We address the problem of a succinct static data structure representing points on anM M grid (M = 2m where m is size of a word) that permits to answer the question of finding the closest point to a query point under the L1 or L1 norm in constant time. Our data structure takes essentially minimum space. These results are extended to d dimensions underL1 .

This paper presents the results of classifying Arabic text documents using the N-gram frequency statistics technique employing a dissimilarity measure called the “Manhattan distance”, and Dice’s measure of similarity. The Dice measure was used for comparison purposes. Results show that N-gram text classification using the Dice measure outperforms classification using the Manhattan measure.

Abstract-In this paper, we investigate the large-times behavior of weak solutions to the fourthorder degenerate parabolic equation ut = -(I@ ~~~~~~ modeling the evolution of thin films. In particular, for all n > 0, we prove exponential decay of u(z, t) towards its mean value (l/If20 Jn u dz in L1-norm for long times and we give the explicit (n-dependent) rate of decay. The result is baaed on c...

for every n ≥ 2, where Fn denotes the set of all polynomials of degree at most n with coefficients from {−1, 0, 1}. Littlewood considered minimization problems of this variety on the unit disk. His most famous, now solved, conjecture was that the L1 norm of an element f ∈ Fn on the unit circle grows at least as fast as c logN , where N is the number of non-zero coefficients in f and c > 0 is an...

We tackle the yearbook ’Face To Age’ challenge to predict the year that a given yearbook photo was taken in. We experiment with three variants of the VGG19 architecture [4], the AlexNet architecture [2], as well as different loss functions and an extensive effort to reduce overfitting. A variant of the AlexNet architecture, that has 2048 neurons in the fully connected layers and is ensembled ov...

Spatial quantiles, based on the L1 norm in a certain sense, provide an appealing vector extension of univariate quantiles and generate a useful “volume” functional based on spatial “central regions” of increasing size. A plot of this functional as a “spatial scale curve” provides a convenient twodimensional characterization of the spread of a multivariate distribution of any dimension. We discu...

We give upper bound estimates for the number of solutions of a certain diophantine equation. Our results can be applied to obtain new lower bound estimates for the L1-norm of certain exponential sums.

For z1, z2, z3 ∈ Z, the tristance d3(z1, z2, z3) is a generalization of the L1-distance on Z to a quantity that reflects the relative dispersion of three points rather than two. A tristance anticode Ad of diameter d is a subset of Z with the property that d3(z1, z2, z3) 6 d for all z1, z2, z3 ∈ Ad. An anticode is optimal if it has the largest possible cardinality for its diameter d. We determin...

It is NP-hard to determine the Radon number of graphs in the geodetic convexity. However, for certain classes of graphs, this well-known convexity parameter can be determined efficiently. In this paper, we focus on geodetic convexity spaces built upon d-dimensional grids, which are the Cartesian products of d paths. After revisiting a result of Eckhoff concerning the Radon number of Rd in the c...

In this work we approach the problem of model comparison between skew families. For the univariate skew model, we measure the sensitivity of the skewness parameter using the L1-distance between symmetric and asymmetric models and we obtain explicit expressions for some of these models. The main result is that the L1-distance between a representable elliptical distribution and a representable sk...