Non-local Data Research Articles

A problem with nonlocal initial data for one-dimensional hyperbolic equation

In this paper we consider a boundary-value problem for one-dimensional hyperbolic equation with nonlocal initial data in integral form. We prove the existence and uniqueness of the generalized solution.

On a time nonlocal problem for inhomogeneous evolution equations

Under consideration is some problem for inhomogeneous differential evolution equation in Banach space with an operator that generates a C 0-continuous semigroup and a nonlocal integral condition in the sense of Stieltjes. In case the operator has continuous inhomogeneity in the graph norm. We give the necessary and sufficient conditions for existence of a generalized solution for the problem of whether the nonlocal data belong to the generator domain. Estimates on solution stability are given, and some conditions are obtained for existence of the classical solution of the nonlocal problem. All results are extended to a Sobolev-type linear equation, the equation in Banach space with a degenerate operator at the derivative. The time nonlocal problem for the partial differential equation, modeling a filtrating liquid free surface, illustrates the general statements.

Efficient parallel CFD-DEM simulations using OpenMP

The paper describes parallelization strategies for the Discrete Element Method (DEM) used for simulating dense particulate systems coupled to Computational Fluid Dynamics (CFD). While the field equations of CFD are best parallelized by spatial domain decomposition techniques, the N-body particulate phase is best parallelized over the number of particles. When the two are coupled together, both modes are needed for efficient parallelization. It is shown that under these requirements, OpenMP thread based parallelization has advantages over MPI processes. Two representative examples, fairly typical of dense fluid–particulate systems are investigated, including the validation of the DEM-CFD and thermal-DEM implementation with experiments. Fluidized bed calculations are performed on beds with uniform particle loading, parallelized with MPI and OpenMP. It is shown that as the number of processing cores and the number of particles increase, the communication overhead of building ghost particle lists at processor boundaries dominates time to solution, and OpenMP which does not require this step is about twice as fast as MPI. In rotary kiln heat transfer calculations, which are characterized by spatially non-uniform particle distributions, the low overhead of switching the parallelization mode in OpenMP eliminates the load imbalances, but introduces increased overheads in fetching non-local data. In spite of this, it is shown that OpenMP is between 50–90% faster than MPI.

Adaptive regularization of the NL-means: application to image and video denoising.

Image denoising is a central problem in image processing and it is often a necessary step prior to higher level analysis such as segmentation, reconstruction, or super-resolution. The nonlocal means (NL-means) perform denoising by exploiting the natural redundancy of patterns inside an image; they perform a weighted average of pixels whose neighborhoods (patches) are close to each other. This reduces significantly the noise while preserving most of the image content. While it performs well on flat areas and textures, it suffers from two opposite drawbacks: it might over-smooth low-contrasted areas or leave a residual noise around edges and singular structures. Denoising can also be performed by total variation minimization-the Rudin, Osher and Fatemi model-which leads to restore regular images, but it is prone to over-smooth textures, staircasing effects, and contrast losses. We introduce in this paper a variational approach that corrects the over-smoothing and reduces the residual noise of the NL-means by adaptively regularizing nonlocal methods with the total variation. The proposed regularized NL-means algorithm combines these methods and reduces both of their respective defaults by minimizing an adaptive total variation with a nonlocal data fidelity term. Besides, this model adapts to different noise statistics and a fast solution can be obtained in the general case of the exponential family. We develop this model for image denoising and we adapt it to video denoising with 3D patches.

Updating Markov chain models using the ensemble Kalman filter

The problem we address is how to condition discrete variables with a prior described by a Markov chain model to a set of continuous, nonlocal observations. This is motivated by the need for improved approaches to condition geological facies descriptions of a reservoir to production data. In this study, we assume that the spatial arrangement of facies can be modeled by a Markov chain model. The conditioning to nonlocal observations consists of two primary steps. First, the ensemble Kalman filter is used to assimilate data without regard for the discrete nature of the variables, or the probability of transition from one state to another. Second, the updated realizations are projected onto the discrete state space using an algorithm for finding the sequence of states with maximum probability. The method, which is based on the Viterbi algorithm, is not iterative and is capable of assimilating nonlocal data such as production data with some limitations. We demonstrate the application of the method first with an example in which the data are nonlocal but linear. The second example is a nonlinear fluid flow example in which data are assimilated sequentially. For the linear problem, the distribution of conditional realizations from the approximate algorithm was found to be indistinguishable from the distribution of realizations from an exact sampling algorithm (McMC). Finally, we discuss how to generalize the methodology from the 1D example presented here to more general cases.

