Advanced mean field methods:theory and practice

A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

When electronic management tools work - and don't work - in social-based distribution channels:a study of IT manufacturers and resellers

Electronic information tools have become increasingly popular with channel manufacturers in their efforts to manage resellers. Although these tools have been found to increase the efficiency of communications, researchers and practitioners alike have questioned their effectiveness. To investigate how top-down electronic information affects social channel relationships we consider the use of such tools in information technology distribution channels. Using electronic communications theory and channel governance theory we hypothesize that the usefulness of the tools is a function of the type of information inherent in each tool (demand creation information or supply fulfillment information) and the particular communications characteristics of this information.

Two sides to attitudinal commitment:the effect of calculative and loyalty commitment on enforcement mechanism in distribution channels

Previous conceptualizations of attitudinal commitment are extended by considering two very different components of a manufacturer’s attachment to an independent channel intermediary. Relying on commitment theory, a model is developed that describes how attitudinal commitment may reside in either the instrumental or the social strain of a manufacturer’s relationship with its distributor. For each strain, the developmental role played by key facets of the channel setting—relative dependence, pledges, and trust—are shown. Furthermore, the nature of the attachment bond is posited to motivate very different governance mechanisms as the distribution agreement is enforced by either social or contractual means. Empirical support for the model demonstrates that an expanded view of attitudinal commitment is important in understanding the complex nature of attachment in channel relationships.

Size frequency distribution of senile plaques in post-mortem brains of five patients with senile dementia of the Alzheimer type (SDAT)

Numerous senile plaques are one of the most characteristic histological findings in SDAT brains. Large classical plaques may develop from smaller uncored forms. There is no strong evidence that, once formed, plaques disappear from the tissue. We have examined cresyl-violet stained sections of the parahippocampal gyrus (PHG), hippocampus, frontal lobe and temporal lobe of five SDAT patients. The frequency of various sizes of plaques were determined in each of these brain regions. Statistical analysis showed that the ratio of large plaques to small plaques was greater in the hippocampal formation (especially the PHG) than in the neocortex. One explanation of these results is that plaques grow more rapidly in the hippocampal formation than elsewhere. Alternatively, if the rate of plaque growth is much the same in different brain regions, the data suggest that plaques develop first in the hippocampal formation (especially the PHG) and only later spread to the neocortex. This interpretation is also consistent with the theory that the neuropathology of SDAT spreads from the olfactory cortex via the hippocampal formation to the neocortex. Further development of this technique may help identify the site of the primary lesion in SDAT.

Productivity analysis and measurement

The state of the art in productivity measurement and analysis shows a gap between simple methods having little relevance in practice and sophisticated mathematical theory which is unwieldy for strategic and tactical planning purposes, -particularly at company level. An extension is made in this thesis to the method of productivity measurement and analysis based on the concept of added value, appropriate to those companies in which the materials, bought-in parts and services change substantially and a number of plants and inter-related units are involved in providing components for final assembly. Reviews and comparisons of productivity measurement dealing with alternative indices and their problems have been made and appropriate solutions put forward to productivity analysis in general and the added value method in particular. Based on this concept and method, three kinds of computerised models two of them deterministic, called sensitivity analysis and deterministic appraisal, and the third one, stochastic, called risk simulation, have been developed to cope with the planning of productivity and productivity growth with reference to the changes in their component variables, ranging from a single value 'to• a class interval of values of a productivity distribution. The models are designed to be flexible and can be adjusted according to the available computer capacity expected accuracy and 'presentation of the output. The stochastic model is based on the assumption of statistical independence between individual variables and the existence of normality in their probability distributions. The component variables have been forecasted using polynomials of degree four. This model is tested by comparisons of its behaviour with that of mathematical model using real historical data from British Leyland, and the results were satisfactory within acceptable levels of accuracy. Modifications to the model and its statistical treatment have been made as required. The results of applying these measurements and planning models to the British motor vehicle manufacturing companies are presented and discussed.

What determines the size frequency distribution of β-amyloid (Aβ) deposits in Alzheimer's disease patients?

The factors determining the size of individual β-amyloid (A,8) deposits and their size frequency distribution in tissue from Alzheimer's disease (AD) patients have not been established. In 23/25 cortical tissues from 10 AD patients, the frequency of Aβ deposits declined exponentially with increasing size. In a random sample of 400 Aβ deposits, 88% were closely associated with one or more neuronal cell bodies. The frequency distribution of (Aβ) deposits which were associated with 0,1,2,...,n neuronal cell bodies deviated significantly from a Poisson distribution, suggesting a degree of clustering of the neuronal cell bodies. In addition, the frequency of Aβ deposits declined exponentially as the number of associated neuronal cell bodies increased. Aβ deposit area was positively correlated with the frequency of associated neuronal cell bodies, the degree of correlation being greater for pyramidal cells than smaller neurons. These data suggested: (1) the number of closely adjacent neuronal cell bodies which simultaneously secrete Aβ was an important factor determining the size of an Aβ deposit and (2) the exponential decline in larger Aβ deposits reflects the low probability that larger numbers of adjacent neurons will secrete Aβ simultaneously to form a deposit. © 1995.

