Local models for Galois deformation rings and applications

We construct projective varieties in mixed characteristic whose singularities model, in generic cases, those of tamely potentially crystalline Galois deformation rings for unramified extensions of $\mathbb{Q}_p$ with small regular Hodge-Tate weights. We establish several significant facts about their geometry including a unibranch property at special points and a representation theoretic description of the irreducible components of their special fibers. We derive from these geometric results a number of local and global consequences: the Breuil-M\'ezard conjecture in arbitrary dimension for tamely potentially crystalline deformation rings with small Hodge-Tate weights (with appropriate genericity conditions), the weight part of Serre's conjecture for $U(n)$ as formulated by Herzig (for global Galois representations which satisfy the Taylor-Wiles hypotheses and are sufficiently generic at $p$), and an unconditional formulation of the weight part of Serre's conjecture for wildly ramified representations

Metastability of Asymptotically Well-Behaved Potential Games

One of the main criticisms to game theory concerns the assumption of full rationality. Logit dynamics is a decentralized algorithm in which a level of irrationality (a.k.a. "noise") is introduced in players' behavior. In this context, the solution concept of interest becomes the logit equilibrium, as opposed to Nash equilibria. Logit equilibria are distributions over strategy profiles that possess several nice properties, including existence and uniqueness. However, there are games in which their computation may take time exponential in the number of players. We therefore look at an approximate version of logit equilibria, called metastable distributions, introduced by Auletta et al. [SODA 2012]. These are distributions that remain stable (i.e., players do not go too far from it) for a super-polynomial number of steps (rather than forever, as for logit equilibria). The hope is that these distributions exist and can be reached quickly by logit dynamics. We identify a class of potential games, called asymptotically well-behaved, for which the behavior of the logit dynamics is not chaotic as the number of players increases so to guarantee meaningful asymptotic results. We prove that any such game admits distributions which are metastable no matter the level of noise present in the system, and the starting profile of the dynamics. These distributions can be quickly reached if the rationality level is not too big when compared to the inverse of the maximum difference in potential. Our proofs build on results which may be of independent interest, including some spectral characterizations of the transition matrix defined by logit dynamics for generic games and the relationship of several convergence measures for Markov chains

Effect of alloying on mechanical properties of as cast ferritic nodular cast irons

The development of low temperature applications for ferritic nodular cast irons calls for improved materials in the as cast state, e.g. for off-shore windmills components. Within this line of work, a series of 68 castings were prepared with the same casting procedure and slight changes in composition. The tensile properties at room temperature, as well as the impact energy for rupture at room temperature, 220 °C and 240 °C, were measured. Outputs from multivariate analysis performed on the data are then discussed and compared to literature results, putting emphasis on the properties of the ferritic matrix

Entanglement Entropy, decoherence, and quantum phase transition of a dissipative two-level system

The concept of entanglement entropy appears in multiple contexts, from black hole physics to quantum information theory, where it measures the entanglement of quantum states. We investigate the entanglement entropy in a simple model, the spin-boson model, which describes a qubit (two-level system) interacting with a collection of harmonic oscillators that models the environment responsible for decoherence and dissipation. The entanglement entropy allows to make a precise unification between entanglement of the spin with its environment, decoherence, and quantum phase transitions. We derive exact analytical results which are confirmed by Numerical Renormalization Group arguments both for an ohmic and a subohmic bosonic bath. Those demonstrate that the entanglement entropy obeys universal scalings. We make comparisons with entanglement properties in the quantum Ising model and in the Dicke model. We also emphasize the possibility of measuring this entanglement entropy using charge qubits subject to electromagnetic noise; such measurements would provide an empirical proof of the existence of entanglement entropy.Comment: 38 pages, 8 figures, related to cond-mat/0612095 and arXiv:0705.0957; final version to appear in Annals of Physic

Vector Competence of the Tick Ixodes ricinus for Transmission of Bartonella birtlesii