A non-local fuzzy segmentation method: Application to brain MRI

The Fuzzy C-Means (FCM) algorithm is a widely used and flexible approach to automated image segmentation, especially in the field of brain tissue segmentation from 3D MRI, where it addresses the problem of partial volume effects. In order to improve its robustness to classical image deterioration, namely noise and bias field artifacts, which arise in the MRI acquisition process, we propose to integrate into the FCM segmentation methodology concepts inspired by the non-local (NL) framework, initially defined and considered in the context of image restoration. The key algorithmic contributions of this article are the definition of an NL data term and an NL regularisation term to efficiently handle intensity inhomogeneities and noise in the data. The resulting new energy formulation is then built into an NL-FCM brain tissue segmentation algorithm. Experiments performed on both synthetic and real MRI data, leading to the classification of brain tissues into grey matter, white matter and cerebrospinal fluid, indicate a significant improvement in performance in the case of higher noise levels, when compared to a range of standard algorithms.

Generalised Nonlocal Image Smoothing

We propose a discrete variational approach for image smoothing consisting of nonlocal data and smoothness constraints that penalise general dissimilarity measures defined on image patches. One of such dissimilarity measures is the weighted L 2 distance between patches. In such a case we derive an iterative neighbourhood filter that induces a new similarity measure in the photometric domain. It can be regarded as an extended patch similarity measure that evaluates not only the patch similarity of two chosen pixels, but also the similarity of their corresponding neighbours. This leads to a more robust smoothing process since the pixels selected for averaging are more coherent with the local image structure. By slightly modifying the way the similarities are computed we obtain two related filters: The NL-means filter of Buades et al. (SIAM Multiscale Model. Simul. 4(2):490–530, 2005b) and the NDS filter of Mrázek et al. (Geometric Properties for Incomplete Data, Computational Imaging and Vision, vol. 31, pp. 335–352, Springer, Dordrecht, 2006). In fact, the proposed approach can be considered as a generalisation of the latter filter to the space of patches. We also provide novel insights into relations of the NDS filter with diffusion/regularisation methods as well as with some recently proposed graph regularisation techniques. We evaluate our method for the task of denoising greyscale and colour images degraded with Gaussian and salt-and-pepper noise, demonstrating that it compares very well to other more sophisticated approaches.

Efficient and Resilient Backbones for Multihop Wireless Networks

We consider the problem of finding in multihop wireless networks. The backbone provides end-to-end connectivity, allowing nonbackbone nodes to save energy since they do not have to route nonlocal data or participate in the routing protocol. Ideally, such a backbone would be small, consist primarily of high capacity nodes, and remain connected even when nodes are mobile or fail. Unfortunately, it is often infeasible to construct a backbone that has all of these properties; e.g., a small optimal backbone is often too sparse to handle node failures or high mobility. We present a parameterized backbone construction algorithm that permits explicit trade-offs between backbone size, resilience to node movement and failure, energy consumption, and path lengths. We prove that our scheme can construct essentially best possible backbones (with respect to energy consumption and backbone size) when the network is relatively static. We generalize our scheme to build more robust structures better suited to networks with higher mobility. We present a distributed protocol based upon our algorithm and show that this protocol builds and maintains a connected backbone in dynamic networks. Finally, we present detailed packet-level simulation results to evaluate and compare our scheme with existing energy-saving techniques. Our results show that, depending on the network environment, our scheme increases network lifetimes by 20 percent to 220 percent without adversely affecting delivery ratio or end-to-end latency.

Towards a more efficient implementation of OpenMP for clusters via translation to global arrays

This paper discusses a novel approach to implementing OpenMP on clusters. Traditional approaches to do so rely on Software Distributed Shared Memory systems to handle shared data. We discuss these and then introduce an alternative approach that translates OpenMP to Global Arrays (GA), explaining the basic strategy. GA requires a data distribution. We do not expect the user to supply this; rather, we show how we perform data distribution and work distribution according to the user-supplied OpenMP static loop schedules. An inspector–executor strategy is employed for irregular applications in order to gather information on accesses to potentially non-local data, group non-local data transfers and overlap communications with local computations. Furthermore, a new directive INVARIANT is proposed to provide information about the dynamic scope of data access patterns. This directive can help us generate efficient codes for irregular applications using the inspector–executor approach. We also illustrate how to deal with some hard cases containing reshaping and strided accesses during the translation. Our experiments show promising results for the corresponding regular and irregular GA codes.

A Detailed Cost Analysis in a Mature Drug Court Setting

Assessing the costs of drug court in relation to benefits has become an important issue for policy makers. Past cost-benefit studies have often relied on proxy estimates, client self-reports and/or non-local data to provide their estimates. This is less than helpful to policy makers particularly at the local level who are trying to understand both their actual investment into drug court and the real local cost savings. This study is an intensive examination of investment costs and benefits resulting from the operation of a single court. Data were collected in a manner that allowed costs and benefit to be assessed both overall and agency-by-agency, and the value of less intensive approaches in providing similar estimates. The study used a Transactional Cost economic model that examines complex multiple agency contributions to costs. The results of this study demonstrate that drug courts can be a cost effective use of taxpayer resources.

