For the system formed by a relativistic electron beam and its plasma return current, we investigate the effects of both transverse and parallel beam and plasma temperatures on the linear stability of collective electromagnetic modes. We focus on nonrelativistic temperatures and wave-vector orientations ranging from two-stream to filamentation instabilities. Water-bag distributions are used to m...

The term modular form, generically, is very broad. These objects most naturally exist within the scope of number theory and play central roles in its various branches, yet they also play important roles in other fields of mathematics. For example, modular forms might conjure up such diverse thoughts as Fermat’s Last Theorem, the Langlands program, the Riemann Hypothesis, arithmetic applications...

In the rodent hippocampus, a phase precession phenomena of place cell firing with the local field potential (LFP) theta is called "theta phase precession" and is considered to contribute to memory formation with spike time dependent plasticity (STDP). On the other hand, in the primate hippocampus, the existence of theta phase precession is unclear. Our computational studies have demonstrated th...

Cortical theta band oscillations (4-8 Hz) in EEG signals have been shown to be important for a variety of different cognitive control operations in visual attention paradigms. However the synchronization source of these signals as defined by fMRI BOLD activity and the extent to which theta oscillations play a role in multimodal attention remains unknown. Here we investigated the extent to which...

Individual neurons in the medial septum and diagonal band fire in phase with, and appear to act as a 'pacemaker' of, the hippocampal theta rhythm. We investigated the relationships of periodic EEG both among various parts of the septum and with dorsal hippocampal theta recorded concurrently in freely moving rats. Most septal sites showed theta rhythm concurrent with hippocampal theta during loc...

is a modular form of weight n/2 on Γ0(N), where N is the level of Q, i.e. NQ−1 is integral and NQ−1 has even diagonal entries. This was proved by Schoeneberg [5] for even n and by Pfetzer [3] for odd n. Shimura [6] uses the Poisson summation formula to generalize their results for arbitrary n and he also computes the theta multiplier explicitly. Stark [8] gives a different proof by converting θ...

The catalytic core of Escherichia coli DNA polymerase III holoenzyme contains three subunits: alpha, epsilon, and theta. The alpha subunit contains the polymerase, and the epsilon subunit contains the exonucleolytic proofreading function. The small (8-kDa) theta subunit binds only to epsilon. Its function is not well understood, although it was shown to exert a small stabilizing effect on the e...

A major tool in understanding how the brain processes information is the analysis of neuronal output at each hierarchical level along the pathway of signal propagation. Theta rhythm and head directionality are the two main signals found across all levels of Papez's circuit, which supports episodic memory formation. Here, we provide evidence that the functional interaction between both signals o...

Performance of memory tasks is impaired by lesions to either the medial prefrontal cortex (mPFC) or the hippocampus (HPC); although how these two areas contribute to successful performance is not well understood. mPFC unit activity is temporally affected by hippocampal-theta oscillations, with almost half the mPFC population entrained to theta in behaving animals, pointing to theta interactions...