Individual Vertices Research Articles

Dual strip weaving

We introduce Dual Strip Weaving , a novel concept for the interactive design of quad layouts, i.e. partitionings of freeform surfaces into quadrilateral patch networks. In contrast to established tools for the design of quad layouts or subdivision base meshes, which are often based on creating individual vertices, edges, and quads, our method takes a more global perspective, operating on a higher level of abstraction: the atomic operation of our method is the creation of an entire cyclic strip, delineating a large number of quad patches at once. The global consistency-preserving nature of this approach reduces demands on the user's expertise by requiring less advance planning. Efficiency is achieved using a novel method at the heart of our system, which automatically proposes geometrically and topologically suitable strips to the user. Based on this we provide interaction tools to influence the design process to any desired degree and visual guides to support the user in this task.

Towards Scene Understanding with Detailed 3D Object Representations

Current approaches to semantic image and scene understanding typically employ rather simple object representations such as 2D or 3D bounding boxes. While such coarse models are robust and allow for reliable object detection, they discard much of the information about objects’ 3D shape and pose, and thus do not lend themselves well to higher-level reasoning. Here, we propose to base scene understanding on a high-resolution object representation. An object class—in our case cars—is modeled as a deformable 3D wireframe, which enables fine-grained modeling at the level of individual vertices and faces. We augment that model to explicitly include vertex-level occlusion, and embed all instances in a common coordinate frame, in order to infer and exploit object-object interactions. Specifically, from a single view we jointly estimate the shapes and poses of multiple objects in a common 3D frame. A ground plane in that frame is estimated by consensus among different objects, which significantly stabilizes monocular 3D pose estimation. The fine-grained model, in conjunction with the explicit 3D scene model, further allows one to infer part-level occlusions between the modeled objects, as well as occlusions by other, unmodeled scene elements. To demonstrate the benefits of such detailed object class models in the context of scene understanding we systematically evaluate our approach on the challenging KITTI street scene dataset. The experiments show that the model’s ability to utilize image evidence at the level of individual parts improves monocular 3D pose estimation w.r.t. both location and (continuous) viewpoint.

Description and performance of track and primary-vertex reconstruction with the CMS tracker

A description is provided of the software algorithms developed for the CMS tracker both for reconstructing charged-particle trajectories in proton-proton interactions and for using the resulting tracks to estimate the positions of the LHC luminous region and individual primary-interaction vertices. Despite the very hostile environment at the LHC, the performance obtained with these algorithms is found to be excellent. For tt̄ events under typical 2011 pileup conditions, the average track-reconstruction efficiency for promptly-produced charged particles with transverse momenta of pT > 0.9GeV is 94% for pseudorapidities of |η| < 0.9 and 85% for 0.9 < |η| < 2.5. The inefficiency is caused mainly by hadrons that undergo nuclear interactions in the tracker material. For isolated muons, the corresponding efficiencies are essentially 100%. For isolated muons of pT = 100GeV emitted at |η| < 1.4, the resolutions are approximately 2.8% in pT, and respectively, 10μm and 30μm in the transverse and longitudinal impact parameters. The position resolution achieved for reconstructed primary vertices that correspond to interesting pp collisions is 10–12μm in each of the three spatial dimensions. The tracking and vertexing software is fast and flexible, and easily adaptable to other functions, such as fast tracking for the trigger, or dedicated tracking for electrons that takes into account bremsstrahlung.

Parallel processing of filtered queries in attributed semantic graphs

Execution of complex analytic queries on massive semantic graphs is a challenging problem in big-data analytics that requires high-performance parallel computing. In a semantic graph, vertices and edges carry attributes of various types and the analytic queries typically depend on the values of these attributes. Thus, the computation must view the graph through a filter that passes only those individual vertices and edges of interest. Previous investigations have developed Knowledge Discovery Toolbox (KDT), a sophisticated Python library for parallel graph computations. In KDT, the user can write custom graph algorithms by specifying operations between edges and vertices (semiring operations). The user can also customize existing graph algorithms by writing filters. Although the high-level language for this customization enables domain scientists to productively express their graph analytics requirements, the customized queries perform poorly due to the overhead of having to call into the Python virtual machine for each vertex and edge.In this work, we use the Selective Embedded Just-In-Time Specialization (SEJITS) approach to automatically translate semiring operations and filters defined by programmers into a lower-level efficiency language, bypassing the upcall into Python. We evaluate our approach by comparing it with the high-performance Combinatorial BLAS engine and show that our approach combines the benefits of programming in a high-level language with executing in a low-level parallel environment. We increase the system’s flexibility by developing techniques that provide users with the ability to define new vertex and edge types from Python. We also present a new Roofline model for graph traversals and show that we achieve performance that is significantly closer to the bounds suggested by the Roofline. Finally, to further understand the complex interaction with the underlying architecture, we present an analysis using performance counters that quantifies the improvement in hardware behavior in the context our SEJITS methodology. Overall, we demonstrate the first known solution to the problem of obtaining high performance from a productivity language when applying graph algorithms selectively on semantic graphs with hundreds of millions of edges and scaling to thousands of processors for graphs.

Trail making test performance in youth varies as a function of anatomical coupling between the prefrontal cortex and distributed cortical regions.

While researchers have gained a richer understanding of the neural correlates of executive function in adulthood, much less is known about how these abilities are represented in the developing brain and what structural brain networks underlie them. Thus, the current study examined how individual differences in executive function, as measured by the Trail Making Test (TMT), relate to structural covariance in the pediatric brain. The sample included 146 unrelated, typically developing youth (80 females), ages 9–14 years, who completed a structural MRI scan of the brain and the Halstead-Reitan TMT (intermediate form). TMT scores used to index executive function included those that evaluated set-shifting ability: Trails B time (number-letter sequencing) and the difference in time between Trails B and A (number sequencing only). Anatomical coupling was measured by examining correlations between mean cortical thickness (MCT) across the entire cortical ribbon and individual vertex thickness measured at ~81,000 vertices. To examine how TMT scores related to anatomical coupling strength, linear regression was utilized and the interaction between age-normed TMT scores and both age and sex-normed MCT was used to predict vertex thickness. Results revealed that stronger Trails B scores were associated with greater anatomical coupling between a large swath of prefrontal cortex and the rest of cortex. For the difference between Trails B and A, a network of regions in the frontal, temporal, and parietal lobes was found to be more tightly coupled with the rest of cortex in stronger performers. This study is the first to highlight the importance of structural covariance in in the prediction of individual differences in executive function skills in youth. Thus, it adds to the growing literature on the neural correlates of childhood executive functions and identifies neuroanatomic coupling as a biological substrate that may contribute to executive function and dysfunction in childhood.

Sparse approximation of 3D shapes via spectral graph wavelets

This paper investigates the compressive representation of 3D meshes and articulates a novel sparse approximation method for 3D shapes based on spectral graph wavelets. The originality of this paper is centering on the first attempt of exploiting spectral graph wavelets in the sparse representation for 3D shape geometry. Conventional spectral mesh compression employs the eigenfunctions of mesh Laplacian as shape bases. The Laplacian eigenbases, generalizing the Fourier bases from Euclidean domain to manifold, exhibit global support and are neither efficient nor precise in representing local geometry. To ameliorate, we advocate an innovative approach to 3D mesh compression using spectral graph wavelets as dictionary to encode mesh geometry. In contrast to Laplacian eigenbases, the spectral graph wavelets are locally defined at individual vertices and can better capture local shape information in a more accurate way. Nonetheless, the multiscale spectral graph wavelets form a redundant dictionary as shape bases, therefore we formulate the compression of 3D shape as a sparse approximation problem that can be readily handled by powerful algorithms such as orthogonal matching pursuit. Various experiments demonstrate that our method is superior to the existing spectral mesh compression methods.

A General Reduction Theorem with Applications to Pathwidth and the Complexity of MAX 2-CSP

We prove a general reduction theorem which allows us to extend bounds for certain graph parameters on cubic graphs to bounds for general graphs taking into account the individual vertex degrees. As applications, we give an algorithm for Max \(2\)-CSP whose complexity matches the algorithm of Scott and Sorkin in the case of \(d\)-regular graphs, \(d \le 5\), but is otherwise faster. It also improves on the previously fastest known algorithm in terms of the average degree, given by Golovnev and Kutzkov. Also from the general theorem, we derive a bound for the pathwidth of a general graph which equals that of Fomin et al. and Gaspers for graphs of degree at most \(6\), but is smaller otherwise, and use this to give an improved exponential-space algorithm for Max \(2\)-CSP. Finally we use the general result to give a faster algorithm for Max \(2\)-CSP on claw-free graphs.

