Small Subregions Research Articles

Continuous amortization and extensions: With applications to bisection-based root isolation

Subdivision-based algorithms recursively subdivide an input region until the smaller subregions can be processed. It is a challenge to analyze the complexity of such algorithms because the work they perform is not uniform across the input region. Continuous amortization was introduced in Burr et al. (2009) as a way to bound the complexity of subdivision-based algorithms. The main features of this new technique are that (1) the technique can be applied, uniformly, to a variety of subdivision-based algorithms, (2) the technique considers a function directly related to the subdivision-based algorithm under consideration, and (3) the output of the technique is often explicitly expressed in terms of the intrinsic complexity of the problem instance.In this paper, the theory of continuous amortization is generalized and applied in several directions. The theory is generalized (1) to allow the domain to be higher dimensional or an abstract measure space, (2) to allow more general subdivisions than bisections, and (3) to bound the value of general functions on the regions of the final partition. The theory is applied to seven examples of subdivision-based algorithms. These applications include (1) bounding the number of subdivisions performed by algorithms for isolating real and complex roots of polynomials, (2) bounding the bit-complexity of subdivision-based algorithms for isolating the real roots of polynomials, and (3) bounding the expected run-time of an algorithm for approximating a biased coin. In each of these applications, by using continuous amortization, we achieve or improve the best-known complexity bounds.

Numerical Homogenization of Elliptic Multiscale Problems by Subspace Decomposition

Numerical homogenization tries to approximate solutions of elliptic partial differential equations with strongly oscillating coefficients by the solution of localized problems over small subregions. We develop and analyze a rapidly convergent iterative method for numerical homogenization that shares this feature with existing approaches and is modeled after the Schwarz method. The method is highly parallelizable and of lower computational complexity than comparable methods that as ours do not make explicit or implicit use of a scale separation.

Geometric partitioning and robust ad-hoc network design

We present fast approximation algorithms for the problem of dividing a given convex geographic region into smaller sub-regions so as to distribute the workloads of a set of vehicles. Our objective is to partition the region in such a fashion as to ensure that vehicles are capable of communicating with one another under limited communication radii. We consider variations of this problem in which sub-regions are constrained to have equal area or be convex, and as a side consequence, our approach yields a factor 1.99 approximation algorithm for the continuous k-centers problem on a convex polygon.

Singularity-consistent payload locations for parallel manipulators

Parallel manipulators are practically confined to a dramatically small subregion of their workspace due to type II singularities. Around such configurations, the actuator forces tend to infinity and, consequently, the controllability is lost. Therefore, in recent years, growing attention is devoted to develop methods for parallel manipulators to pass through these singular positions while the required actuator efforts remain bounded and continuous. With this aim, in this paper the singularity-consistent payload locations are analytically studied. First, it is shown for three-degree-of-freedom planar parallel manipulators that, in general, the corresponding locus describes a circle in the end-effector plane, whereas it will be a straight line if the angular acceleration of the end-effector platform is prescribed to be zero at the singular configuration. Then, it is proved for spatial six-degree-of-freedom parallel manipulators that the locus of interest represents a quadric surface, whereas it degenerates to a plane if the end-effector platform is prescribed to be in pure translation. The developed payload placement method is outlined as four theorems and one corollary, and its effectiveness is demonstrated through numerical simulations.

Photometric metallicity map of the Large Magellanic Cloud

We have estimated a metallicity map of the Large Magellanic Cloud (LMC) using the Magellanic Cloud Photometric Survey (MCPS) and Optical Gravitational Lensing Experiment (OGLE III) photometric data. This is a first of its kind map of metallicity up to a radius of 4 - 5 degrees, derived using photometric data and calibrated using spectroscopic data of Red Giant Branch (RGB) stars. We identify the RGB in the V, (V$-$I) colour magnitude diagrams of small subregions of varying sizes in both data sets. We use the slope of the RGB as an indicator of the average metallicity of a subregion, and calibrate the RGB slope to metallicity using spectroscopic data for field and cluster red giants in selected subregions. The average metallicity of the LMC is found to be [Fe/H] = $-$0.37 dex ($\sigma$[Fe/H] = 0.12) from MCPS data, and [Fe/H] = $-$0.39 dex ($\sigma$[Fe/H] = 0.10) from OGLE III data. The bar is found be the most metal-rich region of the LMC. Both the data sets suggest a shallow radial metallicity gradient up to a radius of 4 kpc ($-$0.049$\pm$0.002 dex kpc$^{-1}$ to $-$0.066$\pm$0.006 dex kpc$^{-1}$). Subregions in which the mean metallicity differs from the surrounding areas do not appear to correlate with previously known features; spectroscopic studies are required in order to assess their physical significance.

