Regular Substructures Research Articles

Spiral arms in broad-line regions of active galactic nuclei

There is growing evidence that broad-line regions (BLRs) in active galactic nuclei (AGNs) have regular substructures, such as spiral arms. This is supported by the fact that the radii of BLRs measured by reverberation mapping (RM) observations are generally consistent with the self-gravitating regions of accretion disks. We showed in Paper I that the spiral arms excited by the gravitational instabilities in these regions may exist in some disk-like BLRs. Here, in the second paper of the series, we investigate the loosely wound spiral arms excited by gravitational instabilities in disk-like BLRs and present their observational characteristics. We solve the governing integro-differential equation by a matrix scheme. The emission-line profiles, velocity-delay maps, and velocity-resolved lags of the BLR spiral arms are calculated. We find that the spiral arms can explain some of the phenomena seen in observations: (1) different asymmetries in the emission-line profiles in the mean and rms spectra; (2) complex subfeatures (incomplete ellipse) in some velocity-delay maps, for example that of NGC 5548; and (3) the short timescales of the asymmetry changes in emission-line profiles (rms spectra). These features are attractive for modeling the observed line profiles and the properties of reverberation, and for revealing the details of the BLR geometry and kinematics.

Substructures in the Isolated Galaxy clusters

The isolated clusters are special objects for understanding the ways of forming observed large-scale distributions of matter. One can consider the isolated clusters as objects evolving without any external influence. We present the results of the analysis of the 2D distribution of galaxies in 31 isolated galaxy clusters with redshifts z < 0.15 and the distance to the nearest neighbor less than 60h−1Mpc. We defined the morphological types of these clusters accordingly to advance Panko’s classification scheme using the “Cluster Cartography” set. The main part of these clusters belongs to the open O-type clusters without any signs of a complex structure. However, we detected the presence of the inner regular substructures for 10 clusters. They are linear substructures, X- and Y-type crosses, and compact short chains. All substructures were detected on a statistically significant level. The detected substructures have special orientations of galaxies, which note to their 3D type. Practically all studied galaxy clusters are young.

IMAGE INTERPOLATION ON THE CPU AND GPU USING LINE RUN SEQUENCES

Abstract. This paper describes an efficient implementation of an image interpolation algorithm based on inverse distance weighting (IDW). The time-consuming search for support pixels bordering the voids to be filled is facilitated through gapless sweeps of different directions over the image. The scanlines needed for the sweeps are constructed from a path prototype per orientation whose regular substructures get reused and shifted to produce aligned duplicates covering the entire input bitmap. The line set is followed concurrently to detect existing samples around nodata patches and compute the distance to the pixels to be newly set. Since the algorithm relies on integer line rasterization only and does not need auxiliary data structures beyond the output image and weight aggregation bitmap for intensity normalization, it will run on multi-core central and graphics processing units (CPUs and GPUs). Also, occluded support pixels of non-convex void patches are ignored, and over- or undersampling close-by and distant valid neighbors is compensated. Runtime and accuracy compared to generated IDW ground truth get evaluated for the CPU and GPU implementation of the algorithm on single-channel and multispectral bitmaps of various filling degrees.

LOCK-FREE MULTITHREADED SEMI-GLOBAL MATCHING WITH AN ARBITRARY NUMBER OF PATH DIRECTIONS

Abstract. This paper describes an efficient implementation of the semi-global matching (SGM) algorithm on multi-core processors that allows a nearly arbitrary number of path directions for the cost aggregation stage. The scanlines for each orientation are discretized iteratively once, and the regular substructures of the obtained template are reused and shifted to concurrently sum up the path cost in at most two sweeps per direction over the disparity space image. Since path overlaps do not occur at any time, no expensive thread synchronization will be needed. To further reduce the runtime on high counts of path directions, pixel-wise disparity gating is applied, and both the cost function and disparity loop of SGM are optimized using current single instruction multiple data (SIMD) intrinsics for two major CPU architectures. Performance evaluation of the proposed implementation on synthetic ground truth reveals a reduced height error if the number of aggregation directions is significantly increased or when the paths start with an angular offset. Overall runtime shows a speedup that is nearly linear to the number of available processors.