Theory and data for area summation of contrast with and without uncertainty:evidence for a noisy energy model

Contrast sensitivity improves with the area of a sine-wave grating, but why? Here we assess this phenomenon against contemporary models involving spatial summation, probability summation, uncertainty, and stochastic noise. Using a two-interval forced-choice procedure we measured contrast sensitivity for circular patches of sine-wave gratings with various diameters that were blocked or interleaved across trials to produce low and high extrinsic uncertainty, respectively. Summation curves were steep initially, becoming shallower thereafter. For the smaller stimuli, sensitivity was slightly worse for the interleaved design than for the blocked design. Neither area nor blocking affected the slope of the psychometric function. We derived model predictions for noisy mechanisms and extrinsic uncertainty that was either low or high. The contrast transducer was either linear (c1.0) or nonlinear (c2.0), and pooling was either linear or a MAX operation. There was either no intrinsic uncertainty, or it was fixed or proportional to stimulus size. Of these 10 canonical models, only the nonlinear transducer with linear pooling (the noisy energy model) described the main forms of the data for both experimental designs. We also show how a cross-correlator can be modified to fit our results and provide a contemporary presentation of the relation between summation and the slope of the psychometric function.

Work-life balance benefits:employee attitudes and behaviors through the lens of social exchange theory

The question of what to provide employees in order that they reciprocate with desirable behaviors in the work place has resulted in a great amount of work in the area of social exchange. Although offering fair compensation, including salary or wages and employee benefits, has been extensively studied, the effects of offering specific types of benefits, such as work-life balance benefits, and the intangible rewards that such an offering inadvertently offers, has only been minimally explored. Utilizing past literature, this current research examined the offering of work-life balance benefits, the value employees place on those benefits, the communication of the benefits by the organization to employees, and their effect on employee attitudes and behaviors. The goal was to identify the effect on desirable outcomes when work-life balance benefits are offered to determine the usefulness to the organization of offering such benefits. To test these effects, a study of an organization known to offer a strong work-life balance benefits package was undertaken. This was accomplished through the distribution of questionnaires to identify the possible relationships involving 408 employee respondents and their 79 supervisors. This was followed with interviews of 12 individuals to ascertain the true reasons for links observed through analysis. Analysis of the data was accomplished through correlation analysis, multilevel analysis and regression analysis generated by SPSS. The results of the quantitative analysis showed support for a relationship between the offering of work-life balance benefits and perceived organizational support, perceived distributive justice, job satisfaction and OCBO. The analysis also showed a lack of support for a relationship between the offering of work-life balance benefits and organizational commitment, OCBI and IRB. The interviews offered possible reasons for the lack of support regarding the relationship between the offering of work-life balance benefits and organizational commitment as well as organizational citizenship behaviors (OCBI and IRB). The implications of these findings on future research, theory and practice in the offering of work-life balance benefits are discussed.

Benevolent sexism at work:gender differences in the distribution of challenging developmental experiences

The current research draws from ambivalent sexism theory to examine potential gender differences in the quantity and quality of developmental work experiences. In a sample of managers in the energy industry, men and women reported participating in a similar number of developmental experiences (with comparable levels of support), but men rated these experiences as more challenging and received more negative feedback than did women. Similarly, a sample of female managers in the health care industry reported comparable amounts, but less challenging types, of developmental experiences than their male counterparts'. The results of three complementary experiments suggest that benevolent sexism is negatively related to men's assignment of challenging experiences to female targets but that men and women were equally likely to express interest in challenging experiences. Taken together, these results suggest that stereotype-based beliefs that women should be protected may limit women's exposure to challenging assignments, which in turn may partially explain the underrepresentation of women at the highest levels of organizations. © The Author(s) 2012.

Incorporating social role theory into topic models for social media content analysis

In this paper, we explore the idea of social role theory (SRT) and propose a novel regularized topic model which incorporates SRT into the generative process of social media content. We assume that a user can play multiple social roles, and each social role serves to fulfil different duties and is associated with a role-driven distribution over latent topics. In particular, we focus on social roles corresponding to the most common social activities on social networks. Our model is instantiated on microblogs, i.e., Twitter and community question-answering (cQA), i.e., Yahoo! Answers, where social roles on Twitter include "originators" and "propagators", and roles on cQA are "askers" and "answerers". Both explicit and implicit interactions between users are taken into account and modeled as regularization factors. To evaluate the performance of our proposed method, we have conducted extensive experiments on two Twitter datasets and two cQA datasets. Furthermore, we also consider multi-role modeling for scientific papers where an author's research expertise area is considered as a social role. A novel application of detecting users' research interests through topical keyword labeling based on the results of our multi-role model has been presented. The evaluation results have shown the feasibility and effectiveness of our model.

Theory of optimal power budget in quasi-linear dispersion-managed fibre links

A theory of an optimal distribution of the gain of in-line amplifiers in dispersion-managed transmission systems is developed. As an example of the application of the general method, a design of the line with periodically imbalanced in-line amplification is proposed.

Statnote 39: The binomial distribution: comparing two proportions

Many populations consist of two classes only, e.g., alive or dead, present or absent, clean or dirty, infected or non-infected, and it is the proportion or percentage of observations that fall into one of these classes that is of interest to an investigator. An observation that falls into one of the two classes is considered a ‘success’ (S), and ‘p’ is defined as the proportion of observations falling into that class. If a random sample of size ‘n’ is obtained from a population, the probability of obtaining 0, 1, 2, 3, etc., successes is then given by the binomial distribution. The binomial distribution can be used as the basis of a number of statistical tests but is most useful when comparing two proportions. This statnote describes two such scenarios in which the binomial distribution is used to compare: (1) two proportions when the samples are independent and (2) two proportions when the samples are paired.

Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws

* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.

Problems and Theorems in the Theory of Multiplier Sequences

The purpose of this paper is (1) to highlight some recent and heretofore unpublished results in the theory of multiplier sequences and (2) to survey some open problems in this area of research. For the sake of clarity of exposition, we have grouped the problems in three subsections, although several of the problems are interrelated. For the reader’s convenience, we have included the pertinent definitions, cited references and related results, and in several instances, elucidated the problems by examples.

On the Coherence Between Probability and Possibility Measures

* This paper is supported by CICYT (Spain) under Project TIN 2005-08943-C02-01.