Coarse Representation Research Articles

A coupled time domain random walk approach for transport in media characterized by broadly-distributed heterogeneity length scales

We develop a time domain random walk approach for conservative solute transport in heterogeneous media where medium properties vary over a distribution of length scales. The spatial transition lengths are equal to the heterogeneity length scales, and thus determined by medium geometry. We derive analytical expressions for the associated transition times and probabilities in one spatial dimension. This approach determines the coarse-grained solute concentration at the interfaces between regions; we derive a generalized master equation for the evolution of the coarse-grained concentration and reconstruct the fine-scale concentration using the propagator of the subscale transport mechanism. The performance of this approach is demonstrated for diffusion under random retardation in power-law media characterized by heavy-tailed lengthscale and retardation distributions. The coarse representation preserves the correct late-time scaling of concentration variance, and the reconstructed fine-scale concentration is essentially identical to that obtained by direct numerical simulation by random walk particle tracking.

Spatio-temporal summarization of dance choreographies

An important issue in performing dance analysis is the automatic extraction of its choreographic patterns, since these elements provide an abstract representation of the semantics of the dance and encode the overall dance storytelling. However, application of conventional video summarization algorithms on dance sequences cannot appropriately retrieve their choreographic patterns, since a dance is composed of an ordered set of sequential elements which are often repeated in time. Additionally, 3D geometry is lost using color information. For this reason, in this paper we propose a new dance summarization scheme of 3D motion captured data (in the form of skeleton joints coordinates) recorded using the Vicon motion capture system. The proposed key frame extraction method implements a hierarchical scheme that exploits spatio-temporal variations of dance features. Initially, global holistic descriptors are extracted to localize the key choreographic steps of a dance (coarse representation). Then, each segment is further decomposed into finer sub-segments to improve dance representativity (fine representation). The abstraction scheme exploits the concepts of a Sparse Modeling Representative Selection (SMRS) appropriately modified to enable spatio-temporal modelling of the dance sequences through a hierarchical decomposition algorithm. Our approach is evaluated on thirty folkloric dance sequences recorded at the Aristotle University of Thessaloniki under the framework of Terpsichore project representing five different choreographies and on publicly available datasets from Carnegie–Mellon University, which depict performances on theatrical kinesiology. Comparisons with other traditional video summarization methods indicate a clear superiority of the proposed hierarchical spatio-temporal decomposition scheme.

A Data-Driven Perspective on the Hierarchical Assembly of Molecular Structures.

Macromolecular systems are composed of a very large number of atomic degrees of freedom. There is strong evidence suggesting that structural changes occurring in large biomolecular systems at long time scale dynamics may be captured by models coarser than atomistic, although a suitable or optimal coarse-graining is a priori unknown. Here we propose a systematic approach to learning a coarse representation of a macromolecule from microscopic simulation data. In particular, the definition of effective coarse variables is achieved by partitioning the degrees of freedom both in the structural (physical) space and in the conformational space. The identification of groups of microscopic particles forming dynamical coherent states in different metastable states leads to a multiscale description of the system, in space and time. The application of this approach to the folding dynamics of two proteins provides a revised view of the classical idea of prestructured regions (foldons) that combine during a protein-folding process and suggests a hierarchical characterization of the assembly process of folded structures.

Environment model adaptation for mobile robot exploration

In this work, we propose a methodology to adapt a mobile robot’s environment model during exploration as a means of decreasing the computational complexity associated with information metric evaluation and consequently increasing the speed at which the system is able to plan actions and travel through an unknown region given finite computational resources. Recent advances in exploration compute control actions by optimizing information-theoretic metrics on the robot’s map. These metrics are generally computationally expensive to evaluate, limiting the speed at which a robot is able to explore. To reduce computational cost, we propose keeping two representations of the environment: one full resolution representation for planning and collision checking, and another with a coarse resolution for rapidly evaluating the informativeness of planned actions. To generate the coarse representation, we employ the Principal of Relevant Information from rate distortion theory to compress a robot’s occupancy grid map. We then propose a method for selecting a coarse representation that sacrifices a minimal amount of information about expected future sensor measurements using the Information Bottleneck Method. We outline an adaptive strategy that changes the robot’s environment representation in response to its surroundings to maximize the computational efficiency of exploration. On computationally constrained systems, this reduction in complexity enables planning over longer predictive horizons, leading to faster navigation. We simulate and experimentally evaluate mutual information based exploration through cluttered indoor environments with exploration rates that adapt based on environment complexity leading to an order-of-magnitude increase in the maximum rate of exploration in contrast to non-adaptive techniques given the same finite computational resources.

