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

Strategies, innovations and characteristics specific to organic farmers. Elements of sociological analysis related to professional organic farming

How can we approach strategies and innovations specific to organic farmers? Is the appearance of new practices evidence of a modification of the structure of professional organic farming? On the basis of a field study carried out in the Midi-Pyrénées region in France, sociological analysis casts light on several examples of strategies and innovations specific to the world of organic farming and from which they arise. The strategic courses of action taken by organic farmers are therefore analysed in relation to organic farming characteristics, defined as the set of issues, interests, representations and other specific characteristics that structure this socio-professional field. Organic farming innovations are the result of interactions between the socio-technical framework, the result of how this field is structured, and the practices of organic farmers (having, to some extent, incorporated these same properties). The emergence of innovative practices as a result of new inputs (converted or used for the first time) is proof of the structural modifications taking place within the area of professional organic farming. Although they may appear to “enrich” organic farming diversity, these new practices are partially derived from traditional farming practices not used in organic farming. They raise the question of the use and the transformation of certain properties that characterise professional organic farming

Which Local Governments Cooperate on Public Safety?: Lessons from Michigan

Despite the increased interest in voluntary services cooperation, little is known about the factors that encourage local governments to enter into collaborative services arrangements with each other. This paper addresses this question through an analysis of interlocal contracting arrangements for police and fire services reported by 464 local governments in Michigan. While the contracting of public services is increasing common in local governments across the country, collaborations on police and fire services have proved far more difficult to achieve. Public safety contracting presents a dilemma for public managers. On one hand, local governments devote a substantial part of their budgets to police and fire, and public safety employees may approach 25 percent of the unit’s workforce and 40 percent of its total payroll. Given the importance of public safety expenditures in the budgets of local governments, it may be impossible to reduce the costs of local government without reducing spending on police and fire services. Yet the fear of lost jobs and lower quality services will often make contracting for police and fire highly controversial in the community. Also, collaborations involving police and fire services may become entangled with the “politics of place.” Unlike other services areas where the contractor may be a private or nonprofit organization, public safety contractors are other local governments, and the baggage of past conflicts and rivalries attach to the issue. We group the factors expected to influence the incentives and feasibility of local governments to collaborate on public services into the following categories: the organization of local governments in the county and variations in the unit’s administrative structure, community demographics, and the fiscal capacity of the local unit. Using logistic and negative binomial regression, we analyze the effect of these factors on the frequency and extent of cooperation reported for police and fire services. We find important differences in the role played by these factors in the frequency and extent of cooperation reported across the two different service areas and within the different types of local units (city, village, and township)

Controlling the potential landscape and normal modes of ion Coulomb crystals by a standing wave optical potential

Light-induced control of ions within small Coulomb crystals is investigated. By intense intracavity optical standing wave fields, subwavelength localization of individual ions is achieved for one-, two-, and three-dimensional crystals. Based on these findings, we illustrate numerically how the application of such optical potentials can be used to tailor the normal mode spectra and patterns of multi-dimensional Coulomb crystals. The results represent, among others, important steps towards controlling the crystalline structure of Coulomb crystals, investigating heat transfer processes at the quantum limit and quantum simulations of many-body systems.Comment: 6+12 pages. arXiv admin note: substantial text overlap with arXiv:1703.0508

Explaining Local Government Cooperation on Public Works: Evidence from Michigan

In recent years, analysts have begun to study cooperation on public services among local governments. These studies have often concluded that services with scale economies are likely candidates for shared service delivery. This article contributes to the emerging literature on this topic by examining interlocal service arrangements for ten public works services in Michigan. Despite the fact that public works exhibit substantial scale economies, many local governments do not cooperate on these services. Empirical studies of local government contracting suggest four groups of factors that may help explain why local governments opt to collaborate on public services: local economic factors, characteristics of the communities in areas adjacent to the local government, demographic characteristics of the local government, and the influence of policy and planning networks. We use data on the service delivery arrangements from 468 general-purpose local governments in Michigan to examine the role played by the factors in explaining interlocal cooperation on public works

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

Pinning an Ion with an Intracavity Optical Lattice

We report one-dimensional pinning of a single ion by an optical lattice. The lattice potential is produced by a standing-wave cavity along the rf-field-free axis of a linear Paul trap. The ion's localization is detected by measuring its fluorescence when excited by standing-wave fields with the same period, but different spatial phases. The experiments agree with an analytical model of the localization process, which we test against numerical simulations. For the best localization achieved, the ion's average coupling to the cavity field is enhanced from 50% to 81(3)% of its maximum possible value, and we infer that the ion is bound in a lattice well with over 97% probability.Comment: 5 pages, 4 figures; Text edited for clarity, results unchange

Area limit laws for symmetry classes of staircase polygons

We derive area limit laws for the various symmetry classes of staircase polygons on the square lattice, in a uniform ensemble where, for fixed perimeter, each polygon occurs with the same probability. This complements a previous study by Leroux and Rassart, where explicit expressions for the area and perimeter generating functions of these classes have been derived.Comment: 18 pages, 3 figure