From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity

The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa. We also briefly recall the known bounds for the removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free nondeterministic devices. Moreover, we report on recent results on the average case descriptional complexity bounds for the conversion of regular expressions to finite automata and brand new developments on the state elimination algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527

A Complexity-Brightness Correlation in Gamma Ray Bursts

We observe strong correlations between the temporal properties of gamma ray bursts (GRBs) and their apparent peak brightness. The strongest effect (with a significance level of 10^{-6}) is the difference between the brightness distributions of simple bursts (dominated by a single smooth pulse) and complex bursts (consisting of overlapping pulses). The latter has a break at a peak flux of 1.5 ph/cm^2/s, while the distribution of simple bursts is smooth down to the BATSE threshold. We also observe brightness dependent variations in the shape of the average peak aligned time profile (ATP) of GRBs. The decaying slope of the ATP shows time dilation when comparing bright and dim bursts while the rising slope hardly changes. Both slopes of the ATP are deformed for weak bursts as compared to strong bursts. The interpretation of these effects is simple: a complex burst where a number of independent pulses overlap in time appears intrinsically stronger than a simple burst. Then the BATSE sample of complex bursts covers larger redshifts where some cosmological factor causes the break in the peak brightness distribution. This break could correspond to the peak in the star formation rate that was recently shown to occur at a redshift of z~1.5.Comment: 13 pages; 11 figures; replaced with the published versio

Small NFAs from Regular Expressions: Some Experimental Results

Regular expressions (res), because of their succinctness and clear syntax, are the common choice to represent regular languages. However, efficient pattern matching or word recognition depend on the size of the equivalent nondeterministic finite automata (NFA). We present the implementation of several algorithms for constructing small epsilon-free NFAss from res within the FAdo system, and a comparison of regular expression measures and NFA sizes based on experimental results obtained from uniform random generated res. For this analysis, nonredundant res and reduced res in star normal form were considered.Comment: Proceedings of 6th Conference on Computability in Europe (CIE 2010), pages 194-203, Ponta Delgada, Azores, Portugal, June/July 201

Complexity, Centralization, and Fragility in Economic Networks

Trade networks, across which countries distribute their products, are crucial components of the globalized world economy. Their structure is strongly heterogeneous across products, given the different features of the countries which buy and sell goods. By using a diversified pool of indicators from network science and product complexity theory, we quantitatively confirm the intuition that, overall, products with higher complexity -- i.e., with larger technological content and number of components -- are traded through a more centralized network -- i.e., with a small number of countries concentrating most of the export flow. Since centralized networks are known to be more vulnerable, we argue that the current composition of production and trading is associated to high fragility at the level of the most complex -- thus strategic -- products

Molecules in galaxies

The main achievements, current developments and prospects of molecular studies in external galaxies are reviewed. They are put in the context of the results of several decades of studies of molecules in local interstellar medium, their chemistry and their importance for star formation. CO observations have revealed the gross structure of molecular gas in galaxies. Together with other molecules, they are among the best tracers of star formation at galactic scales. Our knowledge about molecular abundances in various local galactic environments is progressing. They trace physical conditions and metallicity, and they are closely related to dust processes and large aromatic molecules. Major recent developments include mega-masers, and molecules in Active Galactic Nuclei; millimetre emission of molecules at very high redshift; and infrared H2 emission as tracer of warm molecular gas, shocks and photodissociation regions. The advent of sensitive giant interferometers from the centimetre to sub-millimetre range, especially ALMA in the near future in the mm/submm range, will open a new area for molecular studies in galaxies and their use to trace star formation at all distances.Comment: 96 pages, 11 figure

Principal manifolds and graphs in practice: from molecular biology to dynamical systems

We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the Kohonen's self-organizing maps, a class of artificial neural networks. On several examples we show advantages of using non-linear objects for data approximation in comparison to the linear ones. We propose four numerical criteria for comparing linear and non-linear mappings of datasets into the spaces of lower dimension. The examples are taken from comparative political science, from analysis of high-throughput data in molecular biology, from analysis of dynamical systems.Comment: 12 pages, 9 figure

The First Galaxies: Chemical Enrichment, Mixing, and Star Formation

Using three-dimensional cosmological simulations, we study the assembly process of one of the first galaxies, with a total mass of 10^8 M_sun, collapsing at z = 10. Our main goal is to trace the transport of the heavy chemical elements produced and dispersed by a pair-instability supernova exploding in one of the minihalo progenitors. To this extent, we incorporate an efficient algorithm into our smoothed particle hydrodynamics code which approximately models turbulent mixing as a diffusion process. We study this mixing with and without the radiative feedback from Population III stars that subsequently form in neighboring minihalos. Our simulations allow us to constrain the initial conditions for second-generation star formation, within the first galaxy itself, and inside of minihalos that virialize after the supernova explosion. We find that most minihalos remain unscathed by ionizing radiation or the supernova remnant, while some are substantially photoheated and enriched to supercritical levels, likely resulting in the formation of low-mass Population III or even Population II stars. At the center of the newly formed galaxy, 10^5 M_sun of cold, dense gas uniformly enriched to 10^-3 Z_sun are in a state of collapse, suggesting that a cluster of Population II stars will form. The first galaxies, as may be detected by the James Webb Space Telescope, would therefore already contain stellar populations familiar from lower redshifts.Comment: 13 pages, 9 figures, published in Ap