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Transfers of material by a water flow are simulated using different models, owing for the various processes involved. This gave rise to the development of numerous models (and associated computer codes). This diversity may be apparent only: because models are being used in different fields of hydrology and because they are written in different ways, they look different but could, indeed, be identical. A set of equations, termed transfer equations, is proposed to model various transfers of materials between the soil and surface water through an exchange layer. Its implementation in the open-source software FullSWOF 1D is verified against the approximation of an exact solution, assuring its proper functioning. Subsequent results show that the transfer equations can represent independently-published models in scientific issues as different as soil erosion , river bedload, and chemical transport. Hence, the transfer equations are a unifying transfer model, allowing various processes to be represented by a single model and to simulate the fate of both particles and chemicals using a single computer code. The use of the unifying transfer equations will decrease the number of models to be used, and will help to limit the number of computer codes to be developed. They will also help in drawing parallels between different fields of hydrology.

We argue that the enhancement in the spin polarization of anti-hyperons compared to the polarization of the hyperons in noncentral relativistic heavy-ion collisions arises as a result of an interplay between the chiral and helical vortical effects. The chiral vortical effect generates the axial current of quarks along the vorticity axis while the recently found helical vortical effect generates the helicity flow -- the projection of the quark's polarization vector onto its momentum -- along the same axis. For massless fermions, the helical charge corresponds to a difference in the contributions of particles and anti-particles to the axial charge. Assuming that the spin of light quarks transfers to the strange quarks via the vector kaon states ("the spin-vector dominance"), we are able to describe the ratio of the (anti)hyperon spin polarizations, obtained by the STAR group, without fitting parameters. We also argue that the helical vortical effect dominates over the chiral vortical effect and the chiral magnetic effect in the generation of the electric current., Comment: 9 pages, 3 figures; v2: discussions expanded, chiral magnetic effect and helical vortical effect are compared

We consider a recurrent random walk on a rooted tree in random environment given by a branching random walk. Up to the first return to the root, its edge local times form a Multi-type Galton-Watson tree with countably infinitely many types. When the walk is the diffusive or sub-diffusive, by studying the maximal type of this Galton-Watson tree, we establish the asymptotic behaviour of the largest local times of this walk during n excursions, under the annealed law., Comment: 61 pages, 18 ref

The set of finite binary matrices of a given size is known to carry a finite type A bicrystal structure. We first review this classical construction, explain how it yields a short proof of the equality between Kostka polynomials and one-dimensional sums together with a natural generalisation of the 2M -- X Pitman transform. Next, we show that, once the relevant formalism on families of infinite binary matrices is introduced, this is a particular case of a much more general phenomenon. Each such family of matrices is proved to be endowed with Kac-Moody bicrystal and tricrystal structures defined from the classical root systems. Moreover, we give an explicit decomposition of these multicrystals, reminiscent of the decomposition of characters yielding the Cauchy identities., Comment: 37 pages, 44 ref

International audience; We give an invariance principle for very general additive functionals of conditioned Bienaymé-Galton-Watson trees in the global regime when the offspring distribution lies in the domain of attraction of a stable distribution, the limit being an additive functional of a stable Lévy tree. This includes the case when the offspring distribution has finite variance (the Lévy tree being then the Brownian tree). We also describe, using an integral test, a phase transition for toll functions depending on the size and height.

We investigate the advantages of machine learning techniques to recognize the dynamics of topological objects in quantum field theories. We consider the compact U(1) gauge theory in three spacetime dimensions as the simplest example of a theory that exhibits confinement and mass gap phenomena generated by monopoles. We train a neural network with a generated set of monopole configurations to distinguish between confinement and deconfinement phases, from which it is possible to determine the deconfinement transition point and to predict several observables. The model uses a supervised learning approach and treats the monopole configurations as three-dimensional images (holograms). We show that the model can determine the transition temperature with accuracy, which depends on the criteria implemented in the algorithm. More importantly, we train the neural network with configurations from a single lattice size before making predictions for configurations from other lattice sizes, from which a reliable estimation of the critical temperatures are obtained., Comment: 15 pages, 36 figures; minor revisions, published version

Vacuum fluctuations of quantum fields between physical objects depend on the shapes, positions, and internal composition of the latter. For objects of arbitrary shapes, even made from idealized materials, the calculation of the associated zero-point (Casimir) energy is an analytically intractable challenge. We propose a new numerical approach to this problem based on machine-learning techniques and illustrate the effectiveness of the method in a (2+1) dimensional scalar field theory. The Casimir energy is first calculated numerically using a Monte-Carlo algorithm for a set of the Dirichlet boundaries of various shapes. Then, a neural network is trained to compute this energy given the Dirichlet domain, treating the latter as black-and-white pixelated images. We show that after the learning phase, the neural network is able to quickly predict the Casimir energy for new boundaries of general shapes with reasonable accuracy., 7 pages, 4 figures; minor changes, published version

The dual space of the Cartan subalgebra in a Kac-Moody algebra has a partial ordering defined by the rule that two elements are related if and only if their difference is a non-negative or non-positive integer linear combination of simple roots. In this paper, we study the subposet formed by dominant weights in affine Kac-Moody algebras. We give a more explicit description of the covering relations in this poset. We also study the structure of basic cells in this poset of dominant weights for untwisted affine Kac-Moody algebras of type A., 16 pages

