Birational Mappings and Matrix Sub-algebra from the Chiral Potts Model

We study birational transformations of the projective space originating from lattice statistical mechanics, specifically from various chiral Potts models. Associating these models to \emph{stable patterns} and \emph{signed-patterns}, we give general results which allow us to find \emph{all} chiral $q$-state spin-edge Potts models when the number of states $q$ is a prime or the square of a prime, as well as several $q$-dependent family of models. We also prove the absence of monocolor stable signed-pattern with more than four states. This demonstrates a conjecture about cyclic Hadamard matrices in a particular case. The birational transformations associated to these lattice spin-edge models show complexity reduction. In particular we recover a one-parameter family of integrable transformations, for which we give a matrix representationComment: 22 pages 0 figure The paper has been reorganized, splitting the results into two sections : results pertaining to Physics and results pertaining to Mathematic

A Case of Bowen’s Disease and Small-Cell Lung Carcinoma: Long-Term Consequences of Chronic Arsenic Exposure in Chinese Traditional Medicine

Chronic arsenic toxicity occurs primarily through inadvertent ingestion of contaminated water and food or occupational exposure, but it can also occur through medicinal ingestion. This case features a 53-year-old lifetime nonsmoker with chronic asthma treated for 10 years in childhood with Chinese traditional medicine containing arsenic. The patient was diagnosed with Bowen’s disease and developed extensive-stage small-cell carcinoma of the lung 10 years and 47 years, respectively, after the onset of arsenic exposure. Although it has a long history as a medicinal agent, arsenic is a carcinogen associated with many malignancies including those of skin and lung. It is more commonly associated with non–small-cell lung cancer, but the temporal association with Bowen’s disease in the absence of other chemical or occupational exposure strongly points to a causal role for arsenic in this case of small-cell lung cancer. Individuals with documented arsenic-induced Bowen’s disease should be considered for more aggressive screening for long-term complications, especially the development of subsequent malignancies

On the complexity of some birational transformations

Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines, and relies mainly on univariate polynomial algebra, the second approach is a singularity analysis, and the third method is more numerical, using integer arithmetics. Each method has its own domain of application, but they give corroborating results, and lead us to a conjecture on the complexity of a class of maps constructed from matrix inversions

Mechanisms of gap gene expression canalization in the Drosophila blastoderm

<p>Abstract</p> <p>Background</p> <p>Extensive variation in early gap gene expression in the <it>Drosophila </it>blastoderm is reduced over time because of gap gene cross regulation. This phenomenon is a manifestation of canalization, the ability of an organism to produce a consistent phenotype despite variations in genotype or environment. The canalization of gap gene expression can be understood as arising from the actions of attractors in the gap gene dynamical system.</p> <p>Results</p> <p>In order to better understand the processes of developmental robustness and canalization in the early <it>Drosophila </it>embryo, we investigated the dynamical effects of varying spatial profiles of Bicoid protein concentration on the formation of the expression border of the gap gene <it>hunchback</it>. At several positions on the anterior-posterior axis of the embryo, we analyzed attractors and their basins of attraction in a dynamical model describing expression of four gap genes with the Bicoid concentration profile accounted as a given input in the model equations. This model was tested against a family of Bicoid gradients obtained from individual embryos. These gradients were normalized by two independent methods, which are based on distinct biological hypotheses and provide different magnitudes for Bicoid spatial variability. We showed how the border formation is dictated by the biological initial conditions (the concentration gradient of maternal Hunchback protein) being attracted to specific attracting sets in a local vicinity of the border. Different types of these attracting sets (point attractors or one dimensional attracting manifolds) define several possible mechanisms of border formation. The <it>hunchback </it>border formation is associated with intersection of the spatial gradient of the maternal Hunchback protein and a boundary between the attraction basins of two different point attractors. We demonstrated how the positional variability for <it>hunchback </it>is related to the corresponding variability of the basin boundaries. The observed reduction in variability of the <it>hunchback </it>gene expression can be accounted for by specific geometrical properties of the basin boundaries.</p> <p>Conclusion</p> <p>We clarified the mechanisms of gap gene expression canalization in early <it>Drosophila </it>embryos. These mechanisms were specified in the case of <it>hunchback </it>in well defined terms of the dynamical system theory.</p

Herbivore-induced shifts in carbon and nitrogen allocation in red oak seedlings

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65993/1/j.1469-8137.2008.02420.x.pd

Structural and electrical transport properties of superconducting Au{0.7}In{0.3} films: A random array of superconductor-normal metal-superconductor (SNS) Josephson junctions

The structural and superconducting properties of Au{0.7}In{0.3} films, grown by interdiffusion of alternating Au and In layers, have been studied. The films were found to consist of a uniform solid solution of Au{0.9}In{0.1}, with excess In precipitated in the form of In-rich grains of various Au-In phases (with distinct atomic compositions), including intermetallic compounds. As the temperature was lowered, these individual grains became superconducting at a particular transition temperature (Tc), determined primarily by the atomic composition of the grain, before a fully superconducting state of zero resistance was established. From the observed onset Tc, it was inferred that up to three different superconducting phases could have formed in these Au{0.7}In{0.3} films, all of which were embedded in a uniform Au{0.9}In{0.1} matrix. Among these phases, the Tc of a particular one, 0.8 K, is higher than any previously reported for the Au-In system. The electrical transport properties were studied down to low temperatures. The transport results were found to be well correlated with those of the structural studies. The present work suggests that Au{0.7}In{0.3} can be modeled as a random array of superconductor-normal metal-superconductor (SNS) Josephson junctions. The effect of disorder and the nature of the superconducting transition in these Au{0.7}In{0.3} films are discussed.Comment: 8 text pages, 10 figures in one separate PDF file, submitted to PR

