4,635 research outputs found
Biotechnology Process Patents: Is Special Legislation Needed?
The authors review administrative and court decisions prompting proposed changes to the patent law. After reviewing pros and cons, they argue that, on balance, pending bills can easily cause more problems than they solve
Characteristic polynomials of random matrices at edge singularities
We have discussed earlier the correlation functions of the random variables
\det(\la-X) in which is a random matrix. In particular the moments of the
distribution of these random variables are universal functions, when measured
in the appropriate units of the level spacing. When the \la's, instead of
belonging to the bulk of the spectrum, approach the edge, a cross-over takes
place to an Airy or to a Bessel problem, and we consider here these modified
classes of universality.
Furthermore, when an external matrix source is added to the probability
distribution of , various new phenomenons may occur and one can tune the
spectrum of this source matrix to new critical points. Again there are
remarkably simple formulae for arbitrary source matrices, which allow us to
compute the moments of the characteristic polynomials in these cases as well.Comment: 22 pages, late
Current moments of 1D ASEP by duality
We consider the exponential moments of integrated currents of 1D asymmetric
simple exclusion process using the duality found by Sch\"utz. For the ASEP on
the infinite lattice we show that the th moment is reduced to the problem of
the ASEP with less than or equal to particles.Comment: 13 pages, no figur
Increasing subsequences and the hard-to-soft edge transition in matrix ensembles
Our interest is in the cumulative probabilities Pr(L(t) \le l) for the
maximum length of increasing subsequences in Poissonized ensembles of random
permutations, random fixed point free involutions and reversed random fixed
point free involutions. It is shown that these probabilities are equal to the
hard edge gap probability for matrix ensembles with unitary, orthogonal and
symplectic symmetry respectively. The gap probabilities can be written as a sum
over correlations for certain determinantal point processes. From these
expressions a proof can be given that the limiting form of Pr(L(t) \le l) in
the three cases is equal to the soft edge gap probability for matrix ensembles
with unitary, orthogonal and symplectic symmetry respectively, thereby
reclaiming theorems due to Baik-Deift-Johansson and Baik-Rains.Comment: LaTeX, 19 page
Random walks and random fixed-point free involutions
A bijection is given between fixed point free involutions of
with maximum decreasing subsequence size and two classes of vicious
(non-intersecting) random walker configurations confined to the half line
lattice points . In one class of walker configurations the maximum
displacement of the right most walker is . Because the scaled distribution
of the maximum decreasing subsequence size is known to be in the soft edge GOE
(random real symmetric matrices) universality class, the same holds true for
the scaled distribution of the maximum displacement of the right most walker.Comment: 10 page
{\bf -Function Evaluation of Gap Probabilities in Orthogonal and Symplectic Matrix Ensembles}
It has recently been emphasized that all known exact evaluations of gap
probabilities for classical unitary matrix ensembles are in fact
-functions for certain Painlev\'e systems. We show that all exact
evaluations of gap probabilities for classical orthogonal matrix ensembles,
either known or derivable from the existing literature, are likewise
-functions for certain Painlev\'e systems. In the case of symplectic
matrix ensembles all exact evaluations, either known or derivable from the
existing literature, are identified as the mean of two -functions, both
of which correspond to Hamiltonians satisfying the same differential equation,
differing only in the boundary condition. Furthermore the product of these two
-functions gives the gap probability in the corresponding unitary
symmetry case, while one of those -functions is the gap probability in
the corresponding orthogonal symmetry case.Comment: AMS-Late
ATP-independent Control of Vac8 Palmitoylation by a SNARE Subcomplex on Yeast Vacuoles
Yeast vacuole fusion requires palmitoylated Vac8. We previously showed that Vac8 acylation occurs early in the fusion reaction, is blocked by antibodies against Sec18 (yeast N-ethylmaleimide-sensitive fusion protein (NSF)), and is mediated by the R-SNARE Ykt6. Here we analyzed the regulation of this reaction on purified vacuoles. We show that Vac8 acylation is restricted to a narrow time window, is independent of ATP hydrolysis by Sec18, and is stimulated by the ion chelator EDTA. Analysis of vacuole protein complexes indicated that Ykt6 is part of a complex distinct from the second R-SNARE, Nyv1. We speculate that during vacuole fusion, Nyv1 is the classical R-SNARE, whereas the Ykt6-containing complex has a novel function in Vac8 palmitoylation
Growth models, random matrices and Painleve transcendents
The Hammersley process relates to the statistical properties of the maximum
length of all up/right paths connecting random points of a given density in the
unit square from (0,0) to (1,1). This process can also be interpreted in terms
of the height of the polynuclear growth model, or the length of the longest
increasing subsequence in a random permutation. The cumulative distribution of
the longest path length can be written in terms of an average over the unitary
group. Versions of the Hammersley process in which the points are constrained
to have certain symmetries of the square allow similar formulas. The derivation
of these formulas is reviewed. Generalizing the original model to have point
sources along two boundaries of the square, and appropriately scaling the
parameters gives a model in the KPZ universality class. Following works of Baik
and Rains, and Pr\"ahofer and Spohn, we review the calculation of the scaled
cumulative distribution, in which a particular Painlev\'e II transcendent plays
a prominent role.Comment: 27 pages, 5 figure
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
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