We study properties of positive functions satisfying (E) --$��$u + u p -- M |$\nabla$u| q = 0 is a domain $��$ or in R N + when p > 1 and 1 < q < min{p, 2}. We concentrate our research on the solutions of (E) vanishing on the boundary except at one point. This analysis depends on the existence of separable solutions in R N +. We consruct various types of positive solutions with an isolated singularity on the boundary. We also study conditions for the removability of compact boundary sets and the Dirichlet problem associated to (E) with a measure for boundary data., 44 pages, 26 ref

We consider two-dimensional stochastic differential equations, describing the motion of a slowly and periodically forced overdamped particle in a double-well potential, subjected to weak additive noise. We give sharp asymptotics of Eyring-Kramers type for the expected transition time from one potential well to the other one. Our results cover a range of forcing frequencies that are large with respect to the maximal transition rate between potential wells of the unforced system. The main difficulty of the analysis is that the forced system is non-reversible, so that standard methods from potential theory used to obtain Eyring-Kramers laws for reversible diffusions do not apply. Instead, we use results by Landim, Mariani and Seo that extend the potential-theoretic approach to non-reversible systems., 57 pages, 6 figures. Revised version

Entanglement in finite and semi-infinite free Fermionic chains is studied. A parallel is drawn with the analysis of time and band limiting in signal processing. It is shown that a tridiagonal matrix commuting with the entanglement Hamiltonian can be found using the algebraic Heun operator construct in instances when there is an underlying bispectral problem. Cases corresponding to the Lie algebras $\mathfrak{su}(2)$ and $\mathfrak{su}(1,1)$ as well as to the q-deformed algebra $\mathfrak{so}_q(3)$ at $q$ a root of unity are presented.

We show that the nonlocal two-flavor Nambu--Jona-Lasinio model predicts the enhancement of both chiral and axial symmetry breaking as the chiral imbalance of hot QCD matter, regulated by a chiral chemical potential $\mu_5$, increases. The two crossovers are reasonably close to each other in the range of $\mu_5$ examined here and the pseudocritical temperatures rise with $\mu_5$. The curvatures of the chiral and axial crossovers for the chiral quark chemical potential approximately coincide and give $\kappa_5 \simeq - 0.011$. We point out that the presence of $\mu_5$ in thermodynamic equilibrium is inconsistent with the fact that the chiral charge is not a Noether-conserved quantity for massive fermions. The chiral chemical potential should not, therefore, be considered as a true chemical potential that sets a thermodynamically stable environment in the massive theory, but rather than as a new coupling that may require a renormalization in the ultraviolet domain. The divergence of an unrenormalized chiral density, \corr{coming from zero-point fermionic fluctuations,} is a consequence of this property. We propose a solution to this problem via a renormalization procedure., Comment: 15 pages, 5 figures

We review the fate of the Ostrogradsky ghost in higher-order theories. We start by recalling the original Ostrogradsky theorem and illustrate, in the context of classical mechanics, how higher-derivatives Lagrangians lead to unbounded Hamiltonians and then lead to (classical and quantum) instabilities. Then, we extend the Ostrogradsky theorem to higher-derivatives theories of several dynamical variables and show the possibility to evade the Ostrogradsky instability when the Lagrangian is "degenerate", still in the context of classical mechanics. In particular, we explain why higher-derivatives Lagrangians and/or higher-derivatives Euler-Lagrange equations do not necessarily lead to the propagation of an Ostrogradsky ghost. We also study some quantum aspects and illustrate how the Ostrogradsky instability shows up at the quantum level. Finally, we generalize our analysis to the case of higher order covariant theories where, as the Hamiltonian is vanishing and thus bounded, the question of Ostrogradsky instabilities is subtler., 30 pages, 2 figures; few typos corrected

25 pages, 16 ref.; International audience; In the spirit of the Schur-Weyl duality, we study the connections between the Racah algebra and the centralizers of tensor products of three (possibly different) irreducible representations of su(2). As a first step we show that the Racah algebra always surjects onto the centralizer. We then offer a conjecture regarding the description of the kernel of the map, which depends on the irreducible representations. If true, this conjecture would provide a presentation of the centralizer as a quotient of the Racah algebra. We prove this conjecture in several cases. In particular, while doing so, we explicitly obtain the Temperley-Lieb algebra, the Brauer algebra and the one-boundary Temperley-Lieb algebra as quotients of the Racah algebra.

Let (Z n) n≥0 with Z n = (Z n (i, j)) 1≤i,j≤p be a p multi-type critical branching process in random environment, and let M n be the expectation of Z n given a fixed environment. We prove theorems on convergence in distribution of sequences of branching processes Zn |Mn| /|Z n | > 0 and ln Zn √ n /|Z n | > 0. These theorems extend similar results for single-type critical branching process in random environment.; Soit (Z n) n≥0 , avec Z n = (Z n (i, j)) 1≤i,j≤p, un processus de branchement multi-type et critique en environnement aléatoire. Soit M n la matrice moyenne de Z n à environnement fixé. Nous démontrons des théorèmes de convergence en distribution des suites (Zn/ |Mn| ) et ( Zn /√ n) conditionnellement à la non extinction (|Z n | > 0). Ces théorèmes étendent dans le cadre multi-type des résultats antérieurs connus pour des processus uni-type.

