And if that is true, then selection for adaptive variants indirectly shapes neighboring genomic regions, leading to "a situation where neutral alleles have their frequencies determined by more than genetic drift, and instead have a new layer of stochasticity induced by selection," Kern explained by email: Linked selection would produce more variance between generations than one would expect under neutrality.
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Unlike demographic and genetic stochasticity, environmental stochasticity tends to affect populations of all sizes. ; Natural catastrophes : An extension of environmental stochasticity, natural disasters are random, large scale events such as blizzards, droughts, storms, or fires that reduce a population directly within a short period of time. Natural catastrophes are the hardest events to predict, and MVP models often have difficulty factoring these in. ; Genetic stochasticity : Small populations are vulnerable to genetic stochasticity, the random change in allele frequencies over time, also known as genetic drift.
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Demographic stochasticity refers to variability in population growth arising from sampling random births and deaths in a population of finite size. In small populations, demographic stochasticity will decrease the population growth rate, causing an effect similar to the Allee effect, which will increase the risk of population extinction. Whether or not demographic stochasticity can be considered a part of Allee effect is somewhat contentious however. The most current definition of Allee effect considers the correlation between population density and mean individual fitness.
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This is in contrast to most of the works in the learning literature, where stochasticity is explicitly accounted through a noise term.
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In 1912, the Laysan duck had an effective population size of 7 at most. Small populations are at a greater risk of extinction than larger populations due to small populations having less capacity to recover from adverse stochastic (i.e. random) events. Such events may be divided into four sources: ; Demographic stochasticity : Demographic stochasticity is often only a driving force toward extinction in populations with fewer than 50 individuals.
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Recently, ant colonies are also studied and modeled for their relevance in machine learning, complex interactive networks, stochasticity of encounter and interaction networks, parallel computing, and other computing fields.
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Johan Paulsson is a Swedish mathematician and systems biologist at Harvard Medical School. He is a leading researcher in systems biology and stochastic processes, specializing in stochasticity in gene networks and plasmid reproduction.
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Random events influence the fecundity and survival of individuals in a population, and in larger populations these events tend to be stabilized toward a steady growth rate. However, in small populations there is much more relative variance, which can in turn cause extinction. ; Environmental stochasticity : Small, random changes in the abiotic and biotic components of the ecosystem that a population inhabits fall under environmental stochasticity. Examples are changes in climate over time, and arrival of another species that competes for resources.
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Mixed Poisson processes are doubly stochastic in the sense that in a first step, the value of the random variable X is determined. This value then determines the "second order stochasticity" by increasing or decreasing the original intensity measure \mu .
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Hochberg works on interdisciplinary applications of evolutionary theory including host-parasite coevolution, antibiotic resistance, social evolution, and cancer evolution. Beginning in 2013, Hochberg began to work on evolutionary rescue, a relatively new theory about how organisms escape extinction that integrates traditional adaptation theory with stochasticity and demographics.
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This allows the model to be as simple and verifiable as possible. # Stochasticity: Biological systems exhibit behavior that appears to be random. The probability of a particular behavior can be determined for a system as a whole and then be translated into rules for the individual agents.
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Benettin, G., Christodoulidi, H., and Ponno, A. (2013). The Fermi–Pasta–Ulam Problem and Its Underlying Integrable Dynamics. Journal of Statistical Physics, 1–18Casetti, L., Cerruti-Sola, M., Pettini, M., and Cohen, E. G. D. (1997). The Fermi–Pasta–Ulam problem revisited: stochasticity thresholds in nonlinear Hamiltonian systems.
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By including stochasticity in the choosing of the side the player must use, the game becomes fair and winnable by all players but is subject to chance. By making the choice of the player piece (x or o) subject to chance, the game becomes fair and winnable by all players.
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Fewer than 100 mature plants are known and, extrapolating to suitable habitat, fewer than 250 mature plants are likely to exist in the wild. Because of its small population size, limited habitat and susceptibility to environmental and demographic stochasticity, the species is listed as Endangered under New South Wales’ Threatened Species Conservation Act 1995.
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Saltz, D. (1996) Minimizing extinction probability due to demographic stochasticity in a reintroduced herd of Persian Fallow Deer Dama dama mesopotamica. Biological Conservation, 75(1):27-33. After a successful breeding program, many hundreds of deer have been derived from this original stock. It was later feared that the animals taken by Israel from Semeskandeh consisted of hybrids.
