DESIGNING VLSI SIGNAL PROCESSING CHIPS USING DATA DEPENDENCE GRAPHS.

The highly structured nature of many digital signal processing operations allows these to be directly implemented as regular VLSI circuits. This feature has been successfully exploited in the design of a number of commercial chips, some examples of which are described. While many of the architectures on which such chips are based were originally derived on heuristic basis, there is an increasing interest in the development of systematic design techniques for the direct mapping of computations onto regular VLSI arrays. The purpose of this paper is to show how the the technique proposed by Kung can be readily extended to the design of VLSI signal processing chips where the organisation of computations at the level of individual data bits is of paramount importance. The technique in question allows architectures to be derived using the projection and retiming of data dependence graphs.

HDL composition and HDL antioxidant capacity in patients on regular haemodialysis

Recent evidence suggests that HDL can directly inhibit LDL oxidation, a key early stage in atherogenesis. Patients with chronic renal failure are at increased cardiovascular risk, have reduced HDL levels and altered HDL composition. We have therefore investigated whether compositional changes in HDL lead to decreased HDL antioxidant capacity in these patients. In comparison to control subject HDL, patient HDL contained less total cholesterol, cholesterol esters, phospholipids and alpha-tocopherol. LDL, HDL and LDL + HDL were standardised for protein and oxidised in the presence of Cu2+. The rate of propagation during HDL oxidation was reduced in the patient group (3.28 +/- 0.65 x 10(-5) vs. 4.60 +/- 0.97 x 10(-5) abs. U/min, P

Graphs of relations and Hilbert series

We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by $n$ generators and $\frac {n(n-1)}{2}$ relations for $n \leq 7$. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated to each color are pairwise 2-isomorphic.

The outflow ranking method for weighted directed graphs

A ranking method assigns to every weighted directed graph a (weak) ordering of the nodes. In this paper we axiomatize the ranking method that ranks the nodes according to their outflow using four independent axioms. Besides the well-known axioms of anonymity and positive responsiveness we introduce outflow monotonicity – meaning that in pairwise comparison between two nodes, a node is not doing worse in case its own outflow does not decrease and the other node’s outflow does not increase – and order preservation – meaning that adding two weighted digraphs such that the pairwise ranking between two nodes is the same in both weighted digraphs, then this is also their pairwise ranking in the ‘sum’ weighted digraph. The outflow ranking method generalizes the ranking by outdegree for directed graphs, and therefore also generalizes the ranking by Copeland score for tournaments.