Universal and nonuniversal contributions to block-block entanglement in many-fermion systems

We calculate the entanglement entropy of blocks of size x embedded in a larger system of size L, by means of a combination of analytical and numerical techniques. The complete entanglement entropy in this case is a sum of three terms. One is a universal x- and L-dependent term, first predicted by Calabrese and Cardy, the second is a nonuniversal term arising from the thermodynamic limit, and the third is a finite size correction. We give an explicit expression for the second, nonuniversal, term for the one-dimensional Hubbard model, and numerically assess the importance of all three contributions by comparing to the entropy obtained from fully numerical diagonalization of the many-body Hamiltonian. We find that finite-size corrections are very small. The universal Calabrese-Cardy term is equally small for small blocks, but becomes larger for x > 1. In all investigated situations, however, the by far dominating contribution is the nonuniversal term stemming from the thermodynamic limit.

Intermediate motions as studied by solid-state separated local field NMR experiments

In this report, the application of a class of separated local field NMR experiments named dipolar chemical shift correlation (DIPSHIFT) for probing motions in the intermediate regime is discussed. Simple analytical procedures based on the Anderson-Weiss (AW) approximation are presented. In order to establish limits of validity of the AW based formulas, a comparison with spin dynamics simulations based on the solution of the stochastic Liouville-von-Neumann equation is presented. It is shown that at short evolution times (less than 30% of the rotor period), the AW based formulas are suitable for fitting the DIPSHIFT curves and extracting kinetic parameters even in the case of jumplike motions. However, full spin dynamics simulations provide a more reliable treatment and extend the frequency range of the molecular motions accessible by DIPSHIFT experiments. As an experimental test, molecular jumps of imidazol methyl sulfonate and trimethylsulfoxonium iodide, as well as the side-chain motions in the photoluminescent polymer poly[2-methoxy-5-(2(')-ethylhexyloxy)-1,4-phenylenevinylene], were characterized. Possible extensions are also discussed. (c) 2008 American Institute of Physics.

Effect of spatial inhomogeneity on the mapping between strongly interacting fermions and weakly interacting spins

A combined analytical and numerical study is performed of the mapping between strongly interacting fermions and weakly interacting spins, in the framework of the Hubbard, t-J, and Heisenberg models. While for spatially homogeneous models in the thermodynamic limit the mapping is thoroughly understood, we here focus on aspects that become relevant in spatially inhomogeneous situations, such as the effect of boundaries, impurities, superlattices, and interfaces. We consider parameter regimes that are relevant for traditional applications of these models, such as electrons in cuprates and manganites, and for more recent applications to atoms in optical lattices. The rate of the mapping as a function of the interaction strength is determined from the Bethe-Ansatz for infinite systems and from numerical diagonalization for finite systems. We show analytically that if translational symmetry is broken through the presence of impurities, the mapping persists and is, in a certain sense, as local as possible, provided the spin-spin interaction between two sites of the Heisenberg model is calculated from the harmonic mean of the onsite Coulomb interaction on adjacent sites of the Hubbard model. Numerical calculations corroborate these findings also in interfaces and superlattices, where analytical calculations are more complicated.

Analytical results on Muller's ratchet effect in growing populations

Fontanari introduced [Phys. Rev. Lett. 91, 218101 (2003)] a model for studying Muller's ratchet phenomenon in growing asexual populations. They studied two situations, either including a death probability for each newborn or not, but were able to find analytical (recursive) expressions only in the no-decay case. In this Brief Report a branching process formalism is used to find recurrence equations that generalize the analytical results of the original paper besides confirming the interesting effects their simulations revealed.

Constraints on the infrared behavior of the ghost propagator in Yang-Mills theories

We present rigorous upper and lower bounds for the momentum-space ghost propagator G(p) of Yang-Mills theories in terms of the smallest nonzero eigenvalue (and of the corresponding eigenvector) of the Faddeev-Popov matrix. We apply our analysis to data from simulations of SU(2) lattice gauge theory in Landau gauge, using the largest lattice sizes to date. Our results suggest that, in three and in four space-time dimensions, the Landau gauge ghost propagator is not enhanced as compared to its tree-level behavior. This is also seen in plots and fits of the ghost dressing function. In the two-dimensional case, on the other hand, we find that G(p) diverges as p(-2-2 kappa) with kappa approximate to 0.15, in agreement with A. Maas, Phys. Rev. D 75, 116004 (2007). We note that our discussion is general, although we make an application only to pure gauge theory in Landau gauge. Our simulations have been performed on the IBM supercomputer at the University of Sao Paulo.

