Real and Stochastic Analysis: New Perspectives (Trends in Mathematics)

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Stochastic processes may be used in music to compose a fixed piece or may be produced in performance. Stochastic music was pioneered by Iannis Xenakis , who coined the term stochastic music. Earlier, John Cage and others had composed aleatoric or indeterminate music , which is created by chance processes but does not have the strict mathematical basis Cage's Music of Changes , for example, uses a system of charts based on the I-Ching. Modern electronic music production techniques make these processes relatively simple to implement, and many hardware devices such as synthesizers and drum machines incorporate randomization features.

Generative music techniques are therefore readily accessible to composers, performers, and producers. Stochastic social science theory is similar to systems theory in that events are interactions of systems, although with a marked emphasis on unconscious processes. The event creates its own conditions of possibility, rendering it unpredictable if simply for the number of variables involved. Stochastic social science theory can be seen as an elaboration of a kind of 'third axis' in which to situate human behavior alongside the traditional 'nature vs. See Julia Kristeva on her usage of the 'semiotic', Luce Irigaray on reverse Heideggerian epistemology, and Pierre Bourdieu on polythetic space for examples of stochastic social science theory.


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The term "Stochastic Terrorism" has fallen into frequent use [42] with regard to Lone wolf terrorism. Scripted violence is where a person who has a national platform describes the kind of violence that they want to be carried out. He identifies the targets and leaves it up to the listeners to carry out this violence. It is a form of terrorism. It is an act and a social phenomenon where there is an agreement to inflict massive violence on a whole segment of society.

Again, this violence is led by people in high-profile positions in the media and the government. Think of it like Charles Manson and his followers. He just had his followers carry them out. When color reproductions are made, the image is separated into its component colors by taking multiple photographs filtered for each color.

One resultant film or plate represents each of the cyan, magenta, yellow, and black data. Color printing is a binary system, where ink is either present or not present, so all color separations to be printed must be translated into dots at some stage of the work-flow. A stochastic or frequency modulated dot pattern creates a sharper image. From Wikipedia, the free encyclopedia. For use in technical analysis of financial instruments, see Stochastic oscillator. Randomly determined process. See also: Stochastic theory of hematopoiesis. Oxford University Press.

Adler; Jonathan E. Taylor 29 January Random Fields and Geometry. Stochastic Processes and Models. Cambridge University Press. Random Processes. Foundations of Modern Probability. Bressloff 22 August Stochastic Processes in Cell Biology.

Van Kampen 30 August Stochastic Processes in Physics and Chemistry. Stochastic Population Dynamics in Ecology and Conservation.

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Stochastic Methods in Neuroscience. OUP Oxford. Stochastic Processes: From Physics to Finance. Dougherty Polychotomous outcomes can be combined into groups to create binary outcomes.

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One might, for example, be interested in longevity in any of the three categories H, C, and I. The total number of such conditions is. Other groupings may also be useful, however.

N might be relevant. In any case, however, the prevalence of a combination is the sum of the prevalences of the component outcomes. When nominal and ordinal measures are reduced to binary outcomes, prevalence data is sufficient to determine all the moments of the reward matrices, and thus to calculate the statistics of healthy longevity, however that may be defined. Quantitative measures, on the other hand, do not generally imply a relation between the mean and the other moments, and thus individual data are required. Survey data provide this kind of information, and the reward matrices are created by empirically calculating the moments of the health outcome measure.

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If r i denotes the health outcome for age class i , then. Caswell and Kluge [ 26 ] applied this approach to calculate the moments of lifetime income and expenditures using individual data from the German Income and Expenditure Survey. Our example below will use grip strength measurements from the SHARE survey in European countries, but the principles are identical. The variance among individuals in lifetime healthy longevity arises from two sources: differences among the trajectories taken by individuals through their lives, and differences in health status at each age or stage within the life cycle.

The overall variance in Eq. The variance among trajectories is calculated by eliminating the variance at each age within trajectories, by fixing the rewards at their mean values [ 24 , 25 ]. Suppose that the prevalence of a condition at some age is, say, 0. Then the rewards calculated in 19 and 20 imply that an individual will spend a year with the condition with probability 0. This is obviously a source of variance among individuals. In this hypothetical situation, the mean reward is the same 0. Thus the variance calculated over the lifetime is due only to differences in the pathways that individuals follow through their lives.

In a purely age-classified model, the pathway is exactly the length of life. In a model that included some other stages imagine, for example, marital status combined with age , pathways can be more complicated, but the concept is the same. The reward matrix R 1 for fixed rewards is unchanged, but the higher moments become.

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Disability-adjusted life years are a fundamental component of perhaps the most extensive health demography study ever attempted, the Global Burden of Disease GBD study [ 27 , 28 ]. DALYs differ from simple calculations of healthy longevity in several ways. First, they are computed on a cause-specific basis, to calculate the health burden of a specific disease or condition. In principle, nothing prevents DALYs from being calculated for all causes combined. A larger value of DALY implies poorer health and a greater burden of mortality and morbidity due to the cause under consideration.

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Years lost due to mortality. An individual who dies from the cause under consideration loses some number of years of remaining life. The expectation of this loss is the remaining life expectancy at the age of death.

The GBD project calculates this from a synthetic life table based on the lowest death rates for each age group among all locations with total population exceeding 5 million [ 29 ], p.

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