Search

Living cells constantly monitor their external and internal environments for changing conditions, stresses or developmental cues. Networks of genetically encoded components sense and process these signals following pre-defined rules in such a way that specific combinations of the presence or absence of certain signals activate suitable responses. Many biological signal integration mechanisms approximate Boolean logic operations, whereby presence or absence of signals are computed as variables with values described as either true or false, respectively. Boolean logic gates are commonly used in algebra and in computer sciences, and have long been recognized as useful information processing devices in electronic circuits. In these circuits, logic gates integrate multiple input values and produce an output signal according to pre-defined Boolean logic operations. Recent implementation of these logic operations using genetic components to process information in living cells has allowed genetic circuits to enable novel traits with decision-making capabilities. Although several literature reports describe the design and use of these logic gates to introduce new functions in bacterial, yeast and mammalian cells, similar approaches in plants remain scarce, likely due to challenges posed by the complexity of plants and the lack of some technological advances, e.g. , species-independent genetic transformation. In this mini review, we have surveyed recent reports describing synthetic genetic Boolean logic operators in plants and the different gate architectures used. We also briefly discuss the potential of deploying these genetic devices in plants to bring to fruition a new generation of resilient crops and improved biomanufacturing platforms. • Boolean logic operators are commonly used in algebra and computer sciences. • Many biological processes can be modeled as Boolean logic operations. • Genetically encoded Boolean logic operators are powerful tools in synthetic biology. • Only recently Boolean logic has been applied to plant synthetic biology. • Different genetic parts and topologies can be combined to build logic operators. [ABSTRACT FROM AUTHOR]

High performance computing system, which takes an interconnection network as its infrastructure topology, has been utilized in scientific computing, big data analysis as well as artificial intelligence. With the rapid growth of infrastructure topology (interconnection network) in high performance computing system, the probability of network element malfunction increases dramatically. Generally, the reliability of interconnection network is measured by the traditional (edge) connectivity, which is limited by the minimum degree of the network. In order to overcome the defect, the matroidal connectivity has been newly proposed to extend the edge connectivity. For the regular network G , let B k (G) = { B 1 , B 2 , ... , B k } be a fixed edge partition ordered sequence of G and χ k = (x 1 , x 2 , ... , x k) be a sequence of k integers. For any D ⊆ E (G) , if | D ∩ B i | ≤ x i (i ∈ [ k ]) and G − D is disconnected, then D is named matroidal cut set of G. The matroidal connectivity of G , denoted by λ (G , B k (G)) , is the minimum size of matroidal cut set of G. In this work, we characterize the matroidal connectivity of a class of n -dimensional regular networks G n. To be more specific, we show that λ (G n , B n (G n)) = (k − l + 1) f (l + j) , where f (n) is a function about n , and l , k , n are positive integers (l ≥ 1), j = n − k. As empirical analysis, we directly determine the matroidal connectivity of some well-known interconnection networks, such as hypercube Q n , star graph S T n and alternating group graph A G n. • High performance computing system, which takes interconnection network as its infrastructure topology, has been utilized in scientific computing, big data analysis as well as artificial intelligence. For the regular networks G , we use λ (G , B k (G)) to denote matroidal connectivity of G (where B k (G) = { B 1 , B 2 , ... , B k } is a fixed edge partition ordered sequence of G), which is the minimum size of edge cut set D ⊆ ∪ i = 1 k B i so that G − D is disconnected. In this work, we characterize the matroidal connectivity of a class of n -dimensional regular networks G n. That is, λ (G n , B k (G n)) = (k − l + 1) f (l + j) , where l , k , j (l ≤ k ≤ n) are integers. As empirical analysis, we determine the matroidal connectivity of some kinds of well-known interconnection networks, such as hypercubes (Q n), star graph (S T n) and alternating group graph (A G n). [ABSTRACT FROM AUTHOR]

Due to the complex behavior arising from non-uniqueness, symmetry, and bifurcations in the solution space, solving inverse problems of nonlinear differential equations (DEs) with multiple solutions is a challenging task. To address this, we propose homotopy physics-informed neural networks (HomPINNs), a novel framework that leverages homotopy continuation and neural networks (NNs) to solve inverse problems. The proposed framework begins with the use of NNs to simultaneously approximate unlabeled observations across diverse solutions while adhering to DE constraints. Through homotopy continuation, the proposed method solves the inverse problem by tracing the observations and identifying multiple solutions. The experiments involve testing the performance of the proposed method on one-dimensional DEs and applying it to solve a two-dimensional Gray-Scott simulation. Our findings demonstrate that the proposed method is scalable and adaptable, providing an effective solution for solving DEs with multiple solutions and unknown parameters. Moreover, it has significant potential for various applications in scientific computing, such as modeling complex systems and solving inverse problems in physics, chemistry, biology, etc. • Physics-informed neural networks are used to estimate unknown parameters with physical constraints. • HomPINNs helps to identify multiple solutions and solve inverse problems. • Numerical examples demonstrate its scalability and adaptability. • HomPINNs facilitates the discovery of previously unknown solutions. [ABSTRACT FROM AUTHOR]

