Universal R-matrices for generalized Jordanian r-matrices

Quantization of classical integrable models by the Quantum Inverse Scattering Method requires transition from classical r -matrices to the quantum ones. The twists are the special elements in the algebra of observables, which help to build new classical and quantum r -matrices. In this thesis we develop an approach to explicit derivation of quasiclassical twists for higher dimensional analogs of Jordanian r -matrices. The twists are obtained as limits of more general quantum twists which allow a simple description. The considered class of r -matrices includes the skew-symmetric Cremmer-Gervais r -matrices as well as the extended Jordanian ones. The quantum analogs for both twists are obtained

Bethe ansatz for the deformed Gaudin model

A deformation of the sl(2) Gaudin model by a Jordanian r-matrix depending on the spectral parameter is constructed. The energy spectrum is preserved and recurrent creation operators are proposed

Ex2^2MCMC: Sampling through Exploration Exploitation

We develop an Explore-Exploit Markov chain Monte Carlo algorithm ($\operatorname{Ex^2MCMC}$) that combines multiple global proposals and local moves. The proposed method is massively parallelizable and extremely computationally efficient. We prove $V$-uniform geometric ergodicity of $\operatorname{Ex^2MCMC}$ under realistic conditions and compute explicit bounds on the mixing rate showing the improvement brought by the multiple global moves. We show that $\operatorname{Ex^2MCMC}$ allows fine-tuning of exploitation (local moves) and exploration (global moves) via a novel approach to proposing dependent global moves. Finally, we develop an adaptive scheme, $\operatorname{FlEx^2MCMC}$, that learns the distribution of global moves using normalizing flows. We illustrate the efficiency of $\operatorname{Ex^2MCMC}$ and its adaptive versions on many classical sampling benchmarks. We also show that these algorithms improve the quality of sampling GANs as energy-based models

One-dimensional Particle Processes with Acceleration/Braking Asymmetry

The slow-to-start mechanism is known to play an important role in the particular shape of the Fundamental diagram of traffic and to be associated to hysteresis effects of traffic flow.We study this question in the context of exclusion and queueing processes,by including an asymmetry between deceleration and acceleration in the formulation of these processes. For exclusions processes, this corresponds to a multi-class process with transition asymmetry between different speed levels, while for queueing processes we consider non-reversible stochastic dependency of the service rate w.r.t the number of clients. The relationship between these 2 families of models is analyzed on the ring geometry, along with their steady state properties. Spatial condensation phenomena and metastability is observed, depending on the level of the aforementioned asymmetry. In addition we provide a large deviation formulation of the fundamental diagram (FD) which includes the level of fluctuations, in the canonical ensemble when the stationary state is expressed as a product form of such generalized queues.Comment: 28 pages, 8 figure

Production of He-4 and (4) in Pb-Pb collisions at root(NN)-N-S=2.76 TeV at the LHC

Results on the production of He-4 and (4) nuclei in Pb-Pb collisions at root(NN)-N-S = 2.76 TeV in the rapidity range vertical bar y vertical bar <1, using the ALICE detector, are presented in this paper. The rapidity densities corresponding to 0-10% central events are found to be dN/dy4(He) = (0.8 +/- 0.4 (stat) +/- 0.3 (syst)) x 10(-6) and dN/dy4 = (1.1 +/- 0.4 (stat) +/- 0.2 (syst)) x 10(-6), respectively. This is in agreement with the statistical thermal model expectation assuming the same chemical freeze-out temperature (T-chem = 156 MeV) as for light hadrons. The measured ratio of (4)/He-4 is 1.4 +/- 0.8 (stat) +/- 0.5 (syst). (C) 2018 Published by Elsevier B.V.Peer reviewe

Exactly Solvable Stochastic Processes for Traffic Modelling

We investigate different available methods in the study of exactly solvable stochastic models and their application to the construction of models with acceleration/deceleration dynamics relevant to the road traffic modelling. We consider two family of models: one consisting in multi-speed exclusion processes with acceleration/braking transitions preserving pairwise neighbours locality; a second family of models consisting of tandem queues, with rates coupled dynamically to the flow of clients and enabling for a spontaneous hysteresis mechanism between acceleration and braking phases along the flow.Nous passons en revue différentes méthodes dans l'étude des processus stochastiques exactement solubles, et leur application à la construction de modèles contenant une dynamique d'accélération/décélération cruciale dans la modélisation du traffic routier. Nous considérons deux familles de modèles: la première consiste en des processus d'exclusion à plusieurs types de particules avec des transitions d'accélérations/décélérations préservant la localité de voisinage imédiat de la dynamique stochastique; la seconde consiste en des systèmes de files d'attente assemblées en tandem, dont les taux de service sont couplés dynamiquement au flot des clients, permettant ainsi la mise en place spontannée d'un méchanisme d'hystéresis entre la phase d'accélération et de décélaration le long du flot