Related papers: Three Random Intercepts of a Segment

Rejection sampling is a popular method used to generate numbers that follow some given distribution. We study the use of this method to generate random numbers in the unit interval from increasing probability density functions. We focus on…

Nandakumar asked whether there is a tiling of the plane by pairwise non-congruent triangles of equal area and equal perimeter. Here a weaker result is obtained: there is a tiling of the plane by pairwise non-congruent triangles of equal…

In real-world scenarios classification models are often required to perform robustly when predicting samples belonging to classes that have not appeared during its training stage. Open Set Recognition addresses this issue by devising models…

General regression and classification models are constructed as linear combinations of simple rules derived from the data. Each rule consists of a conjunction of a small number of simple statements concerning the values of individual input…

This paper explores and proves the one-seventh area triangle using a purely algebraic approach as opposed to a geometric one. A triangle set purely in the complex plane is used so that we can utilise features of the complex number system to…

Statistical samples, in order to be representative, have to be drawn from a population in a random and unbiased way. Nevertheless, it is common practice in the field of model-based diagnosis to make estimations from (biased) best-first…

In recent years, learning-based approaches have revolutionized motion planning. The data generation process for these methods involves caching a large number of high quality paths for different queries (start, goal pairs) in various…

We construct classes of homogeneous random fields on a three-dimensional Euclidean space that take values in linear spaces of tensors of a fixed rank and are isotropic with respect to a fixed orthogonal representation of the group of…

While generalizing well over natural inputs, neural networks are vulnerable to adversarial inputs. Existing defenses against adversarial inputs have largely been detached from the real world. These defenses also come at a cost to accuracy.…

As the World Wide Web is growing rapidly, it is getting increasingly challenging to gather representative information about it. Instead of crawling the web exhaustively one has to resort to other techniques like sampling to determine the…

A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…

Linear approximations to the decision boundary of a complex model have become one of the most popular tools for interpreting predictions. In this paper, we study such linear explanations produced either post-hoc by a few recent methods or…

Machine-learning models are ubiquitous. In some domains, for instance, in medicine, the models' predictions must be interpretable. Decision trees, classification rules, and subgroup discovery are three broad categories of supervised…

There is a widespread method to represent the envelope when a given hyperplane family creates an envelope. However, one sometimes encounters cases when the widespread method fails to represent the desired envelope precisely, and is…

Sampling formulas describe probability laws of exchangeable combinatorial structures like partitions and compositions. We give a brief account of two known parametric families of sampling formulas and add a new family to the list.

Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…

We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…

We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy…

Interpretable rationales for model predictions play a critical role in practical applications. In this study, we develop models possessing interpretable inference process for structured prediction. Specifically, we present a method of…

The number of triangles in a graph is useful to deduce a plethora of important features of the network that the graph is modeling. However, finding the exact value of this number is computationally expensive. Hence, a number of…