Journal articles: 'Curves, Algebraic. Gaussian distribution'

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SMALL, ANTHONY. "ON ALGEBRAIC MINIMAL SURFACES IN ℝ3 DERIVING FROM CHARGE 2 MONOPOLE SPECTRAL CURVES." International Journal of Mathematics 16, no. 02 (February 2005): 173–80. http://dx.doi.org/10.1142/s0129167x05002771.

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We give formulae for minimal surfaces in ℝ3 deriving, via classical osculation duality, from elliptic curves in a line bundle over ℙ1. Specialising to the case of charge 2 monopole spectral curves we find that the distribution of Gaussian curvature on the auxiliary minimal surface reflects the monopole's structure. This is elucidated by the behaviour of the surface's Gauss map.

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Faifman, Dmitry, and Zeév Rudnick. "Statistics of the zeros of zeta functions in families of hyperelliptic curves over a finite field." Compositio Mathematica 146, no. 1 (December 11, 2009): 81–101. http://dx.doi.org/10.1112/s0010437x09004308.

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AbstractWe study the fluctuations in the distribution of zeros of zeta functions of a family of hyperelliptic curves defined over a fixed finite field, in the limit of large genus. According to the Riemann hypothesis for curves, the zeros all lie on a circle. Their angles are uniformly distributed, so for a curve of genus g a fixed interval ℐ will contain asymptotically 2g∣ℐ∣ angles as the genus grows. We show that for the variance of number of angles in ℐ is asymptotically (2/π2)log (2g∣ℐ∣) and prove a central limit theorem: the normalized fluctuations are Gaussian. These results continue to hold for shrinking intervals as long as the expected number of angles 2g∣ℐ∣ tends to infinity.

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Wahl, Jonathan. "Gaussian maps on algebraic curves." Journal of Differential Geometry 32, no. 1 (1990): 77–98. http://dx.doi.org/10.4310/jdg/1214445038.

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Ballico, E., and C. Keem. "Ramified coverings and Gaussian maps of smooth algebraic curves." Kodai Mathematical Journal 28, no. 1 (March 2005): 92–98. http://dx.doi.org/10.2996/kmj/1111588038.

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Kalita, Gautam. "Values of Gaussian hypergeometric series and their connections to algebraic curves." International Journal of Number Theory 14, no. 01 (November 21, 2017): 1–18. http://dx.doi.org/10.1142/s179304211850001x.

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In this paper, we explicitly evaluate certain special values of [Formula: see text] hypergeometric series. These evaluations are based on some summation transformation formulas of Gaussian hypergeometric series. We find expressions of the number of points on certain algebraic curves over [Formula: see text] in terms of Gaussian hypergeometric series, which play the vital role in deducing the transformation results.

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BARMAN, RUPAM, and GAUTAM KALITA. "CERTAIN VALUES OF GAUSSIAN HYPERGEOMETRIC SERIES AND A FAMILY OF ALGEBRAIC CURVES." International Journal of Number Theory 08, no. 04 (May 16, 2012): 945–61. http://dx.doi.org/10.1142/s179304211250056x.

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Let λ ∈ ℚ\{0, -1} and l ≥ 2. Denote by Cl, λ the nonsingular projective algebraic curve over ℚ with affine equation given by [Formula: see text] In this paper, we give a relation between the number of points on Cl, λ over a finite field and Gaussian hypergeometric series. We also give an alternate proof of a result of [D. McCarthy, 3F2 Hypergeometric series and periods of elliptic curves, Int. J. Number Theory6(3) (2010) 461–470]. We find some special values of 3F2 and 2F1 Gaussian hypergeometric series. Finally we evaluate the value of 3F2(4) which extends a result of [K. Ono, Values of Gaussian hypergeometric series, Trans. Amer. Math. Soc.350(3) (1998) 1205–1223].

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Kalita, Gautam, and Arijit Jana. "Certain character sums, Gaussian hypergeometric series, and their connections to algebraic curves." Finite Fields and Their Applications 72 (June 2021): 101832. http://dx.doi.org/10.1016/j.ffa.2021.101832.

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Quang, Si Duc, Do Duc Thai, and Pham Duc Thoan. "Distribution value of algebraic curves and the Gauss maps on algebraic minimal surfaces." International Journal of Mathematics 32, no. 05 (March 25, 2021): 2150028. http://dx.doi.org/10.1142/s0129167x21500282.

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In this paper, we first establish a degeneracy second main theorem for algebraic curves from compact complex Riemann surfaces into projective varieties intersecting hypersurfaces in subgeneral position. We then use it to study the ramified values for the Gauss map of the complete (regular) minimal surfaces in [Formula: see text] with finite total curvature in the case where the Gauss map may be algebraic degenerate. Our results generalize and improve the previous results in the field.

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Bloom, Thomas, and Norman Levenberg. "Distribution of nodes on algebraic curves in ${\Bbb C}^N$." Annales de l’institut Fourier 53, no. 5 (2003): 1365–85. http://dx.doi.org/10.5802/aif.1982.

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Awange, J. L., B. Palancz, R. Lewis, T. Lovas, B. Heck, and Y. Fukuda. "An algebraic solution of maximum likelihood function in case of Gaussian mixture distribution." Australian Journal of Earth Sciences 63, no. 2 (February 17, 2016): 193–203. http://dx.doi.org/10.1080/08120099.2016.1143876.

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Riveros, Alberto, and Gustavo Castellano. "Gaussian ϕ(ρz) curves: Comparison with other models." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 2 (August 12, 1990): 192–93. http://dx.doi.org/10.1017/s0424820100134557.

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X ray characteristic intensity Ii , emerging from element i in a bulk sample irradiated with an electron beam may be obtained throughwhere the function ϕi(ρz) is the distribution of ionizations for element i with the mass depth ρz, ψ is the take-off angle and μi the mass absorption coefficient to the radiation of element i.A number of models has been proposed for ϕ(ρz), involving several features concerning the interaction of electrons with matter, e.g. ionization cross section, stopping power, mean ionization potential, electron backscattering, mass absorption coefficients (MAC’s). Several expressions have been developed for these parameters, on which the accuracy of the correction procedures depends.A great number of experimental data and Monte Carlo simulations show that the general shape of ϕ(ρz) curves remains substantially the same when changing the incident electron energy or the sample material. These variables appear in the parameters involved in the expressions for ϕ(ρz). A good description of this function will produce an adequate combined atomic number and absorption correction.

