Global Partition Research Articles

Scalable 3D Spatial Queries for Analytical Pathology Imaging with MapReduce.

3D analytical pathology imaging examines high resolution 3D image volumes of human tissues to facilitate biomedical research and provide potential effective diagnostic assistance. Such approach - quantitative analysis of large-scale 3D pathology image volumes - generates tremendous amounts of spatially derived 3D micro-anatomic objects, such as 3D blood vessels and nuclei. Spatial exploration of such massive 3D spatial data requires effective and efficient querying methods. In this paper, we present a scalable and efficient 3D spatial query system for querying massive 3D spatial data based on MapReduce. The system provides an on-demand spatial querying engine which can be executed with as many instances as needed on MapReduce at runtime. Our system supports multiple types of spatial queries on MapReduce through 3D spatial data partitioning, customizable 3D spatial query engine, and implicit parallel spatial query execution. We utilize multi-level spatial indexing to achieve efficient query processing, including global partition indexing for data retrieval and on-demand local spatial indexing for spatial query processing. We evaluate our system with two representative queries: 3D spatial joins and 3D k-nearest neighbor query. Our experiments demonstrate that our system scales to large number of computing nodes, and efficiently handles data-intensive 3D spatial queries that are challenging in analytical pathology imaging.

Influence of spatial resolution and contrast agent dosage on myocardial T1 relaxation times.

Our aim was to study the influence of small variations in spatial resolution and contrast agent dosage on myocardial T1 relaxation time. Twenty-nine healthy volunteers underwent cardiovascular magnetic resonance at 3T twice, including a modified look-locker inversion recovery (MOLLI) technique-3(3)3(3)5-for T1 mapping. Native T1 was assessed in three spatial resolutions (voxel size 1.4×1.4×6, 1.6×1.6×6, 1.7×1.7×6mm3), and postcontrast T1 after 0.1 and 0.2mmol/kg gadobutrol. Partition coefficient was calculated based on myocardial and blood T1. T1 analysis was done per segment, per slice, and for the whole heart. Native T1 values did not differ with varying spatial resolution per segment (p=0.116-0.980), per slice (basal: p=0.772; middle: p=0.639; apex: p=0.276), and globally (p=0.191). Postcontrast T1 values were significantly lower with higher contrast agent dosage (p<0.001). The global partition coefficient was 0.43±0.3 for 0.2 and 0.1mmol gadobutrol (p=0.079). Related to the tested MOLLI technique at 3T, very small variations in spatial resolution (voxel sizes between 1.4×1.4×6 and 1.7×1.7×6mm3) remained without effect on the native T1 relaxation times. Postcontrast T1 values were naturally shorter with higher contrast agent dosage while the partition coefficient remained constant. Further studies are necessary to test whether these conclusions hold true for larger matrix sizes and in larger cohorts.

MTP: discovering high quality partitions in real world graphs

Given a real world graph, how can we find a large subgraph whose partition quality is much better than the original? How can we use a partition of that subgraph to discover a high quality global partition? Although graph partitioning especially with balanced sizes has received attentions in various applications, it is known NP-hard, and also known that there is no good cut at a large scale for real graphs. In this paper, we propose a novel approach for graph partitioning. Our first focus is on finding a large subgraph with high quality partitions, in terms of conductance. Despite the difficulty of the task for the whole graph, we observe that there is a large connected subgraph whose partition quality is much better than the original. Our proposed method MTP finds such a subgraph by removing "hub" nodes with large degrees, and taking the remaining giant connected component. Further, we extend MTP to gb MTP (Global Balanced MTP) for discovering a global balanced partition. gb MTP attaches the excluded nodes in MTP to the partition found by MTP in a greedy way. In experiments, we demonstrate that MTP finds a subgraph of a large size with low conductance graph partitions, compared with competing methods. We also show that the competitors cannot find connected subgraphs while our method does, by construction. This improvement in partition quality for the subgraph is especially noticeable for large scale cuts--for a balanced partition, down to 14 % of the original conductance with the subgraph size 70 % of the total. As a result, the found subgraph has clear partitions at almost all scales compared with the original. Moreover, gb MTP generally discovers global balanced partitions whose conductance are lower than those found by METIS, the state-of-the-art graph partitioning method.

Strategic balance in graphs

For a given graph G, a nonempty subset S contained in V(G) is an alliance iff for each vertex v∈S there are at least as many vertices from the closed neighbourhood of v in S as in V(G)−S. An alliance is global if it is also a dominating set of G. The alliance partition number of G was defined in Hedetniemi et al. (2004) to be the maximum number of sets in a partition of V(G) such that each set is an alliance. Similarly, in Eroh and Gera (2008) the global alliance partition number is defined for global alliances, where the authors studied the problem for (binary) trees.In the paper we introduce a new concept of strategic balance in graphs: for a given graph G, determine whether there is a partition of vertex set V(G) into three subsets N, S and I such that both N and S are global alliances. We give a survey of its general properties, e.g., showing that a graph G has a strategic balance iff its global alliance partition number equals at least 2. We construct a linear time algorithm for solving the problem in trees (thus giving an answer to the open question stated in Eroh and Gera (2008)) and studied this problem for many classes of graphs: paths, cycles, wheels, stars, complete graphs and complete k-partite graphs. Moreover, we prove that this problem is NP-complete for graphs with a degree bounded by 4 and state an open question regarding subcubic graphs.

Global aerosol mixtures and their multiyear and seasonal characteristics

The optical and microphysical characteristics of distinct aerosol types in the atmosphere are not yet specified at the level of detail required for climate forcing studies. What is even less well known are the characteristics of mixtures of aerosol and, in particular, their precise global spatial distribution. Here, cluster analysis is applied to seven years of 3-hourly, gridded 2.5° × 2° aerosol optical depth data from the Goddard Chemistry Aerosol Radiation and Transport (GOCART) model, one of the most-studied global simulations of aerosol type currently available, to construct a spatial partition of the globe into a finite number of aerosol mixtures. The optimal number of aerosol mixtures is obtained with a k-means algorithm with smart seeding in conjunction with a stopping condition based on applying the ‘law of diminishing returns’ to the norm of the Euclidean distance to provide upper and lower bounds on the number of clusters. Each cluster has a distinct composition in terms of the proportion of biomass burning, sulfate, dust and marine (sea salt) aerosol and this leads rather naturally to a taxonomy for labeling aerosol mixtures. In addition, the assignment of primary colors to constituent aerosol types enables true color-mixing and the production of easy-to-interpret maps of their distribution. The mean multiyear global partition as well as partitions deduced on the seasonal timescale are used to extract aerosol robotic network (AERONET) Level 2.0 Version 2 inversion products in each cluster for estimating the values of key optical and microphysical parameters to help characterize aerosol mixtures. On the multiyear timescale, the globe can be spatially partitioned into 10 distinct aerosol mixtures, with only marginally more variability on the seasonal timescale. In the context of the observational constraints and uncertainties associated with AERONET retrievals, bivariate analysis suggests that mixtures dominated by dust and marine aerosol can be detected with reference to their single scattering albedo and Angstrom exponent at visible wavelengths in conjunction with their fine mode fraction and sphericity. Existing multivariate approaches at classification appear to be more ambiguous. The approach presented here provides gridded (1° × 1°) mean compositions of aeorosol mixtures as well as tentative estimates of mean aerosol optical and microphysical parameters in planetary regions where AERONET sites do not yet exist. Spreadsheets of gridded cluster indices for multiyear and seasonal partitions are provided to facililate further study of the global distribution of aerosol mixtures and possibly for the selection of new AERONET site locations.

Self-Optimal Clustering Technique Using Optimized Threshold Function

This paper presents a self-optimal clustering (SOC) technique which is an advanced version of improved mountain clustering (IMC) technique. The proposed clustering technique is equipped with major changes and modifications in its previous versions of algorithm. SOC is compared with some of the widely used clustering techniques such as K-means, fuzzy C-means, Expectation and Maximization, and K-medoid. Also, the comparison of the proposed technique is shown with IMC and its last updated version. The quantitative and qualitative performances of all these well-known clustering techniques are presented and compared with the aid of case studies and examples on various benchmarked validation indices. SOC has been evaluated via cluster compactness within itself and separation with other clusters. The optimizing factor in the threshold function is computed via interpolation and found to be effective in forming better quality clusters as verified by visual assessment and various standard validation indices like the global silhouette index, partition index, separation index, and Dunn index.

