All functions are (locally) ss-harmonic (up to a small error) - and applications

The classical and the fractional Laplacians exhibit a number of similarities, but also some rather striking, and sometimes surprising, structural differences. A quite important example of these differences is that any function (regardless of its shape) can be locally approximated by functions with locally vanishing fractional Laplacian, as it was recently proved by Serena Dipierro, Ovidiu Savin and myself. This informal note is an exposition of this result and of some of its consequences

Cumulative signal transmission in nonlinear reaction-diffusion networks

Quantifying signal transmission in biochemical systems is key to uncover the mechanisms that cells use to control their responses to environmental stimuli. In this work we use the time-integral of chemical species as a measure of a network’s ability to cumulatively transmit signals encoded in spatiotemporal concentrations. We identify a class of nonlinear reaction-diffusion networks in which the time-integrals of some species can be computed analytically. The derived time-integrals do not require knowledge of the solution of the reaction-diffusion equation, and we provide a simple graphical test to check if a given network belongs to the proposed class. The formulae for the time-integrals reveal how the kinetic parameters shape signal transmission in a network under spatiotemporal stimuli. We use these to show that a canonical complex-formation mechanism behaves as a spatial low-pass filter, the bandwidth of which is inversely proportional to the diffusion length of the ligand

Delayed backbending in the pi h(9/2) band of Ir-187

High-spin states of Ir-187 have been populated in the Yb-176(N-15,4n) reaction and measured with the YRAST Ball spectrometer. The pih(9/2) rotational band has been extended beyond the first alignment crossing, which was found at rotational frequency (h) over bar omega(c) approximate to0.39 MeV . Two different scenarios for describing this crossing are considered: the alignment of an h(9/2) proton or i(13/2) neutron pair and it is concluded that a proton band crossing is more likely. A systematic study of the rotational alignment crossings in the pih(9/2) bands in the N=104,106,108 isotopes of Ta-73,Re-75,Ir-77, and Au-79 is presented