On points at infinity of real spectra of polynomial rings

Let R be a real closed field and A=R[x_1,...,x_n]. Let sper A denote the real spectrum of A. There are two kinds of points in sper A : finite points (those for which all of |x_1|,...,|x_n| are bounded above by some constant in R) and points at infinity. In this paper we study the structure of the set of points at infinity of sper A and their associated valuations. Let T be a subset of {1,...,n}. For j in {1,...,n}, let y_j=x_j if j is not in T and y_j=1/x_j if j is in T. Let B_T=R[y_1,...,y_n]. We express sper A as a disjoint union of sets of the form U_T and construct a homeomorphism of each of the sets U_T with a subspace of the space of finite points of sper B_T. For each point d at infinity in U_T, we describe the associated valuation v_{d*} of its image d* in sper B_T in terms of the valuation v_d associated to d. Among other things we show that the valuation v_{d*} is composed with v_d (in other words, the valuation ring R_d is a localization of R_{d*} at a suitable prime ideal)

On the Pierce-Birkhoff Conjecture

This paper represents a step in our program towards the proof of the Pierce--Birkhoff conjecture. In the nineteen eighties J. Madden proved that the Pierce-Birkhoff conjecture for a ring A$is equivalent to a statement about an arbitrary pair of points$\alpha,\beta\in\sper\ A$and their separating ideal$$; we refer to this statement as the Local Pierce-Birkhoff conjecture at$\alpha,\beta$. In this paper, for each pair$(\alpha,\beta)$with$ht()=\dim A$, we define a natural number, called complexity of$(\alpha,\beta)$. Complexity 0 corresponds to the case when one of the points$\alpha,\beta$is monomial; this case was already settled in all dimensions in a preceding paper. Here we introduce a new conjecture, called the Strong Connectedness conjecture, and prove that the strong connectedness conjecture in dimension n-1 implies the connectedness conjecture in dimension n in the case when$ht()$is less than n-1. We prove the Strong Connectedness conjecture in dimension 2, which gives the Connectedness and the Pierce--Birkhoff conjectures in any dimension in the case when$ht()$less than 2. Finally, we prove the Connectedness (and hence also the Pierce--Birkhoff) conjecture in the case when dimension of A is equal to$ht()=3$, the pair$(\alpha,\beta)$is of complexity 1 and$A$ is excellent with residue field the field of real numbers

A social barometer

International audienceThe new deal in local development and employment public policies lead more and more to a territorial organization. USGERES wishes to endow the employers of the social economy with a new method for a labormanagement dialog, answering the objectives of satisfaction of the beneficiaries of the activity, but also the individual development of the employees. A process, called social barometer, was experimented. It is based on qualitative and quantitative inquiries, analyzed by a steering committee. It allows building new actions for the quality of the employment and the development of activity, and also introduces a new dynamics of professional and local animation

Reduced graphs for min-cut/max-flow approaches in image segmentation

International audienceIn few years, min-cut/max-flow approach has become a leading method for solving a wide range of problems in computer vision. However, min-cut/max-flow approaches involve the construction of huge graphs which sometimes do not fit in memory. Currently, most of the max-flow algorithms are impracticable to solve such large scale problems. In this paper, we introduce a new strategy for reducing exactly graphs in the image segmentation context. During the creation of the graph, we test if the node is really useful to the max-flow computation. Numerical experiments validate the relevance of this technique to segment large scale images

Oviposition behavior of the mirid Macrolophus pygmaeus under risk of intraguild predation and cannibalism

Zoophytophagous mirid species, that feed and develop either on prey or plant resources, are often found simultaneously on the same host. Hence, these species can engage in both intraguild predation and cannibalism, which can pose a threat to mirid eggs. Ovipositing females may respond to such risks of predation on their eggs by reducing the number of eggs laid or selecting safer oviposition sites. We tested the oviposition behaviour of Macrolophus pygmaeus (Rambur) (Hemiptera: Miridae) females under the risk of cannibalism by M. pygmaeus males and intraguild predation by Nesidiocoris tenuis (Reuter) males (Hemiptera: Miridae) under laboratory conditions. Intraguild predators and cannibals were introduced during or after the oviposition period. The number of eggs laid (using counts of newly hatched nymphs) and their proportion on each part of a tomato plant were both measured. The results reveal that only cannibalism by M. pygmaeus males after the period of oviposition significantly decreased the number of hatched eggs. Cannibalism thus represents a greater risk to mirid eggs than intraguild predation. The M. pygmaeus female responded to the presence of potential intraguild predators (or competitors) by decreasing the number of eggs laid in the upper leaves. The results suggest that M. pygmaeus females avoid competition by N. tenuis, by laying fewer eggs on upper leaves. Cannibalism could regulate zoophytophagous predator populations under prey scarcity conditions and minimize the risk of crop damage associated with those biological control agents.info:eu-repo/semantics/acceptedVersio