The "funny" current (I(f)) inhibition by ivabradine at membrane potentials encompassing spontaneous depolarization in pacemaker cells

Recent clinical trials have shown that ivabradine (IVA), a drug that inhibits the funny current (I(f)) in isolated sinoatrial nodal cells (SANC), decreases heart rate and reduces morbidity and mortality in patients with cardiovascular diseases. While IVA inhibits I(f), this effect has been reported at essentially unphysiological voltages, i.e., those more negative than the spontaneous diastolic depolarization (DD) between action potentials (APs). We tested the relative potency of IVA to block I(f) over a wide range of membrane potentials, including those that encompass DD governing to the SANC spontaneous firing rate. A clinically relevant IVA concentration of 3 μM to single, isolated rabbit SANC slowed the spontaneous AP firing rate by 15%. During voltage clamp the maximal I(f) was 18 ± 3 pA/pF (at -120 mV) and the maximal I(f) reduction by IVA was 60 ± 8% observed at -92 ± 4 mV. At the maximal diastolic depolarization (~-60 mV) I(f) amplitude was only -2.9 ± 0.4 pA/pF, and was reduced by only 41 ± 6% by IVA. Thus, I(f) amplitude and its inhibition by IVA at physiologically relevant membrane potentials are substantially less than that at unphysiological (hyperpolarized) membrane potentials. This novel finding more accurately describes how IVA affects SANC function and is of direct relevance to numerical modeling of SANC automaticity.     

One‐Bit Compressed Sensing by Linear Programming

We give the first computationally tractable and almost optimal solution to the problem of one‐bit compressed sensing, showing how to accurately recover an s‐sparse vector \input amssym $x \in {\Bbb R}^n$ from the signs of $O(s \log^2(n/s))$ random linear measurements of x. The recovery is achieved by a simple linear program. This result extends to approximately sparse vectors x. Our result is universal in the sense that with high probability, one measurement scheme will successfully recover all sparse vectors simultaneously. The argument is based on solving an equivalent geometric problem on random hyperplane tessellations.     

Mass differences in baryon isomultiplets with Jp=1+ /2

The mass differences in baryon isomultiplets with J^p=1⁺ /2 were calculated with allowance for the contribution of weak interactions to the Okubo Reggeized tadpole models and violated isotopic Lipmanov symmetry.Translated from Izvestiya VUZ. Fizika, Vol. 11, No. 8, pp. 100–105, August, 1968.In conclusion the author expresses his deep appreciation to A. S. Shekhter and his colleagues at the Department of Theoretical Physics at Saratov State University for their discussion and to N. G. Fadeev (Joint Institute for Nuclear Research, Dubna) for his help in performing the numerical calculations.     

Higher dimensional Euclidean and hyperbolic matrix spaces

Journal d'Analyse Mathématique -     

Noise induced complexity: from subthreshold oscillations to spiking in coupled excitable systems

We study the stochastic dynamics of an ensemble of N globally coupled excitable elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is disturbed by independent Gaussian noise. In simulations of the Langevin dynamics we characterize the collective behavior of the ensemble in terms of its mean field and show that with the increase of noise the mean field displays a transition from a steady equilibrium to global oscillations and then, for sufficiently large noise, back to another equilibrium. In the course of this transition diverse regimes of collective dynamics ranging from periodic subthreshold oscillations to large-amplitude oscillations and chaos are observed. In order to understand the details and mechanisms of these noise-induced dynamics we consider the thermodynamic limit N-->infinity of the ensemble, and derive the cumulant expansion describing temporal evolution of the mean field fluctuations. In Gaussian approximation this allows us to perform the bifurcation analysis; its results are in good qualitative agreement with dynamical scenarios observed in the stochastic simulations of large ensembles.     

Separating convex sets in the plane

Given a setA inR ² and a collectionS of plane sets, we say that a lineL separatesA fromS ifA is contained in one of the closed half-planes defined byL, while every set inS is contained in the complementary closed half-plane.We prove that, for any collectionF ofn disjoint disks inR ², there is a lineL that separates a disk inF from a subcollection ofF with at least (n–7)/4 disks. We produce configurationsH _n andG _n , withn and 2n disks, respectively, such that no pair of disks inH _n can be simultaneously separated from any set with more than one disk ofH _n , and no disk inG _n can be separated from any subset ofG _n with more thann disks.We also present a setJ _m with 3m line segments inR ², such that no segment inJ _m can be separated from a subset ofJ _m with more thanm+1 elements. This disproves a conjecture by N. Alonet al. Finally we show that ifF is a set ofn disjoint line segments in the plane such that they can be extended to be disjoint semilines, then there is a lineL that separates one of the segments from at least n/3+1 elements ofF.