Algorithms for Robust Pole Assignment in Singular Systems

The solution of the pole assignment problem by feedback in singular systems is parameterized and conditions are given which guarantee the regularity and maximal degree of the closed loop pencil. A robustness measure is defined, and numerical procedures are described for selecting the free parameters in the feedback to give optimal robustness.

Feeding rumen-inert fats differing in their degree of saturation decreases intake and increases plasma concentrations of gut peptides in lactating dairy cows

Our objective was to determine the effect of feeding rumen-inert fats differing in their degree of saturation on dry matter intake (DMI), milk production, and plasma concentrations of insulin, glucagon-like peptide 1 (7-36) amide (GLP-1), glucose-dependent insulinotropic polypeptide (GIP), and cholecystokinin (CCK) in lactating dairy cows. Four midlactation, primiparous Holstein cows were used in a 4 x 4 Latin square experiment with 2-wk periods. Cows were fed a control mixed ration ad libitum, and treatments were the dietary addition (3.5% of ration dry matter) of 3 rumen-inert fats as sources of mostly saturated fatty acids (SFA), monounsaturated fatty acids (MUFA), or polyunsaturated fatty acids (PUFA). Daily DMI, milk yield, and composition were measured on the last 4 d of each period. Jugular vein blood was collected every 30 min over a 7-h period on d 12 and 14 of each period for analysis of plasma concentrations of hormones, glucose, and nonesterified fatty acids. Feeding fat decreased DMI, and the decrease tended to be greater for MUFA and PUFA compared with SFA. Plasma concentration of GLP-1 increased when fat was fed and was greater for MUFA and PUFA. Feeding fat increased plasma glucose-dependent insulinotropic polypeptide and CCK concentrations and decreased plasma insulin concentration. Plasma CCK concentration was greater for MUFA and PUFA than for SFA and was greater for MUFA than PUFA. Decreases in DMI in cows fed fat were associated with increased plasma concentrations of GLP-1 and CCK and a decreased insulin concentration. The role of these peptides in regulating DMI in cattle fed fat requires further investigation.

Degree of oxidation of low density lipoprotein affects expression of CD36 and PPAR gamma, but not cytokine production, by human monocyte-macrophages

Oxidized low-density lipoprotein (oxLDL) exhibits many atherogenic effects, including the promotion of monocyte recruitment to the arterial endothelium and the induction of scavenger receptor expression. However, while atherosclerosis involves chronic inflammation within the arterial intima, it is unclear whether oxLDL alone provides a direct inflammatory stimulus for monocyte-macrophages. Furthermore, oxLDL is not a single, well-defined entity, but has structural and physical properties which vary according to the degree of oxidation. We tested the hypothesis that the biological effects of oxLDL will vary according to its degree of oxidation and that some species of oxLDL will have atherogenic properties, while other species may be responsible for its inflammatory activity. The atherogenic and inflammatory properties of LDL oxidized to predetermined degrees (mild, moderate and extensive oxidation) were investigated in a single system using human monocyte-derived macrophages. Expression of CD36 mRNA was up-regulated by mildly- and moderately-oxLDL, but not highly-oxLDL. The expression of the transcription factor, proliferator-activated receptor-gamma (PPARgamma), which has been proposed to positively regulate the expression of CD36, was increased to the greatest degree by highly-oxLDL. However, the DNA binding activity of PPARgamma was increased only by mildly- and moderately-oxLDL. None of the oxLDL species appeared to be pro-inflammatory towards monocytes, either directly or indirectly through mediators derived from lymphocytes, regardless of the degree of oxidation. (C) 2003 Published by Elsevier Science Ireland Ltd.

Modelling the interdependence between the stoichiometry of receptor oligomerization and ligand binding for a coexisting dimer/tetramer receptor system

Many G protein-coupled receptors have been shown to exist as oligomers, but the oligomerization state and the effects of this on receptor function are unclear. For some G protein-coupled receptors, in ligand binding assays, different radioligands provide different maximal binding capacities. Here we have developed mathematical models for co-expressed dimeric and tetrameric species of receptors. We have considered models where the dimers and tetramers are in equilibrium and where they do not interconvert and we have also considered the potential influence of the ligands on the degree of oligomerization. By analogy with agonist efficacy, we have considered ligands that promote, inhibit or have no effect on oligomerization. Cell surface receptor expression and the intrinsic capacity of receptors to oligomerize are quantitative parameters of the equations. The models can account for differences in the maximal binding capacities of radioligands in different preparations of receptors and provide a conceptual framework for simulation and data fitting in complex oligomeric receptor situations.

