Some results on chromatic number as a function of triangle count

A variety of powerful extremal results have been shown for the chromatic number of triangle-free graphs. Three noteworthy bounds are in terms of the number of vertices, edges, and maximum degree given by Poljak \& Tuza (1994), and Johansson. There have been comparatively fewer works extending these types of bounds to graphs with a small number of triangles. One noteworthy exception is a result of Alon et. al (1999) bounding the chromatic number for graphs with low degree and few triangles per vertex; this bound is nearly the same as for triangle-free graphs. This type of parametrization is much less rigid, and has appeared in dozens of combinatorial constructions. In this paper, we show a similar type of result for $\chi(G)$ as a function of the number of vertices $n$, the number of edges $m$, as well as the triangle count (both local and global measures). Our results smoothly interpolate between the generic bounds true for all graphs and bounds for triangle-free graphs. Our results are tight for most of these cases; we show how an open problem regarding fractional chromatic number and degeneracy in triangle-free graphs can resolve the small remaining gap in our bounds

Deterministic parallel algorithms for bilinear objective functions

Many randomized algorithms can be derandomized efficiently using either the method of conditional expectations or probability spaces with low independence. A series of papers, beginning with work by Luby (1988), showed that in many cases these techniques can be combined to give deterministic parallel (NC) algorithms for a variety of combinatorial optimization problems, with low time- and processor-complexity. We extend and generalize a technique of Luby for efficiently handling bilinear objective functions. One noteworthy application is an NC algorithm for maximal independent set. On a graph $G$ with $m$ edges and $n$ vertices, this takes $\tilde O(\log^2 n)$ time and $(m + n) n^{o(1)}$ processors, nearly matching the best randomized parallel algorithms. Other applications include reduced processor counts for algorithms of Berger (1997) for maximum acyclic subgraph and Gale-Berlekamp switching games. This bilinear factorization also gives better algorithms for problems involving discrepancy. An important application of this is to automata-fooling probability spaces, which are the basis of a notable derandomization technique of Sivakumar (2002). Our method leads to large reduction in processor complexity for a number of derandomization algorithms based on automata-fooling, including set discrepancy and the Johnson-Lindenstrauss Lemma

Agricultural Trade Reform and Industry Adjustment in Indonesia

This paper presents a component of a project on industry adjustment to agricultural trade reform in selected developing countries. The aim of the project is to examine the issues affecting the development of industry adjustment policies to manage the impact of trade reform. It will evaluate specific developing country examples of industries that are likely to face significant adjustment pressures from trade policy reform. The study is focused on industry specific policy responses for two reasons. First, many LDC's are concerned about the consequences of future WTO reforms for adjustment in 'sensitive' industries. Governments in developing countries have received advice and assistance on how to comply with the requirements of their WTO commitments from the Uruguay Round of trade negotiations. However, very little attention has been devoted to the domestic effects of trade reform. Second, the implementation of international trade commitments is likely to lead to industry requests for assistance. Adjustment policies used by developed countries may not be directly applicable to LDC situations. Differences in structural characteristics, institutional arrangements and the level of industry development require an investigation of the issues affecting adjustment in developing countries.International Relations/Trade,

Improved algorithms and analysis for the laminar matroid secretary problem

In a matroid secretary problem, one is presented with a sequence of objects of various weights in a random order, and must choose irrevocably to accept or reject each item. There is a further constraint that the set of items selected must form an independent set of an associated matroid. Constant-competitive algorithms (algorithms whose expected solution weight is within a constant factor of the optimal) are known for many types of matroid secretary problems. We examine the laminar matroid and show an algorithm achieving provably 0.053 competitive ratio

The Liberian Truth and Reconciliation Commission: reconciling or re-dividing Liberia?

After 14 years of civil war and violence followed by the momentous and rather unusual elections of 2005, in which a woman defeated a footballer for the presidency, Liberia has seen over six years of state reconstruction and relative peace. Two recent announcements have, however, served as a warning to the extent of progress. The most recent is President Ellen Johnson-Sirleaf’s declaration that she will, despite previous statements to the contrary, stand for re-election in 2011 due to shortcomings in progress. The announcement preceding Johnson-Sirleaf’s was made in the form of the report of the Liberian Truth and Reconciliation Commission (TRC). It recommended that Johnson-Sirleaf, and indeed many others accused of involvement in the war, should be barred from public office for the next 30 years, and still more should stand trial on charges of war crimes. Four important questions arise. First, what was the mandate and findings of the TRC? Second, how has Liberia and the wider international community reacted to the final report? Third, has the TRC fulfilled its mandate and contributed to a process of reconciliation? Finally, and in a much broader sense, where does the TRC stand relative to the much wider liberal peace model

From ‘Warlord’ to ‘Democratic’ President: how Charles Taylor won the 1997 Liberian elections

For the best part of seven years, an increasing number of warring factions fought a vicious civil war for control of the West African state of Liberia. In August 1996, the fourteenth peace accord led to presidential and parliamentary elections in July of the following year. Charles Taylor and his National Patriotic Party (NPP), formed out of the original invasion force, emerged victorious with a landslide 75 per cent of the vote. Given the international reputation of Taylor as a brutal warlord whose sole aim had never wavered from the capture of power in Monrovia, Taylor's across-the-board victory appears difficult to explain. Having concluded that, despite problems and allegations, the election did seem more free and fair than not, the article examines the factors that probably influenced the electorate's choices. The results of this research show an election heavily dependent on an uncertain security situation. However, it suggests that, although a former ‘warlord’ has been rewarded, the voting was a reasoned ploy by the electorate to maximise the possibility of improved living conditions

Post-Conflict Elections or Post-Elections Conflict: Sierra Leone 2002 and Patterns of Voting in Sub-Saharan Africa

Sierra Leone is just one of a growing number of countries that has experienced the current globally popular tool of conflict resolution, the multi-party election. This method of endeav- ouring to put a final cap on a peace process has a mixed record in Africa. There have been some successes, but the installation of unsuitable over-powerful governments and/or the return to war have more often been the case. The article examines firstly the outcomes of the 2002 Sierra Leone elections, and then situates these consequences on a spectrum of African post-conflict elections outcomes. Finally, possibilities for avoiding or mitigating the negative effects of post- conflict polls, particularly those emanating from the inevitable lack of security, are examined and posited

Poliovirus mutant that contains a cold-sensitive defect in viral RNA synthesis

By manipulating an infectious cDNA clone of poliovirus, we have introduced a single-codon insertion into the 3A region of the viral genome which has been proposed to encode a functional precursor of the virion-linked protein VPg. The resulting mutant was cold sensitive in monkey kidney cells. Viral RNA synthesis was poor at 32.5 degrees C, although no other function of the virus was obviously affected. The synthesis of both positive and negative strands was severely depressed. Temperature shift experiments suggest that a normal level of production of the affected function was required only during the early (exponential) phase of RNA synthesis. Analysis of viral polyprotein processing at the nonpermissive temperature revealed that some of the normal cleavages were not made, most likely as a consequence of the defect in RNA synthesis or as a result of the concomitant reduction in the level of virally encoded proteases