Three dimensional structure from intensity correlations

We develop the analysis of x-ray intensity correlations from dilute ensembles of identical particles in a number of ways. First, we show that the 3D particle structure can be determined if the particles can be aligned with respect to a single axis having a known angle with respect to the incident beam. Second, we clarify the phase problem in this setting and introduce a data reduction scheme that assesses the integrity of the data even before the particle reconstruction is attempted. Finally, we describe an algorithm that reconstructs intensity and particle density simultaneously, thereby making maximal use of the available constraints.Comment: 17 pages, 9 figure

Ordering monomial factors of polynomials in the product representation

The numerical construction of polynomials in the product representation (as used for instance in variants of the multiboson technique) can become problematic if rounding errors induce an imprecise or even unstable evaluation of the polynomial. We give criteria to quantify the effects of these rounding errors on the computation of polynomials approximating the function $1/s$. We consider polynomials both in a real variable $s$ and in a Hermitian matrix. By investigating several ordering schemes for the monomials of these polynomials, we finally demonstrate that there exist orderings of the monomials that keep rounding errors at a tolerable level.Comment: Latex2e file, 7 figures, 32 page

Global convergence of a non-convex Douglas-Rachford iteration

We establish a region of convergence for the proto-typical non-convex Douglas-Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration [2] was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given

Magnetic Properties of Undoped C60C_{60}

The Heisenberg antiferromagnet, which arises from the large $U$ Hubbard model, is investigated on the $C_{60}$ molecule and other fullerenes. The connectivity of $C_{60}$ leads to an exotic classical ground state with nontrivial topology. We argue that there is no phase transition in the Hubbard model as a function of $U/t$, and thus the large $U$ solution is relevant for the physical case of intermediate coupling. The system undergoes a first order metamagnetic phase transition. We also consider the S=1/2 case using perturbation theory. Experimental tests are suggested.Comment: 12 pages, 3 figures (included

Quantum spin models with exact dimer ground states

Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground state configuration of all the members of the family on a periodic chain. The ground state is two-fold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh hamiltonian with two-fold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.Comment: 10 pages, 8 figures, revtex, to appear in Phys. Rev.

Cost–benefit analysis of controlling rabies: placing economics at the heart of rabies control to focus political will

Rabies is an economically important zoonosis. This paper describes the extent of the economic impacts of the disease and some of the types of economic analyses used to understand those impacts, as well as the trade-offs between efforts to manage rabies and efforts to eliminate it. In many cases, the elimination of rabies proves more cost-effective over time than the continual administration of postexposure prophylaxis, animal testing and animal vaccination. Economic analyses are used to inform and drive policy decisions and focus political will, placing economics at the heart of rabies control

The sloppy model universality class and the Vandermonde matrix

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy; the system behavior depends only on a few `stiff' combinations of the parameters and is unchanged as other `sloppy' parameter combinations vary by orders of magnitude. We contrast examples of sloppy models (from systems biology, variational quantum Monte Carlo, and common data fitting) with systems which are not sloppy (multidimensional linear regression, random matrix ensembles). We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form, with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.Comment: New content adde

Testing the Growth Rate Hypothesis in Vascular Plants with Above- and Below-Ground Biomass

The growth rate hypothesis (GRH) proposes that higher growth rate (the rate of change in biomass per unit biomass, μ) is associated with higher P concentration and lower C∶P and N∶P ratios. However, the applicability of the GRH to vascular plants is not well-studied and few studies have been done on belowground biomass. Here we showed that, for aboveground, belowground and total biomass of three study species, μ was positively correlated with N∶C under N limitation and positively correlated with P∶C under P limitation. However, the N∶P ratio was a unimodal function of μ, increasing for small values of μ, reaching a maximum, and then decreasing. The range of variations in μ was positively correlated with variation in C∶N∶P stoichiometry. Furthermore, μ and C∶N∶P ranges for aboveground biomass were negatively correlated with those for belowground. Our results confirm the well-known association of growth rate with tissue concentration of the limiting nutrient and provide empirical support for recent theoretical formulations

Low-energy sector of the S=1/2 Kagome antiferromagnet

Starting from a modified version of the the S=1/2 Kagome antiferromagnet to emphasize the role of elementary triangles, an effective Hamiltonian involving spin and chirality variables is derived. A mean-field decoupling that retains the quantum nature of these variables is shown to yield a Hamiltonian that can be solved exactly, leading to the following predictions: i) The number of low lying singlet states increase with the number of sites N like 1.15 to the power N; ii) A singlet-triplet gap remains in the thermodynamic limit; iii) Spinons form boundstates with a small binding energy. By comparing these properties with those of the regular Kagome lattice as revealed by numerical experiments, we argue that this description captures the essential low energy physics of that model.Comment: 4 pages including 3 figure