Beura, Shradhananda; Majhi, Banshidhar; Dash, Ratnakar; Roy, Susnata
2015-04-01
An efficient approach for classification of mammograms for detection of breast cancer is presented. The approach utilises the two-dimensional discrete orthonormal S-transform (DOST) to extract the coefficients from the digital mammograms. A feature selection algorithm based the on null-hypothesis test with statistical 'two-sample t-test' method has been suggested to select most significant coefficients from a large number of DOST coefficients. The selected coefficients are used as features in the classification of mammographic images as benign or malignant. This scheme utilises an AdaBoost algorithm with random forest as its base classifier. Two standard databases Mammographic Image Analysis Society (MIAS) and Digital Database for Screening Mammography (DDSM) are used for the validation of the proposed scheme. Simulation results show an optimal classification performance with respect to accuracies of 98.3 and 98.8% and AUC (receiver operating characteristic) values of 0.9985 and 0.9992 for MIAS and DDSM, respectively. Comparative analysis shows that the proposed scheme outperforms its competent schemes. PMID:26609404
Majhi, Banshidhar; Dash, Ratnakar; Roy, Susnata
2015-01-01
An efficient approach for classification of mammograms for detection of breast cancer is presented. The approach utilises the two-dimensional discrete orthonormal S-transform (DOST) to extract the coefficients from the digital mammograms. A feature selection algorithm based the on null-hypothesis test with statistical ‘two-sample t-test’ method has been suggested to select most significant coefficients from a large number of DOST coefficients. The selected coefficients are used as features in the classification of mammographic images as benign or malignant. This scheme utilises an AdaBoost algorithm with random forest as its base classifier. Two standard databases Mammographic Image Analysis Society (MIAS) and Digital Database for Screening Mammography (DDSM) are used for the validation of the proposed scheme. Simulation results show an optimal classification performance with respect to accuracies of 98.3 and 98.8% and AUC (receiver operating characteristic) values of 0.9985 and 0.9992 for MIAS and DDSM, respectively. Comparative analysis shows that the proposed scheme outperforms its competent schemes. PMID:26609404
Symmetric Discrete Orthonormal Stockwell Transform
NASA Astrophysics Data System (ADS)
Wang, Yanwei; Orchard, Jeff
2008-09-01
The Stockwell Transform (ST) is a time-frequency signal decomposition that is gaining in popularity, likely because of its direct relation with the Fourier Transform (FT). A discrete and non-redundant version of the ST, denoted the Discrete Orthonormal Stockwell Transform (DOST), has made the use of the ST more feasible. However, the matrix multiplication required by the DOST can still be a formidable computation, especially for high-dimensional data. Moreover, the symmetric property of the ST and FT is not present in the DOST. In this paper, we investigate a new Symmetric Discrete Orthonormal Stockwell Transform (SDOST) that still keeps the non-redundant multiresolution features of the DOST, while maintaining a symmetry property similar to that of the FT. First, we give a brief introduction for the ST and the DOST. Then we analyze the DOST coefficients and modify the transform to get a symmetric version. A small experiment shows that the SDOST has kept the abilities of the DOST and demonstrates the advantage of symmetry when applying the SDOST.
Local distinguishability of generic unentangled orthonormal bases
NASA Astrophysics Data System (ADS)
Lebl, Jiří; Shakeel, Asif; Wallach, Nolan
2016-01-01
An orthonormal basis consisting of unentangled (pure tensor) elements in a tensor product of Hilbert spaces is an unentangled orthonormal basis (UOB). In general, for n qubits, we prove that in its natural structure as a real variety, the space of UOB is a bouquet of products of Riemann spheres parametrized by a class of edge colorings of hypercubes. Its irreducible components of maximum dimension are products of 2n-1 two spheres. Using a theorem of Walgate and Hardy, we observe that the UOB whose elements are distinguishable by local operations and classical communication (called locally distinguishable or LOCC distinguishable UOB) are exactly those in the maximum dimensional components. Bennett et al. [Phys. Rev. A 59, 1070 (1999)., 10.1103/PhysRevA.59.1070], in their in-depth study of quantum nonlocality without entanglement, include a specific three-qubit example UOB which is not LOCC distinguishable; we construct certain generalized counterparts of this UOB in n qubits.
Approximation and compression with sparse orthonormal transforms.
Sezer, Osman Gokhan; Guleryuz, Onur G; Altunbasak, Yucel
2015-08-01
We propose a new transform design method that targets the generation of compression-optimized transforms for next-generation multimedia applications. The fundamental idea behind transform compression is to exploit regularity within signals such that redundancy is minimized subject to a fidelity cost. Multimedia signals, in particular images and video, are well known to contain a diverse set of localized structures, leading to many different types of regularity and to nonstationary signal statistics. The proposed method designs sparse orthonormal transforms (SOTs) that automatically exploit regularity over different signal structures and provides an adaptation method that determines the best representation over localized regions. Unlike earlier work that is motivated by linear approximation constructs and model-based designs that are limited to specific types of signal regularity, our work uses general nonlinear approximation ideas and a data-driven setup to significantly broaden its reach. We show that our SOT designs provide a safe and principled extension of the Karhunen-Loeve transform (KLT) by reducing to the KLT on Gaussian processes and by automatically exploiting non-Gaussian statistics to significantly improve over the KLT on more general processes. We provide an algebraic optimization framework that generates optimized designs for any desired transform structure (multiresolution, block, lapped, and so on) with significantly better n -term approximation performance. For each structure, we propose a new prototype codec and test over a database of images. Simulation results show consistent increase in compression and approximation performance compared with conventional methods. PMID:25823033
A family of orthonormal wavelet bases with dilation factor 4
NASA Astrophysics Data System (ADS)
Karoui, Abderrazek
2006-05-01
In this paper, we study a method for the construction of orthonormal wavelet bases with dilation factor 4. More precisely, for any integer M>0, we construct an orthonormal scaling filter mM([xi]) that generates a mother scaling function [phi]M, associated with the dilation factor 4. The computation of the different coefficients of mM([xi])2 is done by the use of a simple iterative method. Also, this work shows how this construction method provides us with a whole family of compactly supported orthonormal wavelet bases with arbitrary high regularity. A first estimate of [alpha](M), the asymptotic regularity of [phi]M is given by [alpha](M)~0.25M. Examples are provided to illustrate the results of this work.
Orthonormal filters for identification in active control systems
NASA Astrophysics Data System (ADS)
Mayer, Dirk
2015-12-01
Many active noise and vibration control systems require models of the control paths. When the controlled system changes slightly over time, adaptive digital filters for the identification of the models are useful. This paper aims at the investigation of a special class of adaptive digital filters: orthonormal filter banks possess the robust and simple adaptation of the widely applied finite impulse response (FIR) filters, but at a lower model order, which is important when considering implementation on embedded systems. However, the filter banks require prior knowledge about the resonance frequencies and damping of the structure. This knowledge can be supposed to be of limited precision, since in many practical systems, uncertainties in the structural parameters exist. In this work, a procedure using a number of training systems to find the fixed parameters for the filter banks is applied. The effect of uncertainties in the prior knowledge on the model error is examined both with a basic example and in an experiment. Furthermore, the possibilities to compensate for the imprecise prior knowledge by a higher filter order are investigated. Also comparisons with FIR filters are implemented in order to assess the possible advantages of the orthonormal filter banks. Numerical and experimental investigations show that significantly lower computational effort can be reached by the filter banks under certain conditions.
Zhao, Chunyu; Burge, James H
2013-12-16
Zernike polynomials are an orthonormal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. In optical testing, slope or curvature of a surface or wavefront is sometimes measured instead, from which the surface or wavefront map is obtained. Previously we derived an orthonormal set of vector polynomials that fit to slope measurement data and yield the surface or wavefront map represented by Zernike polynomials. Here we define a 3-element curvature vector used to represent the second derivatives of a continuous surface, and derive a set of orthonormal curvature basis functions that are written in terms of Zernike polynomials. We call the new curvature functions the C polynomials. Closed form relations for the complete basis set are provided, and we show how to determine Zernike surface coefficients from the curvature data as represented by the C polynomials. PMID:24514717
Orthonormal mode sets for the two-dimensional fractional Fourier transformation.
Alieva, Tatiana; Bastiaans, Martin J
2007-05-15
A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre-Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincaré sphere are studied. PMID:17440542
PAC learning using Nadaraya-Watson estimator based on orthonormal systems
Qiao, Hongzhu; Rao, N.S.V.; Protopopescu, V.
1997-08-01
Regression or function classes of Euclidean type with compact support and certain smoothness properties are shown to be PAC learnable by the Nadaraya-Watson estimator based on complete orthonormal systems. While requiring more smoothness properties than typical PAC formulations, this estimator is computationally efficient, easy to implement, and known to perform well in a number of practical applications. The sample sizes necessary for PAC learning of regressions or functions under sup norm cost are derived for a general orthonormal system. The result covers the widely used estimators based on Haar wavelets, trignometric functions, and Daubechies wavelets.
An Automatic Orthonormalization Method for Solving Stiff Boundary-Value Problems
NASA Astrophysics Data System (ADS)
Davey, A.
1983-08-01
A new initial-value method is described, based on a remark by Drury, for solving stiff linear differential two-point cigenvalue and boundary-value problems. The method is extremely reliable, it is especially suitable for high-order differential systems, and it is capable of accommodating realms of stiffness which other methods cannot reach. The key idea behind the method is to decompose the stiff differential operator into two non-stiff operators, one of which is nonlinear. The nonlinear one is specially chosen so that it advances an orthonormal frame, indeed the method is essentially a kind of automatic orthonormalization; the second is auxiliary but it is needed to determine the required function. The usefulness of the method is demonstrated by calculating some eigenfunctions for an Orr-Sommerfeld problem when the Reynolds number is as large as 10°.
Error estimates of Lagrange interpolation and orthonormal expansions for Freud weights
NASA Astrophysics Data System (ADS)
Kwon, K. H.; Lee, D. W.
2001-08-01
Let Sn[f] be the nth partial sum of the orthonormal polynomials expansion with respect to a Freud weight. Then we obtain sufficient conditions for the boundedness of Sn[f] and discuss the speed of the convergence of Sn[f] in weighted Lp space. We also find sufficient conditions for the boundedness of the Lagrange interpolation polynomial Ln[f], whose nodal points are the zeros of orthonormal polynomials with respect to a Freud weight. In particular, if W(x)=e-(1/2)x2 is the Hermite weight function, then we obtain sufficient conditions for the inequalities to hold:andwhere and k=0,1,2...,r.
Ultrasonic flaw detection using threshold modified S-transform.
Benammar, Abdessalem; Drai, Redouane; Guessoum, Abderrezak
2014-02-01
Interference noising originating from the ultrasonic testing defect signal seriously influences the accuracy of the signal extraction and defect location. Time-frequency analysis methods are mainly used to improve the defects detection resolution. In fact, the S-transform, a hybrid of the Short time Fourier transform (STFT) and wavelet transform (WT), has a time frequency resolution which is far from ideal. In this paper, a new modified S-transform based on thresholding technique, which offers a better time frequency resolution compared to the original S-transform is proposed. The improvement is achieved by the introduction of a new scaling rule for the Gaussian window used in S-transform. Simulation results are presented and show correct time frequency information of multiple Gaussian echoes under low signal-to-noise ratio (SNR) environment. In addition, experimental results demonstrate better and reliable detection of close echoes drowned in the noise. PMID:24120270
NASA Astrophysics Data System (ADS)
Ma, Jun; Parhi, Keshab K.; Hekstra, Gerben J.; Deprettere, Ed F. A.
1998-10-01
CORDIC based IIR digital filters are orthogonal filters whose internal computations consist of orthogonal transformations. These filters possess desirable properties for VLSI implementations such as regularity, local connection, low sensitivity to finite word-length implementation, and elimination of limit cycles. Recently, fine-grain pipelined CORDIC based IIR digital filter architectures which can perform the filtering operations at arbitrarily high sample rates at the cost of linear increase in hardware complexity have been developed. These pipelined architectures consists of only Givens rotations and a few additions which can be mapped onto CORDIC arithmetic based processors. However, in practical applications, implementations of GIvens rotations using traditional CORDIC arithmetic are quite expensive. For example, for 16 bit accuracy, using floating point data format with 16 bit mantissa and 5 bit exponent, it will require approximately 20 pairs of shift-add operations for one Givens rotation. In this paper, we propose an efficient implementation of pipelined CORDIC based IIR digital filters based on fast orthonormal (mu) -rotations. Using this method, the Givens rotations are approximated by angel corresponding to orthonormal (mu) -rotations, which are based on the idea of CORDIC and can perform rotation with minimal number of shift-add operations. We present various methods of construction for such orthonormal (mu) -rotations. A significant reduction of the number of required shift-add operations is achieved. All types of fast rotations can be implemented as a cascade of only four basic types of shift-add stages. These stages can be executed on a modified floating-point CORDIC architecture, making the pipelined filter highly suitable for VLSI implementations.
Takagi-Sugeno fuzzy models in the framework of orthonormal basis functions.
Machado, Jeremias B; Campello, Ricardo J G B; Amaral, Wagner Caradori
2013-06-01
An approach to obtain Takagi-Sugeno (TS) fuzzy models of nonlinear dynamic systems using the framework of orthonormal basis functions (OBFs) is presented in this paper. This approach is based on an architecture in which local linear models with ladder-structured generalized OBFs (GOBFs) constitute the fuzzy rule consequents and the outputs of the corresponding GOBF filters are input variables for the rule antecedents. The resulting GOBF-TS model is characterized by having only real-valued parameters that do not depend on any user specification about particular types of functions to be used in the orthonormal basis. The fuzzy rules of the model are initially obtained by means of a well-known technique based on fuzzy clustering and least squares. Those rules are then simplified, and the model parameters (GOBF poles, GOBF expansion coefficients, and fuzzy membership functions) are subsequently adjusted by using a nonlinear optimization algorithm. The exact gradients of an error functional with respect to the parameters to be optimized are computed analytically. Those gradients provide exact search directions for the optimization process, which relies solely on input-output data measured from the system to be modeled. An example is presented to illustrate the performance of this approach in the modeling of a complex nonlinear dynamic system. PMID:23096073
Analytical Derivation of Row-Orthonormal Hyperspherical Harmonics for Triatomic Systems
NASA Astrophysics Data System (ADS)
Wang, Desheng; Kuppermann, Aron
2009-12-01
Hyperspherical harmonics for triatomic systems as functions of row-orthonormal hyperspherical coordinates, (also called democratic hyperspherical harmonics) are obtained explicitly in terms of Jacobi polynomials and trigonometeric functions. These harmonics are regular at the poles of the triatomic kinetic energy operator, are complete, and are not highly oscillatory. They constitute an excellent basis set for calculating the local hyperspherical surface functions in the strong interaction region of nuclear configuration space. This basis set is, in addition, numerically very efficient and should permit benchmark-quality calculations of state-to-state differential and integral cross sections for those systems. The approach used for their derivation is new and should be applicable to systems of more than three atoms.
Statistical denoising of signals in the S-transform domain
NASA Astrophysics Data System (ADS)
Weishi, Man; Jinghuai, Gao
2009-06-01
In this paper, the denoising of stochastic noise in the S-transform (ST) and generalized S-transform (GST) domains is discussed. First, the mean power spectrum (MPS) of white noise is derived in the ST and GST domains. The results show that the MPS varies linearly with the frequency in the ST and GST domains (with a Gaussian window). Second, the local power spectrum (LPS) of red noise is studied by employing the Monte Carlo method in the two domains. The results suggest that the LPS of Gaussian red noise can be transformed into a chi-square distribution with two degrees of freedom. On the basis of the difference between the LPS distribution of signals and noise, a denoising method is presented through hypothesis testing. The effectiveness of the method is confirmed by testing synthetic seismic data and a chirp signal.
Ocean Domains and Maximum Degree of Spherical Harmonic and Orthonormal Expansions
NASA Technical Reports Server (NTRS)
Rapp, R.
1999-01-01
Ocean domains used for the orthonormal (ON) systems are studied to determine the maximum degree of spherical harmonic and orthonormal expansions that can be constructed. Although it was shown that one domain was restricted to degree 24, others were shown could be constructed to determine expansions to at least degree 36. Since 1991 the maximum degree expansion used for several Ohio State studies has been 24. In this report it is shown that the maximum degree for the ocean domain used by Wang and Rapp [1994] was 32 and 29 for the domain used by Rapp, Zhang, Yi [1996]. A modification of the former domain was developed (D1e) that enabled a solution to degree 36 to be determined. A modification of the Rapp, Zhang, Yi domain (D7d) enabled a degree 30 solution to be made. Combination coefficients were developed for domain D1e, to degree 36, and to degree 30 for domain D7d. The degree 30 spherical harmonic expansion provided by Pavlis [1998] of the POCM_4B dynamic ocean topography (DOT), and the degree 30 part of the degree 360 expansion [Rapp. 1998] of the POCM_4B model was converted to an ON expansion valid for the D7d domain. The degree 36 part of the degree 360 expansion was converted to the ON expansion for the D1e domain. The square root of the degree variances of the various solutions were compared. The root mean square value of DOT from the Pai,lis expansion, after conversion to the ON system, was + or - 66.52 cm (D7d domain). The value from the degree 30 part of the 360 expansion was + or - 66.65 cm. The value based on the actual POCM-4B data, in the D7d domain, was + or - 66.74 cm showing excellent agreement with the ON results. If the spherical harmonic coefficients had been used the implied root mean square value was + or - 60.76 cm [Pavlis] and + or -59.70 cm [Rapp].
On representing rotations by Rodrigues parameters in non-orthonormal reference systems.
Morawiec, A
2016-09-01
A Rodrigues vector is a triplet of real numbers used for parameterizing rotations or orientations in three-dimensional space. Because of its properties (e.g. simplicity of fundamental regions for misorientations) this parameterization is frequently applied in analysis of orientation maps of polycrystalline materials. By conventional definition, the Rodrigues parameters are specified in orthonormal coordinate systems, whereas the bases of crystal lattices are generally non-orthogonal. Therefore, the definition of Rodrigues parameters is extended so they can be directly linked to non-Cartesian bases of a crystal. The new parameters are co- or contravariant components of vectors specified with respect to the same basis as atomic positions in a unit cell. The generalized formalism allows for redundant crystallographic axes. The formulas for rotation composition and the relationship to the rotation matrix are similar to those used in the Cartesian case, but they have a wider range of applicability: calculations can be performed with an arbitrary metric tensor of the crystal lattice. The parameterization in oblique coordinate frames of lattices is convenient for crystallographic applications because the generalized parameters are directly related to indices of rotation-invariant lattice directions and rotation-invariant lattice planes. PMID:27580203
On the decoding of intracranial data using sparse orthonormalized partial least squares
NASA Astrophysics Data System (ADS)
van Gerven, Marcel A. J.; Chao, Zenas C.; Heskes, Tom
2012-04-01
It has recently been shown that robust decoding of motor output from electrocorticogram signals in monkeys over prolonged periods of time has become feasible (Chao et al 2010 Front. Neuroeng. 3 1-10 ). In order to achieve these results, multivariate partial least-squares (PLS) regression was used. PLS uses a set of latent variables, referred to as components, to model the relationship between the input and the output data and is known to handle high-dimensional and possibly strongly correlated inputs and outputs well. We developed a new decoding method called sparse orthonormalized partial least squares (SOPLS) which was tested on a subset of the data used in Chao et al (2010) (freely obtainable from neurotycho.org (Nagasaka et al 2011 PLoS ONE 6 e22561)). We show that SOPLS reaches the same decoding performance as PLS using just two sparse components which can each be interpreted as encoding particular combinations of motor parameters. Furthermore, the sparse solution afforded by the SOPLS model allowed us to show the functional involvement of beta and gamma band responses in premotor and motor cortex for predicting the first component. Based on the literature, we conjecture that this first component is involved in the encoding of movement direction. Hence, the sparse and compact representation afforded by the SOPLS model facilitates interpretation of which spectral, spatial and temporal components are involved in successful decoding. These advantages make the proposed decoding method an important new tool in neuroprosthetics.
Du, Hubing; Gao, Honghong
2016-08-20
Affected by the height dependent effects, the phase-shifting shadow moiré can only be implemented in an approximate way. In the technique, a fixed phase step around π/2 rad between two adjacent frames is usually introduced by a grating translation in its own plane. So the method is not flexible in some situations. Additionally, because the shadow moiré fringes have a complex intensity distribution, computing the introduced phase shift from the existing arccosine function or arcsine function-based phase shift extraction algorithm always exhibits instability. To solve it, we developed a Gram-Schmidt orthonormalization approach based on a three-frame self-calibration phase-shifting algorithm with equal but unknown phase steps. The proposed method using the arctangent function is fast and can be implemented robustly in many applications. We also do optical experiments to demonstrate the correction of the proposed method by referring to the result of the conventional five-step phase-shifting shadow moiré. The results show the correctness of the proposed method. PMID:27556993
The gradient of potential vorticity, quaternions and an orthonormal frame for fluid particles
NASA Astrophysics Data System (ADS)
Gibbon, J. D.; Holm, D. D.
2011-04-01
The gradient of potential vorticity (PV) is an important quantity because of the way PV (denoted as $q$) tends to accumulate locally in the oceans and atmospheres. Recent analysis by the authors has shown that the vector quantity $\\bdB = \\bnabla q\\times \\bnabla\\theta$ for the three-dimensional incompressible rotating Euler equations evolves according to the same stretching equation as for $\\bom$ the vorticity and $\\bB$, the magnetic field in magnetohydrodynamics (MHD). The $\\bdB$-vector therefore acts like the vorticity $\\bom$ in Euler's equations and the $\\bB$-field in MHD. For example, it allows various analogies, such as stretching dynamics, helicity, superhelicity and cross helicity. In addition, using quaternionic analysis, the dynamics of the $\\bdB$-vector naturally allow the construction of an orthonormal frame attached to fluid particles\\,; this is designated as a quaternion frame. The alignment dynamics of this frame are particularly relevant to the three-axis rotations that particles undergo as they traverse regions of a flow when the PV gradient $\\bnabla q$ is large.
