Geometric Phase and Modulo Relations for Probability Amplitudes as Functions on Complex Parameter Spaces

We investigate general differential relations connecting the respective behavior s of the phase and modulo of probability amplitudes of the form \amp{\psi_f}{\psi}, where $\ket{\psi_f}$ is a fixed state in Hilbert space and $\ket{\psi}$ is a section of a holomorphic line bundle over some complex parameter space. Amplitude functions on such bundles, while not strictly holomorphic, nevertheless satisfy generalized Cauchy-Riemann conditions involving the U(1) Berry-Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulo, therefore allowing for the reconstruction of the phase from the modulo (or vice-versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space ${\cal R} = {\mathbb C}P^n$, where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini-Study metric. In conjunction with the generalized Cauchy-Riemann conditions, this geodesic interpretation leads to additional relations, in particular a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established.Comment: 11 pages, 1 figure, revtex

Influence of MWCNT/surfactant dispersions on the mechanical properties of Portland cement pastes

This work studies the reinforcing effect of Multi Walled Carbon Nanotubes (MWCNT) on cement pastes. A 0.35% solid concentration of MWCNT in powder was dispersed in deionized water with sodium dodecyl sulfate (cationic surfactant), cetylpyridinium chloride (anionic surfactant) and triton X-100 (amphoteric surfactant) using an ultrasonic tip processor. Three concentrations of each surfactant (1mM, 10mM and 100mM) were tested, and all samples were sonicated until an adequate dispersion degree was obtained. Cement pastes with additions of carbon nanotubes of 0.15% by mass of cement were produced in two steps; first the dispersions of MWCNT were combined with the mixing water using an ultrasonic tip processor to guarantee homogeneity, and then cement was added and mixed until a homogeneous paste was obtained. Direct tensile strength, apparent density and open porosity of the pastes were measured after 7 days of curing. It was found that the MWCNT/surfactants dispersions decrease the mechanical properties of the cement based matrix due to an increased porosity caused by the presence of surfactants. © Published under licence by IOP Publishing Ltd

The uses and abuses of tree thinking in cultural evolution

Modern phylogenetic methods are increasingly being used to address questions about macro-level patterns in cultural evolution. These methods can illuminate the unobservable histories of cultural traits and identify the evolutionary drivers of trait-change over time, but their application is not without pitfalls. Here we outline the current scope of research in cultural tree thinking, highlighting a toolkit of best practices to navigate and avoid the pitfalls and ‘abuses’ associated with their application. We emphasise two principles that support the appropriate application of phylogenetic methodologies in cross-cultural research: researchers should (1) draw on multiple lines of evidence when deciding if and which types of phylogenetic methods and models are suitable for their cross-cultural data, and (2) carefully consider how different cultural traits might have different evolutionary histories across space and time. When used appropriately phylogenetic methods can provide powerful insights into the processes of evolutionary change that have shaped the broad patterns of human history.1. Introduction 2. Are the data appropriate for comparative phylogenetic analysis? 3. Tree construction: are phylogenetic trees accurate representations of cultural histories? 4. Mapping other cultural features to lexical trees: divergent evolutionary histories, mechanistic (un)identifiability, and model shortcomings 4.1 Do different cultural traits have different evolutionary histories? 4.2 When is the use of methods that require historical coherence justified? 4.3 What about methods that detect yet do not require tree-like structure in the data? 4.4 Are there correlations between the drivers of cross-cultural similarity that create a false impression of ‘fit’ to the language tree? 4.5 Are model shortcomings giving unwarranted precedence to tree-like inheritance patterns? 5. Conclusio

High-throughput analysis of adaptation using barcoded strains of Saccharomyces cerevisiae