52 pages, 22 ref.; We present in this paper the algebra of fused permutations and its deformation the fused Hecke algebra. The first one is defined on a set of combinatorial objects that we call fused permutations, and its deformation on a set of topological objects that we call fused braids. We use these algebras to prove a Schur-Weyl duality theorem for any tensor products of any symmetrised powers of the natural representation of U q (gl N). Then we proceed to the study of the fused Hecke algebras and in particular, we describe explicitely the irreducible representations and the branching rules. Finally, we aim to an algebraic description of the centralisers of the tensor products of U q (gl N)-representations under consideration. We exhibit a simple explicit element that we conjecture to generate the kernel from the fused Hecke algebra to the centraliser. We prove this conjecture in some cases and in particular, we obtain a description of the centraliser of any tensor products of any finite-dimensional representations of U q (sl 2).

46 pages, 30 ref.; International audience; We characterize braided commutative Yetter-Drinfeld C *-algebras over weak Hopf C *-algebras in categorical terms. Using this, we then study quotient type coideal subalgebras of a given weak Hopf C *-algebra G and coideal subalgebras invariant with respect to the adjoint action of G. Finally, as an example, we explicitly describe quotient type coideal subalgebras of the weak Hopf C *-algebras associated with Tambara-Yamagami categories.

23 pages, 3 figures, 27 ref.; The submonoid of the $3$-strand braid group $\mathcal{B}_3$ generated by $\sigma_1$ and $\sigma_1 \sigma_2$ is known to yield an exotic Garside structure on $\mathcal{B}_3$. We introduce and study an infinite family $(M_n)_{n\geq 1}$ of Garside monoids generalizing this exotic Garside structure, i.e., such that $M_2$ is isomorphic to the above monoid. The corresponding Garside group $\mathcal{G}_n$ is an extension of the $(n+1)$-strand braid group, isomorphic to $\mathcal{B}_3$ when $n=2$ and to the complex braid group of the complex reflection group $G_{12}$ when $n=3$. In general, the Garside monoid $M_n$ sujects onto the submonoid $\Sigma_n$ of $\mathcal{B}_{n+1}$ generated by $\sigma_1, \sigma_1 \sigma_2, \dots, \sigma_1 \sigma_2\cdots \sigma_n$, which is not a Garside monoid when $n>2$. Using a new presentation of $\mathcal{B}_{n+1}$ similar to the presentation of $\mathcal{G}_n$, we nevertheless check that $\Sigma_n$ is an Ore monoid with group of fractions isomorphic to $\mathcal{B}_{n+1}$, and give a conjectural presentation of it. We also show that the groups $\mathcal{G}_n$ are isomorphic to groups defined by a cyclic relation; such groups were shown to be Garside groups by Dehornoy and Paris. As a byproduct the monoid $M_n$ yields a new Garside structure for these groups.

We consider a macroscopic two-phase transition model for vehicular traffic flow subject to a point constraint on the density flux. The two phases correspond to light and heavy traffic and their dynamics are described respectively by the Lighthill-Whitham-Richards model and the Aw-Rascle-Zhang model. Their intersection, the so-called metastable phase, is assumed to be non empty. In order to guarantee the control of total variation of solutions, the t-dependent function prescribing the level of the constraint should be piecewise constant. It can be given a priori or it can be computed in a time-discrete way from the solution itself, thus giving rise to nonlocal phase transition models with point constraint in the spirit of LWR-based models described in Andreianov, Donadello, Razafison, Rosini, JMPA (2018). We introduce a new definition of admissible solutions for the Cauchy problem, for which we prove existence and we provide a characterization. In particular, these admissible solutions attain the maximal flux allowed by the constraint whenever it is enforced, which guarantees compatibility of the constructed solutions with the modeling assumption imposed at the level of the Riemann solver. These results rely on the wave front tracking method and on adaptation of the specific entropies and renormalization properties introduced in Andreainov, Donadello, Rosini, M3AS (2016) while dealing with the ARZ system. 2010 Mathematical Subject Classification. Primary: 35L65, 90B20, 35L45

Let (Z n) n≥0 with Z n = (Z n (i, j)) 1≤i,j≤p be a p multi-type critical branching process in random environment, and let M n be the expectation of Z n given a fixed environment. We prove theorems on convergence in distribution of sequences of branching processes Zn |Mn| /|Z n | > 0 and ln Zn √ n /|Z n | > 0. These theorems extend similar results for single-type critical branching process in random environment.; Soit (Z n) n≥0 , avec Z n = (Z n (i, j)) 1≤i,j≤p, un processus de branchement multi-type et critique en environnement aléatoire. Soit M n la matrice moyenne de Z n à environnement fixé. Nous démontrons des théorèmes de convergence en distribution des suites (Zn/ |Mn| ) et ( Zn /√ n) conditionnellement à la non extinction (|Z n | > 0). Ces théorèmes étendent dans le cadre multi-type des résultats antérieurs connus pour des processus uni-type.

