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In 1968, Dashen and Sharp obtained a certain singular Lie algebra of local densities and currents from canonical commutation relations in nonrelativistic quantum field theory. The corresponding Lie group is infinite dimensional: the natural semidirect product of an additive group of scalar functions with a group of diffeomorphisms. Unitary representations of this group describe a wide variety of quantum systems, and have predicted previously unsuspected possibilities; notably, anyons and nonabelian anyons in two space dimensions. We present here foundational reasons why this semidirect product group serves as a universal kinematical group for quantum mechanics. We obtain thus a unified account of all possible quantum kinematics for systems with mass in an arbitrary physical space, and clarify the role played by topology in quantum mechanics. Our development does not require quantization of classical phase space; rather, the classical limit follows from the quantum mechanics. We also consider the relationship of our development to Heisenberg quantization., Comment: This report is based on the presentation by G. A. Goldin at the International Conference on Mathematical Methods in Physics 2023, in Marrakesh, Morocco

Demonstrations of topological photonics have so far largely been confined to infrared wavelengths where imaging technology and access to low-dimensional quantum materials are both limited. Here, we designed and fabricated silicon nitride ring-resonator arrays to demonstrate photonic topological edge states at ~780 nm. We observed edge states corresponding to the integer quantum Hall Hamiltonian with topological protection against fabrication disorder. This demonstration extends the concept of topological edge states to the near-visible regime and paves the way for nonlinear and non-Hermitian topological photonics with the rich library of near-visible quantum emitters., Comment: 7 pages, 4 figures

Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed over non-Euclidean domains, including smooth manifolds appearing in numerous fields such as computer vision, dynamical systems, and neuroscience. However, these approaches assume that the manifold underlying the data is known, limiting their practical utility. We introduce RVGP, a generalisation of GPs for learning vector signals over latent Riemannian manifolds. Our method uses positional encoding with eigenfunctions of the connection Laplacian, associated with the tangent bundle, readily derived from common graph-based approximation of data. We demonstrate that RVGP possesses global regularity over the manifold, which allows it to super-resolve and inpaint vector fields while preserving singularities. Furthermore, we use RVGP to reconstruct high-density neural dynamics derived from low-density EEG recordings in healthy individuals and Alzheimer's patients. We show that vector field singularities are important disease markers and that their reconstruction leads to a comparable classification accuracy of disease states to high-density recordings. Thus, our method overcomes a significant practical limitation in experimental and clinical applications., Comment: ICLR 2024 conference paper. Associated code: https://github.com/agosztolai/RVGP

We discuss the reconstruction of low-energy nuclear reaction kinematics from charged-particle tracks in solenoidal spectrometers working in Active Target Time Projection Chamber mode. In this operation mode, reaction products are tracked within the active gas medium of the Active Target with a three dimensional space point cloud. We have inferred the reaction kinematics from the point cloud using an algorithm based on a linear quadratic estimator (Kalman filter). The performance of this algorithm has been evaluated using experimental data from nuclear reactions measured with the Active Target Time Projection Chamber (AT-TPC) detector.

Free-space modulation of light is crucial for many applications, from light detection and ranging to virtual or augmented reality. Traditional means of modulating free-space light involves spatial light modulators based on liquid crystals and microelectromechanical systems, which are bulky, have large pixel areas (~10 micron x 10 micron), and require high driving voltage. Recent progress in meta-optics has shown promise to circumvent some of the limitations. By integrating active materials with sub-wavelength pixels in a meta-optic, the power consumption can be dramatically reduced while achieving a faster speed. However, these reconfiguration methods are volatile and hence require constant application of control signals, leading to phase jitter and crosstalk. Additionally, to control a large number of pixels, it is essential to implement a memory within each pixel to have a tractable number of control signals. Here, we develop a device with nonvolatile, electrically programmable, phase-only modulation of free-space infrared radiation in transmission using the low-loss phase-change material (PCM) Sb2Se3. By coupling an ultra-thin PCM layer to a high quality (Q)-factor (Q~406) diatomic metasurface, we demonstrate a phase-only modulation of ~0.25pi (~0.2pi) in simulation (experiment), ten times larger than a bare PCM layer of the same thickness. The device shows excellent endurance over 1,000 switching cycles. We then advance the device geometry, to enable independent control of 17 meta-molecules, achieving ten deterministic resonance levels with a 2pi phase shift. By independently controlling the phase delay of pixels, we further show tunable far-field beam shaping. Our work paves the way to realizing non-volatile transmissive phase-only spatial light modulators.