Determination of the molecular weight of proteins in solution from a single small-angle X-ray scattering measurement on a relative scale

This paper describes a new and simple method to determine the molecular weight of proteins in dilute solution, with an error smaller than similar to 10%, by using the experimental data of a single small-angle X-ray scattering (SAXS) curve measured on a relative scale. This procedure does not require the measurement of SAXS intensity on an absolute scale and does not involve a comparison with another SAXS curve determined from a known standard protein. The proposed procedure can be applied to monodisperse systems of proteins in dilute solution, either in monomeric or multimeric state, and it has been successfully tested on SAXS data experimentally determined for proteins with known molecular weights. It is shown here that the molecular weights determined by this procedure deviate from the known values by less than 10% in each case and the average error for the test set of 21 proteins was 5.3%. Importantly, this method allows for an unambiguous determination of the multimeric state of proteins with known molecular weights.

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

Context tree selection: A unifying view

Context tree models have been introduced by Rissanen in [25] as a parsimonious generalization of Markov models. Since then, they have been widely used in applied probability and statistics. The present paper investigates non-asymptotic properties of two popular procedures of context tree estimation: Rissanen's algorithm Context and penalized maximum likelihood. First showing how they are related, we prove finite horizon bounds for the probability of over- and under-estimation. Concerning overestimation, no boundedness or loss-of-memory conditions are required: the proof relies on new deviation inequalities for empirical probabilities of independent interest. The under-estimation properties rely on classical hypotheses for processes of infinite memory. These results improve on and generalize the bounds obtained in Duarte et al. (2006) [12], Galves et al. (2008) [18], Galves and Leonardi (2008) [17], Leonardi (2010) [22], refining asymptotic results of Buhlmann and Wyner (1999) [4] and Csiszar and Talata (2006) [9]. (C) 2011 Elsevier B.V. All rights reserved.

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

Quantification of some nonsteroidal anti-inflammatory drugs as reducing agents of Cu(II)/4,4 '-dicarboxy-2,2 '-biquinoline complexes in cationic micellar medium

A simple method was developed for spectrophotometric determination of some nonsteroidal anti-inflammatory drugs (meloxicam, piroxicam and tenoxicam) based on the reduction of copper(II) in buffered solution (pH 7.0) and micellar medium containing 4,4'-dicarboxy-2,2'-buffered solution (pH 7.0) and micellar medium containing 4,4'-dicarboxy-2,2'-biquinoline acid. The-biquinoline acid. The absorbance values at 558 nm, characteristic of the formed Cu(I)/4,4'-dicarboxy-2,2'-biquinoline complexes, are linear with the concentrations (5.7-40 mmol L(-1), n = 5) of these oxicams (meloxicam r = 0.998; piroxicam and tenoxicam r = 0.999). The limit of detection values, in mmol L(-1), calculated for meloxicam (2.7), piroxicam (1.2) and tenoxicam (1.3) was obtained with 99% confidence level and the relative standard deviations for meloxicam (3.1%), piroxicam (5.1%) and tenoxicam (1.2%) were calculated using a 25 mmol L(-1) solution (n = 7). Mean recovery values for meloxicam, piroxicam and tenoxicam forms were 100 +/- 6.9, 98.6 +/- 3.6 and 99.4 +/- 2.5%, respectively. The conditional potential of Cu(II)/Cu(I) in complex medium of 7.5 mmol L(-1) BCA was determined to be 629 +/- 11 mV vs. NHE.

Simultaneous determination of Cr, Fe, Ni and V in crude oil by emulsion sampling graphite furnace atomic absorption spectrometry

In this work a simple and reliable method for the simultaneous determination of Cr, Fe, Ni and V in crude oil, using emulsion sampling graphite furnace atomic absorption spectrometry is proposed. Under the best conditions, sample masses around 50 mg were weighed in polypropylene tubes and emulsified in a mixture of 0.5% (v v(-1)) hexane + 6% (m v(-1)) Triton X-100 (R). Considering the compromised conditions, the pyrolysis an atomization temperatures for the simultaneous determination of Cr, Fe, Ni and V were 1400 degrees C and 2500 degrees C, respectively. Aliquots of 20 mu L of reference solution and sample emulsion were co-injected into the graphite tube with 10 mu L of 1.0 g L(-1) Mg(NO(3))(2) as chemical modifier. The detection limits (n = 10, 3 sigma) and characteristic masses were, respectively: 0.07 mu g g(-1) and 19 pg for Cr; 2.15 mu g g(-1) and 31 pg for Fe; 1.25 mu g g(-1) and 44 pg for Ni; and 1.15 mu g g(-1) and 149 pg for V. The reliability of the proposed method was checked by fuel oil Standard Reference Material (SRMTriton X-100 (R) 1634c - NIST) analysis. The concentrations found presented no statistical differences compared to the certified values at 95% confidence level.