We study the phenomenology of a class of minimally modified gravity theories called $f(\mathcal{H})$ theories, in which the usual general relativistic Hamiltonian constraint is replaced by a free function of it. After reviewing the construction of the theory and a consistent matter coupling, we analyze the dynamics of cosmology at the levels of both background and perturbations, and present a concrete example of the theory with a $3$-parameter family of the function $f$. Finally, we compare this example model to Planck data as well as some later-time probes, showing that such a realization of $f(\mathcal{H})$ theories fits the data significantly better than the standard $\Lambda$CDM model, in particular by modifying gravity at intermediate redshifts, $z\simeq743$., Comment: 21 pages, 10 figures, matches with published version

International audience; Determinantal point processes (DPPs) are probabilistic models of configurations that favour diversity or repulsion. They have recently gained influence in the machine learning community, mainly because of their ability to elegantly and efficiently subsample large sets of data. In this paper, we consider DPPs from an image processing perspective, meaning that the data we want to subsample are pixels or patches of a given image. To this end, our framework is discrete and finite. First, we adapt their basic definition and properties to DPPs defined on the pixels of an image, that we call determinantal pixel processes (DPixPs). We are mainly interested in the repulsion properties of such a process and we apply DPixPs to texture synthesis using shot noise models. Finally, we study DPPs on the set of patches of an image. Because of their repulsive property, DPPs provide a strong tool to subsample discrete distributions such as that of image patches.

20 pages, 12 ref., 9 fig.; A lubrication equation is obtained for a simplified shear-thinning fluid. The simplified rheology consists of a piecewise linear stress tensor, resulting in a two-viscosity model. This can be interpreted as a modified Bingham fluid, which can be recovered in a specific limit. The lubrication equation is obtained in two steps. First two scalings are performed on the incompressible Navier-Stokes equations, namely the long-wave scaling and the slow motion scaling. Second, the resulting equations are averaged along the vertical direction. Numerical illustations are provided, bringing to light the different possible behaviours.

We discuss the influence of a helicity imbalance on the phase diagram of dense QCD at finite temperature. We argue that the helical chemical potential is a thermodynamically relevant quantity in theories with the mass gap generation. Using the linear sigma model coupled to quarks, we show that the presence of the helical density substantially affects the phase diagram of dense quark matter. A moderate helical density makes the chiral phase transition softer while shifting the critical endpoint towards lower temperatures and higher baryon chemical potentials. As the helical density increases, the segment of the first-order transition disappears, and the chiral transition becomes a soft crossover. At even higher helical chemical potentials, the first-order transition reappears again at the zero-density finite-temperature transition and extends into the interior of the phase diagram. This evolution of the chiral transition reflects the existence of a thermodynamic duality between helical and vector (baryonic) chemical potentials. We also show that the presence of the helicity imbalance of quark matter increases the curvature of the chiral pseudocritical line in QCD., 15 pages, 6 figures

We analyze the Chiral Magnetic Effect for non-Hermitian fermionic systems using the biorthogonal formulation of quantum mechanics. In contrast to the Hermitian chiral counterparts, we show that the Chiral Magnetic Effect may take place in thermal equilibrium of an open non-Hermitian system with, generally, massive fermions. The key observation is that for non-Hermitian charged systems, there is no strict charge conservation as understood in the Hermitian case, so the Bloch theorem preventing currents in the thermodynamic limit in equilibrium does not apply., Comment: 14 pages, 3 figures; v2: discussions extended, version accepted for publication

We prove that star-like limit cycles of any planar polynomial system can also be seen either as solutions defined on a given interval of a new associated planar non-autonomous polynomial system or as heteroclinic solutions of a 3-dimensional polynomial system. We illustrate these points of view with several examples. One of the key ideas in our approach is to decompose the periodic solutions as the sum of two suitable functions. As a first application we use these new approaches to prove that all star-like reversible limit cycles are algebraic. As a second application we introduce a function whose zeroes control the periodic orbits that persist as limit cycles when we perturb a star-like reversible center. As far as we know this is the first time that this question is solved in full generality. Somehow, this function plays a similar role that an Abelian integral for studying perturbations of Hamiltonian systems., 20 pages, 1 figure

The Bannai-Ito algebra $BI(n)$ is viewed as the centralizer of the action of $\mathfrak{osp}(1|2)$ in the $n$-fold tensor product of the universal algebra of this Lie superalgebra. The generators of this centralizer are constructed with the help of the universal $R$-matrix of $\mathfrak{osp}(1|2)$. The specific structure of the $\mathfrak{osp}(1|2)$ embeddings to which the centralizing elements are attached as Casimir elements is explained. With the generators defined, the structure relations of $BI(n)$ are derived from those of $BI(3)$ by repeated action of the coproduct and using properties of the $R$-matrix and of the generators of the symmetric group $\mathfrak S_n$.

