Separability and distillability of multiparticle quantum systems

We present a family of 3-qubit states to which any arbitrary state can be depolarized. We fully classify those states with respect to their separability and distillability properties. This provides a sufficient condition for nonseparability and distillability for arbitrary states. We generalize our results to N-particle states.

Energy and structure of dilute hard- and soft-sphere gases

The energy and structure of dilute hard- and soft-sphere Bose gases are systematically studied in the framework of several many-body approaches, such as the variational correlated theory, the Bogoliubov model, and the uniform limit approximation, valid in the weak-interaction regime. When possible, the results are compared with the exact diffusion Monte Carlo ones. Jastrow-type correlation provides a good description of the systems, both hard- and soft-spheres, if the hypernetted chain energy functional is freely minimized and the resulting Euler equation is solved. The study of the soft-sphere potentials confirms the appearance of a dependence of the energy on the shape of the potential at gas paremeter values of x~0.001. For quantities other than the energy, such as the radial distribution functions and the momentum distributions, the dependence appears at any value of x. The occurrence of a maximum in the radial distribution function, in the momentum distribution, and in the excitation spectrum is a natural effect of the correlations when x increases. The asymptotic behaviors of the functions characterizing the structure of the systems are also investigated. The uniform limit approach is very easy to implement and provides a good description of the soft-sphere gas. Its reliability improves when the interaction weakens.

The nonlinear relaxation time and quasideterministic-theory approaches to characterize the decay of unestable states

We present the relationship between nonlinear-relaxation-time (NLRT) and quasideterministic approaches to characterize the decay of an unstable state. The universal character of the NLRT is established. The theoretical results are applied to study the dynamical relaxation of the Landau model in one and n variables and also a laser model.

Population differentiation and its consequences in the white campion "Silene latifolia" (Caryophyllaceae): a functional analysis