Cluster analysis of accelerated molecular dynamics simulations: A case study of the decahedron to icosahedron transition in Pt nanoparticles.

Modern molecular-dynamics-based techniques are extremely powerful to investigate the dynamical evolution of materials. With the increase in sophistication of the simulation techniques and the ubiquity of massively parallel computing platforms, atomistic simulations now generate very large amounts of data, which have to be carefully analyzed in order to reveal key features of the underlying trajectories, including the nature and characteristics of the relevant reaction pathways. We show that clustering algorithms, such as the Perron Cluster Cluster Analysis, can provide reduced representations that greatly facilitate the interpretation of complex trajectories. To illustrate this point, clustering tools are used to identify the key kinetic steps in complex accelerated molecular dynamics trajectories exhibiting shape fluctuations in Pt nanoclusters. This analysis provides an easily interpretable coarse representation of the reaction pathways in terms of a handful of clusters, in contrast to the raw trajectory that contains thousands of unique states and tens of thousands of transitions.

Continuous Scale Transformations of Linear Features Using Simulated Annealing-Based Morphing

This paper presents a new method for use in performing continuous scale transformations of linear features using Simulated Annealing-Based Morphing (SABM). This study addresses two key problems in the continuous generalization of linear features by morphing, specifically the detection of characteristic points and correspondence matching. First, an algorithm that performs robust detection of characteristic points is developed that is based on the Constrained Delaunay Triangulation (CDT) model. Then, an optimal problem is defined and solved to associate the characteristic points between a coarser representation and a finer representation. The algorithm decomposes the input shapes into several pairs of corresponding segments and uses the simulated annealing algorithm to find the optimal matching. Simple straight-line trajectories are used to define the movements between corresponding points. The experimental results show that the SABM method can be used for continuous generalization and generates smooth, natural and visually pleasing linear features with gradient effects. In contrast to linear interpolation, the SABM method uses the simulated annealing technique to optimize the correspondence between characteristic points. Moreover, it avoids interior distortions within intermediate shapes and preserves the geographical characteristics of the input shapes.

Hierarchical Boltzmann simulations and model error estimation

A hierarchical simulation approach for Boltzmann's equation should provide a single numerical framework in which a coarse representation can be used to compute gas flows as accurately and efficiently as in computational fluid dynamics, but a subsequent refinement allows to successively improve the result to the complete Boltzmann result. We use Hermite discretization, or moment equations, for the steady linearized Boltzmann equation for a proof-of-concept of such a framework. All representations of the hierarchy are rotationally invariant and the numerical method is formulated on fully unstructured triangular and quadrilateral meshes using a implicit discontinuous Galerkin formulation. We demonstrate the performance of the numerical method on model problems which in particular highlights the relevance of stability of boundary conditions on curved domains.The hierarchical nature of the method allows also to provide model error estimates by comparing subsequent representations. We present various model errors for a flow through a curved channel with obstacles.

LES validation of urban flow, part I: flow statistics and frequency distributions

Essential prerequisites for a thorough model evaluation are the availability of problem-specific, quality-controlled reference data and the use of model-specific comparison methods. The work presented here is motivated by the striking lack of proportion between the increasing use of large-eddy simulation (LES) as a standard technique in micro-meteorology and wind engineering and the level of scrutiny that is commonly applied to assess the quality of results obtained. We propose and apply an in-depth, multi-level validation concept that is specifically targeted at the time-dependency of mechanically induced shear-layer turbulence. Near-surface isothermal turbulent flow in a densely built-up city serves as the test scenario for the approach. High-resolution LES data are evaluated based on a comprehensive database of boundary-layer wind-tunnel measurements. From an exploratory data analysis of mean flow and turbulence statistics, a high level of agreement between simulation and experiment is apparent. Inspecting frequency distributions of the underlying instantaneous data proves to be necessary for a more rigorous assessment of the overall prediction quality. From velocity histograms local accuracy limitations due to a comparatively coarse building representation as well as particular strengths of the model to capture complex urban flow features with sufficient accuracy are readily determined. However, the analysis shows that further crucial information about the physical validity of the LES needs to be obtained through the comparison of eddy statistics, which is focused on in part II. Compared with methods that rely on single figures of merit, the multi-level validation strategy presented here supports conclusions about the simulation quality and the model’s fitness for its intended range of application through a deeper understanding of the unsteady structure of the flow.