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Levin, Mordechay B. "On the Gaussian Limiting Distribution of Lattice Points in a Parallelepiped." Uniform distribution theory 11, no. 2 (December 1, 2016): 45–89. http://dx.doi.org/10.1515/udt-2016-0014.

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AbstractLet Γ ⊂ ℝs be a lattice obtained from a module in a totally real algebraic number field. Let ℛ(θ, N) be the error term in the lattice point problem for the parallelepiped [−θ1N1, θ1N1] × . . . × [−θs Ns, θs Ns]. In this paper, we prove that ℛ(θ, N)/σ(ℛ, N) has a Gaussian limiting distribution as N→∞, where θ = (θ1, . . . , θs) is a uniformly distributed random variable in [0, 1]s, N = N1 . . . . Ns and σ(ℛ, N) ≍ (log N)(s−1)/2. We obtain also a similar result for the low discrepancy sequence corresponding to Γ. The main tool is the S-unit theorem.

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FARAHMAND, K. "REAL ZEROS OF ALGEBRAIC POLYNOMIALS WITH STABLE RANDOM COEFFICIENTS." Journal of the Australian Mathematical Society 85, no. 1 (August 2008): 81–86. http://dx.doi.org/10.1017/s1446788708000682.

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AbstractWe consider a random algebraic polynomial of the form Pn,θ,α(t)=θ0ξ0+θ1ξ1t+⋯+θnξntn, where ξk, k=0,1,2,…,n have identical symmetric stable distribution with index α, 0<α≤2. First, for a general form of θk,α≡θk we derive the expected number of real zeros of Pn,θ,α(t). We then show that our results can be used for special choices of θk. In particular, we obtain the above expected number of zeros when $\theta _k={n\choose k}^{1/2}$. The latter generate a polynomial with binomial elements which has recently been of significant interest and has previously been studied only for Gaussian distributed coefficients. We see the effect of α on increasing the expected number of zeros compared with the special case of Gaussian coefficients.

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Davies, John A., Ronald C. Davidson, and George L. Johnston. "Compton and Raman free electron laser stability properties for a warm electron beam propagating through a helical magnetic wiggler." Journal of Plasma Physics 37, no. 2 (April 1987): 255–98. http://dx.doi.org/10.1017/s0022377800012162.

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This paper gives an extensive analytical and numerical characterization of the growth-rate curves (imaginary frequency versus wavenumber) derived from the free electron laser dispersion relation for a warm relativistic electron beam propagating through a constant-amplitude helical magnetic wiggler field. The electron beam is treated as infinite in transverse extent. A detailed mathematical analysis is given of the exact dispersion relation and its Compton approximation for the case of a water-bag equilibrium distribution function (uniform distribution in axial momentum pz). Applicability of the water-bag results to the case of a Gaussian equilibrium distribution in pz is tested numerically. One result of the water-bag analysis is a set of validity conditions for the Compton approximation. Numerical and analytical results indicate that these conditions are applicable to the Gaussian case far outside the parameter range where the individual water-bag and corresponding Gaussian growth rate curves agree.

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Vladimirov, Igor G., Ian R. Petersen, and Matthew R. James. "Parametric randomization, complex symplectic factorizations, and quadratic-exponential functionals for Gaussian quantum states." Infinite Dimensional Analysis, Quantum Probability and Related Topics 22, no. 03 (September 2019): 1950020. http://dx.doi.org/10.1142/s0219025719500206.

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This paper combines probabilistic and algebraic techniques for computing quantum expectations of operator exponentials (and their products) of quadratic forms of quantum variables in Gaussian states. Such quadratic-exponential functionals (QEFs) resemble quantum statistical mechanical partition functions with quadratic Hamiltonians and are also used as performance criteria in quantum risk-sensitive filtering and control problems for linear quantum stochastic systems. We employ a Lie-algebraic correspondence between complex symplectic matrices and quadratic-exponential functions of system variables of a quantum harmonic oscillator. The complex symplectic factorizations are used together with a parametric randomization of the quasi-characteristic or moment-generating functions according to an auxiliary classical Gaussian distribution. This reduces the QEF to an exponential moment of a quadratic form of classical Gaussian random variables with a complex symmetric matrix and is applicable to recursive computation of such moments.

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Veling, E. J. M. "Approximations of impulse response curves based on the generalized moving Gaussian distribution function." Advances in Water Resources 33, no. 5 (May 2010): 546–61. http://dx.doi.org/10.1016/j.advwatres.2010.02.009.

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Jiménez, Javier. "Algebraic probability density tails in decaying isotropic two-dimensional turbulence." Journal of Fluid Mechanics 313 (April 25, 1996): 223–40. http://dx.doi.org/10.1017/s0022112096002194.

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The p.d.f. of the velocity gradients in two-dimensional decaying isotropic turbulence is shown to approach a Cauchy distribution, with algebraic s−2 tails, as the flow becomes dominated by a large number of compact coherent vortices. The statistical argument is independent of the vortex structure, and depends only on general scaling properties. The same argument predicts a Gaussian p.d.f. for the velocity components. The convergence to these limits as a function of the number of vortices is analysed. It is found to be fast in the former case, but slow (logarithmic) in the latter, resulting in residual u−3 tails in all practical cases. The influence of a spread Gaussian vorticity distribution in the cores is estimated, and the relevant dimensionless parameter is identified as the area fraction covered by the cores. A comparison is made with the result of numerical simulations of two-dimensional decaying turbulence. The agreement of the p.d.f.s is excellent in the case of the gradients, and adequate in the case of the velocities. In the latter case the ratio between energy and enstrophy is computed, and agrees with the simulations. All the one-point statistics considered in this paper are consistent with a random arrangement of the vortex cores, with no evidence of energy screening.

