229 research outputs found

    Cortical beta oscillations are associated with motor performance following visuomotor learning

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    © 2019 The Authors People vary in their capacity to learn and retain new motor skills. Although the relationship between neuronal oscillations in the beta frequency range (15–30 Hz) and motor behaviour is well established, the electrophysiological mechanisms underlying individual differences in motor learning are incompletely understood. Here, we investigated the degree to which measures of resting and movement-related beta power from sensorimotor cortex account for inter-individual differences in motor learning behaviour in the young and elderly. Twenty young (18–30 years) and twenty elderly (62–77 years) healthy adults were trained on a novel wrist flexion/extension tracking task and subsequently retested at two different time points (45–60 min and 24 h after initial training). Scalp EEG was recorded during a separate simple motor task before each training and retest session. Although short-term motor learning was comparable between young and elderly individuals, there was considerable variability within groups with subsequent analysis aiming to find the predictors of this variability. As expected, performance during the training phase was the best predictor of performance at later time points. However, regression analysis revealed that movement-related beta activity significantly explained additional variance in individual performance levels 45–60 min, but not 24 h after initial training. In the context of disease, these findings suggest that measurements of beta-band activity may offer novel targets for therapeutic interventions designed to promote rehabilitative outcomes

    Universal Critical Behavior of Aperiodic Ferromagnetic Models

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    We investigate the effects of geometric fluctuations, associated with aperiodic exchange interactions, on the critical behavior of qq-state ferromagnetic Potts models on generalized diamond hierarchical lattices. For layered exchange interactions according to some two-letter substitutional sequences, and irrelevant geometric fluctuations, the exact recursion relations in parameter space display a non-trivial diagonal fixed point that governs the universal critical behavior. For relevant fluctuations, this fixed point becomes fully unstable, and we show the apperance of a two-cycle which is associated with a novel critical behavior. We use scaling arguments to calculate the critical exponent α\alpha of the specific heat, which turns out to be different from the value for the uniform case. We check the scaling predictions by a direct numerical analysis of the singularity of the thermodynamic free-energy. The agreement between scaling and direct calculations is excellent for stronger singularities (large values of qq). The critical exponents do not depend on the strengths of the exchange interactions.Comment: 4 pages, 1 figure (included), RevTeX, submitted to Phys. Rev. E as a Rapid Communicatio

    The Critical Behaviour of the Spin-3/2 Blume-Capel Model in Two Dimensions

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    The phase diagram of the spin-3/2 Blume-Capel model in two dimensions is explored by conventional finite-size scaling, conformal invariance and Monte Carlo simulations. The model in its τ\tau-continuum Hamiltonian version is also considered and compared with others spin-3/2 quantum chains. Our results indicate that differently from the standard spin-1 Blume-Capel model there is no multicritical point along the order-disorder transition line. This is in qualitative agreement with mean field prediction but in disagreement with previous approximate renormalization group calculations. We also presented new results for the spin-1 Blume-Capel model.Comment: latex 18 pages, 4 figure

    Short-Range Ising Spin Glass: Multifractal Properties

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    The multifractal properties of the Edwards-Anderson order parameter of the short-range Ising spin glass model on d=3 diamond hierarchical lattices is studied via an exact recursion procedure. The profiles of the local order parameter are calculated and analysed within a range of temperatures close to the critical point with four symmetric distributions of the coupling constants (Gaussian, Bimodal, Uniform and Exponential). Unlike the pure case, the multifractal analysis of these profiles reveals that a large spectrum of the α\alpha -H\"older exponent is required to describe the singularities of the measure defined by the normalized local order parameter, at and below the critical point. Minor changes in these spectra are observed for distinct initial distributions of coupling constants, suggesting an universal spectra behavior. For temperatures slightly above T_{c}, a dramatic change in the F(α)F(\alpha) function is found, signalizing the transition.Comment: 8 pages, LaTex, PostScript-figures included but also available upon request. To be published in Physical Review E (01/March 97

    Universality and scaling study of the critical behavior of the two-dimensional Blume-Capel model in short-time dynamics

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    In this paper we study the short-time behavior of the Blume-Capel model at the tricritical point as well as along the second order critical line. Dynamic and static exponents are estimated by exploring scaling relations for the magnetization and its moments at early stage of the dynamic evolution. Our estimates for the dynamic exponents, at the tricritical point, are z=2.215(2)z= 2.215(2) and θ=0.53(2)\theta= -0.53(2).Comment: 12 pages, 9 figure

    Field-induced Ordering in Critical Antiferromagnets

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    Transfer-matrix scaling methods have been used to study critical properties of field-induced phase transitions of two distinct two-dimensional antiferromagnets with discrete-symmetry order parameters: triangular-lattice Ising systems (TIAF) and the square-lattice three-state Potts model (SPAF-3). Our main findings are summarised as follows. For TIAF, we have shown that the critical line leaves the zero-temperature, zero -field fixed point at a finite angle. Our best estimate of the slope at the origin is (dTc/dH)T=H=0=4.74±0.15(dT_c/dH)_{T=H=0} = 4.74 \pm 0.15. For SPAF-3 we provided evidence that the zero-field correlation length diverges as ξ(T0,H=0)exp(a/Tx)\xi(T \to 0, H=0) \simeq \exp (a/T^{x}), with x=1.08±0.13x=1.08 \pm 0.13, through analysis of the critical curve at H0H \neq 0 plus crossover arguments. For SPAF-3 we have also ascertained that the conformal anomaly and decay-of-correlations exponent behave as: (a) H=0: c=1,η=1/3c=1, \eta=1/3; (b) H0:c=1/2,η=1/4H \neq 0: c=1/2, \eta=1/4.Comment: RevTex, 7 pages, 4 eps figures, to be published in Phys. Rev.

    Lattice gauge theory with baryons at strong coupling

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    We study the effective Hamiltonian for strong-coupling lattice QCD in the case of non-zero baryon density. In leading order the effective Hamiltonian is a generalized antiferromagnet. For naive fermions, the symmetry is U(4N_f) and the spins belong to a representation that depends on the local baryon number. Next-nearest-neighbor (nnn) terms in the Hamiltonian break the symmetry to U(N_f) x U(N_f). We transform the quantum problem to a Euclidean sigma model which we analyze in a 1/N_c expansion. In the vacuum sector we recover spontaneous breaking of chiral symmetry for the nearest-neighbor and nnn theories. For non-zero baryon density we study the nearest-neighbor theory only, and show that the pattern of spontaneous symmetry breaking depends on the baryon density.Comment: 31 pages, 5 EPS figures. Corrected Eq. (6.1

    Spanning forests and the q-state Potts model in the limit q \to 0

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    We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio
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