The size and distribution of donations: Effects of numbers of potential recipients

Whereas much literature exists on choice overload, little is known about effects of numbers of alternatives in donation decisions. How do these affect both the size and distribution of donations? We hypothesize that donations are affected by the reputation of recipients and increase with their number, albeit at a decreasing rate. Allocations to recipients reflect different concepts of fairness equity and equality. Both may be employed but, since they differ in cognitive and emotional costs, numbers of recipients are important. Using a cognitive (emotional) argument, distributions become more uniform (skewed) as numbers increase. In a survey, respondents indicated how they would donate lottery winnings of 50 Euros. Results indicated that more was donated to NGO s that respondents knew better. Second, total donations increased with the number of recipients albeit at a decreasing rate. Third, distributions of donations became more skewed as numbers increased. We comment on theoretical and practical implications.

On prediction of individual sequences

Sequential randomized prediction of an arbitrary binary sequence isinvestigated. No assumption is made on the mechanism of generating the bit sequence. The goal of the predictor is to minimize its relative loss, i.e., to make (almost) as few mistakes as the best ``expert'' in a fixed, possibly infinite, set of experts. We point out a surprising connection between this prediction problem and empirical process theory. First, in the special case of static (memoryless) experts, we completely characterize the minimax relative loss in terms of the maximum of an associated Rademacher process. Then we show general upper and lower bounds on the minimaxrelative loss in terms of the geometry of the class of experts. As main examples, we determine the exact order of magnitude of the minimax relative loss for the class of autoregressive linear predictors and for the class of Markov experts.

On some geometry and equivalence classes of normal form games

Equivalence classes of normal form games are defined using the geometryof correspondences of standard equilibiurm concepts like correlated, Nash,and robust equilibrium or risk dominance and rationalizability. Resultingequivalence classes are fully characterized and compared across differentequilibrium concepts for 2 x 2 games. It is argued that the procedure canlead to broad and game-theoretically meaningful distinctions of games aswell as to alternative ways of viewing and testing equilibrium concepts.Larger games are also briefly considered.

Sedimentation of pairs of hydrodynamically interacting semiflexible filaments

We describe the effect of hydrodynamic interactions in the sedimentation of a pair of inextensible semiflexible filaments under a uniform constant force at low Reynolds numbers. We have analyzed the different regimes and the morphology of such polymers in simple geometries, which allow us to highlight the peculiarities of the interplay between elastic and hydrodynamic stresses. Cooperative and symmetry breaking effects associated to the geometry of the fibers gives rise to characteristic motion which give them distinct properties from rigid and elastic filaments.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Parametric analysis of different compact tension specimens for fracture toughness characterisation in woven composite materials

Estudi elaborat a partir d’una estada a l’ Imperial College London, entre juliol i novembre de 2006. En aquest treball s’ha investigat la geometria més apropiada per a la caracterització de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. L’objectiu és assegurar la propagació de l’esquerda sense que la proveta falli abans per cap altre mecanisme de dany per tal de permetre la caracterització experimental de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. Amb aquesta fi, s’ha dut a terme l’anàlisi paramètrica de diferents tipus de provetes mitjançant el mètode dels elements finits (FE) combinat amb la virtual crack closure technique (VCCT). Les geometries de les provetes analitzades corresponen a la proveta de l’assaig compact tension (CT) i diferents variacions com la extended compact tension (ECT), la proveta widened compact tension (WCT), tapered compact tension (TCT) i doubly-tapered compact tension (2TCT). Com a resultat d’aquestes anàlisis s’han derivat diferents conclusions per obtenir la geometria de proveta més apropiada per a la caracterització de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. A més, també s’han dut a terme una sèrie d’assaigs experimentals per tal de validar els resultats de les anàlisis paramètriques. La concordança trobada entre els resultats numèrics i experimentals és bona tot i la presència d’efectes no previstos durant els assaigs experimentals.

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table hasn rows and m columns and all probabilities are non-null. This kind of table can beseen as an element in the simplex of n · m parts. In this context, the marginals areidentified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclideanelements of the Aitchison geometry of the simplex can also be translated into the tableof probabilities: subspaces, orthogonal projections, distances.Two important questions are addressed: a) given a table of probabilities, which isthe nearest independent table to the initial one? b) which is the largest orthogonalprojection of a row onto a column? or, equivalently, which is the information in arow explained by a column, thus explaining the interaction? To answer these questionsthree orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independenttwo-way tables and fully dependent tables representing row-column interaction. Animportant result is that the nearest independent table is the product of the two (rowand column)-wise geometric marginal tables. A corollary is that, in an independenttable, the geometric marginals conform with the traditional (arithmetic) marginals.These decompositions can be compared with standard log-linear models.Key words: balance, compositional data, simplex, Aitchison geometry, composition,orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure,contingency table

