The role of noise and initial conditions in the asymptotic solution of a bounded confidence, continuous-opinion model

We study a model for continuous-opinion dynamics under bounded confidence. In particular, we analyze the importance of the initial distribution of opinions in determining the asymptotic configuration. Thus, we sketch the structure of attractors of the dynamical system, by means of the numerical computation of the time evolution of the agents density. We show that, for a given bound of confidence, a consensus can be encouraged or prevented by certain initial conditions. Furthermore, a noisy perturbation is added to the system with the purpose of modeling the free will of the agents. As a consequence, the importance of the initial condition is partially replaced by that of the statistical distribution of the noise. Nevertheless, we still find evidence of the influence of the initial state upon the final configuration for a short range of the bound of confidence parameter

Thermal Conductivity and Specific Heat of the Spin-Ice Compound Dy2_2Ti2_2O7_7: Experimental Evidence for Monopole Heat Transport

Elementary excitations in the spin-ice compound Dy$_2$Ti$_2$O$_7$ can be described as magnetic monopoles propagating independently within the pyrochlore lattice formed by magnetic Dy ions. We studied the magnetic-field dependence of the thermal conductivity {\kappa}(B) for B || [001] and observe clear evidence for magnetic heat transport originating from the monopole excitations. The magnetic contribution {\kappa}_{mag} is strongly field-dependent and correlates with the magnetization M(B). The diffusion coefficient obtained from the ratio of {\kappa}_{mag} and the magnetic specific heat is strongly enhanced below 1 K indicating a high mobility of the monopole excitations in the spin-ice state.Comment: 5 pages, 4 figure

Novel modeling of task versus rest brain state predictability using a dynamic time warping spectrum: comparisons and contrasts with other standard measures of brain dynamics

Dynamic time warping, or DTW, is a powerful and domain-general sequence alignment method for computing a similarity measure. Such dynamic programming-based techniques like DTW are now the backbone and driver of most bioinformatics methods and discoveries. In neuroscience it has had far less use, though this has begun to change. We wanted to explore new ways of applying DTW, not simply as a measure with which to cluster or compare similarity between features but in a conceptually different way. We have used DTW to provide a more interpretable spectral description of the data, compared to standard approaches such as the Fourier and related transforms. The DTW approach and standard discrete Fourier transform (DFT) are assessed against benchmark measures of neural dynamics. These include EEG microstates, EEG avalanches, and the sum squared error (SSE) from a multilayer perceptron (MLP) prediction of the EEG time series, and simultaneously acquired FMRI BOLD signal. We explored the relationships between these variables of interest in an EEG-FMRI dataset acquired during a standard cognitive task, which allowed us to explore how DTW differentially performs in different task settings. We found that despite strong correlations between DTW and DFT-spectra, DTW was a better predictor for almost every measure of brain dynamics. Using these DTW measures, we show that predictability is almost always higher in task than in rest states, which is consistent to other theoretical and empirical findings, providing additional evidence for the utility of the DTW approach

Spin-orbital excitation continuum and anomalous electron-phonon interaction in the Mott insulator LaTiO3_3

Raman scattering experiments on stoichiometric, Mott-insulating LaTiO$_3$ over a wide range of excitation energies reveal a broad electronic continuum which is featureless in the paramagnetic state, but develops a gap of $\sim 800$ cm$^{-1}$ upon cooling below the N\'eel temperature $T_N = 146$ K. In the antiferromagnetic state, the spectral weight below the gap is transferred to well-defined spectral features due to spin and orbital excitations. Low-energy phonons exhibit pronounced Fano anomalies indicative of strong interaction with the electron system for $T > T_N$, but become sharp and symmetric for $T < T_N$. The electronic continuum and the marked renormalization of the phonon lifetime by the onset of magnetic order are highly unusual for Mott insulators and indicate liquid-like correlations between spins and orbitals.Comment: to appear in Phys. Rev. Let

Magnetostrictive Neel ordering of the spin-5/2 ladder compound BaMn2O3: distortion-induced lifting of geometrical frustration

The crystal structure and the magnetism of BaMn$_2$O$_3$ have been studied by thermodynamic and by diffraction techniques using large single crystals and powders. BaMn$_2$O$_3$ is a realization of a $S = 5/2$ spin ladder as the magnetic interaction is dominant along 180$^\circ$ Mn-O-Mn bonds forming the legs and the rungs of a ladder. The temperature dependence of the magnetic susceptibility exhibits well-defined maxima for all directions proving the low-dimensional magnetic character in BaMn$_2$O$_3$. The susceptibility and powder neutron diffraction data, however, show that BaMn$_2$O$_3$ exhibits a transition to antiferromagnetic order at 184 K, in spite of a full frustration of the nearest-neighbor inter-ladder coupling in the orthorhombic high-temperature phase. This frustration is lifted by a remarkably strong monoclinic distortion which accompanies the magnetic transition.Comment: 9 pages, 8 figures, 2 tables; in V1 fig. 2 was included twice and fig. 4 was missing; this has been corrected in V