An Optimal Application Partition Algorithm for Energy Efficient Computation Offloading

In order to alleviate the energy constraint in smartphones, computation offloading is regarded as an effective solution. In computation offloading, how to partition a given application is one of the key issues. On obtaining the best partition, due to the time complexity of partition algorithm, most researchers give up looking for a global optimal solution but to find local optimal. In this paper, a global optimal application partition algorithm is presented, the main strategy is scaling down the problem through merging the correlated nodes firstly, then using 0-1ILP to obtain the partition in order to make the mobile energy consumption achieve global optimal minimum, thus it has less time complexity than 0-1 ILP. Experimental results show that the proposed algorithm made the same global optimal partition results as 0-1 ILP, while it consumed less time and energy than 0-1 ILP.

Symmetric global partition polynomials for reproducing kernel elements

The reproducing kernel element method is a numerical technique that combines finite element and meshless methods to construct shape functions of arbitrary order and continuity, yet retains the Kronecker- $$\delta $$ ? property. Central to constructing these shape functions is the construction of global partition polynomials on an element. This paper shows that asymmetric interpolations may arise due to such things as changes in the local to global node numbering and that may adversely affect the interpolation capability of the method. This issue arises due to the use of incomplete polynomials that are subsequently non-affine invariant. This paper lays out the new framework for generating general, symmetric, truly minimal and complete affine invariant global partition polynomials for triangular and tetrahedral elements. Optimal convergence rates were observed in the solution of Kirchhoff plate problems with rectangular domains.

Unsupervised analysis of top-k core members in poly-relational networks

Poly-relational networks such as social networks are prevalent in the real world. The existing research on poly-relational networks focuses on community detection, aiming to find a global partition of nodes across relations. However, in some real cases, users may be not interested in such a global partition. For example, commercial analysts often care more about the top-k core members in business competitions, and relations among them that are more important to their competitions. Motivated by this, in this paper, we investigate an unsupervised analysis of the top-k core members in a poly-relational network and identify two complementary tasks, namely (1) detection of the top-k core members that are most tightly connected by relevant relations, and (2) identification of the relevant relations via analysis on the importance of each relation to the formation of the top-k core members. Towards this, we propose an optimization framework to jointly deal with the two tasks by maximizing the connectivity between the candidates of the top-k core members across all relations with a synchronously updated weight for each relation. The effectiveness of our framework is verified both theoretically and experimentally.

Reply to “Comment on ‘Application of partition density-functional theory to one-dimensional models’ ”

The Comment by Elliott et al. stresses that partition density-functional theory (PDFT) yields a global partition potential and unique occupation numbers. Our reply points out that both of these results can be obtained, numerically, in model calculations, such as those reported previously to illustrate PDFT by shifting the von Weis\"acker potentials to achieve zero values in the large-$r$ limit.

Amphiphilic Drug-Like Molecules Accumulate in a Membrane below the Head Group Region

The partitioning behavior of drug-like molecules into biomembranes has a crucial impact on the design and efficacy of therapeutic drugs. Thermodynamic properties connected with the interaction of molecules with membranes can be evaluated by calculating free-energy profiles normal to the membrane surface. We calculated the free-energy profiles of 25 drug-like molecules in a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) membrane and free energies of solvation in water and heptane using two methods, molecular dynamics (MD) simulations with the Berger lipid force field and COSMOmic, based on a continuum conductor-like screening model for realistic solvation (COSMO-RS). The biased MD simulations (in total ∼22 μs long) were relatively computationally expensive, whereas the COSMOmic approach offered a significantly less expensive alternative. Both methods provided similar results and showed that the studied amphiphilic drug-like molecules accumulate in the membrane, with the majority localized below the head group region. The MD simulations were more lipophilic and gave free-energy profiles that were systematically deeper than those calculated by COSMOmic. To investigate the physical nature of the increased lipophilicity, we analyzed a water/heptane system and identified that it is most likely caused by overestimation of the attractive term of the Lennard-Jones potential in lipid tails. We concluded that COSMOmic can be successfully used for high-throughput computations of global thermodynamic properties, for example, partition coefficients and energy barrier heights, in phosphocholine membranes. In contrast, MD is better for investigating local properties like molecular positioning and orientation in the membrane because they more accurately reflect the complex structure of lipid bilayers. MD is also useful for studies of highly complex systems, for example, drug-membrane-protein interactions.