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Xiong, Maosheng. "Distribution of zeta zeroes for abelian covers of algebraic curves over a finite field." Journal of Number Theory 147 (February 2015): 789–823. http://dx.doi.org/10.1016/j.jnt.2014.08.008.

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Wu, Jinming, and Chungang Zhu. "The maximum number and its distribution of singular points for parametric piecewise algebraic curves." Journal of Computational and Applied Mathematics 329 (February 2018): 322–30. http://dx.doi.org/10.1016/j.cam.2017.01.023.

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Van Peski, Roger. "Spectral distributions of periodic random matrix ensembles." Random Matrices: Theory and Applications 10, no. 01 (December 19, 2019): 2150011. http://dx.doi.org/10.1142/s2010326321500118.

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Koloğlu, Kopp and Miller compute the limiting spectral distribution of a certain class of real random matrix ensembles, known as [Formula: see text]-block circulant ensembles, and discover that it is exactly equal to the eigenvalue distribution of an [Formula: see text] Gaussian unitary ensemble. We give a simpler proof that under very general conditions which subsume the cases studied by Koloğlu–Kopp–Miller, real-symmetric ensembles with periodic diagonals always have limiting spectral distribution equal to the eigenvalue distribution of a finite Hermitian ensemble with Gaussian entries which is a ‘complex version’ of a [Formula: see text] submatrix of the ensemble. We also prove an essentially algebraic relation between certain periodic finite Hermitian ensembles with Gaussian entries, and the previous result may be seen as an asymptotic version of this for real-symmetric ensembles. The proofs show that this general correspondence between periodic random matrix ensembles and finite complex Hermitian ensembles is elementary and combinatorial in nature.

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Simsek, Burcin, and Satish Iyengar. "Computing tail areas for a high-dimensional Gaussian mixture." Applicable Analysis and Discrete Mathematics 13, no. 3 (2019): 871–82. http://dx.doi.org/10.2298/aadm181222039s.

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We consider the problem of computing tail probabilities - that is, probabilities of regions with low density - for high-dimensional Gaussian mixtures. We consider three approaches: the first is a bound based on the central and non-central ?2 distributions; the second uses Pearson curves with the first three moments of the criterion random variable U; the third embeds the distribution of U in an exponential family, and uses exponential tilting, which in turn suggests an importance sampling distribution. We illustrate each method with examples and assess their relative merits.

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Cui, Jian, Yan Wang, Xue Hong Zhao, and Li Dai. "Comparing Different Means of Signal Treatment for Improving the Detection Power in HPLC-UV-HG-AFS." Applied Mechanics and Materials 239-240 (December 2012): 1045–51. http://dx.doi.org/10.4028/www.scientific.net/amm.239-240.1045.

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The purpose of detecting trace concentrations of analytes often is hindered by occurring noise in the signal curves of analytical methods. This is also a problem when different arsenic species (organic arsenic species such as arsanilic acid, nitarsone and roxarsone) are to be determined in animal meat by HPLC-UV-HG-AFS, which is the basis of this work. In order to improve the detection power, methods of signal treatment may be applied. We show a comparison of convolution with Gaussian distribution curves, Fourier transform, and wavelet transform. It is illustrated how to estimate decisive parameters for these techniques. All methods result in improved limits of detection. Furthermore, applying baselines and evaluating peaks thoroughly is facilitated. However, there are differences. Fourier transform may be applied, but convolution with Gaussian distribution curves shows better results of improvement. The best of the three is wavelet transform, whereby the detection power is improved by factors of about 2.4.

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Tontini, Fabio Caratori, Osvaldo Faggioni, Nicolò Beverini, and Cosmo Carmisciano. "Gaussian envelope for 3D geomagnetic data inversion." GEOPHYSICS 68, no. 3 (May 2003): 996–1007. http://dx.doi.org/10.1190/1.1581071.

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We describe an inversion method for 3D geomagnetic data based on approximation of the source distribution by means of positive constrained Gaussian functions. In this way, smoothness and positivity are automatically imposed on the source without any subjective input from the user apart from selecting the number of functions to use. The algorithm has been tested with synthetic data in order to resolve sources at very different depths, using data from one measurement plane only. The forward modeling is based on prismatic cell parameterization, but the algebraic nonuniqueness is reduced because a relationship among the cells, expressed by the Gaussian envelope, is assumed to describe the spatial variation of the source distribution. We assume that there is no remanent magnetization and that the magnetic data are produced by induced magnetization only, neglecting any demagnetization effects. The algorithm proceeds by minimization of a χ2 misfit function between real and predicted data using a nonlinear Levenberg‐Marquardt iteration scheme, easily implemented on a desktop PC, without any additional regularization. We demonstrate the robustness and utility of the method using synthetic data corrupted by pseudorandom generated noise and a real field data set.

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Taniguchi, Masanobu. "An Asymptotic Expansion for the Distribution of the Likelihood Radio Criterion for a Gaussian Autoregressive Moving Average Process Under a Local Alternative." Econometric Theory 1, no. 1 (April 1985): 73–84. http://dx.doi.org/10.1017/s0266466600011002.

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In this paper, we shall derive the asymptotic expansion for the distribution of the likelihood ratio criterion for a Gaussian autoregressive moving average process under a sequence of local alternative hypotheses converging to the null hypothesis with rate of convergence where n is the sample size. Explicit algebraic formulae are presented for certain special cases, including the ARMA(1,1).

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Kim, Seon Jin, Young Suk Kim, and Sang Woo Kwon. "On Characteristics of Weibull Distribution Parameters of Fatigue Crack Growth Lives." Key Engineering Materials 261-263 (April 2004): 1275–80. http://dx.doi.org/10.4028/www.scientific.net/kem.261-263.1275.

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This paper illustrates the characteristics of parameters for three-parameter Weibull probability distribution of fatigue crack growth lives under constant stress intensity factor control experiments. Applying the statistical properties of the previous experimental results, the fatigue crack curves were simulated by using the non-Gaussian random fields simulation method and analyzed for the different specimen thickness and stress intensity level to determine the probability distributions of the fatigue crack growth life.

