Regions of rationality: Maps for bounded agents

An important problem in descriptive and prescriptive research in decision making is to identify regions of rationality, i.e., the areas for which heuristics are and are not effective. To map the contours of such regions, we derive probabilities that heuristics identify the best of m alternatives (m > 2) characterized by k attributes or cues (k > 1). The heuristics include a single variable (lexicographic), variations of elimination-by-aspects, equal weighting, hybrids of the preceding, and models exploiting dominance. We use twenty simulated and four empirical datasets for illustration. We further provide an overview by regressing heuristic performance on factors characterizing environments. Overall, sensible heuristics generally yield similar choices in many environments. However, selection of the appropriate heuristic can be important in some regions (e.g., if there is low inter-correlation among attributes/cues). Since our work assumes a hit or miss decision criterion, we conclude by outlining extensions for exploring the effects of different loss functions.

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

Geomorphological method in the elaboration of hazard maps for flash-floods in the municipality of Jucuarán (El Salvador)

This work deals with the elaboration of flood hazard maps. These maps reflect the areas prone to floods based on the effects of Hurricane Mitch in the Municipality of Jucuarán of El Salvador. Stream channels located in the coastal range in the SE of El Salvador flow into the Pacific Ocean and generate alluvial fans. Communities often inhabit these fans can be affected by floods. The geomorphology of these stream basins is associated with small areas, steep slopes, well developed regolite and extensive deforestation. These features play a key role in the generation of flash-floods. This zone lacks comprehensive rainfall data and gauging stations. The most detailed topographic maps are on a scale of 1:25 000. Given that the scale was not sufficiently detailed, we used aerial photographs enlarged to the scale of 1:8000. The effects of Hurricane Mitch mapped on these photographs were regarded as the reference event. Flood maps have a dual purpose (1) community emergency plans, (2) regional land use planning carried out by local authorities. The geomorphological method is based on mapping the geomorphological evidence (alluvial fans, preferential stream channels, erosion and sedimentation, man-made terraces). Following the interpretation of the photographs this information was validated on the field and complemented by eyewitness reports such as the height of water and flow typology. In addition, community workshops were organized to obtain information about the evolution and the impact of the phenomena. The superimposition of this information enables us to obtain a comprehensive geomorphological map. Another aim of the study was the calculation of the peak discharge using the Manning and the paleohydraulic methods and estimates based on geomorphologic criterion. The results were compared with those obtained using the rational method. Significant differences in the order of magnitude of the calculated discharges were noted. The rational method underestimated the results owing to short and discontinuous periods of rainfall data with the result that probabilistic equations cannot be applied. The Manning method yields a wide range of results because of its dependence on the roughness coefficient. The paleohydraulic method yielded higher values than the rational and Manning methods. However, it should be pointed out that it is possible that bigger boulders could have been moved had they existed. These discharge values are lower than those obtained by the geomorphological estimates, i.e. much closer to reality. The flood hazard maps were derived from the comprehensive geomorphological map. Three categories of hazard were established (very high, high and moderate) using flood energy, water height and velocity flow deduced from geomorphological and eyewitness reports.

A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Linear and nonlinear terrain deformation maps from a reduced set of interferometric SAR images

In this paper, an advanced technique for the generation of deformation maps using synthetic aperture radar (SAR) data is presented. The algorithm estimates the linear and nonlinear components of the displacement, the error of the digital elevation model (DEM) used to cancel the topographic terms, and the atmospheric artifacts from a reduced set of low spatial resolution interferograms. The pixel candidates are selected from those presenting a good coherence level in the whole set of interferograms and the resulting nonuniform mesh tessellated with the Delauney triangulation to establish connections among them. The linear component of movement and DEM error are estimated adjusting a linear model to the data only on the connections. Later on, this information, once unwrapped to retrieve the absolute values, is used to calculate the nonlinear component of movement and atmospheric artifacts with alternate filtering techniques in both the temporal and spatial domains. The method presents high flexibility with respect to the required number of images and the baselines length. However, better results are obtained with large datasets of short baseline interferograms. The technique has been tested with European Remote Sensing SAR data from an area of Catalonia (Spain) and validated with on-field precise leveling measurements.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions ∇2I(r) and ∇2E(R) are analyzed at the Hartree-Fock (HF) and configuration interaction (CI) levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, IC(r) and EC(R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between IC(r) and EC(R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C2-2, N2, O2+2 molecular series, and the C2H4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of IC(r) and EC(R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, IC(r), EC(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules

The relevance of the Laplacian of intracule and extracule density distributions for analyzing electron-electron interactions in molecules

