7,810 research outputs found
Statistical Curse of the Second Half Rank
In competitions involving many participants running many races the final rank
is determined by the score of each participant, obtained by adding its ranks in
each individual race. The "Statistical Curse of the Second Half Rank" is the
observation that if the score of a participant is even modestly worse than the
middle score, then its final rank will be much worse (that is, much further
away from the middle rank) than might have been expected. We give an
explanation of this effect for the case of a large number of races using the
Central Limit Theorem. We present exact quantitative results in this limit and
demonstrate that the score probability distribution will be gaussian with
scores packing near the center. We also derive the final rank probability
distribution for the case of two races and we present some exact formulae
verified by numerical simulations for the case of three races. The variant in
which the worst result of each boat is dropped from its final score is also
analyzed and solved for the case of two races.Comment: 16 pages, 10 figure
Global fluctuations and Gumbel statistics
We explain how the statistics of global observables in correlated systems can
be related to extreme value problems and to Gumbel statistics. This
relationship then naturally leads to the emergence of the generalized Gumbel
distribution G_a(x), with a real index a, in the study of global fluctuations.
To illustrate these findings, we introduce an exactly solvable nonequilibrium
model describing an energy flux on a lattice, with local dissipation, in which
the fluctuations of the global energy are precisely described by the
generalized Gumbel distribution.Comment: 4 pages, 3 figures; final version with minor change
Effect of sweep angle on the pressure distributions and effectiveness of the ogee tip in diffusing a line vortex
Low-speed wind tunnel tests were conducted to study the influence of sweep angle on the pressure distributions of an ogee-tip configuration with relation to the effectiveness of the ogee tip in diffusing a line vortex. In addition to the pressure data, performance and flow-visualization data were obtained in the wind tunnel tests to evaluate the application of the ogee tip to aircraft configurations. The effect of sweep angle on the performance characteristics of a conventional-tip model, having equivalent planform area, was also investigated for comparison with the ogee-tip configuration. Results of the investigation generally indicate that sweep angle has little effect on the characteristics of the ogee in diffusing a line vortex
Coal desulfurization by low temperature chlorinolysis, phase 2
An engineering scale reactor system was constructed and operated for the evaluation of five high sulfur bituminous coals obtained from Kentucky, Ohio, and Illinois. Forty-four test runs were conducted under conditions of 100 by 200 mesh coal,solvents - methlychloroform and water, 60 to 130 C, 0 to 60 psig, 45 to 90 minutes, and gaseous chlorine flow rate of up to 24 SCFH. Sulfur removals demonstrated for the five coals were: maximum total sulfur removal of 46 to 89% (4 of 5 coals with methylchloroform) and 0 to 24% with water. In addition, an integrated continuous flow mini-pilot plant was designed and constructed for a nominal coal rate of 2 kilograms/hour which will be operated as part of the follow-on program. Equipment flow sheets and design drawings are included for both the batch and continuous flow mini-pilot plants
Dispersion processes
We study a synchronous dispersion process in which particles are
initially placed at a distinguished origin vertex of a graph . At each time
step, at each vertex occupied by more than one particle at the beginning of
this step, each of these particles moves to a neighbour of chosen
independently and uniformly at random. The dispersion process ends once the
particles have all stopped moving, i.e. at the first step at which each vertex
is occupied by at most one particle.
For the complete graph and star graph , we show that for any
constant , with high probability, if , then the
process finishes in steps, whereas if , then
the process needs steps to complete (if ever). We also show
that an analogous lazy variant of the process exhibits the same behaviour but
for higher thresholds, allowing faster dispersion of more particles.
For paths, trees, grids, hypercubes and Cayley graphs of large enough sizes
(in terms of ) we give bounds on the time to finish and the maximum distance
traveled from the origin as a function of the number of particles
Using Classical Probability To Guarantee Properties of Infinite Quantum Sequences
We consider the product of infinitely many copies of a spin-
system. We construct projection operators on the corresponding nonseparable
Hilbert space which measure whether the outcome of an infinite sequence of
measurements has any specified property. In many cases, product
states are eigenstates of the projections, and therefore the result of
measuring the property is determined. Thus we obtain a nonprobabilistic quantum
analogue to the law of large numbers, the randomness property, and all other
familiar almost-sure theorems of classical probability.Comment: 7 pages in LaTe
Probability distribution of residence times of grains in models of ricepiles
We study the probability distribution of residence time of a grain at a site,
and its total residence time inside a pile, in different ricepile models. The
tails of these distributions are dominated by the grains that get deeply buried
in the pile. We show that, for a pile of size , the probabilities that the
residence time at a site or the total residence time is greater than , both
decay as for where
is an exponent , and values of and in the two
cases are different. In the Oslo ricepile model we find that the probability
that the residence time at a site being greater than or equal to ,
is a non-monotonic function of for a fixed and does not obey simple
scaling. For model in dimensions, we show that the probability of minimum
slope configuration in the steady state, for large , varies as where is a constant, and hence .Comment: 13 pages, 23 figures, Submitted to Phys. Rev.
Persistent correlation of constrained colloidal motion
We have investigated the motion of a single optically trapped colloidal
particle close to a limiting wall at time scales where the inertia of the
surrounding fluid plays a significant role. The velocity autocorrelation
function exhibits a complex interplay due to the momentum relaxation of the
particle, the vortex diffusion in the fluid, the obstruction of flow close to
the interface, and the harmonic restoring forces due to the optical trap. We
show that already a weak trapping force has a significant impact on the
velocity autocorrelation function C(t)= at times where the
hydrodynamic memory leads to an algebraic decay. The long-time behavior for the
motion parallel and perpendicular to the wall is derived analytically and
compared to numerical results. Then, we discuss the power spectral densities of
the displacement and provide simple interpolation formulas. The theoretical
predictions are finally compared to recent experimental observations.Comment: 12 pages, 6 figure
Oral Leukoplakia as It Relates to HPV Infection: A Review
Leukoplakia is the most common potentially malignant lesion of the oral cavity and can be categorised according to its clinical appearance as homogeneous or nonhomogenous. Tobacco and areca nut use, either alone or in combination are the most common risk factors for oral leukoplakia, but some oral leukoplakias are idiopathic. Some leukoplakias arise within fields of precancerized oral epithelium in which the keratinocytes may be at different stages of cytogenetic transformation. Leukoplakias may unpredictably regress, may remain stable, or may progress to carcinoma. There is a greater risk of carcinomatous transformation of idiopathic leukoplakia, of non-homogenous leukoplakia, of leukoplakia affecting the floor of the mouth; the ventrolateral surface of the tongue and the maxillary retromolar and adjoining soft palate (collectively called high-risk sites), of leukoplakia with high-grade epithelial dysplasia, and of leukoplakia in which the keratinocytes carry cytogenetic alterations associated with carcinomatous transformation. Although there appears to be some link between human papillomavirus (HPV) and oral leukoplakia, there is little evidence to support a causal relationship either between HPV infection and oral leukoplakia or between HPV-infected leukoplakic keratinocytes and their carcinomatous transformation
- …