Homogeneity in the free group

We show that any non abelian free group \F is strongly $\aleph_0$-homogeneous, i.e. that finite tuples of elements which satisfy the same first-order properties are in the same orbit under \Aut(\F). We give a characterization of elements in finitely generated groups which have the same first-order properties as a primitive element of the free group. We deduce as a consequence that most hyperbolic surface groups are not $\aleph_0$-homogeneous.Comment: 26 page

Hyperbolic towers and independent generic sets in the theory of free groups

We use hyperbolic towers to answer some model theoretic questions around the generic type in the theory of free groups. We show that all the finitely generated models of this theory realize the generic type $p_0$, but that there is a finitely generated model which omits $p_0^{(2)}$. We exhibit a finitely generated model in which there are two maximal independent sets of realizations of the generic type which have different cardinalities. We also show that a free product of homogeneous groups is not necessarily homogeneous.Comment: to appear in Proceedings of the conference "Recent developments in Model Theory", Notre Dame Journal of Formal Logi

Hamiltonian reductions of the one-dimensional Vlasov equation using phase-space moments

We consider Hamiltonian closures of the Vlasov equation using the phase-space moments of the distribution function. We provide some conditions on the closures imposed by the Jacobi identity. We completely solve some families of examples. As a result, we show that imposing that the resulting reduced system preserves the Hamiltonian character of the parent model shapes its phase space by creating a set of Casimir invariants as a direct consequence of the Jacobi identity

Algorithms for network piecewise-linear programs

In this paper a subarea of Piecewise-Linear Programming named network Piecewise-Linear Programming (NPLP) is discussed. Initially the problem formulation, main efinitins and related Concepts are presented. In the sequence of the paper, four specialized algorithms for NPLP, as well as the results of a preliminary computational study, are presented

Higher order Hamiltonian fluid reduction of Vlasov equation

From the Hamiltonian structure of the Vlasov equation, we build a Hamiltonian model for the first three moments of the Vlasov distribution function, namely, the density, the momentum density and the specific internal energy. We derive the Poisson bracket of this model from the Poisson bracket of the Vlasov equation, and we discuss the associated Casimir invariants

The emergence of commercial genomics: analysis of the rise of a biotechnology subsector during the Human Genome Project, 1990 to 2004.

BackgroundDevelopment of the commercial genomics sector within the biotechnology industry relied heavily on the scientific commons, public funding, and technology transfer between academic and industrial research. This study tracks financial and intellectual property data on genomics firms from 1990 through 2004, thus following these firms as they emerged in the era of the Human Genome Project and through the 2000 to 2001 market bubble.MethodsA database was created based on an early survey of genomics firms, which was expanded using three web-based biotechnology services, scientific journals, and biotechnology trade and technical publications. Financial data for publicly traded firms was collected through the use of four databases specializing in firm financials. Patent searches were conducted using firm names in the US Patent and Trademark Office website search engine and the DNA Patent Database.ResultsA biotechnology subsector of genomics firms emerged in parallel to the publicly funded Human Genome Project. Trends among top firms show that hiring, capital improvement, and research and development expenditures continued to grow after a 2000 to 2001 bubble. The majority of firms are small businesses with great diversity in type of research and development, products, and services provided. Over half the public firms holding patents have the majority of their intellectual property portfolio in DNA-based patents.ConclusionsThese data allow estimates of investment, research and development expenditures, and jobs that paralleled the rise of genomics as a sector within biotechnology between 1990 and 2004

Hamiltonian closures for fluid models with four moments by dimensional analysis

Fluid reductions of the Vlasov-Amp{\`e}re equations that preserve the Hamiltonian structure of the parent kinetic model are investigated. Hamiltonian closures using the first four moments of the Vlasov distribution are obtained, and all closures provided by a dimensional analysis procedure for satisfying the Jacobi identity are identified. Two Hamiltonian models emerge, for which the explicit closures are given, along with their Poisson brackets and Casimir invariants