Decomposition and Descriptional Complexity of Shuffle on Words and Finite Languages

We investigate various questions related to the shuffle operation on words and finite languages. First we investigate a special variant of the shuffle decomposition problem for regular languages, namely, when the given regular language is the shuffle of finite languages. The shuffle decomposition into finite languages is, in general not unique. Thatis,therearelanguagesL^,L2,L3,L4withLiluL2= £3luT4but{L\,L2}^ {I/3, L4}. However, if all four languages are singletons (with at least two combined letters), it follows by a result of Berstel and Boasson [6], that the solution is unique; that is {L\,L2} = {L3,L4}. We extend this result to show that if L\ and L2 are arbitrary finite sets and Lz and Z-4 are singletons (with at least two letters in each), the solution is unique. This is as strong as it can be, since we provide examples showing that the solution can be non-unique already when (1) both L\ and L2 are singleton sets over different unary alphabets; or (2) L\ contains two words and L2 is singleton. We furthermore investigate the size of shuffle automata for words. It was shown by Campeanu, K. Salomaa and Yu in [11] that the minimal shuffle automaton of two regular languages requires 2mn states in the worst case (where the minimal automata of the two component languages had m and n states, respectively). It was also recently shown that there exist words u and v such that the minimal shuffle iii DFA for u and v requires an exponential number of states. We study the size of shuffle DFAs for restricted cases of words, namely when the words u and v are both periods of a common underlying word. We show that, when the underlying word obeys certain conditions, then the size of the minimal shuffle DFA for u and v is at most quadratic. Moreover we provide an efficient algorithm, which decides for a given DFA A and two words u and v, whether u lu u C L(A)

A membrane-inserted structural model of the yeast mitofusin Fzo1

Mitofusins are large transmembrane GTPases of the dynamin-related protein family, and are required for the tethering and fusion of mitochondrial outer membranes. Their full-length structures remain unknown, which is a limiting factor in the study of outer membrane fusion. We investigated the structure and dynamics of the yeast mitofusin Fzo1 through a hybrid computational and experimental approach, combining molecular modelling and all-atom molecular dynamics simulations in a lipid bilayer with site-directed mutagenesis and in vivo functional assays. The predicted architecture of Fzo1 improves upon the current domain annotation, with a precise description of the helical spans linked by flexible hinges, which are likely of functional significance. In vivo site-directed mutagenesis validates salient aspects of this model, notably, the long-distance contacts and residues participating in hinges. GDP is predicted to interact with Fzo1 through the G1 and G4 motifs of the GTPase domain. The model reveals structural determinants critical for protein function, including regions that may be involved in GTPase domain-dependent rearrangements

A system for describing and deciding properties of regular languages using input altering transducers

ii, 94 leaves : ill. ; 29 cm.Includes abstract.Includes bibliographical references (leaves 92-94).We present a formal method for describing and deciding code related properties of regular languages using input altering transducers. We also provide an implementation of that method in the form of a web application. We introduce the concept of an input altering transducer. We show how to use such transducers to describe properties of languages and present examples of transducers describing some well known properties (like suffix codes, prefix codes, infix codes, solid codes, and others). We discuss some limitations of our method. In particular, all properties that can be described using input altering transducers are 3-independence properties. We also give an example of a 3-independence property that cannot be represented using a transducer. We explain how our method is a specialisation of a more general method based on language in-equations. We also discuss the relation between our method and a method that uses sets of trajectories to describe properties. In particular, we show how, for any given set of trajectories describing some property, to build an input altering transducer describing the same property. We introduce the concept of counterexample, which is a pair of words that, if a given language does not belong to a given property, illustrate that fact. We show how we can incorporate extracting such counterexample into our method. Finally, we provide some details on the implementation and usage of the web application that was built as a part of this research

