Recently Conrey, Farmer, and Zirnbauer [CFZ1, CFZ2] developed the Lfunctions Ratios conjecture, which gives a recipe that predicts a wealth of statistics, from moments to spacings between adjacent zeros and values of L-functions. The problem with this method is that several of its steps involve ignoring error terms of size comparable to the main term; amazingly, the errors seem to cancel and th...

The concept of a linear ordered orthogonal array is introduced, and its equivalent geometrical configuration is determined when its strength is 3 and 4. Existence of such geometrical configurations is investigated. They are also useful in the study of (T, M, S)-nets.

Using a contrast matching procedure, we measured the perceived contrast of vertical test gratings after adapting to other gratings of either vertical or horizontal orientation. The results show that both parallel and orthogonal adapting gratings reduce perceived contrast and do so proportionally more at low test contrasts than at high. The results are consistent with a single mechanism model pr...

We test the predictions of the L-functions Ratios Conjecture for the family of cuspidal newforms of weight k and level N , with either k fixed and N → ∞ through the primes or N = 1 and k → ∞. We study the main and lower order terms in the 1-level density. We provide evidence for the Ratios Conjecture by computing and confirming its predictions up to a power savings in the family’s cardinality, ...

In the present work we analyze the performance of orthogonal and Biorthogonal wavelet filters for image compression on variety of test images. The test images are of different size and resolution. The compression performance is measured, objectively peak signal to noise ratio and subjectively visual quality of image and it is found that Biorthogonal wavelets outperform the orthogonal ones in bo...