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Achter, Jeffrey D., Daniel Erman, Kiran S. Kedlaya, Melanie Matchett Wood, and David Zureick-Brown. "A heuristic for the distribution of point counts for random curves over a finite field." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2040 (April 28, 2015): 20140310. http://dx.doi.org/10.1098/rsta.2014.0310.

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How many rational points are there on a random algebraic curve of large genus g over a given finite field ? We propose a heuristic for this question motivated by a (now proven) conjecture of Mumford on the cohomology of moduli spaces of curves; this heuristic suggests a Poisson distribution with mean q +1+1/( q −1). We prove a weaker version of this statement in which g and q tend to infinity, with q much larger than g .

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Baraduc, Pierre, and Emmanuel Guigon. "Population Computation of Vectorial Transformations." Neural Computation 14, no. 4 (April 1, 2002): 845–71. http://dx.doi.org/10.1162/089976602317318983.

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Many neurons of the central nervous system are broadly tuned to some sensory or motor variables. This property allows one to assign to each neuron a preferred attribute (PA). The width of tuning curves and the distribution of PAs in a population of neurons tuned to a given variable define the collective behavior of the population. In this article, we study the relationship of the nature of the tuning curves, the distribution of PAs, and computational properties of linear neuronal populations. We show that noise-resistant distributed linear algebraic processing and learning can be implemented by a population of cosine tuned neurons assuming a nonuniform but regular distribution of PAs. We extend these results analytically to the noncosine tuning and uniform distribution case and show with a numerical simulation that the results remain valid for a nonuniform regular distribution of PAs for broad noncosine tuning curves. These observations provide a theoretical basis for modeling general nonlinear sensorimotor transformations as sets of local linearized representations.

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Bérubé, Luc R., Hervé Jouishomme, and Harold C. Jarrell. "The nonrandom binding distribution ofStreptococcus pneumoniaeto type II pneumocytes in culture is dependent on the relative distribution of cells among the phases of the cell cycle." Canadian Journal of Microbiology 44, no. 5 (May 1, 1998): 448–55. http://dx.doi.org/10.1139/w98-025.

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The adherence of Streptococcus pneumoniae to epithelial (A549) lung cells was studied and the bacterial binding distribution was found to be nonrandom (non-Gaussian). Analysis of the dependency of bacterial binding on the cell cycle of A549 cells revealed that approximately 1.8 times more bacteria bind to G2cells than to G0-G1phase cells. Furthermore, bacterial binding curves exhibited a plateau of binding to G2cells at a normalized bacteria to cell ratio approximately 1.8 times larger than that at which the plateau of binding to G0-G1cell was observed. Since G2cells are on average 1.4-1.8 times larger than G0-G1cells, the results indicate that bacterial binding is proportional to cell size and not to the preferential binding (higher affinity) of bacteria to A549 cells in the G2phase. Finally, the non-Gaussian distribution of bacterial binding could be mathematically modeled by a linear combination of three Gaussian distributions each representing bacterial binding to cells in a particular phase of the cell cycle (G0-G1, S, and G2-M). Because the Gaussian function contains a term that takes into account the relative number of cells in each of the phases, this last result implies that the overall (non-Gaussian) binding distribution (and hence the median of bacterial binding) can be highly sensitive to the relative proportion of cells in the various phases of the cell cycle.Key words: bacterial adherence, Streptococcus pneumoniae, flow cytometry, cell cycle.

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Khatoon, Rukaiya, Zahir Shah, Ranjeev Misra, and Rupjyoti Gogoi. "Study of long-term flux and photon index distributions of blazars using RXTE observations." Monthly Notices of the Royal Astronomical Society 491, no. 2 (November 11, 2019): 1934–40. http://dx.doi.org/10.1093/mnras/stz3108.

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ABSTRACT We present a detailed study of flux and index distributions of three blazars [one flat-spectrum radio quasar (FSRQ) and two BL Lacertae objects (BL Lacs)] by using 16 yr of Rossi X-ray Timing Explorer (RXTE) archival data. The three blazars were chosen such that their flux and index distributions have sufficient number of data points (≥90) with relatively less uncertainty $\left(\overline{\sigma _{\rm err}^{2}}/\sigma ^{2} < 0.2\right)$ in light curves. Anderson–Darling (AD) test and histogram fitting show that flux distribution of FSRQ 3C 273 is lognormal, while its photon index distribution is Gaussian. This result is consistent with linear Gaussian perturbation in the particle acceleration time-scale, which produces lognormal distribution in flux. However, for two BL Lacs, viz. Mrk 501 and Mrk 421, AD test shows that their flux distributions are neither Gaussian nor lognormal, and their index distributions are non-normal. The histogram fitting of Mrk 501 and Mrk 421 suggests that their flux distributions are more likely to be a bimodal, and their index distributions are double Gaussian. Since, Sinha et al. had shown that Gaussian distribution of index produces a lognormal distribution in flux, double Gaussian distribution of index in Mrk 501 and Mrk 421 indicates that their flux distributions are probably double lognormal. Observation of double lognormal flux distribution with double Gaussian distribution in index reaffirms two flux states hypothesis. Further, the difference observed in the flux distribution of FSRQ (3C 273) and BL Lacs (Mrk 501 and Mrk 421) at X-rays suggests that the low-energy emitting electrons have a single lognormal flux distribution, while the high-energy ones have a double lognormal flux distribution.

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Xu, Jing, He Zhang, Jian Tao Sun, and Ye Bing Cui. "Research of Facular Energy Distribution for Pulsed Laser Tracking System." Applied Mechanics and Materials 300-301 (February 2013): 504–9. http://dx.doi.org/10.4028/www.scientific.net/amm.300-301.504.

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Due to the distortion is always accorded when the laser facular reaches the four-quadrant detection photosensitive surface of the pulsed laser tracking system, resulting in the decline of the target measuring accuracy. Therefore the effect of facular size and energy distribution for the target azimuth measurement accuracy is researched. The calculation method for laser pot offset is discussed, and the formulas and principle circuit are given. The effect analysis of the laser pot size for measuring linear region and sensitivity are carried out, when the laser spot shows a uniform distribution as well as the Gaussian distribution. The performance of the laser pots under the two energy distribution situations are compared, the corresponding simulation curves are obtained. The simulation results show that the linear region of the Gaussian spot is larger than the uniform spot, but its sensitivity is relatively lower than the uniform spot within the effective dynamic range.

