The literature on statistical learning for time series assumes the asymptotic independence or "mixing" of the data-generating process. These mixing assumptions are never tested, and there are no methods for estimating mixing rates from data. We give an estimator for the beta-mixing rate based on a single stationary sample path and show it is L1-risk consistent.

The literature on statistical learning for time series assumes the asymptotic independence or “mixing’ of the data-generating process. These mixing assumptions are never tested, nor are there methods for estimating mixing rates from data. We give an estimator for the β-mixing rate based on a single stationary sample path and show it is L1-risk consistent.

Abstract We study the rates of estimation of finite mixing distributions, that is, the parameters of the mixture. We prove that under some regularity and strong identifiability conditions, around a given mixing distribution with m0 components, the optimal local minimax rate of estimation of a mixing distribution with m components is n−1/(4(m−m0)+2). This corrects a previous paper by Chen (1995)...

We report a preliminary result for D-D mixing and the doubly Cabibbo suppressed decay rate RD based on an analysis of D 0 → Kπ decays from 57.1 fb of data collected at or just below the Υ (4S) resonance with the BABAR detector at the PEP-II collider. We set 95% confidence limits for the mixing parameters x 2 and y and find that our result is compatible with no mixing and no CP violation. In the...

Bioprocess scale-up is a fundamental component of process development in the biotechnology industry. When scaling up a mammalian cell culture process, it is important to consider factors such as mixing time, oxygen transfer, and carbon dioxide removal. In this study, cell-free mixing studies were performed in production scale 5,000-L bioreactors to evaluate scale-up issues. Using the current bi...

Microelectroosmotic flow is usually restricted to low Reynolds number regime, and mixing in these microfluidic systems becomes problematic due to the negligible inertial effects. To gain an improved understanding of mixing enhancement in microchannels patterned with heterogeneous surface charge, the lattice Boltzmann method has been employed to obtain the electric potential distribution in the ...

We introduce a general-purpose method for optimising the mixing rate of advective fluid flows. An existing velocity field is perturbed in a C1 neighborhood to maximize the mixing rate for flows generated by velocity fields in this neighborhood. Our numerical approach is based on the infinitesimal generator of the flow and is solved by standard linear programming methods. The perturbed flow may ...

This article demonstrates that the rate of mixing can regulate the rate and outcome of both biological and nonbiological autocatalytic reaction systems that display a threshold response to the concentration of an activator. Plug-based microfluidics was used to control the timing of reactions, the rate of mixing, and surface chemistry in blood clotting and its chemical model. Initiation of clott...

a comprehensive mathematical model based on the discrete particle model and computational fluid dynamics was utilized to investigate mixing and segregation of particles in fluidized beds at high pressure. to quantify the extent of mixing in the bed, the lacey mixing index was used. simulations were carried out with different mass fractions of small particles at various pressures ranging from 1 ...

a numerical model for simulating residence time distribution (rtd) of turbulent flows in helical static mixers is proposed and developed to improve the understanding of static mixers. the results of this model is presented in terms of different volumetric flow rate to illustrate the complicated flow patterns that drive the mixing process in helical static mixers. the computed results are also u...