Search

From quasicrystalline alloys to twisted bilayer graphene, the study of material properties arising from quasiperiodic structure has driven advances in theory and applied science. Here we introduce a class of two-phase composites, structured by deterministic Moiré patterns, and we find that these composites display exotic behavior in their bulk electrical, magnetic, diffusive, thermal, and optical properties. With a slight change in the twist angle, the microstructure goes from periodic to quasiperiodic, and the transport properties switch from those of ordered to randomly disordered materials. This transition is apparent when we distill the relationship between classical transport coefficients and microgeometry into the spectral properties of an operator analogous to the Hamiltonian in quantum physics. We observe this order to disorder transition in terms of band gaps, field localization, and mobility edges analogous to Anderson transitions — even though there are no wave scattering or interference effects at play here. Moiré patterns and ordered aperiodic geometries have received significant attention since their observation in twisted bilayer graphene and quasicrystalline alloys. Here, the authors theoretically demonstrate that the same patterns can govern localization in quasiperiodic metal-dielectric composites and can be used to engineer the resultant optical and transport properties. [ABSTRACT FROM AUTHOR]

In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural networkbased learning methodology for such fluid flow reconstruction. Our approach learns an end-to-end mapping between the sensor measurements and the high-dimensional fluid flow field, without any heavy preprocessing on the raw data. No prior knowledge is assumed to be available, and the estimation method is purely data-driven. We demonstrate the performance on three examples in fluid mechanics and oceanography, showing that this modern data-driven approach outperforms traditional modal approximation techniques which are commonly used for flow reconstruction. Not only does the proposed method show superior performance characteristics, it can also produce a comparable level of performance to traditional methods in the area, using significantly fewer sensors. Thus, the mathematical architecture is ideal for emerging global monitoring technologies where measurement data are often limited. [ABSTRACT FROM AUTHOR]

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating between distinct time scales. We demonstrate a robust and scalable SPCA algorithm by formulating it as a value-function optimization problem. This viewpoint leads to a flexible and computationally efficient algorithm. The approach can further leverage randomized methods from linear algebra to extend SPCA to the large-scale (big data) setting. Our proposed innovation also allows for a robust SPCA formulation which obtains meaningful sparse principal components in spite of grossly corrupted input data. The proposed algorithms are demonstrated using both synthetic and real world data, and show exceptional computational efficiency and diagnostic performance. [ABSTRACT FROM AUTHOR]

We demonstrate the effective use of randomized methods for linear algebra to perform network-based analysis of complex vortical flows. Network theoretic approaches can reveal the connectivity structures among a set of vortical elements and analyze their collective dynamics. These approaches have recently been generalized to analyze high-dimensional turbulent flows, for which network computations can become prohibitively expensive. In this work, we propose efficient methods to approximate network quantities, such as the leading eigendecomposition of the adjacency matrix, using randomized methods. Specifically, we use the Nyström method to approximate the leading eigenvalues and eigenvectors, achieving significant computational savings and reduced memory requirements. The effectiveness of the proposed technique is demonstrated on two high-dimensional flow fields: two-dimensional flow past an airfoil and two-dimensional turbulence. We find that quasi-uniform column sampling outperforms uniform column sampling, while both feature the same computational complexity. [ABSTRACT FROM AUTHOR]

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of deterministic algorithms, easing the computational challenges arising in the area of ''big data."" The idea is to derive a small matrix from the highdimensional data, which is then used to efficiently compute the dynamic modes and eigenvalues. The algorithm is presented in a modular probabilistic framework, and the approximation quality can be controlled via oversampling and power iterations. The effectiveness of the resulting randomized DMD algorithm is demonstrated on several benchmark examples of increasing complexity, providing an accurate and efficient approach to extract spatiotemporal coherent structures from big data in a framework that scales with the intrinsic rank of the data, rather than the ambient measurement dimension. For this work we assume that the dynamics of the problem under consideration is evolving on a low-dimensional subspace that is well characterized by a quickly decaying singular value spectrum. [ABSTRACT FROM AUTHOR]

