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Movements, leaders, victories and the continuing fight for equality.
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Wilmington, North Carolina once had a thriving Black middle class and an elected interracial government. In 1898 white supremacists used violence to overthrow that government, kill Black residents and drive many others from the city.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
Dominique Perrin | |
|---|---|
 | |
| Born | November 5, 1946 |
| Education | Paris Diderot University |
| Known for | combinatorics on words coding theory |
| Scientific career | |
| Fields | Formal language theory Combinatorics on words |
| Workplaces | University of Marne-la-Vallée |
| Marcel-Paul Schützenberger | |
Doctoral students | |
Dominique Pierre Perrin[1] (b. 1946) is a French mathematician and theoretical computer scientist known for his contributions to coding theory and to combinatorics on words. He is a professor of the University of Marne-la-Vallée and currently serves as the President of ESIEE Paris.
Perrin earned his PhD from Paris 7 University in 1975. In his early career, he was a CNRS researcher (1970–1977) and taught at the University of Chile (1972–1973). Later, he worked as a professor at the University of Rouen (1977–1983), Paris 7 University (1983–1993), and École Polytechnique (1982–2002). Since 1993, Perrin is a professor at the University of Marne-la-Vallée, and since 2004, he is the President of ESIEE Paris.
Perrin is a member of Academia Europaea since 1989.
Perrin has been a member of the Lothaire group of mathematicians that developed the foundations of combinatorics on words. He has co-authored three scientific monographs: "Theory of Codes" (1985),[2] "Codes and Automata" (2009),[3] and "Infinite Words" (2004),[4] as well as the three Lothaire books.[5][6][7] Perrin has published around 50 research articles in formal language theory.
Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
Dominique Pierre Perrin (b. 1946) is a French mathematician and theoretical computer scientist known for his contributions to coding theory and to combinatorics on words. He is a professor of the University of Marne-la-Vallée and currently serves as the President of ESIEE Paris.
In computer science, the two-way string-matching algorithm (or Crochemore-Perrin string-matching algorithm) is a string-searching algorithm, discovered by Maxime Crochemore and Dominique Perrin in 1991. It searches for copies of a "needle" of length m in a "haystack" of length n. After preprocessing the needle in time O(m), the actual search takes time O(n) linear in the length of the haystack. The two-way algorithm can be viewed as a combination of the forward-going Knuth–Morris–Pratt algorithm (KMP) and the backward-running Boyer–Moore string-search algorithm (BM). Like those two, the two-way algorithm preprocesses the needle to find partially repeating periods and computes “shifts” based on them, indicating what offset to “jump” to in the haystack when a given character is encountered. Unlike BM and KMP, it uses only O(1) additional space to store information about those partial repeats (assuming the transdichotomous model, where an index of ⌈log2(m)⌉ bits is counted as a single word). The preprocessing computes the "period" of the needle, the minimum offset between two consecutive matches (a value between 1 and m), and a "critical factorization" of the needle into a prefix and suffix with particular properties, specified by the length of the prefix (also less than m). The actual matching operation performs at most 2n − m comparisons. Breslauer later published two improved variants performing fewer comparisons, at the cost of storing additional data about the preprocessed needle: The first one performs at most n + ⌊(n − m)/2⌋ comparisons, ⌈(n − m)/2⌉ fewer than the original. It must however store ⌈logφ m⌉ additional offsets into the needle. The second adapts it to only store a constant number of such offsets, denoted c, but must perform n + ⌊(1⁄2 + ε)(n − m)⌋ comparisons, with ε = 1⁄2(Fc+2 − 1)−1 ∈ O(φ−c) going to zero exponentially quickly as c increases. The algorithm is considered fairly efficient in practice, being cache-friendly and using several operations that can be implemented in well-optimized subroutines. It is used by the C standard libraries glibc, newlib, and musl, to implement the memmem and strstr family of substring functions. As with most advanced string-search algorithms, the naïve implementation may be more efficient on small-enough instances; this is especially so if the needle isn't searched in multiple haystacks, which would amortize the preprocessing cost.
In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication is replaced with ordinary addition: x ⊕ y = min { x , y } {\displaystyle x\oplus y=\min\{x,y\}} , x ⊗ y = x + y {\displaystyle x\otimes y=x+y} . So for example, the classical polynomial x 3 + x y + y 4 {\displaystyle x^{3}+xy+y^{4}} would become min { x + x + x , x + y , y + y + y + y } {\displaystyle \min\{x+x+x,\;x+y,\;y+y+y+y\}} . Such polynomials and their solutions have important applications in optimization problems, for example, the problem of optimizing departure times for a network of trains. Tropical geometry is a variant of algebraic geometry in which polynomial graphs resemble piecewise linear meshes, and in which numbers belong to the tropical semiring instead of a field. Because classical and tropical geometry are closely related, results and methods can be converted between them. Algebraic varieties can be mapped to a tropical counterpart and, since this process still retains some geometric information about the original variety, it can be used to help prove and generalize classical results from algebraic geometry, such as the Brill–Noether theorem or computing Gromov–Witten invariants, using the tools of tropical geometry.
In mathematics, more specifically in combinatorics on words, a Sturmian word (Sturmian sequence or billiard sequence) is a certain kind of infinitely long sequence of characters. The concept is named after Jacques Charles François Sturm. Such a sequence can be generated by considering a game of English billiards on a square table. The struck ball will successively hit the vertical and horizontal edges labelled 0 and 1 generating a sequence of letters. This sequence is a Sturmian word.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Shirley Chisholm, elected in 1968.
