Search

Nonlinear independent component analysis is combined with diffusion-map data analysis techniques to detect good observables in high-dimensional dynamic data. These detections are achieved by integrating local principal component analysis of simulation bursts by using eigenvectors of a Markov matrix describing anisotropic diffusion. The widely applicable procedure, a crucial step in model reduction approaches, is illustrated on stochastic chemical reaction network simulations. [ABSTRACT FROM AUTHOR]

An amendment to this paper has been published and can be accessed via a link at the top of the paper. [ABSTRACT FROM AUTHOR]

Abstract We discuss approximation of functions using deep neural nets. Given a function f on a d -dimensional manifold Γ ⊂ R m , we construct a sparsely-connected depth-4 neural network and bound its error in approximating f. The size of the network depends on dimension and curvature of the manifold Γ, the complexity of f , in terms of its wavelet description, and only weakly on the ambient dimension m. Essentially, our network computes wavelet functions, which are computed from Rectified Linear Units (ReLU). [ABSTRACT FROM AUTHOR]

We describe and implement a computer-assisted approach for accelerating the exploration of uncharted effective free-energy surfaces (FESs). More generally, the aim is the extraction of coarsegrained, macroscopic information from stochastic or atomistic simulations, such as molecular dynamics (MD). The approach functionally links the MD simulator with nonlinear manifold learning techniques. The added value comes from biasing the simulator toward unexplored phase-space regions by exploiting the smoothness of the gradually revealed intrinsic low-dimensional geometry of the FES. [ABSTRACT FROM AUTHOR]

Highlights: [•] We tackled the problem of determining the location in the human body of some CT scan images of different patients. [•] We introduce diffusion metrics in a prediction context, useful for working with misaligned data. [•] A comparative study of different methods based on a kNN search was carried out. [•] Our method based on anisotropic diffusion outperforms the state-of-the-art. [ABSTRACT FROM AUTHOR]

Abstract: We introduce a multiscale scheme for sampling scattered data and extending functions defined on the sampled data points, which overcomes some limitations of the Nyström interpolation method. The multiscale extension (MSE) method is based on mutual distances between data points. It uses a coarse-to-fine hierarchy of the multiscale decomposition of a Gaussian kernel. It generates a sequence of subsamples, which we refer to as adaptive grids, and a sequence of approximations to a given empirical function on the data, as well as their extensions to any newly-arrived data point. The subsampling is done by a special decomposition of the associated Gaussian kernel matrix in each scale in the hierarchical procedure. [Copyright &y& Elsevier]

Objective: We propose an automated nutritional assessment algorithm that provides a method for malnutrition risk prediction with high accuracy and reliability. Methods: The database used for this study was a file of 432 patients, where each patient was described by 4 laboratory parameters and 11 clinical parameters. A malnutrition risk assessment of low (1), moderate (2), or high (3) was assigned by a dietitian for each patient. An algorithm for data organization and classification using characteristic metrics for each patient was developed. For each patient, the algorithm characterized the patients' unique profile and built a characteristic metric to identify similar patients who were mapped into a classification. For each patient, the algorithm characterized the patients' classification. Results: The algorithm assigned a malnutrition risk level for different training sizes that were taken from the data. Our method resulted in average errors (distance between the automated score and the real score) of 0.386, 0.3507, 0.3454, 0.34, and 0.2907 for the 10%, 30%, 50%, 70%, and 90% training sizes, respectively. Our method outperformed the compared method even when our method used a smaller training set than the compared method. In addition, we showed that the laboratory parameters themselves were sufficient for the automated risk prediction and organized the patients into clusters that corresponded to low-, low--moderate-, moderate-, moderate--high-, and high-risk areas. The organization and visualization methods provided a tool for the exploration and navigation of the data points. Conclusion: The problem of rapidly identifying risk and severity of malnutrition is crucial for minimizing medical and surgical complications. These are not easily performed or adequately expedited. We characterized for each patient a unique profile and mapped similar patients into a classification. We also found that the laboratory parameters were sufficient for the automated risk prediction. [ABSTRACT FROM AUTHOR]

Abstract: We introduce a method to re-parameterize massive high dimensional data, generated by nonlinear mixing, into its independent physical parameters. Our method enables the identification of the original parameters and their extension to new observations without any knowledge of the true physical model. The suggested approach in this paper is related to spectral independent components analysis (ICA) via the construction of an anisotropic diffusion kernel whose eigenfunctions comprise the independent components. However, we use a novel anisotropic diffusion process, utilizing only a small observed subset , that approximates the isotropic diffusion on the parametric manifold of the full set Y. We employ a Nyström-type extension of the independent components of to the independent components of Y, and provide a validation scheme for our algorithm parameters choice. We demonstrate our method on synthetic examples and on real application examples. [Copyright &y& Elsevier]

Harmonic analysis and diffusion on discrete data has been shown to lead to state-of-the-art algorithms for machine learning tasks, especially in the context of semi-supervised and transductive learning. The success of these algorithms rests on the assumption that the function(s) to be studied (learned, interpolated, etc.) are smooth with respect to the geometry of the data. In this paper we present a method for modifying the given geometry so the function(s) to be studied are smoother with respect to the modified geometry, and thus more amenable to treatment using harmonic analysis methods. Among the many possible applications, we consider the problems of image denoising and transductive classification. In both settings, our approach improves on standard diffusion based methods. [ABSTRACT FROM AUTHOR]