Lu, Yuzhen; Li, Richard; Lu, Renfu
2016-09-01
Structured illumination using sinusoidal patterns has been used for optical imaging of biological tissues in biomedical research, and of horticultural products in food quality evaluation. Implementation of structured-illumination imaging relies on retrieval of amplitude images, which is conventionally achieved by a phase-shifting technique that requires collecting a minimum of three phase-shifted images. In this study, we have proposed Gram-Schmidt orthonormalization (GSO) to retrieve amplitude component (AC) images using only two phase-shifted images. We have proposed two forms of GSO implementation, and prior to GSO processing, we eliminated the direct component (DC) background by subtracting a DC image we recovered using a spiral phase function (SPF) in the Fourier space. We demonstrated the GSO methods through numerical simulations and application examples of detection of bruise defects in apples by structured-illumination reflectance imaging (SIRI). GSO performed comparably to conventional three-phase-based demodulation. It is simple, fast and effective for amplitude retrieval and requires no prior phase information, which could facilitate fast implementation of structured-illumination imaging. PMID:27607260
On the L^p_\\mu-strong property of orthonormal systems
NASA Astrophysics Data System (ADS)
Grigorian, M. G.
2003-10-01
Let \\{\\varphi_n(x)\\} be a system of bounded functions complete and orthonormal in L^2_{ \\lbrack 0,1 \\rbrack } and assume that \\Vert\\varphi_n\\Vert _{p_0}\\leqslant\\mathrm{const}, n\\geqslant 1, for some p_0>2. Then the elements of the system can be rearranged so that the resulting system has the L^p_\\mu-strong property: for each \\varepsilon>0 there exists a (measurable) subset E\\subset \\lbrack 0,1 \\rbrack of measure \\vert E\\vert>1-\\varepsilon and a measurable function \\mu(x), 0<\\mu(x)\\leqslant 1, \\mu(x)=1 on E such that for all p>2 and f(x)\\in L^p_\\mu \\lbrack 0,1 \\rbrack one can find a function g(x)\\in L^1_{ \\lbrack 0,1 \\rbrack } coinciding with f(x) on E such that its Fourier series in the system \\{\\varphi_{\\sigma(k)}(x)\\} converges to g(x) in the L^p_\\mu \\lbrack 0,1 \\rbrack -norm and the sequence of Fourier coefficients of this function belongs to all spaces l^q, q>2.
Homogeneous hierarchies: A discrete analogue to the wavelet-based multiresolution approximation
Mirkin, B.
1996-12-31
A correspondence between discrete binary hierarchies and some orthonormal bases of the n-dimensional Euclidean space can be applied to such problems as clustering, ordering, identifying/testing in very large data bases, or multiresolution image/signal processing. The latter issue is considered in the paper. The binary hierarchy based multiresolution theory is expected to lead to effective methods for data processing because of relaxing the regularity restrictions of the classical theory.
Distributed mean curvature on a discrete manifold for Regge calculus
NASA Astrophysics Data System (ADS)
Conboye, Rory; Miller, Warner A.; Ray, Shannon
2015-09-01
The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector.
Edwards, Lloyd J.; Simpson, Sean L.
2014-01-01
Background The use of 24-hour ambulatory blood pressure monitoring (ABPM) in clinical practice and observational epidemiological studies has grown considerably in the past 25 years. ABPM is a very effective technique for assessing biological, environmental, and drug effects on blood pressure. Objectives In order to enhance the effectiveness of ABPM for clinical and observational research studies via analytical and graphical results, developing alternative data analysis approaches using modern statistical techniques are important. Methods The linear mixed model for the analysis of longitudinal data is particularly well-suited for the estimation of, inference about, and interpretation of both population (mean) and subject-specific trajectories for ABPM data. We propose using a linear mixed model with orthonormal polynomials across time in both the fixed and random effects to analyze ABPM data. Results We demonstrate the proposed analysis technique using data from the Dietary Approaches to Stop Hypertension (DASH) study, a multicenter, randomized, parallel arm feeding study that tested the effects of dietary patterns on blood pressure. Conclusions The linear mixed model is relatively easy to implement (given the complexity of the technique) using available software, allows for straight-forward testing of multiple hypotheses, and the results can be presented to research clinicians using both graphical and tabular displays. Using orthonormal polynomials provides the ability to model the nonlinear trajectories of each subject with the same complexity as the mean model (fixed effects). PMID:24667908
NASA Astrophysics Data System (ADS)
Lee, Hanshin; Hart, Michael; Hill, Gary J.; Rafal, Marc D.
2010-07-01
Wavefront sensing (WFS) is one of the key elements for active alignment of the new Wide-Field Corrector (WFC), as it tracks sidereal motion, with respect to the fixed Hobby-Eberly Telescope (HET) primary mirror. During a track, part of the 10m-pupil of the WFC can lie outside the primary periphery and be clipped off. An additional field-dependent central obscuration by the holes and baffles of the WFC leads to complex pupil geometries. The combination of these is a complicated dynamically varying non-circular telescope pupil. This unique problem to the WFS on the HET needs to be dealt with by choosing an appropriate set of orthonormal aberration polynomials during wavefront reconstruction. In this paper, three ways of computing orthonormal aberration polynomials and their coefficients are discussed. These are based on the Gram-Schmidt (GS) process, but differ in the way of computing key integrals during the GS process. The first method analytically computes the integrals, where a computer algebra program is used. The second uses the Gaussian quadrature over triangulated pupil geometries that approximate the true pupil shape. The last uses indirect numerical estimates of the integrals, which turned out to be natural by-products of the usual least-square Zernike polynomials fit. It is shown that the first method is limited to cases of simple pupil shapes, while the second can be applied to more general pupil shapes. However, when dealing with complicated dynamically varying non-circular pupils, the last method can be vastly more efficient than the second and enables the possibility of estimating orthonormal aberration coefficient on the fly. Also noticed is that the last method naturally takes into account the pixelation effect of pupil geometries due to pixel-based imaging sensors (e.g. CCDs). With these benefits, the last method can be used as a viable tool in real-time wavefront analysis over dynamically changing pupils as in the Hobby- Eberly Telescope, which is
NASA Astrophysics Data System (ADS)
Vivaldi, Franco
2015-12-01
The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.
NASA Astrophysics Data System (ADS)
Vivaldi, Franco
The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.
An asymptotic formula for polynomials orthonormal with respect to a varying weight. II
Komlov, A V; Suetin, S P
2014-09-30
This paper gives a proof of the theorem announced by the authors in the preceding paper with the same title. The theorem states that asymptotically the behaviour of the polynomials which are orthonormal with respect to the varying weight e{sup −2nQ(x)}p{sub g}(x)/√(∏{sub j=1}{sup 2p}(x−e{sub j})) coincides with the asymptotic behaviour of the Nuttall psi-function, which solves a special boundary-value problem on the relevant hyperelliptic Riemann surface of genus g=p−1. Here e{sub 1}
Application of S-transform profilometry in train wheel surface three dimensional measurement
NASA Astrophysics Data System (ADS)
Wang, Haiqing; Zhang, Yu; Li, Jinlong; Hu, Jiayuan
2015-12-01
A three dimensional (3D) measurement method for train wheel surface is proposed based on S-transform profilometry. This method is based on S-transform in fringe analysis. A fringe pattern with a carrier frequency component is projected onto the wheel tread, the deformed fringe patterns caused by the height distribution of wheel surface is recorded as an image, and the fundamental spectrum of S-transform spectra from the image is abstracted by use of weighting filters, then the wrapped phase is obtained by IFFT of the fundamental spectrum. 2D-SRNCP (sorting by reliability following a non-continuous path) phase unwrapping algorithm is used to unwrap phase, which can be used to reconstruct the surface distribution of wheel. Simulation and testing experiment is taken and the result shows that, comparing with light-section method, this method can realize a faster inspection and a higher accuracy measurement of 3D wheel surface.
ERIC Educational Resources Information Center
Ghezzi, Patrick M.
2007-01-01
The advantages of emphasizing discrete trials "teaching" over discrete trials "training" are presented first, followed by a discussion of discrete trials as a method of teaching that emerged historically--and as a matter of necessity for difficult learners such as those with autism--from discrete trials as a method for laboratory research. The…
NASA Astrophysics Data System (ADS)
Cheng, Z.; Chen, Y.; Liu, Y.; Liu, W.; Zhang, G.
2015-12-01
Among those hydrocarbon reservoir detection techniques, the time-frequency analysis based approach is one of the most widely used approaches because of its straightforward indication of low-frequency anomalies from the time-frequency maps, that is to say, the low-frequency bright spots usually indicate the potential hydrocarbon reservoirs. The time-frequency analysis based approach is easy to implement, and more importantly, is usually of high fidelity in reservoir prediction, compared with the state-of-the-art approaches, and thus is of great interest to petroleum geologists, geophysicists, and reservoir engineers. The S transform has been frequently used in obtaining the time-frequency maps because of its better performance in controlling the compromise between the time and frequency resolutions than the alternatives, such as the short-time Fourier transform, Gabor transform, and continuous wavelet transform. The window function used in the majority of previous S transform applications is the symmetric Gaussian window. However, one problem with the symmetric Gaussian window is the degradation of time resolution in the time-frequency map due to the long front taper. In our study, a bi-Gaussian S transform that substitutes the symmetric Gaussian window with an asymmetry bi-Gaussian window is proposed to analyze the multi-channel seismic data in order to predict hydrocarbon reservoirs. The bi-Gaussian window introduces asymmetry in the resultant time-frequency spectrum, with time resolution better in the front direction, as compared with the back direction. It is the first time that the bi-Gaussian S transform is used for analyzing multi-channel post-stack seismic data in order to predict hydrocarbon reservoirs since its invention in 2003. The superiority of the bi-Gaussian S transform over traditional S transform is tested on a real land seismic data example. The performance shows that the enhanced temporal resolution can help us depict more clearly the edge of the
Seizure detection approach using S-transform and singular value decomposition.
Xia, Yudan; Zhou, Weidong; Li, Chengcheng; Yuan, Qi; Geng, Shujuan
2015-11-01
Automatic seizure detection plays a significant role in the diagnosis of epilepsy. This paper presents a novel method based on S-transform and singular value decomposition (SVD) for seizure detection. Primarily, S-transform is performed on EEG signals, and the obtained time-frequency matrix is divided into submatrices. Then, the singular values of each submatrix are extracted using singular value decomposition (SVD). Effective features are constructed by adding the largest singular values in the same frequency band together and fed into Bayesian linear discriminant analysis (BLDA) classifier for decision. Finally, postprocessing is applied to obtain higher sensitivity and lower false detection rate. A total of 183.07 hours of intracranial EEG recordings containing 82 seizure events from 20 patients were used to evaluate the system. The proposed method had a sensitivity of 96.40% and a specificity of 99.01%, with a false detection rate of 0.16/h. PMID:26439656
Detection of near-surface cavities by generalized S-transform of Rayleigh waves
NASA Astrophysics Data System (ADS)
Shao, Guang-zhou; Tsoflias, George P.; Li, Chang-jiang
2016-06-01
The near-surface cavities can cause a huge hidden trouble for urban infrastructure construction, such as, foundation settlement and roadbed subsidence, and so on. So, it is an important task to detect the underground cavities effectively for many engineering projects. At the same time, because of the complexity of near-surface materials and the limited resolution of geophysical methods, detecting the location of the hidden cavities quantitatively is still a technical challenge which needs to be studied further. Base on the study of Xia et al. (Xia et al., 2007), we performed a little modification to the travel time equation for the Rayleigh-wave diffraction. We put forward another way to detect the shallow subsurface voids. The generalized S-transform was adopted to extract the arrival times of the diffracted Rayleigh waves from the near and far-offset boundaries of the void at a certain receiver. Then the arrival times were used to calculate the boundary locations of the void. Three half-space void models and a two-layered void model were used to demonstrate the feasibility and effect of detecting a void with the generalized S-transform. A rotated staggered-grid finite-difference method was adopted in wave field modeling to obtain the synthetic seismic record. Finally, a real world field data was used to verify the detecting effect. The theoretical models and the real world example showed that it is feasible and effective to use the generalized S-transform to detect the near-surface cavities.
Principles of Discrete Time Mechanics
NASA Astrophysics Data System (ADS)
Jaroszkiewicz, George
2014-04-01
1. Introduction; 2. The physics of discreteness; 3. The road to calculus; 4. Temporal discretization; 5. Discrete time dynamics architecture; 6. Some models; 7. Classical cellular automata; 8. The action sum; 9. Worked examples; 10. Lee's approach to discrete time mechanics; 11. Elliptic billiards; 12. The construction of system functions; 13. The classical discrete time oscillator; 14. Type 2 temporal discretization; 15. Intermission; 16. Discrete time quantum mechanics; 17. The quantized discrete time oscillator; 18. Path integrals; 19. Quantum encoding; 20. Discrete time classical field equations; 21. The discrete time Schrodinger equation; 22. The discrete time Klein-Gordon equation; 23. The discrete time Dirac equation; 24. Discrete time Maxwell's equations; 25. The discrete time Skyrme model; 26. Discrete time quantum field theory; 27. Interacting discrete time scalar fields; 28. Space, time and gravitation; 29. Causality and observation; 30. Concluding remarks; Appendix A. Coherent states; Appendix B. The time-dependent oscillator; Appendix C. Quaternions; Appendix D. Quantum registers; References; Index.
Intelligent Power Swing Detection Scheme to Prevent False Relay Tripping Using S-Transform
NASA Astrophysics Data System (ADS)
Mohamad, Nor Z.; Abidin, Ahmad F.; Musirin, Ismail
2014-06-01
Distance relay design is equipped with out-of-step tripping scheme to ensure correct distance relay operation during power swing. The out-of-step condition is a consequence result from unstable power swing. It requires proper detection of power swing to initiate a tripping signal followed by separation of unstable part from the entire power system. The distinguishing process of unstable swing from stable swing poses a challenging task. This paper presents an intelligent approach to detect power swing based on S-Transform signal processing tool. The proposed scheme is based on the use of S-Transform feature of active power at the distance relay measurement point. It is demonstrated that the proposed scheme is able to detect and discriminate the unstable swing from stable swing occurring in the system. To ascertain validity of the proposed scheme, simulations were carried out with the IEEE 39 bus system and its performance has been compared with the wavelet transform-based power swing detection scheme.
Weighted Averaging for Calculating Azimuthal Angles and Filtering Love Waves Using S-transforms
NASA Astrophysics Data System (ADS)
Napoli, V.; Russell, D. R.
2015-12-01
The S-transform methodology is based on Stockwell transforms, which is a form of a short Fourier transform, with a time domain transform window defined by a Gaussian function. The Gaussian function has a standard deviation equal to the frequency of interest. Applying the transform to multiple frequencies of interest results in a time/frequency spectrogram, which has the advantage of being simply invertible back to the time domain. This allows for the calculation of instantaneous frequency/time phase and amplitude measurements, which makes 2D signal filtration of surface waves possible. By solving for the transverse angle of propagation of narrow band filtered Love waves at a range of periods (8-25s) we calculate a vector of possible azimuths, one at each period. We then average over all the bands of interest to determine the mean angle of propagation. To avoid using unreliable low signal-to-noise (SNR) azimuth estimates, we use a SNR weighted average to more accurately reflect the overall signal propagation azimuth. We then use the mean signal azimuth to design a 2D Love wave rejection filter that will reject off-azimuth noise and then invert this to the time domain for an improved signal on the propagation azimuth. We apply this method to the 2009 Democratic People's Republic of Korea nuclear test. After testing the weighted averaging approach, the SNR ratio increases by a factor of 2 overall, and a signal on the transverse component is identified as a Rayleigh wave that "leaked" into the transverse component. Without this method, there could have been improper Love wave signal identification for the event. Using this innovative SNR weighted averaging technique to calculate propagation angle indicates that S-transform filters can lower the noise level by a factor of 2 or more, helping with low SNR events, and remove Rayleigh "leakage" into the transverse channel.
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Synchronous Discrete Harmonic Oscillator
Antippa, Adel F.; Dubois, Daniel M.
2008-10-17
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2{pi} in phase space, is an integral multiple N of the discrete time step {delta}t. It is fully synchronous when N is even. It is pseudo-synchronous when T/{delta}t is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is ''blue shifted'' relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval {delta}t. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
Carlsten, B.E.; Haynes, W.B.
1996-08-01
The authors theoretically and numerically investigate the operation and behavior of the discrete monotron oscillator, a novel high-power microwave source. The discrete monotron differs from conventional monotrons and transit time oscillators by shielding the electron beam from the monotron cavity`s RF fields except at two distinct locations. This makes the discrete monotron act more like a klystron than a distributed traveling wave device. As a result, the oscillator has higher efficiency and can operate with higher beam powers than other single cavity oscillators and has more stable operation without requiring a seed input signal than mildly relativistic, intense-beam klystron oscillators.
ERIC Educational Resources Information Center
Peters, James V.
2004-01-01
Using the methods of finite difference equations the discrete analogue of the parabolic and catenary cable are analysed. The fibonacci numbers and the golden ratio arise in the treatment of the catenary.
Discretizations of axisymmetric systems
NASA Astrophysics Data System (ADS)
Frauendiener, Jörg
2002-11-01
In this paper we discuss stability properties of various discretizations for axisymmetric systems including the so-called cartoon method which was proposed by Alcubierre et al. for the simulation of such systems on Cartesian grids. We show that within the context of the method of lines such discretizations tend to be unstable unless one takes care in the way individual singular terms are treated. Examples are given for the linear axisymmetric wave equation in flat space.
Dynamic deconvolution of seismic data based on generalized S-transform
NASA Astrophysics Data System (ADS)
Zhou, Huailai; Tian, Yaming; Ye, Yan
2014-09-01
The commonly used methods to improve resolution of seismic data are based on stationary convolution model that is inconsistent with the actual propagation law of seismic wavelet in inhomogeneous media. Therefore, to address this artifact, in this paper authors take seismic scattering and attenuation into integrative consideration, and propose an adaptively dynamic deconvolution method based on generalized S-transform (GST). This method introduces the favorable multi-resolution characteristics of GST into the dynamic deconvolution. Firstly, GST of nonstationary seismic trace can be approximately presented as the product of GST of the dynamic propagating wavelet and the reflectivity in time-frequency domain. We then use polynomial fitting to model the time-frequency spectra of nonstationary seismic trace to obtain the estimation of dynamic propagation wavelet and the reflectivity. This method, without calculating directly the value of Q, is applicable to the case when Q varies, and is robust in the presence of noise. Applications to synthetic and field data validate that this method can effectively enhance seismic data resolution without boosting noise, and restore the attenuated energy of nonstationary seismic signal.
NASA Astrophysics Data System (ADS)
Assous, S.; Humeau, A.; Tartas, M.; Abraham, P.; L'Huillier, J. P.
2005-05-01
Conventional signal processing typically involves frequency selective techniques which are highly inadequate for nonstationary signals. In this paper, we present an approach to perform time-frequency selective processing of laser Doppler flowmetry (LDF) signals using the S-transform. The approach is motivated by the excellent localization, in both time and frequency, afforded by the wavelet basis functions. Suitably chosen Gaussian wavelet functions are used to characterize the subspace of signals that have a given localized time-frequency support, thus enabling a time-frequency partitioning of signals. In this paper, the goal is to study the influence of various pharmacological substances taken by the oral way (celecobix (Celebrex®), indomethacin (Indocid®) and placebo) on the physiological activity behaviour. The results show that no statistical differences are observed in the energy computed from the time-frequency representation of LDF signals, for the myogenic, neurogenic and endothelial related metabolic activities between Celebrex and placebo, and Indocid and placebo. The work therefore proves that these drugs do not affect these physiological activities. For future physiological studies, there will therefore be no need to exclude patients having taken cyclo-oxygenase 1 inhibitions.
Fractional S-transform-part 2: Application to reservoir prediction and fluid identification
NASA Astrophysics Data System (ADS)
Du, Zheng-Cong; Xu, De-Ping; Zhang, Jin-Ming
2016-06-01
The fractional S-transform (FRST) has good time-frequency focusing ability. The FRST can identify geological features by rotating the fractional Fourier transform frequency (FRFTfr) axis. Different seismic signals have different optimal fractional parameters which is not conducive to multichannel seismic data processing. Thus, we first decompose the common-frequency sections by the FRST and then we analyze the low-frequency shadow. Second, the combination of the FRST and blind-source separation is used to obtain the independent spectra of the various geological features. The seismic data interpretation improves without requiring to estimating the optimal fractional parameters. The top and bottom of a limestone reservoir can be clearly recognized on the common-frequency section, thus enhancing the vertical resolution of the analysis of the low-frequency shadows compared with traditional ST. Simulations suggest that the proposed method separates the independent frequency information in the time-fractional-frequency domain. We used field seismic and well data to verify the proposed method.
A discrete fractional random transform
NASA Astrophysics Data System (ADS)
Liu, Zhengjun; Zhao, Haifa; Liu, Shutian
2005-11-01
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of the fractional Fourier transform along with some fantastic features of its own. As a primary application, the discrete fractional random transform has been used for image encryption and decryption.
Discrete Newtonian cosmology: perturbations
NASA Astrophysics Data System (ADS)
Ellis, George F. R.; Gibbons, Gary W.
2015-03-01
In a previous paper (Gibbons and Ellis 2014 Discrete Newtonian cosmology Class. Quantum Grav. 31 025003), we showed how a finite system of discrete particles interacting with each other via Newtonian gravitational attraction would lead to precisely the same dynamical equations for homothetic motion as in the case of the pressure-free Friedmann-Lemaître-Robertson-Walker cosmological models of general relativity theory, provided the distribution of particles obeys the central configuration equation. In this paper we show that one can obtain perturbed such Newtonian solutions that give the same linearized structure growth equations as in the general relativity case. We also obtain the Dmitriev-Zel’dovich equations for subsystems in this discrete gravitational model, and show how it leads to the conclusion that voids have an apparent negative mass.
NASA Astrophysics Data System (ADS)
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Discrete breathers in crystals
NASA Astrophysics Data System (ADS)
Dmitriev, S. V.; Korznikova, E. A.; Baimova, Yu A.; Velarde, M. G.