• Propose the aligned storage formats ACSR and AELL. • Put forward a parallel SpMV algorithm based on ACSR and AELL formats. • Theoretically analyze the performance of SpMV on ARM processors. • Evaluate the performance of our optimization on Kunpeng 920 processors. Sparse matrix-vector multiplication (SpMV) has always been a hot topic of research for scientific computing and big data processing, but the sparsity and discontinuity of the nonzero elements in a sparse matrix lead to the memory bottleneck of SpMV. In this paper, we propose aligned CSR (ACSR) and aligned ELL (AELL) formats and a parallel SpMV algorithm to utilize NEON SIMD registers on ARM processors. We analyze the impact of SIMD instruction latency, cache access, and cache misses on SpMV with different formats. In the experiments, our SpMV algorithm based on ACSR achieves 1.18x and 1.56x speedup over SpMV based on CSR and SpMV in PETSc, respectively, and AELL achieves 1.21x speedup over ELL. The deviations between the theoretical results and experimental results in the instruction latency and cache access are 10.26% and 10.51% in ACSR and 5.68% and 2.91% in AELL, respectively. [ABSTRACT FROM AUTHOR]

There is a need for simple, fast, and memory-efficient multidimensional data structures for dense and sparse storage that arise with numerical methods and in software applications. The data structures must perform equally well across multiple computer architectures, including CPUs and GPUs. For this purpose, we developed MATAR, a C++ software library that allows for simple creation and use of intricate data structures that is also portable across disparate architectures using Kokkos. The performance aspect is achieved by forcing contiguous memory layout (or as close to contiguous as possible) for multidimensional and multi-size dense or sparse MAT rix and AR ray (hence, MATAR) types. Our results show that MATAR has the capability to improve memory utilization, performance, and programmer productivity in scientific computing. This is achieved by fitting more work into the available memory, minimizing memory loads required, and by loading memory in the most efficient order. This document describes the purpose of the work, the implementation of each of the data types, and the resulting performance both in some simple baseline test cases and in an application code. • Providing data structures that map problem data efficiently in memory. • Providing an easy to use interface for fast data access and modifier operators. • Creating data structures using Kokkos that run on multiple CPU and GPU architectures in a performant and portable manner. • Example use case of how to use Kokkos to encapsulate complex class hierarchies and virtual functions. [ABSTRACT FROM AUTHOR]

Deep neural networks have been shown to provide accurate function approximations in high dimensions. However, fitting network parameters requires informative training data that are often challenging to collect in science and engineering applications. This work proposes Neural Galerkin schemes based on deep learning that generate training data with active learning for numerically solving high-dimensional partial differential equations. Neural Galerkin schemes build on the Dirac-Frenkel variational principle to train networks by minimizing the residual sequentially over time, which enables adaptively collecting new training data in a self-informed manner that is guided by the dynamics described by the partial differential equations. This is in contrast to other machine learning methods that aim to fit network parameters globally in time without taking into account training data acquisition. Our finding is that the active form of gathering training data of the proposed Neural Galerkin schemes is key for numerically realizing the expressive power of networks in high dimensions. Numerical experiments demonstrate that Neural Galerkin schemes have the potential to enable simulating phenomena and processes with many variables for which traditional and other deep-learning-based solvers fail, especially when features of the solutions evolve locally such as in high-dimensional wave propagation problems and interacting particle systems described by Fokker-Planck and kinetic equations. • Coupling training of deep networks with adaptive data acquisition to solve high-dimensional evolution equations. • Enables predicting local features in high dimensions for which training with classical, uniform data acquisition fails. • Sequentially collects data over time and so avoids requirement of having rich initial data set over the time-space domain. • Suited for transport problems, for which collocation-based deep-network methods with uniform data sampling are inefficient. [ABSTRACT FROM AUTHOR]

Machine learning has been successfully applied to various fields of scientific computing in recent years. For problems with multiscale features such as flows in porous media and mechanical properties of composite materials, however, it remains difficult for machine learning methods to resolve such multiscale features, especially when the small scale information is present. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs) with multiscale coefficients. Inspired by the deep mixed residual method, we rewrite the second-order problem into a first-order system and employ multiple radial basis function neural networks (RBFNNs) to approximate unknown functions in the system. To avoid the overfitting and improve the performance of RBFNN, an additional regularization is introduced in the loss function. Thus the loss function contains two parts: the L 2 loss for the residual of the first-order system and boundary conditions, and the ℓ 1 regularization term for the weights of radial basis functions (RBFs). An algorithm for optimizing the specific loss function is introduced to accelerate the training process. The accuracy and effectiveness of the proposed method are demonstrated through a collection of multiscale problems with scale separation, discontinuity and multiple scales from one to three dimensions. Notably, the ℓ 1 regularization can achieve the goal of representing the solution by fewer RBFs. As a consequence, the total number of RBFs scales like O (ε − n τ) , where ε is the smallest scale, n is the dimensionality, and τ is typically smaller than 1. It is worth mentioning that the proposed method not only has the numerical convergence and thus provides a reliable numerical solution in three dimensions when a classical method is typically not affordable, but also outperforms most other available machine learning methods in terms of accuracy and robustness. Executable files are available at https://github.com/wangzhiwensuda/SRBFNN-for-multiscale-elliptic-problems. The program was implemented in PyTorch and was run on Linux. • A sparse radial basis function neural network (SRBFNN) is proposed to solve multiscale elliptic problems. • SRBFNN achieves higher accuracy in derivatives and solution with fewer basis functions. • The number of basis functions scales as O (ε − τ n) , where ε is the smallest scale, n is the dimensionality, and τ < 1. [ABSTRACT FROM AUTHOR]