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Ahmadi, Omran, and Igor E. Shparlinski. "On the distribution of the number of points on algebraic curves in extensions of finite fields." Mathematical Research Letters 17, no. 4 (2010): 689–99. http://dx.doi.org/10.4310/mrl.2010.v17.n4.a9.

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Xue, Dan, and Weiqi Yuan. "Dynamic Partition Gaussian Crack Detection Algorithm Based on Projection Curve Distribution." Sensors 20, no. 14 (July 17, 2020): 3973. http://dx.doi.org/10.3390/s20143973.

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When detecting the cracks in the tunnel lining image, due to uneven illumination, there are generally differences in brightness and contrast between the cracked pixels and the surrounding background pixels as well as differences in the widths of the cracked pixels, which bring difficulty in detecting and extracting cracks. Therefore, this paper proposes a dynamic partitioned Gaussian crack detection algorithm based on the projection curve distribution. First, according to the distribution of the image projection curve, the background pixels are dynamically partitioned. Second, a new dynamic partitioned Gaussian (DPG) model was established, and the set rules of partition boundary conditions, partition number, and partition corresponding threshold were defined. Then, the threshold and multi-scale Gaussian factors corresponding to different crack widths were substituted into the Gaussian model to detect cracks. Finally, crack morphology and the breakpoint connection algorithm were combined to complete the crack extraction. The algorithm was tested on the lining gallery captured on the site of the Tang-Ling-Shan Tunnel in Liaoning Province, China. The optimal parameters in the algorithm were estimated through the Recall, Precision, and Time curves. From two aspects of qualitative and quantitative analysis, the experimental results demonstrate that this algorithm could effectively eliminate the effect of uneven illumination on crack detection. After detection, Recall could reach more than 96%, and after extraction, Precision was increased by more than 70%.

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le Maire, M., A. Ghazi, J. V. Møller, and L. P. Aggerbeck. "The use of gel chromatography for the determination of sizes and relative molecular masses of proteins. Interpretation of calibration curves in terms of gel-pore-size distribution." Biochemical Journal 243, no. 2 (April 15, 1987): 399–404. http://dx.doi.org/10.1042/bj2430399.

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The separation of proteins by gel-exclusion chromatography has been explained in terms of partitioning of the macromolecules within the gel by a distribution of pores of various radii. The assumption that the distribution of pore sizes is Gaussian has led to the prediction of a linear relationship between the molecular Stokes radius (RS) of the protein and the function erf-1 (1-KD), where KD is the partition coefficient [Ackers (1967) J. Biol. Chem. 242, 3237-3238]. Since careful calibrations of classical (agarose and dextran) gels and h.p.l.c. gels have shown that such a linear relationship is not verified experimentally over a wide range of native protein sizes, we have reinvestigated the model of Ackers (above reference). We show that Ackers' (above reference) derivation is not valid except for a particular Gaussian distribution of pore sizes centred at the origin. Relaxation of this restriction to allow for other types of Gaussian distributions cannot account for the non-linear calibration curves that we have obtained. Instead we show that the pore-size distribution can be calculated from the experimentally determined function KD = f(RS) and that this distribution is bimodal (non-Gaussian). One distribution is centred below 2 nm, whereas the mean value of the second one is around 6-8 nm. The minimum in this bimodal distribution corresponds, for some gels, to a region of poor resolution, which needs to be appreciated for the proper use of gel chromatography in the determination of molecular size.

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Reingold, Eyal M., and Heather Sheridan. "On using distributional analysis techniques for determining the onset of the influence of experimental variables." Quarterly Journal of Experimental Psychology 71, no. 1 (January 2018): 260–71. http://dx.doi.org/10.1080/17470218.2017.1310262.

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Much of the investigation of eye movement control in visual cognition has focused on the influence of experimental variables on mean fixation durations. In this article, we explored the convergence between two distributional analysis techniques that were recently introduced in this domain. First, Staub, White, Drieghe, Hollway and Rayner, proposed fitting the ex-Gaussian distribution to individual participants’ data in order to ascertain whether a variable has a rapid or a slow influence on fixation durations. Second, the divergence point analysis (DPA) procedure was introduced by Reingold, Reichle, Glaholt and Sheridan in order to determine more precisely the earliest discernible impact of a variable on the distribution of fixation durations by contrasting survival curves across two experimental conditions and determining the point at which the two curves begin to diverge. In this article, we introduced a new version of the DPA procedure which is based on ex-Gaussian fitting. We evaluated this procedure by re-analyzing data obtained in previous empirical investigations as well as by conducting a simulation study. We demonstrated that the new ex-Gaussian DPA technique produced estimates that were consistent with estimates produced by prior versions of DPA procedure, and in the present simulation, the ex-Gaussian DPA procedure produced somewhat more accurate individual participant divergence point estimates. Based on the present findings, we also suggest guidelines for best practices in the use of DPA techniques.

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Tarnopolski, Mariusz. "How does the shape of gamma-ray bursts’ pulses affect the duration distribution?" Monthly Notices of the Royal Astronomical Society 507, no. 1 (August 2, 2021): 1450–57. http://dx.doi.org/10.1093/mnras/stab2232.

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ABSTRACT Gamma-ray bursts (GRBs) come in two types, short and long. The distribution of logarithmic durations of long GRBs is asymmetric rather than Gaussian. Such an asymmetry, when modelled with a mixture of Gaussian distributions, requires an introduction of an additional component, often associated with another class of GRBs. However, when modelled with inherently asymmetric distributions, there is no need for such a component. The cosmological dilation was already ruled out as a source of the asymmetry, hence its origin resides in the progenitors. GRB light curves (LCs) are usually well described by a series of fast-rise-exponential-decay pulses. A statistical analysis of ensembles of simulated LCs shows that the asymmetry is a natural consequence of the pulse shape and the multi-pulse character of the LCs.

