The organization objected to what it sees as an overt inclusion of religion in the athletic program, allegedly including the reciting of Scriptural passages, distribution of Bibles and coercion to attend church.
First we describe an idealized scenario — a homogeneous viscous fluid of uniform depth with a particle undergoing passive normal diffusion — where the theory of Brownian motion affords the ability to rigorously specify particle size distributions to meet a prescribed, one-sided, diffusive passage time distribution.
The passage time distribution must be, with high confidence, shorter than the timescales of mucus clearance to maximize drug uptake.
Each structural element is characterized by the passage time distribution function calculated with taking into account the correlations of flows passing through the neighboring pores.
To make the general expressions more concrete it is necessary to introduce a model of structural elements (pores) which determines the passage time distribution.
If we use a first order Taylor approximation, the first passage time distribution (h(t)) is then given by h(t)=-frac{partial S t)}{partial t}, (18) and the relation between the cumulative distribution (S t)) and the FPTD (between two arbitrary times (t_{1}) and (t_{2})) is [35, 36] S(t_{1} -S(t_{2})= int_{t_{1} -St_{2}}hbigl(t^{prime} bigr),dt^{prime}.
The first passage time distribution, also of interest, is less easily discussed deterministically.
Results: Here, we offer a fresh, statistical physics-based perspective focusing on the question of alignment-free comparison, in the process adapting results from 'first passage probability distribution' to summarize statistics of ensemble averaged amino acid propensity values.
At this stage, the focus is on a specific manifestation, that of the 'first passage probability' distribution around the mean value X0 of the data points X t) where 't' is our metaphor for the location of the data point in the time series-like sequence.
As long as we are within the stochastic realm, all prior statistical results, including that for long range correlated stochastic data, suggest the existence of universal power law exponents defining the first passage probability distribution statistics related to t+ and t- transitions.
