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We relate the cohomology of the Orlik-Solomon algebra of a discriminantal arrangement to the local system cohomology of the complement. The Orlik-Solomon algebra of such an arrangement (viewed as a complex) is shown to be a linear approximation of a complex arising from the fundamental group of the complement, the cohomology of which is isomorphic to that of the complement with coefficients in ...

Reed-Solomon codes are examples of error correcting codes, in which redundant information is added to data so that it can be recovered reliably despite errors in transmission or storage and retrieval. The error correction system used on CD’s and DVD’s is based on a Reed-Solomon code. These codes are also used on satellite links and other communications systems. We will first discuss the general...

In the last lecture, we studied codes based on univarite polynomials, also known as Reed-Solomon codes, and on multivariate polynomials, also known as Reed-Muller codes. The Reed-Solomon codes had rate R = 1 − δ, which is optimal (given by the Singleton bound), but required alphabets of large size (|Σ| ≥ n). Multivariate polynomials in a constant number of variables, however, gave codes of posi...

SRA used a language-independent, domain-independent, multipurpose text understanding system as the core of the M UC-5 system for extraction from English and Japanese joint venture texts, SRA 's NLP core systelll, SOLOMON, has been under development since 1986. It has been used for a variety of domains, and was aimed from the start to be language-independent, domain-independent, and application-...

We begin with the definition of Reed-Solomon codes. Definition 1.1 (Reed-Solomon code). Let Fq be a finite field and Fq[x] denote the Fq-space of univariate polynomials where all the coefficients of x are from Fq. Pick {α1, α2, ...αn} distinct elements (also called evaluation points) of Fq and choose n and k such that k ≤ n ≤ q. We define an encoding function for Reed-Solomon code as RS : Fq → ...

In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of the representation of a finite Coxeter group W on the pth graded piece of its Orlik-Solomon algebra as a sum of characters induced from linear characters of centralizers of elements of W . Our refined conjecture relates the character of W on the pth graded piece of its Orlik-Solomon algebra with the ...

In the past few years, all manner of storage systems, ranging from disk array systems to distributed and widearea systems, have started to grapple with the reality of tolerating multiple simultaneous failures of storage nodes. Unlike the single failure case, which is optimally handled with RAID Level-5 parity, the multiple failure case is more difficult because optimal general purpose strategie...

s and Presentations:  UWC Science Research Open Day (2011): Poster Presentation Erasmus N, Solomon MC, Fortuin KA, Henkel RR: Effect of Eurycoma longifolia Jack (Tongkat Ali) extract on human spermatozoa in vitro, Bellville, South Africa; abstract book p. 33.  40 Physiology Society of Southern Africa (2012): Oral Presentation Erasmus N, Solomon MC, Fortuin KA, Henkel RR: Effect of aqueous ext...

The Orlik-Solomon algebra of a matroid M is the quotient of the exterior algebra on the points by the ideal I(M) generated by the boundaries of the circuits of the matroid. There is an isomorphism between the OrlikSolomon algebra of a complex matroid and the cohomology of the complement of a complex arrangement of hyperplanes. In this article a generalization of the Orlik-Solomon algebras, call...