Research on Template Computing Mode of Remote Sensing Image Based on Partition Model

As the amount of data rises and application needs expand, the efficient organization and management of remote sensing data has become a bottleneck restricting the application of remote sensing technology. The Global Partition Theory (GPT) and high performance computing provide an approach to solve the above mentioned problems. GPT studies how the Earth's surface is split into different levels of thickness seamless mesh and how to organize and manage it. Thus, rapid integration of mass remote sensing data of different sources, different types and different resolution can be achieved. Meanwhile, there is a natural segmentation of regional location and distributed storage features in spatial data in the partition organization framework, which makes remote sensing images computing model based on partition inherently parallel attributes. Combing a partition model of the Extended Model Based on Mapping Division (EMD), the researchers study the partition facet of remote sensing image, and propose the conceptual model and data model of partition facet template. Combing with parallel processing framework in high-performance computing of remote sensing image, the researchers design the template-based computing mode of partition facet and the partition process of spatial data. Through analyzing spatial relationship of partition facets, such as containment relationship, neighboring relationship and direction relationship, the researchers propose the basic calculation modes of partition template. There are aggregation, division in longitudinal and extend, conversion in transverse. This research paper is of great significance for expanding the application of GPT, improving the remote sensing technology speed, accelerating spatial information visualization analyzing and decision making speed. It also provides valuable guidance for studying high-performance remote sensing image processing in the future.

Hadoop GIS

Support of high performance queries on large volumes of spatial data becomes increasingly important in many application domains, including geospatial problems in numerous fields, location based services, and emerging scientific applications that are increasingly data- and compute-intensive. The emergence of massive scale spatial data is due to the proliferation of cost effective and ubiquitous positioning technologies, development of high resolution imaging technologies, and contribution from a large number of community users. There are two major challenges for managing and querying massive spatial data to support spatial queries: the explosion of spatial data, and the high computational complexity of spatial queries. In this paper, we present Hadoop-GIS - a scalable and high performance spatial data warehousing system for running large scale spatial queries on Hadoop. Hadoop-GIS supports multiple types of spatial queries on MapReduce through spatial partitioning, customizable spatial query engine RESQUE, implicit parallel spatial query execution on MapReduce, and effective methods for amending query results through handling boundary objects. Hadoop-GIS utilizes global partition indexing and customizable on demand local spatial indexing to achieve efficient query processing. Hadoop-GIS is integrated into Hive to support declarative spatial queries with an integrated architecture. Our experiments have demonstrated the high efficiency of Hadoop-GIS on query response and high scalability to run on commodity clusters. Our comparative experiments have showed that performance of Hadoop-GIS is on par with parallel SDBMS and outperforms SDBMS for compute-intensive queries. Hadoop-GIS is available as a set of library for processing spatial queries, and as an integrated software package in Hive.

Data-aware 3D partitioning for generic shape retrieval

In this paper, we present a new approach for generic 3D shape retrieval based on a mesh partitioning scheme. Our method combines a mesh global description and mesh partition descriptions to represent a 3D shape. The partitioning is useful because it helps us to extract additional information in a more local sense. Thus, part descriptions can mitigate the semantic gap imposed by global description methods. We propose to find spatial agglomerations of local features to generate mesh partitions. Hence, the definition of a distance function is stated as an optimization problem to find the best match between two shape representations. We show that mesh partitions are representative and therefore it helps to improve the effectiveness in retrieval tasks. We present exhaustive experimentation using the SHREC'09 Generic Shape Retrieval Benchmark.

Experimental assessment of mixed-mode partition theories

The propagation of mixed-mode interlaminar fractures is investigated using existing experimental results from the literature and various partition theories. These are (i) a partition theory by Williams (1988) based on Euler beam theory; (ii) a partition theory by Suo (1990) and Hutchinson and Suo (1992) based on 2D elasticity; and (iii) the Wang–Harvey partition theories of the authors based on the Euler and Timoshenko beam theories. The Wang–Harvey Euler beam partition theory seems to offer the best and most simple explanation for all the experimental observations. No recourse to fracture surface roughness or new failure criteria is required. It is in excellent agreement with the linear failure locus and is significantly closer than other partition theories. It is also demonstrated that the global partition of energy release rate when using the Wang–Harvey Timoshenko beam or averaged partition theories or 2D elasticity exactly corresponds with the partition from the Wang–Harvey Euler beam partition theory. It is therefore concluded that the excellent performance of the Wang–Harvey Euler beam partition theory is either due to the failure of materials generally being based on global partitions or that for the specimens tested, the through-thickness shear effect is negligibly small. Further experimental investigations are definitely required.