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Shah, Zahir, Ranjeev Misra, and Atreyee Sinha. "On the determination of lognormal flux distributions for astrophysical systems." Monthly Notices of the Royal Astronomical Society 496, no. 3 (June 18, 2020): 3348–57. http://dx.doi.org/10.1093/mnras/staa1746.

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ABSTRACT Determining whether the flux distribution of an astrophysical source is a Gaussian or a lognormal, provides key insight into the nature of its variability. For light curves of moderate length (<103), a useful first analysis is to test the Gaussianity of the flux and logarithm of the flux, by estimating the skewness and applying the Anderson–Darling (AD) method. We perform extensive simulations of light curves with different lengths, variability, Gaussian measurement errors, and power spectrum index β (i.e. P(f) ∝ f−β), to provide a prescription and guidelines for reliable use of these two tests. We present empirical fits for the expected standard deviation of skewness and tabulated AD test critical values for β = 0.5 and 1.0, which differ from the values given in the literature that are for white noise (β = 0). Moreover, we show that for white noise, for most practical situations, these tests are meaningless, since binning in time alters the flux distribution. For β ≳ 1.5, the skewness variance does not decrease with length and hence the tests are not reliable. Thus, such tests can be applied only to systems with β ≳ 0.5 and β ≲ 1.0. As an example of the prescription given in this work, we reconfirm that the Fermi data of the blazar, 3FGL J0730.2−1141, show that its γ-ray flux is consistent with a lognormal distribution and not with a Gaussian one.

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Ni, Y. Q., Z. G. Ying, and J. M. Ko. "Random Response Analysis of Preisach Hysteretic Systems With Symmetric Weight Distribution." Journal of Applied Mechanics 69, no. 2 (April 18, 2000): 171–78. http://dx.doi.org/10.1115/1.1428333.

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The present study is intended to develop a new method for analyzing nonlinear stochastic dynamic response of the Preisach hysteretic systems based on covariance and switching probability analysis of a nonlocal memory hysteretic constitutive model. A nonlinear algebraic covariance equation is formulated for the single-degree-of-freedom Preisach hysteretic system subjected to stationary Gaussian white noise excitation, from which the stationary mean square response of the system is obtained. The correlation coefficients of hysteretic restoring force with response in the covariance equation are evaluated by using the second moments and switching probabilities that are derived from the disjoint event probability and the mathematical machinery of an exit problem. In recognizing the symmetry of the classical Preisach weighting function, an approximation of equal “up” and “down” switching probabilities is introduced, which greatly simplifies the evaluation of the correlation coefficients. An example of the Preisach hysteretic system with Gaussian distribution weighting function is presented and the analytical results are compared with the digital simulation findings to verify the accuracy of the derived formulas. Computation results show that there exists a sharp drop in the mean square responses with the increase of a hysteresis parameter, and the mean square responses are affected only in a certain range of the Preisach weighting function.

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Malla, Janak Ratna, Walter Saurer, and B. Aryal. "Spatial orientations of angular momentum vectors of galaxies in Supercluster S [173+014+0082]." BIBECHANA 18, no. 1 (January 1, 2021): 26–32. http://dx.doi.org/10.3126/bibechana.v18i1.29165.

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The spin vector orientation of 1302 SDSS (Sloan Digital Sky Survey) galaxies in Supercluster S[173+014+0082] having redshift 0.076 to 0.091 has been analysed. The positions, position angles and inclination angles of galaxies are used to convert two-dimensional observed parameters into three-dimensional angular momentum vectors of the galaxy using the `position angle-inclination' method. The expected isotropic distribution curves are determined performing numerical simulation by generating 107 virtual galaxies. The observed distribution is compared with the expected isotropic distribution curves using three statistical tools namely Chi-square test, auto-correlation test and Fourier test. Redshift map is studied and found that the distributions fit with the Gaussian. No preferred alignment of angular momentum vectors is noticed, supporting Hierarchy model of galaxy formation. BIBECHANA 18 (2021) 26-32

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Morris, Paul J., Nachiketa Chakraborty, and Garret Cotter. "Deviations from normal distributions in artificial and real time series: a false positive prescription." Monthly Notices of the Royal Astronomical Society 489, no. 2 (August 16, 2019): 2117–29. http://dx.doi.org/10.1093/mnras/stz2259.

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ABSTRACT Time-series analysis allows for the determination of the Power Spectral Density (PSD) and Probability Density Function (PDF) for astrophysical sources. The former of these illustrates the distribution of power at various time-scales, typically taking a power-law form, while the latter characterizes the distribution of the underlying stochastic physical processes, with Gaussian and lognormal functional forms both physically motivated. In this paper, we use artificial time series generated using the prescription of Timmer & Koenig to investigate connections between the PDF and PSD. PDFs calculated for these artificial light curves are less likely to be well described by a Gaussian functional form for steep (Γ⪆1) PSD indices due to weak non-stationarity. Using the Fermi LAT monthly light curve of the blazar PKS2155-304 as an example, we prescribe and calculate a false positive rate that indicates how likely the PDF is to be attributed an incorrect functional form. Here, we generate large numbers of artificial light curves with intrinsically normally distributed PDFs and with statistical properties consistent with observations. These are used to evaluate the probabilities that either Gaussian or lognormal functional forms better describe the PDF. We use this prescription to show that PKS2155-304 requires a high prior probability of having a normally distributed PDF, $P(\rm {G})~$ ≥ 0.82, for the calculated PDF to prefer a Gaussian functional form over a lognormal. We present possible choices of prior and evaluate the probability that PKS2155-304 has a lognormally distributed PDF for each.

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Mabrouk, Rostom, François Dubeau, and Layachi Bentabet. "Dynamic Cardiac PET Imaging: Extraction of Time-Activity Curves Using ICA and a Generalized Gaussian Distribution Model." IEEE Transactions on Biomedical Engineering 60, no. 1 (January 2013): 63–71. http://dx.doi.org/10.1109/tbme.2012.2221463.