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A recent study of microbial succession evaluated the balances between stochastic and deterministic processes in the bacterial colonization of a salt marsh chronosequence. The results of this study show that, much like in macro succession, early colonization (primary succession) is mostly influenced by stochasticity while secondary succession of these bacterial communities was more strongly influenced by deterministic factors.
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In queueing theory, Gittins index is used to determine the optimal scheduling of jobs, e.g., in an M/G/1 queue. The mean completion time of jobs under a Gittins index schedule can be determined using the SOAP approach. Note that the dynamics of the queue are intrinsically Markovian, and stochasticity is due to the arrival and service processes.
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Together, these observations tend to suggest that contrary to the prevailing wisdom that phenotype specification is highly deterministic, stochasticity may be a confounding factor in specifying cell fate. This thinking may also help explain how a given cell can reversibly switch phenotypes as seen in EMT and MET or for that matter, a drug-sensitive cell from developing resistance and switching back to drug sensitivity, or the transformation of a normal cell to a malignant one and its reversal to normalcy. Indeed, such stochasticity in phenotypic switching is also thought to underlie cellular differentiation, generation of induced pluripotent stem cells (iPS cells), tumor heterogeneity and emergence of cancer stem cells from non-stem cancer cells. Implicit in the MRK model, the PIN configuration contains information that can specify the cell's phenotype.
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Avian clutch size in relation to rainfall seasonality and stochasticity along an aridity gradient across South Africa. Ostrich 75: 259-268. The rufous-eared warbler spends a large portion of time on the ground, and will run between patches of cover. It often flies between patches of scrubby vegetation low to the ground, and as a result it mistaken for a rodent.
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Random changes in allele frequencies can also be caused by effects other than sampling error, for example random changes in selection pressure. One important alternative source of stochasticity, perhaps more important than genetic drift, is genetic draft. Genetic draft is the effect on a locus by selection on linked loci. The mathematical properties of genetic draft are different from those of genetic drift.
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Unlike in the case of normal cells, state switching in cancer cells is widely believed to arise due to somatic mutations. However, there is growing concern that such a deterministic view of a phenomenon that is reversible is not entirely consistent with multiple lines of evidence which indicate that stochasticity may also play an important role in driving phenotypic plasticity.
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Huffaker's studies of spatial structure and species interactions are an example of early experimentation in metapopulation dynamics. Since the experiments of Huffaker and Levins, models have been created which integrate stochastic factors. These models have shown that the combination of environmental variability (stochasticity) and relatively small migration rates cause indefinite or unpredictable persistence. However, Huffaker's experiment almost guaranteed infinite persistence because of the controlled immigration variable.
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Another example of noise in plants is lateral root behavior. People found that the growth of lateral roots is unpredictable in genetically identical plants which grow in the same environment. One more example of seed germination may illustrate the benefit of developmental noise in plants. Stochasticity in the timing of germination ensures that at least a fraction of the progeny will survive to reproduce.
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For instance, habitat destruction resembling slash-and-burn agriculture is thought to affect rare species rather than poor colonizers. Models that incorporate stochasticity, or random fluctuation in populations, show extinction debt occurring over different time scales than classic models. Most recently, extinction debts have been estimated through the use models derived from neutral theory. Neutral theory has very different assumptions than the metapopulation models described above.
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Traditional population genetic models deal with alleles and genotypes, and are frequently stochastic. In evolutionary game theory, developed first by John Maynard Smith, evolutionary biology concepts may take a deterministic mathematical form, with selection acting directly on inherited phenotypes. These same models can be applied to studying the evolution of human preferences and ideologies. Many variants on these models have been developed, which incorporate weak selection, mutual population structure, stochasticity, etc.
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Differential games have been applied to economics. Recent developments include adding stochasticity to differential games and the derivation of the stochastic feedback Nash equilibrium (SFNE). A recent example is the stochastic differential game of capitalism by Leong and Huang (2010). In 2016 Yuliy Sannikov received the Clark Medal from the American Economic Association for his contributions to the analysis of continuous time dynamic games using stochastic calculus methods.
