Finitely forcible graphons with an almost arbitrary structure

Graphons are analytic objects representing convergent sequences of large graphs. A graphon is said to be finitely forcible if it is determined by finitely many subgraph densities, i.e., if the asymptotic structure of graphs represented by such a graphon depends only on finitely many density constraints. Such graphons appear in various scenarios, particularly in extremal combinatorics. Lovasz and Szegedy conjectured that all finitely forcible graphons possess a simple structure. This was disproved in a strong sense by Cooper, Kral and Martins, who showed that any graphon is a subgraphon of a finitely forcible graphon. We strenghten this result by showing for every ε>0 that any graphon spans a 1−ε proportion of a finitely forcible graphon

A Multivariate Ecological Approach to Delineate Unionid Freshwater Mussel Species

Freshwater mussels represent one of the most imperiled faunal groups on the planet and are critical to freshwater ecosystems. If mussel species are not carefully defined, our conservation plans may miss differences in the habitat needs of different species and the conservation strategies may not be as successful. Because ecological niche models can be used to provide evidence to support similar or dissimilar ecological niches and habitat requirements, I used modelling to forecast suitable habitat for Fusconaia askewi and F. lananensis, two purported threatened Texas species. The modeling results indicated that these species are not ecologically different. Based upon this finding and other information, I treated F. askewi and F. lananensis as synonymous, with F. lananensis as the junior synonym. I combined the occurrence records for F. askewi and F. lananensis to make one ecological niche model for F. askewi. I then ground-validated the model by sampling 25 sites throughout East Texas. My model successfully located F. askewi in five previously unsampled areas, and forecasted suitable habitat in East Texas. On average, the sites where F. askewi was present were significantly higher in habitat suitability than the sites where F. askewi was absent. My study is noteworthy for using a high-resolution, multivariate approach to ecological niche modeling of riverine habitats, which was used to test whether two putative species are ecologically differentiated and to make an improved ecological niche model that combines equivalent entities into a single model. My approach can be used in other studies of closely related groups

Statistical Thermodynamics

Contains a report on a research project.United States Air Force, Office of Scientific Research, Air Research and Development Command (Contract AF49(638)-95

Statistical Thermodynamics

Contains reports on two research projectsU. S. Air Force (Office of Scientific Research, Air Research and Development Command) under Contract AF49(638)-9

Bird's-eye view on Noise-Based Logic

Noise-based logic is a practically deterministic logic scheme inspired by the randomness of neural spikes and uses a system of uncorrelated stochastic processes and their superposition to represent the logic state. We briefly discuss various questions such as (i) What does practical determinism mean? (ii) Is noise-based logic a Turing machine? (iii) Is there hope to beat (the dreams of) quantum computation by a classical physical noise-based processor, and what are the minimum hardware requirements for that? Finally, (iv) we address the problem of random number generators and show that the common belief that quantum number generators are superior to classical (thermal) noise-based generators is nothing but a myth.Comment: paper in pres