2016-05-01
It is well known that periodic discrete defect-containing systems, in addition to traveling waves, support vibrational defect-localized modes. It turned out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Since the nodes of the system are all on equal footing, it is only through the special choice of initial conditions that a group of nodes can be found on which such a mode, called a discrete breather (DB), will be excited. The DB frequency must be outside the frequency range of the small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically conserve its vibrational energy forever provided no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery in them of DBs was only a matter of time. It is well known that periodic discrete defect-containing systems support both traveling waves and vibrational defect-localized modes. It turns out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Because the nodes of the system are all on equal footing, only a special choice of the initial conditions allows selecting a group of nodes on which such a mode, called a discrete breather (DB), can be excited. The DB frequency must be outside the frequency range of small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically preserve its vibrational energy forever if no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery of DBs in them was only a matter of time. Experimental studies of DBs encounter major technical difficulties, leaving atomistic computer simulations as the primary investigation tool. Despite
ERIC Educational Resources Information Center
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
Discreteness induced extinction
NASA Astrophysics Data System (ADS)
dos Santos, Renato Vieira; da Silva, Linaena Méricy
2015-11-01
Two simple models based on ecological problems are discussed from the point of view of non-equilibrium statistical mechanics. It is shown how discrepant may be the results of the models that include spatial distribution with discrete interactions when compared with the continuous analogous models. In the continuous case we have, under certain circumstances, the population explosion. When we take into account the finiteness of the population, we get the opposite result, extinction. We will analyze how these results depend on the dimension d of the space and describe the phenomenon of the "Discreteness Inducing Extinction" (DIE). The results are interpreted in the context of the "paradox of sex", an old problem of evolutionary biology.
A paradigm for discrete physics
Noyes, H.P.; McGoveran, D.; Etter, T.; Manthey, M.J.; Gefwert, C.
1987-01-01
An example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local. Initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity.
NASA Astrophysics Data System (ADS)
Wuensche, Andrew
DDLab is interactive graphics software for creating, visualizing, and analyzing many aspects of Cellular Automata, Random Boolean Networks, and Discrete Dynamical Networks in general and studying their behavior, both from the time-series perspective — space-time patterns, and from the state-space perspective — attractor basins. DDLab is relevant to research, applications, and education in the fields of complexity, self-organization, emergent phenomena, chaos, collision-based computing, neural networks, content addressable memory, genetic regulatory networks, dynamical encryption, generative art and music, and the study of the abstract mathematical/physical/dynamical phenomena in their own right.
NASA Astrophysics Data System (ADS)
Kotulski, Zbigniew; Szczepaski, Janusz
In the paper we propose a new method of constructing cryptosystems utilising a nonpredictability property of discrete chaotic systems. We formulate the requirements for such systems to assure their safety. We also give examples of practical realisation of chaotic cryptosystems, using a generalisation of the method presented in [7]. The proposed algorithm of encryption and decryption is based on multiple iteration of a certain dynamical chaotic system. We assume that some part of the initial condition is a plain message. As the secret key we assume the system parameter(s) and additionally another part of the initial condition.
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2011-08-01
The original continuous-time ''goldfish'' dynamical system is characterized by two neat formulas, the first of which provides the N Newtonian equations of motion of this dynamical system, while the second provides the solution of the corresponding initial-value problem. Several other, more general, solvable dynamical systems ''of goldfish type'' have been identified over time, featuring, in the right-hand (''forces'') side of their Newtonian equations of motion, in addition to other contributions, a velocity-dependent term such as that appearing in the right-hand side of the first formula mentioned above. The solvable character of these models allows detailed analyses of their behavior, which in some cases is quite remarkable (for instance isochronous or asymptotically isochronous). In this paper we introduce and discuss various discrete-time dynamical systems, which are as well solvable, which also display interesting behaviors (including isochrony and asymptotic isochrony) and which reduce to dynamical systems of goldfish type in the limit when the discrete-time independent variable l=0,1,2,... becomes the standard continuous-time independent variable t, 0≤t<∞.
Fault diagnosis of rolling element bearing based on S transform and gray level co-occurrence matrix
NASA Astrophysics Data System (ADS)
Zhao, Minghang; Tang, Baoping; Tan, Qian
2015-08-01
Time-frequency analysis is an effective tool to extract machinery health information contained in non-stationary vibration signals. Various time-frequency analysis methods have been proposed and successfully applied to machinery fault diagnosis. However, little research has been done on bearing fault diagnosis using texture features extracted from time-frequency representations (TFRs), although they may contain plenty of sensitive information highly related to fault pattern. Therefore, to make full use of the textural information contained in the TFRs, this paper proposes a novel fault diagnosis method based on S transform, gray level co-occurrence matrix (GLCM) and multi-class support vector machine (Multi-SVM). Firstly, S transform is chosen to generate the TFRs due to its advantages of providing frequency-dependent resolution while keeping a direct relationship with the Fourier spectrum. Secondly, the famous GLCM-based texture features are extracted for capturing fault pattern information. Finally, as a classifier which has good discrimination and generalization abilities, Multi-SVM is used for the classification. Experimental results indicate that the GLCM-based texture features extracted from TFRs can identify bearing fault patterns accurately, and provide higher accuracies than the traditional time-domain and frequency-domain features, wavelet packet node energy or two-direction 2D linear discriminant analysis based features of the same TFRs in most cases.
NASA Astrophysics Data System (ADS)
Wang, Yuqing; Peng, Zhenming
2016-06-01
As the extension of time-bandwidth product (TBP) in the fractional domain, the generalized time-bandwidth product (GTBP) provides a rotation-independent measure of compactness. A new fractional S transform (FrST) is proposed to avoid missing the physical meaning of the fractional time-frequency plane. FrST is based on the GTBP criterion and the time-frequency rotation property of fractional Fourier transform (FrFT). In addition, we introduce the normalized second-order central moment (NSOCM) calculation method to determine the optimal order. The optimal order searching process can be converted into the NSOCM calculation. Compared with TBP search algorithms, the NSOCM approach has higher computational efficiency. The qualitative advantage of the NSOCM approach in the optimal order selection is demonstrated by a series of model tests. The optimal FrST based on NSOCM (OFrST) can produce more compact time-frequency support than the S transform. The real seismic data spectral decomposition results show that the proposed algorithm can obtain single-frequency visualization with better time-frequency concentration, thereby enhancing the precision of reservoir prediction.
Noyes, H.P. ); Starson, S. )
1991-03-01
Discrete physics, because it replaces time evolution generated by the energy operator with a global bit-string generator (program universe) and replaces fields'' with the relativistic Wheeler-Feynman action at a distance,'' allows the consistent formulation of the concept of signed gravitational charge for massive particles. The resulting prediction made by this version of the theory is that free anti-particles near the surface of the earth will fall'' up with the same acceleration that the corresponding particles fall down. So far as we can see, no current experimental information is in conflict with this prediction of our theory. The experiment crusis will be one of the anti-proton or anti-hydrogen experiments at CERN. Our prediction should be much easier to test than the small effects which those experiments are currently designed to detect or bound. 23 refs.
Discrete Sibson interpolation.
Park, Sung W; Linsen, Lars; Kreylos, Oliver; Owens, John D; Hamann, Bernd
2006-01-01
Natural-neighbor interpolation methods, such as Sibson's method, are well-known schemes for multivariate data fitting and reconstruction. Despite its many desirable properties, Sibson's method is computationally expensive and difficult to implement, especially when applied to higher-dimensional data. The main reason for both problems is the method's implementation based on a Voronoi diagram of all data points. We describe a discrete approach to evaluating Sibson's interpolant on a regular grid, based solely on finding nearest neighbors and rendering and blending d-dimensional spheres. Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional approaches, and generalizes easily to higher dimensions. For large scattered data sets, we achieve two-dimensional (2D) interpolation at interactive rates and 3D interpolation (3D) with computation times of a few seconds. PMID:16509383
Immigration and Prosecutorial Discretion
Apollonio, Dorie; Lochner, Todd; Heddens, Myriah
2015-01-01
Immigration has become an increasingly salient national issue in the US, and the Department of Justice recently increased federal efforts to prosecute immigration offenses. This shift, however, relies on the cooperation of US attorneys and their assistants. Traditionally federal prosecutors have enjoyed enormous discretion and have been responsive to local concerns. To consider how the centralized goal of immigration enforcement may have influenced federal prosecutors in regional offices, we review their prosecution of immigration offenses in California using over a decade's worth of data. Our findings suggest that although centralizing forces influence immigration prosecutions, individual US attorneys' offices retain distinct characteristics. Local factors influence federal prosecutors' behavior in different ways depending on the office. Contrary to expectations, unemployment rates did not affect prosecutors' willingness to pursue immigration offenses, nor did local popular opinion about illegal immigration. PMID:26146530
Discrete Pearson distributions
Bowman, K.O.; Shenton, L.R.; Kastenbaum, M.A.
1991-11-01
These distributions are generated by a first order recursive scheme which equates the ratio of successive probabilities to the ratio of two corresponding quadratics. The use of a linearized form of this model will produce equations in the unknowns matched by an appropriate set of moments (assumed to exist). Given the moments we may find valid solutions. These are two cases; (1) distributions defined on the non-negative integers (finite or infinite) and (2) distributions defined on negative integers as well. For (1), given the first four moments, it is possible to set this up as equations of finite or infinite degree in the probability of a zero occurrence, the sth component being a product of s ratios of linear forms in this probability in general. For (2) the equation for the zero probability is purely linear but may involve slowly converging series; here a particular case is the discrete normal. Regions of validity are being studied. 11 refs.
Discrete stability in stochastic programming
Lepp, R.
1994-12-31
In this lecture we study stability properties of stochastic programs with recourse where the probability measure is approximated by a sequence of weakly convergent discrete measures. Such discrete approximation approach gives us a possibility to analyze explicitly the behavior of the second stage correction function. The approach is based on modern functional analytical methods of an approximation of extremum problems in function spaces, especially on the notion of the discrete convergence of vectors to an essentially bounded measurable function.
Smirnov, Yu. F.; Asherova, R. M.
2011-06-15
The structure of all discrete series of unitary irreducible representations of the U{sub q}(u(3, 1)) and U{sub q}(u(n, 1)) noncompact quantum algebras are investigated with the aid of extremal projection operators and the q-analog of the Mickelsson-Zhelobenko algebra Z(g, g Prime ){sub q}. The orthonormal basis constructed in the infinite-dimensional space of irreducible representations of the U{sub q}(u(n, 1)) Superset-Of-Or-Equal-To U{sub q}(u(n)) algebra is the q-analog of the Gelfand-Graev basis in the space of the corresponding irreducible representations of the u(n, 1) Superset-Of-Or-Equal-To u(n) classical algebra.
Discrete Mathematics and Curriculum Reform.
ERIC Educational Resources Information Center
Kenney, Margaret J.
1996-01-01
Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)
Discrete Mathematics and Its Applications
ERIC Educational Resources Information Center
Oxley, Alan
2010-01-01
The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…
Huang, Z. )
1992-12-01
We examine an interesting scenario to solve the domain-wall problem recently suggested by Preskill, Trivedi, Wilczek, and Wise. The effective potential is calculated in the presence of the QCD axial anomaly. It is shown that some discrete symmetries such as {ital CP} and {ital Z}{sub 2} can be anomalous due to a so-called {ital K} term induced by instantons. We point out that the {ital Z}{sub 2} domain-wall problem in the two-doublet standard model can be resolved by two types of solutions: the {ital CP}-conserving one and the {ital CP}-breaking one. In the first case, there exist two {ital Z}{sub 2}-related local minima whose energy splitting is provided by the instanton effect. In the second case, there is only one unique vacuum so that the domain walls do not form at all. The consequences of this new source of {ital CP} violation are discussed and shown to be well within the experimental limits in weak interactions.
Discreteness inducing coexistence
NASA Astrophysics Data System (ADS)
dos Santos, Renato Vieira
2013-12-01
Consider two species that diffuse through space. Consider further that they differ only in initial densities and, possibly, in diffusion constants. Otherwise they are identical. What happens if they compete with each other in the same environment? What is the influence of the discrete nature of the interactions on the final destination? And what are the influence of diffusion and additive fluctuations corresponding to random migration and immigration of individuals? This paper aims to answer these questions for a particular competition model that incorporates intra and interspecific competition between the species. Based on mean field theory, the model has a stationary state dependent on the initial density conditions. We investigate how this initial density dependence is affected by the presence of demographic multiplicative noise and additive noise in space and time. There are three main conclusions: (1) Additive noise favors denser populations at the expense of the less dense, ratifying the competitive exclusion principle. (2) Demographic noise, on the other hand, favors less dense populations at the expense of the denser ones, inducing equal densities at the quasi-stationary state, violating the aforementioned principle. (3) The slower species always suffers the more deleterious effects of statistical fluctuations in a homogeneous medium.
Khan, M M; Varma, M P; Cleland, J; O'Kane, H O; Webb, S W; Mulholland, H C; Adgey, A A
1981-01-01
Data concerning 17 consecutive patients with discrete subaortic stenosis are recorded. Twelve patients underwent operative resection of the obstructing lesion. Of these all except one were symptomatic and all had electrocardiographic evidence of left ventricular hypertrophy or left ventricular hypertrophy with strain. They had a peak resting systolic left ventricular outflow tract gradient of greater than 50 mmHg as predicted from the combined cuff measurement of systolic blood pressure and the echocardiographically estimated left ventricular systolic pressure and/or as determined by cardiac catheterisation. The outflow tract gradient as predicted from M-mode echocardiography and peak systolic pressure showed close correlation with that measured at cardiac catheterisation or operation. During the postoperative follow-up from one month to 11 years, of 11 patients, one patient required a further operation for recurrence of the obstruction four years after the initial operation. All patients are now asymptomatic. Five patients have not had an operation. The left ventricular outflow tract gradient as assessed at the time of cardiac catheterisation was greater than 50 mmHg. One patient has been lost to follow-up. The remaining four have been followed from four to eight years and have remained asymptomatic and the electrocardiograms have remained unchanged. Careful follow-up of all patients is essential with continuing clinical assessment, electrocardiograms, M-mode and two-dimensional echocardiograms, and if necessary cardiac catheterisation. Prophylaxis against bacterial endocarditis is also essential. Images PMID:6457617
NASA Astrophysics Data System (ADS)
Zandong Sun, Sam; Sun, Xuekai; Wang, Yonggang; Xie, Huiwen
2015-10-01
Pre-stack seismic data is acknowledged to be more favorable in estimating Q values since it carries much more valuable information in traveltime and amplitude than post-stack data. However, the spectrum of reflectors can be strongly altered by nearby reflector or side lobes of the wavelet, which thereby degrades the accuracy of Q estimation based on the pre-stack spectral ratio method. To solve this problem, we propose a method based on the modified S-transform (MST) for estimating Q values from pre-stack gathers, in which Q values can be obtained with regression analysis based on the relationship between spectral ratio slope and the square of offset. Through tests on a numerical model, we first prove advantages of this pre-stack spectral ratio method compared to the traditional post-stack method. Besides, it is also shown that application of MST would lead to a much more focused intercept, which is the kernel for the pre-stack method. Therefore, the accuracy of Q estimation using MST is further improved when compared with that of conventional S-transform (ST). Based on this Q estimation method, we apply relevant processing methods (e.g. inverse Q filtering and dynamic Q migration) in practice, in order to improve imaging resolution and gathering quality with better amplitude and phase relationships. Applications on a carbonate reservoir witness remarkable enhancements of the imaging result, in which features of faults and deep strata are more clearly revealed. Moreover, pre-stack common-reflection-point (CRP) gathers obtained by dynamic Q migration well compensate the amplitude loss and correct the phase. Its ultimate pre-stack elastic inversion result better characterizes the geologic rules of complex carbonate reservoir predominated by secondary-storage-space.
Haydock’s recursive solution of self-adjoint problems. Discrete spectrum
Moroz, Alexander
2014-12-15
Haydock’s recursive solution is shown to underline a number of different concepts such as (i) quasi-exactly solvable models, (ii) exactly solvable models, (iii) three-term recurrence solutions based on Schweber’s quantization criterion in Hilbert spaces of entire analytic functions, and (iv) a discrete quantum mechanics of Odake and Sasaki. A recurrent theme of Haydock’s recursive solution is that the spectral properties of any self-adjoint problem can be mapped onto a corresponding sequence of polynomials (p{sub n}(E)) in energy variable E. The polynomials (p{sub n}(E)) are orthonormal with respect to the density of states n{sub 0}(E) and energy eigenstate |E〉 is the generating function of (p{sub n}(E)). The generality of Haydock’s recursive solution enables one to see the different concepts from a unified perspective and mutually benefiting from each other. Some results obtained within the particular framework of any of (i) to (iv) may have much broader significance.
The discrete variational derivative method based on discrete differential forms
NASA Astrophysics Data System (ADS)
Yaguchi, Takaharu; Matsuo, Takayasu; Sugihara, Masaaki
2012-05-01
As is well known, for PDEs that enjoy a conservation or dissipation property, numerical schemes that inherit this property are often advantageous in that the schemes are fairly stable and give qualitatively better numerical solutions in practice. Lately, Furihata and Matsuo have developed the so-called “discrete variational derivative method” that automatically constructs energy preserving or dissipative finite difference schemes. Although this method was originally developed on uniform meshes, the use of non-uniform meshes is of importance for multi-dimensional problems. On the other hand, the theories of discrete differential forms have received much attention recently. These theories provide a discrete analogue of the vector calculus on general meshes. In this paper, we show that the discrete variational derivative method and the discrete differential forms by Bochev and Hyman can be combined. Applications to the Cahn-Hilliard equation and the Klein-Gordon equation on triangular meshes are provided as demonstrations. We also show that the schemes for these equations are H1-stable under some assumptions. In particular, one for the nonlinear Klein-Gordon equation is obtained by combination of the energy conservation property and the discrete Poincaré inequality, which are the temporal and spacial structures that are preserved by the above methods.
Microscopic derivation of discrete hydrodynamics.
Español, Pep; Anero, Jesús G; Zúñiga, Ignacio
2009-12-28
By using the standard theory of coarse graining based on Zwanzig's projection operator, we derive the dynamic equations for discrete hydrodynamic variables. These hydrodynamic variables are defined in terms of the Delaunay triangulation. The resulting microscopically derived equations can be understood, a posteriori, as a discretization on an arbitrary irregular grid of the Navier-Stokes equations. The microscopic derivation provides a set of discrete equations that exactly conserves mass, momentum, and energy and the dissipative part of the dynamics produces strict entropy increase. In addition, the microscopic derivation provides a practical implementation of thermal fluctuations in a way that the fluctuation-dissipation theorem is satisfied exactly. This paper points toward a close connection between coarse-graining procedures from microscopic dynamics and discretization schemes for partial differential equations. PMID:20059064
Exact discretization by Fourier transforms
NASA Astrophysics Data System (ADS)
Tarasov, Vasily E.
2016-08-01
A discretization of differential and integral operators of integer and non-integer orders is suggested. New type of differences, which are represented by infinite series, is proposed. A characteristic feature of the suggested differences is an implementation of the same algebraic properties that have the operator of differentiation (property of algebraic correspondence). Therefore the suggested differences are considered as an exact discretization of derivatives. These differences have a property of universality, which means that these operators do not depend on the form of differential equations and the parameters of these equations. The suggested differences operators allows us to have difference equations whose solutions are equal to the solutions of corresponding differential equations. The exact discretization of the derivatives of integer orders is given by the suggested differences of the same integer orders. Similarly, the exact discretization of the Riesz derivatives and integrals of integer and non-integer order is given by the proposed fractional differences of the same order.
Novel approach to data discretization
NASA Astrophysics Data System (ADS)
Borowik, Grzegorz; Kowalski, Karol; Jankowski, Cezary
2015-09-01
Discretization is an important preprocessing step in data mining. The data discretization method involves determining the ranges of values for numeric attributes, which ultimately represent discrete intervals for new attributes. The ranges for the proposed set of cuts are analyzed, in order to obtain a minimal set of ranges while retaining the possibility of classification. For this purpose, a special discernibility function can be constructed as a conjunction of alternative cuts set for each pair of different objects of different decisions- cuts discern these objects. However, the data mining methods based on discernibility matrix are insufficient for large databases. The purpose of this paper is the idea of implementation of a new data discretization algorithm that is based on statistics of attribute values and that avoids building the discernibility matrix explicitly. Evaluation of time complexity has shown that the proposed method is much more efficient than currently available solutions for large data sets.
Chaos in Periodic Discrete Systems
NASA Astrophysics Data System (ADS)
Shi, Yuming; Zhang, Lijuan; Yu, Panpan; Huang, Qiuling
This paper focuses on chaos in periodic discrete systems, whose state space may vary with time. Some close relationships between some chaotic dynamical behaviors of a periodic discrete system and its autonomous induced system are given. Based on these relationships, several criteria of chaos are established and some sufficient conditions for no chaos are given for periodic discrete systems. Further, it is shown that a finite-dimensional linear periodic discrete system is not chaotic in the sense of Li-Yorke or Wiggins. In particular, an interesting problem of whether nonchaotic rules may generate a chaotic system is studied, with some examples provided, one of which surprisingly shows that a composition of globally asymptotically stable maps can be chaotic. In addition, some properties of sign pattern matrices of non-negative square matrices are given for convenience of the study.
NASA Astrophysics Data System (ADS)
Jones, J. P.; Carniel, R.; Malone, S.
