Using deep LSD to build operators in GANs latent space with meaning in real space.

Generative models rely on the idea that data can be represented in terms of latent variables which are uncorrelated by definition. Lack of correlation among the latent variable support is important because it suggests that the latent-space manifold is simpler to understand and manipulate than the real-space representation. Many types of generative model are used in deep learning, e.g., variational autoencoders (VAEs) and generative adversarial networks (GANs). Based on the idea that the latent space behaves like a vector space Radford et al. (2015), we ask whether we can expand the latent space representation of our data elements in terms of an orthonormal basis set. Here we propose a method to build a set of linearly independent vectors in the latent space of a trained GAN, which we call quasi-eigenvectors. These quasi-eigenvectors have two key properties: i) They span the latent space, ii) A set of these quasi-eigenvectors map to each of the labeled features one-to-one. We show that in the case of the MNIST image data set, while the number of dimensions in latent space is large by design, 98% of the data in real space map to a sub-domain of latent space of dimensionality equal to the number of labels. We then show how the quasi-eigenvectors can be used for Latent Spectral Decomposition (LSD). We apply LSD to denoise MNIST images. Finally, using the quasi-eigenvectors, we construct rotation matrices in latent space which map to feature transformations in real space. Overall, from quasi-eigenvectors we gain insight regarding the latent space topology.

Prediction of Blood Risk Score in Diabetes Using Deep Neural Networks.

Improving the prediction of blood glucose concentration may improve the quality of life of people living with type 1 diabetes by enabling them to better manage their care. Given the anticipated benefits of such a prediction, numerous methods have been proposed. Rather than attempting to predict glucose concentration, a deep learning framework for prediction is proposed in which prediction is performed using a scale for hypo- and hyper-glycemia risk. Using the blood glucose risk score formula proposed by Kovatchev et al., models with different architectures were trained, including, a recurrent neural network (RNN), a gated recurrent unit (GRU), a long short-term memory (LSTM) network, and an encoder-like convolutional neural network (CNN). The models were trained using the OpenAPS Data Commons data set, comprising 139 individuals, each with tens of thousands of continuous glucose monitor (CGM) data points. The training set was composed of 7% of the data set, while the remaining was used for testing. Performance comparisons between the different architectures are presented and discussed. To evaluate these predictions, performance results are compared with the last measurement (LM) prediction, through a sample-and-hold approach continuing the last known measurement forward. The results obtained are competitive when compared to other deep learning methods. A root mean squared error (RMSE) of 16 mg/dL, 24 mg/dL, and 37 mg/dL were obtained for CNN prediction horizons of 15, 30, and 60 min, respectively. However, no significant improvements were found for the deep learning models compared to LM prediction. Performance was found to be highly dependent on architecture and the prediction horizon. Lastly, a metric to assess model performance by weighing each prediction point error with the corresponding blood glucose risk score is proposed. Two main conclusions are drawn. Firstly, going forward, there is a need to benchmark model performance using LM prediction to enable the comparison between results obtained from different data sets. Secondly, model-agnostic data-driven deep learning models may only be meaningful when combined with mechanistic physiological models; here, it is argued that neural ordinary differential equations may combine the best of both approaches. These findings are based on the OpenAPS Data Commons data set and are to be validated in other independent data sets.

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations.

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

Más Allá de La Filogenética: Evolución Darwiniana de La Actina / Beyond Phylogenetics: Darwinian Evolution of Actin

Resumen La actina es una proteína que se polimeriza para formar citoesqueletos y cuya función es estabilizar y dirigir el movimiento de las paredes celulares. Es una de las proteínas más estables, habiendo evolucionado poco a partir de algas y levaduras, y muy poco desde los peces. Aquí analizamos la evolución de la actina usando las teorías modernas de las interacciones de conformación proteína-agua, y cómo estas han evolucionado para optimizar las funciones de la proteína. Llegamos a la conclusión de que el fracaso del análisis filogenético para identificar positivamente la evolución darwiniana de las proteínas ha sido causado por las limitaciones técnicas propias del siglo XX. Estas limitaciones pueden ser superadas mediante el escalamiento termodinámico y el promedio modular ambos llevados a niveles técnicos del siglo XXI. Los resultados para la actina son especialmente llamativos y reflejan estructuras duales estables, globulares y polimerizadas.

Abstract Actin polymerizes to form cytoskeletons which stabilize and direct motion of cellular walls. It is one of the most stable proteins, having evolved little from algae and yeast, and very little from fish. Here we analyze actin evolution using modern theories of water-protein shaping interactions, and how these have evolved to optimize protein functions. We conclude that the failure of phylogenetic analysis to identify positive Darwinian evolution has been caused by 20th century technical limitations. These are overcome using 21st century thermodynamic scaling and modular averaging. The results for actin are especially striking, and reflect dual stable structures, globular and polymerized.

Escape time, relaxation, and sticky states of a softened Henon-Heiles model: Low-frequency vibrational mode effects and glass relaxation.

Here we study the relaxation of a chain consisting of three masses joined by nonlinear springs and periodic conditions when the stiffness is weakened. This system, when expressed in their normal coordinates, yields a softened Henon-Heiles system. By reducing the stiffness of one low-frequency vibrational mode, a faster relaxation is enabled. This is due to a reduction of the energy barrier heights along the softened normal mode as well as for a widening of the opening channels of the energy landscape in configurational space. The relaxation is for the most part exponential, and can be explained by a simple flux equation. Yet, for some initial conditions the relaxation follows as a power law, and in many cases there is a regime change from exponential to power-law decay. We pinpoint the initial conditions for the power-law decay, finding two regions of sticky states. For such states, quasiperiodic orbits are found since almost for all components of the initial momentum orientation, the system is trapped inside two pockets of configurational space. The softened Henon-Heiles model presented here is intended as the simplest model in order to understand the interplay of rigidity, nonlinear interactions and relaxation for nonequilibrium systems such as glass-forming melts or soft matter. Our softened system can be applied to model ß relaxation in glasses and suggest that local reorientational jumps can have an exponential and a nonexponential contribution for relaxation, the latter due to asymmetric molecules sticking in cages for certain orientations.