A Robust Regression-Based Stock Exchange Forecasting and Determination of Correlation between Stock Markets

Knowledge-based decision support systems for financial management are an important part of investment plans. Investors are avoiding investing in traditional investment areas such as banks due to low return on investment. The stock exchange is one of the major areas for investment presently. Various non-linear and complex factors affect the stock exchange. A robust stock exchange forecasting system remains an important need. From this line of research, we evaluate the performance of a regression-based model to check the robustness over large datasets. We also evaluate the effect of top stock exchange markets on each other. We evaluate our proposed model on the top 4 stock exchanges—New York, London, NASDAQ and Karachi stock exchange. We also evaluate our model on the top 3 companies—Apple, Microsoft, and Google. A huge (Big Data) historical data is gathered from Yahoo finance consisting of 20 years. Such huge data creates a Big Data problem. The performance of our system is evaluated on a 1-step, 6-step, and 12-step forecast. The experiments show that the proposed system produces excellent results. The results are presented in terms of Mean Absolute Error (MAE) and Root Mean Square Error (RMSE)

Detection-Loophole-Free Test of Quantum Nonlocality, and Applications

We present a source of entangled photons that violates a Bell inequality free of the "fair-sampling" assumption, by over 7 standard deviations. This violation is the first experiment with photons to close the detection loophole, and we demonstrate enough "efficiency" overhead to eventually perform a fully loophole-free test of local realism. The entanglement quality is verified by maximally violating additional Bell tests, testing the upper limit of quantum correlations. Finally, we use the source to generate secure private quantum random numbers at rates over 4 orders of magnitude beyond previous experiments.Comment: Main text: 5 pages, 2 figures, 1 table. Supplementary Information: 7 pages, 2 figure

Toda systems in closed string tachyon condensation

We consider $tt^*$ equations appearing in the study of localized tachyon condensations. They are described by various Toda system when we consider the condensation by the lowest tachyon corresponding to the monomial $xy$. The tachyon potential is calculated as a solution to these equations. The Toda system appearing in the deformation of \C^2/\Z_n by $xy$ is identical to that of $D_n$ singularity deformed by $x$. For \C^3/\Z_n with $xyz$ deformation, we find only generic non-simple form, similar to the case appearing in \C/\Z_5\to \C/\Z_3 and we discuss the difficulties in these cases.Comment: 20 pages, no figur