The wave nature of light sets a fundamental diffraction limit that challenges confinement and control of light in nanoscale structures with dimensions significantly smaller than the wavelength. Here, we demonstrate van der Waals MoS_2 nano-photonic devices with dimensions as small as ~ \lambda/16 (~60 nm at 1000 nm excitation wavelength). This deep subwavelength light confinement is achieved by exploiting the coupling between MoS_2 excitons and photons. We validate deep subwavelength light control via far- and near-field measurements. Our near-field measurements reveal detailed imaging of excitation, evolution, and guidance of fields in MoS_2 nanodevices, whereas our far-field study examines highly confined integrated photonics. Exciton-driven nano-photonics at a fraction of a wavelength demonstrated here could dramatically reduce the size of integrated photonic devices and opto-electronic circuits with potential applications in optical information science and engineering., Comment: 39 pages, 32 figures

Engineering the dispersion of light in a metasurface allows for controlling the light-matter interaction strength between light confined in the metasurface and materials placed within its near-field. Specifically, engineering a flatband dispersion increases the photonic density of states thereby enhancing the light-matter interaction. Here, we experimentally demonstrate a metasurface with a flat dispersion at visible wavelengths. We designed and fabricated a suspended one-dimensional gallium phosphide metasurface and measured the photonic band structure via energy-momentum spectroscopy, observing a photonic band that is flat over $10^o$ of half-angle at $\sim 580$nm. We integrated cadmium selenide nanoplatelets with the metasurface, and measured coupled photoluminescence into the flatband. Our demonstration of a photonic flatband will enable the possibility of integrating emerging quantum emitters to the metasurface with possible applications in nonlinear image processing, and topological photonics.

The combination of photonic integrated circuits and free-space meta-optics has the ability to unclasp technological knots that require advanced light manipulation due their conjoined ability to guide and shape electromagnetic waves. The need for large scale access and component interchangeability is essential for rapid prototyping of optical systems. Such capability represents a functional challenge in terms of fabrication and alignment of compound photonic platform. Here, we report a multi-functional interface that demonstrates the capabilities of a flexible and interchangeable combination of a photonic integrated circuit to a free-space coupling chip with different designs of low-loss meta-optics at a wavelength of 780 nm. We show that robustness and fidelity of the designed optical functions can be achieved without prior precise characterization of the free-space input nor stringent alignment between the photonic integrated chip and the meta-optics chip. A diffraction limited spot of approximately 3 micron for a hyperboloid metalens of numerical aperture 0.15 was achieved despite an input Gaussian elliptical deformation of up to 35% and misalignments of the components of up to 20 micron. A holographic display with a peak signal-to-noise ratio of more than 10 compared to its ground truth is also reported using this platform making this work the first interface to shape photonic integrated modes into free space using different diffractive optical functions.

