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

A lower bound for crossing numbers of graphs with applications to Kn, Kp,q, and Q(d)

AbstractIn this paper we obtain a combinatorial lower bound δg(G) for the crossing number crg(G) of a graph G in the closed orientable surface of genus g, and we conjecture that equality holds in a wide range of interesting cases. The lower bound is applied to the crossing number of the 1-skeleton of a d-dimensional cube to show that this crossing number must be at least 4, and a constructive technique is used to show that the crossing number is at most 8. Finally, we show that the crossing number of any graph is at most k2 times the crossing number of the underlying simple graph, where k = maximum multiplicity of an edge

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

Chromatic number and skewness

AbstractIn this note, we solve the problem of determing the chromatic number of planar graphs to which a certain number μ of “extra” edges are attached. We obtain a (best-possible) theorem when μ < 2k for every integer k ≥ 3. The statement of the theorem for k = 2 is the Four-Color Conjecture

Relative colorings of graphs

AbstractIn this paper, the notion of relative chromatic number χ(G, H) for a pair of graphs G, H, with H a full subgraph of G, is formulated; namely, χ(G, H) is the minimum number of new colors needed to extend any coloring of H to a coloring of G. It is shown that the four color conjecture (4CC) is equivalent to the conjecture (R4CC) that χ(G, H) ≤ 4 for any (possibly empty) full subgraph H of a planar graph G and also to the conjecture (CR3CC) that χ(G, H) ≤ 3 if H is a connected and nonempty full subgraph of planar G. Finally, relative coloring theorems on surfaces other than the plane or sphere are proved

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