Probabilistic approach in weighted Markov branching processes

This note provides a new probabilistic approach in discussing the weighted Markov branching process (WMBP) which is a natural generalisation of the ordinary Markov branching process. Using this approach, some important characteristics regarding the hitting times of such processes can be easily obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained. The close link between these newly developed processes and the well-known compound Poisson processes is investigated. It is revealed that any weighted Markov branching process (WMBP) is a random time change of a compound Poisson process.

Serial chimerism analyses indicate that mixed haemopoietic chimerism influences the probability of graft rejection and disease recurrence following allogeneic stem cell transplantation (SCT) for severe aplastic anaemia (SAA): indication for routine assessment of chimerism post SCT for SAA

Ninety-one patients were studied serially for chimeric status following allogeneic stem cell transplantation (SCT) for severe aplastic anaemia (SAA) or Fanconi Anaemia (FA). Short tandem repeat polymerase chain reaction (STR-PCR) was used to stratify patients into five groups: (A) complete donor chimeras (n = 39), (B) transient mixed chimeras (n = 15) (C) stable mixed chimeras (n = 18), (D) progressive mixed chimeras (n = 14) (E) recipient chimeras with early graft rejection (n = 5). As serial sampling was not possible in Group E, serial chimerism results for 86 patients were available for analysis. The following factors were analysed for association with chimeric status: age, sex match, donor type, aetiology of aplasia, source of stem cells, number of cells engrafted, conditioning regimen, graft-versus-host disease (GvHD) prophylaxis, occurrence of acute and chronic GvHD and survival. Progressive mixed chimeras (PMCs) were at high risk of late graft rejection (n = 10, P <0.0001). Seven of these patients lost their graft during withdrawal of immunosuppressive therapy. STR-PCR indicated an inverse correlation between detection of recipient cells post-SCT and occurrence of acute GvHD (P = 0.008). PMC was a bad prognostic indicator of survival (P = 0.003). Monitoring of chimeric status during cyclosporin withdrawal may facilitate therapeutic intervention to prevent late graft rejection in patients transplanted for SAA.

Inverse planned constant dose rate volumetric modulated arc therapy (VMAT) as an efficient alternative to five-field intensity modulated radiation therapy (IMRT) for prostate

Purpose: The aim of this work was to determine if volumetric modulated arc therapy (VMAT) plans, created for constant dose-rate (cdrVMAT) delivery are a viable alternative to step and shoot five-field intensity modulated radiation therapy (IMRT). Materials and methods: The cdrVMAT plans, inverse planned on a treatment planning system with no solution to account for couch top or rails, were created for delivery on a linear accelerator with no variable dose rate control system. A series of five-field IMRT and cdrVMAT plans were created using dual partial arcs (gantry rotating between 260° and 100°) with 4° control points for ten prostate patients with the average rectal constraint incrementally increased. Pareto fronts were compared for the planning target volume homogeneity and average rectal dose between the two techniques for each patient. Also investigated were tumour control probability and normal tissue complication probability values for each technique. The delivery parameters [monitor units (MU) and time] and delivery accuracy of the IMRT and VMAT plans were also compared. Results: Pareto fronts showed that the dual partial arc plans were superior to the five-field IMRT plans, particularly for the clinically acceptable plans where average rectal doses were less for rotational plans (p = 0·009) with no statistical difference in target homogeneity. The cdrVMAT plans had significantly more MU (p = 0·005) but the average delivery time was significantly less than the IMRT plans by 42%. All clinically acceptable cdrVMAT plans were accurate in their delivery (gamma 99·2 ± 1·1%, 3%3 mm criteria). Conclusions Accurate delivery of dual partial arc cdrVMAT avoiding the couch top and rails has been demonstrated.