A topological analysis of intracule and extracule densities and their Laplacians computed within the Hartree-Fock approximation is presented. The analysis of the density distributions reveals that among all possible electron-electron interactions in atoms and between atoms in molecules only very few are located rigorously as local maxima. In contrast, they are clearly identified as local minima in the topology of Laplacian maps. The conceptually different interpretation of intracule and extracule maps is also discussed in detail. An application example to the C2H2, C2H4, and C2H6 series of molecules is presented

Geological and Geomorphological Cartography at Scale 1: 10.000: a Tool of Management for Towns

Geological and geomorphological mapping at scale 1:10.000 besides from being an important source of scientific information it is also a necessary tool for municipal organs in order to make proper decisions when dealing with geo-environmental problems concerning integral territorial development. In this work, detailed information is given on the contents of such maps, their social and economical application, and a balance of the investment and gains that derives from them

Strange nonchaotic attractors in Harper maps

We study the existence of strange nonchaotic attractors (SNA) in the family of Harper maps. We prove that for a set of parameters of positive measure, the map possesses a SNA. However, the set is nowhere dense. By changing the parameter arbitrarily small amounts, the attractor is a smooth curve and not a SNA.

On the bicanonical map of irregular varieties

From the point of view of uniform bounds for the birationality of pluricanonical maps, irregular varieties of general type and maximal Albanese dimension behave similarly to curves. In fact Chen-Hacon showed that, at least when their holomorphic Euler characteristic is positive, the tricanonical map of such varieties is always birational. In this paper we study the bicanonical map. We consider the natural subclass of varieties of maximal Albanese dimension formed by primitive varieties of Albanese general type. We prove that the only such varieties with non-birational bicanonical map are the natural higher-dimensional generalization to this context of curves of genus $2$: varieties birationally equivalent to the theta-divisor of an indecomposable principally polarized abelian variety. The proof is based on the (generalized) Fourier-Mukai transform.

On the bicanonical map of irregular varieties

From the point of view of uniform bounds for the birationality of pluricanonical maps, irregular varieties of general type and maximal Albanese dimension behave similarly to curves. In fact Chen-Hacon showed that, at least when their holomorphic Euler characteristic is positive, the tricanonical map of such varieties is always birational. In this paper we study the bicanonical map. We consider the natural subclass of varieties of maximal Albanese dimension formed by primitive varieties of Albanese general type. We prove that the only such varieties with non-birational bicanonical map are the natural higher-dimensional generalization to this context of curves of genus $2$: varieties birationally equivalent to the theta-divisor of an indecomposable principally polarized abelian variety. The proof is based on the (generalized) Fourier-Mukai transform.

Fair procedures. Evidence from games involving lotteries

Procedural fairness plays a prominent role in the social discourse concerning the marketplace in particular, and social institutions in general. Random procedures are a simple case, and they have found application in several important social allocation decisions. We investigate random procedures in the laboratory. We find that an unbiased random procedure is an acceptable substitute for an unbiased allocation: similar patterns of acceptance and rejection result when either is inserted as a feasible proposal in a sequential battle-of-the-sexes. We also find that unbiasedness, known to be a crucial characteristic of allocation fairness, is important to procedural fairness: in the context of a random offer game, a biased outcome is more readily accepted when chosen by an unbiased random draw than by one that is biased. Procedural fairness is conceptually different than allocation fairness or attribution-based behavior, and none of the current models of fairness and reciprocity captures our results. Post hoc extension of one of these models (ERC) suggests that a deeper understanding of procedural fairness requires further investigation of competing fairness norms.

Catalan Policies and Experiences on Cooperative Repositories

The Centre de Supercomputació de Catalunya (CESCA) together with the Consorci de Biblioteques Universitàries de Catalunya (CBUC) started in 1999 a cooperative repository, named TDR, to file in digital format the full-text of the read thesis at the universities of our country to spread them worldwide in open access preserving the intellectual copyright of the authors. This became operational in 2001 and today it is a service fully consolidated not only among the Catalan universities, but also used by other Spanish universities. Since then, there are four additional cooperative repositories which have been created: RECERCAT, for research papers; RACO, for scientific, cultural and erudite Catalan magazines; PADICAT, for archiving Catalan web sites; and MDC, for Catalan digital collections of pictures, maps, posters, old magazines... These five repositories have some common characteristics: they are open access, that is, they are accessible on the internet for free; they mostly comply with the Open Archive Initiative interoperability protocol for facilitating the efficient dissemination of content; and they have been built in a cooperative manner so that it is easy to adopt common procedures and to share the repository developing and managing costs, it permits more visibility of the indexed documents throughout the search engines, and a better provision for long-term preservation can be made. In this paper we present the common policy established for the Catalan cooperative repositories, we describe the five of them briefly, and we comment on the results obtained of our 6-year experience since the first one became operational.