English

English

Regular Substructures in the Rich Open Galaxy Clusters

We present the results of study the 2D distribution of galaxies in 254 rich open galaxy clusters. The clusters have no concentration to the center, so all kinds of substructures are clearly seen. Regular linear substructures in galaxy clusters were described in Rood & Sastry scheme of morphological types according to positions of 10 brightest galaxies. Another types of regular substructures were missed. Our study fills the lacuna. We have found about 25% of clusters in our data set having four kinds of regular substructures, beyond founded before linear ones. New kinds of regular substructures are: crossing and divaricating filaments or X and Y-type peculiarities, as well as curved strips and short dense chains. We suppose the distribution of dark matter in founded galaxy clusters with substructures have corresponded regular peculiarities. Hot gas distribution in these clusters must be observed distorted X-ray halo. We suppose also the clusters will evolve in the different ways.

DETAILED MORPHOLOGY OF THE RICH CONCENTRATED GALAXY CLUSTERS

The results of the detailed analysis of the 2D distribution of galaxies in 28 rich galaxy clusters with significant concentration to the cluster center are present. The analysis was executed in these directions: the detection of regular substructures and peculiarities in the galaxy distribution. The role of brightest cluster members was taken into account too. The input data were selected from “The Catalogue of Galaxy Clusters and Groups” and list of galaxies of Muenster Red Sky Survey. Concentrated galaxy clusters are evolved, virialized structures. Substructures in this type of clusters must be feeblemarked. Nevertheless we detected ignificant part of concentrated galaxy clusters having different kinds of peculiarities, namely crossing and divaricating filaments or X and Y-type peculiarities, as well as curved strips and short dense chains. 2 clusters having extremely density of galaxies were attributed as superconcentrated/compact type.

On the OBDD representation of some graph classes

Ordered Binary Decision Diagrams (OBDDs) are a popular data structure for Boolean functions. Given the rapid growth of application-based networks, an heuristic approach to deal with very large structured graphs are implicit OBDD-based graph algorithms. Vertices of an input graph are binary encoded and the edge set is represented by its characteristic function. Since OBDDs are able to take advantage of the presence of regular substructures, this approach leads sometimes to sublinear graph representations. By simple counting arguments it is easy to see that almost all graphs on N vertices cannot be represented by OBDDs of polylogarithmic size with respect to N. On the other hand, very simply structured graphs like grid graphs have small OBDD representations. Here, the investigation for which significant graph classes succinct OBDD representations are possible is continued. Using a new method how to use the structure of the adjacency matrix representation of a graph to count subfunctions of the characteristic Boolean function of its edge set, known upper bounds on the OBDD size of interval graphs are improved. Furthermore, the OBDD size for interval bigraphs, (bi)convex graphs, bipartite permutation graphs, chain graphs, threshold graphs, and trees is analyzed. Except for interval graphs, interval bigraphs, and convex graphs the presented bounds are tight. Finally, regular graphs are considered and examples are presented with small and large OBDD size. Moreover, a variable ordering often used in the implicit setting is investigated.

CHANGE DETECTION BASED ON PERSISTENT SCATTERER INTERFEROMETRY – A NEW METHOD OF MONITORING BUILDING CHANGES

Persistent Scatterer Interferometry (PSI) is a technique to detect a network of extracted persistent scatterer (PS) points which feature temporal phase stability and strong radar signal throughout time-series of SAR images. The small surface deformations on such PS points are estimated. PSI particularly works well in monitoring human settlements because regular substructures of man-made objects give rise to large number of PS points. If such structures and/or substructures substantially alter or even vanish due to big change like construction, their PS points are discarded without additional explorations during standard PSI procedure. Such rejected points are called big change (BC) points. On the other hand, incoherent change detection (ICD) relies on local comparison of multi-temporal images (e.g. image difference, image ratio) to highlight scene modifications of larger size rather than detail level. However, image noise inevitably degrades ICD accuracy. We propose a change detection approach based on PSI to synergize benefits of PSI and ICD. PS points are extracted by PSI procedure. A local change index is introduced to quantify probability of a big change for each point. We propose an automatic thresholding method adopting change index to extract BC points along with a clue of the period they emerge. In the end, PS ad BC points are integrated into a change detection image. Our method is tested at a site located around north of Berlin main station where steady, demolished, and erected building substructures are successfully detected. The results are consistent with ground truth derived from time-series of aerial images provided by Google Earth. In addition, we apply our technique for traffic infrastructure, business district, and sports playground monitoring.

