Stable tensor neural networks for efficient deep learning.

Learning from complex, multidimensional data has become central to computational mathematics, and among the most successful high-dimensional function approximators are deep neural networks (DNNs). Training DNNs is posed as an optimization problem to learn network weights or parameters that well-approximate a mapping from input to target data. Multiway data or tensors arise naturally in myriad ways in deep learning, in particular as input data and as high-dimensional weights and features extracted by the network, with the latter often being a bottleneck in terms of speed and memory.

Combining data and theory for derivable scientific discovery with AI-Descartes.

Scientists aim to discover meaningful formulae that accurately describe experimental data. Mathematical models of natural phenomena can be manually created from domain knowledge and fitted to data, or, in contrast, created automatically from large datasets with machine-learning algorithms. The problem of incorporating prior knowledge expressed as constraints on the functional form of a learned model has been studied before, while finding models that are consistent with prior knowledge expressed via general logical axioms is an open problem.

Dynamic graph and polynomial chaos based models for contact tracing data analysis and optimal testing prescription.

In this study, we address three important challenges related to disease transmissions such as the COVID-19 pandemic, namely, (a) providing an early warning to likely exposed individuals, (b) identifying individuals who are asymptomatic, and (c) prescription of optimal testing when testing capacity is limited. First, we present a dynamic-graph based SEIR epidemiological model in order to describe the dynamics of the disease propagation. Our model considers a dynamic graph/network that accounts for the interactions between individuals over time, such as the ones obtained by manual or automated contact tracing, and uses a diffusion-reaction mechanism to describe the state dynamics.

Tensor-tensor algebra for optimal representation and compression of multiway data.

With the advent of machine learning and its overarching pervasiveness it is imperative to devise ways to represent large datasets efficiently while distilling intrinsic features necessary for subsequent analysis. The primary workhorse used in data dimensionality reduction and feature extraction has been the matrix singular value decomposition (SVD), which presupposes that data have been arranged in matrix format. A primary goal in this study is to show that high-dimensional datasets are more compressible when treated as tensors (i.

A modelling study to inform specification and optimal electrode placement for imaging of neuronal depolarization during visual evoked responses by electrical and magnetic detection impedance tomography.

Electrical impedance tomography (EIT) has the potential to achieve non-invasive functional imaging of fast neuronal activity in the human brain due to opening of ion channels during neuronal depolarization. Local changes of resistance in the cerebral cortex are about 1%, but the size and location of changes recorded on the scalp are unknown. The purpose of this work was to develop an anatomically realistic finite element model of the adult human head and use it to predict the amplitude and topography of changes on the scalp, and so inform specification for an in vivo measuring system.

Use of anisotropic modelling in electrical impedance tomography: description of method and preliminary assessment of utility in imaging brain function in the adult human head.

Electrical Impedance Tomography (EIT) is an imaging method which enables a volume conductivity map of a subject to be produced from multiple impedance measurements. It has the potential to become a portable non-invasive imaging technique of particular use in imaging brain function. Accurate numerical forward models may be used to improve image reconstruction but, until now, have employed an assumption of isotropic tissue conductivity.

Design of electrodes and current limits for low frequency electrical impedance tomography of the brain.

For the novel application of recording of resistivity changes related to neuronal depolarization in the brain with electrical impedance tomography, optimal recording is with applied currents below 100 Hz, which might cause neural stimulation of skin or underlying brain. The purpose of this work was to develop a method for application of low frequency currents to the scalp, which delivered the maximum current without significant stimulation of skin or underlying brain. We propose a recessed electrode design which enabled current injection with an acceptable skin sensation to be increased from 100 muA using EEG electrodes, to 1 mA in 16 normal volunteers.

Design and calibration of a compact multi-frequency EIT system for acute stroke imaging.

A new, compact UCLH Mk 2.5 EIT system has been developed and calibrated for EIT imaging of the head. Improvements include increased input and output impedances, increased bandwidth and improved CMRR (80 dB) and linearity over frequencies and load (0.

