The Uncertain generalized probabilistic weighted average and its application in the theory of expertons

A new model for dealing with decision making under risk by considering subjective and objective information in the same formulation is here presented. The uncertain probabilistic weighted average (UPWA) is also presented. Its main advantage is that it unifies the probability and the weighted average in the same formulation and considering the degree of importance that each case has in the analysis. Moreover, it is able to deal with uncertain environments represented in the form of interval numbers. We study some of its main properties and particular cases. The applicability of the UPWA is also studied and it is seen that it is very broad because all the previous studies that use the probability or the weighted average can be revised with this new approach. Focus is placed on a multi-person decision making problem regarding the selection of strategies by using the theory of expertons.

Traces of functions in Fock spaces on lattices of critical density

Following a scheme of Levin we describe the values that functions in Fock spaces take on lattices of critical density in terms of both the size of the values and a cancelation condition that involves discrete versions of the Cauchy and Beurling-Ahlfors transforms.

Hardy’s inequalities for monotone functions on partly ordered measure spaces

We characterize the weighted Hardy inequalities for monotone functions in Rn +. In dimension n = 1, this recovers the standard theory of Bp weights. For n > 1, the result was previously only known for the case p = 1. In fact, our main theorem is proved in the more general setting of partly ordered measure spaces.

Wave-height hazard analysis in Eastern Coast of Spain : Bayesian approach using generalized Pareto distribution

Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated using data from the Mediterranean coast of Spain, where the last years have been extremely disastrous. Thus, it is possible to compare the hazard assessment based on data previous to those years with the analysis including them. With our approach, no significant change is detected when the statistical uncertainty is taken into account. The hazard analysis is carried out with a standard model. Time-occurrence of events is assumed Poisson distributed. The wave-height of each event is modelled as a random variable which upper tail follows a Generalized Pareto Distribution (GPD). Moreover, wave-heights are assumed independent from event to event and also independent of their occurrence in time. A threshold for excesses is assessed empirically. The other three parameters (Poisson rate, shape and scale parameters of GPD) are jointly estimated using Bayes' theorem. Prior distribution accounts for physical features of ocean waves in the Mediterranean sea and experience with these phenomena. Posterior distribution of the parameters allows to obtain posterior distributions of other derived parameters like occurrence probabilities and return periods. Predictives are also available. Computations are carried out using the program BGPE v2.0

Bayes linear spaces

Linear spaces consisting of σ-finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended

Generalized synchronization in directionally coupled systems with identical individual dynamics

A simple chaotic flow is presented, which when driven by an identical copy of itself, for certain initial conditions, is able to display generalized synchronization instead of identical synchronization. Being that the drive and the response are observed in exactly the same coordinate system, generalized synchronization is demonstrated by means of the auxiliary system approach and by the conditional Lyapunov spectrum. This is interpreted in terms of changes in the structure of the system stationary points, caused by the coupling, which modify its global behavior.

Determination of the components of the gyration tensor of quartz by oblique incidence transmission two-modulator generalized ellipsometry

The two independent components of the gyration tensor of quartz, g11 and g33, have been spectroscopically measured using a transmission two-modulator generalized ellipsometer. The method is used to determine the optical activity in crystals in directions other than the optic axis, where the linear birefringence is much larger than the optical activity.

Invisible Environments: Old Age and its spaces

Despite the progressive ageing of a worldwide population, negative attitudes towards old age have proliferated thanks to cultural constructs and myths that, for decades, have presented old age as a synonym of decay, deterioration and loss. Moreover, even though every human being knows he/she will age and that ageing is a process that cannot be stopped, it always seems distant, far off in the future and, therefore, remains invisible. In this paper, I aim to analyse the invisibility of old age and its spaces through two contemporary novels and their ageing females protagonists –Maudie Fowler in Doris Lessing ’s The Diary of a Good Neighbour and Erica March in Rose Tremain ’s The Cupboard. Although invisible to the rest of society, these elderly characters succeed in becoming significant in the lives of younger protagonists who, immersed in their active lives, become aware of the need to enlarge our vision of old age.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

