No part of this book may be reproduced, in any form or by any means, without permission in writing from the author. Cover picture: Three dimensional schematic representation of the steps that lead to controller design. The fish is cloned for scientific purposes only, without permission of the Dutch government.

We show that for each integer h ≥ 2, there exists a least positive integer ch so that if P is a poset having a planar cover graph and the height of P is h, then the dimension of P is at most ch. Trivially, c1 = 2. Also, Felsner, Li and Trotter showed that c2 exists and is 4, but their proof techniques do not seem to apply when h ≥ 3. We focus on establishing the existence of ch, although we sus...

We consider capacitated vertex cover with hard capacity constraints (VC-HC) on hypergraphs. In this problem we are given a hypergraph G = (V,E) with a maximum edge size f . Each edge is associated with a demand and each vertex is associated with a weight (cost), a capacity, and an available multiplicity. The objective is to find a minimum-weight vertex multiset such that the demands of the edge...

Let G = (X, Y; E) be a balanced bipartite graph of order 2n. The path-cover number pc(H) of a graph H is the minimum number of vertex-disjoint paths that use up all the vertices of H. S ⊆ V(G) is called a balanced set of G if |S ∩ X| = |S ∩ Y|. In this paper, we will give some sufficient conditions for a balanced bipartite graph G satisfying that for every balanced set S, there is a bi-cycle of...

This article studies crime rates’ response to economic conditions. Using a longitudinal data set covering about 20 countries over the period 1970-2010, we investigate whether crime rates respond asymmetrically to increases in unemployment and recoveries in economic conditions. We find a positive response of crime rates on variation in unemployment rates, but we do not find compelling evidence o...

In 1988, Seiya Negami published a conjecture stating that a graph G has a finite planar cover (i.e. a homomorphism from some planar graph onto G which maps the vertex neighbourhoods bijectively) if and only if G embeds in the projective plane. Though the ”if” direction is easy, and over ten related research papers have been published during the past 20 years of investigation, this beautiful con...

For a Noetherian local domain (R, m, K), it is an open question whether strong F–regularity deforms. We provide an affirmative answer to this question when the canonical module satisfies certain additional assumptions. The techniques used here involve passing to a Gorenstein ring, using an anti– canonical cover.

Various observation- and reanalysis-based estimates of sea ice mass and ocean heat content trends imply that the energy imbalance of the Arctic climate system was similar [1.0 (0.9,1.2) Wm-2] to the global ocean average during the 2000-2015 period. Most of this extra heat warmed the ocean, and a comparatively small fraction went into sea ice melt. Poleward energy transports and radiation contri...