Efficient estimation of regularization parameters via downsampling and the singular value expansion

The solution, $x$, of the linear system of equations $A x\approx b$ arising from the discretization of an ill-posed integral equation with a square integrable kernel $H(s,t)$ is considered. The Tikhonov regularized solution $ x(\lambda)$ is found as the minimizer of $J( x)=\{ \|A x - b\|_2^2 + \lambda^2 \|L x\|_2^2\}$. $ x(\lambda)$ depends on regularization parameter $\lambda$ that trades off the data fidelity, and on the smoothing norm determined by $L$. Here we consider the case where $L$ is diagonal and invertible, and employ the Galerkin method to provide the relationship between the singular value expansion and the singular value decomposition for square integrable kernels. The resulting approximation of the integral equation permits examination of the properties of the regularized solution $ x(\lambda)$ independent of the sample size of the data. We prove that estimation of the regularization parameter can be obtained by consistently down sampling the data and the system matrix, leading to solutions of coarse to fine grained resolution. Hence, the estimate of $\lambda$ for a large problem may be found by downsampling to a smaller problem, or to a set of smaller problems, effectively moving the costly estimate of the regularization parameter to the coarse representation of the problem. Moreover, the full singular value decomposition for the fine scale system is replaced by a number of dominant terms which is determined from the coarse resolution system, again reducing the computational cost. Numerical results illustrate the theory and demonstrate the practicality of the approach for regularization parameter estimation using generalized cross validation, unbiased predictive risk estimation and the discrepancy principle applied for both the system of equations, and the augmented system of equations.

An iterative learning approach for anticipatory traffic signal control on urban networks

ABSTRACTTraffic signal control on urban road networks offers high opportunity to improve traffic operations. Among others, anticipatory control determines signal timings to optimize network performance, taking into account explicitly the route choice responses and resulting (equilibrium) network flow patterns. However, the optimal control decisions are usually calculated using equilibrium flow models that are in general only a coarse representation of reality. As a result, model–reality mismatch often leads to suboptimal conditions characterized by unexpected congestion effects. This paper presents a novel method to support control decisions for practical applications in real traffic systems that operate repeatedly, for instance from week to week, month to month, and in the presence of flow measurements. The proposed method generates a sequence of control settings to track the real flow response, by observing errors between modeled flows and the measurements. Improvement in the control performance is achieved by learning from this error information. A theoretical analysis on convergence of the control sequence is provided and the impact of different weighting parameters on the convergence performance is discussed. Numerical examples on a test network confirm the effectiveness of the proposed iterative learning approach in tackling modeling error, as well as a main role of model bias correction in tracking reality. The impact of weighting parameters on its convergence is also illustrated.

An estimation model for social relationship strength based on users' profiles, co-occurrence and interaction activities

As the growing popularity of the Internet, the online social network has become an indispensable part and played a more and more important role in our daily life. People in the online social networks would link with their friends through chatting, e-mail, posting, commenting directly, which are built on the mature relationships in reality. However, this link-ship provides only a coarse representation of relationship rather than revealing the relationship strengths. Accurate measurement of social relationship could be applied to many applications, such as project or paper review. In this paper, we propose a probabilistic graphical model to measure the relationship strengths between different users in the social network by taking consideration of the similarities among users profiles, co-occurrence of user names and interaction activities in different activity fields.

AFV refueling stations and the complexity of freeway intersections: the scale dependency of network representation

ABSTRACTAs interest for alternative fuel vehicles (AFVs) in urban areas continues to build, there has been a corresponding focus on the development of methods that can locate initial refueling stations on regional transportation networks in an optimal manner. Recent studies suggest that the behavior of early adopters of AFVs is consistent with the objectives of flow-capturing station location models. One outstanding issue with the further use of these models to locate AFV stations is the relationship between the relatively coarse geographic representation of regional transportation networks used in flow-capturing models and the complexity of the sites they recommend, which are often nodes that represent freeway intersections. Since AFV refueling stations cannot be built directly at freeway intersections, a network GIS method entitled the freeway traffic capture metric (FTCM) is developed to identify locations on proximate local street networks that can effectively capture all traffic passing through a freeway intersection. The FTCM considers deviation from a shortest travel path specifically through a freeway intersection as its metric of convenience for all possible travel routes that pass through it, computing a score for each candidate site on the nearby local street network. The FTCM is tested on nearly 45,000 candidate sites within one mile of 72 freeway intersections in greater Los Angeles, California. Locations that can capture all traffic passing through the nearby freeway intersection are shown to generally be near the intersection’s center, but not necessarily next to freeway entrances or exits. In total, 6.7% of possible station locations near these 72 freeway intersections are convenient for all traffic passing through them, and 22 out of the 72 freeway intersections lack such a site altogether. This indicates that there is high likelihood of inconsistency between regional modeling results and station location effectiveness if this scale dependency between coarse representations of transportation networks and the complexity of local street networks near freeway intersections is not considered when building initial AFV stations near these locations.

