We discuss the problem of computing the volume of a convex body K in R. We review worst-case results which show that it is hard to deterministically approximate voln K and randomised approximation algorithms which show that with randomisation one can approximate very nicely. We then provide some applications of this latter result. •Supported by NATO grant RG0088/89 t Supported by NSF grant CCR-...

Downloa creatic cancer (PC) is a highly lethal disease with complex etiology involving both environmental netic factors. Although cigarette smoking is known to explain 25% of cases, data from recent studies sugat obesity and long-term type II diabetes are twomajor modifiable risk factors for PC. Furthermore, obed diabetes seem to affect the clinical outcome of patients with PC. Understanding th...

This paper investigates the computational complexity of approximating several NPoptimization problems using the number of queries to an NP oracle as a complexity measure. The results show a trade-off between the closeness of the approximation and the number of queries required. For an approximation factor k(n), log logk(n) n queries to an NP oracle can be used to approximate the maximum clique ...

We give a comprehensive and unifying survey of the theoretical aspects of Temporal and Modal Logic Note This paper is to appear in the Handbook of Theoretical Computer Science J van Leeuwen managing editor North Holland Pub Co Work supported in part by US NSF Grant CCR ONR Contract N K and Netherlands ZWO grant nf nfb

Given an undirected graph with non negative edge costs and an inte ger k the k MST problem is that of nding a tree of minimum cost on k nodes This problem is known to be NP hard We present a simple approximation algorithm that nds a solution whose cost is less than times the cost of the optimum This improves upon previous performance ratios for this problem O p k due to Ravi et al O log k due t...

We examined the potential involvement of two CC chemokine receptors (CCRs), CCR-1 and CCR-3, in the functional activation of granulocyte-macrophage colony-stimulating factor (GM-CSF) plus interleukin-4 (IL-4)-generated human peripheral blood monocyte-derived immature dendritic cells (DCs). Flow cytometric analysis showed that CCR-1, CCR-3, CCR-5, and CXC chemokine receptor (CXCR)-4 were express...

Let H be a collection of n hyperplanes in d-space. We will assume that the planes are in general position, meaning that any k planes meet in a d− k-flat, if k = 1, . . . , d, and not at all if k > d. It is not difficult to see that worst-case cell complexity can always be achieved by planes in general position. comBoris says: True, or only asymptotically true?ment Let P be ←− Work on this paper...

Assuming that k and Pk does not have p measure it is shown that BP k P k This implies that the following conditions hold if P does not have p measure i AM co AM is low for P Thus BPP and the graph isomor phism problem are low for P ii If P PH then NP does not have polynomial size circuits This research was supported in part by National Science Foundation Grant CCR with matching funds from Rockw...

One of the most intriguing fa ts about ommuni ation using quantum states is that these states annot be used to transmit more lassi al bits than the number of qubits used, yet in some s enarios there are ways of onveying information with exponentially fewer qubits than possible lassi ally [3, 26℄. Moreover, these methods have a very simple stru ture|they involve only few message ex hanges betwee...