Population density approach

DBS appears to work by freeing thalamocortical and brainstem motor systems from abnormal and disruptive basal ganglia influences ([67], p. 202). At a local scale DBS appears to inhibit the soma of nerve cells and to activate the axons [42]. At an intermediate scale, DBS appears to alter the dynamics in the GPi-STN network [10]. At a distant scale, DBS appears to normalize the activity in the supplementary motor area and in the premotor cortex [67]. While many hypotheses have been formulated, the experimental results are difficult to reconcile especially when several physiological scales are considered. We now present a computational model based on a population density approach. 

Modolo J., Garenne A., Henry J., Beuter A. A new population density approach using the Izhikevich model (in preparation for the / Comput Neurosci). 

Nykamp D. Q., Trandrina D. A population density approach that facilitates large-scale modeling of neural networks analysis and an application to orientation tuning. J Comput Neurosci, 2000, 8(1), 19-50. 

This solution can be obtained explicitly either by matrix diagonalization or by other techniques (see chapter A3.4 and [42, 43]). In many cases the discrete quantum level labels in equation (A3.13.24) can be replaced by a continuous energy variable and the populations by a population density p(E), with replacement of the sum by appropriate integrals [Hj. This approach can be made the starting point of usefiil analytical solutions for certain simple model systems [H, 19, 44, 45 and 46]. 

To factor location into the rankings, multiply the total distances by the average population density in the area surrounding the facility. Where population varies with distance, you may need to vaiy the density by distance. One effective approach is to consider population density in concentric circles of 1 km, 2 km, 5 km, and 10 km radius. 

Basic box models cannot portray effects of nonuniform source patterns. If, for particular chemical species or particular source classes, the dependence of emissions on population density or other identifiable parameters is apparent and significant, we have used modifications to the box modeling approach. As an example, it might be assumed in modeling products of combustion of the lighter fuel oil distillates that source distribution patterns are proportional to population density patterns, because most of such fuel is burned in residential furnaces in cold weather cities. 

The resin system selected to initiate these studies is a step-growth anhydride cured epoxy. The approach to the kinetic analysis is that which is prevalent in the chemical engineering literature on reactor design and analysis. Numerical simulations of oligomeric population density distributions approximate experimental data during the early stages of the cure. Future research will... 

If we examine the current geographical distribution of a mutation, it is hard to estimate the value of the population density n at the position and time where the mutation originates. It makes sense to treat n as a random variable selected from a certain probability density p n). The constraints imposed onp n) are the conservation of the normalization condition f p(n) dn = 1 and the range of variation, noc > n > 0. The maximum information entropy approach leads to a uniform distribution... 

A simple and robust quantitative MO-type approach (as opposed to density approaches) is the ubiquitous Mulliken population analysis [40]. The key concept of this easily programmed and fast method is the distribution of electrons based on occupations of atomic orbitals. The atomic populations do not, however, include electrons from the overlap populations, which are divided exactly in the middle of the bonds, regardless of the bonding type and the electronegativity. As a consequence, differences of atom types are not properly accommodated and the populations per orbital can be larger than 2, which is a violation of the Pauli principle a simple remedy for this error is a Lowdin population analysis that... 

System conditions often allow for the measurement of magma density, and in such cases is should be used as a constraint in evaluating nucleation and growth kinetics from measured population densities. This approach is especially useful in instances of uncertainty in the determination of population densities from sieving or other particle sizing techniques. 

In conclusion to this section, research in the RTD area is always active and the initial concepts of Danckwerts are gradually being completed and extended. The population balance approach provides a theoretical framework for this generalization. However, in spite of the efforts of several authors, simple procedures, easy to use by practitioners, would still be welcome in the field of unsteady state systems (variable volumes and flow rates), multiple inlet/outlet reactors, variable density mixtures, systems in which the mass-flowrate is not conserved, etc... On the other hand, the promising "generalized reaction time distribution" approach could be developed if suitable experimental methods were available for its determination. 

Reference [34] followed by several groups ([49, 51] to name a few) inspired from this statistical approach initiated in physics by Maxwell to develop a similar theory applied to the description of a neural population. Basically a neural population is described by its population density p(w,t) where w is the state of a neuron (scalar in the case of the LIF model, a vector containing the state variables in the case of... 

If erectin can be made available in sufficient quantities for practical use, and if the copulation of males with female dummies bearing erectin can effect the lowering of the population density, this apparent reversal of the sterilized male technique could become a new control approach. 

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