Accelerating IP routing algorithm using graphics processing unit for high speed multimedia communication

This paper presents a Graphics Processing Unit (GPU)-based implementation of a Bellman-Ford (BF) routing algorithm using NVIDIA's Compute Unified Device Architecture (CUDA). In the proposed GPU-based approach, multiple threads run concurrently over numerous streaming processors in the GPU to dynamically update routing information. Instead of computing the individual vertex distances one-by-one, a number of threads concurrently update a larger number of vertex distances, and an individual vertex distance is represented in a single thread. This paper compares the performance of the GPU-based approach to an equivalent CPU implementation while varying the number of vertices. Experimental results show that the proposed GPU-based approach outperforms the equivalent sequential CPU implementation in terms of execution time by exploiting the massive parallelism inherent in the BF routing algorithm. In addition, the reduction in energy consumption (about 99 %) achieved by using the GPU is reflective of the overall merits of deploying GPUs across the entire landscape of IP routing for emerging multimedia communications.

Freeform surface measurement and characterisation using a toolmakers microscope

Current freeform surface (FFS) characterization systems mainly cover aspects related to computer-aided design/manufacture (CAD/CAM). This paper describes a new approach that extends into computer-aided inspection (CAI).The following novel features are addressed:■ Feature recognition and extraction from surface data■ Characterisation of properties of the surface's M and N vectors at individual vertex■ Development of a measuring plan using a toolmakers microscope for the inspection of the FFS■ Inspection of the actual FFS produced by CNC milling■ Verification of the measurement results and comparison with the CAD design dataTests have shown that the deviations between the CAI and CAD data were within the estimated uncertainty limits.

Identifying the Most Connected Vertices in Hidden Bipartite Graphs Using Group Testing

A graph is called hidden if the edges are not explicitly given and edge probe tests are required to detect the presence of edges. This paper studies the k most connected vertices (kMCV) problem on hidden bipartite graphs, which has applications in spatial databases, graph databases, and bioinformatics. There is a prior work on the kMCV problem, which is based on the “2-vertex testing” model, i.e., an edge probe test can only reveal the existence of an edge between two individual vertices. We study the kMCV problem, in the context of a more general edge probe test model called “group testing.” A group test can reveal whether there exists some edge between a vertex and a group of vertices. If group testing is used properly, a single invocation of a group test can reveal as much information as multiple invocations of 2-vertex tests. We discuss the cases and applications where group testing could be used, and present an algorithm, namely, GMCV, that adaptively leverages group testing to solve the kMCV problem.

Canonical granger causality between regions of interest

Estimating and modeling functional connectivity in the brain is a challenging problem with potential applications in the understanding of brain organization and various neurological and neuropsychological conditions. An important objective in connectivity analysis is to determine the connections between regions of interest in the brain. However, traditional functional connectivity analyses have frequently focused on modeling interactions between time series recordings at individual sensors, voxels, or vertices despite the fact that a single region of interest will often include multiple such recordings. In this paper, we present a novel measure of interaction between regions of interest rather than individual signals. The proposed measure, termed canonical Granger causality, combines ideas from canonical correlation and Granger causality analysis to yield a measure that reflects directed causality between two regions of interest. In particular, canonical Granger causality uses optimized linear combinations of signals from each region of interest to enable accurate causality measurements from substantially less data compared to alternative multivariate methods that have previously been proposed for this scenario. The optimized linear combinations are obtained using a variation of a technique developed for optimization on the Stiefel manifold. We demonstrate the advantages of canonical Granger causality in comparison to alternative causality measures for a range of different simulated datasets. We also apply the proposed measure to local field potential data recorded in a macaque brain during a visuomotor task. Results demonstrate that canonical Granger causality can be used to identify causal relationships between striate and prestriate cortexes in cases where standard Granger causality is unable to identify statistically significant interactions.