Summary In his theory On the Origin of Species by Means of Natural Selection (1859), Darwin describes evolution as a gradual change in population over time and that natural selection is a process that caused evolution. Because quantitative variation in species is partly influenced by several genes and thus heritable, association between levels of genetic variation at neutral markers and at quantitative traits and their partitioning within and among populations are important to study mechanisms that drive evolution in populations. Most studies addressing quantitative variation in plants focused on morphological and life history traits but not in traits affecting reproductive success. The aim of this thesis is to better understand how patterns of variation for neutral molecular markers and phenotypic traits drive the evolution of reproduction and defensive mechanisms in six European populations of Silene latifolia, a dioecious plant species. We found evidence for extremely high within and between population variation at six microsatellite loci and at most quantitative traits studied in plants grown under standardized conditions (morphology, life history and reproductive traits). Interestingly, there was clinal variation between age at first flowering and latitude. This pattern is likely due to natural selection since differentiation of this trait was high, heritable and probably higher than differentiation at neutral markers. Our study focused on sex specific selective pressures: mechanisms of intersexual coadaptation and defence mechanism against the seed predator Hadena bicruris. To address divergence at reproductive traits, we studied male and female population of origin effects and in particular pollen competitive ability on male post-pollination success in the study populations with within and between populations crosses. We crossed the same female plant with pollen from a male within the same population of origin and pollen from two males from two distinct populations, using a fixed tester male as a competitor. Additionally, we conducted control crosses with pollen from each male as a single donor. We analysed paternity success of each competitor with two microsatellite loci, seed set and offspring fitness. Male population of origin showed significant among-population variation for siring success at pollen competition. In vitro pollen germination rate showed heritable variation among populations and was positively correlated to siring success. Local or foreign pollen did not have a consistent advantage. Furthermore, female population of origin affected the outcome of pollen competition in some populations. There was no difference of seed set or offspring fitness in within/ between population crosses. This suggests that reproductive divergence may occur via pollen competition in Silene latifolia. The specialist seed predator Hadena bicruris may also induce divergence between populations. We tested potential constitutive and induced defence mechanisms against the specialist predator Hadena bicruris. Because fruit wall thickness is smaller in the invasive range (Northern America) were the moth is absent, this suggests that a thicker fruit wall is a potentially defensive trait against larval attack, and that relaxed selection in the absence of the seed predator has resulted in an evolutionary loss of this defence in the invasive range. Fruit wall thickness was different among three populations. Experimental exposure to moth eggs increased fruit abortion. Fruits built after attack on exposed plants did not have thicker fruit walls compared to fruits on non-exposed plants. Furthermore, fruits with thicker fruit walls were not less profitable, nor did they require longer handling time when exposed to larvae, suggesting no defensive role of fruit wall thickness. Our results show that there is high molecular and phenotypic variation in Silene latifolia and that traits potentially involved in reproductive success both for intra-specific (between sexes) and inter-specific interactions are heritable. Different selective forces may thus interact and cause differential evolution of geographically separated Silene latifolia populations in Europe, leading to the observed differentiation. Résumé Dans sa théorie de l'évolution, L'origine des espèces, ch. 4 (1859), Darwin décrit l'évolution comme un processus continu au cours du temps à l'intérieur de populations et que la sélection naturelle en est le moteur. La variation quantitative est en partie déterminée par plusieurs gènes, donc transmissible à la descendance. Associer le niveau de variation génétique à des marqueurs neutres au niveau de la variation à des traits quantitatifs, ainsi que la répartition à l'intérieur et entre les populations d'une espèce donnée de cette variation, sont importants dans la compréhension des forces évolutives. La plupart des études scientifiques sur la variation quantitative chez les plantes se sont intéressées à la morphologie et à la phénologie mais pas aux caractères impliqués dans le succès reproducteur. L'objectif de cette thèse est de mieux comprendre comment la répartition de la variation à des marqueurs neutres et des caractères quantitatifs influence l'évolution de la reproduction et des mécanismes de défense dans six populations Européennes de l'espèce dioïque Silene latifolia. Nous avons mis en évidence une grande diversité intra et inter-population à six loci microsatellites ainsi qu'à la plupart des caractères quantitatifs mesurés (morphologie, phénologie et traits reproducteurs) sur des plantes cultivées dans des conditions standardisées. Un résultat intéressant est la présence d'un cline latitudinal pour l'âge à la floraison. Ceci est probablement une conséquence de la sélection naturelle, puisque ce caractère est différencié entre les populations étudiées, héritable et que la différenciation de ce trait est supérieure à la différenciation des marqueurs neutres étudiés. Notre étude a ensuite porté plus précisément sur les pressions de sélection spécifiques aux sexes : la coadaptation entre les sexes et les mécanismes de défense contre l'insecte granivore Hadena bicruris. Afin d'évaluer la divergence sur les traits reproducteurs, nous avons étudié les effets des populations d'origine des mâles et des femelles et en particulier le succès reproducteur des mâles après pollinisation à l'aide de croisements inter et intra-population. Nous avons pollinisé la même femelle avec du pollen provenant d'un mâle de la même population ainsi qu'avec le pollen de deux mâles provenant de deux autres populations en situation de compétition avec un pollen provenant d'une population test. Des croisements contrôle ont été réalisés avec les mêmes mâles en pollinisation pure. Nous avons évalué le succès reproducteur de chaque mâle à l'aide d'analyses de paternité ainsi que la production de graines et la fitness de la descendance. L'origine du mâle avait un effet sur la paternité. Le taux de croissance in vitro du pollen est un caractère héritable et a eu un effet positif sur le succès reproducteur. De plus, l'origine de la femelle avait un effet sur le succès des mâles en compétition dans certaines populations. Nos résultats suggèrent qu'une divergence reproductive chez Silene latifolia pourrait apparaître suite à la compétition pollinique. Nous avons ensuite testé des mécanismes potentiels de défense constitutive et induite contre l'herbivore spécialiste Hadena bicruris, un papillon nocturne qui pourrait aussi jouer un rôle dans la différenciation des populations. L'épaisseur des fruits étant plus faible dans les régions où la plante est invasive (Amérique du Nord) et où l'insecte est absent, ce trait pourrait jouer un rôle défensif. Une pression de sélection plus faible causée par l'absence de l'herbivore aurait abouti à une perte de cette défense dans ces régions. Nous avons montré que l'épaisseur du fruit est variable selon les populations. L'infestation artificielle de fruit par l'insecte induit l'abscission sélective des fruits. Les fruits produits après une infestation n'étaient pas plus épais que les fruits issus de plantes non infestées. De plus, les fruits épais n'étaient pas moins nutritifs et ne causaient pas de perte de temps pour la prédation pour les larves, ce qui suggère que l'épaisseur des fruits ne joue pas un rôle défensif. Nos résultats montrent que plusieurs pressions de sélection interviennent et interagissent dans l'évolution de populations distantes, provoquant la divergence des populations Européennes de l'espèce Silene latifolia.

Une vue globale du secteur ambulatoire: étude structurelle et fonctionnelle dans les cantons de Vaud et Fribourg. [A general view of the ambulatory care sector: Structural and functional study in the cantons of Vaud and Fribourg].

The project "Quantification and qualification of ambulatory health care", financed by the Swiss National Science Foundation and covering the Cantons of Vaud and Fribourg, has two main goals: --a structural study of the elements of the ambulatory care sector. This is done through inventories of the professions concerned (physicians, public health nurses, physiotherapists, pharmacists, medical laboratories), allowing to better characterize the "offer". This inventory work includes the collect and analysis of existing statistical data as well as surveys, by questionnaires sent (from September 1980) to the different professions and by interviews. --a functional study, inspired from the US National Ambulatory Medical Care Survey and from similar studies elsewhere, in order to investigate the modes of practice of various providers, with particular regard to interprofessional collaboration (through studying referrals from the ones to the others). The first months of the project have been used for a methodological research in this regard, centered on the use of systems analysis, and for the elaboration of adequate instruments.

Canonical Noether symmetries and commutativity properties for gauge systems

For a dynamical system defined by a singular Lagrangian, canonical Noether symmetries are characterized in terms of their commutation relations with the evolution operators of Lagrangian and Hamiltonian formalisms. Separate characterizations are given in phase space, in velocity space, and through an evolution operator that links both spaces. 2000 American Institute of Physics.

Equivalence Between the Lagrangian and Hamiltonian Formalisms for Constrained Systems

The equivalence between the Lagrangian and Hamiltonian formalism is studied for constraint systems. A procedure to construct the Lagrangian constraints from the Hamiltonian constraints is given. Those Hamiltonian constraints that are first class with respect to the Hamiltonian constraints produce Lagrangian constraints that are FL-projectable.

Lee HWA Chung theorem for presympectic manifolds. Canonical transformations for constrained systems

We generalize the analogous of Lee Hwa Chungs theorem to the case of presymplectic manifolds. As an application, we study the canonical transformations of a canonical system (M, S, O). The role of Dirac brackets as a test of canonicity is clarified.

Higher order Lagrangian systems: Geometric structures, Dynamics, and Constraints

In order to study the connections between Lagrangian and Hamiltonian formalisms constructed from aperhaps singularhigher-order Lagrangian, some geometric structures are constructed. Intermediate spaces between those of Lagrangian and Hamiltonian formalisms, partial Ostrogradskiis transformations and unambiguous evolution operators connecting these spaces are intrinsically defined, and some of their properties studied. Equations of motion, constraints, and arbitrary functions of Lagrangian and Hamiltonian formalisms are thoroughly studied. In particular, all the Lagrangian constraints are obtained from the Hamiltonian ones. Once the gauge transformations are taken into account, the true number of degrees of freedom is obtained, both in the Lagrangian and Hamiltonian formalisms, and also in all the intermediate formalisms herein defined.

Model-Free Reconstruction of Excitatory Neuronal Connectivity from Calcium Imaging Signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.

Design of Optical Systems With Extended Depth of Field: an Educational Approach to Wavefront Coding Techniques

A practical activity designed to introduce wavefront coding techniques as a method to extend the depth of field in optical systems is presented. The activity is suitable for advanced undergraduate students since it combines different topics in optical engineering such as optical system design, aberration theory, Fourier optics, and digital image processing. This paper provides the theoretical background and technical information for performing the experiment. The proposed activity requires students able to develop a wide range of skills since they are expected to deal with optical components, including spatial light modulators, and develop scripts to perform some calculations.

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size M-1. This effect makes a substantial contribution to the total decay rate.

Perturbation theory for classical thermodynamic Green's functions

A systematic time-dependent perturbation scheme for classical canonical systems is developed based on a Wick's theorem for thermal averages of time-ordered products. The occurrence of the derivatives with respect to the canonical variables noted by Martin, Siggia, and Rose implies that two types of Green's functions have to be considered, the propagator and the response function. The diagrams resulting from Wick's theorem are "double graphs" analogous to those introduced by Dyson and also by Kawasaki, in which the response-function lines form a "tree structure" completed by propagator lines. The implication of a fluctuation-dissipation theorem on the self-energies is analyzed and compared with recent results by Deker and Haake.

Interaccion among systems of finite size in predictive relativistic mechanics I. General framework

We derive a Hamiltonian formulation for the three-dimensional formalism of predictive relativistic mechanics. This Hamiltonian structure is used to derive a set of dynamical equations describing the interaction among systems in perturbation theory.

Brownian motion of multidimensional systems in nonpotential velocity-dependent fields of force

We study the Brownian motion in velocity-dependent fields of force. Our main result is a Smoluchowski equation valid for moderate to high damping constants. We derive that equation by perturbative solution of the Langevin equation and using functional derivative techniques.