On the maximal connected component of hypercube with faulty vertices

In evaluating an interconnection network, it is indispensable to estimate the size of the maximal connected components of the underlying graph when the network begins to lose processors. Hypercube is one of the most popular interconnection networks. This article addresses the maximal connected components of an n -dimensional cube with faulty processors. We first prove that an n -cube with a set F of at most 2n - 3 failing processors has a component of size greater than or equal to2(n) - \F\ - 1. We then prove that an n -cube with a set F of at most 3n - 6 missing processors has a component of size greater than or equal to2(n) - \F\ - 2.

On the maximal connected component of hypercube with faulty vertices (II)

evaluating the fault tolerance of an interconnection network, it is essential to estimate the size of a maximal connected component of the network at the presence of faulty processors. Hypercube is one of the most popular interconnection networks. In this paper, we prove that for ngreater than or equal to6, an n-dimensional cube with a set F of at most (4n-10) failing processors has a component of size greater than or equal to2"-\F-3. This result demonstrates the superiority of hypercube in terms of the fault tolerance.

On the maximal connected component of a hypercube with faulty vertices III

Hypercube is one of the most popular topologies for connecting processors in multicomputer systems. In this paper we address the maximum order of a connected component in a faulty cube. The results established include several known conclusions as special cases. We conclude that the hypercube structure is resilient as it includes a large connected component in the presence of large number of faulty vertices.

Diameter of parallelogramic honeycomb torus

The determination of the diameter of an interconnection network is essential in evaluating the performance of the network. Parallelogramic honeycomb torus is an attractive alternative to classical torus network due to smaller vertex degree, and hence, lower implementation cost. In this paper, we present the expression for the diameter of a parallelogramic, honeycomb torus, which extends a known result about rhombic: honeycomb torus. (c) 2005 Elsevier Ltd. All rights reserved.

Vertex splitting and connectivity augmentation in hypergraphs

We consider problems of splitting and connectivity augmentation in hypergraphs. In a hypergraph G = (V +s, E), to split two edges su, sv, is to replace them with a single edge uv. We are interested in doing this in such a way as to preserve a defined level of connectivity in V . The splitting technique is often used as a way of adding new edges into a graph or hypergraph, so as to augment the connectivity to some prescribed level. We begin by providing a short history of work done in this area. Then several preliminary results are given in a general form so that they may be used to tackle several problems. We then analyse the hypergraphs G = (V + s, E) for which there is no split preserving the local-edge-connectivity present in V. We provide two structural theorems, one of which implies a slight extension to Mader’s classical splitting theorem. We also provide a characterisation of the hypergraphs for which there is no such “good” split and a splitting result concerned with a specialisation of the local-connectivity function. We then use our splitting results to provide an upper bound on the smallest number of size-two edges we must add to any given hypergraph to ensure that in the resulting hypergraph we have λ(x, y) ≥ r(x, y) for all x, y in V, where r is an integer valued, symmetric requirement function on V*V. This is the so called “local-edge-connectivity augmentation problem” for hypergraphs. We also provide an extension to a Theorem of Szigeti, about augmenting to satisfy a requirement r, but using hyperedges. Next, in a result born of collaborative work with Zoltán Király from Budapest, we show that the local-connectivity augmentation problem is NP-complete for hypergraphs. Lastly we concern ourselves with an augmentation problem that includes a locational constraint. The premise is that we are given a hypergraph H = (V,E) with a bipartition P = {P1, P2} of V and asked to augment it with size-two edges, so that the result is k-edge-connected, and has no new edge contained in some P(i). We consider the splitting technique and describe the obstacles that prevent us forming “good” splits. From this we deduce results about which hypergraphs have a complete Pk-split. This leads to a minimax result on the optimal number of edges required and a polynomial algorithm to provide an optimal augmentation.