Rank test of location optimal for hyperbolic secant distribution

There are at least two reasons for a symmetric, unimodal, diffuse tailed hyperbolic secant distribution to be interesting in real-life applications. It displays one of the common types of non normality in natural data and is closely related to the logistic and Cauchy distributions that often arise in practice. To test the difference in location between two hyperbolic secant distributions, we develop a simple linear rank test with trigonometric scores. We investigate the small-sample and asymptotic properties of the test statistic and provide tables of the exact null distribution for small sample sizes. We compare the test to the Wilcoxon two-sample test and show that, although the asymptotic powers of the tests are comparable, the present test has certain practical advantages over the Wilcoxon test.

R-estimator of location of the generalized secant hyperbolic distribution

The generalized secant hyperbolic distribution (GSHD) proposed in Vaughan (2002) includes a wide range of unimodal symmetric distributions, with the Cauchy and uniform distributions being the limiting cases, and the logistic and hyperbolic secant distributions being special cases. The current article derives an asymptotically efficient rank estimator of the location parameter of the GSHD and suggests the corresponding one- and two-sample optimal rank tests. The rank estimator derived is compared to the modified MLE of location proposed in Vaughan (2002). By combining these two estimators, a computationally attractive method for constructing an exact confidence interval of the location parameter is developed. The statistical procedures introduced in the current article are illustrated by examples.

Novel approach to tailoring molecular weight distribution and structure with a difunctional RAFT agent

This work has demonstrated that for the first time a single RAFT agent (i. e., difunctional) can be used in conjunction with a radical initiator to obtain a desired M-n and PDI with controlled rates of polymerization. Simulations were used not only to verify the model but also to provide us with a predictive tool to generate other MWDs. It was also shown that all the MWDs prepared in this work could be translated to higher molecular weights through chain extension experiments with little or no compromise in the control of end group functionality. The ratio of monofunctional to difunctional SdC(CH2Ph)S- end groups, XPX and XP (where X) S=C(CH2Ph) S-), can be controlled by simply changing the concentration of initiator, AIBN. Importantly, the amount of dead polymer is extremely low and fulfils the criterion as suggested by Szwarc (Nature 1956) that to meet living requirements nonfunctional polymeric species formed by side reactions in the process should be undetectable by analytical techniques. In addition, this novel methodology will allow the synthesis of AB, ABA, and statistical multiblock copolymers with predetermined ratios to be produced in a one-pot reaction.

3D statistical shape models to embed spatial relationship information

This paper presents the creation of 3D statistical shape models of the knee bones and their use to embed information into a segmentation system for MRIs of the knee. We propose utilising the strong spatial relationship between the cartilages and the bones in the knee by embedding this information into the created models. This information can then be used to automate the initialisation of segmentation algorithms for the cartilages. The approach used to automatically generate the 3D statistical shape models of the bones is based on the point distribution model optimisation framework of Davies. Our implementation of this scheme uses a parameterized surface extraction algorithm, which is used as the basis for the optimisation scheme that automatically creates the 3D statistical shape models. The current approach is illustrated by generating 3D statistical shape models of the patella, tibia and femoral bones from a segmented database of the knee. The use of these models to embed spatial relationship information to aid in the automation of segmentation algorithms for the cartilages is then illustrated.

Statistical mechanics of support vector networks

Using methods of Statistical Physics, we investigate the generalization performance of support vector machines (SVMs), which have been recently introduced as a general alternative to neural networks. For nonlinear classification rules, the generalization error saturates on a plateau, when the number of examples is too small to properly estimate the coefficients of the nonlinear part. When trained on simple rules, we find that SVMs overfit only weakly. The performance of SVMs is strongly enhanced, when the distribution of the inputs has a gap in feature space.

On the annealed VC entropy for margin classifiers: A statistical mechanics study

Using techniques from Statistical Physics, the annealed VC entropy for hyperplanes in high dimensional spaces is calculated as a function of the margin for a spherical Gaussian distribution of inputs.

