Symmetry in Scalar Field Topology

Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. Though geometric symmetry has been well studied within areas like shape processing, identifying symmetry in scalar fields has remained largely unexplored due to the high computational cost of the associated algorithms. We propose a computationally efficient algorithm for detecting symmetric patterns in a scalar field distribution by analysing the topology of level sets of the scalar field. Our algorithm computes the contour tree of a given scalar field and identifies subtrees that are similar. We define a robust similarity measure for comparing subtrees of the contour tree and use it to group similar subtrees together. Regions of the domain corresponding to subtrees that belong to a common group are extracted and reported to be symmetric. Identifying symmetry in scalar fields finds applications in visualization, data exploration, and feature detection. We describe two applications in detail: symmetry-aware transfer function design and symmetry-aware isosurface extraction.

Detecting symmetry in scalar fields using augmented extremum graphs

Visualizing symmetric patterns in the data often helps the domain scientists make important observations and gain insights about the underlying experiment. Detecting symmetry in scalar fields is a nascent area of research and existing methods that detect symmetry are either not robust in the presence of noise or computationally costly. We propose a data structure called the augmented extremum graph and use it to design a novel symmetry detection method based on robust estimation of distances. The augmented extremum graph captures both topological and geometric information of the scalar field and enables robust and computationally efficient detection of symmetry. We apply the proposed method to detect symmetries in cryo-electron microscopy datasets and the experiments demonstrate that the algorithm is capable of detecting symmetry even in the presence of significant noise. We describe novel applications that use the detected symmetry to enhance visualization of scalar field data and facilitate their exploration.

Dynamos driven by weak thermal convection and heterogeneous outer boundary heat flux

We use numerical dynamo models with heterogeneous core-mantle boundary (CMB) heat flux to show that lower mantle lateral thermal variability may help support a dynamo under weak thermal convection. In our reference models with homogeneous CMB heat flux, convection is either marginally supercritical or absent, always below the threshold for dynamo onset. We find that lateral CMB heat flux variations organize the flow in the core into patterns that favour the growth of an early magnetic field. Heat flux patterns symmetric about the equator produce non-reversing magnetic fields, whereas anti-symmetric patterns produce polarity reversals. Our results may explain the existence of the geodynamo prior to inner core nucleation under a tight energy budget. Furthermore, in order to sustain a strong geomagnetic field, the lower mantle thermal distribution was likely dominantly symmetric about the equator. (C) 2015 Elsevier B.V. All rights reserved.

Automatic segmentation of latent fingerprints

Latent fingerprints are routinely found at crime scenes due to the inadvertent contact of the criminals' finger tips with various objects. As such, they have been used as crucial evidence for identifying and convicting criminals by law enforcement agencies. However, compared to plain and rolled prints, latent fingerprints usually have poor quality of ridge impressions with small fingerprint area, and contain large overlap between the foreground area (friction ridge pattern) and structured or random noise in the background. Accordingly, latent fingerprint segmentation is a difficult problem. In this paper, we propose a latent fingerprint segmentation algorithm whose goal is to separate the fingerprint region (region of interest) from background. Our algorithm utilizes both ridge orientation and frequency features. The orientation tensor is used to obtain the symmetric patterns of fingerprint ridge orientation, and local Fourier analysis method is used to estimate the local ridge frequency of the latent fingerprint. Candidate fingerprint (foreground) regions are obtained for each feature type; an intersection of regions from orientation and frequency features localizes the true latent fingerprint regions. To verify the viability of the proposed segmentation algorithm, we evaluated the segmentation results in two aspects: a comparison with the ground truth foreground and matching performance based on segmented region. © 2012 IEEE.

Um Kit de espelhos planos para o ensino de geometria

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Pain drawings in somatoform-functional pain

Background Pain drawings are a diagnostic adjunct to history taking, clinical examinations, and biomedical tests in evaluating pain. We hypothesized that somatoform-functional pain, is mirrored in distinctive graphic patterns of pain drawings. Our aim was to identify the most sensitive and specific graphic criteria as a tool to help identifying somatoform-functional pain. Methods We compared 62 patients with somatoform-functional pain with a control group of 49 patients with somatic-nociceptive pain type. All patients were asked to mark their pain on a pre-printed body diagram. An investigator, blinded with regard to the patients’ diagnoses, analyzed the drawings according to a set of numeric or binary criteria. Results We identified 13 drawing criteria pointing with significance to a somatoform-functional pain disorder (all p-values ≤ 0.001). The most specific and most sensitive criteria combination for detecting somatoform-functional pain included the total number of marks, the length of the longest mark, and the presence of symmetric patterns. The area under the ROC-curve was 96.3% for this criteria combination. Conclusion Pain drawings are an easy-to-administer supplementary technique which helps to identify somatoform-functional pain in comparison to somatic-nociceptive pain.

