Convex Hull of Arithmetic Automata

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata

Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS

Vector Addition Systems with States (VASS) provide a well-known and fundamental model for the analysis of concurrent processes, parameterized systems, and are also used as abstract models of programs in resource bound analysis. In this paper we study the problem of obtaining asymptotic bounds on the termination time of a given VASS. In particular, we focus on the practically important case of obtaining polynomial bounds on termination time. Our main contributions are as follows: First, we present a polynomial-time algorithm for deciding whether a given VASS has a linear asymptotic complexity. We also show that if the complexity of a VASS is not linear, it is at least quadratic. Second, we classify VASS according to quantitative properties of their cycles. We show that certain singularities in these properties are the key reason for non-polynomial asymptotic complexity of VASS. In absence of singularities, we show that the asymptotic complexity is always polynomial and of the form $\Theta(n^k)$, for some integer $k\leq d$, where $d$ is the dimension of the VASS. We present a polynomial-time algorithm computing the optimal $k$. For general VASS, the same algorithm, which is based on a complete technique for the construction of ranking functions in VASS, produces a valid lower bound, i.e., a $k$ such that the termination complexity is $\Omega(n^k)$. Our results are based on new insights into the geometry of VASS dynamics, which hold the potential for further applicability to VASS analysis.Comment: arXiv admin note: text overlap with arXiv:1708.0925

Renormalization : A number theoretical model

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200

Fabrication and Optical Properties of a Fully Hybrid Epitaxial ZnO-Based Microcavity in the Strong Coupling Regime

In order to achieve polariton lasing at room temperature, a new fabrication methodology for planar microcavities is proposed: a ZnO-based microcavity in which the active region is epitaxially grown on an AlGaN/AlN/Si substrate and in which two dielectric mirrors are used. This approach allows as to simultaneously obtain a high-quality active layer together with a high photonic confinement as demonstrated through macro-, and micro-photoluminescence ({\mu}-PL) and reflectivity experiments. A quality factor of 675 and a maximum PL emission at k=0 are evidenced thanks to {\mu}-PL, revealing an efficient polaritonic relaxation even at low excitation power.Comment: 12 pages, 3 figure

Generalized shuffles related to Nijenhuis and TD-algebras

Shuffle and quasi-shuffle products are well-known in the mathematics literature. They are intimately related to Loday's dendriform algebras, and were extensively used to give explicit constructions of free commutative Rota-Baxter algebras. In the literature there exist at least two other Rota-Baxter type algebras, namely, the Nijenhuis algebra and the so-called TD-algebra. The explicit construction of the free unital commutative Nijenhuis algebra uses a modified quasi-shuffle product, called the right-shift shuffle. We show that another modification of the quasi-shuffle product, the so-called left-shift shuffle, can be used to give an explicit construction of the free unital commutative TD-algebra. We explore some basic properties of TD-operators and show that the free unital commutative Nijenhuis algebra is a TD-algebra. We relate our construction to Loday's unital commutative dendriform trialgebras, including the involutive case. The concept of Rota-Baxter, Nijenhuis and TD-bialgebras is introduced at the end and we show that any commutative bialgebra provides such objects.Comment: 20 pages, typos corrected, accepted for publication in Communications in Algebr

LO-phonon assisted polariton lasing in a ZnO based microcavity

Polariton relaxation mechanisms are analysed experimentally and theoretically in a ZnO-based polariton laser. A minimum lasing threshold is obtained when the energy difference between the exciton reservoir and the bottom of the lower polariton branch is resonant with the LO phonon energy. Tuning off this resonance increases the threshold, and exciton-exciton scattering processes become involved in the polariton relaxation. These observations are qualitatively reproduced by simulations based on the numerical solution of the semi-classical Boltzmann equations

Multiscale nature of hysteretic phenomena: Application to CoPt-type magnets

We suggest a workable approach for the description of multiscale magnetization reversal phenomena in nanoscale magnets and apply it to CoPt-type alloys. We show that their hysteretic properties are governed by two effects originating at different length scales: a peculiar splitting of domain walls and their strong pinning at antiphase boundaries. We emphasize that such multiscale nature of hysteretic phenomena is a generic feature of nanoscale magnetic materials.Comment: 4 pages (revtex 4), 2 color EPS figure

