From open resources to educational opportunity

Since MIT’s bold announcement of the OpenCourseWare initiative in 2001, the content of over 700 of its courses have been published on the Web and made available for free to the world. Important infrastructure initiatives have also been launched recently with a view to enabling the sustainable implementation of these educational programmes, through strengthening organizational capacity as well as through building open, standards‐based technology. Each of these initiatives point to a rich palette of transformational possibilities for education; together with the growing open source movement, they offer glimpses of a sustainable ecology of substantial and quality educational resources. This discussion piece will highlight some of the educational opportunity presented by MIT’s current information technology‐enabled educational agenda and related initiatives, along with their strategic underpinnings and implications. It will address various dimensions of their impact on the form and function of education. It will examine how these ambitious programmes achieve a vision characterized by an abundance of sustainable, transformative educational opportunities, not merely pervasive technology

Low Correlation Sequences over the QAM Constellation

This paper presents the first concerted look at low correlation sequence families over QAM constellations of size M^2=4^m and their potential applicability as spreading sequences in a CDMA setting. Five constructions are presented, and it is shown how such sequence families have the ability to transport a larger amount of data as well as enable variable-rate signalling on the reverse link. Canonical family CQ has period N, normalized maximum-correlation parameter theta_max bounded above by A sqrt(N), where 'A' ranges from 1.8 in the 16-QAM case to 3.0 for large M. In a CDMA setting, each user is enabled to transfer 2m bits of data per period of the spreading sequence which can be increased to 3m bits of data by halving the size of the sequence family. The technique used to construct CQ is easily extended to produce larger sequence families and an example is provided. Selected family SQ has a lower value of theta_max but permits only (m+1)-bit data modulation. The interleaved 16-QAM sequence family IQ has theta_max <= sqrt(2) sqrt(N) and supports 3-bit data modulation. The remaining two families are over a quadrature-PAM (Q-PAM) subset of size 2M of the M^2-QAM constellation. Family P has a lower value of theta_max in comparison with Family SQ, while still permitting (m+1)-bit data modulation. Interleaved family IP, over the 8-ary Q-PAM constellation, permits 3-bit data modulation and interestingly, achieves the Welch lower bound on theta_max.Comment: 21 pages, 3 figures. To appear in IEEE Transactions on Information Theory in February 200

N=1 Sigma Models in AdS_4

We study sigma models in AdS_4 with global N=1 supersymmetry and find that they differ significantly from their flat-space cousins -- the target space is constrained to be a Kahler manifold with an exact Kahler form, the superpotential transforms under Kahler transformations, the space of supersymmetric vacua is generically a set of isolated points even when the superpotential vanishes, and the R-symmetry is classically broken by the cosmological constant. Remarkably, the exactness of the Kahler class is also required for the sigma model to arise as a decoupling limit of N=1 supergravity, and ensures the vanishing of gravitational anomalies. As simple applications of these results, we argue that fields with AdS_4 scale masses are ubiquitous in, for example, type IIB N=1 AdS_4 vacua stabilized near large volume; we also show that the Affleck-Dine-Seiberg runaway of N_f < N_c SQCD is regulated by considering the theory in AdS_4.Comment: 32 pages; v2: minor changes and references added; v3: discussion in sect. 5 extended, version published in JHE

Optimal Linear Codes with a Local-Error-Correction Property

Motivated by applications to distributed storage, Gopalan \textit{et al} recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such "local" parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.Comment: 13 pages, Shorter version submitted to ISIT 201

Efficacy of Microalgae on the Removal of Pollutants from Wastewater

Expansion of urban populations, increased coverage of domestic water supply and sewerage give rise to greater quantities of municipal wastewater. With the current emphasis on environmental health and water pollution issues, there is an increasing discharge of waste water in developing countries. Present technologies in developing countries for treating waste water are not sufficient and cost effective. Chlorella vulgaris is a form of green microalgae efficient for pond-based wastewater treatment, rather than bacterial strains for their ability to flocculate Chlorella vulgaris in a culture suspension. A microbial flocculent would be significantly cheaper than traditional flocculants and is believed to be less potentially toxic than synthetic polymers which are currently available. Chlorella vulgaris absorbed more pollutant compared to Chlamydomonas sp., which reveals that Chlorella vulgaris is efficient than Chlamydomonas sp., for treating waste water.

Outer Bounds on the Storage-Repair Bandwidth Tradeoff of Exact-Repair Regenerating Codes

In this paper, three outer bounds on the normalized storage-repair bandwidth (S-RB) tradeoff of regenerating codes having parameter set $\{(n,k,d),(\alpha,\beta)\}$ under the exact-repair (ER) setting are presented. The first outer bound is applicable for every parameter set $(n,k,d)$ and in conjunction with a code construction known as {\em improved layered codes}, it characterizes the normalized ER tradeoff for the case $(n,k=3,d=n-1)$. It establishes a non-vanishing gap between the ER and functional-repair (FR) tradeoffs for every $(n,k,d)$. The second bound is an improvement upon an existing bound due to Mohajer et al. and is tighter than the first bound, in a regime away from the Minimum Storage Regeneraing (MSR) point. The third bound is for the case of $k=d$, under the linear setting. This outer bound matches with the achievable region of {\em layered codes} thereby characterizing the normalized ER tradeoff of linear ER codes when $k=d=n-1$.Comment: Accepted for publication at International Journal of Information and Coding Theory (Special Issue on Information and Coding Theory for Data Storage