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I realized that stochasticity had its limits; there was something else at play in the universe. That realization forced a major alteration of my Stochastic Space-time theory, a modification I call Crypto-stochastic Spacetime theory.” Almost immediately, Crypto- stochastic Space-time theory gave results: he could explain the two-slit experiment, superposition in general, and explain photon polarization (a more compelling explanation than afforded by conventional quantum mechanics).
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The Laguna Mountains skipper's population decline is credited mostly to habitat destruction. Having a single larval host plant makes reproduction difficult if a given Cleveland's horkelia (Horkelia clevelandii) population encounters environmental stochasticity . Habitat destruction and degradation is primarily associated with urban and agricultural development as well as recreational activities. Most common degradation is affiliated with overgrazing and trampling of the Cleveland's horkelia (Horkelia clevelandii) by cattle leading to habitat fragmentation.
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The most direct inspiration for GANs was noise-contrastive estimation, which uses the same loss function as GANs and which Goodfellow studied during his PhD in 2010–2014. Other people had similar ideas but did not develop them similarly. An idea involving adversarial networks was published in a 2010 blog post by Olli Niemitalo. This idea was never implemented and did not involve stochasticity in the generator and thus was not a generative model.
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The helmeted honeyeater is vulnerable to catastrophes such as fire, as fire will most likely cause severe damage to breeding territories. Availability of suitable breeding habitat limits the helmeted honeyeater's reproduction ability. Expansion of habitat and limiting the further loss and degradation of present habitat, and supplementary feeding are key actions for effective management of the species.McCarthy, M.A., Extinction dynamics of the helmeted honeyeater: effects of demography, stochasticity, inbreeding and spatial structure.
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Stochastic metapopulation models take into account stochasticity, which is the non-deterministic or random processes in nature. With this approach a metapopulation may be above the threshold if determined that it is unlikely it will go extinct within a certain time period. The complex nature of these models can result in a small metapopulation that is considered to be above the deterministic extinction threshold, but in reality has a high risk of extinction .
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Transient dynamics, which are effects on the extinction threshold because of instability in either the metapopulation or environmental conditions, is also a large player in modeling results. Landscapes that have recently endured habitat loss and fragmentation may be less able to sustain a metapopulation than previously understood without considering transient dynamics. Finally, environmental stochasticity, which may be spatially correlated, can lead to amplified regional stochastic fluctuations and therefore greatly affect the extinction risk.
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This has important implications for magnetic dynamos. In fact, a very high electrical conductivity translates into high magnetic Reynolds numbers, which indicates that the plasma will be turbulent. In fact, the conventional views on flux freezing in highly conducting plasmas are inconsistent with the phenomenon of spontaneous stochasticity. It has become a standard argument even in textbooks, unfortunately, that magnetic flux freezing should hold better and better as magnetic diffusivity tends to zero (non-dissipative regime).
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Abiotic factors include the physical geography and hydrology of the estuary, including nutrient inputs, sediment load, turbidity, environmental stochasticity, climate and anthropogenic influences. Abiotic factors tend to drive production in the estuarine environment, and are mediated by biotic factors. Biotic factors include nutrient uptake and primary production, secondary production of zooplankton, food web and trophic dynamics, energetic transfer, advection and dispersal in and out of the system, survival and mortality, predation, and competition from introduced species.
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Due to their small, sensitive population size, any manipulation/disturbance to skipper habitat has large impacts on skipper populations. Additionally, the Cleveland's horkelia (Horkelia clevelandii) sees population declines during dry season leading to Laguna Mountains skipper population declines. Because the Laguna Mountains skipper has no known predators, changes in population size is a direct result of habitat manipulation or environmental stochasticity. Furthermore, over collection of Laguna Mountains skipper populations by scientists pose as a potential threat to population size.
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Roughness progression for a road in Texas, US. Blue dots show the times of maintenance. The International Roughness Index (IRI) is the roughness index most commonly obtained from measured longitudinal road profiles. It is calculated using a quarter-car vehicle math model, whose response is accumulated to yield a roughness index with units of slope (in/mi, m/km, etc.). This performance measure has less stochasticity and subjectivity in comparison to other pavement performance indicators, but it is not completely devoid of randomness.
