1,720,968 research outputs found
Convexity and measures of statistical association
Full text linkRecent investigations on the measures of statistical association highlight essential properties such as zero-independence (the measure is zero if and only if the random variables are independent), monotonicity under information refinement, and max-functionality (the measure of association is maximal if and only if we are in the presence of a deterministic (noiseless) dependence). An open question concerns the reasons why measures of statistical associations satisfy one or more of those properties but not others. We show that convexity plays a central role in all properties. Convexity plus a form of strictness (that we are to define) are necessary and sufficient for zero-independence, and convexity and strict convexity on Dirac masses are necessary and sufficient for max-functionality. We apply the findings to study the families of measures of statistical association based on Csisz & aacute;r divergences, optimal transport, kernels, as well as Chatterjee's new correlation coefficient. We further discuss the role of convexity in guaranteeing the asymptotic unbiasedness of given data estimators, prove a central limit theorem for those estimators under independence, and show the rate of convergence under arbitrary dependence. We demonstrate the findings with numerical simulations in a multivariate response context
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Time evolution of the Kardar-Parisi-Zhang equation
Full text linkThe use of the non-linear SPDEs are inevitable in both physics and applied mathematics since many of the physical phenomena in nature can be effectively modeled in random and non-linear way.
The Kardar-Parisi-Zhang (KPZ) equation is well-known for its applications in describing various statistical mechanical models including randomly growing surfaces, directed polymers and interacting particle systems. We consider the upper and lower tail probabilities for the centered (by time) and scaled (according to KPZ time scaling) one-point distribution of the Cole-Hopf solution of the KPZ equation. We provide the first tight bounds on the lower tail probability of the one point distribution of the KPZ equation with narrow wedge initial data. Our bounds hold for all sufficiently large times and demonstrates a crossover between super-exponential decay with exponent (and leading pre-factor ) for tail depth greater than (deep tail), and exponent (with leading pre-factor at least ) for tail depth less than (shallow tail). We also consider the case when the initial data is drawn from a very general class. For the lower tail, we prove an upper bound which demonstrates a crossover from super-exponential decay with exponent in the shallow tail to an exponent in the deep tail. For the upper tail, we prove super-exponential decay bounds with exponent at all depths in the tail. We study the correlation of fluctuations of the narrow wedge solution to the KPZ equation at two different times. We show that when the times are close to each other, the correlation approaches one at a power-law rate with exponent , while when the two times are remote from each other, the correlation tends to zero at a power-law rate with exponent
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
Fractal geometry of the PAM in 2D and 3D with white noise potential
Full text linkWe study the parabolic Anderson model (PAM) \begin{equation}
{\partial \over \partial t}u(t,x) =\frac{1}{2}\Delta u(t,x) + u(t,x)\xi(x),
\quad t>0, x\in \mathbb{R}^d, \quad \text{and} \quad
u(0,x) \equiv 1, \quad \forall x\in \mathbb{R}^d,
\end{equation} where is spatial white noise on with . We show that the peaks of the PAM are macroscopically
multifractal. More precisely, we prove that the spatial peaks of the PAM have
infinitely many distinct values and we compute the macroscopic Hausdorff
dimension (introduced by Barlow and Taylor) of those peaks. As a byproduct, we
obtain the exact spatial asymptotics of the solution of the PAM. We also study
the spatio-temporal peaks of the PAM and show their macroscopic
multifractality. Some of the major tools used in our proof techniques include
paracontrolled calculus and tail probabilities of the largest point in the
spectrum of the Anderson Hamiltonian.Comment: 43 pages, 1 figur
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
On the Convergence Rate of Sinkhorn's Algorithm
Full text linkWe study Sinkhorn's algorithm for solving the entropically regularized
optimal transport problem. Its iterate is shown to satisfy
where denotes relative
entropy and the optimal coupling. This holds for a large class of
cost functions and marginals, including quadratic cost with subgaussian
marginals. We also obtain the rate for the dual suboptimality and
for the marginal entropies. More precisely, we derive
non-asymptotic bounds, and in contrast to previous results on linear
convergence that are limited to bounded costs, our estimates do not deteriorate
exponentially with the regularization parameter. We also obtain a stability
result for as a function of the marginals, quantified in relative
entropy
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
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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