Axially Symmetric Radiation Patterns from Flanged E-Plane Sectoral Horn

A simple technique for obtaining identical E- and H-plane patterns from E-plane sectoral feed horn is presented. Halfpower beam width and gain of the antenna are also improved considerably. Experimental results for a number of horns with flanges of various parameters are also presented. This system may find practical application in radar and space communication systems

Axially Symmetric Radiation Patterns from Corrugated

A modified H-plane sectoral horn antenna with identical E- and'H- plane.patterns over the X-band frequency is discussed. This system has significantly reduced side lobes and hack lobes. Half=power beam width and gain of the antenna are also improved with enhanced matching , Experimental results for a number of horns with various flanges are presented . These find practical application for illuminating symmetric antennas like paraboloids and polarization measurements in radio astronomy, etc. Compared to the fixed pyramidal horns. the present system offers great convenience in trimming the antenna characteristics

Using complex network metrics to predict the persistence of metapopulations with asymmetric connectivity patterns

Almost all metapopulation modelling assumes that connectivity between patches is only a function of distance, and is therefore symmetric. However, connectivity will not depend only on the distance between the patches, as some paths are easy to traverse, while others are difficult. When colonising organisms interact with the heterogeneous landscape between patches, connectivity patterns will invariably be asymmetric. There have been few attempts to theoretically assess the effects of asymmetric connectivity patterns on the dynamics of metapopulations. In this paper, we use the framework of complex networks to investigate whether metapopulation dynamics can be determined by directly analysing the asymmetric connectivity patterns that link the patches. Our analyses focus on “patch occupancy” metapopulation models, which only consider whether a patch is occupied or not. We propose three easily calculated network metrics: the “asymmetry” and “average path strength” of the connectivity pattern, and the “centrality” of each patch. Together, these metrics can be used to predict the length of time a metapopulation is expected to persist, and the relative contribution of each patch to a metapopulation’s viability. Our results clearly demonstrate the negative effect that asymmetry has on metapopulation persistence. Complex network analyses represent a useful new tool for understanding the dynamics of species existing in fragmented landscapes, particularly those existing in large metapopulations.

Vibration of simply-supported trapezoidal plates I. Symmetric trapezoids

A detailed investigation of the natural frequencies and mode shapes of simply supported symmetric trapezoidal plates is undertaken in this paper. For numerical calculations, the relationship that exists between the eigenvalue problem of a polygonal simply supported plate and the eigenvalue problem of polygonal membrane of the same shape is utilized with advantage. The deflection surface is expressed in terms of a Fourier sine series in transformed coordinates and the Galerkin method is used. Results are presented in the form of tables and graphs. Several features like the crossing of frequency curves and the metamorphosis of some of the nodal patterns are observed. By a suitable interpretation of the modes of those symmetric trapezoidal plates which have the median as the nodal line, the results for some of the modes of unsymmetrical trapezoidal plates are also deduced.

Magneto - Transport of electron symmetric and antisymmrtric states in highly doped InGaAs/InAlAs single quantum well

Beating patterns in longitudinal resistance caused by the symmetric and antisymmetric states were observed in a heavily doped InGaAs/InAlAs quantum well by using variable temperature Hall measurement. The energy gap of symmetric and antisymmetric states is estimated to be 4meV from the analysis of beating node positions. In addition, the temperature dependences of the subband electron mobility and concentration were also studied from the mobility spectrum and multicarrier fitting procedure.

Lamella reorientation in thin films of a symmetric poly(L-lactic acid)-block-polystyrene upon crystallization at different temperatures

The thin films of a symmetric crystalline-coil diblock copolymer of poly(L-lactic acid) and polystyrene (PLLA-b-PS) formed lamellae parallel to the substrate surface in melt. When annealed at temperatures well above the glass transition temperature of PLLA block (T-g(PLLA)), the PLLA chains started to crystallize, leading to reorientation of lamellae. Such reorientation behavior exhibited dependence on the correlation between the crystallization temperature (T-c), the glass transition temperature of PS (T-g(PS)), the peak melting point of PLLA crystals (T-m(PLLA)), and the end melting point of PLLA crystals (T-m,end(PLLA)). When annealed at (T-c =) 80 degrees C (T-c < T-g(PS) < T-ODT, order-disorder transition temperature), 123 degrees C (T-g(PS) < T-c < T-m(PLLA) < T-ODT). 165 degrees C (T-g(PS) < T-m(PLLA) < T-c < T-m,end(PLLA) < T-ODT), the parallel lamellae became perpendicular to the substrate surface, exclusively starting at the edge of surface relief patterns. Meanwhile, the corresponding lamellar spacing was significantly enhanced.

Fuzzy ART: Fast Stable Learning and Categorization of Analog Patterns by an Adaptive Resonance System

A Fuzzy ART model capable of rapid stable learning of recognition categories in response to arbitrary sequences of analog or binary input patterns is described. Fuzzy ART incorporates computations from fuzzy set theory into the ART 1 neural network, which learns to categorize only binary input patterns. The generalization to learning both analog and binary input patterns is achieved by replacing appearances of the intersection operator (n) in AHT 1 by the MIN operator (Λ) of fuzzy set theory. The MIN operator reduces to the intersection operator in the binary case. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy set theory play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Learning stops when the input space is covered by boxes. With fast learning and a finite input set of arbitrary size and composition, learning stabilizes after just one presentation of each input pattern. A fast-commit slow-recode option combines fast learning with a forgetting rule that buffers system memory against noise. Using this option, rare events can be rapidly learned, yet previously learned memories are not rapidly erased in response to statistically unreliable input fluctuations.

Wide Band Rectangular Microstrip Antenna using Symmetric T-shaped Feed

Bandwidth enhancement of a rectangular microstrip antenna using a T-shaped microstrip feed is explored in this paper. A 2:1 VSWR impedance bandwidth of 23% is achieved by employing this technique. The far-field patterns are stable across the pass band. The proposed antenna can be used conveniently in broadband communications

FDTD analysis of a symmetric T-strip fed wideband rectangular microstrip antenna

A theoretical analysis of a symmetric T-shaped rnicrostripfed rectangular microstrip antenna using the finite-difference titnedoniain (FDTD) method is presented in this paper. The resonant frequency, return loss, impedance bandwidth, and radiation patterns are predicted and are in good agreement with the measured results