2005-12-01
The time-varying properties of volcanic tremor demand advanced techniques capable of analyzing changes in both time and frequency domains. Specifically, rapid data preprocessing techniques with the ability to distinguish signal from noise are especially valuable in analyzing the temporal, spatial, and spectral properties of these signals. To this end, we use the Discrete Wavelet Packet Transform and the Best Shift Basis algorithm to select an orthonormal basis for continuous volcanic tremor data, then apply a simple statistical test to eliminate frequency bands that primarily consist of Gaussian white noise. We then use the Maximal Overlap Discrete Wavelet Packet Transform to compute and analyze features in the detail coefficients of each "signal" band. Because MODWPT detail coefficients are equivalent to a time series convolved with a zero phase filter, we apply standard polarization and amplitude-based location techniques to each frequency band's detail coefficients to analyze possible source locations and mechanisms. To demonstrate the usefulness of these techniques, we present a sample analysis of data from Erta 'Ale volcano, Ethiopia, recorded on a temporary network in November 2003. Data were sampled at 100 Hz and the DWPT was computed with the LA(16) wavelet to a maximum level of j = 7. The optimal basis for this data set consists of 54 frequency bands, but only 9 contain meaningful "signal" energy. We identify two frequency bands whose locations suggest a distributed source; three frequency bands whose signals may come from the lava lake itself; three high-frequency bands of scattered energy; and one very high frequency band of non-Gaussian instrument noise. Finally, we discuss optimization efforts, computational efficiency, and the feasibility of using similar wavelet methods to preprocess data in real time or near real time.
Nie, Xinhua; Pan, Zhongming; Zhang, Dasha; Zhou, Han; Chen, Min; Zhang, Wenna
2014-01-01
Magnetic anomaly detection (MAD) is a passive approach for detection of a ferromagnetic target, and its performance is often limited by external noises. In consideration of one major noise source is the fractal noise (or called 1/f noise) with a power spectral density of 1/fa (0orthonormal wavelet decomposition can play the role of a Karhunen-Loève-type expansion to the 1/f-type signal by its decorrelation abilities, an effective energy detection method based on undecimated discrete wavelet transform (UDWT) is proposed in this paper. Firstly, the foundations of magnetic anomaly detection and UDWT are introduced in brief, while a possible detection system based on giant magneto-impedance (GMI) magnetic sensor is also given out. Then our proposed energy detection based on UDWT is described in detail, and the probabilities of false alarm and detection for given the detection threshold in theory are presented. It is noticeable that no a priori assumptions regarding the ferromagnetic target or the magnetic noise probability are necessary for our method, and different from the discrete wavelet transform (DWT), the UDWT is shift invariant. Finally, some simulations are performed and the results show that the detection performance of our proposed detector is better than that of the conventional energy detector even utilized in the Gaussian white noise, especially when the spectral parameter α is less than 1.0. In addition, a real-world experiment was done to demonstrate the advantages of the proposed method. PMID:25343484
Analysis and design of modified window shapes for S-transform to improve time-frequency localization
NASA Astrophysics Data System (ADS)
Ma, Jianping; Jiang, Jin
2015-06-01
This paper deals with window design issues for modified S-transform (MST) to improve the performance of time-frequency analysis (TFA). After analyzing the drawbacks of existing window functions, a window design technique is proposed. The technique uses a sigmoid function to control the window width in frequency domain. By proper selection of certain tuning parameters of a sigmoid function, windows with different width profiles can be obtained for multi-component signals. It is also interesting to note that the MST algorithm can be considered as a special case of a generalized method that adds a tunable shaping function to the standard window in frequency domain to meet specific frequency localization needs. The proposed design technique has been validated on a physical vibration test system using signals with different characteristics. The results have demonstrated that the proposed MST algorithm has superior time-frequency localization capabilities over standard ST, as well as other classical TFA methods. Subsequently, the proposed MST algorithm is applied to vibration monitoring of pipes in a water supply process controlled by a diaphragm pump for fault detection purposes.
Distributed Relaxation for Conservative Discretizations
NASA Technical Reports Server (NTRS)
Diskin, Boris; Thomas, James L.
2001-01-01
A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.
Cheraghi-Sohi, Sudeh; Calnan, Michael
2013-11-01
There has much debate about the extent to which professional discretion has been challenged by recent organisational changes such as through the new forms of governance associated with the introduction of the principles of the New Public Management (NPM) into health systems and other public sector services. What appears to be missing from these debates is a detailed analysis of the concept of professional discretion itself. This paper attempts to fill this gap by delineating the key concepts of professional discretion evident in the literature and exploring their significance in an empirical study of the influence of the 2004 new general medical services contract (nGMS) and the introduction of the Quality and Outcomes Framework (QOF), a prescriptive pay-for-performance system designed to standardise the quality of care provision in general medical practice in the United Kingdom. The study adopted a longitudinal design using semi-structured interviews with general practitioners (GPs, N = 62) working in the English National Health Service (NHS) between 2007 and 2009. A multi-dimensional conception of discretion was used to explore how GP discretion might have been influenced by contractual changes and in particular, QOF. The findings suggest that through a complex interplay of factors, a post-QOF reduction in GP discretion was identifiable, highlighting different potential sources of constraint such as in the social, organisational and economic dimensions of discretion. The evidence also suggested the emergence of a new form of organisational medical professionalism within general practice characterised by standardisation, bureaucracy and performance management. PMID:24034951
ERIC Educational Resources Information Center
Langley-Weber, Terri
2012-01-01
This qualitative study examined the influences of teachers' experiences on their perceptions of teaching English language learners (ELLs) framed within Mezirow's transformative learning theory. Eight teachers ranging from pre-Kindergarten to 12th grade participated in long interviews responding to a 10 item questionnaire. Each teacher…
Geometry of discrete quantum computing
NASA Astrophysics Data System (ADS)
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
Reduced discretization error in HZETRN
Slaba, Tony C.; Blattnig, Steve R.; Tweed, John
2013-02-01
The deterministic particle transport code HZETRN is an efficient analysis tool for studying the effects of space radiation on humans, electronics, and shielding materials. In a previous work, numerical methods in the code were reviewed, and new methods were developed that further improved efficiency and reduced overall discretization error. It was also shown that the remaining discretization error could be attributed to low energy light ions (A < 4) with residual ranges smaller than the physical step-size taken by the code. Accurately resolving the spectrum of low energy light particles is important in assessing risk associated with astronaut radiation exposure. In this work, modifications to the light particle transport formalism are presented that accurately resolve the spectrum of low energy light ion target fragments. The modified formalism is shown to significantly reduce overall discretization error and allows a physical approximation to be removed. For typical step-sizes and energy grids used in HZETRN, discretization errors for the revised light particle transport algorithms are shown to be less than 4% for aluminum and water shielding thicknesses as large as 100 g/cm{sup 2} exposed to both solar particle event and galactic cosmic ray environments.
Some discrete multiple orthogonal polynomials
NASA Astrophysics Data System (ADS)
Arvesú, J.; Coussement, J.; van Assche, W.
2003-04-01
In this paper, we extend the theory of discrete orthogonal polynomials (on a linear lattice) to polynomials satisfying orthogonality conditions with respect to r positive discrete measures. First we recall the known results of the classical orthogonal polynomials of Charlier, Meixner, Kravchuk and Hahn (T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978; R. Koekoek and R.F. Swarttouw, Reports of the Faculty of Technical Mathematics and Informatics No. 98-17, Delft, 1998; A.F. Nikiforov et al., Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991). These polynomials have a lowering and raising operator, which give rise to a Rodrigues formula, a second order difference equation, and an explicit expression from which the coefficients of the three-term recurrence relation can be obtained. Then we consider r positive discrete measures and define two types of multiple orthogonal polynomials. The continuous case (Jacobi, Laguerre, Hermite, etc.) was studied by Van Assche and Coussement (J. Comput. Appl. Math. 127 (2001) 317-347) and Aptekarev et al. (Multiple orthogonal polynomials for classical weights, manuscript). The families of multiple orthogonal polynomials (of type II) that we will study have a raising operator and hence a Rodrigues formula. This will give us an explicit formula for the polynomials. Finally, there also exists a recurrence relation of order r+1 for these multiple orthogonal polynomials of type II. We compute the coefficients of the recurrence relation explicitly when r=2.
Discrete implementations of scale transform
NASA Astrophysics Data System (ADS)
Djurdjanovic, Dragan; Williams, William J.; Koh, Christopher K.
1999-11-01
Scale as a physical quantity is a recently developed concept. The scale transform can be viewed as a special case of the more general Mellin transform and its mathematical properties are very applicable in the analysis and interpretation of the signals subject to scale changes. A number of single-dimensional applications of scale concept have been made in speech analysis, processing of biological signals, machine vibration analysis and other areas. Recently, the scale transform was also applied in multi-dimensional signal processing and used for image filtering and denoising. Discrete implementation of the scale transform can be carried out using logarithmic sampling and the well-known fast Fourier transform. Nevertheless, in the case of the uniformly sampled signals, this implementation involves resampling. An algorithm not involving resampling of the uniformly sampled signals has been derived too. In this paper, a modification of the later algorithm for discrete implementation of the direct scale transform is presented. In addition, similar concept was used to improve a recently introduced discrete implementation of the inverse scale transform. Estimation of the absolute discretization errors showed that the modified algorithms have a desirable property of yielding a smaller region of possible error magnitudes. Experimental results are obtained using artificial signals as well as signals evoked from the temporomandibular joint. In addition, discrete implementations for the separable two-dimensional direct and inverse scale transforms are derived. Experiments with image restoration and scaling through two-dimensional scale domain using the novel implementation of the separable two-dimensional scale transform pair are presented.
NASA Astrophysics Data System (ADS)
Varner, R. K.; Graham, K.; Bryce, J. G.; Finkel, L.; Froburg, E.; Hale, S.; Johnson, J. E.; von Damm, K.
2009-12-01
The University of New Hampshire’s Transforming Earth System Science Education (TESSE) project is designed to enrich the education and professional development of in-service and pre-service teachers who currently teach or plan to teach Earth science curricula. A key TESSE program goal is to foster the development of middle and high school students’ Earth System Science (ESS) literacy by engaging teachers in authentic research experiences. As part of TESSE, pre-service teachers are engaged in a research immersion experience (RIE), during which they work alongside a faculty research mentor for an intensive eight week period. The chief goal of this component of the program is to provide these pre-service teachers with authentic research experiences that will sharpen their research skills by providing guidance in designing projects and in gathering and interpreting data. The RIE also includes weekly discussions on pedagogical approaches to research with students, providing a catalyst for taking these research experiences into the classroom. For in-service teachers we have developed a course: “Research Techniques in the Earth System Sciences for Teachers.” Teachers enroll in an intensive ten-day research experience during which they participate in a research cruise on the Great Bay Estuary and collect gas and water samples, measure parameters in the water column, and collect sediment cores in order to answer questions they have posed about the estuary environment. Onshore, teacher teams analyze the water and core samples for gas and trace metal content, grain size, and other sedimentological characteristics. The research experience culminates with a public poster presentation of each team's results. Throughout the experience, teachers are engaged in a variety of discussions about transferring what they have learned about doing research to their classrooms. The integration of authentic research is a key mechanism that the TESSE program uses to help teachers
NASA Astrophysics Data System (ADS)
Guo, Jiming; Zhou, Mingduan; Wang, Chao; Mei, Lianhui
2012-11-01
Based on the model of coordinate S-transformation, a novel method of stability analysis of datum points in high-precision GPS deformation monitoring networks is proposed. The model of coordinate S-transformation is used to calculate seven transformation parameters in adjacent two measurement stages, in order to confirm the stability of stations by coordinate differences. To judge the stability of stations, in comparison to the traditional method by a fixed the same datum point, the "threshold approach" and "statistical test approach" have been developed and applied to evaluate the stability of datum points of a first-order GPS deformation monitoring network of a hydropower station located in the West Region of China.
Systoles in discrete dynamical systems
NASA Astrophysics Data System (ADS)
Fernandes, Sara; Grácio, Clara; Ramos, Carlos Correia
2013-01-01
The fruitful relationship between Geometry and Graph Theory has been explored by several authors benefiting also the Theory of discrete dynamical systems seen as Markov chains in graphs. In this work we will further explore the relation between these areas, giving a geometrical interpretation of notions from dynamical systems. In particular, we relate the topological entropy with the systole, here defined in the context of discrete dynamical systems. We show that for continuous interval maps the systole is trivial; however, for the class of interval maps with one discontinuity point the systole acquires relevance from the point of view of the dynamical behavior. Moreover, we define the geodesic length spectrum associated to a Markov interval map and we compute the referred spectrum in several examples.
Dark Energy from Discrete Spacetime
Trout, Aaron D.
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies. PMID:24312502
Dark energy from discrete spacetime.
Trout, Aaron D
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies. PMID:24312502
Class of discrete Gabor expansion
NASA Astrophysics Data System (ADS)
Li, Shidong; Healy, Dennis M., Jr.
1994-03-01
We present a new approach to studying a discrete Gabor expansion (DGE). We show that, in general, DGE is not the usual biorthogonal decomposition, but belongs to a larger and looser decomposition scheme which we call pseudo frame decomposition. It includes the DGE scheme proposed as a special case. The standard dual frame decomposition is also a special case. We derive algorithms using techniques for Gabor sequences to compute 'biorthogonal' sequences through proper matrix representation. Our algorithms involve solutions to a linear system to obtain the 'biorthogonal' windows. This approach provides a much broader mathematical view of the DGE, and therefore, establishes a wider mathematical foundation towards the theory of DGE. The general algorithm derived also provides a whole class of discrete Gabor expansions, among which 'good' ones can be generated. Simulation results are also provided.
A FORTRAN Program for Discrete Discriminant Analysis
ERIC Educational Resources Information Center
Boone, James O.; Brewer, James K.
1976-01-01
A Fortran program is presented for discriminant analysis of discrete variables. The program assumes discrete, nominal data with no distributional, variance-covariance assumptions. The program handles a maximum of fifty predictor variables and twelve outcome groups. (Author/JKS)
Efficient genetic algorithms using discretization scheduling.
McLay, Laura A; Goldberg, David E
2005-01-01
In many applications of genetic algorithms, there is a tradeoff between speed and accuracy in fitness evaluations when evaluations use numerical methods with varying discretization. In these types of applications, the cost and accuracy vary from discretization errors when implicit or explicit quadrature is used to estimate the function evaluations. This paper examines discretization scheduling, or how to vary the discretization within the genetic algorithm in order to use the least amount of computation time for a solution of a desired quality. The effectiveness of discretization scheduling can be determined by comparing its computation time to the computation time of a GA using a constant discretization. There are three ingredients for the discretization scheduling: population sizing, estimated time for each function evaluation and predicted convergence time analysis. Idealized one- and two-dimensional experiments and an inverse groundwater application illustrate the computational savings to be achieved from using discretization scheduling. PMID:16156928
Anomalies and Discrete Chiral Symmetries
Creutz, M.
2009-09-07
The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.
Discrete vortex representation of magnetohydrodynamics
Kinney, R.; Tajima, T.; Petviashvili, N.; McWilliams, J.C.
1993-02-01
We present an alternative approach to statistical analysis of an intermittent ideal MHD fluid in two dimensions, based on the hydrodynamical discrete vortex model applied to the Elsasser variables. The model contains negative temperature states which predict the formation of magnetic islands, but also includes a natural limit under which the equilibrium states revert to the familiar twin-vortex states predicted by hydrodynamical turbulence theories. Numerical dynamical calculations yield equilibrium spectra in agreement with the theoretical predictions.
Discrete-contact nanowire photovoltaics
NASA Astrophysics Data System (ADS)
Chitambar, Michelle J.; Wen, Wen; Maldonado, Stephen
2013-11-01
A series of finite-element simulations have been performed to assess the operational characteristics of a new semiconductor nanowire solar cell design operating under high-level injection conditions. Specifically, the steady-state current-voltage behavior of a cylindrical silicon (Si) nanowire with a series of discrete, ohmic-selective contacts under intense sunlight illumination was investigated. The scope of the analysis was limited to only the factors that impact the net internal quantum yield for solar to electricity conversion. No evaluations were performed with regards to optical light trapping in the modeled structures. Several aspects in a discrete-contact nanowire device that could impact operation were explored, including the size and density of ohmic-selective contacts, the size of the nanowire, the electronic quality and conductivity of the nanowire, the surface defect density of the nanowire, and the type of ohmic selectivity employed at each contact. The analysis showed that there were ranges of values for each parameter that supported good to excellent photoresponses, with certain combinations of experimentally attainable material properties yielding internal energy conversion efficiencies at the thermodynamic limit for a single junction cell. The merits of the discrete-contact nanowire cell were contrasted with "conventional" nanowire photovoltaic cells featuring a uniform conformal contact and also with planar point-contact solar cells. The unique capacity of the discrete-contact nanowire solar cell design to operate at useful energy conversion efficiencies with low quality semiconductor nanowires (i.e., possessing short charge-carrier lifetimes) with only light doping is discussed. This work thus defines the impetus for future experimental work aimed at developing this photovoltaic architecture.
Interference in discrete Wigner functions
Cormick, Cecilia; Paz, Juan Pablo
2006-12-15
We analyze some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] to represent quantum states of systems with power-of-prime dimensional Hilbert spaces. We consider ''cat'' states obtained as coherent superpositions of states with positive Wigner function; for such states we show that the oscillations of the discrete Wigner function typically spread over the entire discrete phase space (including the regions where the two interfering states are localized). This is a generic property, which is in sharp contrast with the usual attributes of Wigner functions that make them useful candidates to display the existence of quantum coherence through oscillations. However, it is possible to find subsets of cat states with a natural phase-space representation, in which the oscillatory regions remain localized. We show that this can be done for interesting families of stabilizer states used in quantum error-correcting codes, and illustrate this by analyzing the phase-space representation of the five-qubit error-correcting code.
Observability of discretized partial differential equations
NASA Technical Reports Server (NTRS)
Cohn, Stephen E.; Dee, Dick P.
1988-01-01
It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.
Driven discrete time quantum walks
NASA Astrophysics Data System (ADS)
Hamilton, Craig S.; Barkhofen, Sonja; Sansoni, Linda; Jex, Igor; Silberhorn, Christine
2016-07-01
We introduce the driven discrete time quantum walk (QW), where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original QW. These dynamics have two regimes, which we illustrate using the one-dimensional line. Then, we explore a search application which has certain advantages over current search protocols, namely that it does not require a complicated initial state nor a specific measurement time to observe the marked state. Finally, we describe a potential experimental implementation using existing technology.
Discreteness effects in population dynamics
NASA Astrophysics Data System (ADS)
Guevara Hidalgo, Esteban; Lecomte, Vivien
2016-05-01
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of additive observables for stochastic processes. A method commonly used in order to determine such functions is the so-called cloning algorithm which in its non-constant population version essentially reduces to the determination of the growth rate of a population, averaged over many realizations of the dynamics. However, the averaging of populations is highly dependent not only on the number of realizations of the population dynamics, and on the initial population size but also on the cut-off time (or population) considered to stop their numerical evolution. This may result in an over-influence of discreteness effects at initial times, caused by small population size. We overcome these effects by introducing a (realization-dependent) time delay in the evolution of populations, additional to the discarding of the initial transient regime of the population growth where these discreteness effects are strong. We show that the improvement in the estimation of the large deviation function comes precisely from these two main contributions.
Observers for discrete-time nonlinear systems
NASA Astrophysics Data System (ADS)
Grossman, Walter D.
Observer synthesis for discrete-time nonlinear systems with special applications to parameter estimation is analyzed. Two new types of observers are developed. The first new observer is an adaptation of the Friedland continuous-time parameter estimator to discrete-time systems. The second observer is an adaptation of the continuous-time Gauthier observer to discrete-time systems. By adapting these observers to discrete-time continuous-time parameter estimation problems which were formerly intractable become tractable. In addition to the two newly developed observers, two observers already described in the literature are analyzed and deficiencies with respect to noise rejection are demonstrated. Improved versions of these observers are proposed and their performance demonstrated. The issues of discrete-time observability, discrete-time system inversion, and optimal probing are also addressed.
Multigrid methods for isogeometric discretization
Gahalaut, K.P.S.; Kraus, J.K.; Tomar, S.K.
2013-01-01
We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels ℓ, whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order p=4, and for C0 and Cp-1 smoothness. PMID:24511168
Multigrid methods for isogeometric discretization.
Gahalaut, K P S; Kraus, J K; Tomar, S K
2013-01-01
We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels [Formula: see text], whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order [Formula: see text], and for [Formula: see text] and [Formula: see text] smoothness. PMID:24511168
Discrete modelling of drapery systems
NASA Astrophysics Data System (ADS)
Thoeni, Klaus; Giacomini, Anna
2016-04-01
Drapery systems are an efficient and cost-effective measure in preventing and controlling rockfall hazards on rock slopes. The simplest form consists of a row of ground anchors along the top of the slope connected to a horizontal support cable from which a wire mesh is suspended down the face of the slope. Such systems are generally referred to as simple or unsecured draperies (Badger and Duffy 2012). Variations such as secured draperies, where a pattern of ground anchors is incorporated within the field of the mesh, and hybrid systems, where the upper part of an unsecured drapery is elevated to intercept rockfalls originating upslope of the installation, are becoming more and more popular. This work presents a discrete element framework for simulation of unsecured drapery systems and its variations. The numerical model is based on the classical discrete element method (DEM) and implemented into the open-source framework YADE (Šmilauer et al., 2010). The model takes all relevant interactions between block, drapery and slope into account (Thoeni et al., 2014) and was calibrated and validated based on full-scale experiments (Giacomini et al., 2012).The block is modelled as a rigid clump made of spherical particles which allows any shape to be approximated. The drapery is represented by a set of spherical particle with remote interactions. The behaviour of the remote interactions is governed by the constitutive behaviour of the wire and generally corresponds to a piecewise linear stress-strain relation (Thoeni et al., 2013). The same concept is used to model wire ropes. The rock slope is represented by rigid triangular elements where material properties (e.g., normal coefficient of restitution, friction angle) are assigned to each triangle. The capabilities of the developed model to simulate drapery systems and estimate the residual hazard involved with such systems is shown. References Badger, T.C., Duffy, J.D. (2012) Drapery systems. In: Turner, A.K., Schuster R
Classicality in discrete Wigner functions
Cormick, Cecilia; Galvao, Ernesto F.; Gottesman, Daniel; Paz, Juan Pablo; Pittenger, Arthur O.
