On Matrices, Automata, and Double Counting

Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variables M, with the same constraint defined by a finite-state automaton A on each row of M and a global cardinality constraint gcc on each column of M. We give two methods for deriving, by double counting, necessary conditions on the cardinality variables of the gcc constraints from the automaton A. The first method yields linear necessary conditions and simple arithmetic constraints. The second method introduces the cardinality automaton, which abstracts the overall behaviour of all the row automata and can be encoded by a set of linear constraints. We evaluate the impact of our methods on a large set of nurse rostering problem instances

Visualization of Distributed Algorithms Based on Graph Relabelling Systems1 1This work has been supported by the European TMR research network GETGRATS, and by the “Conseil Régional d' Aquitane”.

AbstractIn this paper, we present a uniform approach to simulate and visualize distributed algorithms encoded by graph relabelling systems. In particular, we use the distributed applications of local relabelling rules to automatically display the execution of the whole distributed algorithm. We have developed a Java prototype tool for implementing and visualizing distributed algorithms. We illustrate the different aspects of our framework using various distributed algorithms including election and spanning trees

Distributed Symmetry Breaking in Hypergraphs

Fundamental local symmetry breaking problems such as Maximal Independent Set (MIS) and coloring have been recognized as important by the community, and studied extensively in (standard) graphs. In particular, fast (i.e., logarithmic run time) randomized algorithms are well-established for MIS and $\Delta +1$-coloring in both the LOCAL and CONGEST distributed computing models. On the other hand, comparatively much less is known on the complexity of distributed symmetry breaking in {\em hypergraphs}. In particular, a key question is whether a fast (randomized) algorithm for MIS exists for hypergraphs. In this paper, we study the distributed complexity of symmetry breaking in hypergraphs by presenting distributed randomized algorithms for a variety of fundamental problems under a natural distributed computing model for hypergraphs. We first show that MIS in hypergraphs (of arbitrary dimension) can be solved in $O(\log^2 n)$ rounds ($n$ is the number of nodes of the hypergraph) in the LOCAL model. We then present a key result of this paper --- an $O(\Delta^{\epsilon}\text{polylog}(n))$-round hypergraph MIS algorithm in the CONGEST model where $\Delta$ is the maximum node degree of the hypergraph and $\epsilon > 0$ is any arbitrarily small constant. To demonstrate the usefulness of hypergraph MIS, we present applications of our hypergraph algorithm to solving problems in (standard) graphs. In particular, the hypergraph MIS yields fast distributed algorithms for the {\em balanced minimal dominating set} problem (left open in Harris et al. [ICALP 2013]) and the {\em minimal connected dominating set problem}. We also present distributed algorithms for coloring, maximal matching, and maximal clique in hypergraphs.Comment: Changes from the previous version: More references adde

Logarithmic asymptotics of the densities of SPDEs driven by spatially correlated noise

We consider the family of stochastic partial differential equations indexed by a parameter \eps\in(0,1], \begin{equation*} Lu^{\eps}(t,x) = \eps\sigma(u^\eps(t,x))\dot{F}(t,x)+b(u^\eps(t,x)), \end{equation*} (t,x)\in(0,T]\times\Rd with suitable initial conditions. In this equation, $L$ is a second-order partial differential operator with constant coefficients, $\sigma$ and $b$ are smooth functions and $\dot{F}$ is a Gaussian noise, white in time and with a stationary correlation in space. Let p^\eps_{t,x} denote the density of the law of u^\eps(t,x) at a fixed point (t,x)\in(0,T]\times\Rd. We study the existence of \lim_{\eps\downarrow 0} \eps^2\log p^\eps_{t,x}(y) for a fixed $y\in\R$. The results apply to a class of stochastic wave equations with $d\in\{1,2,3\}$ and to a class of stochastic heat equations with $d\ge1$.Comment: 39 pages. Will be published in the book " Stochastic Analysis and Applications 2014. A volume in honour of Terry Lyons". Springer Verla

A self-organized model for cell-differentiation based on variations of molecular decay rates

