Self-Selection Consistent Functions

This paper studies collective choice rules whose outcomes consist of a collection of simultaneous decisions, each one of which is the only concern of some group of individuals in society. The need for such rules arises in different contexts, including the establishment of jurisdictions, the location of multiple public facilities, or the election of representative committees. We define a notion of allocation consistency requiring that each partial aspect of the global decision taken by society as a whole should be ratified by the group of agents who are directly concerned with this particular aspect. We investigate the possibility of designing envy-free allocation consistent rules, we also explore whether such rules may also respect the Condorcet criterion.Consistency, Condorcet criterion

The Intermediate Scale MSSM, the Higgs Mass and F-theory Unification

Even if SUSY is not present at the Electro-Weak scale, string theory suggests its presence at some scale M_{SS} below the string scale M_s to guarantee the absence of tachyons. We explore the possible value of M_{SS} consistent with gauge coupling unification and known sources of SUSY breaking in string theory. Within F-theory SU(5) unification these two requirements fix M_{SS} ~ 5 x 10^{10} GeV at an intermediate scale and a unification scale M_c ~ 3 x 10^{14} GeV. As a direct consequence one also predicts the vanishing of the quartic Higgs SM self-coupling at M_{SS} ~10^{11} GeV. This is tantalizingly consistent with recent LHC hints of a Higgs mass in the region 124-126 GeV. With such a low unification scale M_c ~ 3 x 10^{14} GeV one may worry about too fast proton decay via dimension 6 operators. However in the F-theory GUT context SU(5) is broken to the SM via hypercharge flux. We show that this hypercharge flux deforms the SM fermion wave functions leading to a suppression, avoiding in this way the strong experimental proton decay constraints. In these constructions there is generically an axion with a scale of size f_a ~ M_c/(4\pi)^2 ~ 10^{12} GeV which could solve the strong CP problem and provide for the observed dark matter. The prize to pay for these attractive features is to assume that the hierarchy problem is solved due to anthropic selection in a string landscape.Comment: 48 pages, 8 figures. v3: further minor correction

Wavelet-based density estimation for noise reduction in plasma simulations using particles

For given computational resources, the accuracy of plasma simulations using particles is mainly held back by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on wavelet analysis is proposed and tested to reduce this noise. The method, known as wavelet based density estimation (WBDE), was previously introduced in the statistical literature to estimate probability densities given a finite number of independent measurements. Its novel application to plasma simulations can be viewed as a natural extension of the finite size particles (FSP) approach, with the advantage of estimating more accurately distribution functions that have localized sharp features. The proposed method preserves the moments of the particle distribution function to a good level of accuracy, has no constraints on the dimensionality of the system, does not require an a priori selection of a global smoothing scale, and its able to adapt locally to the smoothness of the density based on the given discrete particle data. Most importantly, the computational cost of the denoising stage is of the same order as one time step of a FSP simulation. The method is compared with a recently proposed proper orthogonal decomposition based method, and it is tested with three particle data sets that involve different levels of collisionality and interaction with external and self-consistent fields

The Demographics of Broad Line Quasars in the Mass-Luminosity Plane II. Black Hole Mass and Eddington Ratio Functions

We employ a flexible Bayesian technique to estimate the black hole mass and Eddington ratio functions for Type 1 (i.e., broad line) quasars from a uniformly-selected data set of ~58,000 quasars from the SDSS DR7. We find that the SDSS becomes significantly incomplete at M_{BH} < 3 x 10^8 M_{Sun} or L / L_{Edd} < 0.07, and that the number densities of Type 1 quasars continue to increase down to these limits. Both the mass and Eddington ratio functions show evidence of downsizing, with the most massive and highest Eddington ratio black holes experiencing Type 1 quasar phases first, although the Eddington ratio number densities are flat at z < 2. We estimate the maximum Eddington ratio of Type 1 quasars in the observable Universe to be L / L_{Edd} ~ 3. Consistent with our results in Paper I, we do not find statistical evidence for a so-called "sub-Eddington boundary" in the mass-luminosity plane of broad line quasars, and demonstrate that such an apparent boundary in the observed distribution can be caused by selection effect and errors in virial BH mass estimates. Based on the typical Eddington ratio in a given mass bin, we estimate typical growth times for the black holes in Type 1 quasars and find that they are typically comparable to or longer than the age of the universe, implying an earlier phase of accelerated (i.e., with higher Eddington ratios) and possibly obscured growth. The large masses probed by our sample imply that most of our black holes reside in what are locally early type galaxies, and we interpret our results within the context of models of self-regulated black hole growth.Comment: Submitted to ApJ, 25 pages (emulateapj), 15 figures; revised to match accepted version with primary changes to the introduction and discussion, replaced Fig 1

Model Selection with the Loss Rank Principle

A key issue in statistics and machine learning is to automatically select the "right" model complexity, e.g., the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with polynomials. We suggest a novel principle - the Loss Rank Principle (LoRP) - for model selection in regression and classification. It is based on the loss rank, which counts how many other (fictitious) data would be fitted better. LoRP selects the model that has minimal loss rank. Unlike most penalized maximum likelihood variants (AIC, BIC, MDL), LoRP depends only on the regression functions and the loss function. It works without a stochastic noise model, and is directly applicable to any non-parametric regressor, like kNN.Comment: 31 LaTeX pages, 1 figur

Bose-Einstein distribution, condensation transition and multiple stationary states in multiloci evolution of diploid population

The mapping between genotype and phenotype is encoded in the complex web of epistatic interaction between genetic loci. In this rugged fitness landscape, recombination processes, which tend to increase variation in the population, compete with selection processes that tend to reduce genetic variation. Here we show that the Bose-Einstein distribution describe the multiple stationary states of a diploid population under this multi-loci evolutionary dynamics. Moreover, the evolutionary process might undergo an interesting condensation phase transition in the universality class of a Bose-Einstein condensation when a finite fraction of pairs of linked loci, is fixed into given allelic states. Below this phase transition the genetic variation within a species is significantly reduced and only maintained by the remaining polymorphic loci.Comment: (12 pages, 7 figures