The hydrostatic equilibrium is a prominent topic in fluid dynamics and astrophysics. Understanding the stability of perturbations near Boussinesq system helps gain insight into certain weather phenomena. 2D focused here anisotropic involves only horizontal dissipation thermal diffusion. Due to lack vertical dissipation, precise large-time behavior problem difficult. When spatial domain $${\math...

UNLABELLED We have recently described a slow oscillation in the hippocampus of urethane-anesthetized mice, which couples to nasal respiration and is clearly distinct from co-occurring theta oscillations. Here we set out to investigate whether such type of patterned network activity, which we named "hippocampal respiration rhythm" (HRR), also occurs in awake mice. In freely moving mice, instanta...

Theta and gamma rhythms synchronize neurons within and across brain structures. Both rhythms are widespread within the hippocampus during exploratory behavior and rapid-eye-movement (REM) sleep. How synchronous are these rhythms throughout the hippocampus? The present study examined theta and gamma coherence along the septotemporal (long) axis of the hippocampus in rats during REM sleep, a beha...

Here, we report evidence for oscillatory bi-directional interactions between the nucleus accumbens and the neocortex in humans. Six patients performed a demanding covert visual attention task while we simultaneously recorded brain activity from deep-brain electrodes implanted in the nucleus accumbens and the surface electroencephalogram (EEG). Both theta and alpha oscillations were strongly coh...

for any lacunary sequence $theta = (k_{r})$, we define the concepts of $s_{theta}-$limit point and $s_{theta}-$cluster point of a sequence of fuzzy numbers $x = (x_{k})$. we introduce the new sets  $lambda^{f}_{s_{theta}}(x)$, $gamma^{f}_{s_{theta}}(x)$ and prove some inclusion relaions between these and the sets $lambda^{f}_{s}(x)$, $gamma^{f}_{s}(x)$ introduced in ~cite{ayt:slpsfn} by aytar [...

Hippocampal (HPC) theta oscillations have long been linked to various functions of the brain. Many cortical and subcortical areas that also exhibit theta oscillations have been linked to functional circuits with the hippocampus on the basis of coupled activities at theta frequencies. We examine, in freely moving rats, the characteristics of diencephalic theta local field potentials (LFPs) recor...

The theta-gamma neural coding theory suggests that multiple items are represented in working memory (WM) by a superposition of gamma cycles on theta oscillations. To enable a stable, non-interfering representation of multiple items, such a theta-gamma neural code may be reflected by phase-phase coupling, i.e., a precise locking of gamma subcycles to specific theta phases. Recent data have indic...

The rodent medial prefrontal cortex (mPFC) is critical for spatial working memory (SWM), but the underlying neural processes are incompletely understood. During SWM tasks, neural activity in the mPFC becomes synchronized with theta oscillations in the hippocampus, and the strength of hippocampal-prefrontal synchrony is correlated with behavioral performance. However, to what extent the mPFC gen...

We present a neural network model of consolidation focussing on the possible functional roles of theta-and sharp-wave-periods in hippocampal EEG-recordings of rats. Our network implements ideas suggested by Buzss aki concerning two tentative stages of learning in the hippocampal formation: sparse assemblies in region CA3 are weak and transiently potentiated during theta-related exploratory beha...