DNA Gridiron Nanostructures Based on Four-Arm Junctions

Engineering wireframe architectures and scaffolds of increasing complexity is one of the important challenges in nanotechnology. We present a design strategy to create gridiron-like DNA structures. A series of four-arm junctions are used as vertices within a network of double-helical DNA fragments. Deliberate distortion of the junctions from their most relaxed conformations ensures that a scaffold strand can traverse through individual vertices in multiple directions. DNA gridirons were assembled, ranging from two-dimensional arrays with reconfigurability to multilayer and three-dimensional structures and curved objects.

3D-3D Registration of partial capitate bones using spin-images.

It is often necessary to register partial objects in medical imaging. Due to limited FOV, the entirety of an object cannot always be imaged. This study presents a novel application of an existing registration algorithm to this problem. The spin-image algorithm [1] creates pose-invariant representations of global shape with respect to individual mesh vertices. These 'spin-images,' are then compared for two different poses of the same object to establish correspondences and subsequently determine relative orientation of the poses. In this study, the spin-image algorithm is applied to 4DCT-derived capitate bone surfaces to assess the relative accuracy of registration with various amounts of geometry excluded. The limited longitudinal coverage under the 4DCT technique (38.4mm, [2]), results in partial views of the capitate when imaging wrist motions. This study assesses the ability of the spin-image algorithm to register partial bone surfaces by artificially restricting the capitate geometry available for registration. Under IRB approval, standard static CT and 4DCT scans were obtained on a patient. The capitate was segmented from the static CT and one phase of 4DCT in which the whole bone was available. Spin-image registration was performed between the static and 4DCT. Distal portions of the 4DCT capitate (10-70%) were then removed and registration was repeated. Registration accuracy was evaluated by angular errors and the percentage of sub-resolution fitting. It was determined that 60% of the distal capitate could be omitted without appreciable effect on registration accuracy using the spin-image algorithm (angular error < 1.5 degree, sub-resolution fitting > 98.4%).

Residual Closeness in Cycles and Related Networks

Networks are known to be prone to node or link failures. A central issue in the analysis of networks is the assessment of their stability and reliability. The main aim is to understand, predict, and possibly even control the behavior of a networked system under attacks or disfunctions of any type. A central concept that is used to assess stability and robustness of the performance of a network under failures is that of vulnerability. A network is usually represented by an undirected simple graph where vertices represent processors and edges represent links between processors. Different approaches to properly define a measure for graph vulnerability has been proposed so far. In this paper, we study the vulnerability of cycles and related graphs to the failure of individual vertices, using a measure called residual closeness which provides a more sensitive characterization of the graph than some other well-known vulnerability measures.

Graph theoretical analysis of resting magnetoencephalographic functional connectivity networks.

Complex networks have been observed to comprise small-world properties, believed to represent an optimal organization of local specialization and global integration of information processing at reduced wiring cost. Here, we applied magnitude squared coherence to resting magnetoencephalographic time series in reconstructed source space, acquired from controls and patients with schizophrenia, and generated frequency-dependent adjacency matrices modeling functional connectivity between virtual channels. After configuring undirected binary and weighted graphs, we found that all human networks demonstrated highly localized clustering and short characteristic path lengths. The most conservatively thresholded networks showed efficient wiring, with topographical distance between connected vertices amounting to one-third as observed in surrogate randomized topologies. Nodal degrees of the human networks conformed to a heavy-tailed exponentially truncated power-law, compatible with the existence of hubs, which included theta and alpha bilateral cerebellar tonsil, beta and gamma bilateral posterior cingulate, and bilateral thalamus across all frequencies. We conclude that all networks showed small-worldness, minimal physical connection distance, and skewed degree distributions characteristic of physically-embedded networks, and that these calculations derived from graph theoretical mathematics did not quantifiably distinguish between subject populations, independent of bandwidth. However, post-hoc measurements of edge computations at the scale of the individual vertex revealed trends of reduced gamma connectivity across the posterior medial parietal cortex in patients, an observation consistent with our prior resting activation study that found significant reduction of synthetic aperture magnetometry gamma power across similar regions. The basis of these small differences remains unclear.