Rendezvous algorithms encode a communication pattern that is useful when processors sending data do not know who the receiving processors should be, or vice versa. The idea is to define an intermediate decomposition where datums from different sending processors can "rendezvous" to perform a computation, in a manner that both the senders and eventual receivers of the results can identify the appropriate rendezvous processor. Originally designed for interpolating between overlaid grids with independent parallel decompositions (Plimpton et al., 2004), we have recently found rendezvous algorithms useful for a variety of operations in particle- or grid-based simulation codes when running large problems on large numbers of processors. In particular, we show they can perform well when a load-balanced intermediate decomposition is randomized and not spatial, requiring all-to-all communication to move data between processors. In this case rendezvous algorithms leverage the large bisection communication bandwidths which parallel machines provide. We describe how rendezvous algorithms work in a scientific computing context and give specific examples for molecular dynamics and Direct Simulation Monte Carlo codes which result in dramatic performance improvements versus simpler algorithms which do not scale as well. We explain how a generic rendezvous algorithm can be implemented, and also point out similarities with the MapReduce paradigm popularized by Google and Hadoop. • This paper explains how parallel rendezvous algorithms work in the context of large-scale scientific modeling and simulation codes. • It gives several examples of such algorithms. • It presents performance gains of the new algorithms relative to previously used simpler algorithms which were less scalable. [ABSTRACT FROM AUTHOR]

We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct probabilistic representations for the system states, and put forth an adversarial inference procedure for training them on data, while constraining their predictions to satisfy given physical laws expressed by partial differential equations. Such physics-informed constraints provide a regularization mechanism for effectively training deep generative models as surrogates of physical systems in which the cost of data acquisition is high, and training data-sets are typically small. This provides a flexible framework for characterizing uncertainty in the outputs of physical systems due to randomness in their inputs or noise in their observations that entirely bypasses the need for repeatedly sampling expensive experiments or numerical simulators. We demonstrate the effectiveness of our approach through a series of examples involving uncertainty propagation in non-linear conservation laws, and the discovery of constitutive laws for flow through porous media directly from noisy data. • We developed self-supervised deep learning methods for modeling stochastic systems. • Regularized adversarial inference enables learning generative models from small data. • This yields a flexible workflow for characterizing uncertainty in physical systems. • This method bypasses the need for sampling costly simulators for tackling UQ tasks. [ABSTRACT FROM AUTHOR]

We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of a passive scalar (e.g., the concentration of a pollutant). We present two particle methods that leverage the structure of the inverse problem to enable efficient computation of the forward map, one for time evolution problems and one for Dirichlet boundary-value problems. The methods scale in a natural fashion to modern computational architectures, enabling substantial speedup for applications involving sparse observations and high-dimensional unknowns. Numerical examples of applications to Bayesian inference and numerical optimization are provided. • Particle algorithms are presented for PDE-constrained inverse problems. • The methods leverage problem structure to enable fast computation of the forward map. • The methods scale in a natural fashion to modern computational architectures. • Computational complexity for these and traditional two-step algorithms is provided. • Applications to Bayesian inference and numerical optimization are provided. [ABSTRACT FROM AUTHOR]

While deep learning algorithms demonstrate a great potential in scientific computing, its application to multi-scale problems remains to be a big challenge. This is manifested by the "frequency principle" that neural networks tend to learn low frequency components first. Novel architectures such as multi-scale deep neural network (MscaleDNN) were proposed to alleviate this problem to some extent. In this paper, we construct a subspace decomposition based DNN (dubbed SD2NN) architecture for a class of multi-scale problems by combining MscaleDNN algorithms with traditional numerical analysis ideas. The proposed architecture includes one low frequency normal DNN submodule, and one (or a few) high frequency MscaleDNN submodule(s), which are designed to capture the smooth part and the oscillatory part of the multi-scale solutions simultaneously. We demonstrate that the SD2NN outperforms existing models such as MscaleDNN, through several benchmark multi-scale problems in regular or perforated domains. • We propose SD2NN, a new architecture, combining subspace decomposition from numerical analysis and multiscale DNN solvers. • SD2NN has low/high frequency submodules, simultaneously capturing smooth/oscillatory parts of multi-scale solutions. • The new method outperforms state-of-the-art DNN solvers for 1D-3D multiscale PDEs on regular and perforated domains. [ABSTRACT FROM AUTHOR]