CHANGE DETECTION BASED ON PERSISTENT SCATTERER INTERFEROMETRY – A NEW METHOD OF MONITORING BUILDING CHANGES

Abstract. Persistent Scatterer Interferometry (PSI) is a technique to detect a network of extracted persistent scatterer (PS) points which feature temporal phase stability and strong radar signal throughout time-series of SAR images. The small surface deformations on such PS points are estimated. PSI particularly works well in monitoring human settlements because regular substructures of man-made objects give rise to large number of PS points. If such structures and/or substructures substantially alter or even vanish due to big change like construction, their PS points are discarded without additional explorations during standard PSI procedure. Such rejected points are called big change (BC) points. On the other hand, incoherent change detection (ICD) relies on local comparison of multi-temporal images (e.g. image difference, image ratio) to highlight scene modifications of larger size rather than detail level. However, image noise inevitably degrades ICD accuracy. We propose a change detection approach based on PSI to synergize benefits of PSI and ICD. PS points are extracted by PSI procedure. A local change index is introduced to quantify probability of a big change for each point. We propose an automatic thresholding method adopting change index to extract BC points along with a clue of the period they emerge. In the end, PS ad BC points are integrated into a change detection image. Our method is tested at a site located around north of Berlin main station where steady, demolished, and erected building substructures are successfully detected. The results are consistent with ground truth derived from time-series of aerial images provided by Google Earth. In addition, we apply our technique for traffic infrastructure, business district, and sports playground monitoring.

A Multilevel Gamma-Clustering Layout Algorithm for Visualization of Biological Networks

Visualization of large complex networks has become an indispensable part of systems biology, where organisms need to be considered as one complex system. The visualization of the corresponding network is challenging due to the size and density of edges. In many cases, the use of standard visualization algorithms can lead to high running times and poorly readable visualizations due to many edge crossings. We suggest an approach that analyzes the structure of the graph first and then generates a new graph which contains specific semantic symbols for regular substructures like dense clusters. We propose a multilevel gamma-clustering layout visualization algorithm (MLGA) which proceeds in three subsequent steps: (i) a multilevel γ-clustering is used to identify the structure of the underlying network, (ii) the network is transformed to a tree, and (iii) finally, the resulting tree which shows the network structure is drawn using a variation of a force-directed algorithm. The algorithm has a potential to visualize very large networks because it uses modern clustering heuristics which are optimized for large graphs. Moreover, most of the edges are removed from the visual representation which allows keeping the overview over complex graphs with dense subgraphs.

Nanocluster dynamics by mutual grazing with overthermal velocities

A theoretical model of the interaction of two molecules during their mutual grazing is developed. Both molecules in the model are considered to be constructed of identical regular chain-like substructures of diatomic fragments. It is shown that at mutual grazing velocities lower than the Bohr speed in these fragments, which serve as IR radiation antennas, simultaneously with the grazing (∼10−12 s) both excitation and the accumulation of low-energy collective vibrational states (eximoles) occur. Energy transport occurs from antennas to trap-bonds in the same molecules and the energy exchange between molecules leads to their simultaneous fragmentation. The probability functions of the considered processes are derived and investigated.

Regular Substructures of Hom

Extending the notion of von Neumann regular elements in a ring R, a homomorphism f:A→M between R-modules is said to be regular if there exists some g:M → A such that fgf = f. In this paper we report about the use of this term in module theory.

Non-smooth dynamics and stability of mechanical systems featuring a freeplay non-linearity

This paper concerns modelling and time-domain simulation of the dynamics of systems featuring a freeplay non-linearity. The topic of stability is also addressed. We propose to develop a reduced order model based on mode synthesis where the DOF that might have contact are separated from the regular substructures. This formulation allows for a direct application of Moreau's theory for non-smooth dynamics of contact problems. The methodologies developed are applied to a fluid-structure coupled system as given by an aircraft wing with freeplay in the control surface connection.

Regularity and Substructures of Hom

ABSTRACT We define “regular” for maps in a Hom group. This notion specializes to the well-known notions of (Von Neumann) regular in rings and modules. A map f ∈ Hom R (A,M) is regular if and only if Ker(f) ⊆⊕ A and Im(f) ⊆⊕ M. There exists a unique maximal regular End(M)-End(A)-submodule in Hom R (A,M). We study regularity in Hom R (A 1 ⊕ A 2, M 1 ⊕ M 2). The existence of a regular function Hom R (A,M) implies the existence of projective summands of Hom R (A,M) End R (A) and of End R ( M ) Hom R (A,M). We consider regularity in endomorphism rings, and generalize a theorem of Ware-Zelmanowitz. We examine connections between the maximum regular bimodule and other substructures of Hom, mention two generalizations of regularity, and raise some questions.