Complexity and modeling power of insertion-deletion systems

SISTEMAS DE INSERCIÓN Y BORRADO: COMPLEJIDAD Y CAPACIDAD DE MODELADO El objetivo central de la tesis es el estudio de los sistemas de inserción y borrado y su capacidad computacional. Más concretamente, estudiamos algunos modelos de generación de lenguaje que usan operaciones de reescritura de dos cadenas. También consideramos una variante distribuida de los sistemas de inserción y borrado en el sentido de que las reglas se separan entre un número finito de nodos de un grafo. Estos sistemas se denominan sistemas controlados mediante grafo, y aparecen en muchas áreas de la Informática, jugando un papel muy importante en los lenguajes formales, la lingüística y la bio-informática. Estudiamos la decidibilidad/ universalidad de nuestros modelos mediante la variación de los parámetros de tamaño del vector. Concretamente, damos respuesta a la cuestión más importante concerniente a la expresividad de la capacidad computacional: si nuestro modelo es equivalente a una máquina de Turing o no. Abordamos sistemáticamente las cuestiones sobre los tamaños mínimos de los sistemas con y sin control de grafo.COMPLEXITY AND MODELING POWER OF INSERTION-DELETION SYSTEMS The central object of the thesis are insertion-deletion systems and their computational power. More specifically, we study language generating models that use two string rewriting operations: contextual insertion and contextual deletion, and their extensions. We also consider a distributed variant of insertion-deletion systems in the sense that rules are separated among a finite number of nodes of a graph. Such systems are refereed as graph-controlled systems. These systems appear in many areas of Computer Science and they play an important role in formal languages, linguistics, and bio-informatics. We vary the parameters of the vector of size of insertion-deletion systems and we study decidability/universality of obtained models. More precisely, we answer the most important questions regarding the expressiveness of the computational model: whether our model is Turing equivalent or not. We systematically approach the questions about the minimal sizes of the insertiondeletion systems with and without the graph-control

Statistical Mechanics of Horizontal Gene Transfer in Evolutionary Ecology

The biological world, especially its majority microbial component, is strongly interacting and may be dominated by collective effects. In this review, we provide a brief introduction for statistical physicists of the way in which living cells communicate genetically through transferred genes, as well as the ways in which they can reorganize their genomes in response to environmental pressure. We discuss how genome evolution can be thought of as related to the physical phenomenon of annealing, and describe the sense in which genomes can be said to exhibit an analogue of information entropy. As a direct application of these ideas, we analyze the variation with ocean depth of transposons in marine microbial genomes, predicting trends that are consistent with recent observations using metagenomic surveys.Comment: Accepted by Journal of Statistical Physic

Recurrence analysis of extreme event-like data

The identification of recurrences at various timescales in extreme event-like time series is challenging because of the rare occurrence of events which are separated by large temporal gaps. Most of the existing time series analysis techniques cannot be used to analyze an extreme event-like time series in its unaltered form. The study of the system dynamics by reconstruction of the phase space using the standard delay embedding method is not directly applicable to event-like time series as it assumes a Euclidean notion of distance between states in the phase space. The edit distance method is a novel approach that uses the point-process nature of events. We propose a modification of edit distance to analyze the dynamics of extreme event-like time series by incorporating a nonlinear function which takes into account the sparse distribution of extreme events and utilizes the physical significance of their temporal pattern. We apply the modified edit distance method to event-like data generated from point process as well as flood event series constructed from discharge data of the Mississippi River in the USA and compute their recurrence plots. From the recurrence analysis, we are able to quantify the deterministic properties of extreme event-like data. We also show that there is a significant serial dependency in the flood time series by using the random shuffle surrogate method

IST Austria Thesis

The hippocampus is a key brain region for memory and notably for spatial memory, and is needed for both spatial working and reference memories. Hippocampal place cells selectively discharge in specific locations of the environment to form mnemonic represen tations of space. Several behavioral protocols have been designed to test spatial memory which requires the experimental subject to utilize working memory and reference memory. However, less is known about how these memory traces are presented in the hippo campus, especially considering tasks that require both spatial working and long -term reference memory demand. The aim of my thesis was to elucidate how spatial working memory, reference memory, and the combination of both are represented in the hippocampus. In this thesis, using a radial eight -arm maze, I examined how the combined demand on these memories influenced place cell assemblies while reference memories were partially updated by changing some of the reward- arms. This was contrasted with task varian ts requiring working or reference memories only. Reference memory update led to gradual place field shifts towards the rewards on the switched arms. Cells developed enhanced firing in passes between newly -rewarded arms as compared to those containing an unchanged reward. The working memory task did not show such gradual changes. Place assemblies on occasions replayed trajectories of the maze; at decision points the next arm choice was preferentially replayed in tasks needing reference memory while in the pure working memory task the previously visited arm was replayed. Hence trajectory replay only reflected the decision of the animal in tasks needing reference memory update. At the reward locations, in all three tasks outbound trajectories of the current arm were preferentially replayed, showing the animals’ next path to the center. At reward locations trajectories were replayed preferentially in reverse temporal order. Moreover, in the center reverse replay was seen in the working memory task but in the other tasks forward replay was seen. Hence, the direction of reactivation was determined by the goal locations so that part of the trajectory which was closer to the goal was reactivated later in an HSE while places further away from the goal were reactivated earlier. Altogether my work demonstrated that reference memory update triggers several levels of reorganization of the hippocampal cognitive map which are not seen in simpler working memory demand s. Moreover, hippocampus is likely to be involved in spatial decisions through reactivating planned trajectories when reference memory recall is required for such a decision