Parallel Segments Research Articles

A new variant of the barberpole effect: Psychophysical data and computer simulations

The classic barberpole effect shows that perceived direction of motion of parallel line segments depends on the orientation of the frame defined by segment end points. A stimulus configuration was created by crossing two oblique barberpoles. Perceived motion in the crossed portion of the configuration is bi-stable, alternating between two oblique directions defined by the two component barberpoles. Ratings of dominance of perceived motion direction in the crossed portion of two barberpoles of different width and orientation revealed a strong preference for the wider component barberpole and a weak preference for the nearer-to-vertical component barberpole. A network model is presented in which each unit inhibits units with different direction sensitivity and co-extensive receptive fields, and excites units with equal direction sensitivity and neighboring receptive fields. Simulations of the temporal evolution of the spatial activity profile exhibit the effect of barberpole width and the bi-stability of percepts. Fatigue of highly adapted units enables the gradual emergence of non-adapted units. Small initial variations can lead to profound differences in the final state of the system, explaining the quasi-random fluctuation between the two perceptual variants.

Particle Dynamics in Time-Dependent Stadium-Like Billiards

Billiards in the form of a stadium with perturbed boundaries are considered. Investigations are primarily devoted to billiards having a near-rectangle form, but the results regarding the “classical” stadium with the boundary that consists of two semicircles and two parallel segments tangent to them, are also described. In the phase plane, areas corresponding to decrease and increase of the velocity of billiard particles are found. The average velocity of the particle ensemble as a function of the number of collisions with the boundary is obtained.

Two-way plots: I. the case of straight line segments

The two-way plot is a visualization tool for tables by means of intersections of geometrical objects. This paper studies such plots in the case, where the geometrical objects are linear segments. The original two-way plot for additive fits has been introduced in Tukey (1977, Chapter 10E). It consists of two sets of parallel segments, one segment for each row and one segment for each column, chosen in such a manner that all row segments intersect all column segments and such that the ordinates of the intersections are equal to the fitted values. A two-way plot shows immediately and precisely the important features of a fit, not only locally within a single row or column, but also globally. As such it is a very useful tool to go along with the numerical descriptions we generally use. The additive model, however, is too restrictive and this paper generalizes the two-way plot to models with interactive terms. The most general graph we will consider, retains from Tukey's original only the fact that each row and each column is represented by a line segment and that they all mutually intersect each other. The fits that correspond to such a figure turn out to be sums of row and column effects and multiplicative terms involving additional row and column effects. It turns out in practice, that requiring at least one of the row or the column line segments to be parallel or in a fan shape often leads to more visually pleasing charts, without much restricting the quality of the fit.

Minimizing the total projection of a set of vectors, with applications to layered manufacturing

In layered manufacturing (LM), a three-dimensional polyhedral solid is built as a stack of two-dimensional slices. Each slice (a polygon) is built by filling its interior with a sequence of parallel line segments (of some small non-zero width), in a process called hatching. A critical step in hatching is choosing a direction which minimizes the number of segments. In this paper, this problem is approximated as the problem of finding a direction which minimizes the total projected length of a certain set of vectors. Efficient algorithms are proposed for the latter problem, using techniques from computational geometry. Experimental and theoretical analyses show that this approach yields results that approximate closely the optimal solution to the hatching problem. Extensions of these results to several related problems are also discussed.

Femtosecond probing of singlet exciton dynamics in polybithiophene films

The relaxation and transport dynamics of singlet excitons in 100nm-thick, electrochemically prepared polybithiophene films were investigated by monitoring the time evolution of photoinduced bleaching and S1 − Sn absorption with femtosecond transient absorption spectroscopy. The decay dynamics of both bleaching and S 1 − S n absorption between 500 and 800 nm are observed to be independent of the pump pulse wavelength and can be fitted by a biexponential function with the time constants τ1 = 120fs±20fs and τ2 = 2ps±0.3ps. The short time constant τ1 = 120fs was ascribed to the transport dynamics of the initially generated free excitons migrating over parallel aligned polymer segments to structural defects acting as traps. The competing process, occuring predominantly in structurally disordered regions, is structural relaxation of the initially generated free excitons to selftrapped excitons decaying with a lifetime of about 2ps.

