3,996 research outputs found

    Integrable and Nonintegrable Classical Spin Clusters: Integrability Criteria and Analytic Structure of Invariants

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    The nonlinear dynamics is investigated for a system of N classical spins. This represents a Hamiltonian system with N degrees of freedom. According to the Liouville theorem, the complete integrability of such a system requires the existence of N independent integrals of the motion which are mutually in involution. As a basis for the investigation of regular and chaotic spin motions, we have examined in detail the problem of integrability of a two-spin system. It represents the simplest autonomous spin system for which the integrability problem is nontrivial. We have shown that a pair of spins coupled by an anisotropic exchange interaction represents a completely integrable system for any values of the coupling constants. The second integral of the motion (in addition to the Hamiltonian), which ensures the complete integrability, turns out to be quadratic in the spin variables. If, in addition to the exchange anisotropy also single-site anisotropy terms are included in the two-spin Hamiltonian, a second integral of the motion quadratic in the spin variables exists and thus guarantees integrability, only if the model constants satisfy a certain condition. Our numerical calculations strongly suggest that the violation of this condition implies not only the nonexistence of a quadratic integral, but the nonexistence of a second independent integral of motion in general. Finally, as an example of a completely integrable N-spin system we present the Kittel-Shore model of uniformly interacting spins, for which we have constructed the N independent integrals in involution as well as the action-angle variables explicitly

    Oncopeltus fasciatus zen is essential for serosal tissue function in katatrepsis

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    AbstractUnlike most Hox cluster genes, with their canonical role in anterior–posterior patterning of the embryo, the Hox3 orthologue of insects has diverged. Here, we investigate the zen orthologue in Oncopeltus fasciatus (Hemiptera:Heteroptera). As in other insects, the Of-zen gene is expressed extraembryonically, and RNA interference (RNAi) experiments demonstrate that it is functionally required in this domain for the proper occurrence of katatrepsis, the phase of embryonic movements by which the embryo emerges from the yolk and adjusts its orientation within the egg. After RNAi knockdown of Of-zen, katatrepsis does not occur, causing embryos to complete development inside out. However, not all aspects of expression and function are conserved compared to grasshopper, beetle, and fly orthologues. Of-zen is not expressed in the extraembryonic tissue until relatively late, suggesting it is not involved in tissue specification. Within the extraembryonic domain, Of-zen is expressed in the outer serosal membrane, but unlike orthologues, it is not detectable in the inner extraembryonic membrane, the amnion. Thus, the role of zen in the interaction of serosa, amnion, and embryo may differ between species. Of-zen is also expressed in the blastoderm, although this early expression shows no apparent correlation with defects seen by RNAi knockdown

    Parallelizing Gaussian Process Calculations in R

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    We consider parallel computation for Gaussian process calculations to overcome computational and memory constraints on the size of datasets that can be analyzed. Using a hybrid parallelization approach that uses both threading (shared memory) and message-passing (distributed memory), we implement the core linear algebra operations used in spatial statistics and Gaussian process regression in an R package called bigGP that relies on C and MPI. The approach divides the covariance matrix into blocks such that the computational load is balanced across processes while communication between processes is limited. The package provides an API enabling R programmers to implement Gaussian process-based methods by using the distributed linear algebra operations without any C or MPI coding. We illustrate the approach and software by analyzing an astrophysics dataset with n = 67, 275 observations

    Brief assessment of schizotypy: Developing short forms of the Wisconsin Schizotypy Scales

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    The Wisconsin Schizotypy Scales—the Perceptual Aberration, Magical Ideation, Physical Anhedonia, and Revised Social Anhedonia Scales—have been used extensively since their development in the 1970s and 1980s. Based on psychometric analyses using item response theory, the present work presents 15-item short forms of each scale. In addition to being briefer, the short forms omit items with high differential item functioning. Based on data from a sample of young adults (n = 1144), the short forms have strong internal consistency, and they mirror effects found for the longer scales. They thus appear to be a good option for researchers interested in the brief assessment of schizotypic traits. The items are listed in an Appendix A

    Classical Spin Clusters: Integrability and Dynamical Properties

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    A pair of exchange‐coupled classical spins with biaxial exchange and single‐site anisotropy represents a Hamiltonian system with two degrees of freedom for which the integrability question is nontrivial. We have found that such a system is completely integrable if the model parameters satisfy a certain condition. For the integrable cases, the second integral of the motion (in addition to the Hamiltonian), which guarantees integrability, is determined explicitly. It can be reconstructed numerically by means of time averages of dynamical variables over all trajectories. In the nonintegrable cases, the existence of the time averages is still guaranteed, but they no longer define an analytic invariant, and their determination is subject to long‐time anomalies. Our numerical calculation of time averages for two lines of initial conditions reveals a number of interesting features of such nonanalytic invariants

    Conductance anomalies and the extended Anderson model for nearly perfect quantum wires

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    Anomalies near the conductance threshold of nearly perfect semiconductor quantum wires are explained in terms of singlet and triplet resonances of conduction electrons with a single weakly-bound electron in the wire. This is shown to be a universal effect for a wide range of situations in which the effective single-electron confinement is weak. The robustness of this generic behavior is investigated numerically for a wide range of shapes and sizes of cylindrical wires with a bulge. The dependence on gate voltage, source-drain voltage and magnetic field is discussed within the framework of an extended Hubbard model. This model is mapped onto an extended Anderson model, which in the limit of low temperatures is expected to lead to Kondo resonance physics and pronounced many-body effects

    Examining the Proteome of Drosophila Across Organism Lifespan

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    A survey of the proteome of Drosophila melanogaster at nine time points across the adult lifespan based on several mass-spectrometry-based techniques is presented. In total, there is evidence for 5902 unique peptides corresponding to 1699 different proteins. Of hundreds of relatively abundant components, many appear to be highly dynamic as the adult fly ages. Of those proteins that we observe changing with age, a majority, associated with metabolism, reproduction, and development, are downregulated. Other biological pathways such as defense response also show variable changes, where some proteins are down-regulated and others are up-regulated. The observed variations are compared with a report of genome-wide changes at the transcriptome level at different ages and the similarities and differences are presented
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