Number Of Curves Research Articles

On the Bombieri–Pila method over function fields

E. Bombieri and J. Pila introduced a method for bounding the number of integral lattice points that belong to a given arc under several assumptions. In this paper we generalize the Bombieri-Pila method to the case of function fields of genus 0 in one variable. We then apply the result to counting the number of elliptic curves contain in an isomorphism class and with coefficients in a box.

Analysis of Soluble Proteins in Natural Cordyceps sinensis from Different Producing Areas by Sodium Dodecyl Sulfate-Polyacrylamide Gel Electrophoresis and Two-dimensional Electrophoresis.

Background:As one of the bioactive components in Cordyceps sinensis (CS), proteins were rarely used as index components to study the correlation between the protein components and producing areas of natural CS.Objective:Protein components of 26 natural CS samples produced in Qinghai, Tibet, and Sichuan provinces were analyzed and compared to investigate the relationship among 26 different producing areas.Materials and Methods:Proteins from 26 different producing areas were extracted by Tris-HCl buffer with Triton X-100, and separated using sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) and two-dimensional electrophoresis (2-DE).Results:The SDS-PAGE results indicated that the number of protein bands and optical density curves of proteins in 26 CS samples was a bit different. However, the 2-DE results showed that the numbers and abundance of protein spots in protein profiles of 26 samples were obviously different and showed certain association with producing areas.Conclusions:Based on the expression values of matched protein spots, 26 batches of CS samples can be divided into two main categories (Tibet and Qinghai) by hierarchical cluster analysis.SUMMARY The number of protein bands and optical density curves of proteins in 26 Cordyceps sinensis samples were a bit different on the sodium dodecyl sulfate-polyacrylamide gel electrophoresis protein profilesNumbers and abundance of protein spots in protein profiles of 26 samples were obvious different on two-dimensional electrophoresis mapsTwenty-six different producing areas of natural Cordyceps sinensis samples were divided into two main categories (Tibet and Qinghai) by Hierarchical cluster analysis based on the values of matched protein spots. Abbreviations Used: SDS-PAGE: Sodium dodecyl sulfate polyacrylamide gel electrophoresis, 2-DE: Two-dimensional electrophoresis, Cordyceps sinensis: CS, TCMs: Traditional Chinese medicines

Schaeffer's regularity theorem for scalar conservation laws does not extend to systems

Schaeffer’s regularity theorem for scalar conservation laws can be loosely speaking formulated as follows. Assume that the flux is uniformly convex, then for a generic smooth initial datum the admissible solution is smooth outside a locally finite number of curves in the (t, x) plane. Here the term “generic” is to be interpreted in a suitable sense, related to the Baire Category Theorem. Whereas other regularity results valid for scalar conservation laws with convex fluxes have been extended to systems of conservation laws with genuinely nonlinear characteristic fields, in this work we exhibit an explicit counterexample which rules out the possibility of extending Schaeffer’s Theorem. The analysis relies on careful interaction estimates and uses fine properties of the wave front-tracking approximation.

Random regular graphs and the systole of a random surface

We study the systole of a random surface, where by a random surface we mean a surface constructed by randomly gluing together an even number of triangles. We study two types of metrics on these surfaces, the first one coming from using ideal hyperbolic triangles and the second one using triangles that carry a given Riemannian metric. In the hyperbolic case we compute the limit of the expected value of the systole when the number of triangles goes to infinity (approximately 2.484). We also determine the asymptotic probability distribution of the number of curves of any finite length. This turns out to be a Poisson distribution. In the Riemannian case we give an upper bound to the limit supremum and a lower bound to the limit infimum of the expected value of the systole depending only on the metric on the triangle. We also show that this upper bound is sharp in the sense that there is a sequence of metrics for which the limit infimum comes arbitrarily close to the upper bound. The main tool we use is random regular graphs. One of the difficulties in the proof of the limits is controlling the probability that short closed curves are separating. To do this we first prove that the probability that a random cubic graph has a short separating circuit tends to 0 for the number of vertices going to infinity and show that this holds for circuits of a length up to $\log_2$ of the number of vertices.

Connected components of meanders: Ⅰ. bi-rainbow meanders

Closed meanders are planar configurations of one or several disjoint closed Jordan curves intersecting a given line transversely. They arise as shooting curves of parabolic PDEs in one space dimension, as trajectories of Cartesian billiards, and as representations of elements of Temperley-Lieb algebras.Given the configuration of intersections, for example as a permutation or an arc collection, the number of Jordan curves is unknown. We address this question in the special case of bi-rainbow meanders, which are given as non-branched families (rainbows) of nested arcs. Easily obtainable results for small bi-rainbow meanders containing at most four families in total (lower and upper rainbow families) suggest an expression of the number of curves by the greatest common divisor (gcd) of polynomials in the sizes of the rainbow families.We prove however, that this is not the case.On the other hand, we provide a complexity analysis of nose-retraction algorithms. They determine the number of connected components of arbitrary bi-rainbow meanders in logarithmic time. In fact, the nose-retraction algorithms resemble the Euclidean algorithm.Looking for a closed formula of the number of connected components, the nose-retraction algorithm is as good as a gcd-formula and therefore as good as we can possibly expect.

