Robust convergence in pulse coupled oscillators with delays

We show that for pulse coupled oscillators a class of phase response curves with both excitation and inhibition exhibit robust convergence to synchrony on arbitrary aperiodic connected graphs with delays. We describe the basins of convergence and give explicit bounds on the convergence times. These results provide new and more robust methods for synchronization of sensor nets and also have biological implications.Comment: http://prl.aps.org/abstract/PRL/v106/i19/e19410

Amelioration of Proteolipid Protein 139–151-Induced Encephalomyelitis in SJL Mice by Modified Amino Acid Copolymers and Their Mechanisms

Copolymer 1 [Cop1, glatiramer acetate, Copaxone, poly(Y,E,A,K)n] is widely used in the treatment of relapsing/remitting multiple sclerosis in which it reduces the frequency of relapses by ≈30%. In the present study, copolymers with modified amino acid compositions (based on the binding motif of myelin basic protein 85–99 to HLA-DR2) have been developed with the aim of suppressing multiple sclerosis more effectively. The enhanced efficacy of these copolymers in experimental autoimmune encephalomyelitis (EAE) induced in SJL/J mice with proteolipid protein 139–151 was demonstrated by using three protocols: (i) simultaneous administration of autoantigen and copolymer (termed prevention), (ii) pretreatment with copolymers (vaccination), or (iii) administration of copolymers after disease onset (treatment). Strikingly, in the treatment protocol administration of soluble VWAK and FYAK after onset of disease led to stasis of its progression and suppression of histopathological evidence of EAE. The mechanisms by which these effects are achieved have been examined in several types of assays: binding of copolymers to I-As in competition with proteolipid protein 139–151 (blocking), cytokine production by T cells (T helper 2 polarization), and transfer of protection by CD3+ splenocytes or, notably, by copolymer-specific T cell lines (induction of regulatory T cells). The generation of these copolymerspecific regulatory T cells that secrete IL-4 and IL-10 and are independent of the immunizing autoantigen is very prominent among the multiple mechanisms that account for the observed suppressive effect of copolymers in EAE

Observational evidence for cosmological coupling of black holes and its implications for an astrophysical source of dark energy

Observations have found black holes spanning ten orders of magnitude in mass across most of cosmic history. The Kerr black hole solution is however provisional as its behavior at infinity is incompatible with an expanding universe. Black hole models with realistic behavior at infinity predict that the gravitating mass of a black hole can increase with the expansion of the universe independently of accretion or mergers, in a manner that depends on the black hole's interior solution. We test this prediction by considering the growth of supermassive black holes in elliptical galaxies over $0<z\lesssim2.5$. We find evidence for cosmologically coupled mass growth among these black holes, with zero cosmological coupling excluded at 99.98% confidence. The redshift dependence of the mass growth implies that, at $z\lesssim7$, black holes contribute an effectively constant cosmological energy density to Friedmann's equations. The continuity equation then requires that black holes contribute cosmologically as vacuum energy. We further show that black hole production from the cosmic star formation history gives the value of $\Omega_{\Lambda}$ measured by Planck while being consistent with constraints from massive compact halo objects. We thus propose that stellar remnant black holes are the astrophysical origin of dark energy, explaining the onset of accelerating expansion at $z \sim 0.7$.Comment: 10 pages, 3 figures, published in ApJ Letter