In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of some recently proposed proof-systems for these logics.

We use the k-core decomposition to develop algorithms for the analysis of large scale complex networks. This decomposition, based on a recursive pruningof the least connected vertices, allows to disentangle the hierarchical structure of networks by progressively focusing on their central cores.By using this strategy we develop a general visualization algorithm thatcan be used to compare the structural properties of various networks andhighlight their hierarchical structure. The low computational complexity of the algorithm, O(n e), where n is the size of the network, ande is the number of edges, makes it suitable for the visualization of very large sparse networks. We show how the proposed visualization tool allows to find specific structural fingerprints of networks.

We propose a model by which dopamine (DA) and norepinepherine (NE) combine to alternate behavior between relatively exploratory and exploitative modes. The model is developed for a target detection task for which there is extant single neuron recording data available from locus coeruleus (LC) NE neurons. An exploration-exploitation tradeoff is elicited by regularly switching which of the two stimuli are rewarded. DA functions within the model to change synaptic weights according to a reinforcement learning algorithm. Exploration is mediated by the state of LC firing, with higher tonic and lower phasic activity producing greater response variability. The opposite state of LC function, with lower baseline firing rate and greater phasic responses, favors exploitative behavior. Changes in LC firing mode result from combined measures of response conflict and reward rate, where response conflict is monitored using models of anterior cingulate cortex (ACC). Increased long-term response conflict and decreased reward rate, which occurs following reward contingency switch, favors the higher tonic state of LC function and NE release.

Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a non invasive methodfor brain neuronal fibers delineation. Here we show a modification forDT-MRI that allows delineation of neuronal fibers which are infiltrated by edema. We use the Muliple Tensor Variational (MTV) framework which replaces the diffusion model of DT-MRI with a multiple componentmodel and fits it to the signal attenuation with a variational regularizationmechanism. In order to reduce free water contamination weestimate the free water compartment volume fraction in each voxel, remove it, and then calculate the anisotropy of the remaining compartment.

Given a redundant dictionary of basis vectors (or atoms), our goal is to find maximally sparse representations of signals. Previously, we have argued that a sparse Bayesian learning (SBL) framework is particularly well-suited for this task, showing that it has far fewer local minima than other Bayesian-inspired strategies. In this paper, we provide further evidence forthis claim by proving a restricted equivalence condition, based on the distribution of the nonzero generating model weights, whereby the SBL solution will equal the maximally sparse representation. We also prove that if these nonzero weights are drawn from an approximate Jeffreys prior,then with probability approaching one, our equivalence condition issatisfied.

We use the k-core decomposition to develop algorithms for the analysis of large scale complex networks. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by progressively focusing on their central cores. By using this strategy we develop a general visualization algorithm that can be used to compare the structural properties of various networks and highlight their hierarchical structure. The low computational complexity of the algorithm, O(n e), where n is the size of the network, and e is the number of edges, makes it suitable for the visualization of very large sparse networks. We show how the proposed visualization tool allows to find specific structural fingerprints of networks.

We propose a model by which dopamine (DA) and norepinepherine (NE) combine to alternate behavior between relatively exploratory and exploitative modes. The model is developed for a target detection task for which there is extant single neuron recording data available from locus coeruleus (LC) NE neurons. An exploration-exploitation tradeoff is elicited by regularly switching which of the two stimuli are rewarded. DA functions within the model to change synaptic weights according to a reinforcement learning algorithm. Exploration is mediated by the state of LC firing, with higher tonic and lower phasic activity producing greater response variability. The opposite state of LC function, with lower baseline firing rate and greater phasic responses, favors exploitative behavior. Changes in LC firing mode result from combined measures of response conflict and reward rate, where response conflict is monitored using models of anterior cingulate cortex (ACC). Increased long-term response conflict and decreased reward rate, which occurs following reward contingency switch, favors the higher tonic state of LC function and NE release.

Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a non invasive method for brain neuronal fibers delineation. Here we show a modification for DT-MRI that allows delineation of neuronal fibers which are infiltrated by edema. We use the Muliple Tensor Variational (MTV) framework which replaces the diffusion model of DT-MRI with a multiple component model and fits it to the signal attenuation with a variational regularization mechanism. In order to reduce free water contamination we estimate the free water compartment volume fraction in each voxel, remove it, and then calculate the anisotropy of the remaining compartment. The variational framework was applied on data collected with conventional clinical parameters, containing only six diffusion directions. By using the variational framework we were able to overcome the highly ill posed fitting. The results show that we were able to find fibers that were not found by DT-MRI.

Given a redundant dictionary of basis vectors (or atoms), our goal is to find maximally sparse representations of signals. Previously, we have argued that a sparse Bayesian learning (SBL) framework is particularly well-suited for this task, showing that it has far fewer local minima than other Bayesian-inspired strategies. In this paper, we provide further evidence for this claim by proving a restricted equivalence condition, based on the distribution of the nonzero generating model weights, whereby the SBL solution will equal the maximally sparse representation. We also prove that if these nonzero weights are drawn from an approximate Jeffreys prior, then with probability approaching one, our equivalence condition is satisfied. Finally, we motivate the worst-case scenario for SBL and demonstrate that it is still better than the most widely used sparse representation algorithms.

We propose a model by which dopamine (DA) and norepinepherine (NE) combine to alternate behavior between relatively exploratory and exploitative modes. The model is developed for a target detection task for which there is extant single neuron recording data available from locus coeruleus (LC) NE neurons. An exploration-exploitation tradeoff is elicited by regularly switching which of the two stimuli are rewarded. DA functions within the model to change synaptic weights according to a reinforcement learning algorithm. Exploration is mediated by the state of LC firing, with higher tonic and lower phasic activity producing greater response variability. The opposite state of LC function, with lower baseline firing rate and greater phasic responses, favors exploitative behavior. Changes in LC firing mode result from combined measures of response conflict and reward rate, where response conflict is monitored using models of anterior cingulate cortex (ACC). Increased long-term response conflict and decreased reward rate, which occurs following reward contingency switch, favors the higher tonic state of LC function and NE release.