Exponential torsion growth for random 3-manifolds

We show that a random 3-manifold with positive first Betti number admits a tower of cyclic covers with exponential torsion growth

Anti-inflammatory effect of low intensity ultrasound (LIUS) on complete Freund's adjuvant-induced arthritis synovium

SummaryObjectivesArthritis with intra-articular inflammation was accompanied by joint pain, swelling, and stiffness leading to significant functional impairment. Thus, regulation of joint inflammation is a good therapeutic approach for patients with arthritis. In this study, the effect of low intensity ultrasound (LIUS) applied to an adjuvant-induced arthritic rat model on the synovium was investigated.DesignSynovial inflammation was induced by complete Freund's adjuvant (CFA)-injection into the rat knee joint. LIUS (200 mW/cm2) was applied on the ipsilateral knee everyday for 10 min beginning 1 day after inflammation induction. The expression of proinflammatory factors and immunohistochemical staining pattern of the synovium were assessed.ResultsCFA induced an increase of the knee circumference that was significantly diminished by LIUS. Synovial membrane hyperplasia in the ipsilateral joint was also affected by LIUS. The inflammatory mediators, COX-1/2, IL-1β, and iNOS, but not TNF-α, in the synovial membrane were induced after 3 days, and they closely correlated with the degree of edema. In the synovial membrane, the expression of inflammatory mediators was reduced by LIUS. The chemoattractant chemokine receptor CCR5 also was involved. On immunohistochemical analysis, CFA caused increased infiltration of CD11b-positive cells in the synovium. After 3 days, neutrophils, myeloperoxidase (MPO)-positive cells filled the inflammatory core; later, monocytes and macrophages, ionized calcium binding adaptor molecule 1 (Iba1)-positive cells in the periphery infiltrated the core by day 5. LIUS markedly reduced CFA-induced inflammatory cells infiltration.ConclusionLIUS showed a potent anti-inflammatory effect in this animal arthritis model with reduced infiltration of inflammatory cells into the synovium

Extremal statistics of curved growing interfaces in 1+1 dimensions

We study the joint probability distribution function (pdf) of the maximum M of the height and its position X_M of a curved growing interface belonging to the universality class described by the Kardar-Parisi-Zhang equation in 1+1 dimensions. We obtain exact results for the closely related problem of p non-intersecting Brownian bridges where we compute the joint pdf P_p(M,\tau_M) where \tau_M is there the time at which the maximal height M is reached. Our analytical results, in the limit p \to \infty, become exact for the interface problem in the growth regime. We show that our results, for moderate values of p \sim 10 describe accurately our numerical data of a prototype of these systems, the polynuclear growth model in droplet geometry. We also discuss applications of our results to the ground state configuration of the directed polymer in a random potential with one fixed endpoint.Comment: 6 pages, 4 figures. Published version, to appear in Europhysics Letters. New results added for non-intersecting excursion

Airy processes and variational problems

We review the Airy processes; their formulation and how they are conjectured to govern the large time, large distance spatial fluctuations of one dimensional random growth models. We also describe formulas which express the probabilities that they lie below a given curve as Fredholm determinants of certain boundary value operators, and the several applications of these formulas to variational problems involving Airy processes that arise in physical problems, as well as to their local behaviour.Comment: Minor corrections. 41 pages, 4 figures. To appear as chapter in "PASI Proceedings: Topics in percolative and disordered systems

From interacting particle systems to random matrices

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. Some of the fluctuation laws were first discovered in random matrix models. Moreover, the limit process for curved limit shape turned out to show up in a dynamical version of hermitian random matrices, but this analogy does not extend to the case of symmetric matrices. Therefore the connections between growth models and random matrices is only partial.Comment: 18 pages, 8 figures; Contribution to StatPhys24 special issue; minor corrections in scaling of section 2.

