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Law Distribution (law + distribution)
Kinds of Law Distribution Selected AbstractsStatistical behavior of complex cancer karyotypesGENES, CHROMOSOMES AND CANCER, Issue 4 2005Mattias Höglund Epithelial tumors commonly show complex and variable karyotypes that obscure the identification of general patterns of the karyotypic evolution. To overcome some of these problems, we previously systematically analyzed the accumulated cytogenetic data from individual tumor types by using various statistical means. In the present study, we compare previous results obtained for nine tumor types and perform several meta-analyses of data obtained from a number of epithelial tumors, including head and neck, kidney, bladder, breast, colorectal, ovarian, and lung cancer, as well as from malignant melanoma and Wilms tumor, with the specific aim of discovering common patterns of karyotypic evolution. We show that these tumors frequently develop through a hypo- or a hyperdiploid pathway and progress by an increasing number of alternative imbalances through at least two karyotypic phases, Phases I and II, and possibly through a third, Phase III. During Phase I, the karyotypes exhibited a power law distribution of both the number of changes per tumor and the frequency distribution at which bands were involved in breaks. At the transition from Phase I to Phase II/III, the observed power law distributions were lost, indicating a transition from an ordered and highly structured process to a disordered and chaotic pattern. The change in karyotypic orderliness at the transition from Phase I to Phase II/III was also shown by a drastic difference in karyotypic entropy. © 2005 Wiley-Liss, Inc. [source] Temporal Patterns of Atrial Arrhythmia Recurrences in Patients with Implantable Defibrillators: Implications for Assessing Antiarrhythmic TherapiesJOURNAL OF CARDIOVASCULAR ELECTROPHYSIOLOGY, Issue 4 2002LINA A. SHEHADEH M.S. Temporal Patterns of Atrial Arrhythmias.Introduction: The statistical measures commonly used to assess therapies for recurrent atrial arrhythmias (such as time to first recurrence) often assume a uniformly random pattern of arrhythmic events over time. However, the true temporal pattern of atrial arrhythmia recurrences is unknown. The aim of this study was to use linear and nonlinear analyses to characterize the temporal pattern of atrial arrhythmia recurrences in patients with implantable cardioverter defibrillators. Methods and Results: The time and date of atrial tachyarrhythmias recorded in 65 patients with combined atrial and ventricular defibrillators were used to construct a probability density function (PDF) and a model of a Poisson distribution of arrhythmic events for each patient. Average patient age was 66 ± 10 years and follow-up was 7.8 ± 4.8 months. A total of 10,759 episodes of atrial tachyarrhythmias were analyzed (range 43 to 618 episodes per patient). The PDF fit a power law distribution for all 65 patients, with an average r2= 0.89 ± 0.08. The PDF distribution differed significantly from the model Poisson distribution in 47 of 65 patients (P = 0.0002). Differences from the Poisson distribution were noted for patients both taking (30/43 patients; P < 0.015) and not taking (17/22 patients; P < 0.017) antiarrhythmic drugs. Median time between atrial arrhythmia detections for all 65 patients was 10.8 minutes. Conclusion: In implantable cardioverter defibrillator patients, the temporal pattern of frequent recurrences of atrial tachyarrhythmias usually is characterized by a power law distribution. The unique statistical properties of this type of distribution should be considered in designing outcome measures for treatment of atrial tachyarrhythmias. [source] Network of sexual contacts and sexually transmitted HIV infection in Burkina FasoJOURNAL OF MEDICAL VIROLOGY, Issue 6 2006Vito Latora Abstract Two thirds of the people who have been infected by human immunodeficiency virus (HIV) in the world live in Sub-Saharan African countries. The results of a study measuring the degree distribution of the network of sexual contacts in Burkina Faso are described. Such a network is responsible for the spread of sexually transmitted diseases, and in particular of HIV. It has been found that the number of different sexual partners reported by males is a power law distribution with an exponent ,,=,2.9 (0.1). This is consistent with the degree distribution of scale-free networks. On the other hand, the females can be divided into two groups: the prostitutes with an average of 400 different partners per year, and females with a stable partner, having a rapidly decreasing degree distribution. Such a result may have important implications on the control of sexually transmitted diseases and in particular of HIV. Since scale-free networks have no epidemic threshold, a campaign based on prevention and anti-viral treatment of few highly connected nodes can be more successful than any policy based on enlarged but random distribution of the available anti-viral treatments. J. Med. Virol. 78:724,729, 2006. © 2006 Wiley-Liss, Inc. [source] The Self, the symbolic and synchronicity: virtual realities and the emergence of the psycheTHE JOURNAL OF ANALYTICAL PSYCHOLOGY, Issue 3 2005George B. Hogenson Abstract:, Jung's theory of synchronicity is seen as a step in the development of a complete theory of the symbol. In so doing, a number of proposals are made for modelling the symbolic process along lines already in use for modelling a variety of other phenomena, ranging from language to the behaviour of earthquakes. These modelling techniques involve processes of self-organization, and raise issues of scaling in systems including symbolic systems. The proposal is made that symbolic systems obey the same rules of scaling that these other systems obey, and that symbolic systems can therefore be understood as exhibiting the characteristics of a power law distribution,a concept that is explained and developed in the paper. It is finally proposed that synchronicity is an aspect of the symbolic that can be characterized as exhibiting a high degree of ,symbolic density'. [source] Statistical behavior of complex cancer karyotypesGENES, CHROMOSOMES AND CANCER, Issue 4 2005Mattias Höglund Epithelial tumors commonly show complex and variable karyotypes that obscure the identification of general patterns of the karyotypic evolution. To overcome some of these problems, we previously systematically analyzed the accumulated cytogenetic data from individual tumor types by using various statistical means. In the present study, we compare previous results obtained for nine tumor types and perform several meta-analyses of data obtained from a number of epithelial tumors, including head and neck, kidney, bladder, breast, colorectal, ovarian, and lung cancer, as well as from malignant melanoma and Wilms tumor, with the specific aim of discovering common patterns of karyotypic evolution. We show that these tumors frequently develop through a hypo- or a hyperdiploid pathway and progress by an increasing number of alternative imbalances through at least two karyotypic phases, Phases I and II, and possibly through a third, Phase III. During Phase I, the karyotypes exhibited a power law distribution of both the number of changes per tumor and the frequency distribution at which bands were involved in breaks. At the transition from Phase I to Phase II/III, the observed power law distributions were lost, indicating a transition from an ordered and highly structured process to a disordered and chaotic pattern. The change in karyotypic orderliness at the transition from Phase I to Phase II/III was also shown by a drastic difference in karyotypic entropy. © 2005 Wiley-Liss, Inc. [source] | ||||||||||