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Rainfall is an important variable to be able to monitor and forecast across Africa, due to its impact on agriculture, food security, climate related diseases and public health. Numerical Weather Models (NWM) are an important component of this work, due to their complete spatial coverage, high resolution, and ability to forecast into the future. In this study, we seek to evaluate the spatiotemporal skill of short-term rainfall forecasts of rainfall across Africa. Specifically, the European Centre for Medium-Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction-Global Forecast System (NCEP-GFS) forecast models are verified by Rainfall Estimates 2.0 (RFE2) and African Rainfall Climatology Version 2 (ARC2), which are fused products of satellite and in-situ observations and are commonly used in analysis of African rainfall. We found that the model rainfall forecasts show good consistency with the satellite rainfall observations in spatial distribution over Africa on the seasonal timescale. Evaluation metrics show high spatial and seasonal variations over the African continent, including a strong link to the location of the inter-tropical convergence zone (ITCZ) and topographically enhanced precipitation. The rainfall forecasts at one week aggregation time are improved against daily forecasts., Comment: 50 pages, 10 figures, 3 supplementary figures

The unscented transform uses a weighted set of samples called sigma points to propagate the means and covariances of nonlinear transformations of random variables. However, unscented transforms developed using either the Gaussian assumption or a minimum set of sigma points typically fall short when the random variable is not Gaussian distributed and the nonlinearities are substantial. In this paper, we develop the generalized unscented transform (GenUT), which uses 2n+1 sigma points to accurately capture up to the diagonal components of the skewness and kurtosis tensors of most probability distributions. Constraints can be analytically enforced on the sigma points while guaranteeing at least second-order accuracy. The GenUT uses the same number of sigma points as the original unscented transform while also being applicable to non-Gaussian distributions, including the assimilation of observations in the modeling of infectious diseases such as coronavirus (SARS-CoV-2) causing COVID-19., Comment: 15 pages, 4 figures

An optimal filter for Poisson observations is developed as a variant of the traditional Kalman filter. Poisson distributions are characteristic of infectious diseases, which model the number of patients recorded as presenting each day to a health care system. We develop both a linear and nonlinear (extended) filter. The methods are applied to a case study of neonatal sepsis and postinfectious hydrocephalus in Africa, using parameters estimated from publicly available data. Our approach is applicable to a broad range of disease dynamics, including both noncommunicable and the inherent nonlinearities of communicable infectious diseases and epidemics such as from COVID-19., Comment: 19 Pages, 8 Figures

High resolution magnetic resonance (MR) images are desired for accurate diagnostics. In practice, image resolution is restricted by factors like hardware, cost and processing constraints. Recently, deep learning methods have been shown to produce compelling state of the art results for image super-resolution. Paying particular attention to desired hi-resolution MR image structure, we propose a new regularized network that exploits image priors, namely a low-rank structure and a sharpness prior to enhance deep MR image superresolution. Our contributions are then incorporating these priors in an analytically tractable fashion in the learning of a convolutional neural network (CNN) that accomplishes the super-resolution task. This is particularly challenging for the low rank prior, since the rank is not a differentiable function of the image matrix (and hence the network parameters), an issue we address by pursuing differentiable approximations of the rank. Sharpness is emphasized by the variance of the Laplacian which we show can be implemented by a fixed {\em feedback} layer at the output of the network. Experiments performed on two publicly available MR brain image databases exhibit promising results particularly when training imagery is limited., Comment: Accepted to IEEE ICIP 2018

The need for affordable and appropriate medical technologies for developing countries continue to rise as challenges such as inadequate energy supply, limited technical expertise and poor infrastructure persists. Low-field MRI is a technology that can be tailored to meet specific imaging needs within such countries. Its low power requirements and the possibility of operating in minimally shielded or unshielded environments make it especially attractive. Although the technology has been widely demonstrated over several decades, it is yet to be shown that it can be diagnostic and improve patient outcomes in clinical applications. We here demonstrate the robustness of pre-polarizing MRI (PMRI) technology for assembly and deployment in developing countries for the specific application to infant hydrocephalus. Hydrocephalus treatment planning and management requires modest spatial resolution, and only that the brain can be distinguished from fluid - tissue contrast detail within the brain parenchyma is not essential. We constructed an internally shielded PMRI system based on the Lee-Whiting coil system with a 22 cm diameter of spherical volume. In an unshielded room, projection phantom images were acquired at 113 kHz with in-plane resolution of 3 mm x 3 mm, by introducing gradient fields of sufficient magnitude to dominate the 5000ppm inhomogeneity of the readout field. The low cost, straightforward assembly, deployment potential, and maintenance requirements demonstrate the suitability of our PMRI system for developing countries. Further improvement in the image spatial resolution and contrast of low-field MRI will broaden its potential clinical utility beyond hydrocephalus., Comment: 21 pages, 9 figures, 39 references