Bartonella spp. are facultative intracellular vector-borne bacteria associated with several emerging diseases in humans and animals all over the world. The potential for involvement of ticks in transmission of Bartonella spp. has been heartily debated for many years. However, most of the data supporting bartonellae transmission by ticks come from molecular and serological epidemiological surveys in humans and animals providing only indirect evidences without a direct proof of tick vector competence for transmission of bartonellae. We used a murine model to assess the vector competence of Ixodes ricinus for Bartonella birtlesii. Larval and nymphal I. ricinus were fed on a B. birtlesii-infected mouse. The nymphs successfully transmitted B. birtlesii to naïve mice as bacteria were recovered from both the mouse blood and liver at seven and 16 days after tick bites. The female adults successfully emitted the bacteria into uninfected blood after three or more days of tick attachment, when fed via membrane feeding system. Histochemical staining showed the presence of bacteria in salivary glands and muscle tissues of partially engorged adult ticks, which had molted from the infected nymphs. These results confirm the vector competence of I. ricinus for B. birtlesii and represent the first in vivo demonstration of a Bartonella sp. transmission by ticks. Consequently, bartonelloses should be now included in the differential diagnosis for patients exposed to tick bites

Investigating the impact of nicotine on executive functions using a novel virtual reality assessment

Aims Nicotine is known to enhance aspects of cognitive functioning in abstinent smokers but the effects on specific areas of executive functions, and in non-smokers are inconclusive. This may be due in part to the poor sensitivity of tests used to assess executive functions. This study used a new virtual reality assessment of executive functions known as JEF (the Jansari assessment of Executive Functions) to address this issue. Design 2x2 design manipulating group (smokers and never-smokers) and drug (nicotine [4mg for smokers; 2mg for never smokers] vs placebo gum). Setting School of Psychology; University of East LondonParticipants 72 participants (aged 18 to 54). 36 minimally-deprived (2 hr) smokers and 36 never-smokers.Measurements Components of executive function were measured using the virtual reality paradigm JEF, which assesses eight cognitive constructs simultaneously as well as providing an overall performance measure. Results Univariate ANOVAs revealed that nicotine improved overall JEF performance, time-based prospective memory and event-based prospective memory in smokers (p < 0.01) but not in never-smokers. Action-based prospective memory was enhanced in both groups (p < 0.01) and never-smokers out-performed smokers on selective thinking and adaptive thinking (p < 0.01). Conclusions. Overall executive functioning and prospective memory can be enhanced by nicotine gum in abstinent smokers. That smokers were only minimally deprived suggests that JEFis a sensitive measure of executive functioning and that prospective memory is particularly susceptible to disruption by abstinence

The rovibrational spectrum of BeH, MgH and CaH at high temperatures in the X 2Σ+X\,{}^2\Sigma^+ state: a theoretical study

Accurate line lists for three molecules, BeH, MgH and CaH, in their ground electronic states are presented. These line lists are suitable for temperatures relevant to exoplanetary atmospheres and cool stars (up to 2000K). A combination of empirical and \textit{ab initio} methods is used. The rovibrational energy levels of BeH, MgH and CaH are computed using the programs Level and DPotFit in conjunction with `spectroscopic' potential energy curves (PECs). The PEC of BeH is taken from the literature, while the PECs of CaH and MgH are generated by fitting to the experimental transition energy levels. Both spin-rotation interactions (except for BeH, for which it is negligible) and non-adiabatic corrections are explicitly taken into account. Accurate line intensities are generated using newly computed \textit{ab initio} dipole moment curves for each molecule using high levels of theory. Full line lists of rotation-vibration transitions for $^9$BeH, $^{24}$MgH, $^{25}$MgH, $^{26}$MgH and $^{40}$CaH are made available in an electronic form as supplementary data to this article and at \url{www.exomol.com}.Comment: MNRAS (in press

Programmability of Chemical Reaction Networks

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior