Tensor Network Space-Time Spectral Collocation Method for Solving the Nonlinear Convection Diffusion Equation
Not Available
97 MATHEMATICS AND COMPUTING↗
Engineering topics
Alexandrov, Boian S.
Publications and source records attributed to Alexandrov, Boian S..
Tensor Network Space-Time Spectral Collocation Method for Time-Dependent Convection-Diffusion-Reaction Equations
Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions.
97 MATHEMATICS AND COMPUTING↗
Tensor networks for solving the time-independent Boltzmann neutron transport equation
Not Available
97 MATHEMATICS AND COMPUTING↗
Source identification by non-negative matrix factorization combined with semi-supervised clustering
Machine-learning methods and apparatus are provided to solve blind source separation problems with an unknown number of sources and having a signal propagation model with features such as wave-like propagation, medium-dependent velocity, attenuation, diffusion, and/or advection, between sources and sensors. In exemplary embodiments, multiple trials of non-negative matrix factorization are performed for a fixed number of sources, with selection criteria applied to determine successful trials. A semi-supervised clustering procedure is applied to trial results, and the clustering results are evaluated for robustness using measures for reconstruction quality and cluster separation. The number of sources is determined by comparing these measures for different trial numbers of sources. Source locations and parameters of the signal propagation model can also be determined. Disclosed methods are applicable to a wide range of spatial problems including chemical dispersal, pressure transients, and electromagnetic signals, and also to non-spatial problems such as cancer mutation.
Alexandrov, Boian S.↗
Impaired cardiac glycolysis and glycogen depletion are linked to poor myocardial outcomes in juvenile male swine with metabolic syndrome and ischemia
Abstract Obesity continues to rise in the juveniles and obese children are more likely to develop metabolic syndrome (MetS) and related cardiovascular disease. Unfortunately, effective prevention and long‐term treatment options remain limited. We determined the juvenile cardiac response to MetS in a swine model. Juvenile male swine were fed either an obesogenic diet, to induce MetS, or a lean diet, as a control (LD). Myocardial ischemia was induced with surgically placed ameroid constrictor on the left circumflex artery. Physiological data were recorded and at 22 weeks of age the animals underwent a terminal harvest procedure and myocardial tissue was extracted for total metabolic and proteomic LC/MS–MS, RNA‐seq analysis, and data underwent nonnegative matrix factorization for metabolic signatures. Significantly altered in MetS versus. LD were the glycolysis‐related metabolites and enzymes. In MetS compared with LD Glycogen synthase 1 (GYS1)‐glycogen phosphorylases (PYGM/PYGL) expression disbalance resulted in a loss of myocardial glycogen. Our findings are consistent with the concept that transcriptionally driven myocardial changes in glycogen and glucose metabolism‐related enzymes lead to a deficiency of their metabolite products in MetS. This abnormal energy metabolism provides insight into the pathogenesis of the juvenile heart in MetS. This study reveals that MetS and ischemia diminishes ATP availability in the myocardium via altering the glucose‐G6P‐pyruvate axis at the level of metabolites and gene expression of related enzymes. The observed severe glycogen depletion in MetS coincides with disbalance in expression of GYS1 and both PYGM and PYGL. This altered energy substrate metabolism is a potential target of pharmacological agents for improving juvenile myocardial function in MetS and ischemia.
Broadwin, Mark↗
Uncovering novel mutational signatures by de novo extraction with SigProfilerExtractor
Mutational signature analysis is commonly performed in cancer genomic studies. Here, we present SigProfilerExtractor, an automated tool for de novo extraction of mutational signatures, and benchmark it against another 13 bioinformatics tools by using 34 scenarios encompassing 2,500 simulated signatures found in 60,000 synthetic genomes and 20,000 synthetic exomes. For simulations with 5% noise, reflecting high-quality datasets, SigProfilerExtractor outperforms other approaches by elucidating between 20% and 50% more true-positive signatures while yielding 5-fold less false-positive signatures. Applying SigProfilerExtractor to 4,643 whole-genome- and 19,184 whole-exome-sequenced cancers reveals four novel signatures. Two of the signatures are confirmed in independent cohorts, and one of these signatures is associated with tobacco smoking. In summary, this report provides a reference tool for analysis of mutational signatures, a comprehensive benchmarking of bioinformatics tools for extracting signatures, and several novel mutational signatures, including one putatively attributed to direct tobacco smoking mutagenesis in bladder tissues.
59 BASIC BIOLOGICAL SCIENCES↗
Quantum annealing algorithms for Boolean tensor networks
Abstract Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality heuristic solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., $$\{0, 1\}$$ { 0 , 1 } ) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called parallel quantum annealing, we demonstrate that Boolean tensor’s with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer.