2006-01-15
Gibbons et al., [Phys. Rev. A 70, 062101 (2004)] have recently defined discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that such a class of Wigner functions W can be defined so that the only pure states having non-negative W for all such functions are stabilizer states, as conjectured by Galvao, [Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving non-negativity of W for all definitions of W in the class form a subgroup of the Clifford group. This means pure states with non-negative W and their associated unitary dynamics are classical in the sense of admitting an efficient classical simulation scheme using the stabilizer formalism.
Determinant Expressions for Discrete Integrable Maps
NASA Astrophysics Data System (ADS)
Sogo, Kiyoshi
2006-08-01
Explicit formulas for several discrete integrable maps with periodic boundary condition are obtained, which give the sequential time developments in a form of the quotient of successive determinants of tri-diagonal matrices. We can expect that such formulas make the corresponding numerical simulations simple and stable. The cases of discrete Lotka-Volterra and discrete KdV equations are demonstrated by using the common algorithm computing determinants of tri-diagonal matrices.
A discrete event method for wave simulation
Nutaro, James J
2006-01-01
This article describes a discrete event interpretation of the finite difference time domain (FDTD) and digital wave guide network (DWN) wave simulation schemes. The discrete event method is formalized using the discrete event system specification (DEVS). The scheme is shown to have errors that are proportional to the resolution of the spatial grid. A numerical example demonstrates the relative efficiency of the scheme with respect to FDTD and DWN schemes. The potential for the discrete event scheme to reduce numerical dispersion and attenuation errors is discussed.
Scalar discrete nonlinear multipoint boundary value problems
NASA Astrophysics Data System (ADS)
Rodriguez, Jesus; Taylor, Padraic
2007-06-01
In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesus Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119-137; Debra L. Etheridge, Jesus Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127-144].
Peña, J; Solano, E; Mendoza, A; Casals, J; Planell, J A; Gil, F J
2005-01-01
The main objective of this work has been the characterisation and correlation of the wear behaviour of the NiTi shape memory alloys in their different phases. The weight losses for the different alloys in function of the present phase, and of the M(s) transformation temperature are studied. Adhesive wear tests, Pin-on-Disk, according to the ASTM-G99 standard have been carried out. The thermoelastic martensitic transformations that cause the super-elastic effect, the reorientation and coalescence of martensitic plates and the damping effect promotes a high ability to accommodate large deformations without generating permanent damages that causes the wear. The resulting plastic deformation may be accumulated during wear process without generating fracture. The results show that the wear resistance is mainly dependent of the M(s) transformation temperature for both alloys. For the NiTi alloys also the Ni atomic percentage and the hardness of the alloys are important parameters in the wear behavior. PMID:16010037
Current Density and Continuity in Discretized Models
ERIC Educational Resources Information Center
Boykin, Timothy B.; Luisier, Mathieu; Klimeck, Gerhard
2010-01-01
Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schrodinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying…
Discretization vs. Rounding Error in Euler's Method
ERIC Educational Resources Information Center
Borges, Carlos F.
2011-01-01
Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…
Discrete/PWM Ballast-Resistor Controller
NASA Technical Reports Server (NTRS)
King, Roger J.
1994-01-01
Circuit offers low switching loss and automatic compensation for failure of ballast resistor. Discrete/PWM ballast-resistor controller improved shunt voltage-regulator circuit designed to supply power from high-resistance source to low-impedance bus. Provides both coarse discrete voltage levels (by switching of ballast resistors) and continuous fine control of voltage via pulse-width modulation.
Discrete Fractional Diffusion Equation of Chaotic Order
NASA Astrophysics Data System (ADS)
Wu, Guo-Cheng; Baleanu, Dumitru; Xie, He-Ping; Zeng, Sheng-Da
Discrete fractional calculus is suggested in diffusion modeling in porous media. A variable-order fractional diffusion equation is proposed on discrete time scales. A function of the variable order is constructed by a chaotic map. The model shows some new random behaviors in comparison with other variable-order cases.
Discreteness and Gradience in Intonational Contrasts.
ERIC Educational Resources Information Center
Gussenhoven, Carlos
1999-01-01
Three experimental techniques that can be used to investigate the gradient of discrete nature of intonational differences, the semantic task, the imitation task, and the pitch range task are discussed and evaluated. It is pointed out that categorical perception is a sufficient but not a necessary, property of phonological discreteness. (Author/VWL)
Discrete breathers in graphane: Effect of temperature
NASA Astrophysics Data System (ADS)
Baimova, J. A.; Murzaev, R. T.; Lobzenko, I. P.; Dmitriev, S. V.; Zhou, Kun
2016-05-01
The discrete breathers in graphane in thermodynamic equilibrium in the temperature range 50-600 K are studied by molecular dynamics simulation. A discrete breather is a hydrogen atom vibrating along the normal to a sheet of graphane at a high amplitude. As was found earlier, the lifetime of a discrete breather at zero temperature corresponds to several tens of thousands of vibrations. The effect of temperature on the decay time of discrete breathers and the probability of their detachment from a sheet of graphane are studied in this work. It is shown that closely spaced breathers can exchange energy with each other at zero temperature. The data obtained suggest that thermally activated discrete breathers can be involved in the dehydrogenation of graphane, which is important for hydrogen energetics.
Discrete elements method of neutral particle transport
Mathews, K.A.
1983-01-01
A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method.
Active control of turbomachine discrete tones
NASA Astrophysics Data System (ADS)
Fleeter, Sanford
This paper was directed at active control of discrete frequency noise generated by subsonic blade rows through cancellation of the blade row interaction generated propagating acoustic waves. First discrete frequency noise generated by a rotor and stator in a duct was analyzed to determine the propagating acoustic pressure waves. Then a mathematical model was developed to analyze and predict the active control of discrete frequency noise generated by subsonic blade rows through cancellation of the propagating acoustic waves, accomplished by utilizing oscillating airfoil surfaces to generate additional control propagating pressure waves. These control waves interact with the propagating acoustic waves, thereby, in principle, canceling the acoustic waves and thus, the far field discrete frequency tones. This model was then applied to a fan exit guide vane to investigate active airfoil surface techniques for control of the propagating acoustic waves, and thus the far field discrete frequency tones, generated by blade row interactions.
MULTISCALE DISCRETIZATION OF SHAPE CONTOURS
Prasad, L.; Rao, R.
2000-09-01
We present an efficient multi-scale scheme to adaptively approximate the continuous (or densely sampled) contour of a planar shape at varying resolutions. The notion of shape is intimately related to the notion of contour, and the efficient representation of the contour of a shape is vital to a computational understanding of the shape. Any polygonal approximation of a planar smooth curve is equivalent to a piecewise constant approximation of the parameterized X and Y coordinate functions of a discrete point set obtained by densely sampling the curve. Using the Haar wavelet transform for the piecewise approximation yields a hierarchical scheme in which the size of the approximating point set is traded off against the morphological accuracy of the approximation. Our algorithm compresses the representation of the initial shape contour to a sparse sequence of points in the plane defining the vertices of the shape's polygonal approximation. Furthermore, it is possible to control the overall resolution of the approximation by a single, scale-independent parameter.
Seipin Is a Discrete Homooligomer†
Binns, Derk; Lee, SungKyung; Hilton, Christopher L.; Jiang, Qiu-Xing; Goodman, Joel M.
2011-01-01
Seipin is a transmembrane protein that resides in the endoplasmic reticulum and concentrates at junctions between the ER and cytosolic lipid droplets. Mutations in the human seipin gene, including the missense mutation A212P, lead to congenital generalized lipodystrophy (CGL), characterized by the lack of normal adipose tissue and accumulation of fat in liver and muscles. In both yeast and CGL patient fibroblasts, seipin is required for normal lipid droplet morphology; in its absence droplets appear to bud abnormally from the ER. Here we report the first purification and physical characterization of seipin. Yeast seipin is in a large discrete protein complex. Affinity purification demonstrated that seipin is the main if not exclusive protein in the complex. Detergent sucrose gradients in H2O, and D2O and gel filtration were used to determine the size of the seipin complex and account for detergent binding. Both seipin-myc13 (seipin fused to 13 tandem copies of the myc epitope) expressed from the endogenous promoter and overexpressed seipin-mCherry form ~500 kDa proteins consisting of about 9 copies of seipin. The yeast orthologue of the human A212P allele forms only smaller complexes and is unstable; we hypothesize that this accounts for its null phenotype in humans. Seipin appears as a toroid by negative staining electron microscopy. We speculate that seipin plays at least a structural role in organizing droplets or in communication between droplets and ER. PMID:21062080
Compatible Spatial Discretizations for Partial Differential Equations
Arnold, Douglas, N, ed.
2004-11-25
From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical
NASA Astrophysics Data System (ADS)
Hoffmann, Tim
2000-01-01
The equivalence of the discrete isotropic Heisenberg magnet (IHM) model and the discrete nonlinear Schrödinger equation (NLSE) given by Ablowitz and Ladik is shown. This is used to derive the equivalence of their discretization with the one by Izgerin and Korepin. Moreover a doubly discrete IHM is presented that is equivalent to Ablowitz' and Ladiks doubly discrete NLSE.
Discrete flavour symmetries from the Heisenberg group
NASA Astrophysics Data System (ADS)
Floratos, E. G.; Leontaris, G. K.
2016-04-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular, on the PSL2 (p) groups which contain the phenomenologically interesting cases.
Discrete symmetries and de Sitter spacetime
Cotăescu, Ion I. Pascu, Gabriel
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
High-accuracy discrete positioning device
NASA Technical Reports Server (NTRS)
Brooks, John J. (Inventor)
1994-01-01
An article (30) is controllably and precisely positioned at one of three discrete locations defined by a linkage. The positioning apparatus includes two independently driven cranks (34, 42), with a link (50) pivotably connected between the two cranks (34, 42). Another connector (44) is pivotably connected between one of the cranks (34 or 42) and the article (30) to be positioned. The cranks (34, 42) are rotationally adjusted so that the pivot points (52, 54) of the link (50) are collinear with the axes of rotation of the cranks (40, 48), thereby defining one of the three discrete locations. Additional cranks and links can be provided to define additional discrete locations.
Running Parallel Discrete Event Simulators on Sierra
Barnes, P. D.; Jefferson, D. R.
2015-12-03
In this proposal we consider porting the ROSS/Charm++ simulator and the discrete event models that run under its control so that they run on the Sierra architecture and make efficient use of the Volta GPUs.
Motion of Discrete Interfaces Through Mushy Layers
NASA Astrophysics Data System (ADS)
Braides, Andrea; Solci, Margherita
2016-04-01
We study the geometric motion of sets in the plane derived from the homogenization of discrete ferromagnetic energies with weak inclusions. We show that the discrete sets are composed by a `bulky' part and an external `mushy region' composed only of weak inclusions. The relevant motion is that of the bulky part, which asymptotically obeys to a motion by crystalline mean curvature with a forcing term, due to the energetic contribution of the mushy layers, and pinning effects, due to discreteness. From an analytical standpoint, it is interesting to note that the presence of the mushy layers implies only a weak and not strong convergence of the discrete motions, so that the convergence of the energies does not commute with the evolution. From a mechanical standpoint it is interesting to note the geometrical similarity of some phenomena in the cooling of binary melts.
The discrete-time compensated Kalman filter
NASA Technical Reports Server (NTRS)
Lee, W. H.; Athans, M.
1978-01-01
A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete time Kalman filter was derived. The resultant compensated Kalman Filter has the property that steady state bias estimation errors, resulting from modelling errors, were eliminated.
Comparing the Discrete and Continuous Logistic Models
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2008-01-01
The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)
Reducing Neuronal Networks to Discrete Dynamics
Terman, David; Ahn, Sungwoo; Wang, Xueying; Just, Winfried
2008-01-01
We consider a general class of purely inhibitory and excitatory-inhibitory neuronal networks, with a general class of network architectures, and characterize the complex firing patterns that emerge. Our strategy for studying these networks is to first reduce them to a discrete model. In the discrete model, each neuron is represented as a finite number of states and there are rules for how a neuron transitions from one state to another. In this paper, we rigorously demonstrate that the continuous neuronal model can be reduced to the discrete model if the intrinsic and synaptic properties of the cells are chosen appropriately. In a companion paper [1], we analyze the discrete model. PMID:18443649
Discrete Element Modeling of Drop Tests
NASA Astrophysics Data System (ADS)
Wang, Yuannian; Tonon, Fulvio
2012-09-01
A discrete element code with impact model has been developed and calibrated to simulate the dynamic behavior of rock materials, with special regard to rock fragmentation upon impact during rock-fall analysis. The paper summarizes the discrete element code, the calibration algorithms developed to identify the model microparameters, and the impact model. Experimental work on drop tests is then used to validate the code on modeling impact fragmentation. It has been found that the developed discrete element code and impact model can reasonably simulate rock fragmentation in drop tests. The use of the discrete element code and impact model can provide good reference results in evaluating impact fragmentation in rock-fall analysis.
Motion of Discrete Interfaces Through Mushy Layers
NASA Astrophysics Data System (ADS)
Braides, Andrea; Solci, Margherita
2016-08-01
We study the geometric motion of sets in the plane derived from the homogenization of discrete ferromagnetic energies with weak inclusions. We show that the discrete sets are composed by a `bulky' part and an external `mushy region' composed only of weak inclusions. The relevant motion is that of the bulky part, which asymptotically obeys to a motion by crystalline mean curvature with a forcing term, due to the energetic contribution of the mushy layers, and pinning effects, due to discreteness. From an analytical standpoint, it is interesting to note that the presence of the mushy layers implies only a weak and not strong convergence of the discrete motions, so that the convergence of the energies does not commute with the evolution. From a mechanical standpoint it is interesting to note the geometrical similarity of some phenomena in the cooling of binary melts.
Dynamic discretization method for solving Kepler's equation
NASA Astrophysics Data System (ADS)
Feinstein, Scott A.; McLaughlin, Craig A.
2006-09-01
Kepler’s equation needs to be solved many times for a variety of problems in Celestial Mechanics. Therefore, computing the solution to Kepler’s equation in an efficient manner is of great importance to that community. There are some historical and many modern methods that address this problem. Of the methods known to the authors, Fukushima’s discretization technique performs the best. By taking more of a system approach and combining the use of discretization with the standard computer science technique known as dynamic programming, we were able to achieve even better performance than Fukushima. We begin by defining Kepler’s equation for the elliptical case and describe existing solution methods. We then present our dynamic discretization method and show the results of a comparative analysis. This analysis will demonstrate that, for the conditions of our tests, dynamic discretization performs the best.
A discrete control model of PLANT
NASA Technical Reports Server (NTRS)
Mitchell, C. M.
1985-01-01
A model of the PLANT system using the discrete control modeling techniques developed by Miller is described. Discrete control models attempt to represent in a mathematical form how a human operator might decompose a complex system into simpler parts and how the control actions and system configuration are coordinated so that acceptable overall system performance is achieved. Basic questions include knowledge representation, information flow, and decision making in complex systems. The structure of the model is a general hierarchical/heterarchical scheme which structurally accounts for coordination and dynamic focus of attention. Mathematically, the discrete control model is defined in terms of a network of finite state systems. Specifically, the discrete control model accounts for how specific control actions are selected from information about the controlled system, the environment, and the context of the situation. The objective is to provide a plausible and empirically testable accounting and, if possible, explanation of control behavior.
Eigenforms, Discrete Processes and Quantum Processes
NASA Astrophysics Data System (ADS)
Kauffman, Louis H.
2012-05-01
This essay is a discussion of the concept of eigenform, due to Heinz von Foerster, and its relationship with discrete physics and quantum mechanics. We interpret the square root of minus one as a simple oscillatory process - a clock, and as an eigenform. By taking a generalization of this identification of i as a clock and eigenform, we show how quantum mechanics emerges from discrete physics.
Separable two-dimensional discrete Hartley transform
NASA Technical Reports Server (NTRS)
Watson, Andrew B.; Poirson, Allen
1986-01-01
Bracewell has proposed the Discrete Hartley Transform (DHT) as a substitute for the Discrete Fourier Transform (DFT), particularly as a means of convolution. Here, it is shown that the most natural extension of the DHT to two dimensions fails to be separate in the two dimensions, and is therefore inefficient. An alternative separable form is considered, corresponding convolution theorem is derived. That the DHT is unlikely to provide faster convolution than the DFT is also discussed.
`t Hooft anomaly matching for discrete symmetries
Csaki, C.; Murayama, Hitoshi |
1998-05-01
The authors show how to extend the `t Hooft anomaly matching conditions to discrete symmetries. They check these discrete anomally matching conditions on several proposed low-energy spectra of certain strongly interacting gauge theories. The excluded examples include the proposed chirally symmetric vacuum of pure N = 1 supersymmetric yang-Mills theories, certain non-supersymmetric confining theories and some self-dual N = 1 supersymmetric theories based on exceptional groups.
Discrete wavelet analysis of power system transients
Wilkinson, W.A.; Cox, M.D.
1996-11-01
Wavelet analysis is a new method for studying power system transients. Through wavelet analysis, transients are decomposed into a series of wavelet components, each of which is a time-domain signal that covers a specific octave frequency band. This paper presents the basic ideas of discrete wavelet analysis. A variety of actual and simulated transient signals are then analyzed using the discrete wavelet transform that help demonstrate the power of wavelet analysis.
Terminal Dynamics Approach to Discrete Event Systems
NASA Technical Reports Server (NTRS)
Zak, Michail; Meyers, Ronald
1995-01-01
This paper presents and discusses a mathematical formalism for simulation of discrete event dynamic (DED)-a special type of 'man-made' systems to serve specific purposes of information processing. The main objective of this work is to demonstrate that the mathematical formalism for DED can be based upon a terminal model of Newtonian dynamics which allows one to relax Lipschitz conditions at some discrete points.!.
NASA Astrophysics Data System (ADS)
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2016-05-01
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
Discrete differential geometry: The nonplanar quadrilateral mesh
NASA Astrophysics Data System (ADS)
Twining, Carole J.; Marsland, Stephen
2012-06-01
We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.
Discrete differential geometry: the nonplanar quadrilateral mesh.
Twining, Carole J; Marsland, Stephen
2012-06-01
We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids. PMID:23005244
Quantum walks and discrete gauge theories
NASA Astrophysics Data System (ADS)
Arnault, Pablo; Debbasch, Fabrice
2016-05-01
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A family of two-dimensional walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac fermion coupled to arbitrary electromagnetic fields. The electromagnetic interpretation is extended beyond the continuous limit by proving that these discrete-time quantum walks (DTQWs) exhibit an exact discrete local U(1) gauge invariance and possess a discrete gauge-invariant conserved current. A discrete gauge-invariant electromagnetic field is also constructed and that field is coupled to the conserved current by a discrete generalization of Maxwell equations. The dynamics of the DTQWs under crossed electric and magnetic fields is finally explored outside the continuous limit by numerical simulations. Bloch oscillations and the so-called E ×B drift are recovered in the weak-field limit. Localization is observed for some values of the gauge fields.
Seleson, Pablo; Du, Qiang; Parks, Michael L.
2016-08-16
The peridynamic theory of solid mechanics is a nonlocal reformulation of the classical continuum mechanics theory. At the continuum level, it has been demonstrated that classical (local) elasticity is a special case of peridynamics. Such a connection between these theories has not been extensively explored at the discrete level. This paper investigates the consistency between nearest-neighbor discretizations of linear elastic peridynamic models and finite difference discretizations of the Navier–Cauchy equation of classical elasticity. While nearest-neighbor discretizations in peridynamics have been numerically observed to present grid-dependent crack paths or spurious microcracks, this paper focuses on a different, analytical aspect of suchmore » discretizations. We demonstrate that, even in the absence of cracks, such discretizations may be problematic unless a proper selection of weights is used. Specifically, we demonstrate that using the standard meshfree approach in peridynamics, nearest-neighbor discretizations do not reduce, in general, to discretizations of corresponding classical models. We study nodal-based quadratures for the discretization of peridynamic models, and we derive quadrature weights that result in consistency between nearest-neighbor discretizations of peridynamic models and discretized classical models. The quadrature weights that lead to such consistency are, however, model-/discretization-dependent. We motivate the choice of those quadrature weights through a quadratic approximation of displacement fields. The stability of nearest-neighbor peridynamic schemes is demonstrated through a Fourier mode analysis. Finally, an approach based on a normalization of peridynamic constitutive constants at the discrete level is explored. This approach results in the desired consistency for one-dimensional models, but does not work in higher dimensions. The results of the work presented in this paper suggest that even though nearest
PREFACE: 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014)
NASA Astrophysics Data System (ADS)
Di Domenico, Antonio; Mavromatos, Nick E.; Mitsou, Vasiliki A.; Skliros, Dimitri P.
2015-07-01
The DISCRETE 2014: Fourth Symposium in the Physics of Discrete Symmetries took place at King's College London, Strand Campus, London WC2R 2LS, from Tuesday, December 2 2014 till Saturday, December 6 2014. This is the fourth Edition of the DISCRETE conference series, which is a biannual event, having been held previously in Valencia (Discrete'08), Rome (Discrete2010) and Lisbon (Discrete2012). The topics covered at the DISCRETE series of conferences are: T, C, P, CP symmetries; accidental symmetries (B, L conservation); CPT symmetry, decoherence and entangled states, Lorentz symmetry breaking (phenomenology and current bounds); neutrino mass and mixing; implications for cosmology and astroparticle physics, dark matter searches; experimental prospects at LHC, new facilities. In DISCRETE 2014 we have also introduced two new topics: cosmological aspects of non-commutative space-times as well as PT symmetric Hamiltonians (non-Hermitian but with real eigenvalues), a topic that has wide applications in particle physics and beyond. The conference was opened by the King's College London Vice Principal on Research and Innovation, Mr Chris Mottershead, followed by a welcome address by the Chair of DISCRETE 2014 (Professor Nick E. Mavromatos). After these introductory talks, the scientific programme of the DISCRETE 2014 symposium started. Following the tradition of DISCRETE series of conferences, the talks (138 in total) were divided into plenary-review talks (25), invited research talks (50) and shorter presentations (63) — selected by the conveners of each session in consultation with the organisers — from the submitted abstracts. We have been fortunate to have very high-quality, thought stimulating and interesting talks at all levels, which, together with the discussions among the participants, made the conference quite enjoyable. There were 152 registered participants for the event.
