The Rationalist Tradition At Trial

Analysis of Evidence: How to Do Things With Facts Based On Wigmore\u27s Science of Judicial Proof, By Terrence Anderson and William Twining (with an Appendix on Probablity and Proof by Philip Dawid). Little, Brown and Company, and London: George Weidenfeld and Nicolson, Ltd., 1991. Pp. 457. $22.00. (Teacher\u27s Manual. Pp. 181

Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that it leads to mixed state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semi-classical bifurcation. Quantum signatures of the semi-classical limit-cycles are presented.Comment: 36 pages, 18 figure

Optimal strategies for a game on amenable semigroups

The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the semigroup is amenable in the sense of Day and von Neumann, one can extend the set of classical strategies, namely countably additive probability measures on S, to include some finitely additive measures in a natural way. This extended game has a value and the players have optimal strategies. This theorem extends previous results for the multiplication game on a compact group or on the positive integers with a specific payoff. We also prove that the procedure of extending the set of allowed strategies preserves classical solutions: if a semigroup game has a classical solution, this solution solves also the extended game.Comment: 17 pages. To appear in International Journal of Game Theor

Graph Treewidth and Geometric Thickness Parameters

Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for graphs of treewidth $k$, the maximum thickness and the maximum geometric thickness both equal $\lceil{k/2}\rceil$. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth $k$, the maximum book thickness equals $k$ if $k \leq 2$ and equals $k+1$ if $k \geq 3$. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215-221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity.Comment: A preliminary version of this paper appeared in the "Proceedings of the 13th International Symposium on Graph Drawing" (GD '05), Lecture Notes in Computer Science 3843:129-140, Springer, 2006. The full version was published in Discrete & Computational Geometry 37(4):641-670, 2007. That version contained a false conjecture, which is corrected on page 26 of this versio

Implicit Prejudice and its Implications for how Communities should Respond to Racial Injustices

In the spring of 2013, a racially controversial incident occurred on the Washington University Campus. The incident raised questions about the racial tolerance of the university community as well as exactly who should be held responsible for the injustice. Most importantly, the community’s response to the incident exemplified how a community with the potential for substantial collective action can fail to mobilize and improve when they are called upon to do so. This paper examines recent psychological research that studies the existence of subconscious racial prejudices in order to examine its implications in community responses to racial injustices. Results show that the majority of people hold unconscious prejudiced attitudes and are unaware of it, and that these attitudes can lead to discriminatory behavior. This suggests that when a racial injustice occurs in a community, the perpetrators may have been influenced by implicit prejudices held by the communities to which they belong. While literature on structural injustice considers how communities are responsible for the actions of those within them, they are insufficient to deal with issues of race, as they do not account for human reactions to such a sensitive subject. The Community System of Responsibility is introduced as a system that assigns responsibility to community members in a way that is practical in its expectations of individuals and that motivates community progress. Rather than searching for others to accuse, individuals following the community system look inward at consequences of their own behavior and the behavior of the communities to which they belong

Historical Framework for Reviving Constitutional Protection for Property and Contract Rights

Post-New Deal constitutionalism is in search of a theory that justifies judicial intervention on behalf of individual rights while simultaneously avoiding the charge of Lochnerism. \u27 The dominant historical view dismisses post-bellum substantive due process as an anomalous development in the American constitutional tradition. Under this approach, Lochner represents unbounded protection for economic rights that permitted the judiciary to read laissez faire, pro-business policy preferences into the constitutional text. Today\u27s revisionists have mounted a substantial challenge to the dismissive views of traditionalists. Indeed, some claim Lochner reached the right result, but for the wrong reason. The revisionists characterize substantive due process as a genuine, albeit unsuccessful, attempt to apply constitutional protections for property and contract in light of the economic, social and political situation in the late nineteenth century. The revisionist account of Lochnerism is likely to replace the dominant historical view and to transform a central understanding of the American constitutional tradition. In particular, this view of Lochnerism will likely influence the analysis of constitutional protection of economic rights. This Article will demonstrate that both sides have overlooked a key element in the progression of economic rights protection from the early nineteenth century through the Lochner era to the present day: the changing conception of the principle of non-retroactivity. This oversight may not be surprising in one sense, for the modem view-traceable to the Lochner era itself-is that the principle of nonretroactivity is simply a mask for substantive review. But it was not always so. The principle of non-retroactivity, heavily dependent upon the notion of vested rights, was the primary organizing idea in the constitutional economic rights protection that preceded the Lochner era of substantive due process