Ergodicity of a class of truncated elliptical billiards

We consider a class of billiard tables obtained byintersecting elliptical domains x2/a2 + y2⩽1,a>1 withhorizontal strips |y|⩽h<1. The boundary of these tables consists oftwo elliptical arcs connected by two parallel straight segments. We provethat the billiards in these tables have non-vanishing Lyapunov exponentsfor h<min (1/a,1/(2)1/2), and are ergodic for h<1/(1 + a2)1/2.

The prevalence of colinear contours in the real world

Our visual system preferentially groups contour segments that not only have the same orientation but are colinear as well. Long-range horizontal connections are thought to play an important role in context-dependent modifications of neuronal responses. Since the topology of these connections shows a close relation to the perceptual grouping criterion of colinearity, we tested whether the statistical properties of real world images are biased towards colinear contours. By wavelet analysis we detected contours in images of natural environments and calculated their spatial correlations. In urban as well as in natural environments, the correlations between colinear contour segments were larger than the correlations for parallel contour segments. These observations indicate that colinear contour segments dominate real world images and thus might bias the functional and structural development of our visual system.

Structure in magneto-rheological fluids: a theoreticalanalysis

The fundamental mechanism for magneto-rheological clutches, switchesand devices is the ability of magnetic fields to induce relatively thick,linearly extended structures which span the relevant fluid medium.Recent observations have shown these to form via initial thin, linear,chain-like threads along the field lines, which then associate laterally via adiffusion-controlled process into the relatively thick columns which give riseto the enhanced rheology of the fluid. A theoretical analysis is given hereinwhich accounts for these two types of associations. By considering theinteraction energy between parallel aligned free chain segments, the theoryreveals a tendency for the threads to associate at their overlapping ends,thereby forming thick columns. The weak overlapping thus accounts for theability of the columns to disperse rapidly once the field has been removed.Tentative geometries for the initial morphology of these secondary columnclusters are proposed.

Le stade ne minimise pas [formula omitted] parmi les ouverts convexes du plan

In this Note, we are interested in the minimization of the second eigenvalue of the Laplacian with Dirichlet boundary conditions amongst convex plane domains with given area. The natural candidate to be the optimum was the “stadium”, convex hull of two identical tangent disks (Troesch conjecture). We refute this conjecture. Nevertheless, we prove that the optimum has two parallel segments in its boundary.

Order Distance Estimation in Porous Glasses via Transformed Correlation Function of Small-Angle Scattering

A mesoporous two-phase system, consisting of colloidal silica in the cavities of the main silica frame work of a macroporous glass, was investigated by use of Small-Angle X-ray scattering. The transformed correlation function γT(r) was determined for this material for distances r<40 nm. The application of the intrinsic properties of γT(r) yields estimations for two fundamental order distances L 1=11 nm and L 2=120 nm of the~porous glass possessing a clear geometric interpretation: L 1, a short-order-range, is the mean chord length of the mesopores plus the mean chord length in the secondary particles. L 2, a long-order-range, is an estimation of the mean diameter of a macropore plus the mean free distance in the silica framework which separates two nearly parallel segments of two adjacent macropores.

Elliptic islands on the elliptical stadium

The elliptical stadium is a plane region bounded by a curve constructedby joining two half-ellipses with axes $a > 1$ and $b = 1$, by two parallel segments ofequal length $2h$. The corresponding billiard problem defines a two-parameter familyof discrete dynamical systems through the maps $T_{a,h}$.We investigate the existence of elliptic islands for a special family of periodic orbitsof $T_{a,h}$. The hyperbolic character of those orbits were studied in [2] for $1 1$.We prove that, for $a \sqrt 2$ we prove that thereis no upper bound on h for the existence of elliptic islands.