97 MATHEMATICS AND COMPUTING↗
General-Purpose Unsupervised Cyber Anomaly Detection via Non-Negative Tensor Factorization
Distinguishing malicious anomalous activities from unusual but benign activities is a fundamental challenge for cyber defenders. Prior studies have shown that statistical user behavior analysis yields accurate detections by learning behavior profiles from observed user activity. These unsupervised models are able to generalize to unseen types of attacks by detecting deviations from normal behavior, without knowledge of specific attack signatures. However, approaches proposed to date based on probabilistic matrix factorization are limited by the information conveyed in a two-dimensional space. Non-negative tensor factorization, on the other hand, is a powerful unsupervised machine learning method that naturally models multi-dimensional data, capturing complex and multi-faceted details of behavior profiles. Herein, our new unsupervised statistical anomaly detection methodology matches or surpasses state-of-the-art supervised learning baselines across several challenging and diverse cyber application areas, including detection of compromised user credentials, botnets, spam e-mails, and fraudulent credit card transactions.
97 MATHEMATICS AND COMPUTING↗
Finding the Number of Latent Topics With Semantic Non-Negative Matrix Factorization
Not Available
Vangara, Raviteja↗
Tucker-1 Boolean Tensor Factorization with Quantum Annealers
Quantum annealers are an emerging computational architecture that have the potential to address some challenging computational issues that will be left unresolved as we approach the end of the Moore's Law era of computing. D-Wave quantum annealers are designed to solve a challenging set of problems - quadratic unconstrained binary optimization problems. This makes them a natural fit for solving problems with binary or Boolean variables. Here, we explore the use of a quantum annealer to solve Boolean tensor factorization. The goal of Boolean tensor factorization is to represent a high-dimensional tensor filled with Boolean values as a product of Boolean matrices and a Boolean core tensor. We show that a particular Boolean tensor factorization problem (called Tucker-1 factorization) can be decomposed into a sequence of quadratic unconstrained binary optimization problems that can be solved with a D-Wave 2000Q quantum annealer. While quantum annealers specifically and quantum computers in general are at a fairly early stage in their development, they are currently capable of solving these Boolean tensor factorization problems. Importantly, our results show that for fairly small tensors, we are frequently able to obtain an accurate (sometimes exact) factorization using quantum annealing.
97 MATHEMATICS AND COMPUTING↗
Determination of latent dimensionality in international trade flow
Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Moreover, decomposition methods with non-negative constraints are shown to extract more insightful factors. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Particularly, non-negative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Furthermore, estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with non-negative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of non-negative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data. We then apply our method to decompose a network of international trade flows data from International Monetary Fund and shows that with a correct latent dimension determination, the resulting features are able to capture relevant empirical facts from economic literature.
97 MATHEMATICS AND COMPUTING↗
Source identification by non-negative matrix factorization combined with semi-supervised clustering
Machine-learning methods and apparatus are provided to solve blind source separation problems with an unknown number of sources and having a signal propagation model with features such as wave-like propagation, medium-dependent velocity, attenuation, diffusion, and/or advection, between sources and sensors. In exemplary embodiments, multiple trials of non-negative matrix factorization are performed for a fixed number of sources, with selection criteria applied to determine successful trials. A semi-supervised clustering procedure is applied to trial results, and the clustering results are evaluated for robustness using measures for reconstruction quality and cluster separation. The number of sources is determined by comparing these measures for different trial numbers of sources. Source locations and parameters of the signal propagation model can also be determined. Disclosed methods are applicable to a wide range of spatial problems including chemical dispersal, pressure transients, and electromagnetic signals, and also to non-spatial problems such as cancer mutation.
97 MATHEMATICS AND COMPUTING↗
The genomic and epigenomic evolutionary history of papillary renal cell carcinomas
Intratumor heterogeneity (ITH) and tumor evolution have been well described for clear cell renal cell carcinomas (ccRCC), but they are less studied for other kidney cancer subtypes. Here we investigate ITH and clonal evolution of papillary renal cell carcinoma (pRCC) and rarer kidney cancer subtypes, integrating whole-genome sequencing and DNA methylation data. In 29 tumors, up to 10 samples from the center to the periphery of each tumor, and metastatic samples in 2 cases, enable phylogenetic analysis of spatial features of clonal expansion, which shows congruent patterns of genomic and epigenomic evolution. In contrast to previous studies of ccRCC, in pRCC, driver gene mutations and most arm-level somatic copy number alterations (SCNAs) are clonal. These findings suggest that a single biopsy would be sufficient to identify the important genetic drivers and that targeting large-scale SCNAs may improve pRCC treatment, which is currently poor. While type 1 pRCC displays near absence of structural variants (SVs), the more aggressive type 2 pRCC and the rarer subtypes have numerous SVs, which should be pursued for prognostic significance.
59 BASIC BIOLOGICAL SCIENCES↗