Parallel Segments Research Articles

A Note on Caterpillar-Embeddings with No Two Parallel Edges

Let G be a set of n points in general position (i.e., no three points are on a line) in the plane, and let C be a caterpillar on n vertices. We show that one can always find a rectilinear embedding of C in the plane such that the vertices of C are the points of G and no two edges of C go to parallel segments. This proves a conjecture of Robert E. Jamison.

Optimal grid representations

AbstractA graph G is a grid intersection graph if G is the intersection graph of ℋ︁ ∪ ℐ, where ℋ︁ and ℐ are, respectively, finite families of horizontal and vertical linear segments in the plane such that no two parallel segments intersect. (This definition implies that every grid intersection graph is bipartite.) The family ℋ︁ ∪ ℐ is a representation of G. As a consequence of a characterization of grid intersection graphs by Kratochvíl, we observe that when a bipartite graph G = (U ∪ W, E) with minimum degree at least two is a grid intersection graph, then there exists a normalized representation of G on the (r × s)‐grid for r = |U| and s = |W|, that is, a representation in which all end points of segments have integer‐valued coordinates belonging to {(x, y) ∈ N × N | 1 ≤ y ≤ r, 1 ≤ x ≤ s} and the representative segment of each vertex lies on a distinct horizontal or vertical line. A natural problem, with potential applications to circuit layout, is the following: among all the possible normalized representations of G, find a representation ℛ such that the sum of the lengths of the segments in ℛ is minimum. In this work we introduce this problem and present a mixed integer programming formulation to solve it. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(3), 187–193 2004

Domain decomposition method for dynamic faulting under slip-dependent friction

The anti-plane shearing problem on a system of finite faults under a slip-dependent friction in a linear elastic domain is considered. Using a Newmark method for the time discretization of the problem, we have obtained an elliptic variational inequality at each time step. An upper bound for the time step size, which is not a CFL condition, is deduced from the solution uniqueness criterion using the first eigenvalue of the tangent problem. Finite element form of the variational inequality is solved by a Schwarz method assuming that the inner nodes of the domain lie in one subdomain and the nodes on the fault lie in other subdomains. Two decompositions of the domain are analyzed, one made up of two subdomains and another one with three subdomains. Numerical experiments are performed to illustrate convergence for a single time step (convergence of the Schwarz algorithm, influence of the mesh size, influence of the time step), convergence in time (instability capturing, energy dissipation, optimal time step) and an application to a relevant physical problem (interacting parallel fault segments).

A game-theoretic framework for multimetric optimization of interconnect delay, power, and crosstalk noise during wire sizing

The continuous scaling of interconnect wires in deep submicron (DSM) circuits results in increased interconnect delay, power, and crosstalk noise. In this work, we develop a game-theoretic framework and multimetric optimization algorithms for the simultaneous optimization during wire sizing of (i) interconnect delay and crosstalk noise, and (ii) interconnect delay, power, and crosstalk noise. We formulate the wire sizing optimization problem as a normal form-game model and solve it using Nash equilibrium theory. Game theory allows the optimization of multiple metrics with conflicting objectives. This property is exploited in modeling the wire sizing problem while simultaneously optimizing various design parameters like interconnect delay, power, and crosstalk noise, which are conflicting in nature. The nets connecting the driving cell and the driven cell are divided into net segments. The net segments within a channel are modeled as players and the range of possible wire sizes forms the set of strategies. The payoff function is modeled (i) as the geometric mean of interconnect delay and crosstalk noise in the case of first formulation, and (ii) as the weighted sum of interconnect delay, power, and crosstalk noise in the second formulation. The net segments are optimized from the ones closest to the driven cell towards the ones at the driving cell. Complete information about the coupling effects among the nets is extracted after the detailed routing phase. The time and space complexities of the proposed wire sizing formulations are linear in terms of the number of net segments. Experimental results on several medium and large open-core designs indicate that the proposed algorithm for simultaneous optimization of interconnect delay and crosstalk noise yields an average reduction of 21.48% in interconnect delay and a 26.25% reduction in crosstalk noise without any area overhead, over and above the optimization from the Cadence place and route tools. It is shown through experimental results that the algorithm performs significantly better than simulated annealing and genetic search. Further, new simple but accurate models are developed for three parallel interconnect net segments. It is shown that these models yield the same level of accuracy with significantly better run times compared to the models reported in Chen et al. [2004]. A mathematical proof of existence for the Nash equilibrium solution for the proposed wire sizing formulation is also provided.