Diffusion-Weighted Imaging in 3.0 Tesla Breast MRI: Diagnostic Performance and Tumor Characterization Using Small Subregions vs. Whole Tumor Regions of Interest.

IntroductionApparent diffusion coefficient (ADC) values are increasingly reported in breast MRI. As there is no standardized method for ADC measurements, we evaluated the effect of the size of region of interest (ROI) to diagnostic utility and correlation to prognostic markers of breast cancer.MethodsThis prospective study was approved by the Institutional Ethics Board; the need for written informed consent for the retrospective analyses of the breast MRIs was waived by the Chair of the Hospital District. We compared diagnostic accuracy of ADC measurements from whole-lesion ROIs (WL-ROIs) to small subregions (S-ROIs) showing the most restricted diffusion and evaluated correlations with prognostic factors in 112 consecutive patients (mean age 56.2±11.6 years, 137 lesions) who underwent 3.0-T breast MRI.ResultsIntra- and interobserver reproducibility were substantial (κ = 0.616–0.784; Intra-Class Correlation 0.589–0.831). In receiver operating characteristics analysis, differentiation between malignant and benign lesions was excellent (area under curve 0.957–0.962, cut-off ADC values for WL-ROIs: 0.87×10−3 mm2s-1; S-ROIs: 0.69×10−3 mm2s-1, P<0.001). WL-ROIs/S-ROIs achieved sensitivities of 95.7%/91.3%, specificities of 89.5%/94.7%, and overall accuracies of 89.8%/94.2%. In S-ROIs, lower ADC values correlated with presence of axillary metastases (P = 0.03), high histological grade (P = 0.006), and worsened Nottingham Prognostic Index Score (P<0.05). In both ROIs, ADC values correlated with progesterone receptors and advanced stage (P<0.01), but not with HER2, estrogen receptors, or Ki-67.ConclusionsADC values assist in breast tumor characterization. Small ROIs were more accurate than whole-lesion ROIs and more frequently associated with prognostic factors. Cut-off values differed significantly depending on measurement procedure, which should be recognized when comparing results from the literature. Instead of using a whole lesion covering ROI, a small ROI could be advocated in diffusion-weighted imaging.

Projecting changes in regional temperature and precipitation extremes in the United States

Abstract Regional and local climate extremes, and their impacts, result from the multifaceted interplay between large-scale climate forcing, local environmental factors (physiography), and societal vulnerability. In this paper, we review historical and projected changes in temperature and precipitation extremes in the United States, with a focus on strengths and weaknesses of (1) commonly used definitions for extremes such as thresholds and percentiles, (2) statistical approaches to quantifying changes in extremes, such as extreme value theory, and (3) methods for post-processing (downscaling) global climate models (GCMs) to investigate regional and local climate. We additionally derive regional and local estimates of changes in temperature extremes by applying a quantile mapping approach to high-resolution gridded daily temperature data for 6 U.S. sub-regions. Consistent with the background warming in the parent GCMs, we project decreases in regional and local cold extremes and increases in regional and local warm extremes throughout the domain, but the downscaling approach removes bias and produces substantial spatial variability within the relatively small sub-regions. We finish with recommendations for future research on regional climate extremes, suggesting that focus be placed on improving understanding of extremes in the context of large-scale circulation and evaluating the corresponding cascade of scale interactions within GCMs.

Stratified mixture modeling for segmentation of white-matter lesions in brain MR images

Accurate characterization of white-matter lesions from magnetic resonance (MR) images has increasing importance for diagnosis and management of treatment of certain neurological diseases, and can be performed in an objective and effective way by automated lesion segmentation. This usually involves modeling the whole-brain MR intensity distribution, however, capturing various sources of MR intensity variability and lesion heterogeneity results in highly complex whole-brain MR intensity models, thus their robust estimation on a large set of MR images presents a huge challenge. We propose a novel approach employing stratified mixture modeling, where the main premise is that the otherwise complex whole-brain model can be reduced to a tractable parametric form in small brain subregions. We show on MR images of multiple sclerosis (MS) patients with different lesion loads that robust estimators enable accurate mixture modeling of MR intensity in small brain subregions even in the presence of lesions. Recombination of the mixture models across strata provided an accurate whole-brain MR intensity model. Increasing the number of subregions and, thereby, the model complexity, consistently improved the accuracy of whole-brain MR intensity modeling and segmentation of normal structures. The proposed approach was incorporated into three unsupervised lesion segmentation methods and, compared to original and three other state-of-the-art methods, the proposed modeling approach significantly improved lesion segmentation according to increased Dice similarity indices and lower number of false positives on real MR images of 30 patients with MS.