Liu, Yushun; Zhou, Wenjun; Li, Pengfei; Yang, Shuai; Tian, Yan
2016-01-01
Due to electromagnetic interference in power substations, the partial discharge (PD) signals detected by ultrahigh frequency (UHF) antenna sensors often contain various background noises, which may hamper high voltage apparatus fault diagnosis and localization. This paper proposes a novel de-noising method based on the generalized S-transform and module time-frequency matrix to suppress noise in UHF PD signals. The sub-matrix maximum module value method is employed to calculate the frequencies and amplitudes of periodic narrowband noise, and suppress noise through the reverse phase cancellation technique. In addition, a singular value decomposition de-noising method is employed to suppress Gaussian white noise in UHF PD signals. Effective singular values are selected by employing the fuzzy c-means clustering method to recover the PD signals. De-noising results of simulated and field detected UHF PD signals prove the feasibility of the proposed method. Compared with four conventional de-noising methods, the results show that the proposed method can suppress background noise in the UHF PD signal effectively, with higher signal-to-noise ratio and less waveform distortion. PMID:27338409
Liu, Yushun; Zhou, Wenjun; Li, Pengfei; Yang, Shuai; Tian, Yan
2016-01-01
Due to electromagnetic interference in power substations, the partial discharge (PD) signals detected by ultrahigh frequency (UHF) antenna sensors often contain various background noises, which may hamper high voltage apparatus fault diagnosis and localization. This paper proposes a novel de-noising method based on the generalized S-transform and module time-frequency matrix to suppress noise in UHF PD signals. The sub-matrix maximum module value method is employed to calculate the frequencies and amplitudes of periodic narrowband noise, and suppress noise through the reverse phase cancellation technique. In addition, a singular value decomposition de-noising method is employed to suppress Gaussian white noise in UHF PD signals. Effective singular values are selected by employing the fuzzy c-means clustering method to recover the PD signals. De-noising results of simulated and field detected UHF PD signals prove the feasibility of the proposed method. Compared with four conventional de-noising methods, the results show that the proposed method can suppress background noise in the UHF PD signal effectively, with higher signal-to-noise ratio and less waveform distortion. PMID:27338409
Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
NASA Astrophysics Data System (ADS)
Iglesias, David; Marrero, Juan C.; de Diego, David Martín; Martínez, Eduardo
2008-06-01
This paper studies the construction of geometric integrators for nonholonomic systems. We develop a formalism for nonholonomic discrete Euler Lagrange equations in a setting that permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it is necessary to fix a vector subbundle of the Lie algebroid associated to the Lie groupoid. We also discuss the existence of nonholonomic evolution operators in terms of the discrete nonholonomic Legendre transformations and in terms of adequate decompositions of the prolongation of the Lie groupoid. The characterization of the reversibility of the evolution operator and the discrete nonholonomic momentum equation are also considered. Finally, we illustrate with several classical examples the wide range of application of the theory (the discrete nonholonomic constrained particle, the Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a rotating table and the two wheeled planar mobile robot).
Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.
Jason, Peter; Johansson, Magnus
2016-01-01
We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers. PMID:26871085
ERIC Educational Resources Information Center
Rosenstein, Joseph G., Ed.; Franzblau, Deborah S., Ed.; Roberts, Fred S., Ed.
This book is a collection of articles by experienced educators and explains why and how discrete mathematics should be taught in K-12 classrooms. It includes evidence for "why" and practical guidance for "how" and also discusses how discrete mathematics can be used as a vehicle for achieving the broader goals of the major effort now underway to…
The Cauchy-Kovalevskaya Extension Theorem in Discrete Clifford Analysis
NASA Astrophysics Data System (ADS)
De Ridder, H.; De Schepper, H.; Sommen, F.
2010-09-01
Discrete Clifford analysis is a higher dimensional discrete function theory based on skew Weyl relations. It is centered around the study of Clifford algebra valued null solutions, called discrete monogenic functions, of a discrete Dirac operator, i.e. a first order, Clifford vector valued difference operator. In this contribution, we establish a Cauchy-Kovalevskaya extension theorem for discrete monogenic functions defined on the grid Zhm of m-tuples of integer multiples of a variable mesh width h. Convergence to the continuous case is investigated. As illustrative examples we explicitly construct the Cauchy-Kovalevskaya extensions of the discrete delta function and of a discretized exponential.
Discrete photon statistics from continuous microwave measurements
NASA Astrophysics Data System (ADS)
Virally, Stéphane; Simoneau, Jean Olivier; Lupien, Christian; Reulet, Bertrand
2016-04-01
Photocount statistics are an important tool for the characterization of electromagnetic fields, especially for fields with an irrelevant phase. In the microwave domain, continuous rather than discrete measurements are the norm. Using a different approach, we recover discrete photon statistics from the cumulants of a continuous distribution of field quadrature measurements. The use of cumulants allows the separation between the signal of interest and experimental noise. Using a parametric amplifier as the first stage of the amplification chain, we extract useful data from up to the sixth cumulant of the continuous distribution of a coherent field, hence recovering up to the third moment of the discrete statistics associated with a signal with much less than one average photon.
Discrete breathers in hexagonal dusty plasma lattices
Koukouloyannis, V.; Kourakis, I.
2009-08-15
The occurrence of single-site or multisite localized vibrational modes, also called discrete breathers, in two-dimensional hexagonal dusty plasma lattices is investigated. The system is described by a Klein-Gordon hexagonal lattice characterized by a negative coupling parameter epsilon in account of its inverse dispersive behavior. A theoretical analysis is performed in order to establish the possibility of existence of single as well as three-site discrete breathers in such systems. The study is complemented by a numerical investigation based on experimentally provided potential forms. This investigation shows that a dusty plasma lattice can support single-site discrete breathers, while three-site in phase breathers could exist if specific conditions, about the intergrain interaction strength, would hold. On the other hand, out of phase and vortex three-site breathers cannot be supported since they are highly unstable.
Discrete-time Markovian stochastic Petri nets
NASA Technical Reports Server (NTRS)
Ciardo, Gianfranco
1995-01-01
We revisit and extend the original definition of discrete-time stochastic Petri nets, by allowing the firing times to have a 'defective discrete phase distribution'. We show that this formalism still corresponds to an underlying discrete-time Markov chain. The structure of the state for this process describes both the marking of the Petri net and the phase of the firing time for each transition, resulting in a large state space. We then modify the well-known power method to perform a transient analysis even when the state space is infinite, subject to the condition that only a finite number of states can be reached in a finite amount of time. Since the memory requirements might still be excessive, we suggest a bounding technique based on truncation.
The ultimatum game: Discrete vs. continuous offers
NASA Astrophysics Data System (ADS)
Dishon-Berkovits, Miriam; Berkovits, Richard
2014-09-01
In many experimental setups in social-sciences, psychology and economy the subjects are requested to accept or dispense monetary compensation which is usually given in discrete units. Using computer and mathematical modeling we show that in the framework of studying the dynamics of acceptance of proposals in the ultimatum game, the long time dynamics of acceptance of offers in the game are completely different for discrete vs. continuous offers. For discrete values the dynamics follow an exponential behavior. However, for continuous offers the dynamics are described by a power-law. This is shown using an agent based computer simulation as well as by utilizing an analytical solution of a mean-field equation describing the model. These findings have implications to the design and interpretation of socio-economical experiments beyond the ultimatum game.
Numerical discretization for nonlinear diffusion filter
NASA Astrophysics Data System (ADS)
Mustaffa, I.; Mizuar, I.; Aminuddin, M. M. M.; Dasril, Y.
2015-05-01
Nonlinear diffusion filters are famously used in machine vision for image denoising and restoration. This paper presents a study on the effects of different numerical discretization of nonlinear diffusion filter. Several numerical discretization schemes are presented; namely semi-implicit, AOS, and fully implicit schemes. The results of these schemes are compared by visual results, objective measurement e.g. PSNR and MSE. The results are also compared to a Daubechies wavelet denoising method. It is acknowledged that the two preceding scheme have already been discussed in literature, however comparison to the latter scheme has not been made. The semi-implicit scheme uses an additive operator splitting (AOS) developed to overcome the shortcoming of the explicit scheme i.e., stability for very small time steps. Although AOS has proven to be efficient, from the nonlinear diffusion filter results with different discretization schemes, examples shows that implicit schemes are worth pursuing.
Uncertainty relation for the discrete Fourier transform.
Massar, Serge; Spindel, Philippe
2008-05-16
We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=e(i phi) VU. Its most important application is to constrain how much a quantum state can be localized simultaneously in two mutually unbiased bases related by a discrete fourier transform. It provides an uncertainty relation which smoothly interpolates between the well-known cases of the Pauli operators in two dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper's equation, a discrete version of the harmonic oscillator equation. PMID:18518426
An algebra of discrete event processes
NASA Technical Reports Server (NTRS)
Heymann, Michael; Meyer, George
1991-01-01
This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.
Natural discretization in noncommutative field theory
NASA Astrophysics Data System (ADS)
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Tree Ensembles on the Induced Discrete Space.
Yildiz, Olcay Taner
2016-05-01
Decision trees are widely used predictive models in machine learning. Recently, K -tree is proposed, where the original discrete feature space is expanded by generating all orderings of values of k discrete attributes and these orderings are used as the new attributes in decision tree induction. Although K -tree performs significantly better than the proper one, their exponential time complexity can prohibit their use. In this brief, we propose K -forest, an extension of random forest, where a subset of features is selected randomly from the induced discrete space. Simulation results on 17 data sets show that the novel ensemble classifier has significantly lower error rate compared with the random forest based on the original feature space. PMID:26011897
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Discrete Roughness Transition for Hypersonic Flight Vehicles
NASA Technical Reports Server (NTRS)
Berry, Scott A.; Horvath, Thomas J.
2007-01-01
The importance of discrete roughness and the correlations developed to predict the onset of boundary layer transition on hypersonic flight vehicles are discussed. The paper is organized by hypersonic vehicle applications characterized in a general sense by the boundary layer: slender with hypersonic conditions at the edge of the boundary layer, moderately blunt with supersonic, and blunt with subsonic. This paper is intended to be a review of recent discrete roughness transition work completed at NASA Langley Research Center in support of agency flight test programs. First, a review is provided of discrete roughness wind tunnel data and the resulting correlations that were developed. Then, results obtained from flight vehicles, in particular the recently flown Hyper-X and Shuttle missions, are discussed and compared to the ground-based correlations.
The discrete regime of flame propagation
NASA Astrophysics Data System (ADS)
Tang, Francois-David; Goroshin, Samuel; Higgins, Andrew
The propagation of laminar dust flames in iron dust clouds was studied in a low-gravity envi-ronment on-board a parabolic flight aircraft. The elimination of buoyancy-induced convection and particle settling permitted measurements of fundamental combustion parameters such as the burning velocity and the flame quenching distance over a wide range of particle sizes and in different gaseous mixtures. The discrete regime of flame propagation was observed by substitut-ing nitrogen present in air with xenon, an inert gas with a significantly lower heat conductivity. Flame propagation in the discrete regime is controlled by the heat transfer between neighbor-ing particles, rather than by the particle burning rate used by traditional continuum models of heterogeneous flames. The propagation mechanism of discrete flames depends on the spa-tial distribution of particles, and thus such flames are strongly influenced by local fluctuations in the fuel concentration. Constant pressure laminar dust flames were observed inside 70 cm long, 5 cm diameter Pyrex tubes. Equally-spaced plate assemblies forming rectangular chan-nels were placed inside each tube to determine the quenching distance defined as the minimum channel width through which a flame can successfully propagate. High-speed video cameras were used to measure the flame speed and a fiber optic spectrometer was used to measure the flame temperature. Experimental results were compared with predictions obtained from a numerical model of a three-dimensional flame developed to capture both the discrete nature and the random distribution of particles in the flame. Though good qualitative agreement was obtained between model predictions and experimental observations, residual g-jitters and the short reduced-gravity periods prevented further investigations of propagation limits in the dis-crete regime. The full exploration of the discrete flame phenomenon would require high-quality, long duration reduced gravity environment
Model reduction for discrete bilinear systems
NASA Technical Reports Server (NTRS)
King, A. M.; Skelton, R. E.
1987-01-01
A model reduction method for discrete bilinear systems is developed which matches q sets of Volterra and covariance parameters. These parameters are shown to represent both deterministic and stochastic attributes of the discrete bilinear system. A reduced order model which matches these q sets of parameters is defined to be a q-Volterra covariance equivalent realization (q-Volterra COVER). An algorithm is presented which constructs a class of q-Volterra COVERs parameterized by solutions to a Hermitian, quadratic, matrix equation. The algorithm is applied to a bilinear model of a robot manipulator.
1-D EQUILIBRIUM DISCRETE DIFFUSION MONTE CARLO
T. EVANS; ET AL
2000-08-01
We present a new hybrid Monte Carlo method for 1-D equilibrium diffusion problems in which the radiation field coexists with matter in local thermodynamic equilibrium. This method, the Equilibrium Discrete Diffusion Monte Carlo (EqDDMC) method, combines Monte Carlo particles with spatially discrete diffusion solutions. We verify the EqDDMC method with computational results from three slab problems. The EqDDMC method represents an incremental step toward applying this hybrid methodology to non-equilibrium diffusion, where it could be simultaneously coupled to Monte Carlo transport.
Discrete Gabor Filters For Binocular Disparity Measurement
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.
1995-01-01
Discrete Gabor filters proposed for use in determining binocular disparity - difference between positions of same feature or object depicted in stereoscopic images produced by two side-by-side cameras aimed in parallel. Magnitude of binocular disparity used to estimate distance from cameras to feature or object. In one potential application, cameras charge-coupled-device video cameras in robotic vision system, and binocular disparities and distance estimates used as control inputs - for example, to control approaches to objects manipulated or to maintain safe distances from obstacles. Binocular disparities determined from phases of discretized Gabor transforms.
Hybrid Discrete-Continuous Markov Decision Processes
NASA Technical Reports Server (NTRS)
Feng, Zhengzhu; Dearden, Richard; Meuleau, Nicholas; Washington, Rich
2003-01-01
This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.
Applied Behavior Analysis: Beyond Discrete Trial Teaching
ERIC Educational Resources Information Center
Steege, Mark W.; Mace, F. Charles; Perry, Lora; Longenecker, Harold
2007-01-01
We discuss the problem of autism-specific special education programs representing themselves as Applied Behavior Analysis (ABA) programs when the only ABA intervention employed is Discrete Trial Teaching (DTT), and often for limited portions of the school day. Although DTT has many advantages to recommend its use, it is not well suited to teach…
Analysis hierarchical model for discrete event systems
NASA Astrophysics Data System (ADS)
Ciortea, E. M.
2015-11-01
The This paper presents the hierarchical model based on discrete event network for robotic systems. Based on the hierarchical approach, Petri network is analysed as a network of the highest conceptual level and the lowest level of local control. For modelling and control of complex robotic systems using extended Petri nets. Such a system is structured, controlled and analysed in this paper by using Visual Object Net ++ package that is relatively simple and easy to use, and the results are shown as representations easy to interpret. The hierarchical structure of the robotic system is implemented on computers analysed using specialized programs. Implementation of hierarchical model discrete event systems, as a real-time operating system on a computer network connected via a serial bus is possible, where each computer is dedicated to local and Petri model of a subsystem global robotic system. Since Petri models are simplified to apply general computers, analysis, modelling, complex manufacturing systems control can be achieved using Petri nets. Discrete event systems is a pragmatic tool for modelling industrial systems. For system modelling using Petri nets because we have our system where discrete event. To highlight the auxiliary time Petri model using transport stream divided into hierarchical levels and sections are analysed successively. Proposed robotic system simulation using timed Petri, offers the opportunity to view the robotic time. Application of goods or robotic and transmission times obtained by measuring spot is obtained graphics showing the average time for transport activity, using the parameters sets of finished products. individually.
Dimensionality Problem in Discrete Discriminant Analysis
NASA Astrophysics Data System (ADS)
Ferreira, Ana Sousa
2011-09-01
A high dimensional problem is very often in Discrete Discriminant Analysis (DDA) due to the fact that the number of parameters estimated in DDA models is very frequently too large. Then, the main problem is sparseness, in which some of the multinomial cells may have no data in the training sets (for one or several classes). Furthermore, there aren't truly reliable methods for selecting the most discrete discriminative features and often we deal with small sample sizes with classes not well separated. This dimensional DDA problem is often known as the "curse of dimensionality". In this context, a combining models approach seems to be promising since it is known that different DDA models perform differently on different subjects. This approach currently appears in an increasing number of papers aiming to obtain more robust and stable models. Thus, in discrete problems we propose new forms of modeling the conditional probability functions based on linear combinations of reference models (e.g. the Full Multinomial Model (FMM) and the First-order Independence Model (FOIM)). Recently, since class separability is another fundamental problem in discrete supervised problems we have focused in exploring measures for analyzing class separability. We investigate the performance of the present approaches on real and simulated data.
Conjugacy classes in discrete Heisenberg groups
Budylin, R Ya
2014-08-01
We study an extension of a discrete Heisenberg group coming from the theory of loop groups and find invariants of conjugacy classes in this group. In some cases, including the case of the integer Heisenberg group, we make these invariants more explicit. Bibliography: 4 titles.
Bayesian approach to global discrete optimization
Mockus, J.; Mockus, A.; Mockus, L.
1994-12-31
We discuss advantages and disadvantages of the Bayesian approach (average case analysis). We present the portable interactive version of software for continuous global optimization. We consider practical multidimensional problems of continuous global optimization, such as optimization of VLSI yield, optimization of composite laminates, estimation of unknown parameters of bilinear time series. We extend Bayesian approach to discrete optimization. We regard the discrete optimization as a multi-stage decision problem. We assume that there exists some simple heuristic function which roughly predicts the consequences of the decisions. We suppose randomized decisions. We define the probability of the decision by the randomized decision function depending on heuristics. We fix this function with exception of some parameters. We repeat the randomized decision several times at the fixed values of those parameters and accept the best decision as the result. We optimize the parameters of the randomized decision function to make the search more efficient. Thus we reduce the discrete optimization problem to the continuous problem of global stochastic optimization. We solve this problem by the Bayesian methods of continuous global optimization. We describe the applications to some well known An problems of discrete programming, such as knapsack, traveling salesman, and scheduling.
Electrolytic plating apparatus for discrete microsized particles
Mayer, Anton
1976-11-30
Method and apparatus are disclosed for electrolytically producing very uniform coatings of a desired material on discrete microsized particles. Agglomeration or bridging of the particles during the deposition process is prevented by imparting a sufficiently random motion to the particles that they are not in contact with a powered cathode for a time sufficient for such to occur.
Electroless plating apparatus for discrete microsized particles
Mayer, Anton
1978-01-01
Method and apparatus are disclosed for producing very uniform coatings of a desired material on discrete microsized particles by electroless techniques. Agglomeration or bridging of the particles during the deposition process is prevented by imparting a sufficiently random motion to the particles that they are not in contact with each other for a time sufficient for such to occur.
Geometric Representations for Discrete Fourier Transforms
NASA Technical Reports Server (NTRS)
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Discrete Mathematics and the Secondary Mathematics Curriculum.
ERIC Educational Resources Information Center
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
Kinematics of foldable discrete space cranes
NASA Technical Reports Server (NTRS)
Nayfeh, A. H.
1985-01-01
Exact kinematic description of a NASA proposed prototype foldable-deployable discrete space crane are presented. A computer program is developed which maps the geometry of the crane once controlling parameters are specified. The program uses a building block type approach in which it calculates the local coordinates of each repeating cell and then combines them with respect to a global coordinates system.
Neutrino mass and mixing with discrete symmetry
NASA Astrophysics Data System (ADS)
King, Stephen F.; Luhn, Christoph
2013-05-01
This is a review paper about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally, we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A4, S4 and Δ(96).
Discrete Gust Model for Launch Vehicle Assessments
NASA Technical Reports Server (NTRS)
Leahy, Frank B.
2008-01-01
Analysis of spacecraft vehicle responses to atmospheric wind gusts during flight is important in the establishment of vehicle design structural requirements and operational capability. Typically, wind gust models can be either a spectral type determined by a random process having a wide range of wavelengths, or a discrete type having a single gust of predetermined magnitude and shape. Classical discrete models used by NASA during the Apollo and Space Shuttle Programs included a 9 m/sec quasi-square-wave gust with variable wavelength from 60 to 300 m. A later study derived discrete gust from a military specification (MIL-SPEC) document that used a "1-cosine" shape. The MIL-SPEC document contains a curve of non-dimensional gust magnitude as a function of non-dimensional gust half-wavelength based on the Dryden spectral model, but fails to list the equation necessary to reproduce the curve. Therefore, previous studies could only estimate a value of gust magnitude from the curve, or attempt to fit a function to it. This paper presents the development of the MIL-SPEC curve, and provides the necessary information to calculate discrete gust magnitudes as a function of both gust half-wavelength and the desired probability level of exceeding a specified gust magnitude.
Fast mix table construction for material discretization
Johnson, S. R.
2013-07-01
An effective hybrid Monte Carlo-deterministic implementation typically requires the approximation of a continuous geometry description with a discretized piecewise-constant material field. The inherent geometry discretization error can be reduced somewhat by using material mixing, where multiple materials inside a discrete mesh voxel are homogenized. Material mixing requires the construction of a 'mix table,' which stores the volume fractions in every mixture so that multiple voxels with similar compositions can reference the same mixture. Mix table construction is a potentially expensive serial operation for large problems with many materials and voxels. We formulate an efficient algorithm to construct a sparse mix table in O(number of voxels x log number of mixtures) time. The new algorithm is implemented in ADVANTG and used to discretize continuous geometries onto a structured Cartesian grid. When applied to an end-of-life MCNP model of the High Flux Isotope Reactor with 270 distinct materials, the new method improves the material mixing time by a factor of 100 compared to a naive mix table implementation. (authors)
Teaching Discrete Mathematics with Graphing Calculators.
ERIC Educational Resources Information Center
Masat, Francis E.