Dental enamel—a biological ceramic: regular substructures in enamel hydroxyapatite crystals revealed by atomic force microscopy

Hydroxyapatite crystals from developing rat incisor enamel and polished sections of mature human dental enamel were investigated using Atomic and Chemical Force Microscopy. Regular substructures were seen on crystals comprising ∼40 nm wide morphologically and chemically defined bands across the crystal long axes. Exposure to low pH resulted in selective dissolution between bands and the emergence of 2–3 spherical structures within each band. The spherical structures were chemically distinct exhibiting high friction in lateral force mode. Enamel crystals appear to comprise stacks of roughly hexagonal arrays of chemically or structurally distinct spherical subunits.

Self-organization and Fourier selection of optical patterns in a nonlinear photorefractive feedback system

The formation of patterns in two transverse dimensions in photorefractive two-wave mixing with a single feedback mirror is investigated theoretically. We perform numerical simulations of the full (3+1)-dimensional nonlinear model equations, displaying the breakup of the unstable annulus of active modes into hexagonal spots. Analytically we derive amplitude equations of the Landau type for patterns with rhombic- and hexagonal-mode interaction and discuss the stability and coexistence of transverse planforms in the photorefractive feedback system. A strong renormalization for the hexagon amplitude is determined, and its consequences for pattern formation using Landau formalism are discussed. In particular, the stability of regular substructures of a dodecagonal spot arrangement is investigated and square-hexagon competition is predicted. We use an invasive Fourier-filtering technique for the selection of unstable patterns, such as stripes and squares. The longitudinal propagation of the critical and higher-order modes of the self-organized structures and the impact of a Fourier filter on the mode propagation within a nonlinear bulk photorefractive medium is studied in detail.

Quadratic and energy estimates of the partial response of ribbed panels

Two formalisms of the response of a ribbed uniform panel excited by a line drive are considered. In the first a quadratic analysis (QA) of the linear response is obtained. In this response phases among the responses of the bays are preserved and accounted for. (A bay is the portion of the panel that lies between two adjacent ribs.) The preservation of the phases yield responses that exhibit the phenomena of pass and stop bands and of localization and delocalization when the separations between adjacent ribs are equal. In the second an energy analysis (EA) of the response is obtained. The response is estimated in terms of the energy densities in the individual bays. In this formalism the phases among the responses of the bays are inconsequential. Therefore the phenomena of pass and stop bands and of localization and delocalization are not manifested in the EA response. It is thus suggested that formalisms that are akin to the statistical energy analysis (SEA) and SEA itself cannot be expected to exhibit some of the features in the response of a complex structure, especially if the structure is composed of a number of regular substructures; e.g., the identical bays in a ribbed panel. The generic example presented in this paper illustrates that in certain situations and for certain purposes the missing features in the EA response, as compared with the QA response, may be significant.

Global and local partial response of ribbed uniform panels

Two formalisms of the response of a ribbed uniform panel excited by a line drive are considered. In the first, the global response is obtained. In this response, phases among the responses of the bays are preserved and accounted for. (A bay is the portion of the panel that lies between two adjacent ribs.) The preservation of the phases yield responses that exhibit the phenomena of pass and stop bands and of localizations and delocalizations when the separations between adjacent ribs are equal. In the second formalism, the local response is obtained. The response is estimated in terms of the energy densities in the individual bays. In this formalism the phases among the responses of the bays are inconsequential. Therefore, the phenomena of pass and stop bands and of localizations and delocalizations are not manifested in the localized response. It is thus suggested that formalisms that are akin to the statistical energy analysis (SEA) and SEA itself cannot be expected to exhibit some of the features in the response of a complex structure, especially if the structure is composed of a number of regular substructures; e.g., the identical bays in a ribbed panel. Generic examples are presented in this paper to illustrate that in certain situations and for certain purposes the missing features in the local response, as compared with the global response, may be significant.

Regular substructures within homologous transcripts of spread Drosophila germ cells

In this report, the first example of a defined morphological “marker” structure occurring at corresponding sites in closely adjacent transcripts is presented. The analysis of the location of these markers reveals that a linear relationship exists between chromatin length and the distance of the substructures from the axis. This situation allows to draw several conclusions: 1. 1. Heterogeneous length patterns of transcripts in Miller spreads do not necessarily exist in vivo. 2. 2. The DNP RNP length ratio is 4.4. 3. 3. The DNP RNP length ratio is about 8.4. 4. 4. The packing of RNA in non-ribosomal transcription is not different from that of ribosomal transcription as concerns the foreshortening. 5. 5. The length of the transcription unit in this particular picture is at least 400 kilobasepairs.