Rupture by damage accumulation in rocks

The deformation of rocks is associated with microcracks nucleation and propagation, i.e. damage. The accumulation of damage and its spatial localization lead to the creation of a macroscale discontinuity, so-called "fault" in geological terms, and to the failure of the material, i.e. a dramatic decrease of the mechanical properties as strength and modulus. The damage process can be studied both statically by direct observation of thin sections and dynamically by recording acoustic waves emitted by crack propagation (acoustic emission). Here we first review such observations concerning geological objects over scales ranging from the laboratory sample scale (dm) to seismically active faults (km), including cliffs and rock masses (Dm, hm). These observations reveal complex patterns in both space (fractal properties of damage structures as roughness and gouge), time (clustering, particular trends when the failure approaches) and energy domains (power-law distributions of energy release bursts). We use a numerical model based on progressive damage within an elastic interaction framework which allows us to simulate these observations. This study shows that the failure in rocks can be the result of damage accumulation

Network analyses in systems biology: new strategies for dealing with biological complexity

The increasing application of network models to interpret biological systems raises a number of important methodological and epistemological questions. What novel insights can network analysis provide in biology? Are network approaches an extension of or in conflict with mechanistic research strategies? When and how can network and mechanistic approaches interact in productive ways? In this paper we address these questions by focusing on how biological networks are represented and analyzed in a diverse class of case studies. Our examples span from the investigation of organizational properties of biological networks using tools from graph theory to the application of dynamical systems theory to understand the behavior of complex biological systems. We show how network approaches support and extend traditional mechanistic strategies but also offer novel strategies for dealing with biological complexity

Canalization of Gene Expression and Domain Shifts in the Drosophila Blastoderm by Dynamical Attractors

The variation in the expression patterns of the gap genes in the blastoderm of the fruit fly Drosophila melanogaster reduces over time as a result of cross regulation between these genes, a fact that we have demonstrated in an accompanying article in PLoS Biology (see Manu et al., doi:10.1371/journal.pbio.1000049). This biologically essential process is an example of the phenomenon known as canalization. It has been suggested that the developmental trajectory of a wild-type organism is inherently stable, and that canalization is a manifestation of this property. Although the role of gap genes in the canalization process was established by correctly predicting the response of the system to particular perturbations, the stability of the developmental trajectory remains to be investigated. For many years, it has been speculated that stability against perturbations during development can be described by dynamical systems having attracting sets that drive reductions of volume in phase space. In this paper, we show that both the reduction in variability of gap gene expression as well as shifts in the position of posterior gap gene domains are the result of the actions of attractors in the gap gene dynamical system. Two biologically distinct dynamical regions exist in the early embryo, separated by a bifurcation at 53% egg length. In the anterior region, reduction in variation occurs because of stability induced by point attractors, while in the posterior, the stability of the developmental trajectory arises from a one-dimensional attracting manifold. This manifold also controls a previously characterized anterior shift of posterior region gap domains. Our analysis shows that the complex phenomena of canalization and pattern formation in the Drosophila blastoderm can be understood in terms of the qualitative features of the dynamical system. The result confirms the idea that attractors are important for developmental stability and shows a richer variety of dynamical attractors in developmental systems than has been previously recognized

Role of Soil, Crop Debris, and a Plant Pathogen in Salmonella enterica Contamination of Tomato Plants

Background: In the U.S., tomatoes have become the most implicated vehicle for produce-associated Salmonellosis with 12 outbreaks since 1998. Although unconfirmed, trace backs suggest pre-harvest contamination with Salmonella enterica. Routes of tomato crop contamination by S. enterica in the absence of direct artificial inoculation have not been investigated. Methodology/Principal Findings: This work examined the role of contaminated soil, the potential for crop debris to act as inoculum from one crop to the next, and any interaction between the seedbourne plant pathogen Xanthomonas campestris pv. vesicatoria and S. enterica on tomato plants. Our results show S. enterica can survive for up to six weeks in fallow soil with the ability to contaminate tomato plants. We found S. enterica can contaminate a subsequent crop via crop debris; however a fallow period between crop incorporation and subsequent seeding can affect contamination patterns. Throughout these studies, populations of S. enterica declined over time and there was no bacterial growth in either the phyllosphere or rhizoplane. The presence of X. campestris pv. vesicatoria on co-colonized tomato plants had no effect on the incidence of S. enterica tomato phyllosphere contamination. However, growth of S. enterica in the tomato phyllosphere occurred on co-colonized plants in the absence of plant disease. Conclusions/Significance: S. enterica contaminated soil can lead to contamination of the tomato phyllosphere. A six week lag period between soil contamination and tomato seeding did not deter subsequent crop contamination. In the absence o