The structure of the <i>C</i>₇₀ molecule.

<p>(a) The polytope has 105 edges and 12 pentagonal and 25 hexagonal faces. (b) viewed from a direction almost parallel to the plane of and . (c) The structure of viewed from a direction parallel to the plane of and . The column of numbers shows the -coordinate of the orbits of vertices of . The inserted decagon has the -coordinate equal to 0. Surface edges are omitted in (b) and (c).</p

The 12 pentagons of the surface of

<p><b> are shown without the hexagons.</b> The 60 dots are the vertices of . The polytope is oriented as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0084079#pone-0084079-g001" target="_blank">Fig. 1</a>.</p

The structure of the <i>C</i>₆₀ molecule.

<p>(a) The polytope is formed by 60 vertices equidistant from its center. Its surface consists of 12 regular pentagons and 20 regular hexagons. All 90 edges are of the same length. (b) The polytope viewed in the direction almost parallel to the plane spanned by and , which makes the orbits (pentagons and decagons) easy to identify. (c) The polytope viewed in the direction parallel to the plane spanned by and . Surface edges of are omitted in (b) and (c). Horizontal segments are projections of the orbits. The number in a row shows the coordinate of the orbit. The vertical direction is that of .</p

A ring of hexagons from the middle of the surface of

<p><b> and </b><b> unwrapped into the plane.</b> Horizontal lines indicate positions of the four decagons in and five decagons in . The dominant points identify the decagons relative to the basis . Dashed lines are the boundaries of the ring of five inserted hexagons.</p

Reduction of Seizure Occurrence from Exposure to Auditory Stimulation in Individuals with Neurological Handicaps: A Randomized Controlled Trial

<div><h3>Background</h3><p>The purpose of this work was to determine in a clinical trial the efficacy of reducing or preventing seizures in patients with neurological handicaps through sustained cortical activation evoked by passive exposure to a specific auditory stimulus (particular music). The specific type of stimulation had been determined in previous studies to evoke anti-epileptiform/anti-seizure brain activity.</p> <h3>Methods</h3><p>The study was conducted at the Thad E. Saleeby Center in Harstville, South Carolina, which is a permanent residence for individuals with heterogeneous neurological impairments, many with epilepsy. We investigated the ability to reduce or prevent seizures in subjects through cortical stimulation from sustained passive nightly exposure to a specific auditory stimulus (music) in a three-year randomized controlled study. In year 1, baseline seizure rates were established. In year 2, subjects were randomly assigned to treatment and control groups. Treatment group subjects were exposed during sleeping hours to specific music at regular intervals. Control subjects received no music exposure and were maintained on regular anti-seizure medication. In year 3, music treatment was terminated and seizure rates followed. We found a significant treatment effect (p = 0.024) during the treatment phase persisting through the follow-up phase (p = 0.002). Subjects exposed to treatment exhibited a significant 24% decrease in seizures during the treatment phase, and a 33% decrease persisting through the follow-up phase. Twenty-four percent of treatment subjects exhibited a complete absence of seizures during treatment.</p> <h3>Conclusion/Significance</h3><p>Exposure to specific auditory stimuli (i.e. music) can significantly reduce seizures in subjects with a range of epilepsy and seizure types, in some cases achieving a complete cessation of seizures. These results are consistent with previous work showing reductions in epileptiform activity from particular music exposure and offers potential for achieving a non-invasive, non-pharmacologic treatment of epilepsy.</p> <h3>Trial Registration</h3><p>Clinicaltrials.gov <a href="http://clinicaltrials.gov/ct2/show/NCT01459692?term=NCT01459692">NCT01459692</a></p> </div

Protocol of music exposure administered to the treatment group every evening from 9:00 pm until 7:00 am.

<p>The sequence of exposure which was repeated consecutively 3 times each hour was: 1) 9 minute baseline period with no music, 2) K.448 played for 8.5 minutes (complete presentation of first movement), 3) 8.5 minute washout period with no music. The final washout period each hour (8.5 minutes) and the initial baseline period of the next consecutive hour (9 minutes) resulted in a 17.5 minute period of silence between the final music exposure of an hour and the first music exposure of the next hour.</p

Patient Flow Diagram.

<p>Patient Flow Diagram.</p

Seizure changes during study phases.

<p>A) Seizure rates across all phases of the study for the Control group (left) and Treatment group (right). Graphs show 3 month moving averages of seizure rates within each year, averaged across all subjects (i.e. first bar of the graph for each phase represents average seizure counts of months 1 through 3 of that phase, the second bar the average of months 2 through 4, and so on). The solid black horizontal lines indicate the average seizure rate within each phase. In the Control group the average seizure rate can be seen to increase in each consecutive year, while in the Treatment Group the seizure rate decreases from the baseline year rate, and maintains a reduced rate through the post-treatment follow-up year. B) Posterior densities for the treatment rate ratio in the treatment year (left) and in the follow-up year (right). The shift in the distribution of the treatment rate ratio (rate ratio = reduction in seizures in the treatment group/reduction in seizures control group) below 1.0 indicates the significant treatment effect in both the treatment and follow-up years. Posterior density was obtained using Markov Chain Monte Carlo methods and implemented using the rjags package <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045303#pone.0045303-Plummer1" target="_blank">[45]</a> within the R computing environment <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0045303#pone.0045303-R1" target="_blank">[46]</a>. The associated model reflects the model used in the reported GLM analysis. The smoothed plot was constructed by applying the R density function to 50,000 samples of the posterior. C) Posterior densities for the treatment rate ratio in the treatment year (left) for males (blue) and females (red) and in the post-treatment follow-up year (right). It can be seen from the graphs that no differential response from treatment was present as a function of gender. D) Posterior densities for the treatment rate ratio in the treatment year (left) for subjects with symptomatic seizures (blue) and idiopathic seizures (red) and in the post-treatment follow-up year (right). It can be seen from the graphs that while both groups of subjects exhibited a significant reduction in seizures, that subjects with idiopathic seizures exhibited a greater decrease in both treatment and follow-up years than those with symptomatic seizures.</p

Treatment effect from rate model analysis.

<p>A) Estimates of the coefficients from the GLM analysis focusing on the study phase interaction ζ_p,g(s) of the baseline rate model. Estimates are given with the 95% confidence intervals in parenthesis. The results indicate a significant treatment effect is present during the treatment phase (p = 0.024) and the post-treatment follow-up phase (p = 0.002). B) Estimates of the coefficients from the GLM analysis focusing on the study phase interaction ζ_p,g(s of the full model incorporating effects for gender and seizure class interactions with study phase within the treatment group. The results indicate a significant treatment effect is present during the treatment phase (p = 0.033) and the post-treatment follow-up phase (p = 0.006).</p

Distributions of treatment and control group subjects included in final analysis across variables of the study.

<p>The number of subjects in each category is given and the percentage of the group that it represents is indicated in parenthesis. Significance of the difference in the distributions of the groups is indicated on the right (2-sided Fisher Exact test). Note there are no significant differences between groups for any variable. The distribution of neurological impairments of symptomatic subjects is given at the bottom of the table.</p