A statistical-mechanical analysis of coded CDMA with regular LDPC codes

We analyze, using the replica method of statistical mechanics, the theoretical performance of coded code-division multiple-access (CDMA) systems in which regular low-density parity-check (LDPC) codes are used for channel coding.

Statistical mechanics of broadcast channels using low-density parity-check codes

We investigate the use of Gallager's low-density parity-check (LDPC) codes in a degraded broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network communication schemes and is known to provide better performance than simple time sharing methods when algebraic codes are used. The statistical physics based analysis shows that the practical performance of the suggested method, achieved by employing the belief propagation algorithm, is superior to that of LDPC based time sharing codes while the best performance, when received transmissions are optimally decoded, is bounded by the time sharing limit.

Strategic group theory:review, examination and application in the UK pharmaceutical industry

Purpose – The purpose of this paper is to consider the current status of strategic group theory in the light of developments over the last three decades. and then to discuss the continuing value of the concept, both to strategic management research and practising managers. Design/methodology/approach – Critical review of the idea of strategic groups together with a practical strategic mapping illustration. Findings – Strategic group theory still provides a useful approach for management research, which allows a detailed appraisal and comparison of company strategies within an industry. Research limitations/ implications – Strategic group research would undoubtedly benefit from more directly comparable, industry-specific studies, with a more careful focus on variable selection and the statistical methods used for validation. Future studies should aim to build sets of industry specific variables that describe strategic choice within that industry. The statistical methods used to identify strategic groupings need to be robust to ensure that strategic groups are not solely an artefact of method. Practical implications – The paper looks specifically at an application of strategic group theory in the UK pharmaceutical industry. The practical benefits of strategic groups as a classification system and of strategic mapping as a strategy development and analysis tool are discussed. Originality/value – The review of strategic group theory alongside alternative taxonomies and application of the concept to the UK pharmaceutical industry.

Noisy random Boolean formulae:a statistical physics perspective

Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.

Inference and optimization of real edges on sparse graphs:A statistical physics perspective

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory. © 2007 The American Physical Society.

Statistical physics of error-correcting codes

In this thesis we use statistical physics techniques to study the typical performance of four families of error-correcting codes based on very sparse linear transformations: Sourlas codes, Gallager codes, MacKay-Neal codes and Kanter-Saad codes. We map the decoding problem onto an Ising spin system with many-spins interactions. We then employ the replica method to calculate averages over the quenched disorder represented by the code constructions, the arbitrary messages and the random noise vectors. We find, as the noise level increases, a phase transition between successful decoding and failure phases. This phase transition coincides with upper bounds derived in the information theory literature in most of the cases. We connect the practical decoding algorithm known as probability propagation with the task of finding local minima of the related Bethe free-energy. We show that the practical decoding thresholds correspond to noise levels where suboptimal minima of the free-energy emerge. Simulations of practical decoding scenarios using probability propagation agree with theoretical predictions of the replica symmetric theory. The typical performance predicted by the thermodynamic phase transitions is shown to be attainable in computation times that grow exponentially with the system size. We use the insights obtained to design a method to calculate the performance and optimise parameters of the high performance codes proposed by Kanter and Saad.

Managing careers and managing fairness : an organisational justice theory perspective on employee evaluations of, and reactions to, organisational career management practices

This thesis presents the results of a multi-method investigation of employee perceptions of fairness in relation to their career management experiences. Organisational justice theory (OJT) was developed as a theoretical framework and data were gathered via 325 quantitative questionnaires, 20 semi-structured interviews and the analysis of a variety of company documents and materials. The results of the questionnaire survey provided strong support for the salience of employee perceptions of justice in regard to their evaluations of organisational career management (OCM) practices, with statistical support emerging for both an agent-systems and interaction model of organisational justice. The qualitative semi-structured interviews provided more detailed analysis of how fairness was experienced in practice, and confirmed the importance of the OJT constructs of fairness within this career management context. Fairness themes to emerge from this analysis included, equity, needs, voice, bias suppression, consistency, ethicality, respect and feedback drawing on many of the central tenants of distributive, procedural, interpersonal and information justice. For the career management literature there is empirical confirmation of a new theoretical framework for understanding employee evaluations of, and reactions to, OCM practices. For the justice literatures a new contextual domain is explored and confirmed, thus extending further the influence and applicability of the theory. For practitioners a new framework for developing, delivering and evaluating their own OCM policies and systems is presented.

