Activity in human reward-sensitive brain areas is strongly context dependent

Functional neuroimaging research in humans has identified a number of brain areas that are activated by the delivery of primary and secondary reinforcers. The present study investigated how activity in these reward-sensitive regions is modulated by the context in which rewards and punishments are experienced. Fourteen healthy volunteers were scanned during the performance of a simple monetary gambling task that involved a "win" condition (in which the possible outcomes were a large monetary gain, a small gain, or no gain of money) and a "lose" condition (in which the possible outcomes were a large monetary loss, a small loss, or no loss of money). We observed reward-sensitive activity in a number of brain areas previously implicated in reward processing, including the striatum, prefrontal cortex, posterior cingulate, and inferior parietal lobule. Critically, activity in these reward-sensitive areas was highly sensitive to the range of possible outcomes from which an outcome was selected. In particular, these regions were activated to a comparable degree by the best outcomes in each condition-a large gain in the win condition and no loss of money in the lose condition-despite the large difference in the objective value of these outcomes. In addition, some reward-sensitive brain areas showed a binary instead of graded sensitivity to the magnitude of the outcomes from each distribution. These results provide important evidence regarding the way in which the brain scales the motivational value of events by the context in which these events occur

Percolation in invariant Poisson graphs with i.i.d. degrees

Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme that is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components

Bootstrap Percolation on Complex Networks

We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: $f$, the fraction of vertices initially activated, and $p$, the fraction of undamaged vertices in the graph. We observe two transitions: the giant active component appears continuously at a first threshold. There may also be a second, discontinuous, hybrid transition at a higher threshold. Avalanches of activations increase in size as this second critical point is approached, finally diverging at this threshold. We describe the existence of a special critical point at which this second transition first appears. In networks with degree distributions whose second moment diverges (but whose first moment does not), we find a qualitatively different behavior. In this case the giant active component appears for any $f>0$ and $p>0$, and the discontinuous transition is absent. This means that the giant active component is robust to damage, and also is very easily activated. We also formulate a generalized bootstrap process in which each vertex can have an arbitrary threshold.Comment: 9 pages, 3 figure

Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks

We introduce the heterogeneous-$k$-core, which generalizes the $k$-core, and contrast it with bootstrap percolation. Vertices have a threshold $k_i$ which may be different at each vertex. If a vertex has less than $k_i$ neighbors it is pruned from the network. The heterogeneous-$k$-core is the sub-graph remaining after no further vertices can be pruned. If the thresholds $k_i$ are $1$ with probability $f$ or $k \geq 3$ with probability $(1-f)$, the process forms one branch of an activation-pruning process which demonstrates hysteresis. The other branch is formed by ordinary bootstrap percolation. We show that there are two types of transitions in this heterogeneous-$k$-core process: the giant heterogeneous-$k$-core may appear with a continuous transition and there may be a second, discontinuous, hybrid transition. We compare critical phenomena, critical clusters and avalanches at the heterogeneous-$k$-core and bootstrap percolation transitions. We also show that network structure has a crucial effect on these processes, with the giant heterogeneous-$k$-core appearing immediately at a finite value for any $f > 0$ when the degree distribution tends to a power law $P(q) \sim q^{-\gamma}$ with $\gamma < 3$.Comment: 10 pages, 4 figure

Neural dynamics of error processing in medial frontal cortex.

Adaptive behavior requires an organism to evaluate the outcome of its actions, such that future behavior can be adjusted accordingly and the appropriate response selected. During associative learning, the time at which such evaluative information is available changes as learning progresses, from the delivery of performance feedback early in learning to the execution of the response itself during learned performance. Here, we report a learning-dependent shift in the timing of activation in the rostral cingulate zone of the anterior cingulate cortex from external error feedback to internal error detection. This pattern of activity is seen only in the anterior cingulate, not in the pre-supplementary motor area. The dynamics of these reciprocal changes are consistent with the claim that the rostral cingulate zone is involved in response selection on the basis of the expected outcome of an action. Specifically, these data illustrate how the anterior cingulate receives evaluative information, indicating that an action has not produced the desired result. © 2005 Elsevier Inc. All rights reserved

New Magnetic Excitations in the Spin-Density-Wave of Chromium

Low-energy magnetic excitations of chromium have been reinvestigated with a single-Q crystal using neutron scattering technique. In the transverse spin-density-wave phase a new type of well-defined magnetic excitation is found around (0,0,1) with a weak dispersion perpendicular to the wavevector of the incommensurate structure. The magnetic excitation has an energy gap of E ~ 4 meV and at (0,0,1) exactly corresponds to the Fincher mode previously studied only along the incommensurate wavevector.Comment: 4 pages, 4 figure