Given a graph G = (V,E) with n vertices and an integer k 6 n, Max k-Vertex Cover consists of determining a subset K ⊆ V that covers the most of edges in E. We study the polynomial approximation of Max k-Vertex Cover in bipartite graphs by a purely combinatorial algorithm and present an experimental analysis of it that finds the worst case approximation guarantee that is bounded below by 0.794. ...

In this paper, we find the relationship between mincut circuit partitioning and the initial (V, E) pairs distributed condition I entropy on the V-E plain. If a circuit has higher initial potential / entropy, under a nearly max-cut reservation, we have higher probability to aim the mincut. The proposed new method is called Interleaved Cutting Edge-Node Interleaved Sort for Leaching and Envelop (...

Let (X,???X),(Y,???Y) be normed spaces with dim?(X)=n. Bourgain's almost extension theorem asserts that for any ?>0, if N is an ?-net of the unit sphere X and f:N?Y 1-Lipschitz, then there exists O(1)-Lipschitz F:X?Y such ?F(a)?f(a)?Y?n? all a?N. We prove this optimal up to lower order factors, i.e., sometimes maxa?N??F(a)?f(a)?Y?n1?o(1)? every F:X?Y. This improves bound maxa?N??F(a)?f(a)?Y?nc?...

The myosin heavy chain (MHC) and myosin light chain (MLC) isoforms in skeletal muscle of Rana pipiens have been well characterized. We measured the force-velocity (F-V) properties of single intact fast-twitch fibers from R. pipiens that contained MHC types 1 or 2 (MHC1 or MHC2) or coexpressed MHC1 and MHC2 isoforms. Velocities were measured between two surface markers that spanned most of the f...

To investigate the regulation of intramuscular fuel selection, we measured the malonyl-CoA (M-CoA) content in human skeletal muscle at three exercise power outputs [35, 65, and 90% maximal rate of O2 consumption (V˙o 2 max)]. Four males and four females cycled for 10 min at one power output on three separate occasions with muscle biopsies sampled at rest and at 1 and 10 min. The respiratory exc...

Let A, B ⊆ Z be finite, nonempty subsets such that maxB − minB ≤ maxA − minA, gcd(A+B−c) = 1, for some c ∈ A+B, and |A+B| ≤ |A|+2|B|−3−δ(A,B), where δ(A,B) is 1 if x + A ⊆ B for some x ∈ Z, and is 0 otherwise. Assume one of the following conditions holds true: • maxA−minA ≤ |A| + |B|− 3, • gcd(A− a) ≤ 2, for some a ∈ A, • |A + B| ≤ 2|A| + |B|− 3− δ(B,A). Then A+B contains a (|A|+ |B|−1)–term ar...

Brain natriuretic peptide (BNP) reduces the extent of myocardial infarction. We aimed to determine whether BNP may reduce skeletal muscle mitochondrial dysfunctions and oxidative stress through mitochondrial K(ATP) (mK(ATP)) channel opening after ischemia-reperfusion (IR). Wistar rats were assigned to four groups: sham, 3-h leg ischemia followed by 2-h reperfusion (IR), pretreatment with BNP, a...

BACKGROUND Although breathlessness is common in chronic heart failure (CHF), the role of inspiratory muscle dysfunction remains unclear. We hypothesised that inspiratory muscle endurance, expressed as a function of endurance time (Tlim) adjusted for inspiratory muscle load and inspiratory muscle capacity, would be reduced in CHF. METHODS Endurance was measured in 10 healthy controls and 10 pa...

We consider max coloring on hereditary graph classes. The problem is defined as follows. Given a graph G = (V, E) and positive node weights w : V → (0,∞), the goal is to find a proper node coloring of G whose color classes C1, C2, . . . , Ck minimize k ∑ i=1 maxv∈Ci w(v). We design a general framework which allows to convert approximation algorithms for standard node coloring into algorithms fo...