The Beylkin-Cramer Summation Rule and A New Fast Algorithm of Cosmic Statistics for Large Data Sets

Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm that enable us to explore the high order statistics efficiently in large data sets. Central to this technique is to make decomposition both of fields and operators within the framework of multi-resolution analysis (MRA), and realize theirs discrete representations. Accordingly, a homogenous point process could be equivalently described by a operation of a Toeplitz matrix on a vector, which is accomplished by making use of fast Fourier transformation. The algorithm could be applied widely in the cosmic statistics to tackle large data sets. Especially, we demonstrate this novel technique using the spherical, cubic and cylinder counts in cells respectively. The numerical test shows that the algorithm produces an excellent agreement with the expected results. Moreover, the algorithm introduces naturally a sharp-filter, which is capable of suppressing shot noise in weak signals. In the numerical procedures, the algorithm is somewhat similar to particle-mesh (PM) methods in N-body simulations. As scaled with $O(N\log N)$, it is significantly faster than the current particle-based methods, and its computational cost does not relies on shape or size of sampling cells. In addition, based on this technique, we propose further a simple fast scheme to compute the second statistics for cosmic density fields and justify it using simulation samples. Hopefully, the technique developed here allows us to make a comprehensive study of non-Guassianity of the cosmic fields in high precision cosmology. A specific implementation of the algorithm is publicly available upon request to the author.Comment: 27 pages, 9 figures included. revised version, changes include (a) adding a new fast algorithm for 2nd statistics (b) more numerical tests including counts in asymmetric cells, the two-point correlation functions and 2nd variances (c) more discussions on technic

Grover Algorithm with zero theoretical failure rate

In standard Grover's algorithm for quantum searching, the probability of finding the marked item is not exactly 1. In this Letter we present a modified version of Grover's algorithm that searches a marked state with full successful rate. The modification is done by replacing the phase inversion by two phase rotation through angle $\phi$. The rotation angle is given analytically to be $\phi=2 \arcsin(\sin{\pi\over (4J+6)}\over \sin\beta)$, where $\sin\beta={1\over \sqrt{N}}$, $N$ the number of items in the database, and $J$ an integer equal to or greater than the integer part of $({\pi\over 2}-\beta)/(2\beta)$. Upon measurement at $(J+1)$-th iteration, the marked state is obtained with certainty.Comment: 5 pages. Accepted for publication in Physical Review

Development program to produce mullite fiber insulation

Processing methods were utilized to form a mullite fiber-Kaowool felt. The formation of a blended felt using the Rotoformer wet-laying method was successful. Felt products were evaluated for tensile strength, thermal stability, thermal conductivity and structural integrity at 1259 C and 1371 C. Textile processing methods failed in an attempt to form a yarn from staple and multifilament mullite fiber due to fiber damage through mechanical handling. The refractoriness of pure Kaowool ceramic fiber is improved with additions of 30% or greater mullite fiber

Development of fine diameter mullite fiber

Results are presented of a program to develop and evaluate mullite fiber with a mean diameter under two microns. The two micron fiber is produced by a blowing process at room temperature from a low viscosity (10-25 poise) solution. The blown fiber was evaluated for dimensional stability in thermal cycling to 1371 C, and was equivalent to the 5 micron spun B and W mullite fiber. An additive study was conducted to evaluate substitutes for the boron. Three levels of chromium, lithium fluoride, and magnesium were added to the standard composition in place of boron and the fiber produced was evaluated for chemical and dimensional stability in thermal cycling to 1371 C. The magnesium was the most chemically stable, but the chrome additive imparted the best dimensional stability

CP Violation, an experimental perspective

I present a review of current and near-future experimental investigations of CP violation. In this review, I cover limits on particle electric dipole moments (EDMs) and CP violation studies in the K and B systems. The wealth of results from the new B factories provide impressive constraints on the CKM quark mixing matrix elements. Current and future measurements are focusing on processes dominated by loop diagrams, which probe physics at high mass scales in low-energy experiments.Comment: Invited plenary talk, DPF meeting, August 200