We analyzed the regional dependence of ground motion to intensity conversion equations and derived a new global relationship to improve ground motion and intensity estimates for earthquake hazard applications, including those related to the ShakeMap system. For this purpose, we merged several databases collected by other authors in different geographical regions to highlight any systematic regional effects in the relationship between macroseismic intensities and both peak ground velocity and peak ground acceleration. Our database contains macroseismic intensities derived from expert assignments or from the "Did You Feel It?" database, paired with peak ground motions (PGM) from seismic stations. We constrain our intensity-ground-motion pairs to those with a maximum 2 km separation. For each region, we derived invertible relationships between intensities and ground motion using an orthogonal regression. We also derived a global relationship to quantify the regional differences. We investigated the dependence of intensity on predictor variables such as PGM, magnitude, and hypocentral distance. Our analyses indicate that PGM is the most robust predictor variable of intensity. Within one standard deviation, our regional and global results are in agreement with the relations of Worden et al. (2012) for California, Faenza and Michelini (2010) for Italy, Tselentis and Danciu (2008) for Greece, and Atkinson and Kaka (2007) for central-eastern United States. The earthquakes in the study ranged in magnitude from 2.5 to 7.3, and the distances ranged from less than a kilometer to about 200 km from the epicenter.

We study the binary classification problem with hinge loss. We consider classifiers that are linear combinations of base functions. Instead of an ' 2 penalty, which is used by the support vector machine, we put an ' 1 penalty on the coefficients. Under certain conditions on the base functions, hinge loss with this complexity penalty is shown to lead to an oracle inequality involving both model complexity and margin.

Neuronal signal integration and information processing in cortical networks critically depend on the organization of synaptic connectivity. During development, neurons can form synaptic connections when their axonal and dendritic arborizations come within close proximity of each other. Although many signaling cues are thought to be involved in guiding neuronal extensions, the extent to which accidental appositions between axons and dendrites can already account for synaptic connectivity remains unclear. To investigate this, we generated a local network of cortical L2/3 neurons that grew out independently of each other and that were not guided by any extracellular cues. Synapses were formed when axonal and dendritic branches came by chance within a threshold distance of each other. Despite the absence of guidance cues, we found that the emerging synaptic connectivity showed a good agreement with available experimental data on spatial locations of synapses on dendrites and axons, number of synapses by which neurons are connected, connection probability between neurons, distance between connected neurons, and pattern of synaptic connectivity. The connectivity pattern had a small-world topology but was not scale free. Together, our results suggest that baseline synaptic connectivity in local cortical circuits may largely result from accidentally overlapping axonal and dendritic branches of independently outgrowing neurons.

Neuronal signal integration and information processing in cortical neuronal networks critically depend on the organization of synaptic connectivity. Because of the challenges involved in measuring a large number of neurons, synaptic connectivity is difficult to determine experimentally. Current computational methods for estimating connectivity typically rely on the juxtaposition of experimentally available neurons and applying mathematical techniques to compute estimates of neural connectivity. However, since the number of available neurons is very limited, these connectivity estimates may be subject to large uncertainties. We use a morpho-density field approach applied to a vast ensemble of model-generated neurons. A morpho-density field (MDF) describes the distribution of neural mass in the space around the neural soma. The estimated axonal and dendritic MDFs are derived from 100,000 model neurons that are generated by a stochastic phenomenological model of neurite outgrowth. These MDFs are then used to estimate the connectivity between pairs of neurons as a function of their inter-soma displacement. Compared with other density-field methods, our approach to estimating synaptic connectivity uses fewer restricting assumptions and produces connectivity estimates with a lower standard deviation. An important requirement is that the model-generated neurons reflect accurately the morphology and variation in morphology of the experimental neurons used for optimizing the model parameters. As such, the method remains subject to the uncertainties caused by the limited number of neurons in the experimental data set and by the quality of the model and the assumptions used in creating the MDFs and in calculating estimating connectivity. In summary, MDFs are a powerful tool for visualizing the spatial distribution of axonal and dendritic densities, for estimating the number of potential synapses between neurons with low standard deviation, and for obtaining a greater understanding of the relationship between neural morphology and network connectivity.

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