Related papers: A Novel Aprroach to Knot Classification

Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…

In this work we present an algorithm to perform algorithmic differentiation in the context of quantum computing. We present two versions of the algorithm, one which is fully quantum and one which employees a classical step (hybrid…

This paper presents a comprehensive evaluation of the potential of Quantum Convolutional Neural Networks (QCNNs) in comparison to classical Convolutional Neural Networks (CNNs) and Artificial / Classical Neural Network (ANN) models. With…

A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…

As the field of recommender systems has developed, authors have used a myriad of notations for describing the mathematical workings of recommendation algorithms. These notations ap-pear in research papers, books, lecture notes, blog posts,…

The problem of ranking is a multi-billion dollar problem. In this paper we present an overview of several production quality ranking systems. We show that due to conflicting goals of employing the most effective machine learning models and…

Recently, span programs have been shown to be equivalent to quantum query algorithms. It is an open problem whether this equivalence can be utilized in order to come up with new quantum algorithms. We address this problem by providing span…

Optimization is ubiquitous in our daily lives. In the past, (sub-)optimal solutions to any problem have been derived by trial and error, sheer luck, or the expertise of knowledgeable individuals. In our contemporary age, there thankfully…

Unknot recognition is one of the fundamental questions in low dimensional topology. In this work, we show that this problem can be encoded as a validity problem in the existential fragment of the first-order theory of real closed fields.…

Physical knot classification is a challenging fine-grained recognition task in which the intended discriminative cue is rope crossing structure; however, high closed-set accuracy may still arise from low-level appearance shortcuts rather…

In this work we introduce a quantum sorting algorithm with adaptable requirements of memory and circuit depth, and then use it to develop a new quantum version of the classical machine learning algorithm known as k-nearest neighbors (k-NN).…

Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various…

Machine learning assumes a pivotal role in our data-driven world. The increasing scale of models and datasets necessitates quick and reliable algorithms for model training. This dissertation investigates adaptivity in machine learning…

Real networks exhibit heterogeneous nature with nodes playing far different roles in structure and function. To identify vital nodes is thus very significant, allowing us to control the outbreak of epidemics, to conduct advertisements for…

The power of quantum computers is still somewhat speculative. While they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical…

Sorting algorithms have attracted a great deal of attention and study, as they have numerous applications to Mathematics, Computer Science and related fields. In this thesis, we first deal with the mathematical analysis of the Quicksort…

The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…

In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…

We present a computer algorithm to explicitly compute the BGG resolution and its cohomology. We give several applications, in particular computation of various sheaf cohomology groups on flag varieties. An implementation of the algorithm is…

Neural networks with quadratic decision functions have been introduced as alternatives to standard neural networks with affine linear ones. They are advantageous when the objects or classes to be identified are compact and of basic…