We propose an anomaly detection method for multi-variate scientific data based on analysis of high-order joint moments. Using kurtosis as a reliable measure of outliers, we suggest that principal kurtosis vectors, by analogy to principal component analysis (PCA) vectors, signify the principal directions along which outliers appear. The inception of an anomaly, then, manifests as a change in the principal values and vectors of kurtosis. Obtaining the principal kurtosis vectors requires decomposing a fourth order joint cumulant tensor for which we use a simple, computationally less expensive approach that involves performing a singular value decomposition (SVD) over the matricized tensor. We demonstrate the efficacy of this approach on synthetic data, and develop an algorithm to identify the occurrence of a spatial and/or temporal anomalous event in scientific phenomena. The algorithm decomposes the data into several spatial sub-domains and time steps to identify regions with such events. Feature moment metrics, based on the alignments of the principal kurtosis vectors, are computed at each sub-domain and time step for all features to quantify their relative importance towards the overall kurtosis in the data. Accordingly, spatial and temporal anomaly metrics for each sub-domain are proposed using the Hellinger distance of the feature moment metric distribution from a suitable nominal distribution. We apply the algorithm to two turbulent auto-ignition combustion cases and demonstrate that the anomaly metrics reliably capture the occurrence of auto-ignition in relevant spatial sub-domains at the right time steps. • A novel unsupervised anomaly detection method for multi-scale, multi-variate data. • Hypothesis: anomalous events have a signature in the higher order joint moments. • Extends the concept of PCA to higher order moment, specifically kurtosis. • The method identifies principal vectors of kurtosis as directions of anomaly. • The algorithm is designed for distributed large-scale HPC simulations and data. [ABSTRACT FROM AUTHOR]

Abstract The great potential of computational diffusion MRI (dMRI) relies on indirect inference of tissue microstructure and brain connections, since modelling and tractography frameworks map diffusion measurements to neuroanatomical features. This mapping however can be computationally highly expensive, particularly given the trend of increasing dataset sizes and the complexity in biophysical modelling. Limitations on computing resources can restrict data exploration and methodology development. A step forward is to take advantage of the computational power offered by recent parallel computing architectures, especially Graphics Processing Units (GPUs). GPUs are massive parallel processors that offer trillions of floating point operations per second, and have made possible the solution of computationally-intensive scientific problems that were intractable before. However, they are not inherently suited for all problems. Here, we present two different frameworks for accelerating dMRI computations using GPUs that cover the most typical dMRI applications: a framework for performing biophysical modelling and microstructure estimation, and a second framework for performing tractography and long-range connectivity estimation. The former provides a front-end and automatically generates a GPU executable file from a user-specified biophysical model, allowing accelerated non-linear model fitting in both deterministic and stochastic ways (Bayesian inference). The latter performs probabilistic tractography, can generate whole-brain connectomes and supports new functionality for imposing anatomical constraints, such as inherent consideration of surface meshes (GIFTI files) along with volumetric images. We validate the frameworks against well-established CPU-based implementations and we show that despite the very different challenges for parallelising these problems, a single GPU achieves better performance than 200 CPU cores thanks to our parallel designs. Highlights • The computational power offered by GPUs is used to accelerate the analysis of dMRI. • We present a generic and flexible parallel framework for microstructure modelling on GPUs. • And also a framework for performing probabilistic tractography and generating connectomes on GPUs. • A single GPU achieves better performance than 200 CPU cores with our frameworks. [ABSTRACT FROM AUTHOR]

Abstract We introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. In this work, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct types of algorithms, namely continuous time and discrete time models. The first type of models forms a new family of data-efficient spatio-temporal function approximators, while the latter type allows the use of arbitrarily accurate implicit Runge–Kutta time stepping schemes with unlimited number of stages. The effectiveness of the proposed framework is demonstrated through a collection of classical problems in fluids, quantum mechanics, reaction–diffusion systems, and the propagation of nonlinear shallow-water waves. Highlights • We put forth a deep learning framework that enables the synergistic combination of mathematical models and data. • We introduce an effective mechanism for regularizing the training of deep neural networks in small data regimes. • The proposed methods enable scientific prediction and discovery from incomplete models and incomplete data. [ABSTRACT FROM AUTHOR]

We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion Maps on those latent coordinates allows the approximation of the reduced dynamical models. This second round enables mapping the latent space coordinates back to the full ambient space (what is called lifting); it also enables the approximation of full state functions of interest in terms of the reduced coordinates. In our work, we develop and test three different reduced numerical simulation methodologies, either through pre-tabulation in the latent space and integration on the fly or by going back and forth between the ambient space and the latent space. The data-driven latent space simulation results, based on the three different approaches, are validated through (a) the latent space observation of the full simulation through the Nyström Extension formula, or through (b) lifting the reduced trajectory back to the full ambient space, via Latent Harmonics. Latent space modeling often involves additional regularization to favor certain properties of the space over others, and the mapping back to the ambient space is then constructed mostly independently from these properties; here, we use the same data-driven approach to construct the latent space and then map back to the ambient space. • Construction of reduced data-driven dynamical models. • Latent Space modeling through manifold learning. • Latent Harmonics to approximate functions defined in Latent Space (here Diffusion Maps) coordinates. • Latent-Space assisted Scientific Computing. [ABSTRACT FROM AUTHOR]

