Critical edge behavior in the modified Jacobi ensemble and the Painlevé V transcendents

2013 ◽  
Vol 54 (8) ◽  
pp. 083304 ◽  
Author(s):  
Shuai-Xia Xu ◽  
Yu-Qiu Zhao
Keyword(s):  
Jacobi Ensemble ◽  
Critical Edge ◽  
Edge Behavior

scholarly journals Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Massimo Gisonni ◽  
Tamara Grava ◽  
Giulio Ruzza
Keyword(s):  
Generating Functions ◽  
Combinatorial Interpretation ◽  
Hurwitz Numbers ◽  
Jacobi Ensemble ◽  
Matrix Ensembles ◽  
Wilson Polynomials ◽  
Unitary Ensemble ◽  
Topological Expansion

AbstractWe express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix ensembles. We also provide effective formulæ for generating functions of multipoint correlators of the Jacobi Unitary Ensemble in terms of Wilson polynomials, generalizing the known relations between one point correlators and Wilson polynomials.

GLOBAL FLUCTUATIONS FOR LINEAR STATISTICS OF β-JACOBI ENSEMBLES

2012 ◽  
Vol 01 (04) ◽  
pp. 1250013 ◽  
Author(s):  
IOANA DUMITRIU ◽  
ELLIOT PAQUETTE
Keyword(s):  
Gaussian Process ◽  
Covariance Matrix ◽  
Law Of Large Numbers ◽  
Test Functions ◽  
Linear Statistics ◽  
Jacobi Ensemble ◽  
Large Numbers ◽  
The Mean ◽  
Shifted Chebyshev Polynomial ◽  
Global Fluctuations

We study the global fluctuations for linear statistics of the form [Formula: see text] as n → ∞, for C1 functions f, and λ1, …, λn being the eigenvalues of a (general) β-Jacobi ensemble. The fluctuation from the mean [Formula: see text] turns out to be given asymptotically by a Gaussian process. We compute the covariance matrix for the process and show that it is diagonalized by a shifted Chebyshev polynomial basis; in addition, we analyze the deviation from the predicted mean for polynomial test functions, and we obtain a law of large numbers.

Analysis of Concrete Pavement Responses to Temperature and Wheel Loads Measured from Intrumented Slabs

1998 ◽  
Vol 1639 (1) ◽  
pp. 94-101 ◽  
Author(s):  
H. Thomas Yu ◽  
Lev Khazanovich ◽  
Michael I. Darter ◽  
Ahmad Ardani
Keyword(s):  
Structural Response ◽  
Plain Concrete ◽  
Negative Temperature ◽  
Concrete Pavement ◽  
Temperature Gradients ◽  
Critical Conditions ◽  
Test Analysis ◽  
Longitudinal Edge ◽  
Critical Edge ◽  
Using Data

The structural response of jointed plain concrete pavement slabs was evaluated using data obtained from instrumented slabs. The instrumented slabs were a part of newly constructed jointed plain concrete overlay that was constructed on existing asphalt concrete pavement on I–70 in Colorado, near the Kansas–Colorado border. The instrumentation consisted of dial gauges for measuring curling deflections at the slab corner and longitudinal edge and surface-mounted strain gauges for measuring load strains at the longitudinal edge at midslab. The through-thickness temperature profiles in the pavement slabs were also measured at 30-min intervals during the field test. Analysis of the field data showed that the instrumented slabs had a considerable amount of built-in upward curling and that concrete slabs on a stiff base can act completely independent of the base or monolithically with the base, depending on the loading condition. The built-in upward curling of the slabs has the same effect as negative temperature gradients. These findings suggest that the effects of temperature gradients on the critical edge stresses may not be as great as previously thought and that the corner loading, in some cases, may produce more critical conditions for slab cracking. Another important finding of this study is that a physical bond between pavement layers is not required to obtain a bonded response from concrete pavements.

scholarly journals The Mycobacterium tuberculosis PE_PGRS Protein Family Acts as an Immunological Decoy to Subvert Host Immune Response

2022 ◽  
Vol 23 (1) ◽  
pp. 525
Author(s):  
Tarina Sharma ◽  
Anwar Alam ◽  
Aquib Ehtram ◽  
Anshu Rani ◽  
Sonam Grover ◽  
...  
Keyword(s):  
Mycobacterium Tuberculosis ◽  
Immune Responses ◽  
Current Knowledge ◽  
Immune Effector ◽  
Host Immune Responses ◽  
Intrinsically Disordered ◽  
Multiple Strategies ◽  
Latent Stage ◽  
Immune Mediated ◽  
Critical Edge

Mycobacterium tuberculosis (M.tb) is a successful pathogen that can reside within the alveolar macrophages of the host and can survive in a latent stage. The pathogen has evolved and developed multiple strategies to resist the host immune responses. M.tb escapes from host macrophage through evasion or subversion of immune effector functions. M.tb genome codes for PE/PPE/PE_PGRS proteins, which are intrinsically disordered, redundant and antigenic in nature. These proteins perform multiple functions that intensify the virulence competence of M.tb majorly by modulating immune responses, thereby affecting immune mediated clearance of the pathogen. The highly repetitive, redundant and antigenic nature of PE/PPE/PE_PGRS proteins provide a critical edge over other M.tb proteins in terms of imparting a higher level of virulence and also as a decoy molecule that masks the effect of effector molecules, thereby modulating immuno-surveillance. An understanding of how these proteins subvert the host immunological machinery may add to the current knowledge about M.tb virulence and pathogenesis. This can help in redirecting our strategies for tackling M.tb infections.

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