Spatial and temporal resolution of carbon flux estimates for 1983–2002

Abstract. We discuss the spatial and temporal resolution of monthly carbon flux estimates for the period 1983–2002 using a fixed-lag Kalman Smoother technique with a global chemical transport model, and the GLOBALVIEW data product. The observational network has expanded substantially over this period, and the flux estimates are better constrained provided by observations for the 1990's in comparison to the 1980's. The estimated uncertainties also decrease as observational coverage expands. In this study, we use the Globalview data product for a network that changes every 5 yr, rather than using a small number of continually-operating sites (fewer observational constraints) or a large number of sites, some of which may consist almost entirely of extrapolated data. We show that the discontinuities resulting from network changes reflect uncertainty due to a sparse and variable network. This uncertainty effectively limits the resolution of trends in carbon fluxes, and is a potentially significant source of noise in assimilation systems that allow changes in observation distribution between assimilation time steps. The ability of the inversion to distinguish, or resolve, carbon fluxes at various spatial scales is examined using a diagnostic known as the resolution kernel. We find that the global partition between land and ocean fluxes is well-resolved even for the very sparse network of the 1980's, although prior information makes a significant contribution to the resolution. The ability to distinguish zonal average fluxes has improved significantly since the 1980's, especially for the tropics, where the zonal ocean and land biosphere fluxes can be distinguished. Care must be taken when interpreting zonal average fluxes, however, since the lack of air samples for some regions in a zone may result in a large influence from prior flux estimates for these regions. We show that many of the TransCom 3 source regions are distinguishable throughout the period over which estimates are produced. Examples are Boreal and Temperate North America. The resolution of fluxes from Europe and Australia has greatly improved since the 1990's. Other regions, notably Tropical South America and the Equatorial Atlantic remain practically unresolved. Comparisons of the average seasonal cycle of the estimated carbon fluxes with the seasonal cycle of the prior flux estimates reveals a large adjustment of the summertime uptake of carbon for Boreal Eurasia, and an earlier onset of springtime uptake for Temperate North America. In addition, significantly larger seasonal cycles are obtained for some ocean regions, such as the Northern Ocean, North Pacific, North Atlantic and Western Equatorial Pacific, regions that appear to be well-resolved by the inversion.

Tiled top–down combinatorial pyramids for large images representation

AbstractThe uprising number of applications that involve very large images with resolutions greater than 30,000 × 30,000 raises major memory management issues. Firstly, the amount of data usually prevents such images from being processed globally and therefore, designing a global image partition raises several issues. Secondly, a multiresolution approach is necessary since an analysis only based on the highest resolution may miss global features revealed at lower resolutions. This article introduces the tiled top–down pyramidal framework which addresses these two main constraints. Our model provides a full representation of multiresolution images with both geometrical and topological relationships. The advantage of a top–down construction scheme is twofold: the focus of attention only refines regions of interest which results in a reduction of the amount of required memory and in a refinement process that may take into account hierarchical features from previous segmentations. Moreover, the top–down model is combined with decomposition in tiles to provide an accurate memory bounding while allowing global analysis of large images. © 2011Wiley Periodicals, Inc. Int J Imaging Syst Technol, 21, 28–36, 2011.

Partition density-functional theory

Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment densities. An example is given and consequences discussed.

Shortest Paths for a Robot With Nonholonomic and Field-of-View Constraints

This paper presents a complete characterization of shortest paths to a goal position for a robot with unicycle kinematics and an on-board camera with limited field-of-view (FOV), which must keep a given feature in sight. Previous work on this subject has shown that the search for a shortest path can be limited to simple families of trajectories. In this paper, we provide a complete optimal synthesis for the problem, i.e., a language of optimal control words, and a global partition of the motion plane induced by shortest paths, such that a word in the optimal language is univocally associated with a region and completely describes the shortest path from any starting point in that region to the goal point. An efficient algorithm to determine the region in which the robot is at any time is also provided.

A polynomial algorithm for partitioning problems

This article takes a theoretical approach to focus on the algorithmic properties of hardware/software partitioning. It proposes a method with polynomial complexity to find the global optimum of an NP-hard model partitioning problem for 75% of occurrences under some practical conditions. The global optimum is approached with a lower bound distance for the remaining 25%. Furthermore, this approach ensures finding the 2-approximate of the global optimum partition in 97% of instances where technical assumptions exist. The strategy is based on intelligently changing the parameters of the polynomial model of the partitioning problem to force it to produce (or approach) the exact solution to the NP-hard model.