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Qi, Jinyi. "Comparison of Lesion Detection and Quantification in MAP Reconstruction with Gaussian and Non-Gaussian Priors." International Journal of Biomedical Imaging 2006 (2006): 1–10. http://dx.doi.org/10.1155/ijbi/2006/87567.

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Statistical image reconstruction methods based on maximum a posteriori (MAP) principle have been developed for emission tomography. The prior distribution of the unknown image plays an important role in MAP reconstruction. The most commonly used prior are Gaussian priors, whose logarithm has a quadratic form. Gaussian priors are relatively easy to analyze. It has been shown that the effect of a Gaussian prior can be approximated by linear filtering a maximum likelihood (ML) reconstruction. As a result, sharp edges in reconstructed images are not preserved. To preserve sharp transitions, non-Gaussian priors have been proposed. However, their effect on clinical tasks is less obvious. In this paper, we compare MAP reconstruction with Gaussian and non-Gaussian priors for lesion detection and region of interest quantification using computer simulation. We evaluate three representative priors: Gaussian prior, Huber prior, and Geman-McClure prior. We simulate imaging a prostate tumor using positron emission tomography (PET). The detectability of a known tumor in either a fixed background or a random background is measured using a channelized Hotelling observer. The bias-variance tradeoff curves are calculated for quantification of the total tumor activity. The results show that for the detection and quantification tasks, the Gaussian prior is as effective as non-Gaussian priors.

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MORET, M. A., V. de SENNA, M. G. PEREIRA, and G. F. ZEBENDE. "NEWCOMB-BENFORD LAW IN ASTROPHYSICAL SOURCES." International Journal of Modern Physics C 17, no. 11 (November 2006): 1597–604. http://dx.doi.org/10.1142/s0129183106010054.

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We study the behavior of the numbers in 412 light curves of cataclysmic variables, x-ray binary systems, galaxies, pulsars, supernovae remnants and other x-ray sources present in the public data collected by the instrument All Sky Monitor on board of the satellite Rossi x-ray timing explorer. The temporal light curves were analyzed applying Newcomb-Benford Law. The first digit of the x-ray light curves coming from astrophysical systems obeys the Newcomb-Benford Law as an intrinsic behavior. The nonextensive statistical mechanics behavior of astrophysical sources seem to be the cause for these sources to obey the Newcomb-Benford law. Some x-ray binary systems, however, do not follow this behavior. These systems obey either a gaussian or a bimodal distribution.

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Wang, Ya-Qiong, Wei-Kang Kong, and Zhi-Feng Wang. "Effect of Expanding a Rectangular Tunnel on Adjacent Structures." Advances in Civil Engineering 2018 (November 6, 2018): 1–13. http://dx.doi.org/10.1155/2018/1729041.

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The expansion of urban underpass has become the mainstream of development to cope with urban congestion, and the effect on adjacent existing structures during enlarging construction is also an important issue in the construction process. In order to better understand the influence of tunneling on adjacent structures, the pedestrian underpass expanding project above-crossing Xi’an Metro Line 1 was investigated. The aim was to analyze the deformation curves characteristics of adjacent structures by field observation of ground settlement, heave of existing tunnels, and settlement of piles. The results show that the ground settlement curve in the vertical direction of the underpass is similar to the shape of V, and the maximum settlement appearing in the center line of underpass is 18.7 mm. Due to the effect of existing tunnels on the ground deformation, the settlement curve in the parallel direction of the underpass is similar to the shape of M. Above-crossing tunneling would cause the existing tunnels to heave, and the heave mainly occurs in the range of −6 m to 12 m between the pedestrian tunnel face and the center line of each tunnel. The heave curve is similar to the shape of inverted U. The settlement of piles is linear with its axial stress and significantly affected by its location. The settlement curve of piles is similar to the shape of S in two dimensions. On the basis of deformation curves, this paper presents some equations to describe the shape of V, M, inverted U, and S, respectively, by the inverted Gaussian distribution curve, superimposed Gaussian distribution curve, Gaussian distribution curve, and arctangent function.

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DAI, LURU, FEI LIU, and ZHONG-CAN OU-YANG. "END-TO-END DISTANCE DISTRIBUTION OF FORCE STRETCHED CHAINS RECONSTRUCTION BY MAXIMUM-ENTROPY METHOD." International Journal of Modern Physics B 18, no. 17n19 (July 30, 2004): 2365–75. http://dx.doi.org/10.1142/s0217979204025397.

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Using the maximum-entropy method, the end-to-end distance distribution of the force stretched chain is calculated from the moments of the distribution, which can be obtained from the extension-force curves recorded in single-molecule experiments. If one knows force expansion of the extension through the (n-1)th power of force, it is enough information to calculate the n moments of the distribution. The method is examined with force stretched chain models, Gaussian chain and excluded-volume chain on two-dimension lattice. The method reconstructs all distributions precisely. The method also is applied to force stretched complex chain molecules: the hairpin and secondary structure conformations. We find that the distributions of homogeneous chains of two conformations are very different: there are two independent peaks in hairpin distribution; while only one peak is observed in the distribution of secondary structure conformations. Our discussion also shows that the end-to-end distance distribution may discover more critical physical information than the simpler extension-force curves can give.

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CULVER, TIM, JOHN KEYSER, DINESH MANOCHA, and SHANKAR KRISHNAN. "A HYBRID APPROACH FOR DETERMINANT SIGNS OF MODERATE-SIZED MATRICES." International Journal of Computational Geometry & Applications 13, no. 05 (October 2003): 399–417. http://dx.doi.org/10.1142/s0218195903001256.

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Many geometric computations have at their core the evaluation of the sign of the determinant of a matrix. A fast, failsafe determinant sign operation is often a key part of a robust implementation. While linear problems from 3D computational geometry usually require determinants no larger than six, non-linear problems involving algebraic curves and surfaces produce larger matrices. Furthermore, the matrix entries often exceed machine precision, while existing approaches focus on machine-precision matrices. In this paper, we describe a practical hybrid method for computing the sign of the determinant of matrices of order up to 60. The stages include a floating-point filter based on the singular value decomposition of a matrix, an adaptive-precision implementation of Gaussian elimination, and a standard modular arithmetic determinant algorithm. We demonstrate our method on a number of examples encountered while solving polynomial systems.