Effect of positive feedback on Devil's staircase input-output relationship

We consider emerging hysteresis behaviour in a closed loop systemthat includes a nonlinear link $f$ of the Devil's staircase (Cantorfunction) type and a positive feedback. This type of closed loopsarises naturally in analysis of networks where local ``negative''coupling of network elements is combined with ``positive'' couplingat the level of the mean-field interaction (in the limit case whenthe impact of each individual vertex is infinitesimal, while thenumber of vertices is growing). For the Cantor function $f$, takenas a model, and for a monotonically increasing input, we present thecorresponding output of the system explicitly, showing that theoutput is piecewise constant and has a finite number of equal jumps.We then discuss hysteresis loops of the system for genericnon-monotone inputs. The results are presented in the context of differential equations describingnonlinear control systems with almost immediate linear feedback, i.e., in the limit where the time of propagation of the signalthrough the feedback loop tends to zero.

Identifying protein complexes in protein–protein interaction networks by using clique seeds and graph entropy

The identification of protein complexes plays a key role in understanding major cellular processes and biological functions. Various computational algorithms have been proposed to identify protein complexes from protein-protein interaction (PPI) networks. In this paper, we first introduce a new seed-selection strategy for seed-growth style algorithms. Cliques rather than individual vertices are employed as initial seeds. After that, a result-modification approach is proposed based on this seed-selection strategy. Predictions generated by higher order clique seeds are employed to modify results that are generated by lower order ones. The performance of this seed-selection strategy and the result-modification approach are tested by using the entropy-based algorithm, which is currently the best seed-growth style algorithm to detect protein complexes from PPI networks. In addition, we investigate four pairs of strategies for this algorithm in order to improve its accuracy. The numerical experiments are conducted on a Saccharomyces cerevisiae PPI network. The group of best predictions consists of 1711 clusters, with the average f-score at 0.68 after removing all similar and redundant clusters. We conclude that higher order clique seeds can generate predictions with higher accuracy and that our improved entropy-based algorithm outputs more reasonable predictions than the original one.

Anisotropy of Crumbs and aPKC Drives Myosin Cable Assembly during Tube Formation

SummaryThe formation of tubular structures from epithelial sheets is a key process of organ formation in all animals, but the cytoskeletal rearrangements that cause the cell shape changes that drive tubulogenesis are not well understood. Using live imaging and super-resolution microscopy to analyze the tubulogenesis of the Drosophila salivary glands, I find that an anisotropic plasma membrane distribution of the protein Crumbs, mediated by its large extracellular domain, determines the subcellular localization of a supracellular actomyosin cable in the cells at the placode border, with myosin II accumulating at edges where Crumbs is lowest. Laser ablation shows that the cable is under increased tension, implying an active involvement in the invagination process. Crumbs anisotropy leads to anisotropic distribution of aPKC, which in turn can negatively regulate Rok, thus preventing the formation of a cable where Crumbs and aPKC are localized.

Tool path compensation strategies for single point incremental sheet forming using multivariate adaptive regression splines

Single point incremental sheet forming is an emerging sheet metal prototyping process that can produce parts without requiring dedicated tooling per part geometry. One of the major issues with the process concerns the achievable accuracy of parts, which depends on the type of features present in the part and their interactions with one another. In this study, the authors propose a solution to improve the accuracy by using Multivariate Adaptive Regression Splines (MARS) as an error prediction tool to generate continuous error response surfaces for individual features and feature combinations. Two feature types, viz.: planar and ruled, and two feature interactions, viz.: combinations of planar features and combinations of ruled features are studied in detail, with parameters and algorithms to generate response surfaces presented. Validation studies on the generated response surfaces show average deviations of less than 0.3 mm. The predicted response surfaces are then used to generate compensated tool paths by systematically translating the individual vertices in a triangulated surface model of the part available in STL file format orthogonal to the surface of the CAD model, and using the translated model to generate the optimized tool paths. These tool paths bring down the accuracy for most test cases to less than 0.4 mm of average absolute deviations. By further combining the MARS compensated surfaces with a rib offset strategy, the accuracy of planar features is improved significantly with average absolute deviations of less than 0.25 mm.

Stability analysis for impulsive coupled systems on networks

This paper investigates the stability problem of equilibrium for impulsive coupled systems on networks (ICSNs). We provide a systematic method that allows one to construct global Lyapunov functions for large-scale impulsive coupled systems from building blocks of individual vertex systems by using results from graph theory. Consequently, a new asymptotic stability principle and a new exponentially stable principle, which have a close relation to the topology property of the network, are given. As an application to the results, we employ the principle to a class of impulsive coupled systems, and then an easy-verified sufficient condition which guarantees the asymptotic stability and exponential stability are obtained.