An Efficient Object Tracking Method on Quad-/Oc-Trees.

We introduce a fast error-free tracking method applicable to sequences of two and three dimensional images. The core idea is to use Quadtree (resp. Octree) data structures for representing the spatial discretization of an image in two (resp. three) spatial dimensions. This representation enables one to merge into large computational cells the regions that can be faithfully described with such a coarse representation, thus significantly reducing the total number of degrees of freedom that are processed, without compromising accuracy. This encoding is particularly effective in the case of algorithms based on moving fronts, since the adaptive refinement provides a natural means to focus the processing resources on information near the moving front. In this paper, we use an existing contour based tracker and reformulate it to the case of Quad-/Oc-tree data structures. Relevant mathematical assumptions and derivations are presented for this purpose. We then demonstrate that, on standard bio-medical image sequences, a speed up of 5X is easily achieved in 2D and about 10X in 3D.

Analysis of the LIFT Variance-Reduction Method Applied to Monte Carlo Radiation Transport Simulations of a Realistic Nonproliferation Test Problem

The Local Importance Function Transform (LIFT) method is a sophisticated automated variance-reduction technique for Monte Carlo simulation of radiation transport problems. In previous publications, the LIFT method was tested on geometrically simple problems with a coarse representation of radiation energy dependence, and the performance of the method was found to be promising when compared to traditional weight windows–based variance-reduction techniques. In this work, the LIFT method is tested on a spatially complex benchmark test problem with a more realistic representation of energy dependence (50 energy groups) and heterogeneous materials. The performance of the method in comparison with a CADIS (Consistent Adjoint Driven Importance Sampling)–based weight windows method and an analog Monte Carlo simulation is studied. A multigroup Monte Carlo code that utilizes portions of the framework of the deterministic tool Attila has been developed such that the overhead time in implementing the variance-reduction techniques is minimal. The Monte Carlo simulations are performed on an arbitrary tetrahedral mesh created by the mesh generator in Attila. A method to transfer the deterministic solution generated on a finer mesh to a coarser mesh for implementing the hybrid simulations has been developed, and the results are quantified.

Unconscious vision spots the animal but not the dog: Masked priming of natural scenes.

The functional role of consciousness has been traditionally assumed to be related to high-level executive functions, but recent theories of visual consciousness suggest qualitative differences between conscious and unconscious processes also in lower level visual processes. We tested how specific is the information that can be extracted by unconscious processes from natural scenes. Prime images which were suppressed from consciousness by continuous flash suppression facilitated categorization of visible targets at superordinate level (animal vs. non-animal) when the prime shared a category membership with the target. Suppressed prime images did not have any effect on categorization at the basic level (e.g., horse vs. other animal). Priming occurred at basic level categorization only when the prime images were available to consciousness. This pattern supports a "coarse-to-fine" model in which the visual system can unconsciously access coarse representations, but consciousness is needed for finer analysis of visual scenes.

Evaluating Capacity and Delay for Signalized Arterials with Freight Deliveries

Freight deliveries on signalized urban streets are known to cause lane blockages during delivery. Traffic congestion associated with urban freight deliveries has gained increasing attention recently as traffic engineers and planners are tasked with finding solutions to manage increasing demand more sustainably with limited road capacity. The goal of this research is to evaluate two models for quantifying the capacity and delay effects of a lane blocking freight delivery on a signalized urban street. The two methods are: an all-or-nothing model similar to methodology used in the Highway Capacity Manual 2010 (HCM2010) and a detailed analytical model consistent with kinematic wave theory. The purpose is to provide insight on the use of these tools for analysis of urban freight delivery policy. The results of the two models are compared with each. A simulation of 8th Avenue in New York has been calibrated to observed freight deliveries from a six-hour period, and the simulated results confirm effect of delivery location on capacity and delay. The results show that the methods from the HCM2010 to account for the effects of buses stopping for passengers provide only a coarse representation of the capacity and delay effects of urban freight deliveries. The more detailed approach that accounts for the dynamics of queuing provide closed form analytical formulas for delay and capacity that can account for varying locations of deliveries, long delivery durations, and different impacts on different lane groups.

