Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition

Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables. This can be important, with some problems infeasible with one variable ordering but easy with another. Machine learning is the process of fitting a computer model to a complex function based on properties learned from measured data. In this paper we use machine learning (specifically a support vector machine) to select between heuristics for choosing a variable ordering, outperforming each of the separate heuristics.Comment: 16 page

Probability of local bifurcation type from a fixed point: A random matrix perspective

Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal approximators (neural networks). The eigenvalue spectra is considered both numerically and analytically using previous work of Edelman et. al. Based upon the numerical evidence, various conjectures are presented. The conclusion is that in many circumstances, most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues. Nevertheless, surprising situations are presented for which the aforementioned conclusion is not general, e.g. real random matrices with Gaussian elements with a large positive mean and finite variance.Comment: 21 pages, 19 figure

Neural parameters estimation for brain tumor growth modeling

Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the physiological processes that govern the growth of the tumor are considered. To personalize the model, i.e. find a relevant set of parameters, with respect to the tumor dynamics of a particular patient, the model is informed from empirical data, e.g., medical images obtained from diagnostic modalities, such as magnetic-resonance imaging. Existing model-observation coupling schemes require a large number of forward integrations of the biophysical model and rely on simplifying assumption on the functional form, linking the output of the model with the image information. In this work, we propose a learning-based technique for the estimation of tumor growth model parameters from medical scans. The technique allows for explicit evaluation of the posterior distribution of the parameters by sequentially training a mixture-density network, relaxing the constraint on the functional form and reducing the number of samples necessary to propagate through the forward model for the estimation. We test the method on synthetic and real scans of rats injected with brain tumors to calibrate the model and to predict tumor progression

Use of Therapeutic Drug Monitoring, Electronic Health Record Data, and Pharmacokinetic Modeling to Determine the Therapeutic Index of Phenytoin and Lamotrigine

Defining a drug's therapeutic index (TI) is important for patient safety and regulating the development of generic drugs. For many drugs, the TI is unknown. A systematic approach was developed to characterize the TI of a drug using therapeutic drug monitoring and electronic health record (EHR) data with pharmacokinetic (PK) modeling. This approach was first tested on phenytoin, which has a known TI, and then applied to lamotrigine, which lacks a defined TI

colorspace: A Toolbox for Manipulating and Assessing Colors and Palettes

The R package colorspace provides a flexible toolbox for selecting individual colors or color palettes, manipulating these colors, and employing them in statistical graphics and data visualizations. In particular, the package provides a broad range of color palettes based on the HCL (hue-chroma-luminance) color space. The three HCL dimensions have been shown to match those of the human visual system very well, thus facilitating intuitive selection of color palettes through trajectories in this space. Using the HCL color model, general strategies for three types of palettes are implemented: (1) Qualitative for coding categorical information, i.e., where no particular ordering of categories is available. (2) Sequential for coding ordered/numeric information, i.e., going from high to low (or vice versa). (3) Diverging for coding ordered/numeric information around a central neutral value, i.e., where colors diverge from neutral to two extremes. To aid selection and application of these palettes, the package also contains scales for use with ggplot2, shiny and tcltk apps for interactive exploration, visualizations of palette properties, accompanying manipulation utilities (like desaturation and lighten/darken), and emulation of color vision deficiencies. The shiny apps are also hosted online at http://hclwizard.org/

Foreground removal from CMB temperature maps using an MLP neural network

One of the main obstacles in extracting the Cosmic Microwave Background (CMB) signal from observations in the mm-submm range is the foreground contamination by emission from galactic components: mainly synchrotron, free-free and thermal dust emission. Due to the statistical nature of the intrinsic CMB signal it is essential to minimize the systematic errors in the CMB temperature determinations. Following the available knowledge of the spectral behavior of the galactic foregrounds simple, power law-like spectra have been assumed. The feasibility of using a simple neural network for extracting the CMB temperature signal from the combined CMB and foreground signals has been investigated. As a specific example, we have analysed simulated data, like that expected from the ESA Planck Surveyor mission. A simple multilayer perceptron neural network with 2 hidden layers can provide temperature estimates, over more than 80 percent of the sky, that are to a high degree uncorrelated with the foreground signals. A single network will be able to cover the dynamic range of the Planck noise level over the entire sky.Comment: Accepted for publication in Astrophysics and Space Scienc

Anaerobic Antimicrobial Therapy After Necrotizing Enterocolitis in VLBW Infants

To evaluate the effect of anaerobic antimicrobial therapy for necrotizing enterocolitis (NEC) on clinical outcomes in very low birth weight (≤1500 g) infants

Urinary tract infection concordance with positive blood and cerebrospinal fluid cultures in the neonatal intensive care unit

Urinary tract infections (UTI) are common in the neonatal intensive care unit (NICU). Blood, urine, and cerebrospinal fluid (CSF) cultures are frequently obtained to evaluate for infection. We sought to determine the concordance between positive urine cultures and blood or CSF cultures

A new approach in modeling the response of RPC detectors

The response of RPC detectors is highly sensitive to environmental variables. A novel approach is presented to model the response of RPC detectors in a variety of experimental conditions. The algorithm, based on Artificial Neural Networks, has been developed and tested on the CMS RPC gas gain monitoring system during commissioning