Discrete Circles Research Articles

Auditory feedback decreases timing variability for discontinuous and continuous motor tasks in autistic adults.

Autistic individuals demonstrate greater variability and timing error in their motor performance than neurotypical individuals, likely due at least in part to atypical cerebellar characteristics and connectivity. These motor difficulties may differentially affect discrete as opposed to continuous movements in autistic individuals. Augmented auditory feedback has the potential to aid motor timing and variability due to intact auditory-motor pathways in autism and high sensitivity in autistic individuals to auditory stimuli. This experiment investigated whether there were differences in timing accuracy and variability in autistic adults as a function of task (discontinuous vs. continuous movements) and condition (augmented auditory feedback vs. no auditory feedback) in a synchronization-continuation paradigm. Ten autistic young adults aged 17-27 years of age completed the within-subjects study that involved drawing circles at 800 milliseconds intervals on a touch screen. In the discontinuous task, participants traced a series of discrete circles and paused at the top of each circle for at least 60 milliseconds. In the continuous task, participants traced the circles without pausing. Participants traced circles in either a non-auditory condition, or an auditory condition in which they heard a tone each time that they completed a circle drawing. Participants had significantly better timing accuracy on the continuous timing task as opposed to the discontinuous task. Timing consistency was significantly higher for tasks performed with auditory feedback. This research reveals that motor difficulties in autistic individuals affect discrete timing tasks more than continuous tasks, and provides evidence that augmented auditory feedback may be able to mitigate some of the timing variability present in autistic persons' movements. These results provide support for future investigation on the use of music-based therapies involving auditory feedback to address motor dysfunction in autistic individuals.

Periodic discrete Darboux transforms

We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider the integrable reduction to the case of discrete bicycle correspondence. Applying our method to the case of discrete circles, we obtain closed-form discrete parametrisations of all (closed) Darboux transforms and (closed) bicycle correspondences.

Nondipole modification of the ac Stark effect in above-threshold ionization

Above-threshold ionization (ATI) of atoms in intense laser pulses produces photoelectron momentum distributions that exhibit discrete concentric circles related to the absorption of more photons than required to exceed the ionization threshold. Using numerical solutions of the one-electron time-dependent Schr\"odinger equation beyond the electric dipole approximation for circularly polarized laser pulses, we show that the geometric centers of ATI rings are counterintuitively shifted against the propagation direction of the light, i.e., in the direction opposite to the on-average transferred photon momentum. From a comparison with a simple model based on energy considerations, we identify a nondipole modification of the ac Stark effect for electron continuum states as the origin of our observation.

Impact of double defects on seepage behavior of geomembrane lined earth-rock dams

In this study, the unsaturated seepage theory was employed to analyze the effect of different elevations and separations of double defects in geomembrane barrier on the seepage behavior of geomembrane lined earth-rock dams. The results indicated that the separation between the defects has a significant influence on the defect-induced leakage. The increasing separation results in the increase of defect-induced leakage. When the separation reaches 3 m, the defect-induced leakage tends to decrease. The defect-induced leakage increases again when the separation is greater than 3.5 m. And defect-induced leakage increases gradually with decreasing elevation of defect, but is still in the same order of magnitude. In addition, the wetted area near the defects expands with the increasing separation between double defects. The wetted areas can be delineated by a circle, by an ellipse or by two discrete circles depending on the separation and elevation of double defects.

SIMULATION EXPERIMENT ON LANDING SITE SELECTION USING A SIMPLE GEOMETRIC APPROACH

Abstract. Safe landing is an important part of the planetary exploration mission. Even fine scale terrain hazards (such as rocks, small craters, steep slopes, which would not be accurately detected from orbital reconnaissance) could also pose a serious risk on planetary lander or rover and scientific instruments on-board it. In this paper, a simple geometric approach on planetary landing hazard detection and safe landing site selection is proposed. In order to achieve full implementation of this algorithm, two easy-to-compute metrics are presented for extracting the terrain slope and roughness information. Unlike conventional methods which must do the robust plane fitting and elevation interpolation for DEM generation, in this work, hazards is identified through the processing directly on LiDAR point cloud. For safe landing site selection, a Generalized Voronoi Diagram is constructed. Based on the idea of maximum empty circle, the safest landing site can be determined. In this algorithm, hazards are treated as general polygons, without special simplification (e.g. regarding hazards as discrete circles or ellipses). So using the aforementioned method to process hazards is more conforming to the real planetary exploration scenario. For validating the approach mentioned above, a simulated planetary terrain model was constructed using volcanic ash with rocks in indoor environment. A commercial laser scanner mounted on a rail was used to scan the terrain surface at different hanging positions. The results demonstrate that fairly hazard detection capability and reasonable site selection was obtained compared with conventional method, yet less computational time and less memory usage was consumed. Hence, it is a feasible candidate approach for future precision landing selection on planetary surface.

