Integrating Species Traits into Species Pools

Despite decades of research on the species‐pool concept and the recent explosion of interest in trait‐based frameworks in ecology and biogeography, surprisingly little is known about how spatial and temporal changes in species‐pool functional diversity (SPFD) influence biodiversity and the processes underlying community assembly. Current trait‐based frameworks focus primarily on community assembly from a static regional species pool, without considering how spatial or temporal variation in SPFD alters the relative importance of deterministic and stochastic assembly processes. Likewise, species‐pool concepts primarily focus on how the number of species in the species pool influences local biodiversity. However, species pools with similar richness can vary substantially in functional‐trait diversity, which can strongly influence community assembly and biodiversity responses to environmental change. Here, we integrate recent advances in community ecology, trait‐based ecology, and biogeography to provide a more comprehensive framework that explicitly considers how variation in SPFD, among regions and within regions through time, influences the relative importance of community assembly processes and patterns of biodiversity. First, we provide a brief overview of the primary ecological and evolutionary processes that create differences in SPFD among regions and within regions through time. We then illustrate how SPFD may influence fundamental processes of local community assembly (dispersal, ecological drift, niche selection). Higher SPFD may increase the relative importance of deterministic community assembly when greater functional diversity in the species pool increases niche selection across environmental gradients. In contrast, lower SPFD may increase the relative importance of stochastic community assembly when high functional redundancy in the species pool increases the influence of dispersal history or ecological drift. Next, we outline experimental and observational approaches for testing the influence of SPFD on assembly processes and biodiversity. Finally, we highlight applications of this framework for restoration and conservation. This species‐pool functional diversity framework has the potential to advance our understanding of how local‐ and regional‐scale processes jointly influence patterns of biodiversity across biogeographic regions, changes in biodiversity within regions over time, and restoration outcomes and conservation efforts in ecosystems altered by environmental change

An optimal IV technique for identifying continuous-time transfer function model of multiple input systems

An instrumental variable method for continuous-time model identification is proposed for multiple input single output systems where the characteristic polynomials of the transfer functions associated with each input are not constrained to be identical. An associated model order determination procedure is shown to be reasonably successful. Monte Carlo simulation analyses are used to demonstrate the properties and general robustness of the model order selection and parameter estimation schemes. The results obtained to model a winding process and an industrial binary distillation column illustrate the practical applicability of the proposed identification scheme

Spontaneous exciton condensation in 1T-TiSe2: a BCS-like approach

Recently strong evidence has been found in favor of a BCS-like condensation of excitons in 1\textit{T}-TiSe$_2$. Theoretical photoemission intensity maps have been generated by the spectral function calculated within the excitonic condensate phase model and set against experimental angle-resolved photoemission spectroscopy data. Here, the calculations in the framework of this model are presented in detail. They represent an extension of the original excitonic insulator phase model of J\'erome \textit{et al.} [Phys. Rev. {\bf 158}, 462 (1967)] to three dimensional and anisotropic band dispersions. A detailed analysis of its properties and further comparison with experiment are also discussedComment: Submitted to PRB, 11 pages, 7 figure

Temperature dependent photoemission on 1T-TiSe2: Interpretation within the exciton condensate phase model

The charge density wave phase transition of 1T-TiSe2 is studied by angle-resolved photoemission over a wide temperature range. An important chemical potential shift which strongly evolves with temperature is evidenced. In the framework of the exciton condensate phase, the detailed temperature dependence of the associated order parameter is extracted. Having a mean-field-like behaviour at low temperature, it exhibits a non-zero value above the transition, interpreted as the signature of strong excitonic fluctuations, reminiscent of the pseudo-gap phase of high temperature superconductors. Integrated intensity around the Fermi level is found to display a trend similar to the measured resistivity and is discussed within the model.Comment: 8 pages, 6 figure

