A Comparison Of Usual t-Test Statistic and Modified t-Test Statistics on Skewed Distribution Functions

When the sample size n is small, the random variable T= √n(\overline{X} – μ)/S is said to follow a central t distribution with degrees of freedom (n – 1), where \overline{X} is the sample mean and S is the sample standard deviation, provided that the data X ~ N (μ, σ2). The random variable T can be used as a test statistic to hypothesize the population mean μ. Some argue that the t-test statistic is robust against the normality of the distribution and claim that the normality assumption is not necessary. In this article we will use simulation to study whether the t-test is really robust if the population distribution is not normally distributed. In particular, we will study how the skewness of a probability distribution will affect the confidence interval as well as the t-test statistic

Optical studies of carrier and phonon dynamics in Ga_{1-x}Mn_{x}As

We present a time-resolved optical study of the dynamics of carriers and phonons in Ga_{1-x}Mn_{x}As layers for a series of Mn and hole concentrations. While band filling is the dominant effect in transient optical absorption in low-temperature-grown (LT) GaAs, band gap renormalization effects become important with increasing Mn concentration in Ga_{1-x}Mn_{x}As, as inferred from the sign of the absorption change. We also report direct observation on lattice vibrations in Ga1-xMnxAs layers via reflective electro-optic sampling technique. The data show increasingly fast dephasing of LO phonon oscillations for samples with increasing Mn and hole concentration, which can be understood in term of phonon scattering by the holes.Comment: 13 pages, 3 figures replaced Fig.1 after finding a mistake in previous versio

Diversity and Adaptation in Large Population Games

We consider a version of large population games whose players compete for resources using strategies with adaptable preferences. The system efficiency is measured by the variance of the decisions. In the regime where the system can be plagued by the maladaptive behavior of the players, we find that diversity among the players improves the system efficiency, though it slows the convergence to the steady state. Diversity causes a mild spread of resources at the transient state, but reduces the uneven distribution of resources in the steady state.Comment: 8 pages, 3 figure

Observation of the single-electron regime in a highly tunable silicon quantum dot

We report on low-temperature electronic transport measurements of a silicon metal-oxide-semiconductor quantum dot, with independent gate control of electron densities in the leads and the quantum dot island. This architecture allows the dot energy levels to be probed without affecting the electron density in the leads, and vice versa. Appropriate gate biasing enables the dot occupancy to be reduced to the single-electron level, as evidenced by magnetospectroscopy measurements of the ground state of the first two charge transitions. Independent gate control of the electron reservoirs also enables discrimination between excited states of the dot and density of states modulations in the leads.Comment: 4 pages, 3 figures, accepted for Applied Physics Letter

Measurement of Spin Polarization by Andreev Reflection in Ferromagnetic In1-xMnxSb Epilayers

We carried out Point Contact Andreev Reflection (PCAR) spin spectroscopy measurements on epitaxially-grown ferromagnetic In1-xMnxSb epilayers with a Curie temperature of ~9K. The spin sensitivity of PCAR in this material was demonstrated by parallel control studies on its non-magnetic analog, In1-yBeySb. We found the conductance curves of the Sn point contacts with In1-yBeySb to be fairly conventional, with the possible presence of proximity-induced superconductivity effects at the lowest temperatures. The experimental Z-values of interfacial scattering agreed well with the estimates based on the Fermi velocity mismatch between the semiconductor and the superconductor. These measurements provided control data for subsequent PCAR measurements on ferromagnetic In1-xMnxSb, which indicated spin polarization in In1-xMnxSb to be 52 +- 3%