On a Speculated Relation Between Chv\'atal-Sankoff Constants of Several Sequences

It is well known that, when normalized by n, the expected length of a longest common subsequence of d sequences of length n over an alphabet of size sigma converges to a constant gamma_{sigma,d}. We disprove a speculation by Steele regarding a possible relation between gamma_{2,d} and gamma_{2,2}. In order to do that we also obtain new lower bounds for gamma_{sigma,d}, when both sigma and d are small integers.Comment: 13 pages. To appear in Combinatorics, Probability and Computin

SPECIES I: Spectroscopic Parameters and atmosphEric ChemIstriEs of Stars

The detection and subsequent characterisation of exoplanets are intimately linked to the characteristics of their host star. Therefore, it is necessary to study the star in detail in order to understand the formation history and characteristics of their companion(s). Our aims were to develop a community tool that allows the automated calculation of stellar parameters for a large number of stars, using high resolution echelle spectra and minimal photometric magnitudes, and introduce the first results in this work. We measured the equivalent widths of several iron lines and used them to solve the radiative transfer equation assuming local thermodynamic equilibrium to obtain the atmospheric parameters ($T_{\text{eff}}$, [Fe/H], logg and $\xi_t$). We used these values to derive the abundance of 11 chemical elements in the stellar photosphere (Na, Mg, Al, Si, Ca, Ti, Cr, Mn, Ni, Cu and Zn). Rotation and macroturbulent velocity were obtained using temperature calibrators and synthetic line profiles to match the observed spectra of five absorption lines. Finally, by interpolating in a grid of MIST isochrones, we derived the mass, radius and age using a Bayesian approach. SPECIES obtains bulk parameters that are in good agreement with measured values from different existing catalogues, including when different methods are used to derive them. We find excellent agreement with previous works that used similar methodologies. We find discrepancies in the chemical abundances for some elements with respect to other works, which could be produced by differences in $T_{\text{eff}}$, or in the line list or the atomic line data used to derive them. We also obtained analytic relations to describe the correlations between different parameters, and we implemented new methods to better handle these correlations, which provides a better description of the uncertainties associated with the measurements.Comment: 28 pages, 26 figures, resubmitted to A&

Glycemia Regulation: From Feedback Loops to Organizational Closure.

Endocrinologists apply the idea of feedback loops to explain how hormones regulate certain bodily functions such as glucose metabolism. In particular, feedback loops focus on the maintenance of the plasma concentrations of glucose within a narrow range. Here, we put forward a different, organicist perspective on the endocrine regulation of glycaemia, by relying on the pivotal concept of closure of constraints. From this perspective, biological systems are understood as organized ones, which means that they are constituted of a set of mutually dependent functional structures acting as constraints, whose maintenance depends on their reciprocal interactions. Closure refers specifically to the mutual dependence among functional constraints in an organism. We show that, when compared to feedback loops, organizational closure can generate much richer descriptions of the processes and constraints at play in the metabolism and regulation of glycaemia, by making explicit the different hierarchical orders involved. We expect that the proposed theoretical framework will open the way to the construction of original mathematical models, which would provide a better understanding of endocrine regulation from an organicist perspective

The Epstein-Glaser causal approach to the Light-Front QED4_{4}. I: Free theory

In this work we present the study of light-front field theories in the realm of axiomatic theory. It is known that when one uses the light-cone gauge pathological poles $(k^{+}) ^{-n}$ arises, demanding a prescription to be employed in order to tame these ill-defined poles and to have correct Feynman integrals due to the lack of Wick rotation in such theories. In order to shed a new light on this long standing problem we present here a discussion based on the use rigorous mathematical machinery of distributions combined with physical concepts, such as causality, to show how to deal with these singular propagators in a general fashion without making use of any prescription. The first step of our development will consist in showing how analytic representation for propagators arises by requiring general physical properties in the framework of Wightman's formalism. From that we shall determine the equal-time (anti)commutation relations in the light-front form for the scalar, fermionic fields and for the dynamical components of the electromagnetic field. In conclusion, we introduce the Epstein-Glaser causal method in order to have a mathematical rigorous treatment of the free propagators of the theory, allowing us to discuss the general treatment for propagators of the type $(k^{+}) ^{-n}$. Moreover, we show that at given conditions our results reproduce known prescriptions in the literature.Comment: 34 pages, v2 matching the published versio