We study the capability to learn and to generate long-range, power-law correlated sequences by a fully connected asymmetric network. The focus is set on the ability of neural networks to extract statistical features from a sequence. We demonstrate that the average power-law behavior is learnable, namely, the sequence generated by the trained network obeys the same statistical behavior. The inte...

Full simulations of homogeneous isotropic turbulence containing a homogeneous passive scalar were made at low Reynolds numbers and various Prandtl numbers. The results show that the spectral behavior of the two fields are quite similar; both fields decay as power-law functions of time. However. the decay exponent is quite dependent on both the Reynolds and Prandtl numbers. The decay exponent of...

We explore the idea that the power-law tail in the mass function of protostellar condensations and stars arises from the accretion of ambient cloud material on to a condensation, coupled with a nonuniform (exponential) distribution of accretion lifetimes. This model allows for the generation of power-law distributions in all star-forming regions, even if condensations start with a lognormal mas...

To explore the emergence of power laws in social and economic phenomena, the authors discuss the mechanism whereby reversal quasi-symmetry and Gibrat’s law lead to power laws with different powerlaw exponents. Reversal quasi-symmetry is invariance under the exchange of variables in the joint PDF (probability density function). Gibrat’s law means that the conditional PDF of the exchange rate of ...

We study the dynamics of an intriguing crossover from a chaotic to a power-law state as a function of strain rate within the context of a recently introduced model that reproduces the crossover. While the chaotic regime has a small set of positive Lyapunov exponents, interestingly, the scaling regime has a power-law distribution of null exponents which also exhibits a power law. The slow-manifo...

We study hydrogen-bond dynamics in liquid water at low temperatures using molecular dynamics simulations. We find that bond lifetime (“fast dynamics”) has Arrhenius temperature dependence. We also calculate the bond correlation function and find that the correlation time (“slow dynamics”) shows power-law behavior. This power-law behavior, as well as the decay of the bond correlations, is consis...

purpose the aim of this study was to determine the effect of one night's sleep deprivation on anaerobic performance and reaction time of subjects in the morning of the following day. methods eighteen male college student athletes were studied twice in a balanced, randomized design. subjects were measured for peak power, mean power and reaction time. results the performance showed no significant...

This paper studies the ability of salt diapirs to lift large inclusions of dense rocks (rafts). Dense inclusions will be lifted if salt in the diapir rises faster than the inclusions sink. The power-law rheologies of six different salts, and viscosities estimated for Newtonian salt are used to calculate the settling velocity of these inclusions as a function of their radii and density as well a...

Simulated dark matter profiles are often modelled as a ‘NFW’ density profile rather than a single power law. Recently, attention has turned to the rather rigorous power-law behaviour exhibited by the ‘pseudo phase-space density’ of the dark matter halo, which is defined dimensionally in terms of the local density and velocity dispersion of the dark matter particles. The non-power-law behaviour ...

This study provides an approach to predict the springback phenomenon during post-solidification cooling in a functionally graded hybrid composite cylindrical shell with a transverse isotropic structure. Here, the material properties are given with a general parabolic power-law function. During the theoretical analysis, an appropriate transformation is introduced in the equilibrium equation, whi...