The pedunculopontine nucleus is a part of the reticular activating system, and is active during waking and REM sleep. Previous results showed that all PPN cells tested fired maximally at gamma frequencies when depolarized. This intrinsic membrane property was shown to be mediated by high-threshold N- and P/Q-type Ca(2+) channels. Recent studies show that the PPN contains three independent popul...

Bayesian statistical inference is a powerful tool for model-data comparisons and extractions of physical parameters that are often unknown functions system variables. Existing analyses rely on explicit parametrizations the function. It can introduce long-range correlations impose fictitious constraints in regions variable space not probed by experimental data. We develop an information field (I...

let $gamma(s_n)$ be the minimum number of proper subgroups‎ ‎$h_i, i=1‎, ‎dots‎, ‎l $ of the symmetric group $s_n$ such that each element in $s_n$‎ ‎lies in some conjugate of one of the $h_i.$ in this paper we‎ ‎conjecture that $$gamma(s_n)=frac{n}{2}left(1-frac{1}{p_1}right)‎ ‎left(1-frac{1}{p_2}right)+2,$$ where $p_1,p_2$ are the two smallest primes‎ ‎in the factorization of $ninmathbb{n}$ an...

We derive an explicit c-function expansion of a basic hypergeometric function associated to root systems. The basic hypergeometric function in question was constructed as explicit series expansion in symmetric Macdonald polynomials by Cherednik in case the associated twisted affine root system is reduced. Its construction was extended to the nonreduced case by the author. It is a meromorphic We...

Using a recently proposed gauge covariant diagonalization of $\pi a_1$-mixing we show that the low energy theorem $F^{\pi}=e f_\pi^2 F^{3\pi}$ current algebra, relating anomalous form factor $F_{\gamma \to \pi^+\pi^0\pi^-} = and neutral pion $F_{\pi^0 \gamma\gamma}=F^\pi$, is fulfilled in framework Nambu-Jona-Lasinio (NJL) model, solving long standing problem encountered extension including vec...

Let $$S\subset\mathbb R^n$$ be a nonempty set. Given $$d\in [0,n)$$ and cube $$\overline{Q}\subset\mathbb with side length $$l=l(\overline{Q}) \in (0,1]$$ , we show that if the $$d$$ -Hausdorff content $$\mathcal H^d_{\infty}(\overline{Q}\cap S)$$ of set $$\overline{Q}\cap S$$ satisfies inequality S)<\overline{\lambda}l^{d}$$ for some $$\overline{\lambda}\in (0,1)$$ then $$\overline{Q}\setminus...