Duvelisib, An Supreme Relaxation!

The wave activity was calculated as follows. First, the measured phase was spatially unwrapped. Next, we obtain the wave map as the single gradient vector best characterizing the phase gradient across the measurement array. This wave map is then correlated with the measured phase to give the wave activity. We convert the phase into unwrapped phase by taking the discrete spatial derivative and then reintegrating spatially. The chief reason for this is that the spatially unwrapped phases allow the representation of a wave as flupentixol a gradient over a field of scalars. Nearest neighbor edges on the measurement array eij; i, j?��?S, are determined by Delaunay triangulation. For the phase at some t, f, and q, the phase difference on each edge is defined as �Ħ�ij?=?arg(��i)???arg(��j)?+?2k�� with integer k such that �Ħ�ij?��?[??��, ��). We assign unwrapped phase values ��i, i?��?S, using nearest neighbor phase relationships ��i?=?��j?+?�Ħ�ij. Edges are added sequentially, in ascending order of |�Ħ�ij|, to an initially edgeless graph with sites as vertices. If |�Ħ�ij|?click here phase varies smoothly. Unwrapping errors may either reflect legitimate discontinuities in the phase or measurement noise ( Spagnolini, 1995). Adding edges in ascending order of |�Ħ�ij| places unwrapping Selleckchem Duvelisib errors in regions of highest |�Ħ�ij|, i.e. at legitimate discontinuities and high measurement noise. Exploration of phase dynamics using k-means clustering ( Ito et al., 2007) and principal component analysis ( Alexander et al., 2006b) indicated that much of the variance in the unwrapped phases could be explained by linear gradients of phase with the form equation(12) ��S=cos(��(PS�C(o��o��)))��S=cos��PS�Co��o��where (o��, o��) is the location of the origin (bullseye) of the phase gradient on the surface of a sphere, PS gives the coordinates of each measurement site projected onto the surface of a sphere and ��( ) gives the polar angle in the spherical coordinate system. This wave model is linear when expressed in Cartesian coordinates. The principal component analysis of the present data sets confirmed this linear wave model as explaining a large amount of the variance in unwrapped phases (see Results section). We therefore estimated the wave map ( Alexander et al., 2006b?and?Alexander et al., 2009) as a linear gradient in the volume defined by the measurement sites, by solving a regression equation of the form equation(13) ��S=��0+��APCAP+��ISCIS+��LRCLR��S=��0+��APCAP+��ISCIS+��LRCLRwhere �� represents the regression coefficients and (CAP, CIS, CLR) are the Cartesian coordinates of the measurement sites. AP refers to the anterior�Cposterior axis of the measurement array, IS to the inferior�Csuperior axis, and LR to left�Cright axis.