Enumerative Theory for the Tsetlin Library

The Tsetlin library is a well-studied Markov chain on the symmetric group $S_n$. It has stationary distribution $\pi(\sigma)$ the Luce model, a nonuniform distribution on $S_n$, which appears in psychology, horse race betting, and tournament poker. Simple enumerative questions, such as ``what is the distribution of the top $k$ cards?'' or ``what is the distribution of the bottom $k$ cards?'' are long open. We settle these questions and draw attention to a host of parallel questions on the extension to the chambers of a hyperplane arrangement.Comment: 23 pages, 1 figur

Smoluchowski dynamics and the ergodic-nonergodic transition

We use the recently introduced theory for the kinetics of systems of classical particles to investigate systems driven by Smoluchowski dynamics. We investigate the existence of ergodic-nonergodic (ENE) transitions near the liquid-glass transition. We develop a self-consistent perturbation theory in terms of an effective two-body potential. We work to second order in this potential. At second order we have an explicit relationship between the static structure factor and the effective potential. We choose the static structure factor in the case of hard spheres to be given by the solution of the Percus-Yevick approximation for hard spheres. Then using the analytically determined ENE equation for the ergodicity function we find an ENE transition for packing fraction, eta, greater than a critical value eta*=0.76 which is physically unaccessible. The existence of a linear fluctuation-dissipation theorem in the problem is shown and used to great advantage.Comment: 51 pages, 6 figure

Granular clustering in a hydrodynamic simulation

We present a numerical simulation of a granular material using hydrodynamic equations. We show that, in the absence of external forces, such a system phase-separates into high density and low density regions. We show that this separation is dependent on the inelasticity of collisions, and comment on the mechanism for this clustering behavior. Our results are compatible with the granular clustering seen in experiments and molecular dynamic simulations of inelastic hard disks.Comment: 4 pages, 5 figure

Bone regeneration at extraction sockets filled with leukocyte-platelet-rich fibrin:an experimental pre-clinical study

We aimed to histomorphometrically evaluate the effects of Leucocyte-Platelet-Rich Fibrin (L-PRF), with and without the combination of a bone grafting material, for alveolar ridge preservation using an in vivo canine model. Seven dogs (Female Beagles, ~18-month-old) were acquired for the study. L-PRF was prepared from each individual animal by drawing venous blood and spinning them through a centrifuge at 408 RCF-clot (IntrasSpin, Intra-Lock, Boca Raton, FL). L-PRF membranes were obtained from XPression fabrication kit (Biohorizons Implant Systems, Inc., AL, USA). A split mouth approach was adopted with the first molar mesial and distal socket defects treated in an interpolated fashion of the following study groups: 1) Empty socket (negative control); 2) OSS filled defect 3) L-PRF membrane; and 4) Mix of Bio-Oss® with L-PRF. After six weeks, samples were harvested, histologically processed, and evaluated for bone area fraction occupancy (BAFO), vertical/horizontal ridge dimensions (VRD and HRD, respectively), and area of coronal soft tissue infiltration. BAFO was statistically lower for the control group in comparison to all treatment groups. Defects treated with Bio-Oss® were not statistically different then defects treated solely with L-PRF. Collapsed across all groups, L-PRF exhibited higher degrees of BAFO than groups without L-PRF. Defects filled with Bio-Oss® and Bio-Oss® with L-PRF demonstrated greater maintenance of VRD relative to the control group. Collapsed across all groups, Bio-Oss® maintained the VRD and resulted in less area of coronal soft tissue infiltration compared to the empty defect. Soft tissue infiltration observed at the coronal area was not statistically different among defects filled with L-PRF, Bio-Oss®, and Bio-Oss® with L-PRF. Inclusion of L-PRF to particulate xenograft did not promote additional bone heading at 6 weeks in vivo. However, we noted that L-PRF alone promoted alveolar socket regeneration to levels comparable to particulate xenografts, suggesting its potential utilization for socket preservation

Model for Glass Transition in a Binary fluid from a Mode Coupling approach

We consider the Mode Coupling Theory (MCT) of Glass transition for a Binary fluid. The Equations of Nonlinear Fluctuating Hydrodynamics are obtained with a proper choice of the slow variables corresponding to the conservation laws. The resulting model equations are solved in the long time limit to locate the dynamic transition. The transition point from our model is considerably higher than predicted in existing MCT models for binary systems. This is in agreement with what is seen in Computer Simulation of binary fluids. fluids.Comment: 9 Pages, 3 Figure