A quantum phase transition may occur in the ground state of a system at zero temperature when a controlling field or interaction is varied. The resulting quantum fluctuations which trigger the transition produce scaling behaviour of various observables, governed by universal critical exponents. A particularly interesting class of such transitions appear in systems with quantum impurities where ...

Linear compartment models arise in many fields, such as systems biology and pharmacokinetics. These models describe the transport of a given material through a set of compartments, and can be represented by a directed graph. The parameters of a linear compartment model correspond to the transport rates between different compartments, and these are usually estimated by performing an experiment. ...

A two parameter family of multiresolution analyses of L 2 (R 2) each generated by three orthogonal, continuous, compactly supported scaling functions is constructed using fractal interpolation surfaces. The scaling functions remain orthogonal when restricted to certain triangles making them useful for problems with bounded domains. In the usual construction of a wavelet using a multiresolution ...

This work provides a comprehensive scaling law and performance analysis for multi-user massive MIMO relay networks, where the relay is equipped with massive antennas and uses MRC/MRT for lowcomplexity processing. CSI error is considered. First, a sum-rate lower bound is derived which manifests the effect of system parameters including the numbers of relay antennas and users, the CSI quality, an...

We study the dynamical response of a system to a sudden change of the tuning parameter starting or ending at the quantum critical point. In particular, we analyze the scaling of the excitation probability, number of excited quasiparticles, heat and entropy with the quench amplitude, and the system size. We extend the analysis to quenches with arbitrary power law dependence on time of the tuning...

Directional gap probability or gap fraction is a basic parameter in the optical remote sensing modeling. Although some approaches have been proposed to estimate this gap probability from remotely sensed measurements, few efforts have been made to investigate the scaling effects of this parameter. This paper analyzes the scaling effect through aggregating the high-resolution directional gap prob...

We study hyperbolic maps depending on a parameter ε. Each of them has an invariant Cantor set. As ε tends to zero, the map approaches the boundary of hyperbolicity. We analyze the asymptotics of scaling function of the invariant Cantor set as ε goes to zero. We show that there is a limiting scaling function of the limiting map and this scaling function has dense jump discontinuities because the...

Scaling properties of an interface representation of the critical contact process are studied in dimensions 1 3. Simulations confirm the scaling relation βW = 1−θ between the interface-width growth exponent βW and the exponent θ governing the decay of the order parameter. A scaling property of the height distribution, which serves as the basis for this relation, is also verified. The height-hei...

We studied heart rate variability in rats by power scaling spectral analysis (PSSA), autoregressive modeling (AR), and detrended fluctuation analysis (DFA), assessed stability by coefficient of variation between consecutive 6-h epochs, and then compared cross-correlation among techniques. These same parameters were checked from baseline conditions through acute and chronic disease states (strep...