Nematode movement along a chemical gradient in a structurally heterogeneous environment : 2. Theory

L'influence de l'hétérogénéité sur la diffusion chimique et le déplacement des nématodes est étudiée par le biais d'un modèle théorique. Ce modèle prend en compte trois facteurs influant sur le déplacement des nématodes : la structure du sol, la stratégie de recherche de nourriture et la chémotaxie. Utilisant un modèle continu, nous avons mis au point un système discret permettant de simuler les traces des nématodes dans chacune des quatre situations définies par Anderson et al. (1997). Nous avons montré que l'hétérogénéité structurale provoque aussi bien des taux variables de concentrations du composé attractif dans des aires réduites que la reconnaissance de ce composé. L'hétérogénéité structurale du sol limite également la stratégie de recherche de nourriture du nématode lequel adopte alors une stratégie permettant d'éviter les pièges structuraux. Il est démontré que des augmentations localisées de la densité structurale accroissent significativement la reconnaissance du composé attractif. (Résumé d'auteur

Nematode movement along a chemical gradient in a structurally heterogeneous environment : 1 . Experiment

L'interaction entre l'hétérogénéité structurale et les gradients chimiques, ainsi que leur influence sur le déplacement des nématodes, ont été étudiées. Trois dispositifs expérimentaux ont été utilisés qui comprennent un nématode (#Caenorhabditis elegans) placé sur une couche homogène de milieu nutritif gélosé dans une boîte de Petri avec ou sans présence d'une source bactérienne de nourriture (#Escherichia coli) utilisée comme attractif. L'hétérogénéité structurale est réalisée en ajoutant des grains de sable en une seule épaisseur dans chacun des traitements homologues. Toutes les traces ont été relevées à l'aide d'un dispositif de vidéo à séquences temporelles et les données digitalisées avant analyse. Les répartitions des angles de changement de direction et les dimensions fractales des traces sont calculées pour chaque traitement. Il se révèle un effet statistiquement significatif (P inférieur ou égal à 0,01) de tous les traitements sur le déplacement des nématodes. En présence d'un produit attractif, le déplacement du nématode est plus linéaire et dirigé vers la source bactérienne. L'hétérogénéité structurale provoque un déplacement plus linéaire que dans le cas d'un milieu homogène. La dimension fractale des traces du nématode est significativement (P inférieur ou égal à 0,01) plus élevée pour les traitements sans sable ni bactéries que pour les autres traitements. Ces résultats permettent, pour la première fois, de quantifier le degré auquel les nématodes utilisent un comportement de recherche de nourriture au hasard dans un milieu homogène et adoptent un déplacement mieux orienté en présence d'un produit attractif. Finalement, lorsqu'une hétérogénéité est présente, la stratégie de recherche de nourriture devient plutôt une stratégie d'évitement permettant au nématode d'échapper aux "pièges" structuraux, tels les pores en cul-de-sac, et de pouvoir ainsi continuer à réagir à l'attraction. (Résumé d'auteur

Topological representations of matroid maps

The Topological Representation Theorem for (oriented) matroids states that every (oriented) matroid can be realized as the intersection lattice of an arrangement of codimension one homotopy spheres on a homotopy sphere. In this paper, we use a construction of Engstr\"om to show that structure-preserving maps between matroids induce topological mappings between their representations; a result previously known only in the oriented case. Specifically, we show that weak maps induce continuous maps and that the process is a functor from the category of matroids with weak maps to the homotopy category of topological spaces. We also give a new and conceptual proof of a result regarding the Whitney numbers of the first kind of a matroid.Comment: Final version, 21 pages, 8 figures; Journal of Algebraic Combinatorics, 201

Anderson localization as a parametric instability of the linear kicked oscillator

We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric instability of the oscillator, with the localization length determined by an increment of the exponential growth of the energy. Analytical expression for a weak disorder is obtained, which is valid both inside the energy band and at the band edge.Comment: 7 pages, Revtex, no figures, submitted to Phys. Rev.

