Non-stochastic

Buescher M, Yeo SL, Udolph G et al 1998 Binary sibling neuronal cell fate decisions in the Drosophila embryonic central nervous system are non-stochastic and require inscuteable-mediated asymmetry of ganglion mother cells. Genes Dev 12 1858-1870... 

Determine the key chemical parameters that govern non-stochastic behavior. 

Castillo-Garit, J.A., Marrero-Ponce, Y., Torrens, F., Garcia-Domenech, R. Estimation of ADME properties in drug discovery predicting Caco-2 cell permeability using atom-based stochastic and non-stochastic linear indices. J. Pharm. Sci. 2008, 97, 1946-76. 

Averaging is a different kind of operation since it associates with a stochastic variable a non-stochastic or sure number. Alternatively it may be viewed as a projection in the following way. The set of all stochastic variables contains a subset of variables whose probability density is a delta peak. This subset is isomorphic with the sure numbers of the range and may therefore be identified with them. The operation of taking the average is then a projection of the total space of stochastic variables onto this subset. 

Remark. The following difference with ordinary, non-stochastic differential equations needs to be emphasized. All solutions of a non-stochastic equation are obtained by imposing at an arbitrary t0 an initial condition u t0) = a, and then considering all possible values of a. For a stochastic differential equation, however, one gets in this way only a subclass of solutions, namely those that happen to have no dispersion at this particular t0. 

Exercise. Solve the same equation with initial conditions u(t0) = a, u(t0) = / , where t0 0. Show that none of these solutions coincides with any solution found in the preceding exercise, unless F is non-stochastic. 

It must be remembered, however, that the derivation applied to an interval At a 1 after the initial time 0 = 0. This initial time is special because at that time the value of u was given to be equal to a non-stochastic vector a. It is easily seen that the result is equally valid when the initial value is stochastic, provided it is statistically independent of Ax. That fact enables us to apply the same equation (2.7) again to the next interval At. Since the values of At in the next interval are uncorrelated with those in the previous one owing to the shortness of tc. Admittedly there is an overlap at the boundary between both intervals, but this can only give a small error since it extends over a range of order tc out of the total interval At. Hence (2.7) is approximately valid for all times, provided atc 1. Thus the average of u(t) by itself obeys approximately the non-stochastic differential equation (2.7). 

Having treated in the previous two sections linear stochastic differential equations we now return to the general case (1.1). Just as normal differential equations, it can be translated into a linear equation by going to the associated Liouville equation. To do this we temporarily take a single realization y(t) of Y(t) and consider the non-stochastic equation... 

The mathematical description of the modelled process uses a combination of one or more stochastic cores and phenomenological parts related to non-stochastic process components. 

Here (OjoU) accounts for precession arising from both the static field and the non-stochastic motion in the presence of the gradient, wJjf[r o(t), t]. 

In the recommendation published in 1977, basic principles are to prevent detrimental non-stochastic effects and to limit the probability of stochastic effects to levels deemed to be acceptable. Table 6.3 lists the history of the dose limitations. 

Unlike stochastic effects, non-stochastic effects are characterized by a threshold dose below which they do not occur. In addition, the magnitude of the effect is directly proportional to the size of the dose. Furthermore, for non-stochastic effects, there is a clear causal relationship between radiation exposure and the effect. Examples of non-stochastic effects include sterility, erythema (skin reddening), ulceration, and cataract formation. Each of these effects differs from the other in both its threshold dose and in the time over which this dose must be received to cause the effect (i.e. acute vs. chronic exposure). 

Marrero-Ponce, Y. and Castillo-Garit, J.A. (2005) 3D-chiral atom, atom-type, and total non-stochastic and stochastic molecular linear indices and their applications to central chirality codification. 

Marrero-Ponce, Y, Marrero, R.M., Torrens, F., Martinez, Y, Bernal, M.L., Zaldivar, V.R., Castro, E. A. and Abalo, R.G. (2006) Non-stochastic and stochastic linear indices of the molecular pseudograph s atom-adjacency matrix a novel approach for computational in sllico screening and rational selection of new lead antibacterial agents. J. Mol. Model., 12, 255-271. 

Marrero-Ponce, Y, Montero-Torres, A., Zaldivar, C. R., Veitia, M.I., Mayon Perez, M. and Garda Sanchez, R.N. (2005) Non-stochastic and stochastic linear indices of the molecular pseudographs atom adjacency matrix application to in silico studies for the rational discovery of new antimalarial compounds. Bioorg. Med. Chem., 13, 1293—1304. 

Montero-Torres. A.. Vega, M.C., Marrero-Ponce, Y. Rolon. M..Gomez-Barrio, A., Escario, J.A.,Aran. V. J., Martinez-Fernandez, A.R. and Meneses-Marcel. A. (2005) A novel non-stochastic quadratic fingerprints-based approach for the in silico discovery of new antitrypanosomal compounds. Biooig. Med. Chem., 13, 6264—6275. 

Third, the model assumes a non-stochastic default-free interest rate. 

Non-stochastic effects are health effects for which the severity depends upon the dose, and for which there is probably a threshold. 

ICRP (1977) Recommendations of the International Commission on Radiological Protection (ICRP). ICRP publication no. 26. Pergamon, Oxford ICRP (1984) Non-stochastic effects of ionising radiation. Annals of the ICRP publication no. 41. Pergamon, Oxford... 

In accidents, there is a possibility for deterministic (non-stochastic) and stochastic health effects. The principles for planning intervention in the case of a radiation emergency are set out in ICRP Publication 60 and 63 (ICRP 1991a, b, respectively). Intervention is the term applied to steps taken, in an accident situation, to restrict the exposure of member of the public and to minimize the consequences of unavoidable exposure. The assessment of the radiological situation and the implementation of the individual protection measures make up an overall protection strategy that is recommended to be justified and optimized. In the process of optimization, reference levels are to be applied and particular attention should be given to the prevention of severe deterministic health effects. 

When an ALI is defined by the stochastic dose limit, this value alone, is given. When an ALI is determined by the non-stochastic dose limit to an organ, the organ or tissue to which the limit applies is shown, and the ALI for the stochastic limit is shown in parentheses. (Abbreviated organ or tissue designations are used ... 

Consideration of non-stochastic limits has not been included in deriving the air and water effluent concentration limits because non-stochastic effects are presumed not to occur at the dose levels established for individual members of the public. For radionuclides, where the non-stochastic limit was governing in deriving the occupational DAC, the stochastic ALT was used in deriving the corresponding airborne effluent limit in Table 2. For this reason, the DAC and airborne effluent limits are not always proportional as they were the previous Appendix B. 

The label determinism is used in a variety of senses, some of which are seemingly contradictory. Here, we adopt the notion, familiar from automata theory [22], which differs from that in physics, say, of non-stochasticity. One calls a finite-state machine (classical or quantum) deterministic whenever the transition from one state to the next is uniquely determined by the output symbol (or input symbol for recognizers). It is important to realize that a deterministic finite-state machine can still behave stochastically—stochasticity here referring to the positive probability of generating symbols. Once the symbol is determined, though, the transition taken by the machine to the next state is unique. Thus, what is called a stochastic process in dynamical systems theory can be described by a deterministic finite-state generator without contradiction. 

Regarding stochastic effects together with a low individual probability of stochastic effects and a low probability of incurring even one case of stochastic effect in the exposed population. 

According to these references, non-stochastic effects to individuals are prevented if the annual dose equivalent to any organ does not exceed 0.05 Sv, even if repeated year after year. Therefore, 0.05 Sv in one event cannot cause non-stochastic effects. 

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