Communication Generation for Block-Cyclic Distributions

Data-parallel languages such as High Performance Fortran, Vienna Fortran and Fortran D include directives such as alignment and distribution that describe how data and computation are mapped onto the processors in a distributed-memory multiprocessor. A compiler for HPF that generates code for each processor has to compute the sequence of local memory addresses accessed by each processor and the sequence of send and receives for a given processor to access non-local data. In this paper, we present a novel approach for the generation of communication sets that exploits a pttern of send-receive index pairs. In addition, we present an algorithm for code generation. Experimental results demonstrate the viability of this technique.

Efficient Computation of Address Sequences in Data Parallel Programs Using Closed Forms for Basis Vectors

Arrays are mapped to processors through a two-step process—alignment followed by distribution—in data-parallel languages such as High Performance Fortran. This process of mapping creates disjoint pieces of the array that are locally owned by each processor. An HPF compiler that generates code for array statements must compute the sequence of local memory addresses accessed by each processor and the sequence of sends and receives for a given processor to access nonlocal data. In this paper, we present an approach to the address sequence generation problem using the theory of integer lattices. The set of elements referenced can be generated by integer linear combinations of basis vectors. Unlike other work on this problem, we derive closed form expressions for the basis vectors as a function of the mapping of data. Using these basis vectors and exploiting the fact that there is a repeating pattern in the access sequence, we derive highly optimized code that generates the pattern at runtime. The code generated uses table-lookup of the pattern. Experimental results show that our approach is faster than other solutions to this problem.

SUPERB and Vienna Fortran

Distributed-memory systems are powerful tools for solving large-scale scientific and engineering problems. However these machines are difficult to program since the data have to be distributed across the processors and message-passing operations must be inserted for communicating non-local data. In this paper, we discuss SUPERB and Vienna Fortran, two related developments with the objective of providing the user with a higher level programming paradigm while not sacrificing target code performance. The parallelization system SUPERB was developed in the German supercomputer project SUPRENUM from 1985 to 1989. It is based on the Single-Program-Multiple-Data (SPMD) paradigm, allows the use of global addresses, and automatically inserts the necessary communication statements, given a user-supplied data distribution. SUPERB was the first implemented system that translated sequential Fortran 77 into explicitly parallel message-passing Fortran. As a result of the experiences with SUPERB and related research, the language Vienna Fortran was designed within the ESPRIT project GENESIS, in a joint effort of the University of Vienna and ICASE, Nasa Langley Research Center. Vienna Fortran is a machine-independent language extension to Fortran, which includes a broad range of features for the high-level support of advanced application development for distributed-memory multiprocessors. It has significantly influenced the development of High Performance Fortran, a first attempt of language standardization in this area.

Using processor affinity in loop scheduling on shared-memory multiprocessors

Loops are the single largest source of parallelism in many applications. One way to exploit this parallelism is to execute loop iterations in parallel on different processors. Previous approaches to loop scheduling attempted to achieve the minimum completion time by distributing the workload as evenly as possible while minimizing the number of synchronization operations required. The authors consider a third dimension to the problem of loop scheduling on shared-memory multiprocessors: communication overhead caused by accesses to nonlocal data. They show that traditional algorithms for loop scheduling, which ignore the location of data when assigning iterations to processors, incur a significant performance penalty on modern shared-memory multiprocessors. They propose a new loop scheduling algorithm that attempts to simultaneously balance the workload, minimize synchronization, and co-locate loop iterations with the necessary data. They compare the performance of this new algorithm to other known algorithms by using five representative kernel programs on a Silicon Graphics multiprocessor workstation, a BBN Butterfly, a Sequent Symmetry, and a KSR-1, and show that the new algorithm offers substantial performance improvements, up to a factor of 4 in some cases. The authors conclude that loop scheduling algorithms for shared-memory multiprocessors cannot afford to ignore the location of data, particularly in light of the increasing disparity between processor and memory speeds. >

Burgers' equation by non-local shot noise data

We study the scaling limit of random fields which are solutions of a non-linear partial differential equation, known as the Burgers equation, under stochastic initial conditions. These are assumed to be of a non-local shot noise type and driven by a Cox process. Previous work by Bulinskii and Molchanov (1991), Surgailis and Woyczynski (1993a), and Funaki et al. (1994) concentrated on the case of local shot noise data which permitted use of techniques from the theory of random fields with finite range dependence. Those are not available for the non-local case being considered in this paper.Burgers' equation is known to describe various physical phenomena such as non-linear and shock waves, distribution of self-gravitating matter in the universe, and other flow satisfying conservation laws (see e.g. Woyczynski (1993)).