Lots of computational predictors have been developed for fast and large-scale analysis of biological data. However, many of them were developed long time ago when training datasets or sets of input features were rather small. Consequently, the utility of these predictors in much large datasets, which are very common in nowadays, need to be examined carefully. In addition, with the rapid development of scientific research, the expectation on the prediction accuracy of computational predictors is continuously uplifting. Therefore, developing novel strategies to improve the prediction accuracies of computational predictors becomes critical. In this study, the predictive results of existing individual miRNA target predictors were integrated into a decision-tree to make meta-prediction. When the multi-threshold sequential-voting technique was used, the prediction accuracy of the decision-tree was significantly improved by at least thirty percentage points compared to the individual predictors. [ABSTRACT FROM AUTHOR]

In this paper, we study a physics-informed algorithm for Wasserstein Generative Adversarial Networks (WGANs) for uncertainty quantification in solutions of partial differential equations. By using groupsort activation functions in adversarial network discriminators, network generators are utilized to learn the uncertainty in solutions of partial differential equations observed from the initial/boundary data. Under mild assumptions, we show that the generalization error of the computed generator converges to the approximation error of the network with high probability, when the number of samples are sufficiently taken. According to our established error bound, we also find that our physics-informed WGANs have higher requirement for the capacity of discriminators than that of generators. Numerical results on synthetic examples of partial differential equations are reported to validate our theoretical results and demonstrate how uncertainty quantification can be obtained for solutions of partial differential equations and the distributions of initial/boundary data. However, the quality or the accuracy of the uncertainty quantification theory in all the points in the interior is still the theoretical vacancy, and required for further research. • Wasserstein generative adversarial networks need little priors for uncertainty quantifications. • Physics-informed regularization term enforces the satisfaction of governing PDEs. • The proposed probabilistic model (WGAN-PINNs) is able to deal with non-Gaussian and spatially dependent noise. • WGAN-PINNs have good convergence and generalization properties. • Theoretically we have higher requirements on discriminators than generators. [ABSTRACT FROM AUTHOR]

Computational science and engineering application programs are typically large, complex, and dynamic, and are often constrained by distribution limitations. As a means of making tractable rapid explorations of scientific and engineering application programs in the context of new, emerging, and future computing architectures, a suite of “miniapps” has been created to serve as proxies for full scale applications. Each miniapp is designed to represent a key performance characteristic that does or is expected to significantly impact the runtime performance of an application program. In this paper we introduce a methodology for assessing the ability of these miniapps to effectively represent these performance issues. We applied this methodology to three miniapps, examining the linkage between them and an application they are intended to represent. Herein we evaluate the fidelity of that linkage. This work represents the initial steps required to begin to answer the question, “Under what conditions does a miniapp represent a key performance characteristic in a full app?” [ABSTRACT FROM AUTHOR]

The design and implementation of high level tools for parallel programming is a major challenge as the complexity of modern architectures increases. Domain Specific Languages (or DSL) have been proposed as a solution to facilitate this design but few of those DSL s actually take full advantage of said parallel architectures. In this paper, we propose a library-based solution by designing a C++ DSL s using generative programming: NT 2 . By adapting generative programming idioms so that architecture specificities become mere parameters of the code generation process, we demonstrate that our library can deliver high performance while featuring a high level API and being easy to extend over new architectures. [ABSTRACT FROM AUTHOR]

Abstract: Parallelism has become mainstream, in the multicore chip, the GPU, and the internet datacenter running MapReduce. In my field, large-scale scientific computing, parallelism now reigns triumphant. It was no simple, direct route that led to this triumph. Along the way, we were confused by ideas that, in retrospect, turned out to be distractions and errors. The thinking behind them was reasonable, but wrong. One can learn from a dissection of mistakes, so I will retell part of the story here. [Copyright &y& Elsevier]

Abstract: Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented mathematical knowledge that needs to be managed to use such systems effectively. While mathematical knowledge management (MKM) “in the small” is well-studied, scaling up to large, highly interconnected corpora remains difficult. We hold that in order to realize MKM “in the large”, we need representation languages and software architectures that are designed systematically with large-scale processing in mind. Therefore, we have designed and implemented the Mmt language – a module system for mathematical theories. Mmt is designed as the simplest possible language that combines a module system, a foundationally uncommitted formal semantics, and web-scalable implementations. Due to a careful choice of representational primitives, Mmt allows us to integrate existing representation languages for formal mathematical knowledge in a simple, scalable formalism. In particular, Mmt abstracts from the underlying mathematical and logical foundations so that it can serve as a standardized representation format for a formal digital library. Moreover, Mmt systematically separates logic-dependent and logic-independent concerns so that it can serve as an interface layer between computation systems and MKM systems. [Copyright &y& Elsevier]