The Effect of Quantitative Computed Tomography Acquisition Protocols on Bone Mineral Density Estimation.

Osteoporosis is characterized by bony material loss and decreased bone strength leading to a significant increase in fracture risk. Patient-specific quantitative computed tomography (QCT) finite element (FE) models may be used to predict fracture under physiological loading. Material properties for the FE models used to predict fracture are obtained by converting grayscale values from the CT into volumetric bone mineral density (vBMD) using calibration phantoms. If there are any variations arising from the CT acquisition protocol, vBMD estimation and material property assignment could be affected, thus, affecting fracture risk prediction. We hypothesized that material property assignments may be dependent on scanning and postprocessing settings including voltage, current, and reconstruction kernel, thus potentially having an effect in fracture risk prediction. A rabbit femur and a standard calibration phantom were imaged by QCT using different protocols. Cortical and cancellous regions were segmented, their average Hounsfield unit (HU) values obtained and converted to vBMD. Estimated vBMD for the cortical and cancellous regions were affected by voltage and kernel but not by current. Our study demonstrated that there exists a significant variation in the estimated vBMD values obtained with different scanning acquisitions. In addition, the large noise differences observed utilizing different scanning parameters could have an important negative effect on small subregions containing fewer voxels.

Study of the instability of the Poiseuille flow using a thermodynamic formalism

The stability of the plane Poiseuille flow is analyzed using a thermodynamic formalism by considering the deterministic Navier-Stokes equation with Gaussian random initial data. A unique critical Reynolds number, Rec ≈ 2,332, at which the probability of observing puffs in the solution changes from 0 to 1, is numerically demonstrated to exist in the thermodynamic limit and is found to be independent of the noise amplitude. Using the puff density as the macrostate variable, the free energy of such a system is computed and analyzed. The puff density approaches zero as the critical Reynolds number is approached from above, signaling a continuous transition despite the fact that the bifurcation is subcritical for a finite-sized system. An action function is found for the probability of observing puffs in a small subregion of the flow, and this action function depends only on the Reynolds number. The strategy used here should be applicable to a wide range of other problems exhibiting subcritical instabilities.

Towards trustworthy collaboration in spectrum sensing for ad hoc cognitive radio networks

Cognitive radio networks (CRN) make use of dynamic spectrum access to communicate opportunistically in frequency bands otherwise licensed to incumbent primary users such as TV broadcast. To prevent interference to primary users it is vital for secondary users in CRNs to conduct accurate spectrum sensing, which is especially challenging when the transmission range of primary users is shorter compared to the size of the CRN. This task becomes even more challenging in the presence of malicious secondary users that launch spectrum sensing data falsification (SSDF) attacks by providing false spectrum reports. Existing solutions to detect such malicious behaviors cannot be utilized in scenarios where the transmission range of primary users is limited within a small sub-region of the CRN. In this paper, we present a framework for trustworthy collaboration in spectrum sensing for ad hoc CRNs. This framework incorporates a semi-supervised spatio-spectral anomaly/outlier detection system and a reputation system, both designed to detect byzantine attacks in the form of SSDF from malicious nodes within the CRN. The framework guarantees protection of incumbent primary users' communication rights while at the same time making optimal use of the spectrum when it is not used by primary users. Simulation carried out under typical network conditions and attack scenarios shows that our proposed framework can achieve spectrum decision accuracy up to 99.3 % and detect malicious nodes up to 98 % of the time.

Optogenetic and pharmacological suppression of spatial clusters of face neurons reveal their causal role in face gender discrimination

Neurons that respond more to images of faces over nonface objects were identified in the inferior temporal (IT) cortex of primates three decades ago. Although it is hypothesized that perceptual discrimination between faces depends on the neural activity of IT subregions enriched with "face neurons," such a causal link has not been directly established. Here, using optogenetic and pharmacological methods, we reversibly suppressed the neural activity in small subregions of IT cortex of macaque monkeys performing a facial gender-discrimination task. Each type of intervention independently demonstrated that suppression of IT subregions enriched in face neurons induced a contralateral deficit in face gender-discrimination behavior. The same neural suppression of other IT subregions produced no detectable change in behavior. These results establish a causal link between the neural activity in IT face neuron subregions and face gender-discrimination behavior. Also, the demonstration that brief neural suppression of specific spatial subregions of IT induces behavioral effects opens the door for applying the technical advantages of optogenetics to a systematic attack on the causal relationship between IT cortex and high-level visual perception.