CDMA multiuser detection, neural networks, and statistical mechanics

A novel approach, based on statistical mechanics, to analyze typical performance of optimum code-division multiple-access (CDMA) multiuser detectors is reviewed. A `black-box' view ot the basic CDMA channel is introduced, based on which the CDMA multiuser detection problem is regarded as a `learning-from-examples' problem of the `binary linear perceptron' in the neural network literature. Adopting Bayes framework, analysis of the performance of the optimum CDMA multiuser detectors is reduced to evaluation of the average of the cumulant generating function of a relevant posterior distribution. The evaluation of the average cumulant generating function is done, based on formal analogy with a similar calculation appearing in the spin glass theory in statistical mechanics, by making use of the replica method, a method developed in the spin glass theory.

Methods of studying the planar distribution of objects in histological sections of brain tissue

This article reviews the statistical methods that have been used to study the planar distribution, and especially clustering, of objects in histological sections of brain tissue. The objective of these studies is usually quantitative description, comparison between patients or correlation between histological features. Objects of interest such as neurones, glial cells, blood vessels or pathological features such as protein deposits appear as sectional profiles in a two-dimensional section. These objects may not be randomly distributed within the section but exhibit a spatial pattern, a departure from randomness either towards regularity or clustering. The methods described include simple tests of whether the planar distribution of a histological feature departs significantly from randomness using randomized points, lines or sample fields and more complex methods that employ grids or transects of contiguous fields, and which can detect the intensity of aggregation and the sizes, distribution and spacing of clusters. The usefulness of these methods in understanding the pathogenesis of neurodegenerative diseases such as Alzheimer's disease and Creutzfeldt-Jakob disease is discussed. © 2006 The Royal Microscopical Society.

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.

Networking - a statistical physics perspective

Networking encompasses a variety of tasks related to the communication of information on networks; it has a substantial economic and societal impact on a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption requires new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with nonlinear large-scale systems. This review aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications. © 2013 IOP Publishing Ltd.

Statnote 36: Do the data fit the Poisson distribution

In previous Statnotes, many of the statistical tests described rely on the assumption that the data are a random sample from a normal or Gaussian distribution. These include most of the tests in common usage such as the ‘t’ test ), the various types of analysis of variance (ANOVA), and Pearson’s correlation coefficient (‘r’) . In microbiology research, however, not all variables can be assumed to follow a normal distribution. Yeast populations, for example, are a notable feature of freshwater habitats, representatives of over 100 genera having been recorded . Most common are the ‘red yeasts’ such as Rhodotorula, Rhodosporidium, and Sporobolomyces and ‘black yeasts’ such as Aurobasidium pelculans, together with species of Candida. Despite the abundance of genera and species, the overall density of an individual species in freshwater is likely to be low and hence, samples taken from such a population will contain very low numbers of cells. A rare organism living in an aquatic environment may be distributed more or less at random in a volume of water and therefore, samples taken from such an environment may result in counts which are more likely to be distributed according to the Poisson than the normal distribution. The Poisson distribution was named after the French mathematician Siméon Poisson (1781-1840) and has many applications in biology, especially in describing rare or randomly distributed events, e.g., the number of mutations in a given sequence of DNA after exposure to a fixed amount of radiation or the number of cells infected by a virus given a fixed level of exposure. This Statnote describes how to fit the Poisson distribution to counts of yeast cells in samples taken from a freshwater lake.

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.

Revealing statistical properties of quasi-CW fibre lasers in bandwidth-limited measurements

We introduce a general technique how to reveal in experiments of limited electrical bandwidth which is lower than the optical bandwidth of the optical signal under study, whether the statistical properties of the light source obey Gaussian distribution or mode correlations do exist. To do that one needs to perform measurements by decreasing the measurement bandwidth. We develop a simple model of bandwidth-limited measurements and predict universal laws how intensity probability density function and intensity auto-correlation function of ideal completely stochastic source of Gaussian statistics depend on limited measurement bandwidth and measurement noise level. Results of experimental investigation are in good agreement with model predictions. In particular, we reveal partial mode correlations in the radiation of quasi-CW Raman fibre laser.