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Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Packing and Decomposition of Graphs with Trees
No full textAbstractLet H be a tree on h⩾2 vertices. It is shown that if n is sufficiently large and G=(V, E) is an n-vertex graph with δ(G)⩾⌊n/2⌋, then there are ⌊|E|/(h−1)⌋ edge-disjoint subgraphs of G which are isomorphic to H. In particular, if h−1 divides |E| then there is an H-decomposition of G. This result is best possible as there are infinitely many examples of trees on h vertices and graphs G with m(h−1) edges, δ(G)⩾⌊n/2⌋−1, for which G has no H-decomposition
Decomposing oriented graphs into transitive tournaments
No full textAbstractFor an oriented graph G with n vertices, let f(G) denote the minimum number of transitive subtournaments that decompose G. We prove several results on f(G). In particular, if G is a tournament then f(G)<521n2(1+o(1)) and there are tournaments for which f(G)>n2/3000. For general G we prove that f(G)⩽⌊n2/3⌋ and this is tight. Some related parameters are also considered
Variations on the Author
Get PDF“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
Asymptotically optimal Kk-packings of dense graphs via fractional Kk-decompositions
No full textAbstractLet H be a fixed graph. A fractional H-decomposition of a graph G is an assignment of nonnegative real weights to the copies of H in G such that for each e∈E(G), the sum of the weights of copies of H containing e is precisely one. An H-packing of a graph G is a set of edge disjoint copies of H in G. The following results are proved. For every fixed k>2, every graph with n vertices and minimum degree at least n(1-1/9k10)+o(n) has a fractional Kk-decomposition and has a Kk-packing which covers all but o(n2) edges
Arithmetic progressions with constant weight
No full textAbstractLet k⩽n be two positive integers, and let F be a field with characteristic p. A sequence f:{1,…,n}→F is called k-constant, if the sum of the values of f is the same for every arithmetic progression of length k in {1,…,n}. Let V(n,k,F) be the vector space of all k-constant sequences. The constant sequence is, trivially, k-constant, and thus dimV(n,k,F)⩾1. Let m(k,F)=minn=k∞dimV(n,k,F), and let c(k,F) be the smallest value of n for which dimV(n,k,F)=m(k,F). We compute m(k,F) for all k and F and show that the value only depends on k and p and not on the actual field. In particular, we show that if p∤k (in particular, if p=0) then m(k,F)=1 (namely, when n is large enough, only constant functions are k constant). Otherwise, if k=prt where r⩾1 is maximal, then m(k,F)=k−t. We also conjecture that c(k,F)=(k−1)t+φ(t), unless p>t and p divides k, in which case c(k,F)=(k−1)p+1 (in case p∤k we put t=k), where φ(t) is Euler's function. We prove this conjecture in case t is a multiple of at most two distinct prime powers. Thus, in particular, we get that whenever k=q1s1q2s2 where q1,q2 are distinct primes and p≠q1,q2, then every k-constant sequence is constant if and only if n⩾q12s1q22s2−q1s1−1q2s2−1(q1+q2−1). Finally, we establish an interesting connection between the conjecture regarding c(k,F) and a conjecture about the non-singularity of a certain (0,1)-matrix over the integers
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
The number of edge-disjoint transitive triples in a tournament
No full textAbstractWe prove that a tournament with n vertices has more than 0.13n2(1+o(1)) edge-disjoint transitive triples. We also prove some results on the existence of large packings of k-vertex transitive tournaments in an n-vertex tournament. Our proofs combine probabilistic arguments and some powerful packing results due to Wilson and to Frankl and Rödl
All-pairs disjoint paths from a common ancestor in Õ(nω) time
No full textAbstractA common ancestor of two vertices u,v in a directed acyclic graph is a vertex w that can reach both. A {u,v}-junction is a common ancestor w so that there are two paths, one from w to u and the other from w to v, that are internally vertex-disjoint. A lowest common ancestor (LCA) of u and v is a common ancestor w so that no other common ancestor of u and v is reachable from w. Every {u,v}-LCA is a {u,v}-junction, but the converse is not true. Similarly, not every common ancestor is a junction.The all-pairs common ancestor (APCA) problem computes (or determines the non-existence of) a common ancestor for all pairs of vertices. Similarly defined are the all-pairs junction (APJ) and the all-pairs LCA (APLCA) problems. The APCA problem also has an existence version.Bender et al. obtained an algorithm for APCA existence by reduction to transitive closure. Their algorithm runs in Õ(nω) time where ω<2.376 is the exponent of fast Boolean matrix multiplication and n is the number of vertices. Kowaluk and Lingas obtained an algorithm for APLCA whose running time is O(n2+1/(4−ω))≤o(n2.616). Our main result is an Õ(nω) time algorithm for APJ. Thus, junctions for all pairs can also be computed in essentially the time needed for transitive closure.For a subset of vertices S, a common ancestor of S is a vertex that can reach each vertex of S. A lowest common ancestor of S is a common ancestor w of S so that no other common ancestor of S is reachable from w. For k≥2, the k-APCA and the k-APLCA problems are to find, respectively, a common ancestor and a lowest common ancestor for each k-set of vertices. We prove that for all fixed k≥8, the k-APCA problem can be solved in Õ(nk) time, thereby obtaining an essentially optimal algorithm. We also prove that for all k≥4, the k-APLCA problem can be solved in Õ(nk+1/2) time
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