On stability of differential equations with piecewise constant argument using dichotomic maps

This paper deals with the study of the basic theory of existence, uniqueness and continuation of solutions of di®erential equations with piecewise constant argument. Results about asymptotic stability of the equation x(t) =-bx(t) + f(x([t])) with argu- ment [t], where [t] designates the greatest integer function, are established by means of dichotomic maps. Other example is given to illustrate the application of the method. Copyright © 2011 Watam Press.

Coincidences of self-maps on Klein bottle fiber bundles over the circle

The main purpose of this work is to study coincidences of fiber-preserving self-maps over the circle S 1 for spaces which are fiberbundles over S 1 and the fiber is the Klein bottle K. We classify pairs of self-maps over S 1 which can be deformed fiberwise to a coincidence free pair of maps. © 2012 Pushpa Publishing House.

The Lamination of Infinitely Renormalizable Dissipative Gap Maps: Analyticity, Holonomies and Conjugacies

Motivated by return maps near saddles for three-dimensional flows and also by return maps in the torus associated to Cherry flows, we study gap maps with derivative positive and smaller than one outside the discontinuity point. We prove that the lamination of infinitely renormalizable maps (or else maps with irrational rotation numbers) has analytic leaves in a natural subset of a Banach space of analytic maps of this kind. With maps having Hölder continuous derivative and derivative bounded away from zero, we also prove Hölder continuity of holonomies of the lamination and also of conjugacies between maps having the same combinatorics. © 2011 Springer Basel AG.

Virtues and limitations of census maps for identifying critical deficiencies

Includes bibliography

Digital soil mapping: evaluation of sampling systems for soil surveys and refinement of soil maps at lower cost using legacy data

In soil surveys, several sampling systems can be used to define the most representative sites for sample collection and description of soil profiles. In recent years, the conditioned Latin hypercube sampling system has gained prominence for soil surveys. In Brazil, most of the soil maps are at small scales and in paper format, which hinders their refinement. The objectives of this work include: (i) to compare two sampling systems by conditioned Latin hypercube to map soil classes and soil properties; (II) to retrieve information from a detailed scale soil map of a pilot watershed for its refinement, comparing two data mining tools, and validation of the new soil map; and (III) to create and validate a soil map of a much larger and similar area from the extrapolation of information extracted from the existing soil map. Two sampling systems were created by conditioned Latin hypercube and by the cost-constrained conditioned Latin hypercube. At each prospection place, soil classification and measurement of the A horizon thickness were performed. Maps were generated and validated for each sampling system, comparing the efficiency of these methods. The conditioned Latin hypercube captured greater variability of soils and properties than the cost-constrained conditioned Latin hypercube, despite the former provided greater difficulty in field work. The conditioned Latin hypercube can capture greater soil variability and the cost-constrained conditioned Latin hypercube presents great potential for use in soil surveys, especially in areas of difficult access. From an existing detailed scale soil map of a pilot watershed, topographical information for each soil class was extracted from a Digital Elevation Model and its derivatives, by two data mining tools. Maps were generated using each tool. The more accurate of these tools was used for extrapolation of soil information for a much larger and similar area and the generated map was validated. It was possible to retrieve the existing soil map information and apply it on a larger area containing similar soil forming factors, at much low financial cost. The KnowledgeMiner tool for data mining, and ArcSIE, used to create the soil map, presented better results and enabled the use of existing soil map to extract soil information and its application in similar larger areas at reduced costs, which is especially important in development countries with limited financial resources for such activities, such as Brazil.

Optimization of the sampling scheme for maps of physical and chemical properties estimated by kriging

The sampling scheme is essential in the investigation of the spatial variability of soil properties in Soil Science studies. The high costs of sampling schemes optimized with additional sampling points for each physical and chemical soil property, prevent their use in precision agriculture. The purpose of this study was to obtain an optimal sampling scheme for physical and chemical property sets and investigate its effect on the quality of soil sampling. Soil was sampled on a 42-ha area, with 206 geo-referenced points arranged in a regular grid spaced 50 m from each other, in a depth range of 0.00-0.20 m. In order to obtain an optimal sampling scheme for every physical and chemical property, a sample grid, a medium-scale variogram and the extended Spatial Simulated Annealing (SSA) method were used to minimize kriging variance. The optimization procedure was validated by constructing maps of relative improvement comparing the sample configuration before and after the process. A greater concentration of recommended points in specific areas (NW-SE direction) was observed, which also reflects a greater estimate variance at these locations. The addition of optimal samples, for specific regions, increased the accuracy up to 2 % for chemical and 1 % for physical properties. The use of a sample grid and medium-scale variogram, as previous information for the conception of additional sampling schemes, was very promising to determine the locations of these additional points for all physical and chemical soil properties, enhancing the accuracy of kriging estimates of the physical-chemical properties.

