The Dice score is widely used for binary segmentation due to its robustness to class imbalance. Soft generalisations of the Dice score allow it to be used as a loss function for training convolutional neural networks (CNN). Although CNNs trained using mean-class Dice score achieve state-of-the-art results on multi-class segmentation, this loss function does neither take advantage of inter-class...

DICE (the DSPCAD Integrative Command Line Environment) is a package of utilities that facilitates efficient management of software projects. Key areas of emphasis in DICE are cross-platform operation, support for projects that integrate heterogeneous programming languages, and support for applying and integrating different kinds of design and testing methodologies. The package is being develope...

Most RPGs (role-playing games) use some sort of randomizer when resolving actions. Most often dice are used for this, but a few games use cards, rock-paper-scissors or other means of randomization. There are dozens of different ways dice have been used in RPGs, and we are likely to see many more in the future. This is not an evolution from bad methods to better methods – there is no such thing ...

There are two players playing the game, player U and player I. Each player chooses a (distinct) die and rolls – the player with the higher value is the winner. I kindly gives player U the first choice of any one of the three dice. Let us say that U chooses die X. After some thought, I chooses die Z, and then both players roll their dice. What are the possibilities? Because both dice have 6 side...

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.

We analyze a game in which two players choose in turn and roll an n-sided die, each player having his choice of numbering of the faces, subject to certain constraints. The player who rolls the larger number wins. We say die B “dominates” die A if P [B > A] > P [A > B]. The nontransitivity of this dominance relation for dice has been studied by several authors. We analyze the case of n-sided dic...

We present a method to address the challenging problem of segmentation of lumbar vertebrae from CT images acquired with varying fields of view. Our method is based on cascaded 3D Fully Convolutional Networks (FCNs) consisting of a localization FCN and a segmentation FCN. More specifically, in the first step we train a regression 3D FCN (we call it “LocalizationNet”) to find the bounding box of ...

Problem 1. Suppose you have seven dice—each a different color of the rainbow; otherwise the dice are standard, with faces numbered 1 to 6. A roll is a sequence specifying a value for each die in rainbow (ROYGBIV) order. For example, one roll is .3; 1; 6; 1; 4; 5; 2/ indicating that the red die showed a 3, the orange die showed 1, the yellow 6,. . . . For the problems below, describe a bijection...