A comprehensive study of Modulation effects on CMB Polarization

This article does the most general treatment of modulation in Polarization fields. We have considered both linear polarization fields Q and U & also scalar polarization modes E and B. We have shown that any arbitrary modulation in Q and U is allowed but the same can't be done in case of E and B fields. This result also gives a mathematical justification that the masking can only be applied to the Q and U fields and never to E and B fields.Comment: 10 pages, 2 figures, minor corrections, to be submitte

Whole Business Securitization: Secured Lending Repackaged?: A Comment on Hill

We study certain generalized Cauchy integral formulas for gradients of solutions to second order divergence form elliptic systems, which appeared in recent work by P. Auscher and A. Rosén. These are constructed through functional calculus and are in general beyond the scope of singular integrals. More precisely, we establish such Cauchy formulas for solutions u with gradient in weighted L_2(\R^{1+n}_+, t^{\alpha}dtdx) also in the case |\alpha|<1. In the end point cases \alpha= \pm 1, we show how to apply Carleson duality results by T. Hytönen and A. Rosén to establish such Cauchy formulas

An optimal quantum algorithm for the oracle identification problem

In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its dependence on N and M. Our algorithm considerably simplifies and improves the previous best algorithm due to Ambainis et al. Our algorithm also has applications in quantum learning theory, where it improves the complexity of exact learning with membership queries, resolving a conjecture of Hunziker et al. The algorithm is based on ideas from classical learning theory and a new composition theorem for solutions of the filtered $\gamma_2$-norm semidefinite program, which characterizes quantum query complexity. Our composition theorem is quite general and allows us to compose quantum algorithms with input-dependent query complexities without incurring a logarithmic overhead for error reduction. As an application of the composition theorem, we remove all log factors from the best known quantum algorithm for Boolean matrix multiplication.Comment: 16 pages; v2: minor change

Takayasu's arteritis in children : a review

Takayasu's arteritis is an inflammatory disease of unknown origin involving aorta, its primary branches and pulmonary artery. This article briefly reviews the pathology, clinical features and treatment of Takayasu's arteritis, focusing mainly on the disease in children.peer-reviewe

Learning Coverage Functions and Private Release of Marginals

We study the problem of approximating and learning coverage functions. A function $c: 2^{[n]} \rightarrow \mathbf{R}^{+}$ is a coverage function, if there exists a universe $U$ with non-negative weights $w(u)$ for each $u \in U$ and subsets $A_1, A_2, \ldots, A_n$ of $U$ such that $c(S) = \sum_{u \in \cup_{i \in S} A_i} w(u)$. Alternatively, coverage functions can be described as non-negative linear combinations of monotone disjunctions. They are a natural subclass of submodular functions and arise in a number of applications. We give an algorithm that for any $\gamma,\delta>0$, given random and uniform examples of an unknown coverage function $c$, finds a function $h$ that approximates $c$ within factor $1+\gamma$ on all but $\delta$-fraction of the points in time $poly(n,1/\gamma,1/\delta)$. This is the first fully-polynomial algorithm for learning an interesting class of functions in the demanding PMAC model of Balcan and Harvey (2011). Our algorithms are based on several new structural properties of coverage functions. Using the results in (Feldman and Kothari, 2014), we also show that coverage functions are learnable agnostically with excess $\ell_1$-error $\epsilon$ over all product and symmetric distributions in time $n^{\log(1/\epsilon)}$. In contrast, we show that, without assumptions on the distribution, learning coverage functions is at least as hard as learning polynomial-size disjoint DNF formulas, a class of functions for which the best known algorithm runs in time $2^{\tilde{O}(n^{1/3})}$ (Klivans and Servedio, 2004). As an application of our learning results, we give simple differentially-private algorithms for releasing monotone conjunction counting queries with low average error. In particular, for any $k \leq n$, we obtain private release of $k$-way marginals with average error $\bar{\alpha}$ in time $n^{O(\log(1/\bar{\alpha}))}$