The κ− μ / Inverse Gamma Fading Model

Statistical distributions have been extensively used in modeling fading effects in conventional and modern wireless communications. In the present work, we propose a novel κ − µ composite shadowed fading model, which is based on the valid assumption that the mean signal power follows the inverse gamma distribution instead of the lognormal or commonly used gamma distributions. This distribution has a simple relationship with the gamma distribution, but most importantly, its semi heavy-tailed characteristics constitute it suitable for applications relating to modeling of shadowed fading. Furthermore, the derived probability density function of the κ − µ / inverse gamma composite distribution admits a rather simple algebraic representation that renders it convenient to handle both analytically and numerically. The validity and utility of this fading model are demonstrated by means of modeling the fading effects encountered in body centric communications channels, which have been known to be susceptible to the shadowing effect. To this end, extensive comparisons are provided between theoretical and respective real-time measurement results. It is shown that these comparisons exhibit accurate fitting of the new model for various measurement set ups that correspond to realistic communication scenarios.

Alveolar echinococcosis of the liver: Diffusion-weighted MRI findings and potential role in lesion characterisation

PURPOSE: To report the diffusion-weighted MRI findings in alveolar echinococcosis (AE) of the liver and evaluate the potential role of apparent diffusion coefficients (ADCs) in the characterisation of lesions. MATERIALS AND METHODS: We retrospectively included 22 patients with 63 AE liver lesions (≥1cm), examined with 3-T liver MRI, including a free-breathing diffusion-weighted single-shot echo-planar imaging sequence (b-values=50, 300 and 600s/mm(2)). Two radiologists jointly assessed the following lesion features: size, location, presence of cystic and/or solid components (according to Kodama's classification system), relative contrast enhancement, and calcifications (on CT). The ADCtotal, ADCmin and ADCmax were measured in each lesion and the surrounding liver parenchyma. RESULTS: Three type 1, 19 type 2, 17 type 3, three type 4 and 21 type 5 lesions were identified. The mean (±SD) ADCtotal, ADCmin and ADCmax for all lesions were 1.73±0.50, 0.76±0.38 and 2.63±0.76×10(-3)mm(2)/s, respectively. The mean ADCtotal for type 1, type 2, type 3, type 4 and type 5 lesions were 1.97±1.01, 1.76±0.53, 1.73±0.41, 1.15±0.42 and 1.76±0.44×10(-3)mm(2)/s, respectively. No significant differences were found between the five lesion types, except for type 4 (p=0.0363). There was a significant correlation between the presence of a solid component and low ADCmin (r=0.39, p=0.0016), whereas an inverse correlation was found between the relative contrast enhancement and ADCtotal (r=-0.34, p=0.0072). CONCLUSION: The ADCs of AE lesions are relatively low compared to other cystic liver lesions, which may help in the differential diagnosis. Although ADCs are of little use to distinguish between the five lesion types, their low value reflects the underlying solid component.

Armor coats, inverse grading, and streambed scour in selected streams of Southern Ontario and Western New York /

