Inflations of ideal triangulations

Starting with an ideal triangulation of the interior of a compact 3-manifold M with boundary, no component of which is a 2-sphere, we provide a construction, called an inflation of the ideal triangulation, to obtain a strongly related triangulations of M itself. Besides a step-by-step algorithm for such a construction, we provide examples of an inflation of the two-tetrahedra ideal triangulation of the complement of the figure-eight knot in the 3-sphere, giving a minimal triangulation, having ten tetrahedra, of the figure-eight knot exterior. As another example, we provide an inflation of the one-tetrahedron Gieseking manifold giving a minimal triangulation, having seven tetrahedra, of a nonorientable compact 3-manifold with Klein bottle boundary. Several applications of inflations are discussed.Comment: 48 pages, 45 figure

50 TeV HEGRA Sources and Infrared Radiation

The recent observations of 50 TeV gamma radiation by HEGRA have the potential of determining the extragalactic flux of infrared radiation. The fact that radiation is observed in the range between 30 and 100 TeV sets an upper limit on the infrared flux, while a cutoff at $E_{\gamma} \approx 50$ TeV fixes this flux with a good accuracy. If the intrinsic radiation is produced due to interaction of high energy protons with gas or low-energy target photons, then an accompaning high-energy neutrino flux is unavoidable. We calculate this flux and underground muon flux produced by it. The muon flux is dominated by muons with energies about 1 TeV and can be marginally detected by a 1 km$^2$ detector like an expanded AMANDA.Comment: 9 pages, latex2e, 3 eps figure

Quantization in geometric pluripotential theory

The space of K\"ahler metrics can, on the one hand, be approximated by subspaces of algebraic metrics, while, on the other hand, can be enlarged to finite-energy spaces arising in pluripotential theory. The latter spaces are realized as metric completions of Finsler structures on the space of K\"ahler metrics. The former spaces are the finite-dimensional spaces of Fubini--Study metrics of K\"ahler quantization. The goal of this article is to draw a connection between the two. We show that the Finsler structures on the space of K\"ahler potentials can be quantized. More precisely, given a K\"ahler manifold polarized by an ample line bundle we endow the space of Hermitian metrics on powers of that line bundle with Finsler structures and show that the resulting path length metric spaces recover the corresponding metric completions of the Finsler structures on the space of K\"ahler potentials. This has a number of applications, among them a new approach to the rooftop envelopes and Pythagorean formulas of K\"ahler geometry, a new Lidskii type inequality on the space of K\"ahler metrics, and approximation of finite energy potentials, as well as geodesic segments by the corresponding smooth algebraic objects

A model for the fragmentation kinetics of crumpled thin sheets

As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility. Experiments have shown that the total crease length accrues logarithmically when repeatedly compacting and unfolding a sheet of paper. Here, we offer insight to this unexpected result by exploring the correspondence between crumpling and fragmentation processes. We identify a physical model for the evolution of facet area and ridge length distributions of crumpled sheets, and propose a mechanism for re-fragmentation driven by geometric frustration. This mechanism establishes a feedback loop in which the facet size distribution informs the subsequent rate of fragmentation under repeated confinement, thereby producing a new size distribution. We then demonstrate the capacity of this model to reproduce the characteristic logarithmic scaling of total crease length, thereby supplying a missing physical basis for the observed phenomenon.Comment: 11 pages, 7 figures (+ Supplemental Materials: 15 pages, 9 figures); introduced a simpler approximation to model, key results unchanged; added references, expanded supplementary information, corrected Fig. 2 and revised Figs. 4 and 7 for clearer presentation of result

Euler characteristic and quadrilaterals of normal surfaces

Let $M$ be a compact 3-manifold with a triangulation $\tau$. We give an inequality relating the Euler characteristic of a surface $F$ normally embedded in $M$ with the number of normal quadrilaterals in $F$. This gives a relation between a topological invariant of the surface and a quantity derived from its combinatorial description. Secondly, we obtain an inequality relating the number of normal triangles and normal quadrilaterals of $F$, that depends on the maximum number of tetrahedrons that share a vertex in $\tau$.Comment: 7 pages, 1 figur

Love and Suffering: Adolescent Socialization and Suicide in Micronesia

Youth suicide has reached epidemic proportion in Micronesia over the past two decades. Suicides display remarkable cultural patterning in the typical actors, methods, motivational themes, and precipitating social scenarios. The focus of contemporary high rates is among young men aged fifteen to twenty-four, who hang themselves following incidents of conflict with parents. Predominant themes invoked in adolescent suicide accounts involve anger and suffering at the hands of their parents, and feelings of familial rejection juxtaposed with reaffirmations of filial love. Less frequent are themes involving personal shame over violations of fundamental social rules. In situations of both "anger" and "shame" suicides, the primary locus of conflict is within close family relations. The suicides appear as an extreme form of an accustomed pattern of resolving conflict with senior family members by withdrawing from the scene. In this article I employ one paradigmatic case history to provide a description of the cultural construction and social dynamics of contemporary adolescent suicide in Micronesia. The suicide phenomenon is situated within recent changes in the stage of adolescent male socialization in Micronesian societies. For adolescent males of earlier generations, social involvement at the level of lineage and clan activities provided important support. The recent rapid shift from subsistence exchange to cash economy has severely attenuated lineage and clan structures and, by undermining the process of adolescent socialization, has set the stage for high rates of suicide among young men. Finally, I explore the potential for suicide modeling and contagion among Micronesian youth

Dynamic multilateral markets

We study dynamic multilateral markets, in which players' payoffs result from intra-coalitional bargaining. The latter is modeled as the ultimatum game with exogenous (time-invariant) recognition probabilities and unanimity acceptance rule. Players in agreeing coalitions leave the market and are replaced by their replicas, which keeps the pool of market participants constant over time. In this infinite game, we establish payoff uniqueness of stationary equilibria and the emergence of endogenous cooperation structures when traders experience some degree of (heterogeneous) bargaining frictions. When we focus on market games with different player types, we derive, under mild conditions, an explicit formula for each type's equilibrium payoff as the market frictions vanish