Three concurrent variations of the aberrant right subclavian artery, the non-recurrent laryngeal nerve and the right thoracic duct

We herein report a case showing three anatomical variations including the aberrant right subclavian artery (ARSA), the non-recurrent laryngeal nerve (NRLN) and the right thoracic duct in a 59-year-old male cadaver. The right subclavian artery (RSA) arose from the descending aorta next to the left subclavian artery and coursed in between the oesophagus and the thoracic vertebrae. The recurrent laryngeal nerve did not coil around the RSA but directly entered the larynx. Lastly the thoracic duct terminated into the right brachiocephalic vein. This study makes an embryological assumption that the abnormal development of the RSA had happened first and subsequently caused NRLN and the thoracic duct drainage variation. As to our knowledge, only two reports have been made previously concerning such concurrent variations. Therefore, this case report alerts anatomists and clinicians to the possibility of simultaneous occurrence of ARSA, NRLN and the right thoracic duct

Opposite carrier dynamics and optical absorption characteristics under external electric field in nonpolar vs. polar InGaN/GaN based quantum heterostructures

Cataloged from PDF version of article.We report on the electric field dependent carrier dynamics and optical absorption in nonpolar a-plane GaN-based quantum heterostructures grown on r-plane sapphire, which are surprisingly observed to be opposite to those polar ones of the same materials system and similar structure grown on c-plane. Confirmed by their time-resolved photoluminescence measurements and numerical analyses, we show that carrier lifetimes increase with increasing external electric field in nonpolar InGaN/GaN heterostructure epitaxy, whereas exactly the opposite occurs for the polar epitaxy. Moreover, we observe blue-shifting absorption spectra with increasing external electric field as a result of reversed quantum confined Stark effect in these polar structures, while we observe red-shifting absorption spectra with increasing external electric field because of standard quantum confined Stark effect in the nonpolar structures. We explain these opposite behaviors of external electric field dependence with the changing overlap of electron and hole wavefunctions in the context of Fermi's golden rule. (C) 2011 Optical Society of Americ

Best-shot versus weakest-link in political lobbying: an application of group all-pay auction

We analyze a group political lobbying all-pay auction with a group specific public good prize, in which one group follows a weakest-link and the other group follows a best-shot impact function. We completely characterize all semi-symmetric equilibria. There are two types of equilibria: (1) each player in the best-shot group puts mass at the upper bound of the support, whereas each player in the other group puts mass at the lower bound of the support; (2) players in the best-shot group put masses at both the lower and the upper bounds, while the other group randomizes without a mass point. An earlier and longer version of this study was circulated under the title “The Group All-pay Auction with Heterogeneous Impact Functions.” We appreciate the comments of an Associate Editor and two anonymous referees, Kyung Hwan Baik, Walter Enders, Matt Van Essen, Paan Jindapon, David Malueg, Paul Pecorino, Seth Streitmatter, Ted Turocy, the participants at the 2015 conference of ‘Contest: Theory and Evidence’ at the University of East Anglia, and the seminar participants at the University of Alabama and Korea University. Iryna Topolyan gratefully acknowledges the support from the Charles Phelps Taft Research Center. Any remaining errors are our own

Supremum of the Airy2 process minus a parabola on a half line

Let \aip(t) be the Airy$_2$ process. We show that the random variable [\sup_{t\leq\alpha}\{aip(t)-t^2}+\min{0,\alpha}^2] has the same distribution as the one-point marginal of the Airy$_{2\to1}$ process at time $\alpha$. These marginals form a family of distributions crossing over from the GUE Tracy-Widom distribution $F_{\rm GUE}(x)$ for the Gaussian Unitary Ensemble of random matrices, to a rescaled version of the GOE Tracy-Widom distribution $F_{\rm GOE}(4^{1/3}x)$ for the Gaussian Orthogonal Ensemble. Furthermore, we show that for every $\alpha$ the distribution has the same right tail decay $e^{-(4/3)x^{3/2}}$.Comment: To appear in Journal of Statistical Physic

Vicious Walkers and Hook Young Tableaux

We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of walker's movements. Applying the saddle point method, we reveal that the scaling limit gives the Tracy--Widom distribution, which is same with the limit distribution of the largest eigenvalues of the Gaussian unitary ensemble.Comment: 23 pages, 5 figure