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

Investigation of the solid/liquid phase transitions in the U–Pu–O system

Mixed oxides of uranium and plutonium U1-yPuyO2-x are currently studied as reference fuel for Sodium-cooled Fast Reactors (SFRs). To predict the margin to fuel melting, an accurate description of both solidus and liquidus temperatures of these materials is crucial. In this work, after a critical review of the literature data, the parameters of the liquid phase of the CALPHAD models of the Pu–O and U–Pu–O systems are reassessed based on the model of Gu´eneau et al.. A good agreement between the calculated and selected experimental data is obtained. Using this model, the melting behaviour of U1-yPuyO2±x oxides is then studied as a function of plutonium content and oxygen stoichiometry. The congruent melting for the mixed oxides is found to be shifted towards low O/M ratios compared to the end-members (UO1.97 and PuO1.95). The temperature of this congruent melting is nearly constant (3130–3140 K) along a ternary phase boundary from UO1.98 to U0.55Pu0.45O1.82 and then decreases with Pu content to a maximum of approximately 3040 K for PuO1.95. This observation is explained by the stabilisation of the hypo-stoichiometric mixed oxides due to the increase of the configurational entropy at high temperatures by the formation of oxygen vacancies and related cation mixing. The influence of the atmosphere used in the laser heating melting experiments on the oxygen stoichiometry of the sample and its solidus and liquidus temperatures is investigated. The determination of this O/M ratio after laser melting tests using XANES is also reported. The simultaneous presence of U6+, U5+, U4+, Pu3+ and Pu4+ is observed, highlighting the occurrence of charge compensation mechanisms. The samples are highly oxidised in air whereas close to stoichiometry (O/M = 2.00) in argon. These results are in agreement with the computed solidification paths. This work illustrates the complex melting behaviour of the U1-yPuyO2±x fuels and highlights the need for the CALPHAD method to accurately describe and predict the high-temperature transitions of the U–Pu–O system

Precise and simple quantitation of liver steatosis by MRI in an animal model and in patients with NAFLD

International audienc

Analytic and Gevrey Hypoellipticity for Perturbed Sums of Squares Operators

We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying H\"ormander's condition. The first is on the minimal Gevrey regularity: if a sum of squares with analytic coefficients is perturbed with a pseudodifferential operator of order strictly less than its subelliptic index it still has the Gevrey minimal regularity. We also prove a statement concerning real analytic hypoellipticity for the same type of pseudodifferential perturbations, provided the operator satisfies to some extra conditions (see Theorem 1.2 below) that ensure the analytic hypoellipticity

Geometric optics and instability for semi-classical Schrodinger equations

We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the problem cannot be reduced to the study of an o.d.e.Comment: 22 pages. Corollary 1.7 adde

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

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

Noninvasive liver steatosis quantification using MRI techniques combined with blood markers:

Aims: To evaluate the accuracy of different techniques of MRI steatosis quantification, based on histological grading and quantification of liver steatosis.Patients and methods: Twenty-three patients (21 with nonalcoholic fatty liver disease and two controls) were included. Steatosis was evaluated in liver specimens using histological grading (five grades) and steatosis area (% of liver surface) was computed using an inhouse automated image analysis. The following five MRI quantification techniques were performed: two-point Dixon, three-point Dixon, DUAL, spin echo method and a new technique called multi-echo gradient-echo (MFGRE). Interobserver (two observers) and intersite (three different liver sites) agreements were evaluated for the two best-performing methods. Results: Steatosis area was correlated with steatosis grade: Rs (Spearman coefficient)=0.82, P value of less than 0.001. The steatosis area was significantly different between S0–S2 and S3–S4 grades: 4.2±2.4 versus 16.4±8.9% (P<0.001). Correlations between the MRI techniques and steatosis area (or grading) were: MFGRE, Rs=0.72 (0.78); spin echo method, Rs=0.72 (0.76); DUAL, Rs=0.71 (0.76); two-point Dixon, Rs=0.71 (0.75); three-point Dixon, Rs=0.67 (0.77). Interobserver (Ric=0.99) and intersite (Ric=0.97) agreements were excellent for the liver steatosis measurement by MFGRE. The noninvasive diagnosis of the steatosis area was improved by adding blood markers like ALT and triglycerides to MFGRE (aR2: 0.805). Conclusion: MRI, and in particular the MFGRE method, provides accurate and automatic quantification for the noninvasive evaluation of liver steatosis, either as a single measurement or in combination with blood variables

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