Characterization of dynamic solid phase DNA extraction from blood with magnetically controlled silica beads

A novel solid phase extraction technique is described where DNA is bound and eluted from magnetic silica beads in a manner where efficiency is dependent on the magnetic manipulation of the beads and not on the flow of solution through a packed bed. The utility of this technique in the isolation of reasonably pure, PCR-amplifiable DNA from complex samples is shown by isolating DNA from whole human blood, and subsequently amplifying a fragment of the beta-globin gene. By effectively controlling the movement of the solid phase in the presence of a static sample, the issues associated with reproducibly packing a solid phase in a microchannel and maintaining consistent flow rates are eliminated. The technique described here is rapid, simple, and efficient, allowing for recovery of more than 60% of DNA from 0.6 mu L of blood at a concentration which is suitable for PCR amplification. In addition, the technique presented here requires inexpensive, common laboratory equipment, making it easily adopted for both clinical point-of-care applications and on-site forensic sample analysis.

Programmable diagnostic devices made from paper and tape

This paper describes three-dimensional microfluidic paper-based analytical devices (3-D mu PADs) that can be programmed (postfabrication) by the user to generate multiple patterns of flow through them. These devices are programmed by pressing single-use 'on' buttons, using a stylus or a ballpoint pen. Pressing a button closes a small space (gap) between two vertically aligned microfluidic channels, and allows fluids to wick from one channel to the other. These devices are simple to fabricate, and are made entirely out of paper and double-sided adhesive tape. Programmable devices expand the capabilities of mu PADs and provide a simple method for controlling the movement of fluids in paper-based channels. They are the conceptual equivalent of field-programmable gate arrays (FPGAs) widely used in electronics.

Functional specialization of Eucalyptus fine roots: contrasting potential uptake rates for nitrogen, potassium and calcium tracers at varying soil depths

1. Little is known about the role of deep roots in the nutrition of forest trees and their ability to provide a safety-net service taking up nutrients leached from the topsoil. 2. To address this issue, we studied the potential uptake of N, K and Ca by Eucalyptus grandis trees (6 years of age - 25 m mean height), in Brazil, as a function of soil depth, texture and water content. We injected NO(3)(-)- (15)N, Rb(+) (analogue of K(+)) and Sr(2+) (analogue of Ca(2+)) tracers simultaneously in a solution through plastic tubes at 10, 50, 150 and 300 cm in depth in a sandy and a clayey Ferralsol soil. A complete randomized design was set up with three replicates of paired trees per injection depth and soil type. Recently expanded leaves were sampled at various times after tracer injection in the summer, and the experiment was repeated in the winter. Soil water contents were continuously monitored at the different depths in the two soils. 3. Determination of foliar Rb and Sr concentrations and (15)N atom % made it possible to estimate the relative uptake potential (RUP) of tracer injections from the four soil depths and the specific RUP (SRUP), defined as RUP, per unit of fine root length density in the corresponding soil layer. 4. The highest tracer uptake rates were found in the topsoil, but contrasting RUP distributions were observed for the three tracers. Whilst the RUP was higher for NO(3)(-)- (15)N than for Rb(+) and Sr(2+) in the upper 50 cm of soil, the highest SRUP values for Sr(2+) and Rb(+) were found at a depth of 300 cm in the sandy soil, as well as in the clayey soil when gravitational solutions reached that depth. 5. Our results suggest that the fine roots of E. grandis trees exhibit contrasting potential uptake rates with depth depending on the nutrient. This functional specialization of roots might contribute to the high growth rates of E. grandis trees, efficiently providing the large amounts of nutrients required throughout the development of these fast-growing plantations.

Effects of Molybdenum, Nickel, and Nitrogen Sources on the Mineral Nutrition and Growth of Rice Plants

Upland rice plants, cultivar `IAC 202,` were grown in nutrient solution until full tillering. Treatments consisted of ammonium nitrate (AN) or urea (UR) as nitrogen (N) source plus molybdenum (Mo) and/or nickel (Ni): AN + Mo + Ni, AN + Mo - Ni, AN - Mo + Ni, UR + Mo + Ni, UR + Mo - Ni, and UR - Mo + Ni. The experiment was carried out to better understand the effect of these treatments on dry-matter yield, chlorophyll, net photosynthesis rate, nitrate (NO3 --N), total N, in vitro activities of urease and nitrate reductase (NR), and Mo and Ni concentrations. In UR-grown plants, Mo and Ni addition increased yield of dry matter. Regardless of the N source, chlorophyll concentration and net photosynthesis rate were reduced when Mo or Ni were omitted, although not always significantly. The omission of either Mo or Ni led to a decrease in urease activity, independent of N source. Nitrate reductase activity increased in nutrient solutions without Mo, although NO3 --N increased. There was not a consistent variation in total N concentration. Molybdenum and Ni concentration in roots and shoots were influenced by their supply in the nutrient solution. Molybdenum concentration was not influenced by N sources, whereas Ni content in both root and shoots was greater in ammonium nitrate-grown plants. In conclusion, it can be hypothesized that there is a relationship between Mo and Ni acting on photosynthesis, although is an indirect one. This is the first evidence for a beneficial effect of Mo and Ni interaction on plant growth.