On the Functionality and Usefulness of Quadraginta Octants of Naive Sphere

This paper presents a novel study on the functional gradation of coordinate planes in connection with the thinnest and tunnel-free (i.e., naive) discretization of sphere in the integer space. For each of the 48-symmetric quadraginta octants of naive sphere with integer radius and integer center, we show that the corresponding voxel set forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as its functional plane. We use this fundamental property to prove several other theoretical results for naive sphere. First, the quadraginta octants form symmetry groups and subgroups with certain equivalent topological properties. Second, a naive sphere is always unique and consists of fewest voxels. Third, it is efficiently constructible from its functional-plane projection. And finally, a special class of 4-symmetric discrete 3D circles can be constructed on a naive sphere based on back projection from the functional plane.

Characterization of graphomotor functions in individuals with Parkinson's disease and essential tremor.

In this study, we explored the relationship between the clinical features and motor impairments related to the graphomotor function of individuals with Parkinson's disease (PD) and essential tremor (ET). We recruited 46 participants: 12 with PD, 13 with ET, and 21 controls. All participants were asked to perform six graphomotor tasks on a digitizer tablet: drawing straight lines, cursive-connected loops, discrete circles, and continuous circles, and making goal-aimed movements with a stylus in two different directions with three different accuracy constraints. The results showed that although participants with PD were able to draw straight lines slightly faster than controls, they produced cursive-connected loops much slower than controls. In addition, in contrast to controls and individuals with ET, PDs also drew the cursive loops progressively smaller. In the aiming task, we found that equivalent movements with high accuracy constraints were drawn slower by individuals with ET or PD than by controls. However, when performing the equivalent movements with moderate or low accuracy constraints, PDs performed similarly to controls. In contrast to the equivalent movements, PD and ET participants both performed nonequivalent movements slower than controls, no matter the demands arising from the accuracy constraints. The present study shows that simple graphic tasks can differentiate impairments in fine motor function resulting from ET and PD.

On the polyhedra of graceful spheres and circular geodesics

We construct a polyhedral surface called a graceful surface, which provides best possible approximation to a given sphere regarding certain criteria. In digital geometry terms, the graceful surface is uniquely characterized by its minimality while guaranteeing the connectivity of certain discrete (polyhedral) curves defined on it. The notion of “gracefulness” was first proposed in Brimkov and Barneva (1999) and shown to be useful for triangular mesh discretization through graceful planes and graceful lines. In this paper we extend the considerations to a nonlinear object such as a sphere. In particular, we investigate the properties of a discrete geodesic path between two voxels and show that discrete 3D circles, circular arcs, and Mobius triangles are all constructible on a graceful sphere, with guaranteed minimum thickness and the desired connectivity in the discrete topological space.

On different topological classes of spherical geodesic paths and circles in [formula omitted

A discrete spherical geodesic path (DSGP) between two voxels s and t lying on a discrete sphere is a/the shortest path from s to t, comprising voxels of the discrete sphere intersected by the discrete geodesic plane passing through s, t, and the center of the sphere. We consider two classes of discretization, namely naive and standard, for both the sphere and the geodesic plane, which gives rise to four distinct topological classes of DSGP. We show that the naive–naive class does not guarantee the existence of a DSGP, whereas the other three classes do. We derive the upper bounds of the distance of a DSGP belonging to each class, from the real sphere and the real plane, for different neighborhood conditions. We propose an efficient integer-based algorithm to compute the DSGP for any class-and-neighborhood combination. Novel number-theoretic characterization of discrete sphere has been used for searching the voxels comprising a DSGP. The algorithm is output-sensitive, having its time and space complexities both linear in the length of the DSGP. It can also be extended for constructing discrete 3D circles of arbitrary orientations, specified by a few appropriate input parameters. Experimental results and related analysis demonstrate its efficiency and versatility.

A survey of Chinese interpreting studies: who influences who …and why?

This paper describes how scholars in Chinese Interpreting Studies (CIS) interact with each other and form discrete circles of influence. It also discusses what it means to be an influential scholar in the community and the relationship between an author’s choice of research topic and his academic influence. The study examines an all-but-exhaustive collection of 59,303 citations from 1,289 MA theses, 32 doctoral dissertations and 2,909 research papers, combining traditional citation analysis with the newer Social Network Analysis to paint a panorama of CIS. It concludes that the community cannot be broadly divided into Liberal Arts and Empirical Science camps; rather, it comprises several distinct communities with various defining features. The analysis also reveals that the top Western influencers have an array of academic backgrounds and research interests across many different disciplines, whereas their Chinese counterparts are predominantly focused on Interpreting Studies. Last but not least, there is found to be a positive correlation between choosing non-mainstream research topics and having a high level of academic influence in the community.

