1,089 research outputs found
Computation with Polynomial Equations and Inequalities arising in Combinatorial Optimization
The purpose of this note is to survey a methodology to solve systems of
polynomial equations and inequalities. The techniques we discuss use the
algebra of multivariate polynomials with coefficients over a field to create
large-scale linear algebra or semidefinite programming relaxations of many
kinds of feasibility or optimization questions. We are particularly interested
in problems arising in combinatorial optimization.Comment: 28 pages, survey pape
The Ecosystem Approach to Fisheries: Issues, Terminology, Principles, Institutional Foundations, Implementation and Outlook
Ecosystems are complex and dynamic natural units that produce goods and services beyond those of benefit to fisheries. Because fisheries have a direct impact on the ecosystem, which is also impacted by other human activities, they need to be managed in an ecosystem context. The meaning of the terms 'ecosystem management', 'ecosystem based management', 'ecosystem approach to fisheries'(EAF), etc., are still not universally defined and progressively evolving. The justification of EAF is evident in the characteristics of an exploited ecosystem and the impacts resulting from fisheries and other activities. The rich set of international agreements of relevance to EAF contains a large number of principles and conceptual objectives. Both provide a fundamental guidance and a significant challenge for the implementation of EAF. The available international instruments also provide the institutional foundations for EAF. The FAO Code of Conduct for Responsible Fisheries is particularly important in this respect and contains provisions for practically all aspects of the approach. One major difficulty in defining EAF lies precisely in turning the available concepts and principles into operational objectives from which an EAF management plan would more easily be developed. The paper discusses these together with the types of action needed to achieve them. Experience in EAF implementation is still limited but some issues are already apparent, e.g. in added complexity, insufficient capacity, slow implementation, need for a pragmatic approach, etc. It is argued, in conclusion, that the future of EAF and fisheries depends on the way in which the two fundamental concepts of fisheries management and ecosystem management, and their respective stakeholders, will join efforts or collide
Positivity and optimization for semi-algebraic functions
We describe algebraic certificates of positivity for functions belonging to a
finitely generated algebra of Borel measurable functions, with particular
emphasis to algebras generated by semi-algebraic functions. In which case the
standard global optimization problem with constraints given by elements of the
same algebra is reduced via a natural change of variables to the better
understood case of polynomial optimization. A collection of simple examples and
numerical experiments complement the theoretical parts of the article.Comment: 20 page
Organisation spatiale des peuplements ichtyologiques des herbiers Ă Thalassia du Grand Cul-de-Sac Marin en Guadeloupe
Les herbiers à #Thalassia testudinum du Grand Cul-de-Sac Marin en Guadeloupe ont fait l'objet d'une étude de la variabilité spatiale de la faune ichtyologique et de quelques paramÚtres de l'environnement (densité, biomasse et longueur foliaire, agitation, température, oxygÚne dissous, pH et salinité). Les échantillons de poissons ont été prélevés à la senne de plage dans 11 stations réparties de la cÎte (mangrove) à la barriÚre frangeante des récifs coralliens, pendant 12 mois consécutifs (août 1987 à juillet 1988). Les stations non significativement différentes (test de Kruskal-Wallis) pour la température ou le pH, le sont en revanche, pour la densité, la biomasse et la longueur des feuilles de #Thalassia, l'oxygÚne dissous et la salinité, ainsi que pour la richesse spécifique, la régularité et la biomasse ichtyologiqu
Exploiting symmetries in SDP-relaxations for polynomial optimization
In this paper we study various approaches for exploiting symmetries in
polynomial optimization problems within the framework of semi definite
programming relaxations. Our special focus is on constrained problems
especially when the symmetric group is acting on the variables. In particular,
we investigate the concept of block decomposition within the framework of
constrained polynomial optimization problems, show how the degree principle for
the symmetric group can be computationally exploited and also propose some
methods to efficiently compute in the geometric quotient.Comment: (v3) Minor revision. To appear in Math. of Operations Researc
Limitations of Algebraic Approaches to Graph Isomorphism Testing
We investigate the power of graph isomorphism algorithms based on algebraic
reasoning techniques like Gr\"obner basis computation. The idea of these
algorithms is to encode two graphs into a system of equations that are
satisfiable if and only if if the graphs are isomorphic, and then to (try to)
decide satisfiability of the system using, for example, the Gr\"obner basis
algorithm. In some cases this can be done in polynomial time, in particular, if
the equations admit a bounded degree refutation in an algebraic proof systems
such as Nullstellensatz or polynomial calculus. We prove linear lower bounds on
the polynomial calculus degree over all fields of characteristic different from
2 and also linear lower bounds for the degree of Positivstellensatz calculus
derivations.
We compare this approach to recently studied linear and semidefinite
programming approaches to isomorphism testing, which are known to be related to
the combinatorial Weisfeiler-Lehman algorithm. We exactly characterise the
power of the Weisfeiler-Lehman algorithm in terms of an algebraic proof system
that lies between degree-k Nullstellensatz and degree-k polynomial calculus
Systematic InSAR tropospheric phase delay corrections from global meteorological reanalysis data
6p.International audienceDespite remarkable successes achieved by Differential InSAR, estimations of low tectonic strain rates remain challenging in areas where deformation and topography are correlated, mainly because of the topographyârelated atmospheric phase screen (APS). In areas of high relief, empirical removal of the stratified component of the APS may lead to biased estimations of tectonic deformation rates. Here we describe a method to correct interferograms from the effects of the spatial and temporal variations in tropospheric stratification by computing tropospheric delay maps coincident with SAR acquisitions using the ERAâ Interim global meteorological model. The modeled phase delay is integrated along vertical profiles at the ERAâI grid nodes and interpolated at the spatial sampling of the interferograms above the elevation of each image pixel. This approach is validated on unwrapped interferograms. We show that the removal of the atmospheric signal before phase unwrapping reduces the risk of unwrapping errors in areas of rough topography
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