let $(u_n)$ be a sequence of fuzzy numbers.  we recover the slow oscillation of $(u_n)$ of fuzzy numbers from the ces`{a}ro summability of its generator sequence and some additional conditions imposed on $(u_n)$. further, fuzzy analogues of some well known classical tauberian theorems for ces`{a}ro summability method are established as particular cases.

Let $(u_n)$ be a sequence of fuzzy numbers.  We recover the slow oscillation of $(u_n)$ of fuzzy numbers from the Ces`{a}ro summability of its generator sequence and some additional conditions imposed on $(u_n)$. Further, fuzzy analogues of some well known classical Tauberian theorems for Ces`{a}ro summability method are established as particular cases.

Brain rhythms regulate information processing in different states to enable learning and memory formation. The <1 Hz sleep slow oscillation hallmarks slow-wave sleep and is critical to memory consolidation. Here we show in sleeping humans that auditory stimulation in phase with the ongoing rhythmic occurrence of slow oscillation up states profoundly enhances the slow oscillation rhythm, phase-c...

Slow oscillations are important for consolidation of memory during sleep, and Alzheimer's disease (AD) patients experience memory disturbances. Thus, we examined slow oscillation activity in an animal model of AD. APP mice exhibit aberrant slow oscillation activity. Aberrant inhibitory activity within the cortical circuit was responsible for slow oscillation dysfunction, since topical applicati...

Slow oscillation is the main brain rhythm observed during deep sleep in mammals. Although several studies have demonstrated its neocortical origin, the extent of the thalamic contribution is still a matter of discussion. Using electrophysiological recordings in vivo on cats and computational modeling, we found that the local thalamic inactivation or the complete isolation of the neocortical sla...

It is well documented that sleep contributes to memory consolidation and it is also accepted that long-term synaptic plasticity plays a critical role in memory formation. The mechanisms of this sleep-dependent memory formation are unclear. Two main hypotheses are proposed. According to the first one, synapses are potentiated during wake; and during sleep they are scaled back to become available...

The striatum plays an important role in linking cortical activity to basal ganglia outputs. Group I metabotropic glutamate receptors (mGluRs) are densely expressed in the medium spiny projection neurons and may be a therapeutic target for Parkinson's disease. The group I mGluRs are known to modulate the intracellular Ca(2+) signaling. To characterize Ca(2+) signaling in striatal cells, spontane...