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Functional neuroimaging studies have lead to understanding the brain as a collection of spatially segregated functional networks. It is thought that each of these networks is in turn composed of a set of distinct sub-regions that together…

Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…

Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition. We extend these models to the multi-output setting, i.e., for learning vector-valued functions, with application…

We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…

This paper proposes fractional order graph neural networks (FGNNs), optimized by the approximation strategy to address the challenges of local optimum of classic and fractional graph neural networks which are specialised at aggregating…

The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…

The ability to dynamically extend a model to new data and classes is critical for multiple organ and tumor segmentation. However, due to privacy regulations, accessing previous data and annotations can be problematic in the medical domain.…

We propose conditioning field initialization for neural network based topology optimization. In this work, we focus on (1) improving upon existing neural network based topology optimization, (2) demonstrating that by using a prior initial…

Today, deep convolutional neural networks (CNNs) have demonstrated state of the art performance for supervised medical image segmentation, across various imaging modalities and tasks. Despite early success, segmentation networks may still…

First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…

We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

In this work, we develop and analyze a higher-order finite element method for the multidimensional fragmentation equation. To the best of our knowledge, this is the first study to establish a rigorous, conforming finite element framework…

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (1) not naturally amenable to gradient-based optimization, and (2) incompatible…

In addition to being extremely non-linear, modern problems require millions if not billions of parameters to solve or at least to get a good approximation of the solution, and neural networks are known to assimilate that complexity by…

To combine a feedforward neural network (FNN) and Lie group (symmetry) theory of differential equations (DEs), an alternative artificial NN approach is proposed to solve the initial value problems (IVPs) of ordinary DEs (ODEs). Introducing…

Convolutional Neural Networks (CNNs) work very well for supervised learning problems when the training dataset is representative of the variations expected to be encountered at test time. In medical image segmentation, this premise is…

Automatic segmentation of brain glioma from multimodal MRI scans plays a key role in clinical trials and practice. Unfortunately, manual segmentation is very challenging, time-consuming, costly, and often inaccurate despite human expertise…

By promising more accurate diagnostics and individual treatment recommendations, deep neural networks and in particular convolutional neural networks have advanced to a powerful tool in medical imaging. Here, we first give an introduction…

The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution…