Self-diffusion in a monatomic glassforming liquid embedded in the hyperbolic plane

We study by Molecular Dynamics simulation the slowing down of particle motion in a two-dimensional monatomic model: a Lennard-Jones liquid on the hyperbolic plane. The negative curvature of the embedding space frustrates the long-range extension of the local hexagonal order. As a result, the liquid avoids crystallization and forms a glass. We show that, as temperature decreases, the single particle motion displays the canonical features seen in real glassforming liquids: the emergence of a "plateau" at intermediate times in the mean square displacement and a decoupling between the local relaxation time and the (hyperbolic) diffusion constant.Comment: Article for the "11th International Workshop on Complex Systems

Establishment of an in vitro chicken epithelial cell line model to investigate Eimeria tenella gamete development

© 2018 The Author(s). Background: Eimeria tenella infection leads to acute intestinal disorders responsible for important economic losses in poultry farming worldwide. The life-cycle of E. tenella is monoxenous with the chicken as the exclusive host; infection occurs in caecal epithelial cells. However, in vitro, the complete life-cycle of the parasite has only been propagated successfully in primary chicken kidney cells, which comprise undefined mixed cell populations; no cell line model has been able to consistently support the development of the sexual stages of the parasite. We therefore sought to develop a new model to study E. tenella gametogony in vitro using a recently characterised chicken cell line (CLEC-213) exhibiting an epithelial cell phenotype. Methods: CLEC-213 were infected with sporozoites from a precocious strain or with second generation merozoites (merozoites II) from wild type strains. Sexual stages of the parasite were determined both at the gene and protein levels. Results: To our knowledge, we show for the first time in CLEC-213, that sporozoites from a precocious strain of E. tenella were able to develop to gametes, as verified by measuring gene expression and by using antibodies to a microgamete-specific protein (EtFOA1: flagellar outer arm protein 1) and a macrogamete-specific protein (EtGAM-56), but oocysts were not observed. However, both gametes and oocysts were observed when cells were infected with merozoites II from wild type strains, demonstrating that completion of the final steps of the parasite cycle is possible in CLEC-213 cells. Conclusion: The epithelial cell line CLEC-213 constitutes a useful avian tool for studying Eimeria epithelial cell interactions and the effect of drugs on E. tenella invasion, merogony and gametogony

Periodic boundary conditions on the pseudosphere

We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary conditions in the Euclidean plane, we introduce all the needed mathematical notions and sketch a classification of periodic boundary conditions on the hyperbolic plane. We stress the possible applications in statistical mechanics for studying the bulk behavior of physical systems and we illustrate how to implement such periodic boundary conditions in two examples, the dynamics of particles on the pseudosphere and the study of classical spins on hyperbolic lattices.Comment: 30 pages, minor corrections, accepted to J. Phys.

Thermodynamics and structure of simple liquids in the hyperbolic plane

We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk thermodynamic pressure to the pair correlation function and we develop the appropriate setting for extending the integral-equation approach of liquid-state theory in order to describe the fluid structure. We apply the formalism and study the influence of negative space curvature on two types of systems that have been recently considered: Coulombic systems, such as the one- and two-component plasma models, and fluids interacting through short-range pair potentials, such as the hard-disk and the Lennard-Jones models.Comment: 25 pages, 10 Figure

Phase Transition of the Ising model on a Hyperbolic Lattice

The matrix product structure is considered on a regular lattice in the hyperbolic plane. The phase transition of the Ising model is observed on the hyperbolic $(5, 4)$ lattice by means of the corner-transfer-matrix renormalization group (CTMRG) method. Calculated correlation length is always finite even at the transition temperature, where mean-field like behavior is observed. The entanglement entropy is also always finite.Comment: 4 pages, 3 figure

Aging and relaxation near Random Pinning Glass Transitions

Pinning particles at random in supercooled liquids is a promising route to make substantial progress on the glass transition problem. Here we develop a mean-field theory by studying the equilibrium and non-equilibrium dynamics of the spherical p-spin model in presence of a fraction c of pinned spins. Our study shows the existence of two dynamic critical lines: one corresponding to usual Mode Coupling transitions and the other one to dynamic spinodal transitions. Quenches in the portion of the c - T phase diagram delimited by those two lines leads to aging. By extending our results to finite dimensional systems we predict non-interrupted aging only for quenches on the ideal glass transition line and two very different types of equilibrium relaxations for quenches below and above it.Comment: 7 pages, 4 figure

Braided racks, Hurwitz actions and Nichols algebras with many cubic relations

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption turns out to be equivalent to a factorization assumption on the Hilbert series. Besides the known Nichols algebras we obtain a new example. Our method is based on a combinatorial invariant of the Hurwitz orbits with respect to the action of the braid group on three strands.Comment: v2: 35 pages, 6 tables, 14 figure

Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement protocols in a wide range of applications. Using an interdisciplinary approach, we have recently proposed in [arXiv:1109.4424] a strategy that allows compressed sensing to be performed at acquisition rates approaching to the theoretical optimal limits. In this paper, we give a more thorough presentation of our approach, and introduce many new results. We present the probabilistic approach to reconstruction and discuss its optimality and robustness. We detail the derivation of the message passing algorithm for reconstruction and expectation max- imization learning of signal-model parameters. We further develop the asymptotic analysis of the corresponding phase diagrams with and without measurement noise, for different distribution of signals, and discuss the best possible reconstruction performances regardless of the algorithm. We also present new efficient seeding matrices, test them on synthetic data and analyze their performance asymptotically.Comment: 42 pages, 37 figures, 3 appendixe