Surface size analyses of Twenty and Sixteen Mile Creeks, the Grand and Genesee Rivers and Cazenovia Creek show three distinct types of bed-surface sediment: 1) a "continuous" armor coat which has a mean size of -6.5 phi and coarser, 2) a "discontinuous" armor coat which has a mean size of approximately -6.0 phi and 3) a bed with no armor coat which has a mean surface size of -5.0 phi and finer. The continuous armor coat completely covers and protects the subsurface from the flow. The discontinuous armor coat is composed of intermittently-spaced surface clasts, which provide the subsurface with only limited protection from the flow. The bed with no armor coat allows complete exposure of the subsurface to the flow. The subsurface beneath the continuous armor coats of Twenty and Sixteen Mile Creeks is possibly modified by a "vertical winnowing" process when the armor coat is p«natrat«d. This process results in a welld «v«loped inversely graded sediment sequence.vertical winnowing is reduced beneath the discontinuous armor coats of the Grand and Genesee Rivers. The reduction of vertical winnowing results in a more poorly-developed inverse grading than that found in Twenty and sixteen Mile Creeks. The streambed of Cazenovia Creek normally is not armored resulting in a homogeneous subsurface which shows no modification by vertical winnowing. This streambed forms during waning or moderate flows, suggesting it does not represent the maximum competence of the stream. Each population of grains in the subsurface layers of Twenty and sixteen Mile Creeks has been modified by vertical winnowing and does not represent a mode of transport. Each population in the subsurface layers beneath a discontinuous armor coat may partially reflect a transport mode. These layers are still inversely graded suggesting that each population is affected to some degree by vertical winnowing. The populations for sediment beneath a surface which is not armored are probably indicative of transport modes because such sediment has not been modified by vertical winnowing. Bed photographs taken in each of the five streams before and after the 1982-83 snow-melt show that the probability of movement for the surface clasts is a function of grain size. The greatest probability of of clast movement and scour depth of this study were recorded on Cazenovia Creek in areas where no armor coat is present. The scour depth in the armored beds of Twenty and Sixteen Mile Creeks is related to the probability of movement for a given mean surface size.

Flippable Pairs and Subset Comparisons in Comparative Probability Orderings and Related Simple Games

We show that every additively representable comparative probability order on n atoms is determined by at least n - 1 binary subset comparisons. We show that there are many orders of this kind, not just the lexicographic order. These results provide answers to two questions of Fishburn et al (2002). We also study the flip relation on the class of all comparative probability orders introduced by Maclagan. We generalise an important theorem of Fishburn, Peke?c and Reeds, by showing that in any minimal set of comparisons that determine a comparative probability order, all comparisons are flippable. By calculating the characteristics of the flip relation for n = 6 we discover that the regions in the corresponding hyperplane arrangement can have no more than 13 faces and that there are 20 regions with 13 faces. All the neighbours of the 20 comparative probability orders which correspond to those regions are representable. Finally we define a class of simple games with complete desirability relation for which its strong desirability relation is acyclic, and show that the flip relation carries all the information about these games. We show that for n = 6 these games are weighted majority games.

Conventional and Reciprocal Approaches to the Forward and Inverse Problems of Electroencephalography

