Online Updating of Statistical Inference in the Big Data Setting

We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop iterative estimating algorithms and statistical inferences for linear models and estimating equations that update as new data arrive. These algorithms are computationally efficient, minimally storage-intensive, and allow for possible rank deficiencies in the subset design matrices due to rare-event covariates. Within the linear model setting, the proposed online-updating framework leads to predictive residual tests that can be used to assess the goodness-of-fit of the hypothesized model. We also propose a new online-updating estimator under the estimating equation setting. Theoretical properties of the goodness-of-fit tests and proposed estimators are examined in detail. In simulation studies and real data applications, our estimator compares favorably with competing approaches under the estimating equation setting.Comment: Submitted to Technometric

A thermodynamically consistent quasi-particle model without density-dependent infinity of the vacuum zero point energy

In this paper, we generalize the improved quasi-particle model proposed in J. Cao et al., [ Phys. Lett. B {\bf711}, 65 (2012)] from finite temperature and zero chemical potential to the case of finite chemical potential and zero temperature, and calculate the equation of state (EOS) for (2+1) flavor Quantum Chromodynamics (QCD) at zero temperature and high density. We first calculate the partition function at finite temperature and chemical potential, then go to the limit $T=0$ and obtain the equation of state (EOS) for cold and dense QCD, which is important for the study of neutron stars. Furthermore, we use this EOS to calculate the quark-number density, the energy density, the quark-number susceptibility and the speed of sound at zero temperature and finite chemical potential and compare our results with the corresponding ones in the existing literature

An optical fiber tip micrograting thermometer

An ~12 µm long Bragg grating was engraved in an ~5 µm diameter optical fiber tip by focused ion beam (FIB) milling. An ~10-dB extinction was achieved at 1570 nm with only 11 indentations. The grating was used for temperature sensing, and it exhibited a temperature sensitivity of ~22 pm/°C

Finite Temperature Schr\"{o}dinger Equation

We know Schr\"{o}dinger equation describes the dynamics of quantum systems, which don't include temperature. In this paper, we propose finite temperature Schr\"{o}dinger equation, which can describe the quantum systems in an arbitrary temperature. When the temperature T=0, it become Shr\"{o}dinger equation.Comment: 8 page

Quantum theory of light diffraction

At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the approach of relativistic quantum theory. We find that the slit length, slit width, slit thickness and wave-length of light have affected to the diffraction intensity and form of diffraction pattern. However, the effect of slit thickness on the diffraction pattern can not be explained by wave-optical approach, and it can be explained in quantum theory. We compare the theoretical results with single and multiple slits experiment data, and find the theoretical results are accordance with the experiment data. Otherwise, we give some theory prediction. We think all the new prediction will be tested by the light diffraction experiment.Comment: 10 page