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Borwein, Peter B., Weiyu Chen, and Karl Dilcher. "Zeros of Iterated Integrals of Polynomials." Canadian Journal of Mathematics 47, no. 1 (February 1, 1995): 65–87. http://dx.doi.org/10.4153/cjm-1995-004-1.

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AbstractThe operator Im is defined as m-fold indefinite integration with zero constants of integration. The zero distribution of Im(p) for polynomials p is studied in general, and for two special classes of polynomials in detail. The main results are: (i) The zeros of In(Pn), where Pn(𝑧) is the n-th Legendre polynomial, converge to a certain algebraic curve; (ii) the zeros of an integer) converge to pieces of a circle and of two "Szegö curves".

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Wu, Shenghao, Daxiong Liao, Jiming Chen, Qin Chen, and Haitao Pei. "Supersonic Nozzle Optimization Design with Spline Curves Fitting the Nozzle Profiles." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 4 (August 2018): 785–91. http://dx.doi.org/10.1051/jnwpu/20183640785.

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Supersonic nozzle contour optimization design was applied to 0.6m×0.6m continuous transonic wind tunnel to improve flow quality in the test section. The Mach number root mean square deviation with the design value was chosen as optimization target. And the CFD results were verified with experimental results. Cubic spline curves with the optimal interpolating point distribution scheme were used to fit the nozzle contour. Efficient global optimization based on the Gaussian process surrogate model was used to reduce the times of evaluation. Results indicate that, the optimization framework can generate a supersonic nozzle contour with better flow quality and more accurate Mach number and that the optimal Mach number root mean square deviation is 0.001.

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Fitio, Volodymyr, Iryna Yaremchuk, Andriy Bendziak, Michal Marchewka, and Yaroslav Bobitski. "Diffraction of a Gaussian Beam with Limited cross Section by a Volume Phase Grating under Waveguide Mode Resonance." Materials 14, no. 9 (April 27, 2021): 2252. http://dx.doi.org/10.3390/ma14092252.

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In this work, the diffraction of a Gaussian beam on a volume phase grating was researched theoretically and numerically. The proposed method is based on rigorous coupled-wave analysis (RCWA) and Fourier transform. The Gaussian beam is decomposed into plane waves using the Fourier transform. The number of plane waves is determined using the sampling theorem. The complex reflected and transmitted amplitudes are calculated for each RCWA plane wave. The distribution of the fields along the grating for the reflected and transmitted waves is determined using inverse Fourier transform. The powers of the reflected and transmitted waves are determined based on these distributions. Our method shows that the energy conservation law is satisfied for the phase grating. That is, the power of the incident Gaussian beam is equal to the sum of the powers of the reflected and transmitted beams. It is demonstration of our approach correctness. The numerous studies have shown that the spatial shapes of the reflected and transmitted beams differ from the Gaussian beam under resonance. In additional, the waveguide mode appears also in the grating. The spatial forms of the reflected and transmitted beams are Gaussian in the absence of resonance. It was found that the width of the resonance curves is wider for the Gaussian beam than for the plane wave. However, the spectral and angular sensitivities are the same as for the plane wave. The resonant wavelengths are slightly different for the plane wave and the Gaussian beam. Numerical calculations for four refractive index modulation coefficients of the grating medium were carried out by the proposed method. The widths of the resonance curves decrease with the increasing in the refractive index modulation. Moreover, the reflection coefficient also increases.

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Fichtner, Horst, and S. Ranga Sreenivasan. "Exact algebraic dispersion relations for wave propagation in hot magnetized plasmas." Journal of Plasma Physics 49, no. 1 (February 1993): 101–23. http://dx.doi.org/10.1017/s0022377800016858.

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A new model is presented for the treatment of wave propagation along an external magnetic field in a hot collisionless plasma. The analysis is based on the so-called polynomial distribution functions along the magnetic field, and takes account of enhanced fractions of high-energy particles, which are characteristic of rarefied and magnetized astrophysical plasmas, in comparison with the bi-Maxwellian distributions. These new distributions permit the derivation of general dispersion relations that are exactly valid for waves with Im (ω) > 0, and represent good approximations for those with Im (ω) > 0. Furthermore, the explicit form of the dispersion relations is shown to be valid for distribution functions of different shapes. Because of their algebraic structure, the solution of the dispersion relations can be shown to be equivalent to the determination of the roots of complex-valued polynomials. The cold plasma, the Maxwellian plasma and the so-called quasi-Maxwellian plasma appear in this formalism as asymptotic and special cases. The reliability of the model is demonstrated with the calculation of dispersion curves, growth and damping rates for several standard modes, and by comparing it with previous calculations carried out using explicit Maxwellian distributions. Finally, the tendency of the solar wind to generate ion-cyclotron waves is investigated as a first, new application.

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Pessen, Helmut, Thomas F. Kumosinski, and Harold M. Farrell. "Small-angle X-ray scattering investigation of the micellar and submicellar forms of bovine casein." Journal of Dairy Research 56, no. 3 (May 1989): 443–51. http://dx.doi.org/10.1017/s0022029900028922.

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SummarySmall-angle X-ray scattering was performed on whole casein under submicellar (Ca2+ removed) and micellar (Ca2+ re-added) conditions. Submicellar scattering curves showed two Gaussian components which were interpreted in terms of a spherical particle with two concentric regions of different electron density, a relatively compact core of higher electron density and a looser shell. Normalized scattering curves and calculated distance distribution functions were consistent with this picture. Micellar scattering data, which can yield only cross-sectional information related to a window of scattered intensities, could be analysed by a sum of three Gaussians with no residual function. The two Gaussians with the lower radii of gyration were again taken to indicate the two concentric regions of different electron density of inhomogeneous spherical particles; the third Gaussian was shown to reflect the packing number of these particles within a cross-sectional portion of the micelle, which was 3:1 for this system. These results are a strong indication that submicellar inhomogeneous particles containing hydrophobically stabilized inner cores exist within the colloidal micelle.

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Journal articles on the topic 'Curves, Algebraic. Gaussian distribution'

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