Quaternary alluvial terraces in an active tectonic region: the San Juan River Valley, Andean Ranges, San Juan Province, Argentina

The San Juan River, located in San Juan Province (Argentina), crosses the Precordillera and other geologic units including the Ullum tectonic valley and the La Laja Zone between latitudes 31°S and 32°S. The San Juan River is antecedent as is suggested by its two perpendicular segments linked by an almost parallel segment to the main structural trend. Along the Precordillera, the San Juan River valley has many different alluvial fans at the river junctions with its tributaries. The Quaternary alluvial fans display surfaces cut in a series of steps which we consider to be alluvial terraces generated by aggradation and repeated incision episodes. The studied sector includes one area with recent major seismic activity (La Laja Zone), another without major seismic activity (Precordillera area), and a subsident area (Ullum area) where a large lake was formed 6500yr BP. The old San Juan River was captured by the Quebrada de Ullum valley by means of a 25-m incision, which resulted in river-gradient headward erosion. The San Juan River gradient shows some irregularities that, although unrelated to the main structures, are associated with river dynamics, which emphasizes lithologic differences. The main river valley width, the geometry and gradient of each tributary, together with the basement rock lithologies and the size of each local source area are the major factors which control the alluvial terrace generation processes. In the La Laja Zone, where the uppermost terrace is capped by travertine, dating of travertine deposits suggests that the maximum incision rate is 0.9–1mm/yr related to episodic activity on the La Laja Fault.

Affine invariant detection of perceptually parallel 3D planar curves

The problem of parallelism detection between two curves has been formulated in this paper as a line detection problem within an affine-invariant local similarity matrix computed for the two curves. Each element of this matrix gives an affine invariant measure of local parallelism for any pair of curve segments along the two curves. This approach enables the detection of a pair of parallel 3D planar curves as well as parallel 2D curves under general affine transform. Two descriptors were also used here to provide a multi-resolution representation of a curve. Since these two descriptors provide sufficient local and semi-local shape information at every feature point on the curves, the process of detecting parallelism is thus robust against both noise and deformations. Moreover, the proposed technique allows all significant pairs of parallel segments within any two curves in the scene to be detected. Experiments on detecting randomly affine-transformed curves, which are obtained from natural images or artificially generated images, have demonstrated the effectiveness of the technique.

FER Kinase Activation of Stat3 Is Determined by the N-terminal Sequence

p94(fer) and p51(ferT) are two tyrosine kinases that share identical SH2 and kinase domains but differ in their N-terminal regions. To further explore the cellular functions of these two highly related tyrosine kinases, their subcellular distribution profiles and in vivo phosphorylation activity were followed using double immunofluorescence assay. When combined with immunoprecipitation analysis, this assay showed that p94(fer) can lead to the tyrosine phosphorylation and activation of Stat3 but not of Stat1 or Stat2. Native p94(fer) exerted this activity when residing in the cytoplasm. However, modified forms of p94(fer), which are constitutively nuclear, could also lead to the phosphorylation of Stat3. Endogenous Stat3 and p94(fer) co-immunoprecipitated with each other, thus proving the interaction of these two proteins in vivo. Unlike p94(fer), p51(ferT) did not induce the phosphorylation of Stat3 but led to the phosphorylation of other nuclear proteins. Replacing the unique 43-amino acid-long N-terminal tail of p51(ferT) with a parallel segment from the N-terminal tail of p94(fer) did not change the subcellular localization of p51(ferT) but enabled it to activate Stat3. Thus the different N-terminal sequences of p94(fer) and p51(ferT) can affect their ability to induce phosphorylation of Stat3 and most probably direct their different cellular functions.

N-terminal sequences direct the autophosphorylation states of the FER tyrosine kinases in vivo.

