The Rényi Redundancy of Generalized Huffman Codes

Huffman's algorithm gives optimal codes, as measured by average codeword length, and the redundancy can be measured as the difference between the average codeword length and Shannon's entropy. If the objective function is replaced by an exponentially weighted average, then a simple modification of Huffman's algorithm gives optimal codes. The redundancy can now be measured as the difference between this new average and A. Renyi's (1961) generalization of Shannon's entropy. By decreasing some of the codeword lengths in a Shannon code, the upper bound on the redundancy given in the standard proof of the noiseless source coding theorem is improved. The lower bound is improved by randomizing between codeword lengths, allowing linear programming techniques to be used on an integer programming problem. These bounds are shown to be asymptotically equal. The results are generalized to the Renyi case and are related to R.G. Gallager's (1978) bound on the redundancy of Huffman codes

Determining Principal Component Cardinality through the Principle of Minimum Description Length

PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal components. The information-theoreticMDL (Minimum Description Length) principle gives objective compression-based criteria for model selection, but it is difficult to analytically applyits modern definition - NML (Normalized Maximum Likelihood) - to theproblem of PCA. This work shows a general reduction of NML prob-lems to lower-dimension problems. Applying this reduction, it boundsthe NML of PCA, by terms of the NML of linear regression, which areknown.Comment: LOD 201

Low-energy electron scattering from methanol and ethanol

Measured and calculated differential cross sections for elastic (rotationally unresolved) electron scattering from two primary alcohols, methanol (CH3OH) and ethanol (C2H5OH), are reported. The measurements are obtained using the relative flow method with helium as the standard gas and a thin aperture as the collimating target gas source. The relative flow method is applied without the restriction imposed by the relative flow pressure conditions on helium and the unknown gas. The experimental data were taken at incident electron energies of 1, 2, 5, 10, 15, 20, 30, 50, and 100 eV and for scattering angles of 5°–130°. There are no previous reports of experimental electron scattering differential cross sections for CH3OH and C2H5OH in the literature. The calculated differential cross sections are obtained using two different implementations of the Schwinger multichannel method, one that takes all electrons into account and is adapted for parallel computers, and another that uses pseudopotentials and considers only the valence electrons. Comparison between theory and experiment shows that theory is able to describe low-energy electron scattering from these polyatomic targets quite well

Redefining smoking relapse as recovered social identity – secondary qualitative analysis of relapse narratives

Although many people in the general population manage to quit smoking, relapse is common. Theory underpinning the determinants of smoking relapse is under-developed. This article aims to specify theoretical insight into the process of relapse to smoking, to underpin effective intervention development. Secondary qualitative analysis of extended narratives of smoking relapse (n=23) were inductively coded within our conceptual framework of a socially situated narrative theoretical approach to identity. Smoking relapse is conceptualised as a situated rational response to a ‘disruption’ in individual narrative identity formation, and an attempt to recover a lost social identity. Emotional reactions to relapse, such as pleasure, but also guilt and shame, support this assertion by demonstrating the ambivalence of re-engaging in a behaviour that is situated and rational in terms of individual identity formation, yet ostracised and stigmatised by wider culture

The construction of identities in narratives about serious leisure occupations

Engagement in occupation contributes to the shaping of identity throughout the human life. The act of telling about such engagement involves interaction based on symbolic meaning; the speaker constructing an identity by conveying how the occupation is personally meaningful. This study explored meaning in narratives told by people who engage in serious leisure occupations. A total of 78 narratives were extracted from interviews with 17 people who invest considerable time and other resources into their leisure. Analysis focused on the content, structure and performance of each narrative in order to explore meaning. The meanings were organised into a framework based around three dimensions: the located self, the active self and the changing self. Each dimension has facets that the individual might emphasise, constructing a unique identity. The framework offers a structured basis for conceptualising how occupation contributes to the shaping of the internalised self and the socially situated identity

Broadcasting graphic war violence: the moral face of Channel 4

Drawing on empirical data from Channel 4 (C4) regarding the broadcasting of violent war imagery, and positioned within Goffman’s notion of the interaction ritual (1959, 1967), this article investigates how C4 negotiate potentially competing commercial, regulatory and moral requirements through processes of discretionary decision-making. Throughout, the article considers the extent to which these negotiations are presented through a series of ‘imaginings’ – of C4 and its audience – which serve to simultaneously guide and legitimate the decisions made. This manifestation of imaginings moves us beyond more blanket explanations of ‘branding’ and instead allows us to see the final programmes as the end product of a series of complex negotiations and interactions between C4 and those multiple external parties significant to the workings of their organization. The insights gleaned from this case study are important beyond the workings of C4 because they help elucidate how all institutions and organizations may view, organize and justify their practices (to both themselves and others) within the perceived constraints in which they operate

Description of Generalized Continued Fractions by Finite Automata

A generalized continued fraction algorithm associates with every real number x a sequence of integers; x is rational iff the sequence is finite. For a fixed algorithm, call a sequence of integers valid if it is the result of that algorithm on some input x0. We show that, if the algorithm is sufficiently well-behaved, then the set of all valid sequences is accepted by a finite automaton. I. Introduction. It is well known that every real number x has a unique expansion as a simple continued fraction in the form

Renal DCE-MRI model selection using Bayesian probability theory

The goal of this work was to demonstrate the utility of Bayesian probability theory-based model selection for choosing the optimal mathematical model from among 4 competing models of renal dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data. DCE-MRI data were collected on 21 mice with high (n = 7), low (n = 7), or normal (n = 7) renal blood flow (RBF). Model parameters and posterior probabilities of 4 renal DCE-MRI models were estimated using Bayesian-based methods. Models investigated included (1) an empirical model that contained a monoexponential decay (washout) term and a constant offset, (2) an empirical model with a biexponential decay term (empirical/biexponential model), (3) the Patlak–Rutland model, and (4) the 2-compartment kidney model. Joint Bayesian model selection/parameter estimation demonstrated that the empirical/biexponential model was strongly favored for all 3 cohorts, the modeled DCE signals that characterized each of the 3 cohorts were distinctly different, and individual empirical/biexponential model parameter values clearly distinguished cohorts of low and high RBF from one another. The Bayesian methods can be readily extended to a variety of model analyses, making it a versatile and valuable tool for model selection and parameter estimation.</jats:p

'Working out’ identity: distance runners and the management of disrupted identity

This article contributes fresh perspectives to the empirical literature on the sociology of the body, and of leisure and identity, by analysing the impact of long-term injury on the identities of two amateur but serious middle/long-distance runners. Employing a symbolic interactionist framework,and utilising data derived from a collaborative autoethnographic project, it explores the role of ‘identity work’ in providing continuity of identity during the liminality of long-term injury and rehabilitation, which poses a fundamental challenge to athletic identity. Specifically, the analysis applies Snow and Anderson’s (1995) and Perinbanayagam’s (2000) theoretical conceptualisations in order to examine the various forms of identity work undertaken by the injured participants, along the dimensions of materialistic, associative and vocabularic identifications. Such identity work was found to be crucial in sustaining a credible sporting identity in the face of disruption to the running self, and in generating momentum towards the goal of restitution to full running fitness and reengagement with a cherished form of leisure. KEYWORDS: identity work, symbolic interactionism, distance running, disrupted identit