Use and perception of urban green spaces in Barcelona

Background: Although the mechanisms are not well understood yet, evidence exists of the benefits of urban green spaces for human health. As a consequence, one of the concerns of public health interventions must be to promote the use of urban green spaces within cities. Aims: This study aims to explore the citizens’ purposes of use of urban green spaces as well as the elements related to the characteristics of these places that condition their use. Methods: In-depth interviews were conducted with non-hospitalised people living in different areas of Barcelona, with different socioeconomic status and different residential distance to urban green spaces (n = 20). Thematic content analysis of the qualitative data was performed. Results: Physical pursuits and attention restoration were identified as prominent purposes of use of urban green spaces. The natural features of urban green spaces were identified as the most relevant determiners for the use of these places. Conclusions: To promote the use of urban green spaces, qualitative findings from this study suggest that purpose-built places should be provided. Moreover, natural features of urban green spaces must be particularly taken into account when designing and maintaining them.

Sidelobe elimination for generalized synthetic discriminant functions by a two-filter correlation and subsequent postprocessing of the intensity distributions

One of the most important problems in optical pattern recognition by correlation is the appearance of sidelobes in the correlation plane, which causes false alarms. We present a method that eliminate sidelobes of up to a given height if certain conditions are satisfied. The method can be applied to any generalized synthetic discriminant function filter and is capable of rejecting lateral peaks that are even higher than the central correlation. Satisfactory results were obtained in both computer simulations and optical implementation.

The induced generalized OWA operator

We present the induced generalized ordered weighted averaging (IGOWA) operator. It is a new aggregation operator that generalizes the OWA operator by using the main characteristics of two well known aggregation operators: the generalized OWA and the induced OWA operator. Then, this operator uses generalized means and order inducing variables in the reordering process. With this formulation, we get a wide range of aggregation operators that include all the particular cases of the IOWA and the GOWA operator, and a lot of other cases such as the induced ordered weighted geometric (IOWG) operator and the induced ordered weighted quadratic averaging (IOWQA) operator. We further generalize the IGOWA operator by using quasi-arithmetic means. The result is the Quasi-IOWA operator. Finally, we also develop a numerical example of the new approach in a financial decision making problem.

The Emergence of Regional ICT Regulatory Spaces

This paper examines the role that existing Latin American policy institutions and regulatory coordination mechanisms (otherwise referred to as “regional regulatory spaces”) play in innovation and development of the ICT sector. In doing so, it recognizes that sector regulation does not currently match regional development, thereby limiting its potential progress. In order to shed light on the role that the “regional regulatory space” could potentially play, the author addresses three main questions: · Is there a hierarchy of policies by which it is presumed easy to “coordinate within well-defined technical subjects” but extremely challenging to “agree in matters of public policy?” · What would happen if policy divergence became more important than convergence? Is it reasonable to consider creating “regional regulatory spaces?” or should we focus solely on technological coordination? · Do institutions capable of serving as effective regional regulatory spaces already exist in Latin America or should we consider modifying existing institutions or creating new institutions? After analyzing these three overarching areas of concern, this paper then discusses the need to create a regional space in order to harmonize ICT regulatory frameworks and public policies. Ultimately, this work aims to advance the institutional formulation beyond pre-existing efforts.

Generalized three-sided assignment markets: consistency and the core

A class of three-sided markets (and games) is considered, where value is generated by pairs or triplets of agents belonging to different sectors, as well as by individuals. For these markets we analyze the situation that arises when some agents leave the market with some payoff To this end, we introduce the derived market (and game) and relate it to the Davis and Maschler (1965) reduced game. Consistency with respect to the derived market, together with singleness best and individual anti-monotonicity axiomatically characterize the core for these generalized three-sided assignment markets. These markets may have an empty core, but we define a balanced subclass, where the worth of each triplet is defined as the addition of the worths of the pairs it contains. Keywords: Multi-sided assignment market, Consistency, Core, Nucleolus. JEL Classification: C71, C78

Weight filtration on the cohomology of complex analytic spaces

We extend Deligne's weight filtration to the integer cohomology of complex analytic spaces (endowed with an equivalence class of compactifications). In general, the weight filtration that we obtain is not part of a mixed Hodge structure. Our purely geometric proof is based on cubical descent for resolution of singularities and Poincaré-Verdier duality. Using similar techniques, we introduce the singularity filtration on the cohomology of compactificable analytic spaces. This is a new and natural analytic invariant which does not depend on the equivalence class of compactifications and is related to the weight filtration.