Graphing calculator use is often thought of in terms of pre-calculus or continuous topics in mathematics. This paper contains examples and activities that demonstrate useful, interesting, and easy ways to use a graphing calculator with discrete topics. Examples are given for each of the following topics: functions, mathematical induction and…
A deterministic discrete ordinates transport proxy application
Energy Science and Technology Software Center (ESTSC)
2014-06-03
Kripke is a simple 3D deterministic discrete ordinates (Sn) particle transport code that maintains the computational load and communications pattern of a real transport code. It is intended to be a research tool to explore different data layouts, new programming paradigms and computer architectures.
Discrete Events as Units of Perceived Time
ERIC Educational Resources Information Center
Liverence, Brandon M.; Scholl, Brian J.
2012-01-01
In visual images, we perceive both space (as a continuous visual medium) and objects (that inhabit space). Similarly, in dynamic visual experience, we perceive both continuous time and discrete events. What is the relationship between these units of experience? The most intuitive answer may be similar to the spatial case: time is perceived as an…
Core-Generating Discretization for Rough Set Feature Selection
NASA Astrophysics Data System (ADS)
Tian, David; Zeng, Xiao-Jun; Keane, John
Rough set feature selection (RSFS) can be used to improve classifier performance. RSFS removes redundant attributes whilst keeping important ones that preserve the classification power of the original dataset. The feature subsets selected by RSFS are called reducts. The intersection of all reducts is called core. However, RSFS handles discrete attributes only. To process datasets consisting of real attributes, they are discretized before applying RSFS. Discretization controls core of the discrete dataset. Moreover, core may critically affect the classification performance of reducts. This paper defines core-generating discretization, a type of discretization method; analyzes the properties of core-generating discretization; models core-generating discretization using constraint satisfaction; defines core-generating approximate minimum entropy (C-GAME) discretization; models C-GAME using constraint satisfaction and evaluates the performance of C-GAME as a pre-processor of RSFS using ten datasets from the UCI Machine Learning Repository.
Discrete ordinates methods in xy geometry with spatially varying angular discretization
Bal, G.; Warin, X.
1997-10-01
The efficiency of a new quadrature rule adapted to the numerical resolution of a neutron transport problem in xy geometry is presented based on the use of the discrete ordinates method for the angular variable. The purpose of introducing this quadrature rule is to couple two different angular discretizations used on two nonoverlapping subdomains, which is useful for performing local refinement. This coupling and some numerical results of source problems are presented.
Quantum RLC circuits: Charge discreteness and resonance
NASA Astrophysics Data System (ADS)
Utreras-Díaz, Constantino A.
2008-10-01
In a recent article [C.A. Utreras-Díaz, Phys. Lett. A 372 (2008) 5059], we have advanced a semiclassical theory of quantum circuits with discrete charge and electrical resistance. In this work, we present a few elementary applications of this theory. For the zero resistance inductive circuit, we obtain the Stark ladder energies in yet another way; for the circuit driven by a combination d.c. plus a.c. electromotive force (emf) we generalize earlier results by Chandía et al. [K. Chandía, J.C. Flores, E. Lazo, Phys. Lett. A 359 (2006) 693]. As a second application, we investigate the effect of electrical resistance and charge discreteness, in the resonance conditions of a series RLC quantum circuit.
Numerical valuation of discrete double barrier options
NASA Astrophysics Data System (ADS)
Milev, Mariyan; Tagliani, Aldo
2010-03-01
In the present paper we explore the problem for pricing discrete barrier options utilizing the Black-Scholes model for the random movement of the asset price. We postulate the problem as a path integral calculation by choosing approach that is similar to the quadrature method. Thus, the problem is reduced to the estimation of a multi-dimensional integral whose dimension corresponds to the number of the monitoring dates. We propose a fast and accurate numerical algorithm for its valuation. Our results for pricing discretely monitored one and double barrier options are in agreement with those obtained by other numerical and analytical methods in Finance and literature. A desired level of accuracy is very fast achieved for values of the underlying asset close to the strike price or the barriers. The method has a simple computer implementation and it permits observing the entire life of the option.
Discrete shaped strain sensors for intelligent structures
NASA Technical Reports Server (NTRS)
Andersson, Mark S.; Crawley, Edward F.
1992-01-01
Design of discrete, highly distributed sensor systems for intelligent structures has been studied. Data obtained indicate that discrete strain-averaging sensors satisfy the functional requirements for distributed sensing of intelligent structures. Bartlett and Gauss-Hanning sensors, in particular, provide good wavenumber characteristics while meeting the functional requirements. They are characterized by good rolloff rates and positive Fourier transforms for all wavenumbers. For the numerical integration schemes, Simpson's rule is considered to be very simple to implement and consistently provides accurate results for five sensors or more. It is shown that a sensor system that satisfies the functional requirements can be applied to a structure that supports mode shapes with purely sinusoidal curvature.
Discrete instability in the DNA double helix.
Tabi, Conrad Bertrand; Mohamadou, Alidou; Kofané, Timoléon Crépin
2009-12-01
Modulational instability (MI) is explored in the framework of the base-rotor model of DNA dynamics. We show, in fact, that the helicoidal coupling introduced in the spin model of DNA reduces the system to a modified discrete sine-Gordon (sG) equation. The MI criterion is thus modified and displays interesting features because of the helicoidal coupling. In the simulations, we have found that a train of pulses is generated when the lattice is subjected to MI, in agreement with analytical results obtained in a modified discrete sG equation. Also, the competitive effects of the harmonic longitudinal and helicoidal constants on the dynamics of the system are notably pointed out. In the same way, it is shown that MI can lead to energy localization which becomes high for some values of the helicoidal coupling constant. PMID:20059197
Semi-Discrete Ingham-Type Inequalities
Komornik, Vilmos Loreti, Paola
2007-03-15
One of the general methods in linear control theory is based on harmonic and non-harmonic Fourier series. The key of this approach is the establishment of various suitable adaptations and generalizations of the classical Parseval equality. A new and systematic approach was begun in our papers in collaboration with Baiocchi. Many recent results of this kind, obtained through various Ingham-type theorems, were exposed recently. Although this work concentrated on continuous models, in connection with numerical simulations a natural question is whether these results also admit useful discrete versions. The purpose of this paper is to establish discrete versions of various Ingham-type theorems by using our approach. They imply the earlier continuous results by a simple limit process.
Degeneracy and discreteness in cosmological model fitting
NASA Astrophysics Data System (ADS)
Teng, Huan-Yu; Huang, Yuan; Zhang, Tong-Jie
2016-03-01
We explore the problems of degeneracy and discreteness in the standard cosmological model (ΛCDM). We use the Observational Hubble Data (OHD) and the type Ia supernovae (SNe Ia) data to study this issue. In order to describe the discreteness in fitting of data, we define a factor G to test the influence from each single data point and analyze the goodness of G. Our results indicate that a higher absolute value of G shows a better capability of distinguishing models, which means the parameters are restricted into smaller confidence intervals with a larger figure of merit evaluation. Consequently, we claim that the factor G is an effective way of model differentiation when using different models to fit the observational data.
Hydraulically controlled discrete sampling from open boreholes
Harte, Philip T.
2013-01-01
Groundwater sampling from open boreholes in fractured-rock aquifers is particularly challenging because of mixing and dilution of fluid within the borehole from multiple fractures. This note presents an alternative to traditional sampling in open boreholes with packer assemblies. The alternative system called ZONFLO (zonal flow) is based on hydraulic control of borehole flow conditions. Fluid from discrete fractures zones are hydraulically isolated allowing for the collection of representative samples. In rough-faced open boreholes and formations with less competent rock, hydraulic containment may offer an attractive alternative to physical containment with packers. Preliminary test results indicate a discrete zone can be effectively hydraulically isolated from other zones within a borehole for the purpose of groundwater sampling using this new method.
Discrete Abelian gauge symmetries and axions
NASA Astrophysics Data System (ADS)
Honecker, Gabriele; Staessens, Wieland
2015-07-01
We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete ℤn symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/ℤ2N and T6/ℤ2 × ℤ2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent ℤ2 symmetry is identified in a global Pati-Salam model, while global left-right symmetric models give rise to supersymmetric realizations of the DFSZ axion model. In one class of the latter models, the axion as well as Standard Model particles carry a non-trivial ℤ3 charge.
Multiple Autonomous Discrete Event Controllers for Constellations
NASA Technical Reports Server (NTRS)
Esposito, Timothy C.
2003-01-01
The Multiple Autonomous Discrete Event Controllers for Constellations (MADECC) project is an effort within the National Aeronautics and Space Administration Goddard Space Flight Center's (NASA/GSFC) Information Systems Division to develop autonomous positioning and attitude control for constellation satellites. It will be accomplished using traditional control theory and advanced coordination algorithms developed by the Johns Hopkins University Applied Physics Laboratory (JHU/APL). This capability will be demonstrated in the discrete event control test-bed located at JHU/APL. This project will be modeled for the Leonardo constellation mission, but is intended to be adaptable to any constellation mission. To develop a common software architecture. the controllers will only model very high-level responses. For instance, after determining that a maneuver must be made. the MADECC system will output B (Delta)V (velocity change) value. Lower level systems must then decide which thrusters to fire and for how long to achieve that (Delta)V.
Discrete dislocation dynamics simulations in a cylinder
NASA Astrophysics Data System (ADS)
Li, Maosheng; Gao, Chan; Xu, Jianing
2015-02-01
Mechanical properties of material are closely related to the motion of dislocations, and predicting the interactions and resulting collective motion of dislocations is a major task in understanding and modelling plastically deforming materials. A discrete dislocation dynamics model is used to describe the orientation substructure within the microstructure. Discrete dislocation dynamics simulations in three dimensions have been used to examine the role of dislocation multiplication and mobility on the plasticity in small samples under uniaxial compression. In this paper we describe the application of the dislocation dynamics simulations in a cylindrical geometry. The boundary conditions for the simulation were estimated from the distribution of the geometrically necessary dislocation density which was obtained from the orientation map. Numerical studies benchmark could validate the accuracy of the algorithms and the importance of handling the singularity correctly. The results of the simulation explain the formation of the experimentally observed substructure.
Discrete scale invariance in supercritical percolation
NASA Astrophysics Data System (ADS)
Schröder, Malte; Chen, Wei; Nagler, Jan
2016-01-01
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order parameter (Chen et al 2014 Phys. Rev. Lett. 112 155701). Here we report the discovery of macrotransition cascades which follow percolation. The order parameter grows in discrete macroscopic steps with positions that can be randomly distributed even in the thermodynamic limit. These transition positions are, however, correlated and follow scaling laws which arise from discrete scale invariance (DSI) and non self-averaging, both traditionally unrelated to percolation. We reveal the DSI in ensemble measurements of these non self-averaging systems by rescaling of the individual realizations before averaging.
Optimal Discretization Resolution in Algebraic Image Reconstruction
NASA Astrophysics Data System (ADS)
Sharif, Behzad; Kamalabadi, Farzad
2005-11-01
In this paper, we focus on data-limited tomographic imaging problems where the underlying linear inverse problem is ill-posed. A typical regularized reconstruction algorithm uses algebraic formulation with a predetermined discretization resolution. If the selected resolution is too low, we may loose useful details of the underlying image and if it is too high, the reconstruction will be unstable and the representation will fit irrelevant features. In this work, two approaches are introduced to address this issue. The first approach is using Mallow's CL method or generalized cross-validation. For each of the two methods, a joint estimator of regularization parameter and discretization resolution is proposed and their asymptotic optimality is investigated. The second approach is a Bayesian estimator of the model order using a complexity-penalizing prior. Numerical experiments focus on a space imaging application from a set of limited-angle tomographic observations.
Computational frameworks for discrete Gabor analysis
NASA Astrophysics Data System (ADS)
Strohmer, Thomas
1997-10-01
The Gabor transform yields a discrete representation of a signal in the phase space. Since the Gabor transform is non-orthogonal, efficient reconstruction of a signal from its phase space samples is not straightforward and involves the computation of the so- called dual Gabor function. We present a unifying approach to the derivation of numerical algorithms for discrete Gabor analysis, based on unitary matrix factorization. The factorization point of view is notably useful for the design of efficient numerical algorithms. This presentation is the first systematic account of its kind. In particular, it is shown that different algorithms for the computation of the dual window correspond to different factorizations of the frame operator. Simple number theoretic conditions on the time-frequency lattice parameters imply additional structural properties of the frame operator.
On Discrete Lotka-Volterra Type Models
NASA Astrophysics Data System (ADS)
Mukhamedov, Farrukh; Saburov, Mansoor
The Lotka-Volterra (in short LV) model is a second order nonlinear differential equation frequently used to describe the dynamics of biological systems in which two groups of species, predators and their preys interact. One of the basic results of the LV model is that under suitable conditions the LV model can exhibit any asymptotical behavior such as equilibrium states, periodic cycles, and attractors. The discrete analogy of LV model has been considered by many researchers and has been called a quadratic LV model. In a discrete case, one of the unexpected results is that a quadratic LV model cannot exhibit a periodic cycle. In this paper we study nonlinear LV type models which include quadratic LV as a particular case. Unlike quadratic LV models, LV type models can exhibit any asymptotical behavior such as equilibrium states, periodic cycles, and attractors.
A new model for discrete character evolution.
Grafen, A; Ridley, M
1997-01-01
The paper provides an explicit justification for the principle that a uniform taxon should contribute only one datapoint in comparative analyses with discrete variables. The justification is that phylogenetic patterns in variables unincluded in the proposed test vitiate the assumption of independence, both at the level of species and at the level of branch segments. The consequence is that a uniform taxon cannot safely be counted as more than one datapoint. The arguments use a branching discrete Markov process in continuous time, with the new feature that the tested variables are only a subset of the evolving characters. This model is proposed as a useful criterion for measuring the merit of proposed tests, and illustrates the necessity for models in evaluating comparative methods. PMID:9039396
A discrete formulation of the Wigner transport equation
NASA Astrophysics Data System (ADS)
Kim, Kyoung-Youm
2007-12-01
A discrete formulation of the Wigner distribution function (WDF) and the Wigner transport equation (WTE) is proposed, where the "discreteness" of the WDF and WTE is not just a practical, mathematical feature of discretization for the possible computations, but reveals a fundamental physics regarding the maximum correlation length of potentials (an essential quantum-mechanical feature of the WTE): it is set by the positional uncertainty due to the discrete values of momentum in evaluating the discrete WDF. Our formulation also shows that the weighting function to the potential-correlation term can be derived naturally from a mathematical necessity related to the antiperiodicity of the discrete density operator. In addition, we propose a mutually independent discretization scheme for the diagonal and cross-diagonal coordinates of the density operator, which results in a numerically effective discrete WTE in that it requires much less computational resources without significant loss in accuracy.
Performance of the discrete electrode railgun
Usuba, S.; Kakudate, Y.; Yoshida, M.; Aoki, K.; Yamawaki, H.; Fujiwara, S. ); Miyamoto, M. ); Kubota, A. ); Den, M. )
1991-01-01
In this paper a concept of Discrete Electrode (DE) railgun is presented. Plasma acceleration experiments using small DE railguns showed that the DE railgun could regulate the armature current distribution by means of fuses and a velocity of the armature current propagation was significantly higher than that in a normal type railgun. A mechanism of the armature current propagation in the DE railgun was discussed.
DOS: the discrete-ordinates system. [LMFBR
Rhoades, W. A.; Emmett, M. B.
1982-09-01
The Discrete Ordinates System determines the flux of neutrons or photons due either to fixed sources specified by the user or to sources generated by particle interaction with the problem materials. It also determines numerous secondary results which depend upon flux. Criticality searches can be performed. Numerous input, output, and file manipulation facilities are provided. The DOS driver program reads the problem specification from an input file and calls various program modules into execution as specified by the input file.
Discrete sequence prediction and its applications
NASA Technical Reports Server (NTRS)
Laird, Philip
1992-01-01
Learning from experience to predict sequences of discrete symbols is a fundamental problem in machine learning with many applications. We apply sequence prediction using a simple and practical sequence-prediction algorithm, called TDAG. The TDAG algorithm is first tested by comparing its performance with some common data compression algorithms. Then it is adapted to the detailed requirements of dynamic program optimization, with excellent results.
Additive discrete 1D linear canonical transform
NASA Astrophysics Data System (ADS)
Zhao, Liang; Healy, John J.; Guo, Chang-liang; Sheridan, John T.
2015-09-01
The continuous linear canonical transforms (LCT) can describe a wide variety of wave field propagations through paraxial (first order) optical systems. Digital algorithms to numerically calculate the LCT are therefore important in modelling scalar wave field propagations and are also of interest for many digital signal processing applications. The continuous LCT is additive, but discretization can remove this property. In this paper we discuss three special cases of the LCT for which constraints can be identified to ensure the DLCT is additive.
Discrete Bimodal Probes for Thrombus Imaging
Uppal, Ritika; Ciesienski, Kate L.; Chonde, Daniel B.; Loving, Galen S.; Caravan, Peter
2012-01-01
Here we report a generalizable solid/solution phase strategy for the synthesis of discrete bimodal fibrin-targeted imaging probes. A fibrin-specific peptide was conjugated with two distinct imaging reporters at the C- and N-terminus. In vitro studies demonstrated retention of fibrin affinity and specificity. Imaging studies showed that these probes could detect fibrin over a wide range of probe concentrations by optical, magnetic resonance, and positron emission tomography imaging. PMID:22698259
Continuous limit of discrete quantum walks
NASA Astrophysics Data System (ADS)
M N, Dheeraj; Brun, Todd A.
2015-06-01
Quantum walks can be defined in two quite distinct ways: discrete-time and continuous-time quantum walks (DTQWs and CTQWs). For classical random walks, there is a natural sense in which continuous-time walks are a limit of discrete-time walks. Quantum mechanically, in the discrete-time case, an additional "coin space" must be appended for the walk to have nontrivial time evolution. Continuous-time quantum walks, however, have no such constraints. This means that there is no completely straightforward way to treat a CTQW as a limit of a DTQW, as can be done in the classical case. Various approaches to this problem have been taken in the past. We give a construction for walks on d -regular, d -colorable graphs when the coin flip operator is Hermitian: from a standard DTQW we construct a family of discrete-time walks with a well-defined continuous-time limit on a related graph. One can think of this limit as a "coined" continuous-time walk. We show that these CTQWs share some properties with coined DTQWs. In particular, we look at a spatial search by a DTQW over the two-dimensional (2D) torus (a grid with periodic boundary conditions) of size √{N }×√{N } , where it was shown that a coined DTQW can search in time O (√{N }logN ) , but a standard CTQW takes Ω (N ) time to search for a marked element. The continuous limit of the DTQW search over the 2D torus exhibits the O (√{N }logN ) scaling, like the coined walk it is derived from. We also look at the effects of graph symmetry on the limiting walk, and show that the properties are similar to those of the DTQW as shown in Krovi and Brun, Phys. Rev. A 75, 062332 (2007), 10.1103/PhysRevA.75.062332.
Computational requirements for a discrete Kalman filter.
NASA Technical Reports Server (NTRS)
Mendel, J. M.
1971-01-01
Computational requirements - i.e., computing time per cycle (iteration) and required storage - which determine minimum sampling rates and computer memory size, were obtained as functions of the dimensions of the important system matrices for a discrete Kalman filter. Two types of measurement processing are discussed: simultaneous and sequential. It is shown that it is often better to process statistically independent measurements in more than one batch and then use sequential processing than to process them together via simultaneous processing.
High dimensional cohomology of discrete groups.
Brown, K S
1976-06-01
For a large class of discrete groups Gamma, relations are established between the high dimensional cohomology of Gamma and the cohomology of the normalizers of the finite subgroups of Gamma. The results are stated in terms of a generalization of Tate cohomology recently constructed by F. T. Farrell. As an illustration of these results, it is shown that one can recover a cohomology calculation of Lee and Szczarba, which they used to calculate the odd torsion in K(3)(Z). PMID:16592322
High dimensional cohomology of discrete groups
Brown, Kenneth S.
1976-01-01
For a large class of discrete groups Γ, relations are established between the high dimensional cohomology of Γ and the cohomology of the normalizers of the finite subgroups of Γ. The results are stated in terms of a generalization of Tate cohomology recently constructed by F. T. Farrell. As an illustration of these results, it is shown that one can recover a cohomology calculation of Lee and Szczarba, which they used to calculate the odd torsion in K3(Z). PMID:16592322
Joint discrete universality of Hurwitz zeta functions
NASA Astrophysics Data System (ADS)
Laurinčikas, A.
2014-11-01
We obtain a joint discrete universality theorem for Hurwitz zeta functions. Here the parameters of zeta functions and the step of shifts of these functions approximating a given family of analytic functions are connected by some condition of linear independence. Nesterenko's theorem gives an example satisfying this condition. The universality theorem is applied to estimate the number of zeros of a linear combination of Hurwitz zeta functions. Bibliography: 20 titles.
Discrete Atomic Layers at the Molecular Level
NASA Astrophysics Data System (ADS)
Yorimitsu, Hideki; Bhanuchandra, M.
2015-12-01
In this review, we deal with the syntheses of large discrete atomic layers at the molecular level. Spectroscopic measurements as well as X-ray crystallographic analyses lead to unambiguous characterizations of these layers. The molecular atomic layers can be considered to be parts of graphenes and related atomic layers, thereby helping to understand such indefinitely huge atomic layers or serving as seeds for the controlled synthesis of nanocarbons.
Discrete Inverse and State Estimation Problems
NASA Astrophysics Data System (ADS)
Wunsch, Carl
2006-06-01
The problems of making inferences about the natural world from noisy observations and imperfect theories occur in almost all scientific disciplines. This book addresses these problems using examples taken from geophysical fluid dynamics. It focuses on discrete formulations, both static and time-varying, known variously as inverse, state estimation or data assimilation problems. Starting with fundamental algebraic and statistical ideas, the book guides the reader through a range of inference tools including the singular value decomposition, Gauss-Markov and minimum variance estimates, Kalman filters and related smoothers, and adjoint (Lagrange multiplier) methods. The final chapters discuss a variety of practical applications to geophysical flow problems. Discrete Inverse and State Estimation Problems is an ideal introduction to the topic for graduate students and researchers in oceanography, meteorology, climate dynamics, and geophysical fluid dynamics. It is also accessible to a wider scientific audience; the only prerequisite is an understanding of linear algebra. Provides a comprehensive introduction to discrete methods of inference from incomplete information Based upon 25 years of practical experience using real data and models Develops sequential and whole-domain analysis methods from simple least-squares Contains many examples and problems, and web-based support through MIT opencourseware
Police investigations: discretion denied yet undeniably exercised
Belur, J.; Tilley, N.; Osrin, D.; Daruwalla, N.; Kumar, M.; Tiwari, V.