An experimental method for measuring the mean length of cerebellar parallel fibers: validation and derivation of a correction factor by computational simulation and probability analysis

The length of cerebellar parallel fibers is important for information integration by the Purkinje cells. Based on the Copernican principle for analyzing the length of stochastic events, we have recently devised a stochastic method to estimate the mean length of parallel fibers within a given cerebellar region. The purpose of the present report is to provide validation of this methodology via computational simulations. We create virtual parallel fibers with known lengths and program each step of our stochastic method for computational simulation. We then compare the observed mean length obtained from our computational simulation with the known mean length of the virtual parallel fibers. In particular, we investigate the effect of cutting parallel fibers into segments during histological sectioning. Our computational results reveal an over-estimation factor ranging from 1.0 (no correction is necessary) to 2.0 as the parallel fiber segmentation becomes increasingly severe. Based on probability theory considerations, we have confirmed the existence of this over-estimation. We have further determined the cause of this over-estimation to be an artificial consequence of one of the sampling steps in our stochastic method. These results provide validation of our methodology, as well as a correction factor, which can be derived directly from the experimentally measured parameters and used to obtain the true mean length of parallel fibers. Potential applications of the stochastic method include a comparative analysis of the length of parallel fibers as an approach to gain clues about cerebellar circuit principles and function. In addition, the stochastic method may also find promising applications in other functionally important axonal systems in the brain.

Hybrid parallel-slant hole collimators for SPECT imaging

We propose a new collimator geometry, the hybrid parallel-slant (HPS) hole geometry, to improve sensitivity for SPECT imaging with large field of view (LFOV) gamma cameras. A HPS collimator has one segment with parallel holes and one or more segments with slant holes. The collimator can be mounted on a conventional SPECT LFOV system that uses parallel-beam collimators, and no additional detector or collimator motion is required for data acquisition. The parallel segment of the collimator allows for the acquisition of a complete data set of the organs-of-interest and the slant segments provide additional data. In this work, simulation studies of an MCAT phantom were performed with a HPS collimator with one slant segment. The slant direction points from patient head to patient feet with a slant angle of 30/spl deg/. We simulated 64 projection views over 180/spl deg/ with the modeling of nonuniform attenuation effect, and then reconstructed images using an MLEM algorithm that incorporated the hybrid geometry. It was shown that sensitivity to the cardiac region of the phantom was increased by approximately 50% when using the HPS collimator compared with a parallel-hole collimator. No visible artifacts were observed in the myocardium and the signal-to-noise ratio (SNR) of the myocardium walls was improved. Compared with collimators with other geometries, using a HPS collimator has the following advantages: (a) significant sensitivity increase; (b) a complete data set obtained from the parallel segment that allows for artifact-free image reconstruction; and (c) no additional collimator or detector motion. This work demonstrates the potential value of hybrid geometry in collimator design for LFOV SPECT imaging.

Dichotomy between Nodal and Antinodal Quasiparticles in Underdoped(La2−xSrx)CuO4Superconductors

High resolution angle-resolved photoemission measurements on an underdoped (La(2-x)Srx)CuO4 system show that, at energies below 70 meV, the quasiparticle peak is well defined around the (pi/2,pi/2) nodal region and disappears rather abruptly when the momentum is changed from the nodal point to the (pi,0) antinodal point along the underlying "Fermi surface." It indicates that there is an extra low energy scattering mechanism acting upon the antinodal quasiparticles. We propose that this mechanism is the scattering of quasiparticles across the nearly parallel segments of the Fermi surface near the antinodes.

Increased mitogenic and decreased contractile P2 receptors in smooth muscle cells by shear stress in human vessels with intact endothelium.

