheology used in glaciology, and the friction boundary condition enforced at the base of glaciers. Chapter 4 presents a numerical investigation of subglacial cavitation and its application to glacial sliding under steady and unsteady conditions. We reconstruct steady friction laws by calculating several steady cavity shapes. These steady results are validated by comparing them to a linearised analytical method. We then perturb some of these steady states with oscillating water pressures that reveal an interplay between the frequency of the perturbations and the resulting sliding speed and cavity volume. Moreover, we find that if the steady state is located on the downsloping or rate-weakening part of the friction law, the cavity evolves towards the upsloping section, indicating that the downsloping part is unstable. Finally, we explore steady marine ice sheet configurations in Chapter 4. We do so by computing steady states to the parallel slab marine ice sheet problem, which we propose in this chapter. In this problem, a slab of ice of uniform thickness flows down an inclined bedrock into the ocean. We enforce influx conditions that allow us to explore a spectrum of flow regimes, ranging from sliding to shear-dominated flow. We find that the flux-thickness relationship at the grounding line takes the form of power laws with exponents n+1 and n+2 in these two limits, respectively, where n is a non-dimensional parameter in Glen's law, the power law rheology used commonly used in glaciology. We derive analytical approximations in these limits which resemble our numerical findings closely, with visible deviations in some cases. Our numerical results allow us to understand the shortcomings of these commonly used analytical methods. Moreover, in the context of the parallel slab problem, we find that the flux-thickness relationships are strictly monotonically increasing and that the bedrock plays a prominent role in the sliding dominated regime

The socle of a Leavitt path algebra

In this paper we characterize the minimal left ideals of a Leavitt path algebra as those ones which are isomorphic to principal left ideals generated by line point vertices, that is, by vertices whose trees do not contain neither bifurcations nor closed paths. Moreover, we show that the socle of a Leavitt path algebra is the two-sided ideal generated by these line point vertices. This characterization allows us to compute the socle of some algebras that arise as the Leavitt path algebra of some row-finite graphs. A complete description of the socle of a Leavitt path algebra is given: it is a locally matricial algebra.Comment: 13 pg