Loop cluster on discrete circles

The loop clusters of a Poissonian ensemble of Markov loops on a finite or countable graph have been studied in \cite{Markovian-loop-clusters-on-graphs}. In the present article, we study the loop clusters associated with a rotation invariant nearest neighbor walk on the discrete circle $G^{(n)}$ with $n$ vertices. We prove a convergence result of the loop clusters on $G^{(n)}$, as $n\rightarrow\infty$, under suitable condition of the parameters. These parameters are chosen in such a way that the rotation invariant nearest neighbor walk on $G^{(n)}$, as $n\rightarrow\infty$, converges to a Brownian motion on circle $\mathbb{S}^{1}=\mathbb{R}/\mathbb{Z}$ with certain drift and killing rate. In the final section, we show that several limit results are predicted by Brownian loop-soup on $\mathbb{S}^{1}$.

Polar Zernike moments and rotational invariance

Zernike moments (ZM) have potentials in pattern recognition, image analysis/processing, and in computer vision. Their invariance and orthogonality are attractive in many applications. Unfortunately, direct computation of factorials in them is time consuming and discouraging. Also, people have shown poor invariance for Cartesian ZM in the discrete case. Need of a faster computing algorithm with better rotational invariance is already felt in various research communities. To find a solution, we have examined a completely new approach which comprises a unique mapping of a gray-level image on a discrete circular disk to compute Cartesian as well as polar ZM through a new recursive relation. Such a map does not require any special sampling. The proposed new recursion is based on the computational structure of the radial polynomial embedded in the ZM. Fast computation of ZM, in our case, uses the developed new recursion and the properties of discrete circles, e.g., symmetry, uniqueness, and hole-free generation of discrete disk. This discrete circular map helps not only the fast computation of ZM but also lends its support to provide better rotational invariance for polar ZM over that of Cartesian ZM. The invariance is useful in recognition.

Skinning of circles and spheres

Skinning of an ordered set of discrete circles is discussed in this paper. By skinning we mean the geometric construction of two G 1 continuous curves touching each of the circles at a point, separately. After precisely defining the admissible configuration of initial circles and the desired geometric properties of the skin, we construct the touching points and tangents of the skin by applying classical geometric methods, like cyclography and the ancient problem of Apollonius, finding touching circles of three given circles. Comparing the proposed method to a recent technique ( Slabaugh et al., 2008, 2010), larger class of admissible data set and fast computation are the main advantages. Spatial extension of the problem for skinning of spheres by a surface is also discussed in detail.

Fitting nature's basic functions. II. Estimating uncertainties and testing hypotheses

For pt.I see ibid., previous issue. In the last issue we considered a linear statistical model. The development was motivated by global annual average temperature data which were plotted as discrete circles. The two curves are the best-fitting first- and fifth-degree polynomials. The fifth-degree polynomial tracks the data better, but we need more statistical analysis to determine whether the improvement obtained justifies the addition of four new free parameters. This is one of the questions that we address in this installment. We discuss simple diagnostics for the fit, uncertainties in the estimates, estimate correlations, assigning confidence levels, testing hypotheses, and a time series diagnostic.

Role of Vascular Endothelial Cell Growth Factor in Ovarian Hyperstimulation Syndrome