The accurate prognosis for traumatic brain injury (TBI) patients is difficult yet essential to inform therapy, patient management, and long-term after-care. Patient characteristics such as age, motor and pupil responsiveness, hypoxia and hypotension, and radiological findings on computed tomography (CT), have been identified as important variables for TBI outcome prediction. CT is the acute imaging modality of choice in clinical practice because of its acquisition speed and widespread availability. However, this modality is mainly used for qualitative and semi-quantitative assessment, such as the Marshall scoring system, which is prone to subjectivity and human errors. This work explores the predictive power of imaging biomarkers extracted from routinely-acquired hospital admission CT scans using a state-of-the-art, deep learning TBI lesion segmentation method. We use lesion volumes and corresponding lesion statistics as inputs for an extended TBI outcome prediction model. We compare the predictive power of our proposed features to the Marshall score, independently and when paired with classic TBI biomarkers. We find that automatically extracted quantitative CT features perform similarly or better than the Marshall score in predicting unfavourable TBI outcomes. Leveraging automatic atlas alignment, we also identify frontal extra-axial lesions as important indicators of poor outcome. Our work may contribute to a better understanding of TBI, and provides new insights into how automated neuroimaging analysis can be used to improve prognostication after TBI., Comment: Accepted at MLCN MICCAI 2022 workshop

Machine learning models deployed on medical imaging tasks must be equipped with out-of-distribution detection capabilities in order to avoid erroneous predictions. It is unsure whether out-of-distribution detection models reliant on deep neural networks are suitable for detecting domain shifts in medical imaging. Gaussian Processes can reliably separate in-distribution data points from out-of-distribution data points via their mathematical construction. Hence, we propose a parameter efficient Bayesian layer for hierarchical convolutional Gaussian Processes that incorporates Gaussian Processes operating in Wasserstein-2 space to reliably propagate uncertainty. This directly replaces convolving Gaussian Processes with a distance-preserving affine operator on distributions. Our experiments on brain tissue-segmentation show that the resulting architecture approaches the performance of well-established deterministic segmentation algorithms (U-Net), which has not been achieved with previous hierarchical Gaussian Processes. Moreover, by applying the same segmentation model to out-of-distribution data (i.e., images with pathology such as brain tumors), we show that our uncertainty estimates result in out-of-distribution detection that outperforms the capabilities of previous Bayesian networks and reconstruction-based approaches that learn normative distributions. To facilitate future work our code is publicly available., Comment: Published in Journal of Machine Learning for Biomedical Imaging: Special Issue: Information Processing in Medical Imaging (IPMI) 2021

Agitation is one of the neuropsychiatric symptoms with high prevalence in dementia which can negatively impact the Activities of Daily Living (ADL) and the independence of individuals. Detecting agitation episodes can assist in providing People Living with Dementia (PLWD) with early and timely interventions. Analysing agitation episodes will also help identify modifiable factors such as ambient temperature and sleep as possible components causing agitation in an individual. This preliminary study presents a supervised learning model to analyse the risk of agitation in PLWD using in-home monitoring data. The in-home monitoring data includes motion sensors, physiological measurements, and the use of kitchen appliances from 46 homes of PLWD between April 2019-June 2021. We apply a recurrent deep learning model to identify agitation episodes validated and recorded by a clinical monitoring team. We present the experiments to assess the efficacy of the proposed model. The proposed model achieves an average of 79.78% recall, 27.66% precision and 37.64% F1 scores when employing the optimal parameters, suggesting a good ability to recognise agitation events. We also discuss using machine learning models for analysing the behavioural patterns using continuous monitoring data and explore clinical applicability and the choices between sensitivity and specificity in-home monitoring applications., Comment: 13 pages, accepted to Research2Clinics WS @ NeurIPS 2021

Interpreting the environmental, behavioural and psychological data from in-home sensory observations and measurements can provide valuable insights into the health and well-being of individuals. Presents of neuropsychiatric and psychological symptoms in people with dementia have a significant impact on their well-being and disease prognosis. Agitation in people with dementia can be due to many reasons such as pain or discomfort, medical reasons such as side effects of a medicine, communication problems and environment. This paper discusses a model for analysing the risk of agitation in people with dementia and how in-home monitoring data can support them. We proposed a semi-supervised model which combines a self-supervised learning model and a Bayesian ensemble classification. We train and test the proposed model on a dataset from a clinical study. The dataset was collected from sensors deployed in 96 homes of patients with dementia. The proposed model outperforms the state-of-the-art models in recall and f1-score values by 20%. The model also indicates better generalisability compared to the baseline models.