Investigation and numerical solution of some 3D internal Dirichlet generalized harmonic problems in finite domains

A Dirichlet generalized harmonic problem for finite right circular cylindrical domains is considered. The term “generalized” indicates that a boundary function has a finite number of first kind discontinuity curves. It is shown that if a finite domain is bounded by several surfaces and the curves are placed in arbitrary form, then the generalized problem has a unique solution depending continuously on the data. The problem is considered for the simple case when the curves of discontinuity are circles with centers situated on the axis of the cylinder. An algorithm of numerical solution by a probabilistic method is given, which in its turn is based on a computer simulation of the Wiener process. A numerical example is considered to illustrate the effectiveness and simplicity of the proposed method.

Existence of random invariant periodic curves via random semiuniform ergodic theorem

We employ an extension of ergodic theory to the random setting to investigate the existence of random periodic solutions of random dynamical systems. Given that a random dynamical system on a cylinder [Formula: see text] has a dissipative structure, we proved that a random invariant compact set can be expressed as a union of finite of number of random periodic curves. The idea in this paper is closely related to the work recently considered by Zhao and Zheng [46].

Assessment of the effects of expressway geometric design features on the frequency of accident crash rates using high-resolution laser scanning data and GIS

ABSTRACTAccurate information on accidents and on the relevant factors that affect them is critical for establishing the relationship between accident frequency and explanatory factors. In this study, we present a simplified method to extract road geometric features accurately from very high-resolution laser scanning data to analyze accident frequency on the North-South Expressway in Malaysia. Using expressway geometric features (i.e. horizontal and vertical alignments) extracted from laser scanning data and accident histories, this research first developed an APM based on geometric regression and a geographic information system (GIS). Then, an elasticity analysis was conducted to investigate the relationship between accident occurrence and road geometric design features. Results of the case study showed that the length of the road segments (mean = 0.014, elasticity = 0.122), the number of vertical curves in a road section (mean = 4.797, elasticity = 0.999), and the presence of a horizontal curve in a road segment (mean = 2.746, elasticity = 0.877), the average distance to the nearest access point (mean = -0.001, elasticity = −0.035), and AADT (mean = 3.01, elasticity = 0.881) determined accident occurrence, all at a significance level of 5%. This study shows that laser scanning systems can provide an easy and efficient method to collect transportation data, particularly those for accident analysis.

Numerical bifurcation for the capillary Whitham equation

The so-called Whitham equation arises in the modeling of free surface water waves, and combines a generic nonlinear quadratic term with the exact linear dispersion relation for gravity waves on the free surface of a fluid with finite depth.In this work, the effect of incorporating capillarity into the Whitham equation is in focus. The capillary Whitham equation is a nonlocal equation similar to the usual Whitham equation, but containing an additional term with a coefficient depending on the Bond number which measures the relative strength of capillary and gravity effects on the wave motion.A spectral collocation scheme for computing approximations to periodic traveling waves for the capillary Whitham equation is put forward. Numerical approximations of periodic traveling waves are computed using a bifurcation approach, and a number of bifurcation curves are found. Our analysis uncovers a rich structure of bifurcation patterns, including subharmonic bifurcations, as well as connecting and crossing branches. Indeed, for some values of the Bond number, the bifurcation diagram features distinct branches of solutions which intersect at a secondary bifurcation point. The same branches may also cross without connecting, and some bifurcation curves feature self-crossings without self-connections.

Is the tautochrone curve unique?

We show that there are an infinite number of tautochrone curves in addition to the cycloid solution first obtained by Christiaan Huygens in 1658. We begin by reviewing the inverse problem of finding the possible potential energy functions that lead to periodic motions of a particle whose period is a given function of its mechanical energy. There are infinitely many such solutions, called “sheared” potentials. As an interesting example, we show that a Pöschl-Teller potential and the one-dimensional Morse potentials are sheared relative to one another for negative energies, clarifying why they share the same oscillation periods for their bounded solutions. We then consider periodic motions of a particle sliding without friction over a track around its minimum under the influence of a constant gravitational field. After a brief historical survey of the tautochrone problem we show that, given the oscillation period, there is an infinity of tracks that lead to the same period. As a bonus, we show that there are infinitely many tautochrones.