• An approach for training neural networks combined with partial differential equations. • Combines a finite element framework with a machine learning library. • Learns missing physics in the partial differential equation. We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in the optimisation as apposed to making them part of the loss function. The resulting models are discretised in space by the finite element method (FEM). The method applies to both stationary and transient as well as linear/nonlinear PDEs. We describe implementation of the approach as an extension of the existing FEM framework FEniCS and its algorithmic differentiation tool dolfin-adjoint. Through series of examples we demonstrate capabilities of the approach to recover coefficients and missing PDE operators from observations. Further, the proposed method is compared with alternative methodologies, namely, physics informed neural networks and standard PDE-constrained optimisation. Finally, we demonstrate the method on a complex cardiac cell model problem using deep neural networks. [ABSTRACT FROM AUTHOR]

Abstract: The ability to support Quality of Service (QoS) constraints is an important requirement in some scientific applications. With the increasing use of Cloud computing infrastructures, where access to resources is shared, dynamic and provisioned on-demand, identifying how QoS constraints can be supported becomes an important challenge. However, access to dedicated resources is often not possible in existing Cloud deployments and limited QoS guarantees are provided by many commercial providers (often restricted to error rate and availability, rather than particular QoS metrics such as latency or access time). We propose a workflow system architecture which enforces QoS for the simultaneous execution of multiple scientific workflows over a shared infrastructure (such as a Cloud environment). Our approach involves multiple pipeline workflow instances, with each instance having its own QoS requirements. These workflows are composed of a number of stages, with each stage being mapped to one or more physical resources. A stage involves a combination of data access, computation and data transfer capability. A token bucket-based data throttling framework is embedded into the workflow system architecture. Each workflow instance stage regulates the amount of data that is injected into the shared resources, allowing for bursts of data to be injected while at the same time providing isolation of workflow streams. We demonstrate our approach by using the Montage workflow, and develop a Reference net model of the workflow. [Copyright &y& Elsevier]

Abstract: Numerical analysis of Markovian models is relevant for performance evaluation and probabilistic analysis of systems’ behavior from several fields in science and engineering. These models can be represented in a compact fashion using Kronecker algebra. The Vector-Descriptor Product (VDP) is the key operation to obtain stationary and transient solutions of models represented by Kronecker-based descriptors. VDP algorithms are usually CPU intensive, requiring alternatives such as data partitioning to produce results in less time. This paper introduces a set of parallel implementations of a hybrid algorithm for handling descriptors and a detailed performance analysis on four real Markovian models. The implementations are based on different scheduling strategies using OpenMP and existing techniques of static and dynamic load balancing, along with data partitioning presented in the literature. The performance evaluation study contains analysis of speed-up, synchronization and scheduling overheads, task mapping policies, and memory affinity. The results presented here provide insights into different implementation choices for an application on shared-memory systems and how this application benefited from this architecture. [Copyright &y& Elsevier]

Abstract: In parallel adaptive applications, the computational structure of the applications changes over time, leading to load imbalances even though the initial load distributions were balanced. To restore balance and to keep communication volume low in further iterations of the applications, dynamic load balancing (repartitioning) of the changed computational structure is required. Repartitioning differs from static load balancing (partitioning) due to the additional requirement of minimizing migration cost to move data from an existing partition to a new partition. In this paper, we present a novel repartitioning hypergraph model for dynamic load balancing that accounts for both communication volume in the application and migration cost to move data, in order to minimize the overall cost. The use of a hypergraph-based model allows us to accurately model communication costs rather than approximate them with graph-based models. We show that the new model can be realized using hypergraph partitioning with fixed vertices and describe our parallel multilevel implementation within the Zoltan load balancing toolkit. To the best of our knowledge, this is the first implementation for dynamic load balancing based on hypergraph partitioning. To demonstrate the effectiveness of our approach, we conducted experiments on a Linux cluster with 1024 processors. The results show that, in terms of reducing total cost, our new model compares favorably to the graph-based dynamic load balancing approaches, and multilevel approaches improve the repartitioning quality significantly. [Copyright &y& Elsevier]

Abstract: Particle-In-Cell (PIC) methods have been widely used for plasma physics simulations in the past three decades. To ensure an acceptable level of statistical accuracy relatively large numbers of particles are needed. State-of-the-art Graphics Processing Units (GPUs), with their high memory bandwidth, hundreds of SPMD processors, and half-a-teraflop performance potential, offer a viable alternative to distributed memory parallel computers for running medium-scale PIC plasma simulations on inexpensive commodity hardware. In this paper, we present an overview of a typical plasma PIC code and discuss its GPU implementation. In particular we focus on fast algorithms for the performance bottleneck operation of Particle-To-Grid interpolation. [Copyright &y& Elsevier]