Background: Experimental evolution of microbes can be used to empirically address a wide range of questions about evolution and is increasingly employed to study complex phenomena ranging from genetic evolution to evolutionary rescue. Regardless of experimental aims, fitness assays are a central component of this type of research, and low-throughput often limits the scope and complexity of experimental evolution studies. We created an experimental evolution system in Results: We first confirm that barcode insertions do not alter fitness and that barcode sequencing can be used to efficiently detect fitness differences via pooled competition-based fitness assays. Next, we examine the effects of ploidy, chemical stress, and population bottleneck size on the evolutionary dynamics and fitness gains (adaptation) in a total of 76 experimentally evolving, asexual populations by conducting 1,216 fitness assays and analyzing 532 longitudinal-evolutionary samples collected from the evolving populations. In our analysis of these data we describe the strengths of this experimental evolution system and explore sources of error in our measurements of fitness and evolutionary dynamics. Conclusions: Our experimental treatments generated distinct fitness effects and evolutionary dynamics, respectively quantified via multiplexed fitness assays and barcode lineage tracking. These findings demonstrate the utility of this new resource for designing and improving high-throughput studies of experimental evolution. The approach described here provides a framework for future studies employing experimental designs that require high-throughput multiplexed fitness measurements

The ecology of religious beliefs

Although ecological forces are known to shape the expression of sociality across a broad range of biological taxa, their role in shaping human behavior is currently disputed. Both comparative and experimental evidence indicate that beliefs in moralizing high gods promote cooperation among humans, a behavioral attribute known to correlate with environmental harshness in nonhuman animals. Here we combine fine-grained bioclimatic data with the latest statistical tools from ecology and the social sciences to evaluate the potential effects of environmental forces, language history, and culture on the global distribution of belief in moralizing high gods (n = 583 societies). After simultaneously accounting for potential nonindependence among societies because of shared ancestry and cultural diffusion, we find that these beliefs are more prevalent among societies that inhabit poorer environments and are more prone to ecological duress. In addition, we find that these beliefs are more likely in politically complex societies that recognize rights to movable property. Overall, our multimodel inference approach predicts the global distribution of beliefs in moralizing high gods with an accuracy of 91%, and estimates the relative importance of different potential mechanisms by which this spatial pattern may have arisen. The emerging picture is neither one of pure cultural transmission nor of simple ecological determinism, but rather a complex mixture of social, cultural, and environmental influences. Our methods and findings provide a blueprint for how the increasing wealth of ecological, linguistic, and historical data can be leveraged to understand the forces that have shaped the behavior of our own species

An ABS control logic based on wheel force measurement

The paper presents an anti-lock braking system (ABS) control logic based on the measurement of the longitudinal forces at the hub bearings. The availability of force information allows to design a logic that does not rely on the estimation of the tyre-road friction coefficient, since it continuously tries to exploit the maximum longitudinal tyre force. The logic is designed by means of computer simulation and then tested on a specific hardware in the loop test bench: the experimental results confirm that measured wheel force can lead to a significant improvement of the ABS performances in terms of stopping distance also in the presence of road with variable friction coefficien

Mode-Wise Entanglement of Gaussian States

We address the decomposition of a multi-mode pure Gaussian state with respect to a bi-partite division of the modes. For any such division the state can always be expressed as a product state involving entangled two-mode squeezed states and single mode local states at each side. The character of entanglement of the state can therefore be understood modewise; that is, a given mode on one side is entangled with only one corresponding mode of the other, and therefore the total bi-partite entanglement is the sum of the modewise entanglement. This decomposition is generally not applicable to all mixed Gaussian states. However, the result can be extended to a special family of "isotropic" states, characterized by a phase space covariance matrix with a completely degenerate symplectic spectrum.Comment: 4 pages, RevTex4. Replaced with revised version with reference added to a previous related paper. Minor typographical errors correcte

Electron-hydrogen scattering in Faddeev-Merkuriev integral equation approach

Electron-hydrogen scattering is studied in the Faddeev-Merkuriev integral equation approach. The equations are solved by using the Coulomb-Sturmian separable expansion technique. We present $S$- and $P$-wave scattering and reactions cross sections up to the $H(n=4)$ threshold.Comment: 2 eps figure

Analysis of ``Gauge Modes'' in Linearized Relativity

By writing the complete set of $3 + 1$ (ADM) equations for linearized waves, we are able to demonstrate the properties of the initial data and of the evolution of a wave problem set by Alcubierre and Schutz. We show that the gauge modes and constraint error modes arise in a straightforward way in the analysis, and are of a form which will be controlled in any well specified convergent computational discretization of the differential equations.Comment: 11pages LaTe