MatCal: Open Source Bayesian <sup>14</sup>C Age Calibration in Matlab

The matcal function provides radiocarbon ( 14 C) age calibration in Matlab using the Bayesian highest posterior density ( HPD ) . The function produces a probability distribution function (PDF) of calibrated ages, as well as 1 sigma (68.27%) and 2 sigma (95.45%) probability calibrated age credible intervals, calculated using HPD. Publication ready calibration plots are also produced, with the option to save to disk. Calibration output can be in either Cal BP or BCE/CE (BC/AD), and a reservoir age can be specified if necessary. The user can choose from a number of calibration curves, including the latest version of IntCal.

More than simply microbial growth curves

Bacterial growth is a very important piece of information in a wide range of investigation and, in most of the time the data are simply shown directly without any further processing. In a single factor investigation without comparative information to be extracted, this simple approach can be used together with other data to form a comprehensive set of results. When comparison is involved, such direct showing of bacterial growth curves without processing cannot warrant a meaningful comparison thoroughly and further processing of data is necessary. In addition, there is little, if any, quantitative data for the comparison from the display of growth curves and description of a number of curves is not a simple task, especially in a meaningful way for assimilation of the data to readers. With this in mind, I would like to remind of those who plan to show such data as growth curves for their potential publication to carry this further to generate comparative results for a much meaningful interpretation by modeling and calculation from the raw growth data over time of incubation. By calculating with existing equations, the lag phase, growth rate and the biomass can be derived from a series of growth curves for a more effective and meaningful analysis. This approach is not new, but remembrance of such available tool is more important so that research data are shown professionally and also scientifically for meaning presentation and effective assimilation.

Synthesis of Constant Torque Compliant Mechanisms

Constant torque compliant mechanisms produce an output torque that does not change in a large range of input rotation. They have wide applications in aerospace, automobile, timing, gardening, medical, and healthcare devices. Unlike constant force compliant mechanisms, the synthesis of constant torque compliant mechanisms has not been extensively investigated yet. In this paper, a method is presented for synthesizing constant torque compliant mechanisms that have coaxial input rotation and output torque. The same shaft is employed for both input rotation and output torque. A synthesized constant torque compliant mechanism is modeled as a set of variable width spline curves within an annular design domain formed between a rotation shaft and a fixed ring. Interpolation circles are used to define variable width spline curves. The synthesis of constant torque compliant mechanisms is systematized as optimizing the control parameters of the interpolation circles of the variable width spline curves. The presented method is demonstrated by the synthesis of constant torque compliant mechanisms that have different number of variable width spline curves in this paper.

Rational curves in CICYs in products of two projective spaces

ABSTRACTLet X be the product of two projective spaces and consider the general CICY threefold Y in X with configuration matrix A. We prove the finiteness part of the analogue of the Clemens’ conjecture for such a CICY in low bidegrees. More precisely, we prove that the number of smooth rational curves on Y with low bidegree and with nondegenerate birational projection is at most finite (even in cases in which positive dimensional families of degenerate rational curves are known).

Influence of Martensitic Transformation on the Fatigue of Low Temperature Metastable Stainless Steel

The influence of martensitic transformation on the fatigue of AISI 316 type stainless steel, which presents a low temperature metastable behavior, was investigated at-196 and 25°C. Fatigue tests were conducted on both annealed and cold worked conditions. The results from stress versus number of cycles curves showed that the fatigue resistance is not affected by the “dynamically” induced martensite in annealed specimens at both temperatures. On the contrary, the previously induced “static” martensite in work hardened specimens contributes to decrease the fatigue resistance limit. The contribution of the martensite stability is discussed.

A method for psychophysical screening of odorants for use in city gas based on olfactory adaptation tolerance

In many developed nations, natural gas (so-called city gas) is supplied as a utility for cooking, heating, and hot-water supply. Because natural gas is odorless, city gas must be odorized so that it can be detected in the event of a leak. Although high adaptation tolerance is an important criterion for city gas odorants, there is yet no standard method of evaluating the psychophysical suitability of new candidate odorants in terms of olfactory adaptation. In order to address this situation, we developed a method for psychophysical screening of new candidate odorants for use in city gas based on adaptation tolerance. We used the main component of the conventional city gas odor (tertbutylmercaptan, TBM) and six new candidate odorants: cyclohexene (CH), ethyl isobutyrate (EI), isovaleric acid (IVA), 2-hexene (HEX), 1,5-cyclooctadiene (COD), and 1-methylpyrrolidine (MEP). Participants evaluated the perceived intensity of a continuously presented odor at a fixed concentration. After the time-intensity curves were quantitatively classified into fast or slow adaptation patterns, we compared the number of intensity curves classified into each pattern between TBM and each new odorant. Our results revealed that HEX has a significantly higher adaptation tolerance than TBM, and that the other five new candidate odorants were almost equivalent to TBM in terms of adaptation tolerance. We concluded that all of the new candidate odorants used in this study passed the psychophysical screen based on adaptation tolerance, and are therefore suitable for use in city gas.

