786 research outputs found

    Some applications of series expansions in magnetism

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    A double-blind study of the efficacy of apomorphine and its assessment in "off-periods in Parkinson's disease

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    Five patients with idiopathic Parkinson's disease with severe response fluctuations were selected for a randomized double-blind placebo-controlled study, concerning the clinical effects of subcutaneous apomorphine and its assessment in `offÂż-periods. The study was designed as five n = 1 studies, in which every patient was his own control. The effect of apomorphine was studied by using the Columbia rating scale and quantitative assessments, using tapping, walking and pinboard. There was a significant positive effect of apomorphine, in a mean optimal dose of 2.7 mg, with a mean latency of onset of 7.3 min and a mean duration of response of 96 min. After pretreatment with domperidone, no significant adverse effects were observed. Tapping showed the highest correlation with rigidity and bradykinesia. Walking showed a high correlation with stability and gait. Pinboard testing did not give additional information. The first conclusion was that apomorphine proved to be a significantly effective dopamine agonist, proven now also by a double blind placebo-controlled study. Secondly it was concluded that assessment of clinical effect in parkinsonian patients can be performed best by combining the Columbia item tremor with tapping and walking scores

    New algorithm of the high-temperature expansion for the Ising model in three dimensions

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    New algorithm of the finite lattice method is presented to generate the high-temperature expansion series of the Ising model. It enables us to obtain much longer series in three dimensions when compared not only to the previous algorithm of the finite lattice method but also to the standard graphical method. It is applied to extend the high-temperature series of the simple cubic Ising model from beta^{26} to beta^{46} for the free energy and from beta^{25} to beta^{32} for the magnetic susceptibility.Comment: 3 pages, Lattice2002(spin

    Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices

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    We present an efficient algorithm for computing the partition function of the q-colouring problem (chromatic polynomial) on regular two-dimensional lattice strips. Our construction involves writing the transfer matrix as a product of sparse matrices, each of dimension ~ 3^m, where m is the number of lattice spacings across the strip. As a specific application, we obtain the large-q series of the bulk, surface and corner free energies of the chromatic polynomial. This extends the existing series for the square lattice by 32 terms, to order q^{-79}. On the triangular lattice, we verify Baxter's analytical expression for the bulk free energy (to order q^{-40}), and we are able to conjecture exact product formulae for the surface and corner free energies.Comment: 17 pages. Version 2: added 4 further term to the serie

    Higher orders of the high-temperature expansion for the Ising model in three dimensions

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    The new algorithm of the finite lattice method is applied to generate the high-temperature expansion series of the simple cubic Ising model to β50\beta^{50} for the free energy, to β32\beta^{32} for the magnetic susceptibility and to β29\beta^{29} for the second moment correlation length. The series are analyzed to give the precise value of the critical point and the critical exponents of the model.Comment: Lattice2003(Higgs), 3 pages, 2 figure

    Resolving the molecular architecture of the photoreceptor active zone with 3D-MINFLUX

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    Cells assemble macromolecular complexes into scaffoldings that serve as substrates for catalytic processes. Years of molecular neurobiology research indicate that neurotransmission depends on such optimization strategies. However, the molecular topography of the presynaptic active zone (AZ), where transmitter is released upon synaptic vesicle (SV) fusion, remains to be visualized. Therefore, we implemented MINFLUX optical nanoscopy to resolve the AZ of rod photoreceptors. This was facilitated by a novel sample immobilization technique that we name heat-assisted rapid dehydration (HARD), wherein a thin layer of rod synaptic terminals (spherules) was transferred onto glass coverslips from fresh retinal slices. Rod ribbon AZs were readily immunolabeled and imaged in 3D with a precision of a few nanometers. Our 3D-MINFLUX results indicate that the SV release site in rods is a molecular complex of bassoon–RIM2–ubMunc13-2–Cav1.4, which repeats longitudinally on both sides of the ribbon

    Recording electrical activity from the brain of behaving octopus

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    : Octopuses, which are among the most intelligent invertebrates,1,2,3,4 have no skeleton and eight flexible arms whose sensory and motor activities are at once autonomous and coordinated by a complex central nervous system.5,6,7,8 The octopus brain contains a very large number of neurons, organized into numerous distinct lobes, the functions of which have been proposed based largely on the results of lesioning experiments.9,10,11,12,13 In other species, linking brain activity to behavior is done by implanting electrodes and directly correlating electrical activity with observed animal behavior. However, because the octopus lacks any hard structure to which recording equipment can be anchored, and because it uses its eight flexible arms to remove any foreign object attached to the outside of its body, in vivo recording of electrical activity from untethered, behaving octopuses has thus far not been possible. Here, we describe a novel technique for inserting a portable data logger into the octopus and implanting electrodes into the vertical lobe system, such that brain activity can be recorded for up to 12 h from unanesthetized, untethered octopuses and can be synchronized with simultaneous video recordings of behavior. In the brain activity, we identified several distinct patterns that appeared consistently in all animals. While some resemble activity patterns in mammalian neural tissue, others, such as episodes of 2 Hz, large amplitude oscillations, have not been reported. By providing an experimental platform for recording brain activity in behaving octopuses, our study is a critical step toward understanding how the brain controls behavior in these remarkable animals

    Series studies of the Potts model. I: The simple cubic Ising model

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    The finite lattice method of series expansion is generalised to the qq-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained, unlike two-dimensional lattices where the computational requirements grow exponentially with the number of terms. For the Ising (q=2q=2) case we have extended low-temperature series for the partition functions, magnetisation and zero-field susceptibility to u26u^{26} from u20u^{20}. The high-temperature series for the zero-field partition function is extended from v18v^{18} to v22v^{22}. Subsequent analysis gives critical exponents in agreement with those from field theory.Comment: submitted to J. Phys. A: Math. Gen. Uses preprint.sty: included. 24 page
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