Phenomenological Renormalization Group Methods

Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate critical behavior of the model on infinite lattice is obtained through the exact computation of some thermal quantities of the model on finite clusters. In this work some of these methods are reviewed, namely the mean field renormalization group, the effective field renormalization group and the finite size scaling renormalization group procedures. Although special emphasis is given to the mean field renormalization group (since it has been, up to now, much more applied an extended to study a wide variety of different systems) a discussion of their potentialities and interrelations to other methods is also addressed.Comment: Review Articl

How Does the Government (Want to) Fund Science? Politics, Lobbying and Academic Earmarks

This paper examines academic earmarks and their role in the funding of university research. It provides a summary and review of the evidence on the supply of earmarks by legislators. It then discusses the role of university lobbying for earmarks on the demand side. Finally, the paper examines the impact of earmarks on research quantity and quality.

Academic Earmarks and the Returns to Lobbying

Despite a large literature on lobbying and information transmission by interest groups, no prior study has measured returns to lobbying. In this paper, we statistically estimate the returns to lobbying by universities for educational earmarks (which now represent 10 percent of federal funding of university research). The returns to lobbying approximate zero for universities not represented by a member of the Senate Appropriations Committee (SAC) or House Appropriations Committee (HAC). However, the average lobbying university with representation on the SAC receives an average return to one dollar of lobbying of $11-$17; lobbying universities with representation on the HAC obtain $20-$36 for each dollar spent. Moreover, we cannot reject the hypothesis that lobbying universities with SAC or HAC representation set the marginal benefit of lobbying equal to its marginal cost, although the large majority of universities with representation on the HAC and SAC do not lobby, and thus do not take advantage of their representation in Congress. On average, 45 percent of universities are predicted to choose the optimal level of lobbying. In addition to addressing questions about the federal funding of university research, we also discuss the impact of our results for the structure of government.

Edge-colouring and total-colouring chordless graphs

A graph $G$ is \emph{chordless} if no cycle in $G$ has a chord. In the present work we investigate the chromatic index and total chromatic number of chordless graphs. We describe a known decomposition result for chordless graphs and use it to establish that every chordless graph of maximum degree $\Delta\geq 3$ has chromatic index $\Delta$ and total chromatic number $\Delta + 1$. The proofs are algorithmic in the sense that we actually output an optimal colouring of a graph instance in polynomial time

Complexity of colouring problems restricted to unichord-free and \{square,unichord\}-free graphs

A \emph{unichord} in a graph is an edge that is the unique chord of a cycle. A \emph{square} is an induced cycle on four vertices. A graph is \emph{unichord-free} if none of its edges is a unichord. We give a slight restatement of a known structure theorem for unichord-free graphs and use it to show that, with the only exception of the complete graph $K_4$, every square-free, unichord-free graph of maximum degree~3 can be total-coloured with four colours. Our proof can be turned into a polynomial time algorithm that actually outputs the colouring. This settles the class of square-free, unichord-free graphs as a class for which edge-colouring is NP-complete but total-colouring is polynomial