Anisotropic aberration correction using region of interest based digital adaptive optics in Fourier domain OCT.

In this paper a numerical technique is presented to compensate for anisotropic optical aberrations, which are usually present across the lateral field of view in the out of focus regions, in high resolution optical coherence tomography and microscopy (OCT/OCM) setups. The recorded enface image field at different depths in the tomogram is digitally divided into smaller sub-regions or the regions of interest (ROIs), processed individually using subaperture based digital adaptive optics (DAO), and finally stitched together to yield a final image with a uniform diffraction limited resolution across the entire field of view (FOV). Using this method, a sub-micron lateral resolution is achieved over a depth range of 218 [Formula: see text]for a nano-particle phantom sample imaged using a fiber based point scanning spectral domain (SD) OCM system with a limited depth of focus (DOF) of ~7 [Formula: see text]at a numerical aperture (NA) of 0.6. Thus, an increase in DOF by ~30x is demonstrated in this case. The application of this method is also shown in ex vivo mouse adipose tissue.

Measurement of fluid rotation, dilation, and displacement in particle image velocimetry using a Fourier–Mellin cross-correlation

Traditional particle image velocimetry (PIV) uses discrete Cartesian cross correlations (CCs) to estimate the displacements of groups of tracer particles within small subregions of sequentially captured images. However, these CCs fail in regions with large velocity gradients or high rates of rotation. In this paper, we propose a new PIV correlation method based on the Fourier–Mellin transformation (FMT) that enables direct measurement of the rotation and dilation of particle image patterns. In previously unresolvable regions of large rotation, our algorithm significantly improves the velocity estimates compared to traditional correlations by aligning the rotated and stretched particle patterns prior to performing Cartesian correlations to estimate their displacements. Our algorithm, which we term Fourier–Mellin correlation (FMC), reliably measures particle pattern displacement between pairs of interrogation regions with up to ±180° of angular misalignment, compared to 6–8° for traditional correlations, and dilation/compression factors of 0.5–2.0, compared to 0.9–1.1 for a single iteration of traditional correlations.We apply our FMC algorithm to synthetic computer-generated PIV images with known velocity and vorticity fields, and to an experimentally measured flow field. Our results show that combining FMC with discrete window offset (DWO) or iterative image deformation (IID) algorithms decreases the mean and variance of displacement and vorticity errors compared to traditional correlations, and that FMC accelerates the convergence of IID.

Simulated annealing approach with an exhaustive greedy search for the optimal machining region decomposition in CNC roughing tool path generation

For machining various parts, it is important to generate efficient tool paths for productivity. At the stage of roughing, the workspace is sliced and the paths are generated outside the part in each sliced plane. One of important decision variables in planar tool path generation is the direction in which paths are aligned. This paper is about decomposing the machining region and deciding the path direction in each subregion so that machining time can be reduced. The machining region is decomposed into discretized meshes and the path planning problem is formulated as a combinatorial optimization problem. The formulated problem is solved by the simulated annealing technique. To speed up the overall optimization procedure, the annealing procedure is rather prematurely terminated and a clearing algorithm is applied to remove small subregions. This is needed since the cost function of this problem has many ‘flat’ areas and provides ‘narrow’ passages to its optimum.

The stress analysis of a shear wall with matrix displacement method

Finite element method (FEM) is an effective quantitative method to solve complex engineering problems. The basic idea of FEM for a complex problem is to be able to find a solution by reducing the problem made simple. If mathematical tools are inadequate to obtain precise result, even approximate result, FEM is the only method that can be used for structural analyses. In FEM, the domain is divided into a large number of simple, small and interconnected sub-regions called finite elements. FEM has been used commonly for linear and nonlinear analyses of different types of structures to give us accurate results of plane stress and plane strain problems in civil engineering area. In this paper, FEM is used to investigate stress analysis of a shear wall which is subjected to concentrated loads and fundamental principles of stress analysis of the shear wall are presented by using matrix displacement method in this paper. This study is consisting of two parts. In the first part, the shear wall is discretized with constant strain triangular finite elements and stiffness matrix and load vector which is attained from external effects are calculated for each of finite elements using matrix displacement method. As to second part of the study, finite element analysis of the shear wall is made by ANSYS software program. Results obtained in the second part are presented with tables and graphics, also results of each part is compared with each other, so the performance of the matrix displacement method is demonstrated. The solutions obtained by using the proposed method show excellent agreements with the results of ANSYS. The results show that this method is effective and preferable for the stress analysis of shell structures. Further studies should be carried out to be able to prove the efficiency of the matrix displacement method on the solution of plane stress problems using different types of structures.