We investigated the role of shear stress in regulating P2 receptors in human umbilical vein. Using a novel, computerized, biomechanical perfusion model, parallel vessel segments were randomized to simultaneous perfusion under high (25 dyn/cm2) or low (<4 dyn/cm2) shear stress at identical mean perfusion pressure (20 mm Hg) for 6 hours. In the endothelium, no significant P2 receptor mRNA differences were found. In smooth muscle cells (SMCs), high shear stress decreased P2X1 receptors, whereas P2Y2 and P2Y6 receptors were upregulated. These findings were consistent at the mRNA level (real-time reverse transcription-polymerase chain reaction), protein level (Western blot), and morphologically (immunohistochemistry). The changes were more pronounced in the subintimal layer of the media. Our findings suggest that shear stress might regulate gene expression in SMCs more than in the endothelium in intact vessels. Decreased expression of the contractile P2X1 receptor could lead to reduced vascular tonus and increased blood flow. Because P2Y2 and P2Y6 receptors stimulate growth and migration of SMCs, increased expression of these receptors could promote vascular remodeling induced by shear stress. The pattern of upregulation of mitogenic P2Y receptors and downregulation of contractile P2X1 receptor is similar to changes seen in the phenotypic shift from contractile to synthetic SMCs.

Crystallographic‐Orientation‐Dependent Dissolution Behavior of Sapphire in Anorthite Liquid Containing Chromia

A sapphire single crystal was put into anorthite powders containing Cr2O3 and then heat‐treated at 1600°C. The resultant morphologies of the sapphire—anorthite‐liquid interfaces were corrugated and quite different depending on the crystallographic orientation of the sapphire; all the planes perpendicular to the C&gt;‐plane showed fingerlike morphologies, while long parallel segments were detached from the basal C‐plane. The results were interpreted in terms of coherency‐strain‐induced instability of the solid–liquid interface (ISLI) caused by the alloying of Cr2O3 into sapphire. The difference in microstructural evolution depending on crystallographic orientation was explained in terms of strong anisotropy of the solid–liquid interface characteristics.

Analysis of the helical twisted-wire pair running above ground:transfer function evaluation

This paper deals with the analysis of an internally excited three-conductor nonuniform transmission-line system comprising a twisted wire pair (TWP) running above a conducting plane. Research is conducted aimed at the analysis and characterization of the propagation properties of a helical-type TWP system with lossy conductors. Numerical simulation results regarding the attenuation and phase-velocity characteristics of this transmission-line system are obtained by using a TWP model consisting of a cascade of small incremental parallel segments subjected to continuous rotation. Special attention is paid to the derivation and analysis of the frequency-domain voltage transfer function describing the behavior of the TWP structure with a number N of twists. Time-domain results concerning the system response to a pulse train excitation are also obtained by making use of the information conveyed by the transfer function. Both frequency- and time-domain simulation results reported here show that the periodicity arising from wire twisting may dramatically modify the transmission-line system propagation properties as compared to those concerning the untwisted case.

Neuron recognition by parallel Potts segmentation.

Identifying neurons and their spatial coordinates in images of the cerebral cortex is a necessary step in the quantitative analysis of spatial organization in the brain. This is especially important in the study of Alzheimer's disease (AD), in which spatial neuronal organization and relationships are highly disrupted because of neuronal loss. To automate neuron recognition by using high-resolution confocal microscope images from human brain tissue, we propose a recognition method based on statistical physics that consists of image preprocessing, parallel image segmentation, and cluster selection on the basis of shape, optical density, and size. We segment a preprocessed digital image into clusters by applying Monte Carlo simulations of a q-state inhomogeneous Potts model. We then select the range of Potts segmentation parameters to yield an ideal recognition of simplified objects in the test image. We apply our parallel segmentation method to control individuals and to AD patients and achieve recognition of 98% (for a control) and 93% (for an AD patient), with at most 3% false clusters.

Resolving independent ion and ion displacement transport mechanisms in ion channels

Univalent metal ion fluxes in gramicidin channels in bilayer membranes produce linear current–voltage plots. Both independent ion models with first-order rate constants or ion–ion displacement models with pseudo-first-order rate constants reproduce the linear current–voltage behavior. To differentiate the mechanisms, the anomalous behavior of the system at low thallous ion mole fractions is studied using a potential ramp protocol. Under these conditions, the current–voltage plots separate into three linear segments with a low conductance segment at lower potentials and parallel outer segments with higher conductance whose voltage axis intercepts are displaced from zero potential. This displaced threshold potential varies with thallous ion mole fraction but has a constant electrochemical potential for all mole fractions. The current–voltage plots and their properties suggest a low conductance mechanism where thallous ion exclusion from the channel obeys Boltzmann statistics in the electrochemical potential. The higher conductance outer segments for electrochemical potentials that exceed the threshold obey a multi-ion displacement.