Analysis of concurrency-coherency control protocols for distributed transaction processing systems with regional locality

A system structure and protocols for improving the performance of a distributed transaction processing system when there is some regional locality of data reference are presented. A distributed computer system is maintained at each region, and a central computer system with a replication of all databases at the distributed sites is introduced. It provides the advantage of distributed systems principally for local transactions, and has the advantage of centralized systems for transactions accessing nonlocal data. Specialized protocols keep the copies at the distributed and centralized systems consistent without incurring the overhead and delay of generalized protocols for fully replicated databases. The advantages achievable through this system structure and the tradeoffs between protocols for concurrency and coherency control of the duplicate copies of the databases are studied. An approximate analytic model is used to estimate the system performance. It is found that the performance is sensitive to the protocol and that substantial performance improvement can be obtained as compared with distributed systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Parallel Performance of Domain-Decomposed Preconditioned Krylov Methods for PDEswith Locally Uniform Refinement

Preconditioners based on domain decomposition appear natural for the Krylov solution of implicitly discretized partial differential equations (PDEs) on parallel computers. Two-scale preconditioners (involving a global coarse-grid solve, independent solves over interfaces connecting the coarse-grid points, and independent subdomain solves) have been known since the early 1980s to be “near optimal” in the sense of ensuring a bounded, or at most logarithmically growing, iteration count as the mesh is refined. As a result, the refinement of the mesh can be chosen locally on the basis of truncation error, and the granularity of the domain decomposition can be chosen globally on the basis of parallel computing considerations with only mild effects on the convergence rate of the algorithm. However, overall computational complexity depends not only on the algebraic convergence rate, but also on the operation counts of the components of the preconditioner that must be applied at each iteration. The costs of solving the subdomain systems and the crosspoint system show superlinear growth in their respective (and inversely related) sizes. On the subdomains, the superlinear terms arise from arithmetic only; in the crosspoint system the cost of nonlocal data exchange is also superlinear. These factors make the preconditioner granularity and the choice of its components problem- and machine-dependent compromises. The tradeoffs involved are illustrated through numerical experiments on both shared- and distributed-memory computers for convection-diffusion problems. Because of the development of boundary layers, these problems benefit from local mesh refinement, which is straightforward to accommodate within the domain decomposition framework in a locally uniform sense, but which introduces load balancing as a further consideration in selecting the granularity of the preconditioner. In spite of the tradeoffs, cumulative speedups are obtainable out to at least medium-scale granularity (up to 64 processors in our tests). The largest problems involve $\mathcal{O}(10^5 )$ unknowns partitioned into $\mathcal{O}(10^3 )$ subdomains and converge in $\mathcal{O}(10)$ iterations requiring $\mathcal{O}(1)$ seconds on the Intel iPSC/860.

Performance of hashed cache data migration schemes on multicomputers

Many researchers approach the problem of programming distributed memory machines by assuming a global shared name space. Thus the user views the distributed memory of the machine as though it were shared. A major issue that arises at this point is how to manage the memory. When a processor accesses data stored on another processor's memory, data must be moved between the two processors. Once these data are retrieved from another processor's memory, several interesting issues are raised. Where should these data be stored locally? What transformations must be performed to the code to guarantee that the nonlocal accesses reference the correct memory location? What optimizations can be performed to reduce the time spent in accessing the nonlocal data? In this paper we examine various data migration mechanisms that allow an explicit and controlled mapping of data to memory. We describe, experimentally evaluate, and model a set of schemes for storing and retrieving off-processor array elements. The schemes are all based on using hash tables for efficient access of nonlocal data. The three different techniques evaluated are the basic hashed cache, partial enumeration, and full enumeration, the details of which are described in the paper. In all three schemes, nonlocal data are stored in hash tables—the difference is in the amount of memory used by the schemes and the retrieval mechanisms for nonlocal data.

A hybrid distributed centralized system structure for transaction processing

A hybrid system structure comprised of distributed systems to take advantage of locality of reference and a central system to handle transactions that access non-local data is examined. Several transaction processing applications, such as reservation systems, insurance and banking have such regional locality of reference. A concurrency and coherency control protocol that maintains the integrity of the data and performs well for transactions that access local or non-local data is described. It is shown that the performance of the hybrid system is much less sensitive to the fraction of remote accesses than the distributed system and offers similar performance to the distributed system for local transactions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stochastic functional differential equations modelling materials with selective recall

We study a problem in stochastic functional differential equations which, in addition to a standard one-one-parameter noise term involves a random perturbation of the memory. This problem can also be regarded as a first order hyperbolic system of stochastic partial differential equations with given initial data and nonlocal boundary data. Existence and uniqueness of a solution is established and the generator of the associated Markov process is analyzed. Thereafter, for two model problems arising from first- and second-order integro-differential equations suggested by physical applications we establish asymptotic stability in probability of the associated stochastic processes.