Retinal template matching and registration is an important challenge in teleophthalmology with low-cost imaging devices. However, the images from such devices generally have a small field of view (FOV) and image quality degradations, making matching difficult. In this paper, we develop an efficient and accurate retinal matching technique that combines dimension reduction and mutual information (MI), called RetinaMatch. The dimension reduction initializes the MI optimization as a coarse localization process, which narrows the optimization domain and avoids local optima. The effectiveness of RetinaMatch is demonstrated on the open fundus image database STARE with simulated reduced FOV and anticipated degradations, and on retinal images acquired by adapter-based optics attached to a smartphone. RetinaMatch achieves a success rate over 94% on human retinal images with the matched target registration errors below 2 pixels on average, excluding the observer variability, outperforming standard template matching solutions. In the application of measuring vessel diameter repeatedly, single pixel errors are expected. In addition, our method can be used in the process of image mosaicking with area-based registration, providing a robust approach when feature-based methods fail. To the best of our knowledge, this is the first template matching algorithm for retina images with small template images from unconstrained retinal areas. In the context of the emerging mixed reality market, we envision automated retinal image matching and registration methods as transformative for advanced teleophthalmology and long-term retinal monitoring. [ABSTRACT FROM AUTHOR]

We introduce a new set of algorithmic tools capable of producing scalable, low-rank decompositions of global spatiotemporal atmospheric chemistry data. By exploiting emerging randomized linear algebra algorithms, a suite of decompositions are proposed that extract the dominant features from big data sets (i.e., global atmospheric chemistry at longitude, latitude, and elevation) with improved interpretability. Importantly, our proposed algorithms scale with the intrinsic rank of the global chemistry space rather than the ever increasing spatiotemporal measurement space, thus allowing for the efficient representation and compression of the data. In addition to scalability, two additional innovations are proposed for improved interpretability: (i) a nonnegative decomposition of the data for improved interpretability by constraining the chemical space to have only positive expression values (unlike PCA analysis); and (ii) sparse matrix decompositions, which threshold small weights to zero, thus highlighting the dominant, localized spatial activity (again unlike PCA analysis). Our methods are demonstrated on a full year of global chemistry dynamics data, showing the significant improvement in computational speed and interpretability. We show that the decomposition methods presented here successfully extract known major features of atmospheric chemistry, such as summertime surface pollution and biomass burning activities. [ABSTRACT FROM AUTHOR]

We introduce a new set of algorithmic tools capable of producing scalable, low-rank decompositions of global spatio-temporal atmospheric chemistry data. By exploiting emerging randomized linear algebra algorithms, a suite of decompositions are proposed that extract the dominant features from big data sets (i.e. global atmospheric chemistry at longitude, latitude and elevation) with improved interpretability. Importantly, our proposed algorithms scale with the intrinsic rank of the global chemistry space rather than the ever increasing spatio-temporal measurement space, thus allowing for efficient representation and compression of the data. In addition to scalability, two additional innovations are proposed for improved interpretability: (i) a non-negative decomposition of the data for improved interpretability by constraining the chemical space to have only positive expression values (unlike PCA analysis), and (ii) sparse matrix decompositions, which thresholds low-correlations to zero, thus highlighting the dominant, localized spatial activity (again unlike PCA analysis). Our methods are demonstrated on a full year of global chemistry dynamics data, showing its significant improvement in computational speed and interpretability. We show that the here presented decomposition methods successfully extract known major features of atmospheric chemistry, such as summertime surface pollution and biomass burning activities. Indeed, we find that the full annual model output can be reconstructed using only 50-100 principal modes, suggesting that the presented methods offer the potential to archive model data of atmospheric chemistry with compression factors in the range of 200-4000 or greater. In the emerging area of big data, specifically global chemistry monitoring, such technologies are critically enabling for real-time and computationally tractable diagnostics of both large scale simulation and measurement data. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of ‘big data’ has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper presents a randomized hierarchical alternating least squares (HALS) algorithm to compute the NMF. By deriving a smaller matrix from the nonnegative input data, a more efficient nonnegative decomposition can be computed. Our algorithm scales to big data applications while attaining a near-optimal factorization, i.e., the algorithm scales with the target rank of the data rather than the ambient dimension of measurement space. The proposed algorithm is evaluated using synthetic and real world data and shows substantial speedups compared to deterministic HALS. [ABSTRACT FROM AUTHOR]

Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications. Many challenging problems in science and engineering rely on the study of dynamical systems that evolve continuously in time, and yet this feature proves difficult to be captured reliably using modern machine learning (ML) models. This paper develops a convergence test based on numerical analysis and illustrates how this methodology can be combined with existing ML techniques to validate models for science and engineering applications. [ABSTRACT FROM AUTHOR]

Sea ice regulates heat exchange between the ocean and atmosphere in Earth's polar regions. The thermal conductivity of sea ice governs this exchange, and is a key parameter in climate modelling. However, it is challenging to measure and predict due to its sensitive dependence on temperature, salinity and brine microstructure. Moreover, as temperature increases, sea ice becomes permeable, and fluid can flow through the porous microstructure. While models for thermal diffusion through sea ice have been obtained, advective contributions to transport have not been considered theoretically. Here, we homogenize a multiscale advection–diffusion equation that models thermal transport through porous sea ice when fluid flow is present. We consider two-dimensional models of convective flow and use an integral representation to derive bounds on the thermal conductivity as a function of the Péclet number. These bounds guarantee enhancement in the thermal conductivity due to the added flow. Further, we relate the Péclet number to temperature, making these bounds useful for global climate models. Our analytic approach offers a mathematical theory which can not only improve predictions of atmosphere–ice–ocean heat exchanges in climate models, but can provide a theoretical framework for a range of problems involving advection–diffusion processes in various fields of application. [ABSTRACT FROM AUTHOR]

The Anderson transition in solids and optics is a wave phenomenon where disorder induces localization of the wave functions. We find here that the hallmarks of the Anderson transition are exhibited by classical transport at a percolation threshold--without wave interference or scattering effects. As long range order or connectedness develops, the eigenvalue statistics of a key random matrix governing transport cross over toward universal statistics of the Gaussian orthogonal ensemble, and the field eigenvectors delocalize. The transition is examined in resistor networks, human bone, and sea ice structures. [ABSTRACT FROM AUTHOR]

Intimate partner violence (IPV), HIV, and substance use are serious intersecting public health issues. This paper aims to describe the Social Intervention Group (SIG)'s syndemic-focused interventions for women that address the co-occurrence of IPV, HIV, and substance use, referred to as the SAVA syndemic. We reviewed SIG intervention studies from 2000 to 2020 that evaluated the effectiveness of syndemic-focused interventions which addressed two or more outcomes related to reducing IPV, HIV, and substance use among different populations of women who use drugs. This review identified five interventions that co-targeted SAVA outcomes. Of the five interventions, four showed a significant reduction in risks for two or more outcomes related to IPV, substance use, and HIV. The significant effects of SIG's interventions on IPV, substance use, and HIV outcomes among different populations of women demonstrate the potential of using syndemic theory and methods in guiding effective SAVA-focused interventions. [ABSTRACT FROM AUTHOR]

Social support has been identified as a significant factor in addressing treatment barriers and facilitating treatment adherence. Using a descriptive design, this qualitative study aims at sharing personal feelings and social support-related experiences among pulmonary tuberculosis (TB) patients in Western India. A semi-structured interview guide was designed, and thirty-seven in-depth interviews were conducted. Descriptive thematic analysis was employed for reporting the themes and the results. The participants highlighted diverse social support experiences like empathy, compassion, trust, neglect, tangible aid, strained relationships with in-laws, health provider's support, strength, and motivation which influences their treatment adherent behaviour. Contrasting differences of social support experiences among adherent and non-adherent TB patients were also reported. The study has important ramifications for developing patient-centric social support intervention strategies, TB policy, and practice. The study has shown, 'if not for this support', patients would have left the treatment, and it is mainly because this debilitating disease robs people of their physical, social, economic, psychological, and emotional well-being far beyond the period when treatment is being administered. However, we resonate that addressing social support is not the only way, and TB elimination overall will require an optimal mix of enhanced biomedical, social, economic, and policy interventions. [ABSTRACT FROM AUTHOR]