Structural, seismic and hydrothermal features at the border of an active intermittent resurgent block: Ischia Island (Italy)

Resurgent blocks are uplifted parts of volcanoes where most of the deformation (uplift) is accommodated along peripheral faults. The island of Ischia, Italy, has an active resurgent block uplifted ∼1000 m in the last ∼30 ka, which allows us to investigate the deformation associated with a strong uplift in volcanic areas. Air-photo interpretation was matched with field work (1:5000 scale mapping and structural analysis) throughout the resurgent block. These results have been matched with a review of the seismic and hydrothermal activity at Ischia. The results show that the block has a polygonal shape in map view and is characterized by a trapdoor uplift, which results in a ∼15° tilt towards the SE. The northern, most uplifted part is bordered by E–W- and NE–SW-trending faults, arranged in parallel segments over an area ∼1.5 km wide. I 0≥5 MCS degree shallow (1–1.6 km depth) earthquakes focused in correspondence with the outermost set of faults on the northernmost part of the block. Here, variations in the hydrothermal activity have been observed during seismic events. Previously performed analogue models show that resurgent blocks are bordered by inward-dipping high-angle reverse faults (outermost fault system) and outward-dipping normal faults (innermost fault system). We propose a model of trapdoor uplift of a block which induces reverse faulting, responsible for seismicity and hydrothermal variations along the most uplifted part. Outward-dipping normal faults, in the innermost part, form as a consequence of the gravitational sliding of the volumes bordered by the reverse faults. The further reactivation of the outermost reverse faults triggers a new cycle of intermittent trapdoor uplift of the block.

Parallel testing of multi-port static random access memories

This paper presents a novel approach for testing multi-port memories. This approach is based on the parallel execution of the testing process so that inter-port faults (shorts and coupling faults) can be detected at no loss of coverage and with no increase in the number of tests compared with a single-port memory. The parallelization is based on partitioning the memory into so-called segments; in each phase, the operation of a port is restricted to a segment. The proposed approach utilizes parallel segment accesses by arranging the ports on a pair-wise basis (one port for reading and the second port for writing); this permits an efficient utilization of the ports and full coverage of inter-port faults for both normal and mirror layouts. A port assignment process is utilized together with the partitioning of the memory; it considers the functionalities of the ports and their relation with respect to the addresses and the placement of the cells. It is shown that the test complexity of the proposed approach is independent of the number of ports. Simulation results are presented. A BIST circuitry capable of embedding and controlling this parallel approach is also proposed; it is shown that the BIST implementation is O(NlogN) where N is the number of ports.

Seismic-reflection profiles of the central part of the Clarendon–Linden fault system of western New York in relation to regional seismicity

Geological and geophysical research in upstate New York, with few exceptions, has not definitively associated seismicity with specific Proterozoic basement or Paleozoic bedrock structures. The central part of the Clarendon–Linden fault system (CLFS) between Batavia and Dale, NY is one of those exceptions where seismicity has been studied and has been spatially associated with structure. The CLFS is either a complex system of long faults with associated shorter branches and parallel segments, or a region of many short faults aligned north–south from the Lake Ontario shore southward to Allegany County, NY. Interpretation of 38 km of Vibroseis and approximately 56 km of conventional seismic-reflection data along 13 lines suggests that the CLFS is a broad zone of small faults with small displacements in the lower Paleozoic bedrock section that is at least 77 km long and 7–17 km wide and spatially coincident with a north-trending geophysical (combined aeromagnetic and gravity) lineament within the basement. The relative offset across the faults of the system is more than 91 m near Attica, NY. The CLFS is the expression of tectonic crustal adjustments within the Paleozoic rock above the boundary of two basement megablocks of differing petrologic provinces and differing earthquake characteristics that forms the eastern side of the Elzevir–Frontenac boundary zone. Deep seismic-reflection profiles display concave-eastward listric faults that probably merge at depth near the mid-crustal boundary layer. An interpretive vertical section provides the setting for refined definitions of the CLFS, its extensions at depth and its relation to seismicity. Most modern seismicity in western New York and the Niagara Peninsula of Ontario occurs in apparent patterns of randomly dispersed activity. The sole exception is a line of seven epicenters of small earthquakes that trend east from Attica, NY into the Rochester basement megablock. Earthquakes may be triggered at the intersections of north- and east-trending brittle faults within the Niagara basement megablock. Current interpretations of the mechanisms for earthquake generation in western New York and the Niagara Peninsula of Ontario require conservative estimates of seismic hazards that assume that an earthquake the size of the 1929 Attica, NY, event ( M b=5.2) or larger could occur anywhere in the Eastern Great Lakes Basin (EGLB). The broad zone of small-displacement faults that marks the CLFS in the lower Paleozoic sedimentary section and the uppermost basement may not provide the structural environment for generation of earthquakes in western New York. If this interpretation is correct, most seismicity is generated within the Niagara basement megablock beneath or west of the CLFS. Consequently, we may have to look to the deeper tectonic regime of basement megablocks to understand the distribution of modern seismicity in the EGLB.

