In this paper we consider the notions of global-fairness (G-fairness) and bounded-fairness (B-fairness) for arbitrary Petri nets (PNs). G-fairness in a PN guarantees every transition occurs infinitely often in every valid firing sequence of infinite length. B-fairness guarantees a bound on the number of times a transition in the PN can fire without some transition firing at least once. These pr...

We study continuous (strongly) minimal cut generating functions for the model where all variables are integer. We consider both the original Gomory-Johnson setting, as well as a recent extension by Cornuéjols and Yıldız. We show that for any continuous minimal or strongly minimal cut generating function, there exists an extreme cut generating function that approximates the (strongly) minimal fu...

We give an O(n log log n) time algorithm for computing the minimum cut (or equivalently, the shortest cycle) of a weighted directed planar graph. This improves the previous fastest O(n log n) solution [SODA’04]. Interestingly, while in undirected planar graphs both min-cut and min st-cut have O(n log log n) solutions [ESA’11, STOC’11], in directed planar graphs our result makes min-cut faster t...

For a 1-tough graph G we define σ3(G) = min{d(u) + d(v)+ d(w) : {u, v, w} is an independent set of vertices} and NCσ3−n+5(G) = max{ ⋃ σ3−n+5 i=1 N(vi) : {v1, ..., vσ3−n+5} is an independent set of vertices}. We show that every 1-tough graph with σ3(G) ≥ n contains a cycle of length at least min{n, 2NCσ3−n+5(G) + 2}. This result implies some well-known results of Faßbender [2] and of Flandrin, J...

We study computation by formulas over (min,+). We consider the computation of max{x1, . . . , xn} over N as a difference of (min,+) formulas, and show that size n+ n log n is sufficient and necessary. Our proof also shows that any (min,+) formula computing the minimum of all sums of n − 1 out of n variables must have n log n leaves; this too is tight. Our proofs use a complexity measure for (mi...

Pyridostigmine bromide (PB) is a reversible cholinesterase inhibitor. The aim of this study was to determine the effect of orally administration of single dose sustained-released tablet of pyridostigmine bromide (PBSR) on the frequency domain indices of heart rate variability (HRV). Thirty-two healthy young men were participated in this study. They were divided into 2 groups; the pyridostigmine...

A family C of min-wise independent permutations is known to be a useful tool of indexing replicated documents on the Web. For any integer n > 0, a family C of permutations on [n] = {1, 2, . . . , n} is said to be min-wise independent if for any (nonempty) X ⊆ [n] and any x ∈ X, Pr(min{π(X)} = π(x)) = ‖X‖−1 when π is chosen uniformly at random from C, where ‖A‖ is the cardinality of a finite set...

Quantum data locking is a quantum communication primitive that allows the use of short secret key to encrypt much longer message. It guarantees information-theoretical security against an adversary with limited memory. Here we present protocol employs pseudorandom circuits consisting Clifford gates only, which are easier implement fault tolerantly than universal gates. We show information can b...

Abstract We provide an improvement of Calderón and Torchinsky’s version [ 5] the Hörmander multiplier theorem on Hardy spaces $H^p$ ($0<p<\infty $), substituting Sobolev space $L_s^2(A_0)$ by Lorentz–Sobolev $L_s^{\tau ^{(s,p)},\min (1,p) }(A_0)$, where $\tau ^{(s,p)} =\frac{n}{s-(n/\min{(1,p)}-n)}$ $A_0$ is annulus $\{\xi \in{\mathbb{R}}^n:\,\, 1/2<|\xi |<2\}$. Our ...

ghrelin is an orexigenic peptide secreted by the stomach. the aim of this study was to investigate the effect of three weeks of endurance training on plasma and fundus ghrelin as well as growth hormone (gh), cortisol hormone and weight in male wistar rats. 20 male wistar rats (14–16 weeks old) were randomly assigned to control (n =10) and training (n=10) groups. the rats in the training group e...