Reducible braids and Garside theory

We show that reducible braids which are, in a Garside-theoretical sense, as simple as possible within their conjugacy class, are also as simple as possible in a geometric sense. More precisely, if a braid belongs to a certain subset of its conjugacy class which we call the stabilized set of sliding circuits, and if it is reducible, then its reducibility is geometrically obvious: it has a round or almost round reducing curve. Moreover, for any given braid, an element of its stabilized set of sliding circuits can be found using the well-known cyclic sliding operation. This leads to a polynomial time algorithm for deciding the Nielsen-Thurston type of any braid, modulo one well-known conjecture on the speed of convergence of the cyclic sliding operation.Comment: 28 pages, 4 figure

Fast algorithmic Nielsen-Thurston classification of four-strand braids

We give an algorithm which decides the Nielsen-Thurston type of a given four-strand braid. The complexity of our algorithm is quadratic with respect to word length. The proof of its validity is based on a result which states that for a reducible 4-braid which is as short as possible within its conjugacy class (short in the sense of Garside), reducing curves surrounding three punctures must be round or almost round.Comment: One minor error corrected (Example 4.2 was wrong

A Cubic Algorithm for Computing Gaussian Volume

We present randomized algorithms for sampling the standard Gaussian distribution restricted to a convex set and for estimating the Gaussian measure of a convex set, in the general membership oracle model. The complexity of integration is $O^*(n^3)$ while the complexity of sampling is $O^*(n^3)$ for the first sample and $O^*(n^2)$ for every subsequent sample. These bounds improve on the corresponding state-of-the-art by a factor of $n$. Our improvement comes from several aspects: better isoperimetry, smoother annealing, avoiding transformation to isotropic position and the use of the "speedy walk" in the analysis.Comment: 23 page

Roundness Estimation of Sedimentary Rocks Using Eliptic Fourier and Deep Neural Networks

Sedimentary rocks analysis is useful in geological science, economic sector, and risk evaluation. Roundness is a morphological parameter that provide information to characterize and classify sedimentary material. Roundness degrees is estimated from the contour of the particle. Waddell (1932) proposed a remarkable method based on the measurement of particle’s curvature. This method is accurate; evertheless, it is not invariant to scale and rotation. This problem can be solved by mapping the contour to the frequencydomain, however, spectral analysis is a difficult task. Based on these two approaches, we propose to use a deep neural network whose input is the elliptical Fourier spectrum and target is roundness proposed by Wadell. The training database consists of 623 realrocks images from some geological phenomena. We have found the neural networks perform very well on the 88.8% of rocks

Roundness Estimation of Sedimentary Rocks Using Eliptic Fourier and Deep Neural Networks

Sedimentary rocks analysis is useful in geological science, economic sector, and risk evaluation. Roundness is a morphological parameter that provide information to characterize and classify sedimentary material. Roundness degrees is estimated from the contour of the particle. Waddell (1932) proposed a remarkable method based on the measurement of particle’s curvature. This method is accurate; evertheless, it is not invariant to scale and rotation. This problem can be solved by mapping the contour to the frequencydomain, however, spectral analysis is a difficult task. Based on these two approaches, we propose to use a deep neural network whose input is the elliptical Fourier spectrum and target is roundness proposed by Wadell. The training database consists of 623 realrocks images from some geological phenomena. We have found the neural networks perform very well on the 88.8% of rocks

Generating numerical approximations

We describe a computational model for planning phrases like “more than a quarter” and “25.9 per cent” which describe proportions at different levels of precision. The model lays out the key choices in planning a numerical description, using formal definitions of mathematical form (e.g., the distinction between fractions and percentages) and roundness adapted from earlier studies. The task is modeled as a constraint satisfaction problem, with solutions subsequently ranked by preferences (e.g., for roundness). Detailed constraints are based on a corpus of numerical expressions collected in the NUMGEN project, and evaluated through empirical studies in which subjects were asked to produce (or complete) numerical expressions in specified contexts

Identification of Plant Types by Leaf Textures Based on the Backpropagation Neural Network

The number of species of plants or flora in Indonesia is abundant. The wealth of Indonesia's flora species is not to be doubted. Almost every region in Indonesia has one or some distinctive plant(s) which may not exist in other countries. In enhancing the potential diversity of tropical plant resources, good management and utilization of biodiversity is required. Based on such diversity, plant classification becomes a challenge to do. The most common way to recognize between one plant and another is to identify the leaf of each plant. Leaf-based classification is an alternative and the most effective way to do because leaves will exist all the time, while fruits and flowers may only exist at any given time. In this study, the researchers will identify plants based on the textures of the leaves. Leaf feature extraction is done by calculating the area value, perimeter, and additional features of leaf images such as shape roundness and slenderness. The results of the extraction will then be selected for training by using the backpropagation neural network. The result of the training (the formation of the training set) will be calculated to produce the value of recognition accuracy with which the feature value of the dataset of the leaf images is then to be matched. The result of the identification of plant species based on leaf texture characteristics is expected to accelerate the process of plant classification based on the characteristics of the leaves