Statistical theory of relaxation of high energy electrons in quantum Hall edge states

We investigate theoretically the energy exchange between electrons of two co-propagating, out-of-equilibrium edge states with opposite spin polarization in the integer quantum Hall regime. A quantum dot tunnel-coupled to one of the edge states locally injects electrons at high energy. Thereby a narrow peak in the energy distribution is created at high energy above the Fermi level. A second downstream quantum dot performs an energy resolved measurement of the electronic distribution function. By varying the distance between the two dots, we are able to follow every step of the energy exchange and relaxation between the edge states - even analytically under certain conditions. In the absence of translational invariance along the edge, e.g. due to the presence of disorder, energy can be exchanged by non-momentum conserving two-particle collisions. For weakly broken translational invariance, we show that the relaxation is described by coupled Fokker-Planck equations. From these we find that relaxation of the injected electrons can be understood statistically as a generalized drift-diffusion process in energy space for which we determine the drift-velocity and the dynamical diffusion parameter. Finally, we provide a physically appealing picture in terms of individual edge state heating as a result of the relaxation of the injected electrons.Comment: 13 pages plus 6 appendices, 8 figures. Supplemental Material can be found on http://quantumtheory.physik.unibas.ch/people/nigg/supp_mat.htm

Interaction induced edge channel equilibration

The electronic distribution functions of two Coulomb coupled chiral edge states forming a quasi-1D system with broken translation invariance are found using the equation of motion approach. We find that relaxation and thereby energy exchange between the two edge states is determined by the shot noise of the edge states generated at a quantum point contact (QPC). In close vicinity to the QPC, we derive analytic expressions for the distribution functions. We further give an iterative procedure with which we can compute numerically the distribution functions arbitrarily far away from the QPC. Our results are compared with recent experiments of Le Sueur et al..Comment: 10 pages, 7 figures, includes 5 pages of supplementary informatio

Health Knowledge Assessment of College Freshmen Educated in South Dakota K-12

Nothing in life is so taken for granted when possessed, or so missed when lost, as is health. Therefore, it is essential to possess basic facts if each individual is to take advantage of medical science advances, protect himself against quackery, and obtain an optimum level of health. Health education is recognized by leading educators as of vital importance in educating our youth, but health education has not established itself in a way comparable to other subjects. Kilander noted this fact as early as 1937, and yet, 46 years later, South Dakota\u27s health education programs have not been established. Many South Dakota elementary and secondary schools offer little health education. In 1976, South Dakota was one of only three states which did not require health education, and presently, in 1983, still has no legislative requirement. Previous studies have shown that misconceptions and superstitions in a wide variety of health areas were prevalent among investigated populations regardless of their educational level. With health knowledge growing at an unprecedented rate, health educators need to improve the extent and methods of disseminating that knowledge to overcome these misconceptions and superstitions, while introducing newly discovered information. Individuals must have this factual base for their health attitudes and health behaviors. However, for healthful actions to be followed, students need this essential base of scientific knowledge, for they cannot practice what they do not know. Knowledge without action is sterile, and action without knowledge is blind . The purpose of the study was to determine the level of health knowledge of selected college freshmen educated in South Dakota. The subjects attended grades K-12 in only one school district

Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise

This paper shows how to use realised kernels to carry out efficient feasible inference on the ex-post variation of underlying equity prices in the presence of simple models of market frictions. The issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed Gaussian limit theorems. The weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem. Realised kernels can also be selected to (i) be analysed using endogenously spaced data such as that in databases on transactions, (ii) allow for market frictions which are endogenous, (iii) allow for temporally dependent noise. The finite sample performance of our estimators is studied using simulation, while empirical work illustrates their use in practice.Bipower variation, Long run variance estimator, Market frictions, Quadratic variation, Realised variance

Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise

This paper shows how to use realised kernels to carry out efficient feasible inference on the ex-post variation of underlying equity prices in the presence of simple models of market frictions. The issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed Gaussian limit theorems. The weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem. Realised kernels can also be selected to (i) be analysed using endogenously spaced data such as that in databases on transactions, (ii) allow for market frictions which are endogenous, (iii) allow for temporally dependent noise. The finite sample performance of our estimators is studied using simulation, while empirical work illustrates their use in practice.

Subsampling realised kernels

In a recent paper we have introduced the class of realised kernel estimators of the increments of quadratic variation in the presence of noise. We showed that this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend our analysis, looking at the class of subsampled realised kernels and we derive the limit theory for this class of estimators. We find that subsampling is highly advantageous for estimators based on discontinuous kernels, such as the truncated kernel. For kinked kernels, such as the Bartlett kernel, we show that subsampling is impotent, in the sense that subsampling has no effect on the asymptotic distribution. Perhaps surprisingly, for the efficient smooth kernels, such as the Parzen kernel, we show that subsampling is harmful as it increases the asymptotic variance. We also study the performance of subsampled realised kernels in simulations and in empirical work.Bipower variation; Long run variance estimator; Market frictions; Quadratic variation; Realised kernel; Realised variance; Subsampling.

Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise

We consider kernel-based estimators of integrated variances in the presence of independent market microstructure effects. We derive the bias and variance properties for all regular kernel-based estimators and derive a lower bound for their asymptotic variance. Further we show that the subsample-based estimator is closely related to a Bartlett-type kernel estimator. The small difference between the two estimators due to end effects, turns out to be key for the consistency of the subsampling estimator. This observation leads us to a modified class of kernel-based estimators, which are also consistent. We study the efficiency of our new kernel-based procedure. We show that optimal modified kernel-based estimator converges to the integrated variance at the optimal rate, m^1/4, where m is the number of intraday returns.

Multivariate Realised Kernels: Consistent Positive Semi-Definite Estimators of the Covariation of Equity Prices with Noise and Non-Synchronous Trading

We propose a multivariate realised kernel to estimate the ex-post covariation of log-prices. We show this new consistent estimator is guaranteed to be positive semi-definite and is robust to measurement noise of certain types and can also handle non-synchronous trading. It is the first estimator which has these three properties which are all essential for empirical work in this area. We derive the large sample asymptotics of this estimator and assess its accuracy using a Monte Carlo study. We implement the estimator on some US equity data, comparing our results to previous work which has used returns measured over 5 or 10 minutes intervals. We show the new estimator is substantially more precise.HAC estimator, Long run variance estimator, Market frictions, Quadratic variation, Realised variance

Soybeans as a home-grown supplement for dairy cows

Soybeans, grown on the farm, give promise of providing many dairymen with a valuable protein supplement for their dairy herds which will make them independent of the purchase of high-priced protein feeds. Investigations at the Iowa Agricultural Experiment Station show that soybeans make a palatable dairy feed, that they give good results in milk production when fed in place of other protein supplements, and that pound for pound they are a third more valuable than oilmeal, with which direct comparison was made. A home-grown supplement of that kind would be especially valuable to Iowa dairy farms. These farms easily produce all of the roughages needed for the herds in both winter and summer, such as ensilage, clover, alfalfa hay and soiling crops. It is also relatively easy for them to provide the greater portion of the grain ration, as the home-grown corn and oats should form the basis of the concentrates fed. These two feeds, however, are relatively low in protein and so are the roughages, with the exception of the legume hays. It is necessary, therefore, to secure additional concentrates which will provide the extra protein needed, especially in the ration of heavy producing cows. This is one of the main problems of dairy farming today