Risk homeostasis theory in simulated environments

This thesis has two aims. First, it sets out to develop an alternative methodology for the investigation of risk homeostasis theory (RHT). It is argued that the current methodologies of the pseudo-experimental design and post hoc analysis of road-traffic accident data both have their limitations, and that the newer 'game' type simulation exercises are also, but for different reasons, incapable of testing RHT predictions. The alternative methodology described here is based on the simulation of physical risk with intrinsic reward rather than a 'points pay-off'. The second aim of the thesis is to examine a number of predictions made by RHT through the use of this alternative methodology. Since the pseudo-experimental design and post hoc analysis of road-traffic data are both ill-suited to the investigation of that part of RHT which deals with the role of utility in determining risk-taking behaviour in response to a change in environmental risk, and since the concept of utility is critical to RHT, the methodology reported here is applied to the specific investigation of utility. Attention too is given to the question of which behavioural pathways carry the homeostasis effect, and whether those pathways are 'local' to the nature of the change in environmental risk. It is suggested that investigating RHT through this new methodology holds a number of advantages and should be developed further in an attempt to answer the RHT question. It is suggested too that the methodology allows RHT to be seen in a psychological context, rather than the statistical context that has so far characterised its investigation. The experimental findings reported here are in support of hypotheses derived from RHT and would therefore seem to argue for the importance of the individual and collective target level of risk, as opposed to the level of environmental risk, as the major determinant of accident loss.

A statistical analysis of regional variation in adverb position in a corpus of written Standard American English

This paper investigates whether the position of adverb phrases in sentences is regionally patterned in written Standard American English, based on an analysis of a 25 million word corpus of letters to the editor representing the language of 200 cities from across the United States. Seven measures of adverb position were tested for regional patterns using the global spatial autocorrelation statistic Moran’s I and the local spatial autocorrelation statistic Getis-Ord Gi*. Three of these seven measures were indentified as exhibiting significant levels of spatial autocorrelation, contrasting the language of the Northeast with language of the Southeast and the South Central states. These results demonstrate that continuous regional grammatical variation exists in American English and that regional linguistic variation exists in written Standard English.

A Statistical Convergence Aplication for the Hopfield Networks

When Recurrent Neural Networks (RNN) are going to be used as Pattern Recognition systems, the problem to be considered is how to impose prescribed prototype vectors ξ^1,ξ^2,...,ξ^p as fixed points. The synaptic matrix W should be interpreted as a sort of sign correlation matrix of the prototypes, In the classical approach. The weak point in this approach, comes from the fact that it does not have the appropriate tools to deal efficiently with the correlation between the state vectors and the prototype vectors The capacity of the net is very poor because one can only know if one given vector is adequately correlated with the prototypes or not and we are not able to know what its exact correlation degree. The interest of our approach lies precisely in the fact that it provides these tools. In this paper, a geometrical vision of the dynamic of states is explained. A fixed point is viewed as a point in the Euclidean plane R2. The retrieving procedure is analyzed trough statistical frequency distribution of the prototypes. The capacity of the net is improved and the spurious states are reduced. In order to clarify and corroborate the theoretical results, together with the formal theory, an application is presented

Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective

Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.

Matrix-Variate Statistical Distributions and Fractional Calculus

MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthday

Using extreme value theory to value stock market returns

Extreme stock price movements are of great concern to both investors and the entire economy. For investors, a single negative return, or a combination of several smaller returns, can possible wipe out so much capital that the firm or portfolio becomes illiquid or insolvent. If enough investors experience this loss, it could shock the entire economy. An example of such a case is the stock market crash of 1987. Furthermore, there has been a lot of recent interest regarding the increasing volatility of stock prices. ^ This study presents an analysis of extreme stock price movements. The data utilized was the daily returns for the Standard and Poor's 500 index from January 3, 1978 to May 31, 2001. Research questions were analyzed using the statistical models provided by extreme value theory. One of the difficulties in examining stock price data is that there is no consensus regarding the correct shape of the distribution function generating the data. An advantage with extreme value theory is that no detailed knowledge of this distribution function is required to apply the asymptotic theory. We focus on the tail of the distribution. ^ Extreme value theory allows us to estimate a tail index, which we use to derive bounds on the returns for very low probabilities on an excess. Such information is useful in evaluating the volatility of stock prices. There are three possible limit laws for the maximum: Gumbel (thick-tailed), Fréchet (thin-tailed) or Weibull (no tail). Results indicated that extreme returns during the time period studied follow a Fréchet distribution. Thus, this study finds that extreme value analysis is a valuable tool for examining stock price movements and can be more efficient than the usual variance in measuring risk. ^