1,367 research outputs found

    Historic context statement for the City of Salem, Salem, Oregon

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    prepared for the City of Salem, Oregon, by Marianne Kadas.Title from PDF title page (viewed on January 29, 2020).This archived document is maintained by the State Library of Oregon as part of the Oregon Documents Depository Program. It is for informational purposes and may not be suitable for legal purposes.Includes bibliographical references (pages 79-81).Funded by the City of Salem and by a matching grant from the National Park Service, U. S. Department of the Interior, in cooperation with the Oregon State Preservation Office.Mode of access: Internet from the Oregon Government Publications Collection.Text in English

    An efficient sparse adaptation of the polytope method over Fp and a record-high binary bivariate factorisation

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    AbstractA recent bivariate factorisation algorithm appeared in Abu-Salem et al. [Abu-Salem, F., Gao, S., Lauder, A., 2004. Factoring polynomials via polytopes. In: Proc. ISSAC’04. pp. 4–11] based on the use of Newton polytopes and a generalisation of Hensel lifting. Although possessing a worst-case exponential running time like the Hensel lifting algorithm, the polytope method should perform well for sparse polynomials whose Newton polytopes have very few Minkowski decompositions. A preliminary implementation in Abu-Salem et al. [Abu-Salem, F., Gao, S., Lauder, A., 2004. Factoring polynomials via polytopes. In: Proc. ISSAC’04. pp. 4–11] indeed reflects this property, but does not exploit the fact that the algorithm preserves the sparsity of the input polynomial, so that the total amount of work and space required are O(d4) and O(d2) respectively, for an input bivariate polynomial of total degree d. In this paper, we show that the polytope method can be made sensitive to the number of non-zero terms of the input polynomial, so that the input size becomes dependent on both the degree and the number of terms of the input bivariate polynomial. We describe a sparse adaptation of the polytope method over finite fields with prime order, which requires fewer bit operations and memory references given a degree d sparse polynomial whose number of terms t satisfies t<d3/4, and which is known to be the product of two sparse factors. For t<d, and using fast polynomial arithmetic over finite fields, our refinement reduces the amount of work per extension of a coprime dominating edge factorisation and the total spatial cost to O(tλd2+t2λdL(d)+t4λd) bit operations and O(tλd) bits of memory respectively, for some 1/2≤λ<1, and L(d)=logdloglogd. To the best of our knowledge, the sparse binary factorisations achieved using this adaptation are of the highest degree so far, reaching a world record degree of 20000 for a very sparse bivariate polynomial over F2

    Supplemental Material - Potential diagnostic role of circulating MiRNAs in colorectal cancer

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    Supplemental Material for Potential diagnostic role of circulating MiRNAs in colorectal cancer by Dina A El-Sayed, Ahmed MH Salem, Menha M Swellam and Marwa GA Hegazy in International Journal of Immunopathology and Pharmacology</p

    A new construction of Salem polynomials

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    An earlier result of the author on the zeros of reciprocal polynomials is applied to give a new construction of Salem number

    Academic Correspondence, Stanford and Other Universities 1959-1960: Correspondence on Speaking Engagements, October 23, 1959 to January 23, 1960

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    Miscellaneous correspondence about speaking engagements; includes: Ethel Lanestrem to Fayez Sayegh, January 18, 1960; Sayegh to Ethel Lanestrem, January 22, 1960; Sayegh to Rev. J. Richard Spann, January 5, 1960; Sam Salem to Sayegh, January 23, 1960; note by Sayegh on Sam Salem and speaking engagements in Ohio; 2 page biography titled "Notes on Dr. Fayez A. Sayegh, Noted Lecturer and Author on Arab Affairs"; Jean A. Kemble to Sayegh, January 5, 1960; Dr. Nicholas Nyaradi to Sayegh, November 18, 1959; Glen A. Green to Sayegh, January 19, 1960; Glen A. Green to Sayegh, October 23, 1959; Sayegh to Glen A. Green, November 15, 1959

    A new sparse Gaussian elimination algorithm and the Niederreiter linear system for trinomials over F 2

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    An important factorization algorithm for polynomials over finite fields was developed by Niederreiter. The factorization problem is reduced to solving a linear system over the finite field in question, and the solutions are used to produce the complete factorization of the polynomial into irreducibles. One charactersistic feature of the linear system arising in the Niederreiter algorithm is the fact that, if the polynomial to be factorized is sparse, then so is the Niederreiter matrix associated with it. In this paper, we investigate the special case of factoring trinomials over the binary field. We develop a new algorithm for solving the linear system using sparse Gaussian elmination with the Markowitz ordering strategy. Implementing the new algorithm to solve the Niederreiter linear system for trinomials over F 2 suggests that, the system is not only initially sparse, but also preserves its sparsity throughout the Gaussian elimination phase. When used with other methods for extracting the irreducible factors using a basis for the solution set, the resulting algorithm provides a more memory efficient and sometimes faster sequential alternative for achieving high degree trinomial factorizations over F 2.Abu Salem F, 2004, LECT NOTES COMPUT SC, V3019, P217; Berlekamp E. R., 1967, BELL SYST TECH J, V46, P1853; Bonorden O., 2001, ACM SIGSAM B, V35, P16, DOI 10.1145-504331.504333; Curtis A. R., 1971, Journal of the Institute of Mathematics and Its Applications, V8; Duff I. S., 1986, DIRECT METHODS SPARS; Fleischmann P, 2003, MATH COMPUT, V72, P1887, DOI 10.1090-S0025-5718-03-01494-7; FLEISCHMANN P, 1993, LINEAR ALGEBRA APPL, V192, P101, DOI 10.1016-0024-3795(93)90238-J; GAO S, 1994, CONT MATH, V168, P101; GOTTFERT R, 1994, MATH COMPUT, V62, P831, DOI 10.2307-2153543; GUSTAVSON FG, 1972, SPARSE MATRICES THEI, P41; LEE TCY, 1995, APPL ALGEBR ENG COMM, V6, P147, DOI 10.1007-BF01195333; MARKOWITZ HM, 1957, MANAGE SCI, V3, P255, DOI 10.1287-mnsc.3.3.255; NIEDERREITER H, 1993, APPL ALGEBR ENG COMM, V4, P81, DOI 10.1007-BF01386831; NIEDERREITER H, 1993, LINEAR ALGEBRA APPL, V192, P301, DOI 10.1016-0024-3795(93)90247-L; NIEDERREITER H, 1993, J SYMB COMPUT, V16, P401, DOI 10.1006-jsco.1993.1055; NIEDERREITER H, 1994, MATH COMPUT, V62, P819, DOI 10.2307-2153542; Roelse P, 1999, MATH COMPUT, V68, P869, DOI 10.1090-S0025-5718-99-01008-X; VANDERSTAPPEN AF, 1993, SIAM J MATRIX ANAL A, V14, P853, DOI 10.1137-0614059; von zur Gathen J., 1999, MODERN COMPUTER ALGE; VONZURGATHEN J, P ISSAC 96 ZUR, P121
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