Many studies are aimed at identifying dense clusters/subgraphs from protein-protein interaction (PPI) networks for protein function prediction. However, the prediction performance based on the dense clusters is actually worse than a simple guilt-by-association method using neighbor counting ideas. This indicates that the local topological structures and properties of PPI networks are still open...

For a digraph D, let λ(D) be the arc-strong-connectivity of D. For an integer k > 0, a simple digraph Dwith |V (D)| ≥ k + 1 is k-maximal if every subdigraph H of D satisfies λ(H) ≤ k but for adding new arc to D results in a subdigraph H ′ with λ(H ) ≥ k + 1. We prove that if D is a simple k-maximal digraph on n > k + 1 ≥ 2 vertices, then |A(D)| ≥ n 2  + (n − 1)k +  n k + 2   1 + 2k −  k +...

We study the possible Hausdorff limits of Julia sets and filled subsequences sequence dual Chebyshev polynomials a non-polar compact set $$K\subset {\mathbb C}$$ compare such to K. Moreover, we prove that measures maximal entropy for K converges weak* equilibrium measure on

BACKGROUND Among opioids, meperidine (pethidine) also shows local anesthetic activity when applied locally to peripheral nerve fibers and has been used for this effect in the clinical setting for regional anesthesia. This study investigated the blocking effects of meperidine on different ion channels in peripheral nerves. METHODS Experiments were conducted using the outside-out configuration ...

With the help of symbolic computer packages, study cohomological rigidity real solvable Lie algebras rank one with a maximal torus derivations t and eigenvalue spectrum spec(t)=1,k,k+1,⋯,n+k−2 initiated in previous work is continued for arbitrary values k≥2, obtaining new hierarchies rigid algebras.

Introduction. Let G be a reductive Lie group with maximal compact subgroup K and let Γ be a cocompact discrete subgroup of G. We consider the induced representation IndΓ (C), which is the canonical representation on the space L2(Γ\G). The duality theorem of Gelfand [6] states that there is a Frobenius reciprocity as follows: for any irreducible unitary representation π of G it holds HomG,cont(I...

A (d, k) set is a subset of Rd containing a translate of every k-dimensional plane. Bourgain showed that for k ≥ kcr(d), where kcr(d) solves 2kcr−1 + kcr = d, every (d, k) set has positive Lebesgue measure. We give a short proof of this result which allows for an improved Lp estimate of the corresponding maximal operator, and which demonstrates that a lower value of kcr could be obtained if imp...

Clustering is one of the central data mining problems and numerous approaches have been proposed in this field. However, few of these methods focus on categorical data. The categorical techniques that do exist have significant shortcomings in terms of performance, the clusters they detect, and their ability to locate clusters in subspaces. This work introduces a novel algorithm called Click, wh...

Let n and k be integers. A set A ⊂ Z/nZ is k-free if for all x in A, kx / ∈ A. We determine the maximal cardinality of such a set when k and n are coprime. We also study several particular cases and we propose an efficient algorithm for solving the general case. We finally give the asymptotic behaviour of the minimal size of a k-free set in J1, nK which is maximal for inclusion.

Let K be a proper (i.e., closed, pointed, full convex) cone in R. An n × n matrix A is said to be K-primitive if there exists a positive integer k such that A(K \ {0}) ⊆ intK; the least such k is referred to as the exponent of A and is denoted by γ(A). For a polyhedral cone K, the maximum value of γ(A), taken over all K-primitive matrices A, is denoted by γ(K). It is proved that for any positiv...