We propose a non-abelian higher-spin theory in two dimensions for an infinite multiplet of massive scalar fields and infinitely many topological higher-spin gauge fields together with their dilaton-like partners. The spectrum includes local degrees of freedom although the field equations take the form of flatness and covariant constancy conditions because fields take values in a suitable extension of the infinite-dimensional higher-spin algebra $hs[\lambda]$. The corresponding action functional is of BF-type and generalizes the known topological higher-spin Jackiw-Teitelboim gravity., Comment: 15 pages. Main results originally appeared in v1 of arXiv:1911.13212, of which the self-contained section 8 has been extracted and expanded, v2: references and comments added. v3: more detailed abstract, extended discussion of 2d higher-spin dynamics in Introduction, Section 5 now contains more detailed explanation of the spectrum, references and acknowledgements added. Journal version

The Askey–Wilson algebra is realized in terms of the elements of the quantum algebras [Formula: see text] or [Formula: see text]. A new realization of the Racah algebra in terms of the Lie algebras [Formula: see text] or [Formula: see text] is also given. Details for different specializations are provided. The advantage of these new realizations is that one generator of the Askey–Wilson (or Racah) algebra becomes diagonal in the usual representation of the quantum algebras whereas the second one is tridiagonal. This allows us to recover easily the recurrence relations of the associated orthogonal polynomials of the Askey scheme. These realizations involve rational functions of the Cartan generator of the quantum algebras, where they are linear with respect to the other generators and depend on the Casimir element of the quantum algebras.

We provide a lattice regularization of all topological defects in minimal models CFTs using RSOS and anyonic spin chains. For defects of type $(1,s)$, we connect our result with the "topological symmetry" initially identified in Fibonacci anyons [Phys. Rev. Lett. 98, 160409 (2007)], and the center of the affine Temperley-Lieb algebra discussed in [1811.02551]. We show that the topological nature of the defects is exact on the lattice as well. Our defects of type $(r,1)$, in contrast, are only topological in the continuum limit. Identifications are obtained by a mix of algebraic and Bethe-ansatz techniques. Most of our discussion is framed in a Hamiltonian (or transfer matrix) formalism, and direct and crossed channel are both discussed in detail. For defects of type $(1,s)$, we also show how to implement their fusion, which turns out to reproduce the tensor product of the underlying monoidal category used to build the anyonic chain., 42 pages, 4 figures

International audience; The lifespan of refractory results from a complex interaction between chemistry, thermal conditions, and mechanics. The development of numerical models able to predict the results of such complex multi-physics couplings requires an intensive use of the thermodynamics of irreversible processes framework. Today, the main barriers to reach fully predictive simulations are: the access to relevant data at high temperature (chemical kinetics, chemical expansion coefficient, etc), the numerical complexity and the computational time. The theoretical framework is briefly illustrated on refractory lining applications with a focus on the impact of the swelling induced by corrosion. Then, the numerical difficulties to ensure the numerical convergence and the accuracy of the results when solving classical partial differential equations are examined. Finally, a new approach to model the capillary impregnation by slag, based on percolation theory, is proposed. The basics of this method and the first numerical results are presented.

We contribute an answer to the question raised in [Coron, Contemp. Math 2007] concerning the controllability, in the framework of L^2 solutions, of the viscous Burgers equation u_t +(u 2 /2)_x = u_xx for initial and terminal data prescribed for x ∈ (0, 1). In contrast to typical techniques on the controllability of the viscous Burgers equation invoking the heat equation, we combine scaling and compensated compactness arguments along with observations on the non-controllability of the inviscid Burgers equation to point out wide sets of terminal states non-attainable from zero initial data by solutions of restricted size. We prove in particular that, given L ≥ 1, for sufficiently large |C| and T < (1 + ∆)/|C| (where ∆ > 0 depends on L), the constant terminal state u(·, T) := C is not attainable at time T , starting from zero data, by weak solutions of the viscous Burgers equation satisfying an a priori bound of the form ||u||_∞ ≤ L|C|. Further, in order to get closer to the original question we develop a basic well-posedness theory of unbounded entropy solutions to the Cauchy problem for multi-dimensional scalar conservation laws with pure L p data and polynomial growth up to the critical power p of the flux function. The case of the Cauchy-Dirichlet problem for the Burgers equation on an interval is also addressed, in the L^2 solution framework which is considerably simpler than the established L^1 theory of renor-malized solutions to such problems. Local regularity of unbounded entropy solutions is discussed in the one-dimensional case with convex flux. Non-controllability results are then extended to solutions of the viscous Burgers equation in the L^2 setting, under the a priori bound ||u||_2 ≤ LT |C| and an L^2 − L^3_loc regularization assumption.

We study the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary. We derive a local limit theorem in the fluctuation regime., Comment: 37 pages, 2 figures. The previous version of this article (arXiv:1803.09253V2) has been split into two parts: the first part is the new version (arXiv:1803.09253v3) and the second will be part of a joint article with Jetlir Duraj and Vitali Wachtel (to appear soon on arXiv)

Classical Hamiltonian systems with conserved charges and those with constraints often describe dynamics on a pre-symplectic manifold. Here we show that a pre-symplectic manifold is also the proper stage to describe autonomous energy conserving Hamiltonian time crystals. We explain how the occurrence of a time crystal relates to the wider concept of spontaneously broken symmetries; in the case of a time crystal, the symmetry breaking takes place in a dynamical context. We then analyze in detail two examples of time crystalline Hamiltonian dynamics. The first example is a piecewise linear closed string, with dynamics determined by a Lie-Poisson bracket and Hamiltonian that relates to membrane stability. We explain how the Lie-Poisson brackets descents to a time crystalline pre-symplectic bracket, and we show that the Hamiltonian dynamics supports two phases; in one phase we have a time crystal and in the other phase time crystals are absent. The second example is a discrete Hamiltonian variant of the Q-ball Lagrangian of time dependent non-topological solitons. We explain how a Q-ball becomes a time crystal, and we construct examples of time crystalline Q-balls., Comment: 17 pages 4 figures