p94(fer) and p51(ferT) are two tyrosine kinases which share identical SH2 and kinase domains but differ in their N-terminal regions. While p94(fer) is expressed in most mammalian cells, the accumulation of p51(ferT) is restricted to meiotic spermatocytes. Here we show that the different N-terminal tails of p94(fer) and p51(ferT) direct different autophosphorylation states of these two kinases in vivo. N-terminal coiled-coil domains cooperated to drive the oligomerization and autophosphorylation in trans of p94(fer). Moreover, the ectopically expressed N-terminal tail of p94(fer) could act as a dominant negative mutant and associated with the endogenous p94(fer) protein in CHO cells. This increased significantly the percentage of cells residing in the G0/G1 phase, thus suggesting a role for p94(fer) in the regulation of G1 progression. Unlike p94(fer), overexpressed p51(ferT) was not autophosphorylated in COS1 cells. However, removal of the unique N-terminal 43 aa of p51(ferT) or the replacement of this region by a parallel segment from p94(fer) endowed the modified p51(ferT) with the ability to autophosphorylate. The unique N-terminal sequences of p51(ferT) thus interfere with its ability to autophosphorylate in vivo. These experiments indicate that the N-terminal sequences of the FER tyrosine kinases direct their different cellular autophosphorylation states, thereby dictating their different cellular functions.

Branching point effects on the passive properties of the cerebellar granule cell axon

This paper describes a mathematical model of the axon of the cerebellar granule cell as it ascends into the molecular layer and branches into its two parallel fiber segments. We present a theoretical and computational analysis of the input resistance at the branching point and the degree of signal attenuation between the ascending segment of the axon and the parallel fibers. The results suggest considerable passive signal decay in this branch point. If correct, this result has important implications for cerebellar function, as granule cell activation would be expected to always propagate in the ascending but not necessarily the parallel fiber segments of the same axon.

Relaxation of a polymer chain confined in a tube or a slit

Relaxation modes and rates of a single polymer chain confined in a tube or a slit by repulsive walls are studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. The relaxation modes and rates of a polymer chain of N segments in the directions parallel and perpendicular to the walls are estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices of positions of the segments. For the parallel component, the behavior of the pth slowest relaxation rate λ∥ p of a polymer chain of N segments agrees with the scaling prediction λ∥ p ≃ λ b (gp/N) x for gp/N << 1, where x = 2 for a tube and x = 2.5 for a slit. Here, λ b and g are the slowest relaxation rate within each blob and the number of segments per blob, respectively. The corresponding relaxation modes show the Rouse-like behavior. For the perpendicular component, the behavior of the pth slowest relaxation rate λ⊥ p is consistent with the scaling prediction λ⊥ p ≃ λ b for gp/N < 1. The behavior of the corresponding relaxation modes is consistent with the blob picture.

Stimulus segmentation in the visual search task

Four experiments were conducted in order to study the segmentation process in a visual search task with relevant stimuli (target and distractors) randomly distributed among textural elements. The basic idea was that a parallel segmentation process of the relevant stimuli would contribute to the overall reaction time independently of the contribution of the number of relevant stimuli. In the first experiment, with relevant stimuli and textural elements that differed in the orientation of their component lines, texture presence interacted with number of relevant stimuli and with target presence. These results were not favorable to the parallel segmentation hypothesis. In the second and third experiments, in which the relevant and the textural stimuli differed in orientation and in the luminance contrast of their component lines, the results support a parallel segmentation process for the higher contrast conditions. In these experiments, the effect of texture presence was greater on target-absent than on target-present trials. Experiment 4 shows that the search can be restricted to the high-contrast relevant stimuli when the number of these stimuli is constant and the number of textural stimuli changes from trial to trial. The present results suggest that the relevant stimuli can be segmented in parallel and then submitted to a restricted analysis, even when they are scattered among textural stimuli.

POINT AND LINE SEGMENT RECONSTRUCTION FROM VISIBILITY INFORMATION

In general, visibility reconstruction problems involve determining a set of objects in the plane that exhibit a specified set of visibility constraints. In this paper, an algorithm is presented for reconstructing a set of parallel line segments from specified visibility information contained in an extended endpoint visibility graph. The algorithm runs in polynomial time and relies on simple vector arithmetic to generate a system of linear inequalities. A related problem, solvable with the same technique, is the point reconstruction problem, in which the cyclic ordering and the x-coordinates of a set of points is specified. A second contribution is the definition of an extension of the visibility graph called the Stab Graph, which contains extra visibility information.

Adverse Selection and the Economic Limits of Market Substitution: An Application to E-Commerce and Traditional Trade in Used Cars

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. Positive trade in parallel segments implies that 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 vector 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.