ACR Proton Acceleration Associated with Reconnection Processes beyond the Heliospheric Termination Shock

One of the curious observations from the Voyagers is that the intensity of anomalous cosmic rays (ACRs) did not peak at the heliospheric termination shock (HTS) but instead a short distance (within ~1 au) downstream of the HTS. One possible explanation is that the interaction of the wavy heliospheric current sheet with the HTS enhances magnetic reconnection and generates numerous small-scale magnetic flux ropes in the heliosheath immediately downstream of the HTS. Charged particles are accelerated in this region due to Fermi acceleration and the reconnection electric field. In this work, we provide observational evidence of the presence of magnetic flux ropes in the heliosheath region just downstream of the HTS using a wavelet analysis of the reduced magnetic helicity and Grad–Shafranov reconstruction techniques. The Zank et al. kinetic transport theory for particles propagating through the magnetic islands region is employed to fit the observed energetic proton intensities in the post-HTS region. Our modeling results agree reasonably well with the observations, which suggests that stochastic acceleration via reconnection processes can explain the ACR proton peak beyond the HTS

Autonomy and forage grasses in goat farming of western France First results of a sociological survey

International audienceOur communication is based on the results of a multidisciplinary research (PSDR FLECHE-Fromages et Laits issus d'Élevages de Chèvres conduites avec de l'Herbe-2016-2020) which aims to study the potential of grass valorization in goat systems, with the dual objective of strengthening the economic resilience of farms and the social image of the dairy goat sector of Western France. The latter currently represent almost half of the national goat population and 58% of the milk supplied in France. The sociological aspect of the research concerns the representations, value systems, interests and constraint systems (technical, economic, etc.) that guide the practices of all the actors in the sector: farmers, upstream and downstream actors. The objective of this approach is to analyse, at all levels of the value chain, the incentives and obstacles to a possible transition to more grassy feeding systems. Based on 76 semi-directive interviews, this paper presents the first results of this survey by showing how contextual elements (socio-economic, professional, etc.) impact farmers' choices of practices. While, in principle, the whole goat sector seems to be converging towards an agro-ecological transition that ensures its sustainability, in practice, each of its actors is confronted with a system of constraints that limit actual developments. The articulation of these obstacles seems to lead to a kind of inertia, which prevents the adoption of practices that are nevertheless perceived as recommendable by most actors. Autonomie et fourrages herbagers dans les élevages caprins de l'Ouest de la France. Premiers résultats d'une enquête sociologique. Résumé. Notre communication s'inscrit dans le cadre d'une recherche pluridisciplinaire (Programme PSDR-FLECHE-Fromages et Laits issus d'Élevages de Chèvres conduites avec de l'Herbe-2016-2020) qui vise à étudier le potentiel de valorisation de l'herbe dans les systèmes caprins, dans le double objectif de renforcer la résilience économique des exploitations et l'image sociale des filières caprines laitières de l'Ouest de la France. Ces dernières représentent actuellement près de la moitié de l'effectif national de chèvres et 58% du lait livré en France. Le volet sociologique de la recherche porte sur les représentations, les systèmes de valeurs, les intérêts et les systèmes de contraintes (techniques, économiques, etc.) qui orientent les pratiques de l'ensemble des acteurs de la filière : éleveurs, acteurs de l'amont et de l'aval. L'objectif de cette démarche est d'analyser, à tous les niveaux de la filière, les incitations et les freins à une éventuelle transition vers des systèmes alimentaires plus herbagers. A partir de 76 entretiens semi-directifs, ce papier présente les premiers résultats de cette enquête en montrant, notamment, comment les éléments contextuels (socio-économiques, professionnels, etc.) impactent les choix des pratiques des exploitants agricoles. Si, en principe, l'ensemble de la filière caprine semble converger vers une transition agroécologique qui en assure la durabilité, dans la pratique, chacun de ses acteurs est confronté à un univers de contraintes qui limitent les évolutions effectives. L'articulation des freins relevant des différents maillons de la filière, semble ainsi déboucher sur une sorte d'inertie, qui empêche l'adoption de pratiques pourtant perçues comme souhaitables par la plupart des acteurs. Mots-clés. Autonomie-fourrages herbagers-caprins-sociologie