Let $W_0$ be a reflection subgroup of a finite complex reflection group $W$, and let $B_0$ and $B$ be their respective braid groups. In order to construct a Hecke algebra $\widetilde{H}_0$ for the normalizer $N_W(W_0)$, one first considers a natural subquotient $\widetilde{B}_0$ of $B$ which is an extension of $N_W(W_0)/W_0$ by $B_0$. We prove that this extension is split when $W$ is a Coxeter group, and deduce a standard basis for the Hecke algebra $\widetilde{H}_0$. We also give classes of both split and non-split examples in the non-Coxeter case., 22 pages. To appear in Annales de l'Institut Fourier

Ecological community structure, persistence and stability are shaped by multiple forces, acting on multiple scales. These include patterns of resource use and limitation, spatial heterogeneities, drift and migration. Pathogen strains co-circulating in a host population are a special type of an ecological community. They compete for colonization of susceptible hosts, and sometimes interact via altered susceptibilities to co-colonization. Diversity in such pairwise interaction traits enables the multiple strains to create dynamically their niches for growth and persistence, and ‘engineer’ their common environment. How such a network of interactions with others mediates collective coexistence remains puzzling analytically and computationally difficult to simulate. Furthermore, the gradients modulating stability-complexity regimes in such multi-player systems remain poorly understood. In a recent study, we presented an analytic framework for N-type coexistence in an SIS epidemiological system with co-colonization interactions. The multi-strain complexity was reduced from O(N2) dimensions of population structure to only N equations for strain frequency evolution on a long timescale. Here, we examine the key drivers of coexistence regimes in such a system. We find the ratio of single to co-colonization μ critically determines the type of equilibrium for multi-strain dynamics. This key quantity in the model encodes a trade-off between overall transmission intensity R0 and mean interaction coefficient in strain space k. Preserving a given coexistence regime, under fixed trait variation, can only be achieved from a balance between higher competition in favourable environments, and higher cooperation in harsher environments, consistent with the stress gradient hypothesis in ecology. Multi-strain coexistence regimes are more stable when μ is small, whereas as μ increases, dynamics tends to increase in complexity. There is an intermediate ratio that maximizes the existence and stability of a unique coexistence equilibrium between strains. This framework provides a foundation for linking invariant principles in collective coexistence across biological systems, and for understanding critical shifts in community dynamics, driven by simple and random pairwise interactions but potentiated by mean-field and environmental gradients.

We use k-Schur functions to get the minimal boundary of the k-bounded partition poset. This permits to describe the central random walks on affine Grassmannian elements of type A and yields a polynomial expression for their drift. We also recover Rietsch's parametriza-tion of totally nonnegative unitriangular Toeplitz matrices without using quantum cohomology of flag varieties. All the homeomorphisms we define can moreover be made explicit by using the combinatorics of k-Schur functions and elementary computations based on Perron-Frobenius theorem., Comments welcome

The Bekenstein-Hawking (BH) entropy is expected to be modified by certain correction terms in the quantum loop expansion. As is well known the logarithmic terms in the entropy of black holes appear as a one-loop addition to the classical BH entropy. In this note we study the further modifications of the logarithmic terms in the entropy of the Schwarzschild black holes due to higher quantum loops: up to three loops in a general renormalizable theory of gauge fields, scalars and fermions and two loops in quantum gravity. For a large class of field multiplets (including that of the Standard Model) that include graviton and for a certain range in the values of the couplings these modifications manifest themselves in cooling down the black holes at later stages of evaporation and, respectively, in increasing the life time of the black hole. If this picture persists to even higher loops, then the small black holes formed in the early stages of the cosmic evolution do not evaporate completely by now as is predicted in the standard picture. Instead, their long-lived (Planckian mass) remnants should present in abundance in today's Universe., Comment: 12 pages; more comments and references added, to appear in Phys. Lett. B

We use modified traces to renormalize Lyubashenko's closed 3-manifold invariants coming from twist non-degenerate finite unimodular ribbon categories. Our construction produces new topological invariants which we upgrade to 2+1-TQFTs under the additional assumption of factorizability. The resulting functors provide monoidal extensions of Lyubashenko's mapping class group representations, as discussed in arXiv:2010.14852. This general framework encompasses important examples of non-semisimple modular categories coming from the representation theory of quasi-Hopf algebras, which were left out of previous non-semisimple TQFT constructions., 49 pages; v3: added pictures and references

We study the notion of partial action of a locally compact groupoid on a C *-algebra. We show that the semidirect product groupoid associated with a partial action of an amenable locally compact groupoid on a locally compact space is an amenable locally compact groupoid.

