Estimation of functional connectivity from electromagnetic signals and the amount of empirical data required

An increasing number of neuroimaging studies are concerned with the identification of interactions or statistical dependencies between brain areas. Dependencies between the activities of different brain regions can be quantified with functional connectivity measures such as the cross-correlation coefficient. An important factor limiting the accuracy of such measures is the amount of empirical data available. For event-related protocols, the amount of data also affects the temporal resolution of the analysis. We use analytical expressions to calculate the amount of empirical data needed to establish whether a certain level of dependency is significant when the time series are autocorrelated, as is the case for biological signals. These analytical results are then contrasted with estimates from simulations based on real data recorded with magnetoencephalography during a resting-state paradigm and during the presentation of visual stimuli. Results indicate that, for broadband signals, 50-100 s of data is required to detect a true underlying cross-correlations coefficient of 0.05. This corresponds to a resolution of a few hundred milliseconds for typical event-related recordings. The required time window increases for narrow band signals as frequency decreases. For instance, approximately 3 times as much data is necessary for signals in the alpha band. Important implications can be derived for the design and interpretation of experiments to characterize weak interactions, which are potentially important for brain processing.

Spatial and temporal dependencies of cross-orientation suppression in human vision.

A well-known property of orientation-tuned neurons in the visual cortex is that they are suppressed by the superposition of an orthogonal mask. This phenomenon has been explained in terms of physiological constraints (synaptic depression), engineering solutions for components with poor dynamic range (contrast normalization) and fundamental coding strategies for natural images (redundancy reduction). A common but often tacit assumption is that the suppressive process is equally potent at different spatial and temporal scales of analysis. To determine whether it is so, we measured psychophysical cross-orientation masking (XOM) functions for flickering horizontal Gabor stimuli over wide ranges of spatio-temporal frequency and contrast. We found that orthogonal masks raised contrast detection thresholds substantially at low spatial frequencies and high temporal frequencies (high speeds), and that small and unexpected levels of facilitation were evident elsewhere. The data were well fit by a functional model of contrast gain control, where (i) the weight of suppression increased with the ratio of temporal to spatial frequency and (ii) the weight of facilitatory modulation was the same for all conditions, but outcompeted by suppression at higher contrasts. These results (i) provide new constraints for models of primary visual cortex, (ii) associate XOM and facilitation with the transient magno- and sustained parvostreams, respectively, and (iii) reconcile earlier conflicting psychophysical reports on XOM.

Atom transfer radical polymerisation - towards the synthesis of a fully-functional photorefractive polymer

Atom transfer radical polymerisation (ATRP) of styrene in xylene solution initiated with 1-phenylethyl bromide and mediated by CuBr/N-propyl-2- pyridinemethanimine catalyst complex was studied. The polymerisation was ill-controlled, yielding polymers with broad molecular weight distributions and values of number average molecular weight considerably higher than the theoretical values calculated from 100% initiator efficiency. The degree of control afforded over the polymerisation was enhanced by use of a more soluble catalyst complex, CuBr/N-octyl-2-pyridinemethanimine. Furthermore, the use of a more polar solvent, diglyme, generated a homogeneous catalyst complex that facilitated the production of polymers having narrow molecular weight distributions (1.10 < PDi < 1.20). The kinetics of the atom transfer radical polymerisation of methyl methacrylate at 90°C in diglyme solution initiated with ethyl-2-bromoisobutyrate and mediated by CuBr/N-octyl-2-pyridinemethanimine was studied and the orders of the reaction were established. The effect on the rate of polymerisation of the ratio of CuBr:N-octyl-2-pyridinemethanimine was also determined. The temperature dependencies of the rate of polymerisation of methyl methacrylate in diglyme solution and xylene solution were studied, and were found to be non-linear and dependent upon the polarity of the solvent. The use of highly polar aprotic solvents, such as N,N-dimethylformamide and dimethylsulphoxide, was found to be detrimental to the degree of control afforded over the polymerisation of methyl methacrylate. This was circumvented by use of a 5-fold excess, over that conventionally used, of catalyst complex. The atom transfer radical polymerisation of (4-nitrophenyl)-[3-[N-[2- (methacryloyloxy)ethyl]carbazolyl]]diazene in dimethyl sulphoxide solution was studied. Although homopolymerisation yielded only oligomers, copolymerisation of this monomer with methyl methacrylate was found to be readily achievable. Keywords: ATRP, Styrene; Methyl methacrylate; Polar solvents; Fully-functional photorefractive polymer. 2