Average-Case Complexity of Shellsort

We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a $p$-pass Shellsort for any incremental sequence is \Omega (pn^{1 + 1/p) for all $p \leq \log n$. Using similar arguments, we analyze the average-case complexity of several other sorting algorithms.Comment: 11 pages. Submitted to ICALP'9

Assessment of diagnostic value of age for meridional amblyopia with Logistic regression and receiver operating characteristic curve

AIM: To assess the diagnostic value of age for meridional amblyopia by Logistic regression and receiver operating characteristic(ROC)curve.<p>METHODS: A total of 1 005 children(1 910 eyes)with unknown ocular abnormalities other than with-the-rule astigmatism(aged 4-8 years)were recruited. Astigmatism >or =1.00D and sphere < or = 3.00D were present in one or both eyes. The difference of sphere between both eyes was less 1.50D. The difference of astigmatism between both eyes was less 1.00D. All astigmatism was calculated by the absolute value. By analyzing age, sex, astigmatism type, diopter of cylinder and diopter of sphere with Logistic regression, two mathematical models were established. Then the diagnostic efficacy of the model was assessed using the ROC curve.<p>RESULTS: The model 1 included 4 parameters(sex, astigmatism type, diopter of cylinder and diopter of sphere). The model 2 included 5 parameters(the 4 parameters of the model 1 adding age). Using Logistic regression, the diopter of cylinder had an influence on the diagnosis of meridional amblyopia in two models. In model 2, age was another influencing factor on the diagnosis of meridional amblyopia. The model 1 area under ROC curve(AUC)was 0.64, and the model 2 was 0.74. The area of model 2 was greater than the model 1. There was statistical difference in the AUC of two models(<i>P</i><0.05).<p>CONCLUSION: Age might be an influential factor on the diagnosis of meridional amblyopia using Logistic regression and ROC curve

Proportionate Recursive Maximum Correntropy Criterion Adaptive Filtering Algorithms and their Performance Analysis

The maximum correntropy criterion (MCC) has been employed to design outlier-robust adaptive filtering algorithms, among which the recursive MCC (RMCC) algorithm is a typical one. Motivated by the success of our recently proposed proportionate recursive least squares (PRLS) algorithm for sparse system identification, we propose to introduce the proportionate updating (PU) mechanism into the RMCC, leading to two sparsity-aware RMCC algorithms: the proportionate recursive MCC (PRMCC) algorithm and the combinational PRMCC (CPRMCC) algorithm. The CPRMCC is implemented as an adaptive convex combination of two PRMCC filters. For PRMCC, its stability condition and mean-square performance were analyzed. Based on the analysis, optimal parameter selection in nonstationary environments was obtained. Performance study of CPRMCC was also provided and showed that the CPRMCC performs at least as well as the better component PRMCC filter in steady state. Numerical simulations of sparse system identification corroborate the advantage of proposed algorithms as well as the validity of theoretical analysis

Back-action Induced Non-equilibrium Effect in Electron Charge Counting Statistics

We report our study of the real-time charge counting statistics measured by a quantum point contact (QPC) coupled to a single quantum dot (QD) under different back-action strength. By tuning the QD-QPC coupling or QPC bias, we controlled the QPC back-action which drives the QD electrons out of thermal equilibrium. The random telegraph signal (RTS) statistics showed strong and tunable non-thermal-equilibrium saturation effect, which can be quantitatively characterized as a back-action induced tunneling out rate. We found that the QD-QPC coupling and QPC bias voltage played different roles on the back-action strength and cut-off energy.Comment: 4 pages, 4 figures, 1 tabl