A comparative empirical analysis of statistical models for evaluating highway segment crash frequency

Abstract The present study conducted an empirical highway segment crash frequency analysis on the basis of fixed-parameters negative binomial and random-parameters negative binomial models. Using a 4-year data from a total of 158 highway segments, with a total of 11,168 crashes, the results from both models were presented, discussed, and compared. About 58% of the selected variables produced normally distributed parameters across highway segments, while the remaining produced fixed parameters. The presence of a noise barrier along a highway segment would increase mean annual crash frequency by 0.492 for 88.21% of the highway segments, and would decrease crash frequency for 11.79% of the remaining highway segments. Besides, the number of vertical curves per mile along a segment would increase mean annual crash frequency by 0.006 for 84.13% of the highway segments, and would decrease crash frequency for 15.87% of the remaining highway segments. Thus, constraining the parameters to be fixed across all highway segments would lead to an inaccurate conclusion. Although, the estimated parameters from both models showed consistency in direction, the magnitudes were significantly different. Out of the two models, the random-parameters negative binomial model was found to be statistically superior in evaluating highway segment crashes compared with the fixed-parameters negative binomial model. On average, the marginal effects from the fixed-parameters negative binomial model were observed to be significantly overestimated compared with those from the random-parameters negative binomial model.

Reconstruction of an input function from a dynamic PET water image using multiple tissue curves

Quantification of cerebral blood flow (CBF) is important for the understanding of normal and pathologic brain physiology. When CBF is assessed using PET with 15O or C15O2, its calculation requires an arterial input function, which generally requires invasive arterial blood sampling. The aim of the present study was to develop a new technique to reconstruct an image derived input function (IDIF) from a dynamic 15O PET image as a completely non-invasive approach.Our technique consisted of using a formula to express the input using tissue curve with rate constant parameter. For multiple tissue curves extracted from the dynamic image, the rate constants were estimated so as to minimize the sum of the differences of the reproduced inputs expressed by the extracted tissue curves. The estimated rates were used to express the inputs and the mean of the estimated inputs was used as an IDIF. The method was tested in human subjects (n = 29) and was compared to the blood sampling method. Simulation studies were performed to examine the magnitude of potential biases in CBF and to optimize the number of multiple tissue curves used for the input reconstruction.In the PET study, the estimated IDIFs were well reproduced against the measured ones. The difference between the calculated CBF values obtained using the two methods was small as around <8% and the calculated CBF values showed a tight correlation (r = 0.97). The simulation showed that errors associated with the assumed parameters were <10%, and that the optimal number of tissue curves to be used was around 500.Our results demonstrate that IDIF can be reconstructed directly from tissue curves obtained through 15O PET imaging. This suggests the possibility of using a completely non-invasive technique to assess CBF in patho-physiological studies.

A Classification of Spherical Curves Based on Gauss Diagrams

We consider generic smooth closed curves on the sphere $$S^2$$ . These curves (oriented or not) are classified relatively to the group $$\text{ Diff }(S^2)$$ or its subgroup $$\text{ Diff }^+(S^2)$$ ), with the Gauss diagrams as main tool. V. I. Arnold determined the numbers of orbits of curves with n double points when $$n<6$$ . This paper explains how a preliminary classification of the Gauss diagrams of order 5, 6 and 7 allows to draw up the list of the realizable chord diagrams of these orders. For each such diagram $$\Gamma $$ and for each Arnold symmetry type T, we determine the number of orbits of spherical curves of type T realizing $$\Gamma $$ . As a consequence, we obtain the total numbers of curves (oriented or not) with 6 or 7 double points on the sphere (oriented or not) and also the number of curves with special properties (e.g. having no simple loop).

Fidelity vs. simplicity

Vector drawing is a popular representation in graphic design because of the precision, compactness and editability offered by parametric curves. However, prior work on line drawing vectorization focused solely on faithfully capturing input bitmaps, and largely overlooked the problem of producing a compact and editable curve network. As a result, existing algorithms tend to produce overly-complex drawings composed of many short curves and control points, especially in the presence of thick or sketchy lines that yield spurious curves at junctions. We propose the first vectorization algorithm that explicitly balances fidelity to the input bitmap with simplicity of the output, as measured by the number of curves and their degree. By casting this trade-off as a global optimization, our algorithm generates few yet accurate curves, and also disambiguates curve topology at junctions by favoring the simplest interpretations overall. We demonstrate the robustness of our algorithm on a variety of drawings, sketchy cartoons and rough design sketches.