Given a normal subgroup bundle $\mathcal A$ of the isotropy bundle of a groupoid $\Sigma$, we obtain a twisted action of the quotient groupoid $\Sigma/\mathcal A$ on the bundle of group $C^*$-algebras determined by $\mathcal A$ whose twisted crossed product recovers the groupoid $C^*$-algebra $C^*(\Sigma)$. Restricting to the case where $\mathcal A$ is abelian, we describe $C^*(\Sigma)$ as the $C^*$-algebra associated to a $\mathbf T$-groupoid over the tranformation groupoid obtained from the canonical action of $\Sigma/\mathcal A$ on the Pontryagin dual space of $\mathcal A$. We give some illustrative examples of this result., Comment: 28 Pages. This is a substantially revised version of the original with a new title. Section 4 of the old version will appear separately

For a given dimension d $\ge$ 2 and a finite measure $\nu$ on (0, +$\infty$), we consider $\xi$ a Poisson point process on R d x (0, +$\infty$) with intensity measure dc $\otimes$ $\nu$ where dc denotes the Lebesgue measure on R d. We consider the Boolean model $\Sigma$ = $\cup$ (c,r)$\in$$\xi$ B(c, r) where B(c, r) denotes the open ball centered at c with radius r. For every x, y $\in$ R d we define T (x, y) as the minimum time needed to travel from x to y by a traveler that walks at speed 1 outside $\Sigma$ and at infinite speed inside $\Sigma$. By a standard application of Kingman sub-additive theorem, one easily shows that T (0, x) behaves like $\mu$ x when x goes to infinity, where $\mu$ is a constant named the time constant in classical first passage percolation. In this paper we investigate the regularity of $\mu$ as a function of the measure $\nu$ associated with the underlying Boolean model.

International audience; Salmonella strains colonize the digestive tract of farm livestock, such as chickens or pigs, without affecting them, and potentially infect food products, representing a threat for human health ranging from food poisoning to typhoid fever. It has been shown that the ability to excrete the pathogen in the environment and contaminate other animals is variable. This heterogeneity in pathogen carriage and shedding results from interactions between the host's immune response, the pathogen and the commensal intestinal microbiota. In this paper we propose a novel generic multiscale modeling framework of heterogeneous pathogen transmission in an animal population. At the intra-host level, the model describes the interaction between the commensal microbiota, the pathogen and the inflammatory response. Random fluctuations in the ecological dynamics of the individual microbiota and transmission at between-host scale are added to obtain a drift-diffusion PDE model of the pathogen distribution at the population level. The model is further extended to represent transmission between several populations. The asymptotic behavior as well as the impact of control strategies including cleaning and antimicrobial administration are investigated through numerical simulation. Résumé. Les salmonelles colonisent le tube digestif des animaux d'élevage, comme les poulets ou les porcs, sans les affecter, et peuvent infecter les productions alimentaires. Elles constituent une menace pour la santé humaine allant de l'intoxication alimentaireà la fièvre typhoïde. Il aété démontré que la capacitéà excréter le pathogène dans l'environnement et contaminer d'autres animaux est variable. Cette hétérogénéité dans le portage et l'excrétion du pathogène résulte des interactions entre la réponse immunitaire de l'hôte, le pathogène et le microbiote intestinal commensal. Dans cet article, nous proposons un nouveau cadre générique de modélisation multi-échelle de la transmission hétérogène d'un pathogène dans une population animale. Au niveau intra-hôte, le modèle décrit l'interaction entre le microbiote commensal, le pathogène et la réponse inflammatoire. L'ajout de fluctuations aléatoires dans la dynamiqueécologique du microbiote des individus et d'une transmissionà l'échelle inter-individuelle permet d'obtenir un modèle EDP de transport-diffusion de la distribution des pathogènesà l'échelle de la population. Le modèle est encoreétendu pour représenter la transmission entre plusieurs populations. Le comportement asymptotique ainsi que l'impact des stratégies de contrôle,comprenant la désinfection de l'environnement et l'administration d'antimicrobiens, sontétudiés par simulation numérique.

9 pages, 27 ref.; We propose a model for self-organized traffic flow at bottlenecks that consists of a scalar conservation law with a nonlocal constraint on the flux. The constraint is a function of an organization marker which evolves through an ODE depending on the upstream traffic density and its variations. We prove well-posedness for the problem, construct and analyze a finite volume scheme, perform numerical simulations and discuss the model and related perspectives.

The Lukash metric is a homogeneous gravitational wave which at late times approximates the behaviour of a generic class of spatially homogenous cosmological models with monotonically decreasing energy density. The transcription from Brinkmann to Baldwin-Jeffery-Rosen (BJR) to Bianchi coordinates is presented and the relation to a Sturm-Liouville equation is explained. The 6-parameter isometry group is derived. In the Bianchi VII range of parameters we have two BJR transciptions. However using either of them induces a mere relabeling of the geodesics and isometries. Following pioneering work of Siklos, we provide a self-contained account of the geometry and global structure of the spacetime. The latter contains a Killing horizon to the future of which the spacetime resembles an anisotropic version of the Milne cosmology and to the past of which it resemble the Rindler wedge., Comment: Revised version. 34 pages, 5 figures. To be published in JCAP

