Optimal generalized quantum measurements for arbitrary spin systems

Positive-operator-valued measurements on a finite number of N identically prepared systems of arbitrary spin J are discussed. Pure states are characterized in terms of Bloch-like vectors restricted by a SU(2J+1) covariant constraint. This representation allows for a simple description of the equations to be fulfilled by optimal measurements. We explicitly find the minimal positive-operator-valued measurement for the N=2 case, a rigorous bound for N=3, and set up the analysis for arbitrary N.

Hysteresis in a system driven by either generalized force or displacement variables: martensitic phase transition in single-crystalline Cu-Zn-Al

We report on experiments aimed at comparing the hysteretic response of a Cu-Zn-Al single crystal undergoing a martensitic transition under strain-driven and stress-driven conditions. Strain-driven experiments were performed using a conventional tensile machine while a special device was designed to perform stress-driven experiments. Significant differences in the hysteresis loops were found. The strain-driven curves show reentrant behavior yield point which is not observed in the stress-driven case. The dissipated energy in the stress-driven curves is larger than in the strain-driven ones. Results from recently proposed models qualitatively agree with experiments.

Newton-Hooke algebras, nonrelativistic branes, and generalized pp-wave metrics

The Newton-Hooke algebras in d dimensions are constructed as contractions of dS(AdS) algebras. Nonrelativistic brane actions are WZ terms of these Newton-Hooke algebras. The NH algebras appear also as subalgebras of multitemporal relativistic conformal algebras, SO(d+1,p+2). We construct generalizations of pp-wave metrics from these algebras.

Minimal optimal generalized quantum measurements

Optimal and finite positive operator valued measurements on a finite number N of identically prepared systems have recently been presented. With physical realization in mind, we propose here optimal and minimal generalized quantum measurements for two-level systems. We explicitly construct them up to N = 7 and verify that they are minimal up to N = 5.

Generalized Schmidt decomposition and classification of three-quantum-bit states

We prove for any pure three-quantum-bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.

Geometric morphometric analyses provide evidence for the adaptive character of the Tanganyikan cichlid fish radiations.

The cichlids of East Africa are renowned as one of the most spectacular examples of adaptive radiation. They provide a unique opportunity to investigate the relationships between ecology, morphological diversity, and phylogeny in producing such remarkable diversity. Nevertheless, the parameters of the adaptive radiations of these fish have not been satisfactorily quantified yet. Lake Tanganyika possesses all of the major lineages of East African cichlid fish, so by using geometric morphometrics and comparative analyses of ecology and morphology, in an explicitly phylogenetic context, we quantify the role of ecology in driving adaptive speciation. We used geometric morphometric methods to describe the body shape of over 1000 specimens of East African cichlid fish, with a focus on the Lake Tanganyika species assemblage, which is composed of more than 200 endemic species. The main differences in shape concern the length of the whole body and the relative sizes of the head and caudal peduncle. We investigated the influence of phylogeny on similarity of shape using both distance-based and variance partitioning methods, finding that phylogenetic inertia exerts little influence on overall body shape. Therefore, we quantified the relative effect of major ecological traits on shape using phylogenetic generalized least squares and disparity analyses. These analyses conclude that body shape is most strongly predicted by feeding preferences (i.e., trophic niches) and the water depths at which species occur. Furthermore, the morphological disparity within tribes indicates that even though the morphological diversification associated with explosive speciation has happened in only a few tribes of the Tanganyikan assemblage, the potential to evolve diverse morphologies exists in all tribes. Quantitative data support the existence of extensive parallelism in several independent adaptive radiations in Lake Tanganyika. Notably, Tanganyikan mouthbrooders belonging to the C-lineage and the substrate spawning Lamprologini have evolved a multitude of different shapes from elongated and Lamprologus-like hypothetical ancestors. Together, these data demonstrate strong support for the adaptive character of East African cichlid radiations.

Effects of common origin and common rearing environment on variance in ectoparasite load and phenotype of nestling Alpine swifts

Knowledge of the quantitative genetics of resistance to parasitism is key to appraise host evolutionary responses to parasite selection. Here, we studied effects of common origin (i.e. genetic and pre-hatching parental effects) and common rearing environment (i.e. post-hatching parental effects and other environment effects) on variance in ectoparasite load in nestling Alpine swifts (Apus melba). This colonial bird is intensely parasitized by blood sucking louse-flies that impair nestling development and survival. By cross-fostering half of the hatchlings between pairs of nests, we show strong significant effect of common rearing environment on variance (90.7% in 2002 and 90.9% in 2003) in the number of louse-flies per nestling and no significant effect of common origin on variance in the number of louse-flies per nestling. In contrast, significant effects of common origin were found for all the nestling morphological traits (i.e. body mass, wing length, tail length, fork length and sternum length) under investigation. Hence, our study suggests that genetic and pre-hatching parental effects play little role in the distribution of parasites among nestling Alpine swifts, and thus that nestlings have only limited scope for evolutionary responses against parasites. Our results highlight the need to take into consideration environmental factors, including the evolution of post-hatching parental effects such as nest sanitation, in our understanding of host-parasite relationships.

Yield gains of coffee plants from phosphorus fertilization may not be generalized for high density planting

Inconclusive responses of the adult coffee plant to phosphorus fertilization have been reported in the literature, especially when dealing with application of this nutrient in high density planting systems. Thus, this study was carried out for the purpose of assessing the response of adult coffee plants at high planting density in full production (in regard to yield and their biennial cycle/stability) to the addition of different sources and application rates of P in the Zona da Mata region of Minas Gerais, Brazil. The experiment with coffee plants of the Catucaí Amarelo 6/30 variety was carried out over four growing seasons. Treatments were arranged in a full factorial design [(4 × 3) + 1] consisting of four P sources (monoammonium phosphate, simple superphosphate, natural reactive rock phosphate from Algeria (Djebel-Onk), and FH 550®), three P rates (100, 200, and 400 kg ha-1 year-1 of P2O5), and an additional treatment without application of the nutrient (0 kg ha-¹ year-¹). A randomized block experimental design was used with three replicates. The four seasons were evaluated as subplots in a split plot experiment. The P contents in soil and leaves increased with increased rates of P application. However, there was no effect from P application on the yield and its biennial cycle/stability regardless of the source used over the four seasons assessed.

Generalized Weyl solutions

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyls construction is generalized here to arbitrary dimension D>~4. The general solution of the D-dimensional vacuum Einstein equations that admits D-2 orthogonal commuting non-null Killing vector fields is given either in terms of D-3 independent axisymmetric solutions of Laplaces equation in three-dimensional flat space or by D-4 independent solutions of Laplaces equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat black ring with an event horizon of topology S1S2 held in equilibrium by a conical singularity in the form of a disk.

Generalized Onsager symmetry

Onsager's symmetry theorem for transport near equilibrium is extended in two directions. A corresponding symmetry is obtained for linear transport near nonequilibrium stationary states, and the class of transport laws is extended to include nonlocality in both space and time. The results are formally exact and independent of any specific model for the nonequilibrium state.

Generalized percolation in random directed networks

We develop a general theory for percolation in directed random networks with arbitrary two-point correlations and bidirectional edgesthat is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.