This paper proves that shadowing solutions can be almost surely nonphysical. This finding invalidates the argument that small perturbations in a chaotic system can only have a small impact on its statistical behavior. This theoretical finding has implications for many applications in which chaotic dynamics plays an important role. It suggests, for example, that we can control the climate through subtle perturbations. It also suggests that numerical simulations of chaotic dynamics, such as turbulent flows and global atmosphere and ocean circulation, may fail to predict the true long-term or statistical behavior. • Shadowing orbits may not be typical orbits or physical solutions. • This atypicality implies shadowing-based sensitivity can be biased. • Numerical solutions of chaotic dynamical systems can be statistically inconsistent. • Minor parameter changes can significantly alter the statistics of a chaotic system. [ABSTRACT FROM AUTHOR]

Abstract: We present a scalable framework for parallelizing greedy graph coloring algorithms on distributed-memory computers. The framework unifies several existing algorithms and blends a variety of techniques for creating or facilitating concurrency. The latter techniques include exploiting features of the initial data distribution, the use of speculative coloring and randomization, and a BSP-style organization of computation and communication. We experimentally study the performance of several specialized algorithms designed using the framework and implemented using MPI. The experiments are conducted on two different platforms and the test cases include large-size synthetic graphs as well as real graphs drawn from various application areas. Computational results show that implementations that yield good speedup while at the same time using about the same number of colors as a sequential greedy algorithm can be achieved by setting parameters of the framework in accordance with the size and structure of the graph being colored. Our implementation is freely available as part of the Zoltan parallel data management and load-balancing library. [Copyright &y& Elsevier]

Abstract: We propose an architecture to harness the comparatively low computational power of geographically concentrated mobile devices (such as in a wireless ad hoc network, especially a sensor network) to build a wireless ad hoc lattice computer (WAdL). The primary contribution of the WAdL design is the ability to maintain, despite the mobility of the participating devices, a virtual lattice where the devices represent lattice points. WAdL is a cellular automaton-like architecture designed to carry out simulations of the unfolding of physical phenomena (e.g., fluid flow, system of moving, interacting objects, etc.) in the bounded region of Euclidean space represented by the underlying virtual lattice of WAdL. We present the design and algorithms of the WAdL architecture, and demonstrate its use with an example application (lift and drag on an airplane wing in flight) implemented on a simulated WAdL environment. We also discuss current issues and future directions of work on the WAdL architecture. [Copyright &y& Elsevier]

The exploitation of idle cycles on pervasive desktop PC systems offers the opportunity to increase the available computing power by orders of magnitude (10×–1000×). However, for desktop PC distributed computing to be widely accepted within the enterprise, the systems must achieve high levels of efficiency, robustness, security, scalability, manageability, unobtrusiveness, and openness/ease of application integration.We describe the Entropia distributed computing system as a case study, detailing its internal architecture and philosophy in attacking these key problems. Key aspects of the Entropia system include the use of: (1) binary sandboxing technology for security and unobtrusiveness, (2) a layered architecture for efficiency, robustness, scalability and manageability, and (3) an open integration model to allow applications from many sources to be incorporated.Typical applications for the Entropia System includes molecular docking, sequence analysis, chemical structure modeling, and risk management. The applications come from a diverse set of domains including virtual screening for drug discovery, genomics for drug targeting, material property prediction, and portfolio management. In all cases, these applications scale to many thousands of nodes and have no dependences between tasks. We present representative performance results from several applications that illustrate the high performance, linear scaling, and overall capability presented by the Entropia system. [Copyright &y& Elsevier]

Having its origin in theoretical computer science, the Kannan-Lovász-Simonovits (KLS) conjecture is one of the major open problems in asymptotic convex geometry and high-dimensional probability theory today. In this work, we establish a connection between this conjecture and the study of large and moderate deviations for isotropic log-concave random vectors. We then study the moderate deviations for the Euclidean norm of random orthogonally projected random vectors in an ℓ p n –ball. This leads to a number of interesting observations: (A) the ℓ 1 n –ball is critical for the new approach; (B) for p ≥ 2 the rate function in the moderate deviations principle undergoes a phase transition, depending on whether the scaling is below the square-root of the subspace dimensions or comparable; (C) for 1 ≤ p < 2 and comparable subspace dimensions, the rate function again displays a phase transition depending on its growth relative to n p / 2. [ABSTRACT FROM AUTHOR]

The slice-rank method, introduced by Tao as a symmetrized version of the polynomial method of Croot, Lev and Pach and Ellenberg and Gijswijt, has proved to be a useful tool in a variety of combinatorial problems. Explicit tensors have been introduced in different contexts but little is known about the limitations of the method. In this paper, building upon a method presented by Tao and Sawin, it is proved that the asymptotic slice rank of any k -tensor in any field is either 1 or at least k / (k − 1) (k − 1) / k. This provides evidence that straight-forward application of the method cannot give useful results in certain problems for which non-trivial exponential bounds are already known. An example, actually a motivation for starting this work, is the problem of bounding the size of sets of trifferent sequences, which constitutes a long-standing open problem in information theory and in theoretical computer science. [ABSTRACT FROM AUTHOR]