Parallel image segmentation with adaptive mesh

AbstractWe propose a parallel segmentation algorithm for general images which does not require advance knowledge of the image and where no initial assumptions about the number and position of regions are needed. This algorithm splits the image into a set of small triangular regions with uniform image properties, and the hierarchical construction is based on a parallel adaptive mesh algorithm. Based on a recursive binary traversal of discontinuities of image properties, hierarchical binary split and merge processing is performed. In this paper, a region is defined as space of the image where the features have smooth variation. By evaluating the homogeneity of the region using local differential properties representing the smoothness of the image, the problems of the starting point of processing and of order dependence are solved. Matching between blocks is ensured by sharing the small overlapping space that is needed to preserve the continuity of local properties. Further, it is possible to extract a region boundary line that matches the discontinuities of the local properties. Experiments performed on artificial intensity images, color real images, and range real images confirmed the universality and effectiveness of the proposed algorithm. © 2002 Wiley Periodicals, Inc. Syst Comp Jpn, 33(10): 95–104, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.1161

Adverse Selection and Market Substitution by Electronic Trade

Adverse selection induces economic limits to market substitution. If quality uncertainty persists in both Internet and traditional marketplaces, a second-best equilibrium with parallel market segments may arise. The information cost advantage of one marketplace is exactly offset by a more severe adverse selection problem associated with non-observable quality variables. The electronic marketplace providing dominant search means contains all segments, while the traditional market may lack some segments. These missing segments are characterized by low quality expectations given the set of advertised quality signals. The analytic results are confirmed by an empirical investigation of used-car trade. Thus the study also provides an estimate of the price differential between the electronic and the traditional marketplace.

Protein structure comparison using bipartite graph matching and its application to protein structure classification.

A measure of protein structure similarity is calculated from the matching of pairs of secondary structure elements between two proteins. The interaction of each pair was estimated from their axial line segments and combined with other geometric features to produce an optimal discrimination between intrafamily and interfamily relationships. The matching used a fast bipartite graph-matching algorithm that avoids the computational complexity of searching for the full subgraph isomorphism between the two sets of interactions. The main algorithm used was the "stable marriage" algorithm, which works on the ranked "preferences" of one interaction for another. The method takes 1/10 of a second for a typical comparison making it suitable as a fast pre-filter for slower, more exhaustive approaches. An application to protein structure classification is described.

On computing the upper envelope of segments in parallel

Given a collection of segments in the plane, if we regard the segments as opaque barriers, their upper envelope consists of the portions of the segments visible from point (0, +/spl infin/). In this paper, we present deterministic parallel methods for constructing the upper envelope of segments on the weakest shared-memory model, the EREW PRAM. We show that we can find the upper envelope of n line segments optimally in 0(logn) time using 0(n) processors. Furthermore, if the segments are nonintersecting and their endpoints are sorted in x-coordinate, then we can reduce the number of processors to 0(n/ logn). Our method implies that we can find the upper envelope sequentially in 0(n log log n) time, which improves previous results. We also show that we can find the upper envelope of n k-intersecting segments (any pair of the segments intersects at most k times) with a slightly larger time and processor bound.

Ordered Arrangements of Semiflexible Polymers at the Interface with Solids

The molecular arrangements and conformations of dense systems of semiflexible polymer chains near solid surfaces have been investigated by Monte Carlo simulations. At variance with the results obtained for more flexible chains, the mean square end-to-end distance and the mean square radius of gyration of chains in contact with the surfaces are found to be much higher than in the bulk. This is related to the increased length of the surface trains and to the increased tendency of such trains to form rod-like strands. As a result, the first layer of polymer units in contact with the surfaces consists of two-dimensional domains of locally parallel chain segments. The width of these domains is several times the transverse diameter of the chains.