We propose a local conformal autoencoder (LOCA) for standardized data coordinates. LOCA is a deep learning-based method for obtaining standardized data coordinates from scientific measurements. Data observations are modeled as samples from an unknown, nonlinear deformation of an underlying Riemannian manifold, which is parametrized by a few normalized, latent variables. We assume a repeated measurement sampling strategy, common in scientific measurements, and present a method for learning an embedding in Rd that is isometric to the latent variables of the manifold. The coordinates recovered by our method are invariant to diffeomorphisms of the manifold, making it possible to match between different instrumental observations of the same phenomenon. Our embedding is obtained using LOCA, which is an algorithm that learns to rectify deformations by using a local z-scoring procedure, while preserving relevant geometric information. We demonstrate the isometric embedding properties of LOCA in various model settings and observe that it exhibits promising interpolation and extrapolation capabilities, superior to the current state of the art. Finally, we demonstrate LOCA's efficacy in single-site Wi-Fi localization data and for the reconstruction of three-dimensional curved surfaces from two-dimensional projections. [ABSTRACT FROM AUTHOR]

The high-dimensional data created by high-throughput technologies require visualization tools that reveal data structure and patterns in an intuitive form. We present PHATE, a visualization method that captures both local and global nonlinear structure using an information-geometric distance between data points. We compare PHATE to other tools on a variety of artificial and biological datasets, and find that it consistently preserves a range of patterns in data, including continual progressions, branches and clusters, better than other tools. We define a manifold preservation metric, which we call denoised embedding manifold preservation (DEMaP), and show that PHATE produces lower-dimensional embeddings that are quantitatively better denoised as compared to existing visualization methods. An analysis of a newly generated single-cell RNA sequencing dataset on human germ-layer differentiation demonstrates how PHATE reveals unique biological insight into the main developmental branches, including identification of three previously undescribed subpopulations. We also show that PHATE is applicable to a wide variety of data types, including mass cytometry, single-cell RNA sequencing, Hi-C and gut microbiome data. PHATE, a new data visualization tool, better preserves patterns in high-dimensional data after dimensionality reduction. [ABSTRACT FROM AUTHOR]

Highlights: [•] We tested if a relationship between distant parts of the default mode network (DMN), a resting state network defined by fMRI studies, could be observed in the intracranial EEG. [•] Relationship was measured with linear and non-linear relationship measures of the intracranial EEG and an evaluation of the gamma power envelope. [•] The relationship within the DMN was not greater than the relationship from DMN locations to a control location outside it, suggesting a lack of intracranial EEG support for the fMRI defined DMN. [Copyright &y& Elsevier]

Experimental work across species has demonstrated that spontaneously generated behaviors are robustly coupled to variations in neural activity within the cerebral cortex. Functional magnetic resonance imaging data suggest that temporal correlations in cortical networks vary across distinct behavioral states, providing for the dynamic reorganization of patterned activity. However, these data generally lack the temporal resolution to establish links between cortical signals and the continuously varying fluctuations in spontaneous behavior observed in awake animals. Here, we used wide-field mesoscopic calcium imaging to monitor cortical dynamics in awake mice and developed an approach to quantify rapidly time-varying functional connectivity. We show that spontaneous behaviors are represented by fast changes in both the magnitude and correlational structure of cortical network activity. Combining mesoscopic imaging with simultaneous cellular-resolution two-photon microscopy demonstrated that correlations among neighboring neurons and between local and large-scale networks also encode behavior. Finally, the dynamic functional connectivity of mesoscale signals revealed subnetworks not predicted by traditional anatomical atlas-based parcellation of the cortex. These results provide new insights into how behavioral information is represented across the neocortex and demonstrate an analytical framework for investigating time-varying functional connectivity in neural networks., (© 2023. The Author(s), under exclusive licence to Springer Nature America, Inc.)

Confinement breaks translational and rotational symmetry in materials and makes all physical properties functions of position. Such spatial variations are key to modulating material properties at the nanoscale, and characterizing them accurately is therefore an intense area of research in the molecular simulations community. This is relatively easy to accomplish for basic mechanical observables. Determining spatial profiles of transport properties, such as diffusivity, is, however, much more challenging, as it requires calculating position-dependent autocorrelations of mechanical observables. In our previous paper (Domingues, T.S.; Coifman, R.; Haji-Akbari, A. J. Phys. Chem. B 2023 , 127 , 5273 10.1021/acs.jpcb.3c00670), we analytically derive and numerically validate a set of filtered covariance estimators (FCEs) for quantifying spatial variations of the diffusivity tensor from stochastic trajectories. In this work, we adapt these estimators to extract diffusivity profiles from MD trajectories and validate them by applying them to a Lennard-Jones fluid within a slit pore. We find our MD-adapted estimator to exhibit the same qualitative features as its stochastic counterpart, as it accurately estimates the lateral diffusivity across the pore while systematically underestimating the normal diffusivity close to hard boundaries. We introduce a conceptually simple and numerically efficient correction scheme based on simulated annealing and diffusion maps to resolve the latter artifact and obtain normal diffusivity profiles that are consistent with the self-part of the van Hove correlation functions. Our findings demonstrate the potential of this MD-adapted estimator in accurately characterizing spatial variations of diffusivity in confined materials.