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These global value assignments may deterministically depend on some 'hidden' classical variable which, in turn, may vary stochastically for some classical reason (as in statistical mechanics). The measured assignments of observables may therefore finally stochastically change. This stochasticity is however epistemic and not ontic as in the standard formulation of quantum mechanics. # Value assignments pre-exist and are independent of the choice of any other observables which, in standard quantum mechanics, are described as commuting with the measured observable, and they are also measured.
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Prior integrate-and-fire models with stochastic characteristics relied on including a noise to simulate stochasticity. The Galves–Löcherbach model distinguishes itself because it is inherently stochastic, incorporating probabilistic measures directly in the calculation of spikes. It is also a model that may be applied relatively easily, from a computational standpoint, with a good ratio between cost and efficiency. It remains a non-Markovian model, since the probability of a given neuronal spike depends on the accumulated activity of the system since the last spike.
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There are no concrete explanations for the evolution of trophic eggs. The two main conflicting arguments are: #They are an evolved maternal phenotype #They are simply a failed generation of offspring, produced as a result of reproductive stochasticity. If they have evolved (and are now distinct) from functionless by-products of failed reproduction, then trophic eggs should be more easily available and provide more nutrients to the offspring than their evolutionary predecessors. There seems to be clear evidence of this adaptation in many species.
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1\. LIANTI has been used to probe stochastic firing of DNA replication origins in single cells. LIANTI was performed in single human fibroblast cells in early S phase, enabling direct observation of DNA replication origin firing and replicon formation based on the detection of single-cell copy-number gain with kilobase resolution. Certain level of cell-to-cell heterogeneity was observed, suggesting a large degree of stochasticity in replication origin firing in early S phase. 2\. LIANTI has been used to characterize UV-induced SNVs in single cells.
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Tigers have become extinct in some areas because of extrinsic factors such as habitat destruction, poaching, disease, floods, fires and drought, decline of prey species for the same reasons, as well as intrinsic factors such as demographic stochasticity and genetic deterioration. Recognizing the conservation reliance of tigers, Project Tiger is establishing a national science-based framework for monitoring tiger population trends in order to manage the species more effectively. India now has 28 tiger reserves, located in 17 states. These reserves cover including 1.14% of the total land area of the country.
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Minimum viable population (MVP) is a lower bound on the population of a species, such that it can survive in the wild. This term is commonly used in the fields of biology, ecology, and conservation biology. MVP refers to the smallest possible size at which a biological population can exist without facing extinction from natural disasters or demographic, environmental, or genetic stochasticity. The term "population" is defined as a group of interbreeding individuals in similar geographic area that undergo negligible gene flow with other groups of the species.
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Patterning mechanisms such as those described by the French flag model can be perturbed at many levels (production and stochasticity of the diffusion of the morphogen, production of the receptor, stochastic of the signaling cascade, etc). Patterning is therefore inherently noisy. Robustness against this noise and genetic perturbation is therefore necessary to ensure proper that cells measure accurately positional information. Studies of the zebrafish neural tube and antero-posterior patternings has shown that noisy signaling leads to imperfect cell differentiation that is later corrected by transdifferentiation, migration or cell death of the misplaced cells.
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Jefferson Antonio Galves, known simply as Antonio Galves, is a Brazilian mathematician, professor of the Institute of Mathematics and Statistics of the University of São Paulo and member of the Brazilian Academy of Sciences. His field of studies is related to statistician issues models, in particular models that have stochasticity and variable range of memory. In 2007 he won the National Order of Scientific Merit. Professor Galves is also the leader of NeuroMat, a research center established in 2013 at the University of São Paulo that is dedicated to integrating mathematical modeling and theoretical neuroscience.
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Stochasticity associated with linkage to other genes that are under selection is not the same as sampling error, and is sometimes known as genetic draft in order to distinguish it from genetic drift. When the allele frequency is very small, drift can also overpower selection even in large populations. For example, while disadvantageous mutations are usually eliminated quickly in large populations, new advantageous mutations are almost as vulnerable to loss through genetic drift as are neutral mutations. Not until the allele frequency for the advantageous mutation reaches a certain threshold will genetic drift have no effect.
