The theory of neuronal firing in Stein’s model is outlined as well as the corresponding theory for a diffusion approximation which has the same first two infinitesimal moments. The diffusion approximation is derived from the discontinuous model in the limit of large input frequencies and small postsynaptic potential amplitudes. A comparison of the calculated mean interspike intervals is made fo...

The satisfiability threshold for constraint satisfaction problems is that value of the ratio of constraints (or clauses) to variables, above which the probability that a random instance of the problem has a solution is zero in the large system limit. Two different approaches to obtaining this threshold have been discussed in the literature using first or second-moment methods which give rigorou...

We formulate a theory for shot noise in quantum nanoelectromechanical systems. As a specific example, the theory is applied to a quantum shuttle, and the zero-frequency noise, measured by the Fano factor F, is computed. F reaches very low values (F approximately 10(-2)) in the shuttling regime even in the quantum limit, confirming that shuttling is universally a low noise phenomenon. In approac...

Epidemiological investigations of health effects related to chronic low-level exposures or other circumstances often face the difficult task of dealing with levels of biomarkers that are hard to detect and/or quantify. In these cases instrumentation may not adequately measure biomarker levels. Reasons include a failure of instruments to detect levels below a certain value or, alternatively, int...

Exposure to metals at workplaces is well known and in many cases occupational studies led to an adoption of limit values. For airborne concentrations of substances as metals refer to the "Maximaleo Arbeitsplatz-Konzentration" (MAK) in Germany or the "Threshold Limit Value" (TLV) in USA. Biological monitoring consists of an assessment of overall exposure to chemicals at the workplace and in the ...

In this work we discuss a parameter $\sigma$ on weighted $k$-element multisets of $[n]= \{1,\dots ,n\}$. The sums $k$-multisets are related to $k$-subsets, $k$-multisets, as well special instances truncated interpolated multiple zeta values. We study properties using symbolic combinatorics. (re)derive and extend certain identities for $\zeta^{t}_n(\{m\}_k)$. Moreover, introduce random variables...