Generation of a random partition of a finite set by an urn model

AbstractA random partition of Nn = {1,…,n} may be generated by putting the elements of Nn at random into a stochastic number of cells. This representations is used to prove asymptotic results about the random partition for n → ∞

Polynomials of binomial type and compound Poisson processes

AbstractLet qnand sn, n ϵ N, respectively, be a set of polynomials of binomial type and a Sheffer set related to it, both having positive coefficients. Then qn(x), x > 0 is connected with the probability that a compound Poisson process starting at zero is in state n at time τx andqn(x)qn(1) is the probability generating function of the number of jumps of this process in [0, τ] given that it is in state n at time τ. The sn admit similar interpretations when the initial distribution of the compound Poisson process is not concentrated at zero. The possible limits for n → ∞ ofqn(x)qn(1)andsn(x)sn(1) are studied

Independent poisson processes generated by record values and inter-record times

AbstractThe mth-order upper record values of a sequence of independent random variables with common continuous distribution function, that are kth but not (k-1)th-order record values and that precede inter-record times of length j, form a Poisson process, the processes for different (k,j) being independent, k = 1,..., m, j = 1,2,.... The records with record epochs after r\2>m, have a similar property if we condition with respect to the mth decreasing order statistic of the sample for times 1,..., r. These results extend theorems by Ignatov

Convergence in distribution of quotients of order statistics

AbstractLet X1, X2,… be i.i.d. random variables with continuous distribution function F < 1. It is known that if 1 - F(x) varies regularly of order - p, the successive quotients of the order statistics in decreasing order of X1,…,Xn are asymptotically independent, as n→∞, with distribution functions xkp, k = 1, 2, …. A strong converse is proved, viz. convergence in distribution of this type of one of the quotients implies regular varation of 1 - F(x)

Asymptotic expansions for renewal measures in the plane

Let P be a distribution in the plane and define the renewal measure R=ΣP *n where * denotes convolution. The main results of this paper are three term asymptotic expansions for R far from the origin. As an application, expansions are obtained for distributions in linear boundary crossing problems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47655/1/440_2004_Article_BF00348749.pd

Volumes of Restricted Minkowski Sums and the Free Analogue of the Entropy Power Inequality

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality has a counterpart for the free analogue of entropy . The free entropy (introduced recently by the second named author), consistently with Boltzmann's formula $S=k\log W$, was defined via volumes of matricial microstates. Proving the free entropy power inequality naturally becomes a geometric question. Restricting the Minkowski sum of two sets means to specify the set of pairs of points which will be added. The relevant inequality, which holds when the set of "addable" points is sufficiently large, differs from the Brunn-Minkowski inequality by having the exponent $1/n$ replaced by $2/n$. Its proof uses the rearrangement inequality of Brascamp-Lieb-L\"uttinger

Systemic toxicity and cytokine/acute phase protein levels in patients after isolated limb perfusion with tumor necrosis factor-alpha complicated by high leakage

BACKGROUND: Since the introduction of high-dose tumor necrosis factor-alpha (TNFalpha) in the setting of isolated limb perfusion (ILP) in the clinic, prevention of leakage to the body of the patient is monitored with great precision for fear of TNF-mediated toxicity. That we observed remarkably little toxicity in patients with and without leakage prompted us to determine patterns of cytokines and acute phase proteins in patients with high leakage and in patients without any leakage. METHODS: TNFalpha, interleukin (IL)-6, IL-8, C-reactive protein, and secretory (s)-phospholipase A2 were measured at several time points during and after (until 7 days) ILP in 10 patients with a leakage to the systemic circulation varying in percentage from 12% to 65%. As a control, the same measurements, both in peripheral blood and in perfusate, were performed in nine patients without systemic leakage. RESULTS: In patients with systemic leakage, levels of TNFalpha increased during ILP, reaching values to 277 ng/ml. IL-6 and IL-8 peaked 3 hours after ILP with values significantly higher compared with patients without systemic leakage. C-reactive protein and s-phospholipase A2 peaked at day 1 in both patient groups, s-phospholipase A2 with significant higher levels and C-reactive protein, in contrast, with lower levels in the leakage patients. CONCLUSIONS: High leakage of TNFalpha to the systemic circulation, caused by a complicated ILP, led to 10-fold to more than 100-fold increased levels of TNFalpha, IL-6, and IL-8 in comparison with patients without leakage. The increase of the acute phase proteins was limited. Even when high leakage occurs, this procedure should not

Information dynamics: Temporal behavior of uncertainty measures

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory methods and inequalities satisfied by Fisher and Shannon information measures. We focus on a compatibility of these inequalities with the prescribed (deterministic, random or quantum) temporal behavior of pertinent probability densities.Comment: Incorporates cond-mat/0604538, title, abstract changed, text modified, to appear in Cent. Eur. J. Phy

Metabolic response of blood vessels to TNF alpha

TNF alpha signaling in the vascular endothelium elicits multiple inflammatory responses that drive vascular destabilization and leakage. Bioactive lipids are main drivers of these processes. In vitro mechanistic studies of bioactive lipids have been largely based on two-dimensional endothelial cell cultures that, due to lack of laminar flow and the growth of the cells on noncompliant stiff substrates, often display a pro-inflammatory phenotype. This complicates the assessment of inflammatory processes. Three-dimensional microvessels-on-a-chip models provide a unique opportunity to generate endothelial microvessels in a more physiological environment. Using an optimized targeted liquid chromatography-tandem mass spectrometry measurements of a panel of pro- and anti-inflammatory bioactive lipids, we measure the profile changes upon administration of TNF alpha. We demonstrate that bioactive lipid profiles can be readily detected from three-dimensional microvessels-on-a-chip and display a more dynamic, less inflammatory response to TNF alpha, that resembles more the human situation, compared to classical two-dimensional endothelial cell cultures.Analytical BioScience