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The minimum viable population (MVP) is a lower bound on the population of a species, such that it can survive in the wild. More specifically MVP is the smallest possible size at which a biological population can exist without facing extinction from natural disasters or demographic, environmental, or genetic stochasticity. The term "population" refers to the population of a species in the wild. As a reference standard, MVP is usually given with a population survival probability of somewhere between ninety and ninety-five percent and calculated for between one hundred and one thousand years into the future.
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Models that oversimplify reality can result in biased data. Multiple parameters such as number of mutations accumulated since introduction, stochasticity, the genetic difference of strains introduced, and the sampling effort can make unbiased estimates of CST difficult even with whole-genome sequences, especially if sampling is limited, mutation rates are low, or if pathogens were recently introduced. More information on the factors that influence CST rates is needed for the contraction of more appropriate models to study these events. The process of using genetic markers to estimate CST rates should take into account several important factors to reduce bias.
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However, in age and stage-structured models, a constant MSY does not always exist. In such cases, cyclic harvest is optimal where the yield and resource fluctuate in size, through time. In addition, environmental stochasticity interacts with demographically structured populations in fundamentally different ways than for unstructured populations when determining optimal harvest. In fact, the optimal biomass to be left in the ocean, when fished at MSY, can be either higher or lower than in analogous deterministic models, depending on the details of the density dependent recruitment function, if stage-structure is also included in the model.
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Therefore, random variation resulting from birth and death events would not be considered part of Allee effect as the increased risk of extinction is not a consequence of the changing fates of individuals within the population. Meanwhile, when demographic stochasticity results in fluctuations of sex ratios, it arguably reduces the mean individual fitness as population declines. For example, a fluctuation in small population that causes a scarcity in one sex would in turn limit the access of mates for the opposite sex, decreasing the fitness of the individuals within the population. This type of Allee effect will likely be more prevalent in monogamous species than polygynous species.
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Causes of raptor mortality in Crete. Raptors Worldwide. World Working Group on Birds of Prey/MME, Budapest, 849-860. Increasing powerline collisions resulting in electrocution from highly dangerous pylons are a major cause of mortality, resulting in unsustainably high population turnover. In one Spanish study area, 56% of juveniles and 13% of adults were killed by electrocution. In France, 44% of radio-tagged post-dispersal juveniles were killed by electrocution.Mañosa, S. (2001). Strategies to identify dangerous electricity pylons for birds. Biodiversity & Conservation, 10(11), 1997-2012.Soutullo, A., López-López, P., & Urios, V. (2008). Incorporating spatial structure and stochasticity in endangered Bonelli’s eagle’s population models: implications for conservation and management. Biological Conservation, 141(4), 1013-1020.
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In oxygenated amorphous carbon, oxygen is added as a dopant to facilitate the breaking of the carbon filaments because it is known that carbon-based materials, when exposed to oxygen, break down by so- called Joule heating. Very recently, he and his team have focused on mimicking the unprecedented computational capabilities of the human brain to build ultra-low power cognitive computing systems. They have built artificial synapses and spiking neurons using phase-change materials, and showed that the inherent stochasticity of these neurons enables population-based computation, similar to the way the human brain processes information. Using the all phase- change neuromorphic architecture, they demonstrated the basic computational primitive of a temporal correlation detector.
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Johan Paulsson was born in 1973, in Kristinehamn, a small city in the Swedish province of Värmland. He studied at Uppsala University, where he obtained a BSc in Mathematics in 1996, a Masters of Science in Molecular Biology in 1996, and a Ph.D. in Molecular Biology in 2000 on stochasticity in intracellular circuits, in particular in plasmid copy control, under the supervision of Profs. Mans Ehrenberg and Kurt Nordström. In 2000 he moved to Princeton University, where he was a Lewis-Thomas Fellow in Biophysics, where he did the research for his paper "Summing up the noise in genetic networks", which received wide attention because it gave a firm theoretical footing to the budding field of genetic noise.
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They found myelination to be a characteristics of each neural subtype reflecting random interaction between neurons and oligodendrocytes, myelinating cells of the CNS. Arlotta and her team propose that this diversity and stochasticity of myelination underlies the diverse array of communication patterns that arise in the cortex. Arlotta also develops and applies brain organoids to test various aspects of brain development and neurogenesis in models that better recapitulate the CNS but are more malleable to testing. Arlotta led a team of researchers towards developing organoids that were able to grow for up to 9 months, generate dendritic spines, as well as a broad array of diverse cells types as would be observed in the human brain.
