Related papers: A Novel Aprroach to Knot Classification

Despite the highest classification accuracy in wide varieties of application areas, artificial neural network has one disadvantage. The way this Network comes to a decision is not easily comprehensible. The lack of explanation ability…

This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…

Despite the promise that fault-tolerant quantum computers can efficiently solve classically intractable problems, it remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy,…

In recent years, there has been considerable innovation in the world of predictive methodologies. This is evident by the relative domination of machine learning approaches in various classification competitions. While these algorithms have…

Real-world events exhibit a high degree of interdependence and connections, and hence data points generated also inherit the linkages. However, the majority of AI/ML techniques leave out the linkages among data points. The recent surge of…

We study algebraic tangles as fundamental components in knot theory, developing a systematic approach to classify and tabulate prime tangles using a novel canonical representation. The canonical representation enables us to distinguish…

We make use of the 3D nature of knots and links to find savings in computational complexity when computing knot invariants such as the linking number and, in general, most finite type invariants. These savings are achieved in comparison…

Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…

Subgraph isomorphism is a well-known NP-hard problem which is widely used in many applications, such as social network analysis and knowledge graph query. Its performance is often limited by the inherent hardness. Several insightful works…

Quantum machine learning is considered one of the current research fields with immense potential. In recent years, Havl\'i\v{c}ek et al. [Nature 567, 209-212 (2019)] have proposed a quantum machine learning algorithm with quantum-enhanced…

We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…

Although taxonomy is often used informally to evaluate the results of phylogenetic inference and find the root of phylogenetic trees, algorithmic methods to do so are lacking. In this paper we formalize these procedures and develop…

We propose a taxonomy for quantum algorithms grounded in the fundamental symmetries, both continuous and discrete, underlying quantum state spaces, oracles, and circuit dynamics. By organizing algorithms according to their symmetry groups…

The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers are difficult to compute and no general algorithm…

In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…

In this paper we present a novel tool to evaluate problem solving systems. Instead of using a system to solve a problem, we suggest using the problem to evaluate the system. By finding a numerical representation of a problem's complexity,…

Graph neural networks have achieved state-of-the-art accuracy for graph node classification. However, GNNs are difficult to scale to large graphs, for example frequently encountering out-of-memory errors on even moderate size graphs. Recent…

We introduce a novel approach to description of networks/graphs. It is based on an analogue physical model which is dynamically evolved. This evolution depends on the connectivity matrix and readily brings out many qualitative features of…

This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance…

In recent years, many neural network models have been proposed for pattern classification, function approximation and regression problems. This paper presents an approach for classifying patterns from simplified NNs. Although the predictive…