Detecting the Transition From Pop III to Pop II Stars

We discuss the cosmological significance of the transition from the Pop III to Pop II mode of star formation in the early universe, and when and how it may occur in primordial galaxies. Observations that could detect this transition include those of element abundances in metal-poor Galactic halo stars, and of the helium reionization and associated heating of the intergalactic medium. We suggest that gamma-ray bursts may be a better probe of the end of the first-stars epoch than of Pop III stars.Comment: 10 pages, 3 figures; to appear in New Astronomy Reviews as proceedings of "First Light and Reionization Workshop", eds. A. Cooray & E. Barton, Irvine, CA, May 19-21, 200

Optimal rate list decoding via derivative codes

The classical family of $[n,k]_q$ Reed-Solomon codes over a field \F_q consist of the evaluations of polynomials f \in \F_q[X] of degree $< k$ at $n$ distinct field elements. In this work, we consider a closely related family of codes, called (order $m$) {\em derivative codes} and defined over fields of large characteristic, which consist of the evaluations of $f$ as well as its first $m-1$ formal derivatives at $n$ distinct field elements. For large enough $m$, we show that these codes can be list-decoded in polynomial time from an error fraction approaching $1-R$, where $R=k/(nm)$ is the rate of the code. This gives an alternate construction to folded Reed-Solomon codes for achieving the optimal trade-off between rate and list error-correction radius. Our decoding algorithm is linear-algebraic, and involves solving a linear system to interpolate a multivariate polynomial, and then solving another structured linear system to retrieve the list of candidate polynomials $f$. The algorithm for derivative codes offers some advantages compared to a similar one for folded Reed-Solomon codes in terms of efficient unique decoding in the presence of side information.Comment: 11 page

Linear-algebraic list decoding of folded Reed-Solomon codes

Folded Reed-Solomon codes are an explicit family of codes that achieve the optimal trade-off between rate and error-correction capability: specifically, for any \eps > 0, the author and Rudra (2006,08) presented an n^{O(1/\eps)} time algorithm to list decode appropriate folded RS codes of rate $R$ from a fraction 1-R-\eps of errors. The algorithm is based on multivariate polynomial interpolation and root-finding over extension fields. It was noted by Vadhan that interpolating a linear polynomial suffices if one settles for a smaller decoding radius (but still enough for a statement of the above form). Here we give a simple linear-algebra based analysis of this variant that eliminates the need for the computationally expensive root-finding step over extension fields (and indeed any mention of extension fields). The entire list decoding algorithm is linear-algebraic, solving one linear system for the interpolation step, and another linear system to find a small subspace of candidate solutions. Except for the step of pruning this subspace, the algorithm can be implemented to run in {\em quadratic} time. The theoretical drawback of folded RS codes are that both the decoding complexity and proven worst-case list-size bound are n^{\Omega(1/\eps)}. By combining the above idea with a pseudorandom subset of all polynomials as messages, we get a Monte Carlo construction achieving a list size bound of O(1/\eps^2) which is quite close to the existential O(1/\eps) bound (however, the decoding complexity remains n^{\Omega(1/\eps)}). Our work highlights that constructing an explicit {\em subspace-evasive} subset that has small intersection with low-dimensional subspaces could lead to explicit codes with better list-decoding guarantees.Comment: 16 pages. Extended abstract in Proc. of IEEE Conference on Computational Complexity (CCC), 201

MOUTH FRESHNERS - Useful or harmful?

From periods best known to man, aroma or pleasant smell is always welcomed while bad odor withresent. Many methods have been adopted to avoid or mask malodour. Bad odor is considered asdisgusting especially during the periods of intimacy or closer association with others.  This article attempts to explain the role played by these mouth freshners.

A Woman\u27s Kind of Love: Female Longing in the Tamil Alvar Poetry

In the eighth section of Andal\u27s Nacciyar Tirumoli, a woman calls to the clouds and bids them to take a message of love to her delinquent lover, Vishnu, here figured as the lord of Venkatam. In the opening verse of the decad, she begins by plaintively questioning the clouds of her beloved\u27s whereabouts only to end with a bitter complaint about her sullied womanhood -- pen-nirmai. Bracketed by her eager questions -- has the lord of Venkatam come with you -- and her bitter complaint -- how does this bring him pride -- is the landscape of her body. Her tears are waterfalls, her breasts mountains, and just as the waterfalls erode the soil from the mountain slopes, her tears erase her womanhood. The black mark against the unrepentant divine lover is not just her (implied) lost chastity, but the gradual corrosion of her very self

Development of an Oxygen Saturation Monitoring System by Embedded Electronics

Measuring Oxygenation of blood (SaO2) plays a vital role in patient’s health monitoring. This is often measured by pulse oximeter, which is standard measure during anesthesia, asthma, operative and post-operative recoveries. Despite all, monitoring Oxygen level is necessary for infants with respiratory problems, old people, and pregnant women and in other critical situations. This paper discusses the process of calculating the level of oxygen in blood and heart-rate detection using a non-invasive photo plethysmography also called as pulsoximeter using the MSP430FG437 microcontroller (MCU). The probe uses infrared lights to measure and should be in physical contact with any peripheral points in our body. The percentage of oxygen in the body is worked by measuring the intensity from each frequency of light after it transmits through the body and then calculating the ratio between these two intensities

Optimal Column-Based Low-Rank Matrix Reconstruction

We prove that for any real-valued matrix $X \in \R^{m \times n}$, and positive integers $r \ge k$, there is a subset of $r$ columns of $X$ such that projecting $X$ onto their span gives a $\sqrt{\frac{r+1}{r-k+1}}$-approximation to best rank-$k$ approximation of $X$ in Frobenius norm. We show that the trade-off we achieve between the number of columns and the approximation ratio is optimal up to lower order terms. Furthermore, there is a deterministic algorithm to find such a subset of columns that runs in $O(r n m^{\omega} \log m)$ arithmetic operations where $\omega$ is the exponent of matrix multiplication. We also give a faster randomized algorithm that runs in $O(r n m^2)$ arithmetic operations.Comment: 8 page