Geometric variational problems of statistical mechanics and of combinatorics

We present the geometric solutions of the various extremal problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape of a typical Young diagram and of a typical skyscraper.Comment: 10 page

Sponges of Navassa

This photographic guide was compiled from data collected during the 2004 NOAA survey of the coral reefs of Navassa and does not represent a comprehensive list of all Porifera in Navassa. Specifically missing are taxa that inhabit caves, overhangs, vertical walls; species that live in the interstices of the reef framework; and species found at depths greater than 50 meters. Specimens were identified by Janie Wulff and Timothy Swain of Florida State University using a combination of digital photography, field observations, and microscopic examination of siliceous spicules. Genera are organized into higher taxa according to Systema Porifera, Hooper & van Soest (ed.) 2002. We have purposefully erred on the side of splitting similar taxa for which a species designation could not be definitively assigned, in order to demonstrate the range of forms observed in this survey. Some species are shown with symbiotic zoanthids on the surface of the sponge, but zoanthids are not always present and should not be relied on for identification of the sponge taxa

Adaptive information search and decision making over single and repeated plays

For over 50 years expected value and expected utility theory has been challenged by behavioral findings in repeated and single plays of risky gambles. The inherent long-term nature of these models has been found to be at odds with preferences indicating short-term maximization in single play situations. With the present study we provide further evidence on the distinction between long-term and short-term oriented behavior. Evaluating experiencedbased decisions over repeated and single play situations we demonstrate that both choice preferences and search behavior change in response to long and short-term framing. This suggests different cognitive approaches for single and repeated play situations, with single decisions often favoring risk-aversion and therefore the underweighting of rare events. These findings are in line with alternative models of risky choice as for example proposed by Lopes (1996) and also the literature on statedependent foraging

A novel method for evaluating the critical nucleus and the surface tension in systems with first order phase transition

We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable surrounding. The frozen configuration creates a pinning field on the surface of the free sphere. The pinning field forces the sphere to stay in the metastable phase as long as its size is smaller than the critical nucleus. We test our method in two first-order systems, both on a two-dimensional lattice: a system where the parameter tuning the transition is the magnetic field, and a second system where the tuning parameter is the temperature. In both cases the results are satisfying. Unlike previous techniques, our method does not require an infinite volume limit to compute the surface tension, and it therefore gives reliable estimates even by using relatively small systems. However, our method cannot be used at, or close to, the critical point, i.e. at coexistence, where the critical nucleus becomes infinitely large.Comment: 12 pages, 15 figure

Cognitive network science: A review of research on cognition through the lens of network representations, processes, and dynamics

10.1155/2019/2108423Complexity2019210842