A radiance cache method for highly glossy surfaces

Radiance caching methods have proven to be efficient for global illumination. Their goal is to compute precisely illumination values (incident radiance or irradiance) at a reasonable number of points lying on the scene surfaces. These points, called records, are stored in a cache used for estimating illumination at other points in the scene. Unfortunately, with records lying on glossy surfaces, the irradiance value alone is not sufficient to evaluate the reflected radiance; each record should also store the incident radiance for all incident directions. Memory storage can be reduced with projection techniques using spherical harmonics or other basis functions. These techniques provide good results for low shininess BRDFs. However, they get impractical for shininess of even moderate value, since the number of projection coefficients increases drastically. In this paper, we propose a new radiance caching method that handles highly glossy surfaces while requiring a low memory storage. Each cache record stores a coarse representation of the incident illumination thanks to a new data structure, called Equivalent Area light Sources, capable of handling fuzzy mirror surfaces. In addition, our method proposes a new simplification of the interpolation process, since it avoids the need for expressing and evaluating complex gradients.

Intertwining agents and environments

Connections between human agents and dynamic natural and physical environments can be difficult to explore, particularly for critical scenarios in which evidence is often scarce. For these scenarios, we often turn to modeling and simulation as sandboxes for our inquiry. However, in the absence of fine-grain ground truth about events and phenomena that are often extraordinary in the human experience, our models have settled upon a tradition of coarse representation. In this paper, we introduce a method for developing rich connections between agents and environment. We present a scheme for Virtual Geographic Environments, which puts them to use as a platform for intertwining diverse spatial data from Geographic Information Systems, three-dimensional mesh models of built settings, agent-based models of human cognition and movement, and richly specified process models for physical phenomena and human behavior. To demonstrate the usefulness of the scheme, we will present a unified model of human–physical response to built damage following a simulated earthquake.

The Anatomical and Functional Organization of the Human Visual Pulvinar.

The anatomical organization and basic response properties of the visual pulvinar have been extensively studied in nonhuman primates. Yet, relatively little is known about the functional and anatomical organization of the human pulvinar. Using neuroimaging, we found multiple representations of visual space within the ventral human pulvinar and extensive topographically organized connectivity with visual cortex. This organization is similar to other nonhuman primates and provides additional support that the general organization of the pulvinar is consistent across the primate phylogenetic tree. These results suggest that the human pulvinar, like other primates, is well positioned to regulate corticocortical communication.

Simulated South Atlantic transports and their variability during 1958–2007

South Atlantic transports, as simulated by a global ocean-sea ice model forced with the Coordinated Ocean-ice Reference Experiments version 2 (CORE-II) interannually varying air-sea reanalysis data sets, are analyzed for the period 1958–2007. The ocean-sea ice model is configured at three different resolutions: from eddy-permitting to coarsened grid spacing. A particular focus is given to the effect of eddy fluxes and inter-ocean exchanges on the South Atlantic Meridional Overturning Circulation (SAMOC), as well as on the main factors contributing to the interannual variability during the integration period. Differences between refined and coarsened grid spacing models are more evident in coastal areas and in regions of high eddy activities. Major discrepancies are associated to both the parameterization of eddy fluxes and the coarse representation of the bathymetry. The refined grid spacing model produces higher values of both SAMOC index, defined as the maximum of the zonally-integrated northward cumulative volume transport (CVT) from surface to bottom across ∼34° S, and meridional heat transport (MHT). All models show high correlations between SAMOC index and MHT, as well as a strengthening of the transports in the 1980–2007 period. The strengthening of the SAMOC index is mainly dominated by surface and mode waters in all models. In surface and intermediate layers, the regions contributing to this trend are located east of 40° W. These changes are compensated by the strengthening of the poleward transport in deeper layers, mostly in the western part of the basin. The MHT trend is connected with the combined effect of a heat transport increase through the Drake Passage and a reduction of the heat loss through the eastern section between Africa and Antarctica, mainly associated with a strengthening in heat entering into the basin through the Agulhas system.