Colorful Strips

Given a planar point set and an integer $k$, we wish to color the points with $k$ colors so that any axis-aligned strip containing enough points contains all colors. The goal is to bound the necessary size of such a strip, as a function of $k$. We show that if the strip size is at least $2k{-}1$, such a coloring can always be found. We prove that the size of the strip is also bounded in any fixed number of dimensions. In contrast to the planar case, we show that deciding whether a 3D point set can be 2-colored so that any strip containing at least three points contains both colors is NP-complete. We also consider the problem of coloring a given set of axis-aligned strips, so that any sufficiently covered point in the plane is covered by $k$ colors. We show that in $d$ dimensions the required coverage is at most $d(k{-}1)+1$. Lower bounds are given for the two problems. This complements recent impossibility results on decomposition of strip coverings with arbitrary orientations. Finally, we study a variant where strips are replaced by wedges

THE CURRENT MACROECONOMIC CRISIS

Professor Crotty once casually observed that in his view economics could not be properly thought of as a science. This paper investigates the implications of this view in light of the question of how the scientific method has recently contributed to the evolution of economic practice. It is argued that agent-based models might provide a platform for an integration of recent micro and macroeconomic theories.Agent-based models, macroeconomics, Keynes, James Crotty.

The Top Three Patent Cases of 2012

New Year’s Day prompts us to reflect on what the last 12 months have brought, so I’ve taken the opportunity to think back on 2012’s intellectual property developments. It’s been a busy year, with patent reform, new technologies, multilateral treaties, and more. To make my task more manageable, I’m going to focus on three important patent law cases – one at the Supreme Court level, one at the appellate level, and one at the trial court level. I’ll conclude with an extra-special bonus: the Case To Watch for patent law in 2013. Then, in my next entry in this series, I’ll do the same for copyright. My choice at the Supreme Court is Mayo Collaborative Services v. Prometheus Laboratories, Inc., in which the Court confronted the issue of patent-eligible subject matter. That’s an issue the Court ignored for almost 30 years. It resurfaced in 2010, when the Court decided Bilski v. Kappos. Bilski was mostly about software and business-method patents, and it relied on the long-standing restriction on patenting “abstract ideas.” In Prometheus, the Court addressed another important industry – medicine and biotech – and it did so by relying on another categorical exclusion: “laws of nature.” [...

Scene and Surface in the Cinema : Implications for Realism

Dans l'organisation visuelle d'un film, on peut distinguer deux ensembles distincts d'informations, l'un relatif à l'événement diégétique en trois dimensions (la scène) et l'autre, à l'écran bidimensionnel sur lequel le film est projeté (la surface). L'auteur, en collaboration avec ses collègues du Digital Arts and Imaging Lab, a essayé de déterminer quelle information était perçue comme faisant partie de la scène et quelle autre était considérée comme faisant partie de la surface. S'appuyant sur les travaux de James J. Gibson, il conclut en mettant en question l'application de la théorie du réalisme au cinéma.The visual array of a motion picture contains two separable sets of information, one for a three-dimensional diegetic event (scene) and another set of information which specifies the two-dimensional screen upon which the film is projected (surface). The author and his colleagues of the Digital Arts and Imaging Lab have attempted to sort out which information is seen as part of the scene and which as part of the surface. Based on the works of James J. Gibson, their conclusions question the application of the theory of realism to films

Pragmatic Evolutions of the Kantian a priori: From the Mental to the Bodily

In this article, I review textual evidence demonstrating that James and Dewey incorporated Kant’s ideas, even while criticizing him. I specifically argue that the pragmatic evolution of the Kantian a priori carried out by James and Dewey is a transition from the mental to the bodily. I further argue that the parallels between pragmatists and Kant, along with the transition from the mental to bodily, relate to scientific contexts in which all developed their outlooks. Though historically grounded, my ultimate goal is to show that pragmatism and by extension Kantianism mesh with and indeed contribute to cutting edge ideas in fields ranging from neuropathology to robotics and AI to cognitive science, whether in the form of Gibsonian theory or enactivism

Measurement of the B_s^0→K^+K^- lifetime relative to the B_d^0→K^+π^- lifetime

The study of B decays to charmless charged hadrons offers an opportunity to improve our understanding CP violation and to search for New Physics beyond the Standard Model. We present an analysis to make a measurement of the B_s^0→K^+K^- lifetime relative to B_d^0 lifetime which removes systematic bias introduced to the lifetime by distance of flight based selections

Los Materiales contra la materialidad

This article seeks to reverse the emphasis, in current studies of material culture, on the materiality of objects, as against the properties of material. Drawing on James Gibson`s tripartite division of the inhabited environment into médium, substances and surfaces, it is argued that the forms of things are not imposed from without upon an inert substrate of matter, but are continually generated and disolved within the fluxes of materials across the interface between substances and the medium that surrounds them. Thus things are active not because they are imbued with agency but because of ways in wich they are caught up in these currents of the lifeworld. The properties of materials, then, are not fixed attributes of matter but are processual and relational. To describe these properties means telling their stories