49 research outputs found
Moments of unconditional logarithmically concave vectors
We derive two-sided bounds for moments of linear combinations of coordinates
od unconditional log-concave vectors. We also investigate how well moments of
such combinations may be approximated by moments of Gaussian random variables.Comment: 14 page
Exponential and moment inequalities for U-statistics
A Bernstein-type exponential inequality for (generalized) canonical
U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen
inequalities for sums of independent random variables are extended to
(generalized) U-statistics of any order whose kernels are either nonnegative or
canonicalComment: 22 page
Shaping bursting by electrical coupling and noise
Gap-junctional coupling is an important way of communication between neurons
and other excitable cells. Strong electrical coupling synchronizes activity
across cell ensembles. Surprisingly, in the presence of noise synchronous
oscillations generated by an electrically coupled network may differ
qualitatively from the oscillations produced by uncoupled individual cells
forming the network. A prominent example of such behavior is the synchronized
bursting in islets of Langerhans formed by pancreatic \beta-cells, which in
isolation are known to exhibit irregular spiking. At the heart of this
intriguing phenomenon lies denoising, a remarkable ability of electrical
coupling to diminish the effects of noise acting on individual cells.
In this paper, we derive quantitative estimates characterizing denoising in
electrically coupled networks of conductance-based models of square wave
bursting cells. Our analysis reveals the interplay of the intrinsic properties
of the individual cells and network topology and their respective contributions
to this important effect. In particular, we show that networks on graphs with
large algebraic connectivity or small total effective resistance are better
equipped for implementing denoising. As a by-product of the analysis of
denoising, we analytically estimate the rate with which trajectories converge
to the synchronization subspace and the stability of the latter to random
perturbations. These estimates reveal the role of the network topology in
synchronization. The analysis is complemented by numerical simulations of
electrically coupled conductance-based networks. Taken together, these results
explain the mechanisms underlying synchronization and denoising in an important
class of biological models
On limit theorems for continued fractions
It is shown that for sums of functionals of digits in continued fraction
expansion the Kolmogorov-Feller weak laws of large numbers and the
Khinchine-L\'evy-Feller-Raikov characterization of the domain of attraction of
the normal law hold.Comment: 16 page
On a conjecture of J. Zinn
The article contains no abstrac
Moment inequalities for sums of certain independent symmetric random variables
This paper gives upper and lower bounds for moments of sums of independent random variables which satisfy the condition , where are concave functions. As a consequence we obtain precise information about the tail probabilities of linear combinations of independent random variables for which for some fixed 0 < r ≤ 1. This complements work of Gluskin and Kwapień who have done the same for convex functions N