The effect of counterpoise correction and relaxation energy term to the internal rotation barriers: application to the BF3 ...NH3 and C2H4 ...SO2 dimers

The relevance of the fragment relaxation energy term and the effect of the basis set superposition error on the geometry of the BF3⋯NH3 and C2H4⋯SO2 van der Waals dimers have been analyzed. Second-order Møller-Plesset perturbation theory calculations with the d95(d,p) basis set have been used to calculate the counterpoise-corrected barrier height for the internal rotations. These barriers have been obtained by relocating the stationary points on the counterpoise-corrected potential energy surface of the processes involved. The fragment relaxation energy can have a large influence on both the intermolecular parameters and barrier height. The counterpoise correction has proved to be important for these systems

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Centralnotations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform.In this way very elaborated aspects of mathematical statistics can be understoodeasily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating,combination of likelihood and robust M-estimation functions are simple additions/perturbations in A2(Pprior). Weighting observations corresponds to a weightedaddition of the corresponding evidence.Likelihood based statistics for general exponential families turns out to have aparticularly easy interpretation in terms of A2(P). Regular exponential families formfinite dimensional linear subspaces of A2(P) and they correspond to finite dimensionalsubspaces formed by their posterior in the dual information space A2(Pprior).The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P.The discussion of A2(P) valued random variables, such as estimation functionsor likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Optical-geometrical effects on the photoluminescence spectra of Si nanocrystals embedded in SiO2

We demonstrate that thickness, optical constants, and details of the multilayer stack, together with the detection setting, strongly influence the photoluminescence spectra of Si nanocrystals embedded in SiO2. Due to multiple reflections of the visible light against the opaque silicon substrate, an interference pattern is built inside the oxide layer, which is responsible for the modifications in the measured spectra. This interference effect is complicated by the depth dependence of (i) the intensity of the excitation laser and (ii) the concentration of the emitting nanocrystals. These variations can give rise to apparent features in the recorded spectra, such as peak shifts, satellite shoulders, and even splittings, which can be mistaken as intrinsic material features. Thus, they can give rise to an erroneous attribution of optical bands or estimate of the average particle size, while they are only optical-geometrical artifacts. We have analyzed these effects as a function of material composition (Si excess fraction) and thickness, and also evaluated how the geometry of the detection setup affects the measurements. To correct the experimental photoluminescence spectra and extract the true spectral shape of the emission from Si nanocrystals, we have developed an algorithm based on a modulation function, which depends on both the multilayer sequence and the experimental configuration. This procedure can be easily extended to other heterogeneous systems.

Quantum dynamics of crystals of molecular nanomagnets inside a resonant cavity

It is found that crystals of molecular nanomagnets exhibit enhanced magnetic relaxation when placed inside a resonant cavity. A strong dependence of the magnetization curve on the geometry of the cavity has been observed, providing indirect evidence of the coherent microwave radiation by the crystals. A similar dependence has been found for a crystal placed between the Fabry-Perot superconducting mirrors.

Topological magnetic irreversibility in superconducting Pb samples of various shapes

The magnetic-field dependence of the magnetization of cylinders, disks, and spheres of pure type-I superconducting lead was investigated by means of isothermal measurements of first magnetization curves and hysteresis cycles. Depending on the geometry of the sample and the direction and intensity of the applied magnetic field, the intermediate state exhibits different irreversible features that become particularly highlighted in minor hysteresis cycles. The irreversibility is noticeably observed in cylinders and disks only when the magnetic field is parallel to the axis of revolution and is very subtle in spheres. When the magnetic field decreases from the normal state, the irreversibility appears at a temperature-dependent value whose distance to the thermodynamic critical field depends on the sample geometry. The irreversible features in the disks are altered when they are submitted to an annealing process. These results agree well with very recent high-resolution magneto-optical experiments in similar materials that were interpreted in terms of transitions between different topological structures for the flux configuration in the intermediate state. A discussion of the relative role of geometrical barriers for flux entry and exit and pinning effects as responsible for the magnetic irreversibility is given.

Dimerization of polyacetylene treated as a spin-Peierls distortion of the Heisenberg Hamiltonian

Extracting a bond-length-dependent Heisenberg-like Hamiltonian from the potential-energy surfaces of the two lowest states of ethylene, it is possible to study the geometry of polyacetylene by minimization of the cohesive energy, using both variational-cluster and Rayleigh-Schrödinger perturbative expansions. The dimerization amplitude is satisfactorily reproduced. Optimizing the variational-cluster-expansion total energy with the equal-bond-length constraint, the barrier to reversal of alternation is obtained. The alternating-to-regular phase transition is treated from the Néel-state starting function and appears to be of second order.