On the Linearization of the First and Second Painleve' Equations

We found Fuchs--Garnier pairs in 3X3 matrices for the first and second Painleve' equations which are linear in the spectral parameter. As an application of our pairs for the second Painleve' equation we use the generalized Laplace transform to derive an invertible integral transformation relating two its Fuchs--Garnier pairs in 2X2 matrices with different singularity structures, namely, the pair due to Jimbo and Miwa and the one found by Harnad, Tracy, and Widom. Together with the certain other transformations it allows us to relate all known 2X2 matrix Fuchs--Garnier pairs for the second Painleve' equation with the original Garnier pair.Comment: 17 pages, 2 figure

Dilute ferrimagnetic semiconductors in Fe-substituted spinel ZnGa2_2O4_4

Solid solutions of nominal composition [ZnGa$_2$O$_4$]$_{1-x}$[Fe$_3$O$_4$]$_x$, of the semiconducting spinel ZnGa$_2$O$_4$ with the ferrimagnetic spinel Fe$_3$O$_4$ have been prepared with $x$ = 0.05, 0.10, and 0.15. All samples show evidence for long-range magnetic ordering with ferromagnetic hysteresis at low temperatures. Magnetization as a function of field for the $x$ = 0.15 sample is S-shaped at temperatures as high as 200 K. M\"ossbauer spectroscopy on the $x$ = 0.15 sample confirms the presence of Fe$^{3+}$, and spontaneous magnetization at 4.2 K. The magnetic behavior is obtained without greatly affecting the semiconducting properties of the host; diffuse reflectance optical spectroscopy indicates that Fe substitution up to $x$ = 0.15 does not affect the position of the band edge absorption. These promising results motivate the possibility of dilute ferrimagnetic semiconductors which do not require carrier mediation of the magnetic moment.Comment: 9 pages and 6 figure

Collapse of a Bose-Einstein condensate induced by fluctuations of the laser intensity

The dynamics of a metastable attractive Bose-Einstein condensate trapped by a system of laser beams is analyzed in the presence of small fluctuations of the laser intensity. It is shown that the condensate will eventually collapse. The expected collapse time is inversely proportional to the integrated covariance of the time autocorrelation function of the laser intensity and it decays logarithmically with the number of atoms. Numerical simulations of the stochastic 3D Gross-Pitaevskii equation confirms analytical predictions for small and moderate values of mean field interaction.Comment: 13 pages, 7 eps figure

Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature

An infinite family of classical superintegrable Hamiltonians defined on the N-dimensional spherical, Euclidean and hyperbolic spaces are shown to have a common set of (2N-3) functionally independent constants of the motion. Among them, two different subsets of N integrals in involution (including the Hamiltonian) can always be explicitly identified. As particular cases, we recover in a straightforward way most of the superintegrability properties of the Smorodinsky-Winternitz and generalized Kepler-Coulomb systems on spaces of constant curvature and we introduce as well new classes of (quasi-maximally) superintegrable potentials on these spaces. Results here presented are a consequence of the sl(2) Poisson coalgebra symmetry of all the Hamiltonians, together with an appropriate use of the phase spaces associated to Poincare and Beltrami coordinates.Comment: 12 page

Universal singularity at the closure of a gap in a random matrix theory

We consider a Hamiltonian $H = H_0+ V$, in which $H_0$ is a given non-random Hermitian matrix,and $V$ is an $N \times N$ Hermitian random matrix with a Gaussian probability distribution.We had shown before that Dyson's universality of the short-range correlations between energy levels holds at generic points of the spectrum independently of $H_{0}$. We consider here the case in which the spectrum of $H_{0}$ is such that there is a gap in the average density of eigenvalues of $H$ which is thus split into two pieces. When the spectrum of $H_{0}$ is tuned so that the gap closes, a new class of universality appears for the energy correlations in the vicinity of this singular point.Comment: 20pages, Revtex, to be published in Phys. Rev.

Rational Solutions of the Painleve' VI Equation

In this paper, we classify all values of the parameters $\alpha$, $\beta$, $\gamma$ and $\delta$ of the Painlev\'e VI equation such that there are rational solutions. We give a formula for them up to the birational canonical transformations and the symmetries of the Painlev\'e VI equation.Comment: 13 pages, 1 Postscript figure Typos fixe