1,720,967 research outputs found
Singularities of massless scattering and cluster algebras
No full textPartial flag varieties arise in the context of massless scattering kinematics. They can be associated to both spinor-helicity variables and momentum twistor variables in two separate yet natural ways. Here we report on evidence at five and six points that the cluster algebras associated to these partial flag varieties contain information relevant to non-dual conformal massless scattering amplitudes and related observables. At five points both spinor-helicity and momentum twistor cluster structures capture similar information about symbol alphabets. At six points we demonstrate that the momentum twistor structure captures a larger subset of the alphabet compared to the spinor-helicity one. We also observe that the associated cluster structures correctly predict the appearance of certain triples of symbol letters related to cluster mutation relations
Una aplicación del teorema de Sturmfels en la familia de ideales de grafos
No full textEn este trabajo se realiza una aplicación del teorema 3.1 (véase en 1.1) de Brend Sturmfels, en su artículo [9] “Gröbner Bases of Toric Varieties” (Bases de Groebner de variedades tóricas), donde estudia las variedades tóricas proyectivas desde una perspectiva combinatoria. Este teorema caracteriza los radicales de los ideales iniciales de una variedad tórica como los ideales de Stanley-Reisner de cierta triangulación inducida por un vector de pesos. La autora utiliza dicho resultado tomando la configuración de puntos como los vértices de los grafos K- completos K4 y K5. Por medio de una implementación computacional con el software algebraico Macaulay2 calcula invariantes combinatorias como los f-vectores, complejos simpliciales y ´orbitas de los ideales iniciales resultantes de la acción de los grupos simétricos S4 y S5 respectivamente, encontrando que para el caso de los ideales iniciales del ideal tórico asociado a K4, tienen un único f-vector y todos los ideales iniciales que resultan de la acción del grupo simétrico se encuentran en una única ´orbita. Para el caso de la aplicación computacional de la configuración de K5, encuentra tres f-vectores distintos de los complejos iniciales, y además, tres tipos de ´orbitas de los ideales iniciales con respecto a la acción del grupo simétrico S5.PregradoMATEMATICO(A
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
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
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe 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
Tropical totally positive cluster varieties
Full text linkWe study the relation between the integer tropical points of a cluster
variety (satisfying the full Fock-Goncharov conjecture) and the totally
positive part of the tropicalization of an ideal presenting the corresponding
cluster algebra. Suppose we are given a presentation of the cluster algebra by
a Khovanskii basis for a collection of -vector valuations associated
with several seeds related by mutations. In presence of a full rank fully
extended exchange matrix we construct the rays of a subfan of the totally
positive part of the tropicalization of the ideal that coincides
combinatorially with the subgraph of the exchange graph of the cluster algebra
corresponding to the collection of seeds. Moreover, geometric information about
Gross-Hacking-Keel-Kontsevich's toric degenerations associated with seeds gets
identified with the Gr\"obner toric degenerations obtained from maximal cones
in the tropicalization. As application we prove a conjecture about the relation
between Rietsch-Williams' valuations for Grassmannians arising from plabic
graphs \cite{RW17} to Kaveh-Manon's work on valuations from the tropicalization
of an ideal \cite{KM16}. In a second application we give a partial answer to
the question if the Feigin-Fourier-Littelmann-Vinberg degeneration of the full
flag variety in type is isomorphic to a degeneration obtained from
the cluster structure.Comment: Comments are very welcom
Toric degenerations: a bridge between representation theory, tropical geometry and cluster algebras
Full text linkIn this thesis we study toric degenerations of projective varieties. We compare
different constructions to understand how and why they are related. In focus are toric degenerations
obtained from representation theory, tropical geometry or cluster algebras. Often
those rely on valuations and the theory of Newton-Okounkov bodies. Toric degenerations can
be seen as a combinatorial shadow of the original objects. The goal is therefore to understand
why the different theories are so closely related, by understanding the toric degenerations they
yield first. We choose Grassmannians, flag varieties and Schubert varieties as starting point
as here many different constructions are applicable. One of our main results shows how toric
degenerations obtained using full-rank valuations, independent of how these are constructed,
can (under certain conditions) be realized using tropical geometry
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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