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Concept learning is a general task with applications in various domains. As a motivating example we consider the application of music playlist generation, where a playlist is represented as a concept (e.g., `relaxing music') rather than as…

In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support vector machines,…

Calculating intermolecular charge transfer integrals in organic semiconductors requires substantial computer resource for each individual calculation. We might alternatively construct a machine learning model for transfer integrals, which…

Deep generative models (DGMs) have recently demonstrated remarkable success in capturing complex probability distributions over graphs. Although their excellent performance is attributed to powerful and scalable deep neural networks, it is,…

Let $\Mod \CS$ denote the category of $\CS$-modules, where $\CS$ is a small category. In the first part of this paper, we provide a version of Rickard's theorem on derived equivalence of rings for $\Mod \CS$. This will have several…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

Significant efforts are being spent on building a quantum computer. At the same time, developments in quantum software are rapidly progressing. Insufficient quantum resources often are the problem when running quantum algorithms. New…

Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The…

We achieve new results on skew polynomial rings and their quotients, including the first explicit example of a skew polynomial ring where the ratio of the degree of a skew polynomial to the degree of its bound is not extremal. These methods…

This paper presents a systematic study on developing multi-template machine learning (ML) surrogate models and applying them to the inverse design of transformers (XFMRs) in radio-frequency integrated circuits (RFICs). Our study starts with…

Monte Carlo simulations of systems of particles such as hard spheres or soft spheres with singular kernels can display around a phase transition prohibitively long convergence times when using traditional Hasting-Metropolis reversible…

It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem…

We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to…

Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…

Machine learning potentials (MLPs) developed from extensive datasets constructed from density functional theory (DFT) calculations have become increasingly appealing for many researchers. This paper presents a framework of polynomial-based…

Recurrent neural networks (RNNs) are more suitable for learning non-linear dependencies in dynamical systems from observed time series data. In practice all the external variables driving such systems are not known a priori, especially in…

Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are…

Reverse Monte Carlo (RMC) is an algorithm that incorporates stochastic modification of the action as part of the process that updates the fields in a Monte Carlo simulation. Such update moves have the potential of lowering or eliminating…

Neural networks are widely used as a model for classification in a large variety of tasks. Typically, a learnable transformation (i.e. the classifier) is placed at the end of such models returning a value for each class used for…

The pharmaceutical industry has witnessed exponential growth in transforming operations towards continuous manufacturing to effectively achieve increased profitability, reduced waste, and extended product range. Model Predictive Control…