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As an evolutionary theory, key innovations has come under critical scrutiny due to the fact that it is hard to test. Identification depends on finding correlation between the innovation and increased diversity by comparing sister taxa, but this does not prove causality or isolate other causes of diversity such as stochasticity or habitat, and it is possible to 'cherry pick' examples that fit the hypothesis. In addition the retrospective identification of key innovations offers little in terms of understanding the processes and pressures that resulted in the adaptation, and may identify a very complex evolutionary process as a single event. An example of this is the evolution of avian flight, which was identified as a key innovation in 1963 by Ernst Mayr.
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Although loose definitions of superspreader events exist, some effort has been made at defining what qualifies as a superspreader event (SSEV). Lloyd-Smith et al. (2005) define a protocol to identify a superspreader event as follows: # estimate the effective reproductive number, R, for the disease and population in question; # construct a Poisson distribution with mean R, representing the expected range of Z due to stochasticity without individual variation; # define an SSEV as any infected person who infects more than Z(n) others, where Z(n) is the nth percentile of the Poisson(R) distribution. This protocol defines a 99th-percentile SSEV as a case which causes more infections than would occur in 99% of infectious histories in a homogeneous population.
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Stochastic quantum mechanics (or the stochastic interpretation) is an interpretation of quantum mechanics. The modern application of stochastics to quantum mechanics involves the assumption of spacetime stochasticity, the idea that the small-scale structure of spacetime is undergoing both metric and topological fluctuations (John Archibald Wheeler's "quantum foam"), and that the averaged result of these fluctuations recreates a more conventional- looking metric at larger scales that can be described using classical physics, along with an element of nonlocality that can be described using quantum mechanics. A stochastic interpretation of quantum mechanics is due to persistent vacuum fluctuation. The main idea is that vacuum or spacetime fluctuations are the reason for quantum mechanics and not a result of it as it is usually considered.
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This theory has been supported by experiments showing that within a population of mouse haematopoietic progenitor cells, underlying stochastic variability in the distribution of Sca-1, a stem cell factor, subdivides the population into groups exhibiting variable rates of cellular differentiation. For example, under the influence of erythropoietin (an erythrocyte-differentiation factor), a subpopulation of cells (as defined by the levels of Sca-1) differentiated into erythrocytes at a sevenfold higher rate than the rest of the population. Furthermore, it was shown that if allowed to grow, this subpopulation re- established the original subpopulation of cells, supporting the theory that this is a stochastic, reversible process. Another level at which stochasticity may be important is in the process of apoptosis and self-renewal.
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A metapopulation is generally considered to consist of several distinct populations together with areas of suitable habitat which are currently unoccupied. In classical metapopulation theory, each population cycles in relative independence of the other populations and eventually goes extinct as a consequence of demographic stochasticity (fluctuations in population size due to random demographic events); the smaller the population, the more chances of inbreeding depression and prone to extinction. Although individual populations have finite life-spans, the metapopulation as a whole is often stable because immigrants from one population (which may, for example, be experiencing a population boom) are likely to re-colonize habitat which has been left open by the extinction of another population. They may also emigrate to a small population and rescue that population from extinction (called the rescue effect).
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Social sequence analysts are interested in a number of quantifiable properties of ordered social processes, and measured have been developed to reflect these. They include measures of stochasticity or sequential connection (whether and to what extent sequentially adjacent status depend on each other, in a Markovian sense, sequential recurrence (whether specific events or status can occur more than one in the course of a given sequence), the extent to which states are logically prerequisites of each other (an issue that is explored in both event structure analysis and other forms of prerequisite analysis, such as PERT analysis), stationarity (whether the relationship between two sequence states or elements differs depending on where in the sequence that relationship is evaluated), the presence of spells (whether given states or elements are “sticky” or have inertia and therefore tend to reoccur and remain once they occur), and homogeneity (whether sequence characteristics like stationarity are similar, and thus whether sequences have the same structure, across subjects that belong to different social groupings, such as race, gender, or socioeconomic status).Gottman, John Mordechai, and Anup Kumar Roy. 1990. Sequential Analysis: A Guide for Behavioral Researchers.
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