Poisson Structures of Calogero-Moser and Ruijsenaars-Schneider Models

We examine the Hamiltonian structures of some Calogero-Moser and Ruijsenaars-Schneider N-body integrable models. We propose explicit formulations of the bihamiltonian structures for the discrete models, and field-theoretical realizations of these structures. We discuss the relevance of these realizations as collective-field theory for the discrete models.Comment: 15 pages, no figures; v2 references added, typos correcte

A Model of the Cellular Iron Homeostasis Network Using Semi-Formal Methods for Parameter Space Exploration

This paper presents a novel framework for the modeling of biological networks. It makes use of recent tools analyzing the robust satisfaction of properties of (hybrid) dynamical systems. The main challenge of this approach as applied to biological systems is to get access to the relevant parameter sets despite gaps in the available knowledge. An initial estimate of useful parameters was sought by formalizing the known behavior of the biological network in the STL logic using the tool Breach. Then, once a set of parameter values consistent with known biological properties was found, we tried to locally expand it into the largest possible valid region. We applied this methodology in an effort to model and better understand the complex network regulating iron homeostasis in mammalian cells. This system plays an important role in many biological functions, including erythropoiesis, resistance against infections, and proliferation of cancer cells.Comment: In Proceedings HSB 2012, arXiv:1208.315

Discrete bands of petroleum hydrocarbons and molecular organic markers identified within massive coral skeletons

The tissues of corals deposit an aragonite exoskeleton beneath their outer living film at a rate dependent on growth and hence on environmental conditions. This typically results in annual (seasonal) bands being formed within colonies. By analysing molecular organic markers within these bands, our research suggests that coral skeletons record contamination from oil and potentially could be used to investigate other anthropogenic and biogenic organic inputs. Our analyses of sections from within corals (Porites lutea) sampled from the Gulf coasts of Kuwait and Saudi Arabia demonstrate discrete bands of oil contamination which, using selected terpenoid biomarkers, can be source-indexed to specific oil fields (i.e. Kuwait, Iranian or Arabian crude oils). Together with dating using microscopic and X-ray inspection, this offers the potential to investigate contamination during recent years. Further research is, however, necessary to elucidate degradation mechanisms during, and following, the occlusion process of organics within coral skeletons

A new dynamical reflection algebra and related quantum integrable systems

We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang-Baxter equations, coactions, fusions, and commuting traces are derived. Explicit examples are given and quantum integrable Hamiltonians are constructed. They exhibit features similar to the Ruijsenaars-Schneider Hamiltonians.Comment: 16 pages v2: signs in the classical reflection algebra correcte

Developmental perspectives on interpersonal affective touch

In the last decade, philosophy, neuroscience and psychology alike have paid increasing attention to the study of interpersonal affective touch, which refers to the emotional and motivational facets of tactile sensation. Some aspects of affective touch have been linked to a neurophysiologically specialised system, namely the C tactile (CT) system. While the role of this sys-tem for affiliation, social bonding and communication of emotions have been widely investigated, only recently researchers have started to focus on the potential role of interpersonal affective touch in acquiring awareness of the body as our own, i.e. as belonging to our psychological ‘self’. We review and discuss recent developmental and adult findings, pointing to the central role of interpersonal affective touch in body awareness and social cognition in health and disorders. We propose that interpersonal affective touch, as an interoceptive modality invested of a social nature, can uniquely contribute to the ongoing debate in philosophy about the primacy of the relational nature of the minimal self

Some remarks on blueprints and F1{\pmb {{\mathbb {F}}}_1}-schemes

Over the past two decades several different approaches to defining a geometry over F-1 have been proposed. In this paper, relying on Toen and Vaquies formalism (J.K-Theory 3: 437-500, 2009), we investigate a new category Sch((B) over tilde) of schemes admitting a Zariski cover by affine schemes relative to the category of blueprints introduced by Lorscheid (Adv. Math. 229: 1804-1846, 2012). A blueprint, which may be thought of as a pair consisting of a monoid M and a relation on the semiring M circle times(F1), N, is a monoid object in a certain symmetric monoidal category B, which is shown to be complete, cocomplete, and closed. We prove that every B-scheme Sigma can be associated, through adjunctions, with both a classical scheme Ez and a scheme (Sigma) under bar over F-1 in the sense of Deitmar (in van der Geer G., Moonen B., Schoof R. (eds.) Progress in mathematics 239, Birkhauser, Boston, 87-100, 2005), together with a natural transformation Lambda : Sigma(Z) -> (Sigma) under bar circle times(F1) Z. Furthermore, as an application, we show that the category of "F-1-schemes" defined by Connes and Consani in (Compos. Math. 146: 1383-1415, 2010) can be naturally merged with that of (B) over tilde -schemes to obtain a larger category, whose objects we call "F-1-schemes with relations"

Some remarks on blueprints and mathbfF1mathbf{F}_1-schemes

Over the past two decades several different approaches to defining a geometry over F-1 have been proposed. In this paper, relying on Toen and Vaquies formalism (J.K-Theory 3: 437-500, 2009), we investigate a new category Sch((B) over tilde) of schemes admitting a Zariski cover by affine schemes relative to the category of blueprints introduced by Lorscheid (Adv. Math. 229: 1804-1846, 2012). A blueprint, which may be thought of as a pair consisting of a monoid M and a relation on the semiring M circle times(F1), N, is a monoid object in a certain symmetric monoidal category B, which is shown to be complete, cocomplete, and closed. We prove that every B-scheme Sigma can be associated, through adjunctions, with both a classical scheme Ez and a scheme (Sigma) under bar over F-1 in the sense of Deitmar (in van der Geer G., Moonen B., Schoof R. (eds.) Progress in mathematics 239, Birkhauser, Boston, 87-100, 2005), together with a natural transformation Lambda : Sigma(Z) -> (Sigma) under bar circle times(F1) Z. Furthermore, as an application, we show that the category of "F-1-schemes" defined by Connes and Consani in (Compos. Math. 146: 1383-1415, 2010) can be naturally merged with that of (B) over tilde -schemes to obtain a larger category, whose objects we call "F-1-schemes with relations"

A millisecond coarse-grained simulation approach to decipher allosteric cannabinoid binding at the glycine receptor α1

International audienceGlycine receptors (GlyR) are regulated by small-molecule binding at several allosteric sites. Cannabinoids like tetrahydrocannabinol (THC) and N-arachidonyl-ethanol-amide (AEA) potentiate the GlyR response but their mechanism of action is not fully established. By combining millisecond coarse-grained (CG) MD simulations powered by Martini 3 with backmapping to all-atom representations, we have characterized the cannabinoid-binding site(s) at the zebrafish GlyR-α1 active state with atomic resolution. Based on hundreds of thousand ligand-binding events, we find that cannabinoids bind to the transmembrane domain of the receptor at both intrasubunit and intersubunit sites. For THC, the intrasubunit binding mode predicted in simulation is in excellent agreement with recent cryo-EM structures, while intersubunit binding recapitulates in full previous mutagenesis experiments. Intriguingly, AEA is predicted to bind at the same intersubunit site despite the strikingly different chemistry. Statistical analyses of the ligand-receptor interactions highlight potentially relevant residues for GlyR potentiation, offering experimentally testable predictions. The predictions for AEA have been validated by electrophysiology recordings of rationally designed mutants. The results highlight the existence of multiple cannabinoid-binding sites for the allosteric regulation of GlyR and put forward an effective strategy for the identification and structural characterization of allosteric binding sites