Darwin observed that multiple, lowly organized, rudimentary, or exaggerated structures show increased relative variability. However, the cellular basis for these laws has never been investigated. Some animals, such as the nematode Caenorhabditis elegans, are famous for having organs that possess the same number of cells in all individuals, a property known as eutely. But for most multicellular ...

4 Power-Laws of the Internet 8 4.1 Rank power-law . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.2 Degree power-law . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.3 Eigen power-law . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.4 The doubts and settlement . . . . . . . . . . . . . . . . . . . . . 12 4.5 Network analysis before power-laws . . . . . . . . . . ...

We analytically calculate the secular precession of the pericenter of a test particle orbiting a central body surrounded by a continuous distribution of Dark Matter (DM) by using some commonly adopted spherically symmetric density profiles for it. We obtain exact expressions without resorting to a-priori simplifying assumptions on the orbital geometry of the test particle. Our formulas allow us...

I propose a new measure of common, time-varying tail risk for large cross sections of stock returns. Stock return tails are described by a power law in which the power law exponent is allowed to transition smoothly through time as a function of recent data. It is motivated by asset pricing theory and is estimable via quasi-maximum likelihood. Estimates indicate substantial time variation in sto...

Power law cumulative number-size distributions are widely used to describe the scaling properties of data sets and to establish scale invariance. We derive the relationships between the scaling exponents of non-cumulative and cumulative number-size distributions for linearly binned and logarithmically binned data. Cumulative number-size distributions for data sets of many natural phenomena exhi...

Abstract We show that some gapped quantum many-body systems have a ground state degeneracy is stable to long-range (e.g. power-law) perturbations, in the sense any energy splitting induced by such perturbations exponentially small system size. More specifically, we consider an Ising symmetry-breaking Hamiltonian with several exactly degenerate states and gap, then perturb symmetric interactions...

The combined effect of non-Newtonian rheology and irreversible boundary reaction on dispersion in a Herschel-Bulkley fluid through a conduit (pipe/channel) is studied by using generalized dispersion model. The study explains the development of dispersive transport following the injection of a tracer in terms of three effective transport coefficients namely exchange, convective and dispersion co...