121,952 research outputs found
Singular integrals along lacunary directions in Rn
No full textA recent result by Parcet and Rogers is that finite order lacunarity characterizes the boundedness of the maximal averaging operator associated to an infinite set of directions in Rn. Their proof is based on geometric-combinatorial coverings of fat hyperplanes by two-dimensional wedges. Seminal results by Nagel-Stein-Wainger relied on geometric coverings of n-dimensional nature. In this article we find the sharp cardinality estimate for singular integrals along finite subsets of finite order lacunary sets in all dimensions. Previous results only covered the special case of the directional Hilbert transform in dimensions two and three. The proof is new in all dimensions and relies, among other ideas, on a precise covering of the n-dimensional Nagel-Stein-Wainger cone by two-dimensional Parcet-Rogers wedges
Maximal subspace averages
No full textWe study maximal operators associated to singular averages along finite subsets of the Grassmannian of -dimensional subspaces of . The well studied case corresponds to the the directional maximal function with respect to arbitrary finite subsets of . We provide a systematic study of all cases and prove essentially sharp bounds for the maximal subspace averaging operator in terms of the cardinality of , with no assumption on the structure of . In the codimension case, that is , we prove the precise critical weak -bound.
Drawing on the analogy between maximal subspace averages and -Nikodym maximal averages, we also formulate the appropriate maximal Nikodym conjecture for general . In this context, we prove the best possible -bound for the -Nikodym maximal function for all combinations of dimension and codimension.
Our estimates rely on Fourier analytic almost orthogonality principles, combined with polynomial partitioning, but we also use spatial analysis based on the precise calculation of intersections of -dimensional plates in .40 pages, 1 figure, submitted for publicatio
Maximal directional operators along algebraic varieties
No full textWe establish the sharp growth order, up to epsilon losses, of the -norm of the maximal directional averaging operator along a finite subset of a polynomial variety of arbitrary dimension , in terms of cardinality. This is an extension of the works by Córdoba, for one-dimensional manifolds, Katz for the circle in two dimensions, and Demeter for the 2-sphere. For the case of directions on the two-dimensional sphere we improve by a factor of on the best known bound, due to Demeter, and we obtain a sharp estimate for our model operator. Our results imply new -estimates for Kakeya-type maximal functions with tubes pointing along polynomial directions. Our proof technique is novel and in particular incorporates an iterated scheme of polynomial partitioning on varieties adapted to directional operators, in the vein of Guth, Guth-Katz, and Zahl.34 pages, final version, incorporates the comments of the anonymous referees; to appear in Amer. J. Mat
INGUINO-FEMORAL LYMPHADENECTOMY FOR VULVAR CARCINOMA WITH OR WITHOUT SAPHENECTOMY: A RANDOMISED STUDY
No full textOn the maximal directional hilbert transform in three dimensions
No full textWe establish the sharp growth rate, in terms of cardinality, of the Lp norms of the maximal Hilbert transform Hω along finite subsets of a finite order lacunary set of directions ω c R3, answering a question of Parcet and Rogers in dimension n = 3. Our result is the first sharp estimate for maximal directional singular integrals in dimensions greater than 2. The proof relies on a representation of the maximal directional Hilbert transform in terms of a model maximal operator associated to compositions of 2D angular multipliers, as well as on the usage of weighted norm inequalities, and their extrapolation, in the directional setting
Singular integrals along variable codimension one subspaces
No full textThis article deals with maximal operators on formed by taking
arbitrary rotations of tensor products of a -dimensional H\"ormander--Mihlin
multiplier with the identity in coordinates, in the particular
codimension 1 case . These maximal operators are naturally connected to
differentiation problems and maximally modulated singular integrals such as
Sj\"olin's generalization of Carleson's maximal operator. Our main result, a
weak-type -estimate on band-limited functions, leads to
several corollaries. The first is a sharp estimate for the
maximal operator restricted to a finite set of rotations in terms of the
cardinality of the finite set. The second is a version of the
Carleson--Sj\"olin theorem. In addition, we obtain that functions in the Besov
space , , may be recovered from their
averages along a measurable choice of codimension subspaces, a form of
Zygmund's conjecture in general dimension .Comment: Published version on Ars Inveniendi Analytic
A Multi-Language Comparison of Influences on Author Verification using Character N-Grams
No full textWe create a new multi-language corpus for author verification based on Wikipedia talkpages, and evaluate the influence that differences in topic and time have on character n-gram author profiles. Topic alignment between two texts is found to increase author verification precision, and an authors writing style is found to change over time, but not more significantly after 3 years than after 1 year.Information ArchitectureWISElectrical Engineering, Mathematics and Computer Scienc
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe 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
A metric approach to sparse domination
No full textWe present a general approach to sparse domination based on single-scale Lp-improving as a key assumption. The results are formulated in the setting of metric spaces of homogeneous type and avoid completely the use of dyadic-probabilistic techniques as well as of Christ–Hytönen–Kairema cubes. Among the applications of our general principle, we recover sparse domination of Dini-continuous Calderón–Zygmund kernels on spaces of homogeneous type, we prove a family of sparse bounds for maximal functions associated to convolutions with measures exhibiting Fourier decay, and we deduce sparse estimates for Radon transforms along polynomial submanifolds of Rn
The vanishing author in computer-generated works: a critical analysis of recent Australian case law
No full textAbstract
The use of software is ubiquitous in the creation of many copyright works, yet the requirement in copyright law that every work have a human author who engages in independent intellectual effort means that its use may prevent copyright subsistence. Several recent Australian cases have refocused attention on authorship as an essential criterion of copyright subsistence, and these cases suggest that much computer-produced output may be authorless and thus lack copyright protection. This article, the first in a two-part series, analyses how each case deals with the question of authorship of computer-produced works and why the use of software diminishes copyright protection for a significant number of computer-generated works. The article critiques the application of conventional notions of human authorship developed in the pre-computer age to modern productions and suggests alternative approaches to authorship that satisfy both the major objectives of copyright policy and the need to adapt to the computer age. The article argues that, without a broader judicial approach to authorship of computer-generated works, Parliament must remedy the lacuna in protection for these ‘authorless’ works. Possible solutions for reform are suggested. In a forthcoming article, the author comprehensively examines those reform proposals
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