Theta oscillations within the hippocampus-amygdala-medial prefrontal cortex (HPC-AMY-mPFC) circuit have been consistently implicated in the regulation of anxiety behaviors, including risk-assessment. To study if theta activity during risk-assessment was correlated with exploratory behavior in an approach/avoidance paradigm we recorded simultaneous local field potentials from this circuit in rat...

ity. Afterdischarges were less likely to be induced by direct hippocampal stimulation during periods when the hippocampal LFP had already been suppressed with preceding preparatory stimulation. Evoked potentials produced in the hippocampus by thalamic stimulation were also suppressed when preparatory direct hippocampal stimulation was provided. The authors were also able to demonstrate 2 novel ...

A biased graph consists of a graph T and a subclass B of the polygons of T, such that no theta subgraph of T contains exactly two members of B. A subgraph is balanced when all its polygons belong to B. A vertex is a balancing vertex if deleting it leaves a balanced graph. We give a construction for unbalanced biased graphs having a balancing vertex and we show that an unbalanced biased graph ha...

It is shown that if $\gamma: [a,b] \to S^2$ $C^3$ with $\det(\gamma, \gamma', \gamma'') \neq 0$, and $A \subseteq \mathbb{R}^3$ a Borel set, then $\dim \pi_{\theta} (A) \geq \min\left\{ 2,\dim A, \frac{ \dim A}{2} + \frac{3}{4} \right\}$ for a.e. $\theta \in [a,b]$, where $\pi_{\theta}$ denotes projection onto the orthogonal complement of $\gamma(\theta)$ ``$\dim$'' refers to Hausdorff dimensio...