We propose a parameter efficient Bayesian layer for hierarchical convolutional Gaussian Processes that incorporates Gaussian Processes operating in Wasserstein-2 space to reliably propagate uncertainty. This directly replaces convolving Gaussian Processes with a distance-preserving affine operator on distributions. Our experiments on brain tissue-segmentation show that the resulting architecture approaches the performance of well-established deterministic segmentation algorithms (U-Net), which has never been achieved with previous hierarchical Gaussian Processes. Moreover, by applying the same segmentation model to out-of-distribution data (i.e., images with pathology such as brain tumors), we show that our uncertainty estimates result in out-of-distribution detection that outperforms the capabilities of previous Bayesian networks and reconstruction-based approaches that learn normative distributions.

Behavioural symptoms and urinary tract infections (UTI) are among the most common problems faced by people with dementia. One of the key challenges in the management of these conditions is early detection and timely intervention in order to reduce distress and avoid unplanned hospital admissions. Using in-home sensing technologies and machine learning models for sensor data integration and analysis provides opportunities to detect and predict clinically significant events and changes in health status. We have developed an integrated platform to collect in-home sensor data and performed an observational study to apply machine learning models for agitation and UTI risk analysis. We collected a large dataset from 88 participants with a mean age of 82 and a standard deviation of 6.5 (47 females and 41 males) to evaluate a new deep learning model that utilises attention and rational mechanism. The proposed solution can process a large volume of data over a period of time and extract significant patterns in a time-series data (i.e. attention) and use the extracted features and patterns to train risk analysis models (i.e. rational). The proposed model can explain the predictions by indicating which time-steps and features are used in a long series of time-series data. The model provides a recall of 91\% and precision of 83\% in detecting the risk of agitation and UTIs. This model can be used for early detection of conditions such as UTIs and managing of neuropsychiatric symptoms such as agitation in association with initial treatment and early intervention approaches. In our study we have developed a set of clinical pathways for early interventions using the alerts generated by the proposed model and a clinical monitoring team has been set up to use the platform and respond to the alerts according to the created intervention plans., Comment: 11 pages

Machine learning techniques combined with in-home monitoring technologies provide a unique opportunity to automate diagnosis and early detection of adverse health conditions in long-term conditions such as dementia. However, accessing sufficient labelled training samples and integrating high-quality, routinely collected data from heterogeneous in-home monitoring technologies are main obstacles hindered utilising these technologies in real-world medicine. This work presents a semi-supervised model that can continuously learn from routinely collected in-home observation and measurement data. We show how our model can process highly imbalanced and dynamic data to make robust predictions in analysing the risk of Urinary Tract Infections (UTIs) in dementia. UTIs are common in older adults and constitute one of the main causes of avoidable hospital admissions in people with dementia (PwD). Health-related conditions, such as UTI, have a lower prevalence in individuals, which classifies them as sporadic cases (i.e. rare or scattered, yet important events). This limits the access to sufficient training data, without which the supervised learning models risk becoming overfitted or biased. We introduce a probabilistic semi-supervised learning framework to address these issues. The proposed method produces a risk analysis score for UTIs using routinely collected data by in-home sensing technologies., Comment: 11 pages

Stacking Gaussian Processes severely diminishes the model's ability to detect outliers, which when combined with non-zero mean functions, further extrapolates low non-parametric variance to low training data density regions. We propose a hybrid kernel inspired from Varifold theory, operating in both Euclidean and Wasserstein space. We posit that directly taking into account the variance in the computation of Wasserstein-2 distances is of key importance towards maintaining outlier status throughout the hierarchy. We show improved performance on medium and large scale datasets and enhanced out-of-distribution detection on both toy and real data.