Objective: Hydrocephalus is a medical condition in which there is an abnormal accumulation of cerebrospinal fluid (CSF) in the brain. Segmentation of brain imagery into brain tissue and CSF (before and after surgery, i.e. pre-op vs. postop) plays a crucial role in evaluating surgical treatment. Segmentation of pre-op images is often a relatively straightforward problem and has been well researched. However, segmenting post-operative (post-op) computational tomographic (CT)-scans becomes more challenging due to distorted anatomy and subdural hematoma collections pressing on the brain. Most intensity and feature based segmentation methods fail to separate subdurals from brain and CSF as subdural geometry varies greatly across different patients and their intensity varies with time. We combat this problem by a learning approach that treats segmentation as supervised classification at the pixel level, i.e. a training set of CT scans with labeled pixel identities is employed. Methods: Our contributions include: 1.) a dictionary learning framework that learns class (segment) specific dictionaries that can efficiently represent test samples from the same class while poorly represent corresponding samples from other classes, 2.) quantification of associated computation and memory footprint, and 3.) a customized training and test procedure for segmenting post-op hydrocephalic CT images. Results: Experiments performed on infant CT brain images acquired from the CURE Children's Hospital of Uganda reveal the success of our method against the state-of-the-art alternatives. We also demonstrate that the proposed algorithm is computationally less burdensome and exhibits a graceful degradation against number of training samples, enhancing its deployment potential., Comment: IEEE Transactions on Biomedical Engineering, 2018

In 2013, the US National Oceanographic and Atmospheric Agency refined the historical rainfall estimates over the African Continent and produced the African Rainfall Climate version 2.0 (ARC2) estimator. ARC2 offers a nearly complete record of daily rainfall estimates since 1983 at 0.1 x 0.1 degree resolution. Despite short-term anomalies in twice-yearly rainy season intensities in Uganda, we identify an overall decrease in average rainfall of about 12% during the past 34 years. Spatiotemporally, these decreases are greatest in agricultural regions of central and western Uganda, but are also reflective of rainfall decreases in the gorilla habitat within the Bwindi Forest in Southwest Uganda. The findings carry significant implications for agriculture, food security, and wildlife habitat., Comment: 19 pages, 5 figures

Neonatal sepsis (NS) is responsible for over a 1 million yearly deaths worldwide. In the developing world NS is often treated without an identified microbial pathogen. Amplicon sequencing of the bacterial 16S rRNA gene can be used to identify organisms that are difficult to detect by routine microbiological methods. However, contaminating bacteria are ubiquitous in both hospital settings and research reagents, and must be accounted for to make effective use of these data. In the present study, we sequenced the bacterial 16S rRNA gene obtained from blood and cerebrospinal fluid (CSF) of 80 neonates presenting with NS to the Mbarara Regional Hospital in Uganda. Assuming that patterns of background contamination would be independent of pathogenic microorganism DNA, we applied a novel quantitative approach using principal orthogonal decomposition to separate background contamination from potential pathogens in sequencing data. We designed our quantitative approach contrasting blood, CSF, and control specimens, and employed a variety of statistical random matrix bootstrap hypotheses to estimate statistical significance. These analyses demonstrate that Leptospira appears present in some infants presenting within 48 hr of birth, indicative of infection in utero, and up to 28 days of age, suggesting environmental exposure. This organism cannot be cultured in routine bacteriological settings, and is enzootic in the cattle that the rural peoples of western Uganda often live in close proximity. Our findings demonstrate that statistical approaches to remove background organisms common in 16S sequence data can reveal putative pathogens in small volume biological samples from newborns. This computational analysis thus reveals an important medical finding that has the potential to alter therapy and prevention efforts in a critically ill population., Comment: 23 pages, 2 figures