Systemic properties of living cells are the result of molecular dynamics governed by so-called genetic regulatory networks (GRN). These networks capture all possible features of cells and are responsible for the immense levels of adaptation characteristic to living systems. At any point in time only small subsets of these networks are active. Any active subset of the GRN leads to the expression of particular sets of molecules (expression modes). The subsets of active networks change over time, leading to the observed complex dynamics of expression patterns. Understanding of this dynamics becomes increasingly important in systems biology and medicine. While the importance of transcription rates and catalytic interactions has been widely recognized in modeling genetic regulatory systems, the understanding of the role of degradation of biochemical agents (mRNA, protein) in regulatory dynamics remains limited. Recent experimental data suggests that there exists a functional relation between mRNA and protein decay rates and expression modes. In this paper we propose a model for the dynamics of successions of sequences of active subnetworks of the GRN. The model is able to reproduce key characteristics of molecular dynamics, including homeostasis, multi-stability, periodic dynamics, alternating activity, differentiability, and self-organized critical dynamics. Moreover the model allows to naturally understand the mechanism behind the relation between decay rates and expression modes. The model explains recent experimental observations that decay-rates (or turnovers) vary between differentiated tissue-classes at a general systemic level and highlights the role of intracellular decay rate control mechanisms in cell differentiation.Comment: 16 pages, 5 figure

Learning Mazes with Aliasing States: An LCS Algorithm with Associative Perception

Learning classifier systems (LCSs) belong to a class of algorithms based on the principle of self-organization and have frequently been applied to the task of solving mazes, an important type of reinforcement learning (RL) problem. Maze problems represent a simplified virtual model of real environments that can be used for developing core algorithms of many real-world applications related to the problem of navigation. However, the best achievements of LCSs in maze problems are still mostly bounded to non-aliasing environments, while LCS complexity seems to obstruct a proper analysis of the reasons of failure. We construct a new LCS agent that has a simpler and more transparent performance mechanism, but that can still solve mazes better than existing algorithms. We use the structure of a predictive LCS model, strip out the evolutionary mechanism, simplify the reinforcement learning procedure and equip the agent with the ability of associative perception, adopted from psychology. To improve our understanding of the nature and structure of maze environments, we analyze mazes used in research for the last two decades, introduce a set of maze complexity characteristics, and develop a set of new maze environments. We then run our new LCS with associative perception through the old and new aliasing mazes, which represent partially observable Markov decision problems (POMDP) and demonstrate that it performs at least as well as, and in some cases better than, other published systems

Can majority support save an endangered language? A case study of language attitudes in Guernsey

Many studies of minority language revitalisation focus on the attitudes and perceptions of minorities, but not on those of majority group members. This paper discusses the implications of these issues, and presents research into majority andf minority attitudes towards the endangered indigenous vernacular of Guernsey, Channel Islands. The research used a multi-method approach (questionnaire and interview) to obtain attitudinal data from a representative sample of the population that included politicians and civil servants (209 participants). The findings suggested a shift in language ideology away from the post-second world war ‘culture of modernisation’ and monolingual ideal, towards recognition of the value of a bi/trilingual linguistic heritage. Public opinion in Guernsey now seems to support the maintenance of the indigenous language variety, which has led to a degree of official support. The paper then discusses to what extent this ‘attitude shift’ is reflected in linguistic behaviour and in concrete language planning measures

Cytosine-to-Uracil Deamination by SssI DNA Methyltransferase

The prokaryotic DNA(cytosine-5)methyltransferase M.SssI shares the specificity of eukaryotic DNA methyltransferases (CG) and is an important model and experimental tool in the study of eukaryotic DNA methylation. Previously, M.SssI was shown to be able to catalyze deamination of the target cytosine to uracil if the methyl donor S-adenosyl-methionine (SAM) was missing from the reaction. To test whether this side-activity of the enzyme can be used to distinguish between unmethylated and C5-methylated cytosines in CG dinucleotides, we re-investigated, using a sensitive genetic reversion assay, the cytosine deaminase activity of M.SssI. Confirming previous results we showed that M.SssI can deaminate cytosine to uracil in a slow reaction in the absence of SAM and that the rate of this reaction can be increased by the SAM analogue 5’-amino-5’-deoxyadenosine. We could not detect M.SssI-catalyzed deamination of C5-methylcytosine (m5C). We found conditions where the rate of M.SssI mediated C-to-U deamination was at least 100-fold higher than the rate of m5C-to-T conversion. Although this difference in reactivities suggests that the enzyme could be used to identify C5-methylated cytosines in the epigenetically important CG dinucleotides, the rate of M.SssI mediated cytosine deamination is too low to become an enzymatic alternative to the bisulfite reaction. Amino acid replacements in the presumed SAM binding pocket of M.SssI (F17S and G19D) resulted in greatly reduced methyltransferase activity. The G19D variant showed cytosine deaminase activity in E. coli, at physiological SAM concentrations. Interestingly, the C-to-U deaminase activity was also detectable in an E. coli ung+ host proficient in uracil excision repair