Consolidation of the genetic and cytogenetic maps of turbot (Scophthalmus maximus) using FISH with BAC clones

Bacterial artificial chromosomes (BAC) have been widely used for fluorescence in situ hybridization (FISH) mapping of chromosome landmarks in different organisms, including a few in teleosts. In this study, we used BAC-FISH to consolidate the previous genetic and cytogenetic maps of the turbot (Scophthalmus maximus), a commercially important pleuronectiform. The maps consisted of 24 linkage groups (LGs) but only 22 chromosomes. All turbot LGs were assigned to specific chromosomes using BAC probes obtained from a turbot 5x genomic BAC library. It consisted of 46,080 clones with inserts of at least 100 kb and < 5 % empty vectors. These BAC probes contained gene-derived or anonymous markers, most of them linked to quantitative trait loci (QTL) related to productive traits. BAC clones were mapped by FISH to unique marker-specific chromosomal positions, which showed a notable concordance with previous genetic mapping data. The two metacentric pairs were cytogenetically assigned to LG2 and LG16, and the nucleolar organizer region (NOR)-bearing pair was assigned to LG15. Double-color FISH assays enabled the consolidation of the turbot genetic map into 22 linkage groups by merging LG8 with LG18 and LG21 with LG24. In this work, a first-generation probe panel of BAC clones anchored to the turbot linkage and cytogenetical map was developed. It is a useful tool for chromosome traceability in turbot, but also relevant in the context of pleuronectiform karyotypes, which often show small hardly identifiable chromosomes. This panel will also be valuable for further integrative genomics of turbot within Pleuronectiformes and teleosts, especially for fine QTL mapping for aquaculture traits, comparative genomics, and whole-genome assembly.

Amazon forest biomass density maps: tackling the uncertainty in carbon emission estimates

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation

Convergence to a period one fixed point is investigated for both logistic and cubic maps. For the logistic map the relaxation to the fixed point is considered near a transcritical bifurcation while for the cubic map it is near a pitchfork bifurcation. We confirmed that the convergence to the fixed point in both logistic and cubic maps for a region close to the fixed point goes exponentially fast to the fixed point and with a relaxation time described by a power law of exponent -1. At the bifurcation point, the exponent is not universal and depends on the type of the bifurcation as well as on the nonlinearity of the map.

COINCIDENCES OF FIBREWISE MAPS BETWEEN SPHERE BUNDLES OVER THE CIRCLE

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Precision of distances and ordering of microsatellite markers in consensus linkage maps of chromosomes 1, 3 and 4 from two reciprocal chicken populations using bootstrap sampling

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Self-Organizing Maps of Molecular Descriptors for Sesquiterpene Lactones and Their Application to the Chemotaxonomy of the Asteraceae Family

The Asteraceae, one of the largest families among angiosperms, is chemically characterised by the production of sesquiterpene lactones (SLs). A total of 1,111 SLs, which were extracted from 658 species, 161 genera, 63 subtribes and 15 tribes of Asteraceae, were represented and registered in two dimensions in the SISTEMATX, an in-house software system, and were associated with their botanical sources. The respective 11 block of descriptors: Constitutional, Functional groups, BCUT, Atom-centred, 2D autocorrelations, Topological, Geometrical, RDF, 3D-MoRSE, GETAWAY and WHIM were used as input data to separate the botanical occurrences through self-organising maps. Maps that were generated with each descriptor divided the Asteraceae tribes, with total index values between 66.7% and 83.6%. The analysis of the results shows evident similarities among the Heliantheae, Helenieae and Eupatorieae tribes as well as between the Anthemideae and Inuleae tribes. Those observations are in agreement with systematic classifications that were proposed by Bremer, which use mainly morphological and molecular data, therefore chemical markers partially corroborate with these classifications. The results demonstrate that the atom-centred and RDF descriptors can be used as a tool for taxonomic classification in low hierarchical levels, such as tribes. Descriptors obtained through fragments or by the two-dimensional representation of the SL structures were sufficient to obtain significant results, and better results were not achieved by using descriptors derived from three-dimensional representations of SLs. Such models based on physico-chemical properties can project new design SLs, similar structures from literature or even unreported structures in two-dimensional chemical space. Therefore, the generated SOMs can predict the most probable tribe where a biologically active molecule can be found according Bremer classification.

Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = {0}. Let S(V) be the sphere of V and suppose f: S(V) -> W is a G-equivariant mapping. We give an estimate for the dimension of the set f(-1){0} in terms of V and W. This extends the Bourgin-Yang version of the Borsuk-Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G-coincidences set of a continuous map from S(V) into a real vector space W'.

On the existence of G-equivariant maps

Let G be a compact Lie group. Let X, Y be free G-spaces. In this paper, by using the numerical index i (X; R), under cohomological conditions on the spaces X and Y, we consider the question of the existence of G-equivariant maps f: X -> Y.

Secondary nontwist phenomena in area-preserving maps

Phenomena as reconnection scenarios, periodic-orbit collisions, and primary shearless tori have been recognized as features of nontwist maps. Recently, these phenomena and secondary shearless tori were analytically predicted for generic maps in the neighborhood of the tripling bifurcation of an elliptic fixed point. In this paper, we apply a numerical procedure to find internal rotation number profiles that highlight the creation of periodic orbits within islands of stability by a saddle-center bifurcation that emerges out a secondary shearless torus. In addition to the analytical predictions, our numerical procedure applied to the twist and nontwist standard maps reveals that the atypical secondary shearless torus occurs not only near a tripling bifurcation of the fixed point but also near a quadrupling bifurcation. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4750040]