Observability and controllability are essential concepts to the design of predictive observer models and feedback controllers of networked systems. For example, noncontrollable mathematical models of real systems have subspaces that influence model behavior, but cannot be controlled by an input. Such subspaces can be difficult to determine in complex nonlinear networks. Since almost all of the present theory was developed for linear networks without symmetries, here we present a numerical and group representational framework, to quantify the observability and controllability of nonlinear networks with explicit symmetries that shows the connection between symmetries and nonlinear measures of observability and controllability. We numerically observe and theoretically predict that not all symmetries have the same effect on network observation and control. Our analysis shows that the presence of symmetry in a network may decrease observability and controllability, although networks containing only rotational symmetries remain controllable and observable. These results alter our view of the nature of observability and controllability in complex networks, change our understanding of structural controllability, and affect the design of mathematical models to observe and control such networks., Comment: 19 pages, 9 figures

We describe a geometric method to quantify wave patterns observed in the nervous system, which are non-stationary and with a mixture of spiral, target, plane and irregular waves. The method analyzes fluctuations of the energy angular distribution in two-dimensional Fourier spectrum of wave patterns, which reflects changes of the orientation distribution of wavefronts. We show that the number of the genuine peaks in generalized phase spectrum is close to the number of the coherent space-time clusters arising in wave patterns, and propose to use the number as a complexity measure., Comment: 16 pages, 3 figures, 1 video

In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. We seek to study these dynamics with respect to the following compartments: neurons, glia, and extracellular space. We are particularly interested in the slower time-scale dynamics that determine overall excitability, and set the stage for transient episodes of persistent oscillations, working memory, or seizures. In this second of two companion papers, we present an ionic current network model composed of populations of Hodgkin-Huxley type excitatory and inhibitory neurons embedded within extracellular space and glia, in order to investigate the role of micro-environmental ionic dynamics on the stability of persistent activity. We show that these networks reproduce seizure-like activity if glial cells fail to maintain the proper micro-environmental conditions surrounding neurons, and produce several experimentally testable predictions. Our work suggests that the stability of persistent states to perturbation is set by glial activity, and that how the response to such perturbations decays or grows may be a critical factor in a variety of disparate transient phenomena such as working memory, burst firing in neonatal brain or spinal cord, up states, seizures, and cortical oscillations., Comment: Post-review revision. 5 figures. This is the second of a pair of related papers; see also arXiv:0806.3738

In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. In this first paper, we construct a mathematical model consisting of a single conductance-based neuron together with intra- and extracellular ion concentration dynamics. We formulate a reduction of this model that permits a detailed bifurcation analysis, and show that the reduced model is a reasonable approximation of the full model. We find that competition between intrinsic neuronal currents, sodium-potassium pumps, glia, and diffusion can produce very slow and large-amplitude oscillations in ion concentrations similar to what is seen physiologically in seizures. Using the reduced model, we identify the dynamical mechanisms that give rise to these phenomena. These models reveal several experimentally testable predictions. Our work emphasizes the critical role of ion concentration homeostasis in the proper functioning of neurons, and points to important fundamental processes that may underlie pathological states such as epilepsy., Comment: Post-review revision. 8 figures. This is the first of a pair of related papers; see also arXiv:0806.3741

Recent work has identified nonlinear deterministic structure in neuronal dynamics using periodic orbit theory. Troublesome in this work were the significant periods of time where no periodic orbits were extracted - "dynamically dark" regions. Tests for periodic orbit structure typically require that the underlying dynamics are differentiable. Since continuity of a mathematical function is a necessary but insufficient condition for differentiability, regions of observed differentiability should be fully contained within regions of continuity. We here verify that this fundamental mathematical principle is reflected in observations from mammalian neuronal activity. First, we introduce a null Jacobian transformation to verify the observation of differentiable dynamics when periodic orbits are extracted. Second, we show that a less restrictive test for deterministic structure requiring only continuity demonstrates widespread nonlinear deterministic structure only partially appreciated with previous approaches., Comment: 4 Pages, RevTex, 3 Figures