A Geometry-aware Data Partitioning Algorithm for Parallel Quad Mesh Generation on Large-scale 2D Regions

We develop a partitioning algorithm to decompose complex 2D data into small simple subregions for effective parallel quad meshing. We formulate the partitioning problem for effective parallel quad meshing as a quadratic integer optimization problem with linear constraints. Directly solving this problem is expensive for large-scale data partitioning. Hence, we suggest a more efficient two-step algorithm to obtain an approximate solution. First, we partition the region into a set of cells using L∞ Centroidal Voronoi Tessellation (CVT), then we solve a graph partitioning on the dual graph of this CVT to minimize the total partitioning boundary length, while enforcing the load balancing and each subregion's connectivity. With this decomposition, subregions are distributed to multiple processors for parallel quadrilateral mesh generation. We demonstrate that our decomposition algorithm outperforms existing approaches by offering a higher-quality partitioning, and therefore, improved performance and quality in mesh generation.

A geometric semantic genetic programming system for the electoral redistricting problem

Redistricting consists in dividing a geographic space or region of spatial units into smaller subregions or districts. In this paper, a Genetic Programming framework that addresses the electoral redistricting problem is proposed. The method uses new genetic operators, called geometric semantic genetic operators, that employ semantic information directly in the evolutionary search process with the objective of improving its optimization ability. The system is compared to several different redistricting techniques, including evolutionary and non-evolutionary methods. The simulations were made on ten real data-sets and, even though the studied problem does not belong to the classes of problems for which geometric semantic operators induce a unimodal fitness landscape, the results we present demonstrate the effectiveness of the proposed technique.

Variability in results from negative binomial models for lyme disease measured at different spatial scales

Lyme disease has been the subject of many studies due to increasing incidence rates year after year and the severe complications that can arise in later stages of the disease. Negative binomial models have been used to model Lyme disease in the past with some success. However, there has been little focus on the reliability and consistency of these models when they are used to study Lyme disease at multiple spatial scales. This study seeks to explore how sensitive/consistent negative binomial models are when they are used to study Lyme disease at different spatial scales (at the regional and sub-regional levels). The study area includes the thirteen states in the Northeastern United States with the highest Lyme disease incidence during the 2002–2006 period. Lyme disease incidence at county level for the period of 2002–2006 was linked with several previously identified key landscape and climatic variables in a negative binomial regression model for the Northeastern region and two smaller sub-regions (the New England sub-region and the Mid-Atlantic sub-region). This study found that negative binomial models, indeed, were sensitive/inconsistent when used at different spatial scales. We discuss various plausible explanations for such behavior of negative binomial models. Further investigation of the inconsistency and sensitivity of negative binomial models when used at different spatial scales is important for not only future Lyme disease studies and Lyme disease risk assessment/management but any study that requires use of this model type in a spatial context.

Comprehensive and Efficient Design Parameter Selection for Soft Error Resilient Processors via Universal Rules

Soft errors have been significantly degrading the reliability of current processors whose feature sizes and supply voltages are fast scaling down. In this paper, we propose two effective approaches to characterize processor reliability against soft errors at presilicon stage. By utilizing a rule search strategy named Patient Rule Induction Method (PRIM), we are capable of generating a set of selective rules on key design parameters. These rules quantify the design space subregion with the lowest effective soft error rate (SER), thus providing useful guidelines in designing reliable processors. Furthermore, we also propose to use Classification and Regression Trees (CART) to partition the design space into a number of small subregions each being associated with a representative SER value. This gives the processor designer a global view of the SER distribution, enabling a comprehensive analysis over the entire design space. More importantly, both approaches generate “universal” models whose effectiveness is validated with a set of test programs unseen to training. Compared to traditional application-specific design space studies, our models’ cross-program capability can save great training effort in the era of multithreading. Finally, a case study on multiprocessors is performed to simultaneously balance multiple design metrics, including reliability, performance, and power.