International audience; Special Issue of the journal "Markov Processes and Related Fields" containing papers presented at the meeting: Large Random Networks and Constrained Random Walks, In honor of Guy Fayolle, on the occasion of his 75th birthday (Dijon, August 27-28, 2018). Editors: Kilian Raschel, Ellen Saada. pp. 535-542: Introduction. pp. 543-544: V.A. Malyshev, "Best Feelings to True Friend". pp. 545-552: G. Ruget, "Pour un Ami". pp. 553-566: A. Bensoussan, S.R. Hoe, Z. Yan, "Capital Accumulation with Constraint: A Mean Field TypeControl Framework". pp. 567-612: M. Falconnet, N. Gantert, E. Saada, "Ergodicity of Some Dynamics of DNA Sequences". pp. 613-635: S. Foss, M. Miyazawa, "Tails in a Fixed-Point Problem for a Branching Process with State-Independent Immigration". pp. 637-658: A. de La Fortelle, "Generalized Inverses of Increasing Functions and Lebesgue Decomposition". pp. 659-686: J.-F. Le Gall, A. Riera, "Some Explicit Distributions for Brownian Motion Indexed by theBrownian Tree". pp. 687-710: A. Marin, I. Mitrani, M. Elahi, C. Williamson, "The SRPT Service Policy with Frequency Scaling: Modeling, Evaluation and Optimization". pp. 711-756: K. Raschel, P. Tarrago, "Boundary Behavior of Random Walks in Cones". pp. 757-778: M. Saxena, O.J. Boxma, M. Mandjes, "An Infinite-Server System with Lévy Shot-Noise Modulation: Moments and Asymptotics".

We study the free motion of a massive particle moving in the background of a Finslerian deformation of a plane gravitational wave in Einstein's General Relativity. The deformation is a curved version of a one-parameter family of Relativistic Finsler structures introduced by Bogoslovsky, which are invariant under a certain deformation of Cohen and Glashow's Very Special Relativity group ISIM(2). The partially broken Carroll Symmetry we derive using Baldwin-Jeffery-Rosen coordinates allows us to integrate the geodesics equations. The transverse coordinates of timelike Finsler-geodesics are identical to those of the underlying plane gravitational wave for any value of the Bogoslovsky-Finsler parameter $b$. We then replace the underlying plane gravitational wave by a homogenous pp-wave solution of the Einstein-Maxwell equations. We conclude by extending the theory to the Finsler-Friedmann-Lemaitre model., Comment: v4: Published version. 42 pages, 6 figures

Bipolar orientations of planar maps have recently attracted some interest in combinatorics, probability theory and theoretical physics. Plane bipolar orientations with $n$ edges are known to be counted by the $n$th Baxter number $b(n)$, which can be defined by a linear recurrence relation with polynomial coefficients. Equivalently, the associated generating function $\sum_n b(n)t^n$ is D-finite. In this paper, we address a much refined enumeration problem, where we record for every $r$ the number of faces of degree $r$. When these degrees are bounded, we show that the associated generating function is given as the constant term of a multivariate rational series, and thus is still D-finite. We also provide detailed asymptotic estimates for the corresponding numbers. The methods used earlier to count all plane bipolar orientations, regardless of their face degrees, do not generalize easily to record face degrees. Instead, we start from a recent bijection, due to Kenyon et al., that sends bipolar orientations onto certain lattice walks confined to the first quadrant. Due to this bijection, the study of bipolar orientations meets the study of walks confined to a cone, which has been extremely active in the past 15 years. Some of our proofs rely on recent developments in this field, while others are purely bijective. Our asymptotic results also involve probabilistic arguments., Comment: 64 pages. Special issue of the S\'eminaire Lotharingien de Combinatoire, dedicated to Christian Krattenthaler's 60th birthday

International audience; We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean–Vlasov equation depending on ε, the scaling parameter separating the time scale of the slow variable from the time scale of the fast variable. Its atypical behavior is encapsulated in a large N Large Deviation Principle with a rate functional Iε. We study the Γ-convergence of Iε as ε→0 and show it converges to the rate functional appearing in the Macroscopic Fluctuations Theory for diffusive systems.

Many recent and often (Adaptive) Markov Chain Monte Carlo (A)MCMC methods are associated in practice to unknown rates of convergence. We propose a simulation-based methodology to estimate and compare MCMC's performance, using a Kullback divergence criterion requiring an estimate of the entropy of the algorithm densities at each iteration, computed from iid simulated chains. In previous works, we proved some consistency results in MCMC setup for an entropy estimate based on Monte-Carlo integration of a kernel density estimate proposed by Györfi and Van Der Meulen (1989), and we investigate an alternative Nearest Neighbor (NN) entropy estimate from Kozachenko and Leonenko (1987). This estimate has been used mostly in univariate situations until recently when entropy estimation in higher dimensions has been considered in other fields like neuroscience or system biology. Unfortunately, in higher dimensions, both estimators converge slowly with a noticeable bias. The present work goes several steps further, with bias reduction and automatic (A)MCMC convergence criterion in mind. First, we apply in our situation a recent, "crossed NN-type" nonparametric estimate of the Kullback divergence between two densities, based on iid samples from each, introduced by Wang et al. (2006, 2009). We prove the consistency of these entropy estimates under recent uniform control conditions, for the successive densities of a generic class of MCMC algorithm to which most of the methods proposed in the recent literature belong. Secondly, we propose an original solution based on a PCA for reducing relevant dimension and bias in even higher dimensions. All our algorithms for MCMC simulation and entropy estimation are implemented in an R package taking advantage of recent advances in high performance (parallel) computing.