Le problème inverse en électroencéphalographie (EEG) est la localisation de sources de courant dans le cerveau utilisant les potentiels de surface sur le cuir chevelu générés par ces sources. Une solution inverse implique typiquement de multiples calculs de potentiels de surface sur le cuir chevelu, soit le problème direct en EEG. Pour résoudre le problème direct, des modèles sont requis à la fois pour la configuration de source sous-jacente, soit le modèle de source, et pour les tissues environnants, soit le modèle de la tête. Cette thèse traite deux approches bien distinctes pour la résolution du problème direct et inverse en EEG en utilisant la méthode des éléments de frontières (BEM): l’approche conventionnelle et l’approche réciproque. L’approche conventionnelle pour le problème direct comporte le calcul des potentiels de surface en partant de sources de courant dipolaires. D’un autre côté, l’approche réciproque détermine d’abord le champ électrique aux sites des sources dipolaires quand les électrodes de surfaces sont utilisées pour injecter et retirer un courant unitaire. Le produit scalaire de ce champ électrique avec les sources dipolaires donne ensuite les potentiels de surface. L’approche réciproque promet un nombre d’avantages par rapport à l’approche conventionnelle dont la possibilité d’augmenter la précision des potentiels de surface et de réduire les exigences informatiques pour les solutions inverses. Dans cette thèse, les équations BEM pour les approches conventionnelle et réciproque sont développées en utilisant une formulation courante, la méthode des résidus pondérés. La réalisation numérique des deux approches pour le problème direct est décrite pour un seul modèle de source dipolaire. Un modèle de tête de trois sphères concentriques pour lequel des solutions analytiques sont disponibles est utilisé. Les potentiels de surfaces sont calculés aux centroïdes ou aux sommets des éléments de discrétisation BEM utilisés. La performance des approches conventionnelle et réciproque pour le problème direct est évaluée pour des dipôles radiaux et tangentiels d’excentricité variable et deux valeurs très différentes pour la conductivité du crâne. On détermine ensuite si les avantages potentiels de l’approche réciproquesuggérés par les simulations du problème direct peuvent êtres exploités pour donner des solutions inverses plus précises. Des solutions inverses à un seul dipôle sont obtenues en utilisant la minimisation par méthode du simplexe pour à la fois l’approche conventionnelle et réciproque, chacun avec des versions aux centroïdes et aux sommets. Encore une fois, les simulations numériques sont effectuées sur un modèle à trois sphères concentriques pour des dipôles radiaux et tangentiels d’excentricité variable. La précision des solutions inverses des deux approches est comparée pour les deux conductivités différentes du crâne, et leurs sensibilités relatives aux erreurs de conductivité du crâne et au bruit sont évaluées. Tandis que l’approche conventionnelle aux sommets donne les solutions directes les plus précises pour une conductivité du crâne supposément plus réaliste, les deux approches, conventionnelle et réciproque, produisent de grandes erreurs dans les potentiels du cuir chevelu pour des dipôles très excentriques. Les approches réciproques produisent le moins de variations en précision des solutions directes pour différentes valeurs de conductivité du crâne. En termes de solutions inverses pour un seul dipôle, les approches conventionnelle et réciproque sont de précision semblable. Les erreurs de localisation sont petites, même pour des dipôles très excentriques qui produisent des grandes erreurs dans les potentiels du cuir chevelu, à cause de la nature non linéaire des solutions inverses pour un dipôle. Les deux approches se sont démontrées également robustes aux erreurs de conductivité du crâne quand du bruit est présent. Finalement, un modèle plus réaliste de la tête est obtenu en utilisant des images par resonace magnétique (IRM) à partir desquelles les surfaces du cuir chevelu, du crâne et du cerveau/liquide céphalorachidien (LCR) sont extraites. Les deux approches sont validées sur ce type de modèle en utilisant des véritables potentiels évoqués somatosensoriels enregistrés à la suite de stimulation du nerf médian chez des sujets sains. La précision des solutions inverses pour les approches conventionnelle et réciproque et leurs variantes, en les comparant à des sites anatomiques connus sur IRM, est encore une fois évaluée pour les deux conductivités différentes du crâne. Leurs avantages et inconvénients incluant leurs exigences informatiques sont également évalués. Encore une fois, les approches conventionnelle et réciproque produisent des petites erreurs de position dipolaire. En effet, les erreurs de position pour des solutions inverses à un seul dipôle sont robustes de manière inhérente au manque de précision dans les solutions directes, mais dépendent de l’activité superposée d’autres sources neurales. Contrairement aux attentes, les approches réciproques n’améliorent pas la précision des positions dipolaires comparativement aux approches conventionnelles. Cependant, des exigences informatiques réduites en temps et en espace sont les avantages principaux des approches réciproques. Ce type de localisation est potentiellement utile dans la planification d’interventions neurochirurgicales, par exemple, chez des patients souffrant d’épilepsie focale réfractaire qui ont souvent déjà fait un EEG et IRM.

Some Properties of Weighted Distributions for Truncated Random Variables

The present study gave emphasis on characterizing continuous probability distributions and its weighted versions in univariate set up. Therefore a possible work in this direction is to study the properties of weighted distributions for truncated random variables in discrete set up. The problem of extending the measures into higher dimensions as well as its weighted versions is yet to be examined. As the present study focused attention to length-biased models, the problem of studying the properties of weighted models with various other weight functions and their functional relationships is yet to be examined.

