Extremal geometry of a Brownian porous medium

Abstract: Omitted [too many formulae]. Keywords: Brownian motion, random set, capacity, largest inradius, cover time, principal Dirichlet eigenvalue, large deviation principle

Isovector and isoscalar superfluid phases in rotating nuclei

The subtle interplay between the two nuclear superfluids, isovector T=1 and isoscalar T=0 phases, are investigated in an exactly soluble model. It is shown that T=1 and T=0 pair-modes decouple in the exact calculations with the T=1 pair-energy being independent of the T=0 pair-strength and vice-versa. In the rotating-field, the isoscalar correlations remain constant in contrast to the well known quenching of isovector pairing. An increase of the isoscalar (J=1, T=0) pair-field results in a delay of the bandcrossing frequency. This behaviour is shown to be present only near the N=Z line and its experimental confirmation would imply a strong signature for isoscalar pairing collectivity. The solutions of the exact model are also discussed in the Hartree-Fock-Bogoliubov approximation.Comment: 5 pages, 4 figures, submitted to PR

Degree distribution of shortest path trees and bias of network sampling algorithms

In this article, we explicitly derive the limiting distribution of the degree distribution of the shortest path tree from a single source on various random network models with edge weights. We determine the power-law exponent of the degree distribution of this tree and compare it to the degree distribution of the original graph. We perform this analysis for the complete graph with edge weights that are powers of exponential random variables (weak disorder in the stochastic mean-field model of distance) as well as on the configuration model with edge-weights drawn according to any continuous distribution. In the latter, the focus is on settings where the degrees obey a power law, and we show that the shortest path tree again obeys a power law with the same degree power-law exponent. We also consider random r-regular graphs for large r, and show that the degree distribution of the shortest path tree is closely related to the shortest path tree for the stochastic mean field model of distance. We use our results to explain an empirically observed bias in network sampling methods. This is part of a general program initiated in previous works by Bhamidi, van der Hofstad and Hooghiemstra [7, 8, 6] of analyzing the effect of attaching random edge lengths on the geometry of random network models

Extremal geometry of a Brownian porous medium

Analysis and Stochastic

Degeneracies when T=0 Two Body Matrix Elements are Set Equal to Zero and Regge's 6j Symmetry Relations

The effects of setting all T=0 two body interaction matrix elements equal to a constant (or zero) in shell model calculations (designated as $=0$) are investigated. Despite the apparent severity of such a procedure, one gets fairly reasonable spectra. We find that using $=0$ in single j shell calculations degeneracies appear e.g. the $I={1/2} ^{-}$ and ${13/2}^{-}$ states in $^{43}$Sc are at the same excitation energies; likewise the I=$3_{2}^{+}$,$7_{2}^{+}$,9$^{+}_{1}$ and 10$^{+}_{1}$ states in $^{44}$Ti. The above degeneracies involve the vanishing of certain 6j and 9j symbols. The symmetry relations of Regge are used to explain why these vanishings are not accidental. Thus for these states the actual deviation from degeneracy are good indicators of the effects of the T=0 matrix elements. A further indicator of the effects of the T=0 interaction in an even - even nucleus is to compare the energies of states with odd angular momentum with those that are even

Perceptual Pluralism

Perceptual systems respond to proximal stimuli by forming mental representations of distal stimuli. A central goal for the philosophy of perception is to characterize the representations delivered by perceptual systems. It may be that all perceptual representations are in some way proprietarily perceptual and differ from the representational format of thought (Dretske 1981; Carey 2009; Burge 2010; Block ms.). Or it may instead be that perception and cognition always trade in the same code (Prinz 2002; Pylyshyn 2003). This paper rejects both approaches in favor of perceptual pluralism, the thesis that perception delivers a multiplicity of representational formats, some proprietary and some shared with cognition. The argument for perceptual pluralism marshals a wide array of empirical evidence in favor of iconic (i.e., image-like, analog) representations in perception as well as discursive (i.e., language-like, digital) perceptual object representations

Latent class analysis variable selection

We propose a method for selecting variables in latent class analysis, which is the most common model-based clustering method for discrete data. The method assesses a variable's usefulness for clustering by comparing two models, given the clustering variables already selected. In one model the variable contributes information about cluster allocation beyond that contained in the already selected variables, and in the other model it does not. A headlong search algorithm is used to explore the model space and select clustering variables. In simulated datasets we found that the method selected the correct clustering variables, and also led to improvements in classification performance and in accuracy of the choice of the number of classes. In two real datasets, our method discovered the same group structure with fewer variables. In a dataset from the International HapMap Project consisting of 639 single nucleotide polymorphisms (SNPs) from 210 members of different groups, our method discovered the same group structure with a much smaller number of SNP

Assessing the number of users who are excluded by domestic heating controls

This is the pre-print version of the Article. This Article is also referred to as: "Assessing the 'Design Exclusion' of Heating Controls at a Low-Cost, Low-Carbon Housing Development". - Copyright @ 2011 Taylor & FrancisSpace heating accounts for almost 60% of the energy delivered to housing which in turn accounts for nearly 27% of the total UK's carbon emissions. This study was conducted to investigate the influence of heating control design on the degree of ‘user exclusion’. This was calculated using the Design Exclusion Calculator, developed by the Engineering Design Centre at the University of Cambridge. To elucidate the capability requirements of the system, a detailed hierarchical task analysis was produced, due to the complexity of the overall task. The Exclusion Calculation found that the current design placed excessive demands upon the capabilities of at least 9.5% of the UK population over 16 years old, particularly in terms of ‘vision’, ‘thinking’ and ‘dexterity’ requirements. This increased to 20.7% for users over 60 years old. The method does not account for the level of numeracy and literacy and so the true exclusion may be higher. Usability testing was conducted to help validate the results which indicated that 66% of users at a low-carbon housing development could not programme their controls as desired. Therefore, more detailed analysis of the cognitive demands placed upon the users is required to understand where problems within the programming process occur. Further research focusing on this cognitive interaction will work towards a solution that may allow users to behave easily in a more sustainable manner