Ovarian hyperstimulation syndrome (OHSS) is the most serious problem that occurs when gonadotropins are used to induce ovulation. The ovaries enlarge and vascular permeability increases, causing protein-rich fluid to leave the intravascular space. This may explain accumulating peritoneal fluid, edema, hypovolemia, and subsequent anuria or hypertension in the most severe cases. A vasoactive substance released by the stimulated ovary has been postulated, in part because follicular fluid (FF) from patients at risk significantly enhances the permeability of endothelial cells (ECs) in vitro. One candidate is the glycoprotein vascular endothelial cell growth factor (VEGF). This study sought to determine whether VEGF induces EC permeability by analyzing fluid samples from 80 infertile women undergoing hormonal ovulation induction. Samples of FF were categorized according to the number of oocytes retrieved. Endothelial cell permeability was estimated using bovine aortic ECs seeded on filters exposed to mannitol. The EC barrier became significantly more permeable to mannitol within 4 hours of exposure to VEGF (Table 1). A peak increase exceeding 60 percent was noted at 24 hours. The effect of VEGF on EC permeability was dose-related. Permeability induced by FF correlated directly with the number of oocytes produced by indi- vidual patients (Fig. 1). Antibody against VEGF reversed FF-stimulated permeability (Table 2). The VEGF-stimulated permeability was reversed by nearly half by an inhibitor of nitrous oxide production. Concentrations of VEGF increased progressively with the number of oocytes produced (Fig. 2) . Incubating EC with VEGF (or with FF from women producing numerous oocytes) led the actin fibers to span the entire cell transversely, forming stress fibers. Again, VEGF antibody substantially reversed this effect. Table 1: Effects of exogenous VEGF on endothelial cell permeability in vitro*Fig. 1: A, Correlation of number of oocytes retrieved from women after hormonal stimulation of the ovary with in vitro endothelial cell permeability stimulated by their individual ovarian follicular fluid (FF). Each circle represents the permeability to mannitol that transgresses an endothelial cell monolayer in culture at 24 hours as a function of the number of oocytes produced. FF samples from 80 women were studied, but only 65 discrete circles are shown because of overlapping values. B, Group correlations for oocyte production and FF-induced permeability. Some patient values overlap and hence are not shown as discrete circles.Table 2: Stimulation of in vitro endothelial cell permeability by follicular fluids and reversed by VEGF antibody*Fig. 2: VEGF concentrations in the follicular fluids of patients in groups I through IV. Each bar is the mean ± SEM of the samples in the group. Asterisks indicate P < .05 by ANOVA plus Scheffe’s F-test versus group I.These findings suggest that VEGF is the factor accounting for the major clinical consequences of OHSS. The disorder might be prevented using receptor antagonists or substances inhibiting VEGF synthesis. J Clin Invest 1998;102:1978–1985

Discrete circles, rings and spheres

This paper presents a new approach to discrete circles, rings, and an immediate extension to spheres. The circle, called arithmetical circle is defined by diophantine equations. The integer radius circles with the same centre pave the plane. It is easy to determine if a point is on, inside, or outside a circle. This was not easy to do with previous definitions of circles, like Bresenham's. We show that the arithmetical circle extends Bresenham's circle. We give an efficient incremental generation algorithm. The arithmetical circle has many extensions. We present briefly half-integer centered circles with a generation algorithm, 4-connected circles, and a general ring definition. We finish with the arithmetical sphere, an immediate 3D extension of arithmetical circle. We give elements to build a algorithm for generating the sphere.

Random walks on discrete and continuous circles

We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the ‘generation gap' process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the continuous circle S1.

Random walks on discrete and continuous circles

We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the ‘generation gap' process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the continuous circle S 1.

Localization of the meningococcal receptors for human transferrin

The interaction between gold-labelled human transferrin (Au-HTF) with live meningococci after growth in vivo or in different in vitro conditions was examined by electron microscopy to localize and quantify the numbers of HTF-binding sites on the cell surface. It was clearly demonstrated that HTF binds to the surface of live meningococci (of different serogroups and serotypes) after growth in either iron-sufficient or iron-restricted cultures, although the degree of labelling was always higher (2- to 35-fold) in the latter case. The commensal Neisseria polysaccharea behaved similarly. Ultrathin sections showed that Au-HTF was localized predominantly on the outer membrane of the cells and vesicles, with hardly any internalization. Au-HTF labelling on meningococci was significantly reduced after incubation with unlabelled HTF or with rabbit antiserum containing antibodies against transferrin-binding proteins (TBPs), demonstrating the specificity of the interaction. These sera also blocked binding between HTF and outer membrane proteins on Western immunoblots. Direct evidence of the expression of the TBPs (Western blots) and localization of the HTF receptor (electron microscopy) on in vivo-grown meningococci was obtained from organisms derived without laboratory culturing from the cerebrospinal fluid of a patient. There was considerable cell-to-cell variation in the amount of labelling present on cells of the same sample (in vitro- or in vivo-grown organisms) and between different strains. The degree of binding varied with time of incubation of the cells with Au-HTF. The gold particles frequently formed discrete circles on the cell surfaces of the in vitro-grown organisms; these circles appear to be associated with outer membrane vesicle formation. The results show that the TBPs, which form part of the active components of the HTF receptor(s), are expressed in vivo and are surface exposed and immunogenic and that antibodies against them can interfere with the HTF binding of the meningococcal cells, which may affect iron utilization. This study further supports the concept of regarding the TBPs as future vaccine candidates.

On the properties of discrete circles, rings, and disks

This paper is about formal properties of discrete circles (defined as Freeman digitizations of circles with integer radius and center coordinates), discrete disks (defined as discrete circles with filled-in interiors), and discrete rings (defined as differences between consecutive discrete disks). Such objects are important in applications involving distance transforms and propagation methods. Several properties of these objects are derived, namely, conditions for occurrence of certain point configurations, formulas for the number of raster points in these objects, and their perimeters and areas. These parameters are also related to corresponding properties of ideal (nondiscrete) circles, and some limit theorems (for radius approaching infinity) are stated.