A study on semigroup action on fuzzy subsets, inverse fuzzy automata and related topics

This thesis comprises five chapters including the introductory chapter. This includes a brief introduction and basic definitions of fuzzy set theory and its applications, semigroup action on sets, finite semigroup theory, its application in automata theory along with references which are used in this thesis. In the second chapter we defined an S-fuzzy subset of X with the extension of the notion of semigroup action of S on X to semigroup action of S on to a fuzzy subset of X using Zadeh's maximal extension principal and proved some results based on this. We also defined an S-fuzzy morphism between two S-fuzzy subsets of X and they together form a category S FSETX. Some general properties and special objects in this category are studied and finally proved that S SET and S FSET are categorically equivalent. Further we tried to generalize this concept to the action of a fuzzy semigroup on fuzzy subsets. As an application, using the above idea, we convert a _nite state automaton to a finite fuzzy state automaton. A classical automata determine whether a word is accepted by the automaton where as a _nite fuzzy state automaton determine the degree of acceptance of the word by the automaton. 1.5. Summary of the Thesis 17 In the third chapter we de_ne regular and inverse fuzzy automata, its construction, and prove that the corresponding transition monoids are regular and inverse monoids respectively. The languages accepted by an inverse fuzzy automata is an inverse fuzzy language and we give a characterization of an inverse fuzzy language. We study some of its algebraic properties and prove that the collection IFL on an alphabet does not form a variety since it is not closed under inverse homomorphic images. We also prove some results based on the fact that a semigroup is inverse if and only if idempotents commute and every L-class or R-class contains a unique idempotent. Fourth chapter includes a study of the structure of the automorphism group of a deterministic faithful inverse fuzzy automaton and prove that it is equal to a subgroup of the inverse monoid of all one-one partial fuzzy transformations on the state set. In the fifth chapter we define min-weighted and max-weighted power automata study some of its algebraic properties and prove that a fuzzy automaton and the fuzzy power automata associated with it have the same transition monoids. The thesis ends with a conclusion of the work done and the scope of further study.

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

An LDA and probability-based classifier for the diagnosis of Alzheimer's Disease from structural MRI

In this paper a custom classification algorithm based on linear discriminant analysis and probability-based weights is implemented and applied to the hippocampus measurements of structural magnetic resonance images from healthy subjects and Alzheimer’s Disease sufferers; and then attempts to diagnose them as accurately as possible. The classifier works by classifying each measurement of a hippocampal volume as healthy controlsized or Alzheimer’s Disease-sized, these new features are then weighted and used to classify the subject as a healthy control or suffering from Alzheimer’s Disease. The preliminary results obtained reach an accuracy of 85.8% and this is a similar accuracy to state-of-the-art methods such as a Naive Bayes classifier and a Support Vector Machine. An advantage of the method proposed in this paper over the aforementioned state of the art classifiers is the descriptive ability of the classifications it produces. The descriptive model can be of great help to aid a doctor in the diagnosis of Alzheimer’s Disease, or even further the understand of how Alzheimer’s Disease affects the hippocampus.

Destructive weighted Poisson cure rate models

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow a compound weighted Poisson distribution. This model is more flexible in terms of dispersion than the promotion time cure model. Moreover, it gives an interesting and realistic interpretation of the biological mechanism of the occurrence of event of interest as it includes a destructive process of the initial risk factors in a competitive scenario. In other words, what is recorded is only from the undamaged portion of the original number of risk factors.

The exponentiated generalized inverse Gaussian distribution

The modeling and analysis of lifetime data is an important aspect of statistical work in a wide variety of scientific and technological fields. Good (1953) introduced a probability distribution which is commonly used in the analysis of lifetime data. For the first time, based on this distribution, we propose the so-called exponentiated generalized inverse Gaussian distribution, which extends the exponentiated standard gamma distribution (Nadarajah and Kotz, 2006). Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters. The usefulness of the new model is illustrated by means of a real data set. (c) 2010 Elsevier B.V. All rights reserved.

A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis - latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.