Factors limiting the application of electrical impedance tomography for identification of regional conductivity changes using scalp electrodes during epileptic seizures in humans.

Electrical impedance tomography (EIT) has the potential to produce images during epileptic seizures. This might improve the accuracy of the localization of epileptic foci in patients undergoing presurgical assessment for curative neurosurgery. It has already been shown that impedance increases by up to 22% during induced epileptic seizures in animal models, using cortical or implanted electrodes in controlled experiments.

Multi-frequency electrical impedance tomography (EIT) of the adult human head: initial findings in brain tumours, arteriovenous malformations and chronic stroke, development of an analysis method and calibration.

MFEIT (multi-frequency electrical impedance tomography) could distinguish between ischaemic and haemorrhagic stroke and permit the urgent use of thrombolytic drugs in patients with ischaemic stroke. The purpose of this study was to characterize the UCLH Mk 2 MFEIT system, designed for this purpose, with 32 electrodes and a multiplexed 2 kHz to 1.6 MHz single impedance measuring circuit.

Diffuse photon propagation in multilayered geometries.

Diffuse optical tomography (DOT) is an emerging functional medical imaging modality which aims to recover the optical properties of biological tissue. The forward problem of the light propagation of DOT can be modelled in the frequency domain as a diffusion equation with Robin boundary conditions. In the case of multilayered geometries with piecewise constant parameters, the forward problem is equivalent to a set of coupled Helmholtz equations.

Applications of GRID in clinical neurophysiology and Electrical Impedance Tomography of brain function.

The computational requirements in Neurophysiology are increasing with the development of new analysis methods. The resources the GRID has to offer are ideally suited for this complex processing. A practical implementation of the GRID, Condor, has been assessed using a local cluster of 920 PCs.

Generating accurate finite element meshes for the forward model of the human head in EIT.

The use of realistic anatomy in the model used for image reconstruction in EIT of brain function appears to confer significant improvements compared to geometric shapes such as a sphere. Accurate model geometry may be achieved by numerical models based on magnetic resonance images (MRIs) of the head, and this group has elected to use finite element meshing (FEM) as it enables detailed internal anatomy to be modelled and has the capability to incorporate information about tissue anisotropy. In this paper a method for generating accurate FEMs of the human head is presented where MRI images are manually segmented using custom adaptation of industry standard commercial design software packages.

Using the GRID to improve the computation speed of electrical impedance tomography (EIT) reconstruction algorithms.

In our group at University College London, we have been developing electrical impedance tomography (EIT) of brain function. We have attempted to improve image quality by the use of realistic anatomical meshes and, more recently, non-linear reconstruction methods. Reconstruction with linear methods, with pre-processing, may take up to a few minutes per image for even detailed meshes.

Digital subtraction versus film-screen angiography for detecting acute pulmonary emboli: evaluation in a porcine model.

Purpose: To compare the diagnostic performance of digital subtraction angiography (DSA) to that of film-screen angiography (FSA) for detecting acute pulmonary embolism (PE) in a porcine model.

Materials And Methods: DSA and FSA were performed in 13 pigs before and after central venous administration of autologous emboli. Results were compared to findings at necropsy with use of ex vivo pulmonary angiography to guide pathologic sectioning.

Depiction of pulmonary emboli with spiral CT: optimization of display window settings in a porcine model.

Purpose: To determine optimal spiral computed tomographic (CT) image display for depiction of pulmonary emboli (PE).

Materials And Methods: Autologous PE detected in 10 pigs with contrast material-enhanced spiral CT were displayed with six display window settings (standard mediastinal window and five modified windows referenced to attenuation values in pulmonary artery [PA] branches). The thrombus gray level and gray level contrast and separability of PE versus those of the local PA branch were computed for each window setting; results were compared with repeated measured analysis of variance.