Detection of embryo mortality and hatch using thermal differences among incubated chicken eggs

Accurate diagnosis of both the stage of embryonic mortality and the hatch process in incubated eggs is a fundamental component in troubleshooting and hatchery management. However, traditional methods disturb incubation, destroy egg samples, risk contamination, are time and labour-intensive and require specialist knowledge and training. Therefore, a new method to accurately detect embryonic mortality and hatching time would be of significant interest for the poultry industry if it could be done quickly, cheaply and be fully integrated into the process. In this study we have continuously measured individual eggshell temperatures and the corresponding micro-environmental air temperatures throughout the 21 days of incubation using standard low-cost temperature sensors. Moreover, we have quantified the thermal interaction between eggs and air by calculating thermal profile changes (temperature drop time, drop length and drop magnitude) that allowed us to detect four categories of egg status (infertile/early death, middle death, late death and hatch) during incubation. A decision tree induction classification model accurately (93.3%) predicted the status of 105 sampled eggs in comparison to the classical hatch residue breakout analyses. With this study we have provided a major contribution to the optimisation of incubation processes by introducing an alternative method for the currently practiced hatch residue breakout analyses.status: publishe

Black Hole Entropy is Noether Charge

We consider a general, classical theory of gravity in $n$ dimensions, arising from a diffeomorphism invariant Lagrangian. In any such theory, to each vector field, $\xi^a$, on spacetime one can associate a local symmetry and, hence, a Noether current $(n-1)$-form, ${\bf j}$, and (for solutions to the field equations) a Noether charge $(n-2)$-form, ${\bf Q}$. Assuming only that the theory admits stationary black hole solutions with a bifurcate Killing horizon, and that the canonical mass and angular momentum of solutions are well defined at infinity, we show that the first law of black hole mechanics always holds for perturbations to nearby stationary black hole solutions. The quantity playing the role of black hole entropy in this formula is simply $2 \pi$ times the integral over $\Sigma$ of the Noether charge $(n-2)$-form associated with the horizon Killing field, normalized so as to have unit surface gravity. Furthermore, we show that this black hole entropy always is given by a local geometrical expression on the horizon of the black hole. We thereby obtain a natural candidate for the entropy of a dynamical black hole in a general theory of gravity. Our results show that the validity of the ``second law" of black hole mechanics in dynamical evolution from an initially stationary black hole to a final stationary state is equivalent to the positivity of a total Noether flux, and thus may be intimately related to the positive energy properties of the theory. The relationship between the derivation of our formula for black hole entropy and the derivation via ``Euclidean methods" also is explained.Comment: 16 pages, EFI 93-4

Nucleosome repositioning via loop formation

Active (catalysed) and passive (intrinsic) nucleosome repositioning is known to be a crucial event during the transcriptional activation of certain eucaryotic genes. Here we consider theoretically the intrinsic mechanism and study in detail the energetics and dynamics of DNA-loop-mediated nucleosome repositioning, as previously proposed by Schiessel et al. (H. Schiessel, J. Widom, R. F. Bruinsma, and W. M. Gelbart. 2001. {\it Phys. Rev. Lett.} 86:4414-4417). The surprising outcome of the present study is the inherent nonlocality of nucleosome motion within this model -- being a direct physical consequence of the loop mechanism. On long enough DNA templates the longer jumps dominate over the previously predicted local motion, a fact that contrasts simple diffusive mechanisms considered before. The possible experimental outcome resulting from the considered mechanism is predicted, discussed and compared to existing experimental findings

Instabilities in a Two-Component, Species Conserving Condensate

We consider a system of two species of bosons of equal mass, with interactions $U^{a}(|x|)$ and $U^{x}(|x|)$ for bosons of the same and different species respectively. We present a rigorous proof -- valid when the Hamiltonian does not include a species switching term -- showing that, when $U^{x}(|x|)>U^{a}(|x|)$, the ground state is fully "polarized" (consists of atoms of one kind only). In the unpolarized phase the low energy excitation spectrum corresponds to two linearly dispersing modes that are even a nd odd under species exchange. The polarization instability is signaled by the vani shing of the velocity of the odd modes.Comment: To appear in Phys. Rev.

Some comments on "The Mathematical Universe"

I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of which lies in the acceptance that mathematics is (at least in part) a human construction, and discuss concrete consequences of this--at first sight purely philosophical--difference in point of view.Comment: 11 page

Symmetry justification of Lorenz' maximum simplification

In 1960 Edward Lorenz (1917-2008) published a pioneering work on the `maximum simplification' of the barotropic vorticity equation. He derived a coupled three-mode system and interpreted it as the minimum core of large-scale fluid mechanics on a `finite but unbounded' domain. The model was obtained in a heuristic way, without giving a rigorous justification for the chosen selection of modes. In this paper, it is shown that one can legitimate Lorenz' choice by using symmetry transformations of the spectral form of the vorticity equation. The Lorenz three-mode model arises as the final step in a hierarchy of models constructed via the component reduction by means of symmetries. In this sense, the Lorenz model is indeed the `maximum simplification' of the vorticity equation.Comment: 8 pages, minor correction