1,721,272 research outputs found
Support Vector Machines in R
Full text linkBeing among the most popular and efficient classification and regression methods currently available, implementations of support vector machines exist in almost every popular programming language. Currently four R packages contain SVM related software. The purpose of this paper is to present and compare these implementations. (author's abstract)Series: Research Report Series / Department of Statistics and Mathematic
Support Vector Machines in R
Full text linkBeing among the most popular and efficient classification and regression methods currently available, implementations of support vector machines exist in almost every popular programming language. Currently four R packages contain SVM related software. The purpose of this paper is to present and compare these implementations.
Nonsingularity of matrices associated with classes of arithmetical functions on lcm-closed sets
No full textAbstractLet S={x1,…,xn} be a set of n distinct positive integers and f be an arithmetical function. Let [f(xi,xj)] denote the n×n matrix having f evaluated at the greatest common divisor (xi,xj) of xi and xj as its i,j-entry and (f[xi,xj]) denote the n×n matrix having f evaluated at the least common multiple [xi,xj] of xi and xj as its i,j-entry. The set S is said to be lcm-closed if [xi,xj]∈S for all 1⩽i, j⩽n. For an integer x>1, let ω(x) denote the number of distinct prime factors of x. Define ω(1)=0. In this paper, we show that if S={x1,…,xn} is an lcm-closed set satisfying maxx∈S{ω(lcm(S)x)}⩽2, and if f is a strictly increasing (resp. decreasing) completely multiplicative function, or if f is a strictly decreasing (resp. increasing) completely multiplicative function satisfying 0<f(p)⩽1p (resp. f(p)⩾p) for any prime p, then the matrix [f(xi,xj)] (resp. (f[xi,xj])) defined on S is nonsingular. By using the concept of least-type multiple introduced in [S. Hong, J. Algebra 281 (2004) 1–14], we also obtain reduced formulas for det(f(xi,xj)) and det(f[xi,xj]) when f is completely multiplicative and S is lcm-closed. We also establish several results about the nonsingularity of LCM matrices and reciprocal GCD matrices
Nonsingularity of matrices associated with classes of arithmetical functions
No full textAbstractLet S={x1,…,xn} be a set of n distinct positive integers. Let f be an arithmetical function. Let [f(xi,xj)] denote the n×n matrix having f evaluated at the greatest common divisor (xi,xj) of xi and xj as its i,j-entry and (f[xi,xj]) denote the n×n matrix having f evaluated at the least common multiple [xi,xj] of xi and xj as its i,j-entry. The set S is said to be gcd-closed if (xi,xj)∈S for all 1⩽i,j⩽n. For an integer x, let ν(x) denote the number of distinct prime factors of x. In this paper, by using the concept of greatest-type divisor introduced by S. Hong in [Adv. Math. (China) 25 (1996) 566–568; J. Algebra 218 (1999) 216–228], we obtain a new reduced formula for detf[(xi,xj)] if S is gcd-closed. Then we show that if S={x1,…,xn} is a gcd-closed set satisfying maxx∈S{ν(x)}⩽2, and if f is a strictly increasing (respectively decreasing) completely multiplicative function, or if f is a strictly decreasing (respectively increasing) completely multiplicative function satisfying 0<f(p)⩽1p (respectively f(p)⩾p) for any prime p, then the matrix [f(xi,xj)] (respectively (f[xi,xj])) defined on S is nonsingular. As a corollary, we show the following interesting result: The LCM matrix ([xi,xj]) defined on a gcd-closed set is nonsingular if maxx∈S{ν(x)}⩽2
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Divisibility of matrices associated with multiplicative functions
No full textAbstractLet S={x1,…,xn} be a set of n distinct positive integers. For x,y∈S and y<x, we say the y is a greatest-type divisor of x in S if y∣x and it can be deduced that z=y from y∣z,z∣x,z<x and z∈S. For x∈S, let GS(x) denote the set of all greatest-type divisors of x in S. For any arithmetic function f, let (f(xi,xj)) denote the n×n matrix having f evaluated at the greatest common divisor (xi,xj) of xi and xj as its i,j-entry and let (f[xi,xj]) denote the n×n matrix having f evaluated at the least common multiple [xi,xj] of xi and xj as its i,j-entry. In this paper, we assume that S is a gcd-closed set and maxx∈S{|GS(x)|}=1. We show that if f is a multiplicative function such that (f∗μ)(d)∈Z whenever d|lcm(S) and f(a)|f(b) whenever a|b and a,b∈S and (f(xi,xj)) is nonsingular, then the matrix (f(xi,xj)) divides the matrix (f[xi,xj]) in the ring Mn(Z) of n×n matrices over the integers. As a consequence, we show that (f(xi,xj)) divides (f[xi,xj]) in the ring Mn(Z) if (f∗μ)(d)∈Z whenever d|lcm(S) and f is a completely multiplicative function such that (f(xi,xj)) is nonsingular. This confirms a conjecture of Hong raised in 2004
Bounds for determinants of matrices associated with classes of arithmetical functions
No full textAbstractLet be an arithmetical function and S = x1, xn a set of distinct positive integers. Let ((xi,xj)) denote the n × n matrix having evaluated at the greatest common divisor of and as its entry and denote the matrix having evaluated at the least common multiple [xi, xj] of xi and xj as its i, j entry. In this paper, we show for a certain class of arithmetical functions new bounds for det [(xi, xj]), which improve the results obtained by Bourque and Ligh in 1993. As a corollary, we get new lower bounds for det[(xi, xj)], which improve the results obtained by Rajarama Bhat in 1991. We also show for a certain class of semi-multiplicative function new bounds for det([xi, xj]), which improve the results obtained by Bourque and Ligh in 1995
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions
No full textLet f be an arithmetic function and S= {x1, …, xn} be a set of n distinct positive integers. By (f(xi, xj)) (resp. (f[xi, xj])) we denote the n × n matrix having f evaluated at the greatest common divisor (xi, xj) (resp. the least common multiple [xi, xj]) of x, and xj as its (i, j)-entry, respectively. The set S is said to be gcd closed if (xi, xj) ∈ S for 1 ≤ i, j ≤ n. In this paper, we give formulas for the determinants of the matrices (f(xi, xj)) and (f[xi, xj]) if S consists of multiple coprime gcd-closed sets (i.e., S equals the union of S1, …, Sk with k ≥ 1 being an integer and S1, …, Sk being gcd-closed sets such that (lcm(Si), lcm(Sj)) = 1 for all 1 ≤ i ≠ j ≤ k). This extends the Bourque-Ligh, Hong’s and the Hong-Loewy formulas obtained in 1993, 2002 and 2011, respectively. It also generalizes the famous Smith’s determinant
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