Learning non-linear systems from noisy, limited, and/or dependent data is an important task across various scientific fields including statistics, engineering, computer science, mathematics, and many more. In general, this learning task is ill-posed; however, additional information about the data's structure or on the behavior of the unknown function can make the task well-posed. In this work, we study the problem of learning nonlinear functions from corrupted and weakly dependent data. The learning problem is recast as a sparse robust linear regression problem where we incorporate both the unknown coefficients and the corruptions in a basis pursuit framework. The main contribution of our paper is to provide a reconstruction guarantee for the associated ℓ 1 -optimization problem where the sampling matrix is formed from weakly dependent data. Specifically, we prove that the sampling matrix satisfies the null space property and the stable null space property, provided that the data is compact and satisfies a suitable concentration inequality. We show that our recovery results are applicable to various types of weakly dependent data such as exponentially strongly α -mixing data, geometrically C -mixing data, and uniformly ergodic Markov chain. Our theoretical results are verified via several numerical simulations. [ABSTRACT FROM AUTHOR]

• This numerical scheme is devised by the primal-dual weak Galerkin(PDWG) framework. • The PDWG method can be interpreted as a constraint optimization process. • The PDWG scheme conserves mass locally on each element. • Optimal order error estimates are derived for the PDWG solution. This article devises a new numerical method for first-order transport problems by using the primal-dual weak Galerkin (PD-WG) finite element method recently developed in scientific computing. The PD-WG method is based on a variational formulation of the modeling equation for which the differential operator is applied to the test function so that low regularity for the exact solution of the original equation is sufficient for computation. The PD-WG finite element method indeed yields a symmetric system involving both the original equation for the primal variable and its dual for the dual variable (also known as Lagrangian multiplier). For the linear transport problem, it is shown that the PD-WG method offers numerical solutions that conserve mass locally on each element. Optimal order error estimates in various norms are derived for the numerical solutions arising from the PD-WG method with weak regularity assumptions on the modelling equations. A variety of numerical results are presented to demonstrate the accuracy and stability of the new method. [ABSTRACT FROM AUTHOR]

• Boys negatively evaluate peers who challenge group norms related to computing. • Children expect groups to negatively evaluate challenges to science gender norms. • Perceptions of group evaluation predict how boys individually evaluate their peers. Women are drastically underrepresented within computer science, which is in part informed by societal ideas of who can and should belong in the sciences. Less is known about how children evaluate their peers who challenge gendered expectations of who can and should take part in computer science. The current study asked children (N = 213; 110 girls) in middle childhood (M age = 8.71 years; n = 108) and late childhood (M age = 10.56 years; n = 105) to evaluate a gender-matched peer who challenged a group norm related to either computer science (male-gendered domain) or biology (less male-gendered domain). Male participants most negatively evaluated a peer who wanted to take part in a biology activity when the rest of the group wanted to do a programming activity. Furthermore, male participants expected their group to negatively evaluate this deviant peer in the programming condition. Mediation analysis revealed that for boys in the computer science condition, perceived group evaluation predicted individual evaluation. Female participants, in contrast, did not negatively evaluate someone who challenged a STEM (science, technology, engineering, and math) peer group norm. This study demonstrates that male peer groups may perpetuate the idea that computer science is for men through negative evaluation of in-group members who challenge those ideas and, in turn, maintain their dominant position as the high-status group. Achieving equity in the computer science field will require a greater understanding of these peer group norms. [ABSTRACT FROM AUTHOR]

This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation errors, for example in the creation of implicit Large Eddy schemes, we introduce the Sparse Identification of Truncation Errors (SITE) framework to automatically identify the terms of the modified differential equation from simulation data. We build on recent advances in the field of data-driven discovery and control of complex systems and combine it with classical work on modified differential equation analysis of Warming, Hyett, Lerat and Peyret. We augment a sparse regression-rooted approach with appropriate preconditioning routines to aid in the identification of the individual modified differential equation terms. The construction of such a custom algorithm pipeline allows attenuating of multicollinearity effects as well as automatic tuning of the sparse regression hyperparameters using the Bayesian information criterion (BIC). As proof of concept, we constrain the analysis to finite difference schemes and leave other numerical schemes open for future inquiry. Test cases include the linear advection equation with a forward-time, backward-space discretization, the Burgers' equation with a MacCormack predictor-corrector scheme and the Korteweg-de Vries equation with a Zabusky and Kruska discretization scheme. Based on variation studies, we derive guidelines for the selection of discretization parameters, preconditioning approaches and sparse regression algorithms. The results showcase highly accurate predictions underlining the promise of SITE for the analysis and optimization of discretization schemes, where analytic derivation of modified differential equations is infeasible. • Sparse regression based framework to automatically identify truncation error terms. • Proving modified differential equations can be identified from simulation data. • Preconditioning at multiple stages attenuates multicollinearity effects. • Highly accurate results for test cases with main limit being machine precision. [ABSTRACT FROM AUTHOR]