2014-01-01
Police investigations involve determining whether a crime has been committed, and if so what type of crime, who has committed it and whether there is the evidence to charge the perpetrators. Drawing on fieldwork in Delhi and Mumbai, this paper explores how police investigations unfolded in the specific context of women’s deaths by burning in India. In particular, it focuses on the use of discretion despite its denial by those exercising it. In India, there are distinctive statutes relating to women’s suspicious deaths, reflecting the widespread expectation that the bride’s family will pay a dowry to the groom’s family and the tensions to which this may on occasion give rise in the early years of a marriage. Often, there are conflicting claims influencing how the woman’s death is classified. These in turn affect police investigation. The nature and direction of police discretion in investigating women’s deaths by burning reflect in part the unique nature of the legislation and the particular sensitivities in relation to these types of death. They also highlight processes that are liable to be at work in any crime investigation. It was found that police officers exercised unacknowledged discretion at seven specific points in the investigative process, with potentially significant consequences for the achievement of just outcomes: first response, recording the victim’s ‘dying declaration’, inquest, registering of the ‘First Information Report’, collecting evidence, arrest and framing of the charges. PMID:26376482
Discrete Deterministic and Stochastic Petri Nets
NASA Technical Reports Server (NTRS)
Zijal, Robert; Ciardo, Gianfranco
1996-01-01
Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.
An essay on discrete foundations for physics
Noyes, H.P.; McGoveran, D.O.
1988-07-01
We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non-uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs.
An essay on discrete foundations for physics
Noyes, H.P.; McGoveran, D.O.
1988-10-05
We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non- uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs.
Light Adaptation of Discrete Waves in the Limulus Photoreceptor
Srebro, Richard; Behbehani, Mahmood
1972-01-01
Light adaptation affects discrete waves in two ways. It reduces their average size and decreases the probability that a photon incident at the cornea causes a discrete wave. There is no effect of light adaptation on the latency of discrete waves, or on their time-course. PMID:5042025
How to detect the integrability of discrete systems
NASA Astrophysics Data System (ADS)
Grammaticos, B.; Halburd, R. G.; Ramani, A.; Viallet, C.-M.
2009-10-01
Several integrability tests for discrete equations will be reviewed. All tests considered can be applied directly to a given discrete equation and do not rely on the a priori knowledge of the existence of related structures such as Lax pairs. Specifically, singularity confinement, algebraic entropy, Nevanlinna theory, Diophantine integrability and discrete systems over finite fields will be described.
5 CFR 7.1 - Discretion in filling vacancies.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 5 Administrative Personnel 1 2010-01-01 2010-01-01 false Discretion in filling vacancies. 7.1 Section 7.1 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE RULES GENERAL PROVISIONS (RULE VII) § 7.1 Discretion in filling vacancies. In his discretion, an appointing officer may fill...
Breaking and Restoring of Diffeomorphism Symmetry in Discrete Gravity
Bahr, B.; Dittrich, B.
2009-12-15
We discuss the fate of diffeomorphism symmetry in discrete gravity. Diffeomorphism symmetry is typically broken by the discretization. This has repercussions for the observable content and the canonical formulation of the theory. It might however be possible to construct discrete actions, so-called perfect actions, with exact symmetries and we will review first steps towards this end.
Fluctuations and discreteness in diffusion limited growth
NASA Astrophysics Data System (ADS)
Devita, Jason P.
This thesis explores the effects of fluctuations and discreteness on the growth of physical systems where diffusion plays an important role. It focuses on three related problems, all dependent on diffusion in a fundamental way, but each with its own unique challenges. With diffusion-limited aggregation (DLA), the relationship between noisy and noise-free Laplacian growth is probed by averaging the results of noisy growth. By doing so in a channel geometry, we are able to compare to known solutions of the noise-free problem. We see that while the two are comparable, there are discrepancies which are not well understood. In molecular beam epitaxy (MBE), we create efficient computational algorithms, by replacing random walkers (diffusing atoms) with approximately equivalent processes. In one case, the atoms are replaced by a continuum field. Solving for the dynamics of the field yields---in an average sense---the dynamics of the atoms. In the other case, the atoms are treated as individual random-walking particles, but the details of the dynamics are changed to an (approximately) equivalent set of dynamics. This approach involves allowing adatoms to take long hops. We see approximately an order of magnitude speed up for simulating island dynamics, mound growth, and Ostwald ripening. Some ideas from the study of MBE are carried over to the study of front propagation in reaction-diffusion systems. Many of the analytic results about front propagation are derived from continuum models. It is unclear, however, that these results accurately describe the properties of a discrete system. It is reasonable to think that discrete systems will converge to the continuum results when sufficiently many particles are included. However, computational evidence of this is difficult to obtain, since the interesting properties tend to depend on a power law of the logarithm of the number of particles. Thus, the number of particles included in simulations must be exceedingly large. By
Projected discrete ordinates methods for numerical transport problems
Larsen, E.W.
1985-01-01
A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.
Discretization of Continuous Time Discrete Scale Invariant Processes: Estimation and Spectra
NASA Astrophysics Data System (ADS)
Rezakhah, Saeid; Maleki, Yasaman
2016-07-01
Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a second continuous time DSI process which provides a proper approximation of the first one. This enables us to provide a bilateral relation between covariance functions of the subsidiary process and the new continuous time processes. The time varying spectral representation of such continuous time DSI process is characterized, and its spectrum is estimated. Also, a new method for estimation time dependent Hurst parameter of such processes is provided which gives a more accurate estimation. The performance of this estimation method is studied via simulation. Finally this method is applied to the real data of S & P500 and Dow Jones indices for some special periods.
Efficient discretization in finite difference method
NASA Astrophysics Data System (ADS)
Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris
2015-04-01
Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.
Efficient Associative Computation with Discrete Synapses.
Knoblauch, Andreas
2016-01-01
Neural associative networks are a promising computational paradigm for both modeling neural circuits of the brain and implementing associative memory and Hebbian cell assemblies in parallel VLSI or nanoscale hardware. Previous work has extensively investigated synaptic learning in linear models of the Hopfield type and simple nonlinear models of the Steinbuch/Willshaw type. Optimized Hopfield networks of size n can store a large number of about n(2)/k memories of size k (or associations between them) but require real-valued synapses, which are expensive to implement and can store at most C = 0.72 bits per synapse. Willshaw networks can store a much smaller number of about n(2)/k(2) memories but get along with much cheaper binary synapses. Here I present a learning model employing synapses with discrete synaptic weights. For optimal discretization parameters, this model can store, up to a factor ζ close to one, the same number of memories as for optimized Hopfield-type learning--for example, ζ = 0.64 for binary synapses, ζ = 0.88 for 2 bit (four-state) synapses, ζ = 0.96 for 3 bit (8-state) synapses, and ζ > 0.99 for 4 bit (16-state) synapses. The model also provides the theoretical framework to determine optimal discretization parameters for computer implementations or brainlike parallel hardware including structural plasticity. In particular, as recently shown for the Willshaw network, it is possible to store C(I) = 1 bit per computer bit and up to C(S) = log n bits per nonsilent synapse, whereas the absolute number of stored memories can be much larger than for the Willshaw model. PMID:26599711
Synaptic plasticity with discrete state synapses
NASA Astrophysics Data System (ADS)
Abarbanel, Henry D. I.; Talathi, Sachin S.; Gibb, Leif; Rabinovich, M. I.
2005-09-01
Experimental observations on synaptic plasticity at individual glutamatergic synapses from the CA3 Shaffer collateral pathway onto CA1 pyramidal cells in the hippocampus suggest that the transitions in synaptic strength occur among discrete levels at individual synapses [C. C. H. Petersen , Proc. Natl. Acad. Sci. USA 85, 4732 (1998); O’Connor, Wittenberg, and Wang, D. H. O’Connor , Proc. Natl. Acad. Sci. USA (to be published); J. M. Montgomery and D. V. Madison, Trends Neurosci. 27, 744 (2004)]. This happens for both long term potentiation (LTP) and long term depression (LTD) induction protocols. O’Connor, Wittenberg, and Wang have argued that three states would account for their observations on individual synapses in the CA3-CA1 pathway. We develop a quantitative model of this three-state system with transitions among the states determined by a competition between kinases and phosphatases shown by D. H. O’Connor , to be determinant of LTP and LTD, respectively. Specific predictions for various plasticity protocols are given by coupling this description of discrete synaptic α -amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor ligand gated ion channel conductance changes to a model of postsynaptic membrane potential and associated intracellular calcium fluxes to yield the transition rates among the states. We then present various LTP and LTD induction protocols to the model system and report the resulting whole cell changes in AMPA conductance. We also examine the effect of our discrete state synaptic plasticity model on the synchronization of realistic oscillating neurons. We show that one-to-one synchronization is enhanced by the plasticity we discuss here and the presynaptic and postsynaptic oscillations are in phase. Synaptic strength saturates naturally in this model and does not require artificial upper or lower cutoffs, in contrast to earlier models of plasticity.
Interventional tool tracking using discrete optimization.
Heibel, Hauke; Glocker, Ben; Groher, Martin; Pfister, Marcus; Navab, Nassir
2013-03-01
This work presents a novel scheme for tracking of motion and deformation of interventional tools such as guide-wires and catheters in fluoroscopic X-ray sequences. Being able to track and thus to estimate the correct positions of these tools is crucial in order to offer guidance enhancement during interventions. The task of estimating the apparent motion is particularly challenging due to the low signal-to-noise ratio (SNR) of fluoroscopic images and due to combined motion components originating from patient breathing and tool interactions performed by the physician. The presented approach is based on modeling interventional tools with B-splines whose optimal configuration of control points is determined through efficient discrete optimization. Each control point corresponds to a discrete random variable in a Markov random field (MRF) formulation where a set of labels represents the deformation space. In this context, the optimal curve corresponds to the maximum a posteriori (MAP) estimate of the MRF energy. The main motivation for employing a discrete approach is the possibility to incorporate a multi-directional search space which is robust to local minima. This is of particular interest for curve tracking under large deformation. This work analyzes feasibility of employing efficient first-order MRFs for tracking. In particular it shows how to achieve a good compromise between energy approximations and computational efficiency. Experimental results suggest to define both the external and internal energy in terms of pairwise potential functions. The method was successfully applied to the tracking of guide-wires in fluoroscopic X-ray sequences of several hundred frames which requires extremely robust techniques. Comparisons with state-of-the-art guide-wire tracking algorithms confirm the effectiveness of the proposed method. PMID:23232412
Optical tomography with discretized path integral.
Yuan, Bingzhi; Tamaki, Toru; Kushida, Takahiro; Mukaigawa, Yasuhiro; Kubo, Hiroyuki; Raytchev, Bisser; Kaneda, Kazufumi
2015-07-01
We present a framework for optical tomography based on a path integral. Instead of directly solving the radiative transport equations, which have been widely used in optical tomography, we use a path integral that has been developed for rendering participating media based on the volume rendering equation in computer graphics. For a discretized two-dimensional layered grid, we develop an algorithm to estimate the extinction coefficients of each voxel with an interior point method. Numerical simulation results are shown to demonstrate that the proposed method works well. PMID:26839903
Discrete Analysis of Clay Layer Tensile Strength
NASA Astrophysics Data System (ADS)
Lê, T. N. H.; Plé, O.; Villard, P.; Gotteland, P.; Gourc, J. P.
2009-06-01
The Discrete Element Method is used to investigate the tensile behaviour and cracks mechanisms of a clay material submitted to bending loading. It is the case of compacted clay liners in landfill cap cover application. Such as the soil tested in this study is plastic clay, the distinct elements model was calibrated with previous data results by taking into account cohesive properties. Various contact and cohesion laws are tested to show that the numerical model is able to reproduce the failure mechanism. Numerical results are extending to simulate a landfill cap cover.
Discrete computer analysis in petroleum geology
Zakharian, A.Z.
1995-08-01
Computer analysis must not be resembling on geologist`s work, having its own way because of uncertainty and shortness of geological information even on mature stage of exploration, when our original system of formal discrete computer analysis, realised on {open_quotes}FoxPro for Windows{close_quotes} with not substantial but probabilistic (without ever driving the usual maps) representation of geological situation was used for picking out the sets of best points for exploration drilling in south part of Dheprovsko-Donetzky oil-gas basin.
Discrete time modelization of human pilot behavior
NASA Technical Reports Server (NTRS)
Cavalli, D.; Soulatges, D.
1975-01-01
This modelization starts from the following hypotheses: pilot's behavior is a time discrete process, he can perform only one task at a time and his operating mode depends on the considered flight subphase. Pilot's behavior was observed using an electro oculometer and a simulator cockpit. A FORTRAN program has been elaborated using two strategies. The first one is a Markovian process in which the successive instrument readings are governed by a matrix of conditional probabilities. In the second one, strategy is an heuristic process and the concepts of mental load and performance are described. The results of the two aspects have been compared with simulation data.
Discrete analog computing with rotor-routers.
Propp, James
2010-09-01
Rotor-routing is a procedure for routing tokens through a network that can implement certain kinds of computation. These computations are inherently asynchronous (the order in which tokens are routed makes no difference) and distributed (information is spread throughout the system). It is also possible to efficiently check that a computation has been carried out correctly in less time than the computation itself required, provided one has a certificate that can itself be computed by the rotor-router network. Rotor-router networks can be viewed as both discrete analogs of continuous linear systems and deterministic analogs of stochastic processes. PMID:20887076
Construction of Discrete Time Shadow Price
Rogala, Tomasz Stettner, Lukasz
2015-12-15
In the paper expected utility from consumption over finite time horizon for discrete time markets with bid and ask prices and strictly concave utility function is considered. The notion of weak shadow price, i.e. an illiquid price, depending on the portfolio, under which the model without bid and ask price is equivalent to the model with bid and ask price is introduced. Existence and the form of weak shadow price is shown. Using weak shadow price usual (called in the paper strong) shadow price is then constructed.
Compartmentalization analysis using discrete fracture network models
La Pointe, P.R.; Eiben, T.; Dershowitz, W.; Wadleigh, E.
1997-08-01
This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph the theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.
Discrete Space Theory of Radiative Transfer: Application
NASA Astrophysics Data System (ADS)
Rao, M. Srinivasa
2010-06-01
The method of obtaining the solution of radiative transfer equation using discrete space theory (DST) is described with (1) interaction principle for different geometries (2) star product (3) calculation of radiation field at internal points. Some of the important steps to obtain the solution of radiative transfer equation in spherical symmetry are also mentioned. Applications of DST are discussed with their results in two cases (a) study of reflection effect in close binary systems and (b) to compute KI 769.9 nm emission line profiles from N-type stars.
Discrete Space Theory of Radiative Transfer: Application
NASA Astrophysics Data System (ADS)
Rao, M. Srinivasa
The method of obtaining the solution of radiative transfer equation using discrete space theory (DST) is described with (1) interaction principle for different geometries (2) star product (3) calculation of radiation field at internal points. Some of the important steps to obtain the solution of radiative transfer equation in spherical symmetry are also mentioned. Applications of DST are discussed with their results in two cases (a) study of reflection effect in close binary systems and (b) to compute KI 769.9 nm emission line profiles from N-type stars.
Discrete Wigner functions and quantum computational speedup
Galvao, Ernesto F.
2005-04-01
Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize the set C{sub d} of states having non-negative W simultaneously in all definitions of W in this class. For d{<=}5 I show C{sub d} is the convex hull of stabilizer states. This supports the conjecture that negativity of W is necessary for exponential speedup in pure-state quantum computation.
Coagulation and fragmentation with discrete mass loss
NASA Astrophysics Data System (ADS)
Blair, Pamela N.; Lamb, Wilson; Stewart, Iain W.
2007-05-01
A nonlinear integro-differential equation that models a coagulation and multiple fragmentation process in which discrete fragmentation mass loss can occur is examined using the theory of strongly continuous semigroups of operators. Under the assumptions that the coagulation kernel is bounded and the fragmentation rate function a satisfies a linear growth condition, global existence and uniqueness of solutions that lose mass in accordance with the model are established. In the case when no coagulation is present and the fragmentation process is governed by power-law kernels, an explicit formula is given for the substochastic semigroup associated with the resulting mass-loss fragmentation equation.
Compartmentalization analysis using discrete fracture network models
La Pointe, P.R.; Eiben, T.; Dershowitz, W.; Wadleigh, E.
1997-12-31
This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.
Partitioning technique for discrete quantum systems
Jin, L.; Song, Z.
2011-06-15
We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show that the effective Hamiltonian on the central graph can be constructed by adding additional potentials on the branch-root nodes, which generates the same result as does the the original Hamiltonian on the entire graph. Exactly solvable models are presented to demonstrate the main points of this paper.
Time Discretization Approach to Dynamic Localization Conditions
NASA Astrophysics Data System (ADS)
Papp, E.
An alternative wavefunction to the description of the dynamic localization of a charged particle moving on a one-dimensional lattice under the influence of a periodic time dependent electric field is written down. For this purpose the method of characteristics such as applied by Dunlap and Kenkre [Phys. Rev. B 34, 3625 (1986)] has been modified by using a different integration variable. Handling this wavefunction one is faced with the selection of admissible time values. This results in a conditionally exactly solvable problem, now by accounting specifically for the implementation of a time discretization working in conjunction with a related dynamic localization condition. In addition, one resorts to the strong field limit, which amounts to replace, to leading order, the large order zeros of the Bessel function J0(z), used before in connection with the cosinusoidal modulation, by integral multiples of π. Here z stands for the ratio between the field amplitude and the frequency. The modulation function of the electric field vanishes on the nodal points of the time grid, which stands for an effective field-free behavior. This opens the way to propose quickly tractable dynamic localization conditions for arbitrary periodic modulations. We have also found that the present time discretization approach produces the minimization of the mean square displacement characterizing the usual exact wavefunction. Other realizations and comparisons have also been presented.
A Discrete Model for Color Naming
NASA Astrophysics Data System (ADS)
Menegaz, G.; Le Troter, A.; Sequeira, J.; Boi, J. M.
2006-12-01
The ability to associate labels to colors is very natural for human beings. Though, this apparently simple task hides very complex and still unsolved problems, spreading over many different disciplines ranging from neurophysiology to psychology and imaging. In this paper, we propose a discrete model for computational color categorization and naming. Starting from the 424 color specimens of the OSA-UCS set, we propose a fuzzy partitioning of the color space. Each of the 11 basic color categories identified by Berlin and Kay is modeled as a fuzzy set whose membership function is implicitly defined by fitting the model to the results of an ad hoc psychophysical experiment (Experiment 1). Each OSA-UCS sample is represented by a feature vector whose components are the memberships to the different categories. The discrete model consists of a three-dimensional Delaunay triangulation of the CIELAB color space which associates each OSA-UCS sample to a vertex of a 3D tetrahedron. Linear interpolation is used to estimate the membership values of any other point in the color space. Model validation is performed both directly, through the comparison of the predicted membership values to the subjective counterparts, as evaluated via another psychophysical test (Experiment 2), and indirectly, through the investigation of its exploitability for image segmentation. The model has proved to be successful in both cases, providing an estimation of the membership values in good agreement with the subjective measures as well as a semantically meaningful color-based segmentation map.
Harmonic Pinnacles in the Discrete Gaussian Model
NASA Astrophysics Data System (ADS)
Lubetzky, Eyal; Martinelli, Fabio; Sly, Allan
2016-06-01
The 2 D Discrete Gaussian model gives each height function {η : Z^2to{Z}} a probability proportional to {exp(-β {H}(η))}, where {β} is the inverse-temperature and {{H}(η) = sum_{x˜ y}(η_x-η_y)^2} sums over nearest-neighbor bonds. We consider the model at large fixed {β}, where it is flat unlike its continuous analog (the Discrete Gaussian Free Field). We first establish that the maximum height in an {L× L} box with 0 boundary conditions concentrates on two integers M, M + 1 with {M˜ √{(1/2πβ)log Llog log L}}. The key is a large deviation estimate for the height at the origin in {{Z}2}, dominated by "harmonic pinnacles", integer approximations of a harmonic variational problem. Second, in this model conditioned on {η≥ 0} (a floor), the average height rises, and in fact the height of almost all sites concentrates on levels H, H + 1 where {H˜ M/√{2}}. This in particular pins down the asymptotics, and corrects the order, in results of Bricmont et al. (J. Stat. Phys. 42(5-6):743-798, 1986), where it was argued that the maximum and the height of the surface above a floor are both of order {√{log L}}. Finally, our methods extend to other classical surface models (e.g., restricted SOS), featuring connections to p-harmonic analysis and alternating sign matrices.
Discrete distributed strain sensing of intelligent structures
NASA Technical Reports Server (NTRS)
Anderson, Mark S.; Crawley, Edward F.
1992-01-01
Techniques are developed for the design of discrete highly distributed sensor systems for use in intelligent structures. First the functional requirements for such a system are presented. Discrete spatially averaging strain sensors are then identified as satisfying the functional requirements. A variety of spatial weightings for spatially averaging sensors are examined, and their wave number characteristics are determined. Preferable spatial weightings are identified. Several numerical integration rules used to integrate such sensors in order to determine the global deflection of the structure are discussed. A numerical simulation is conducted using point and rectangular sensors mounted on a cantilevered beam under static loading. Gage factor and sensor position uncertainties are incorporated to assess the absolute error and standard deviation of the error in the estimated tip displacement found by numerically integrating the sensor outputs. An experiment is carried out using a statically loaded cantilevered beam with five point sensors. It is found that in most cases the actual experimental error is within one standard deviation of the absolute error as found in the numerical simulation.
Discrete quantum spectrum of black holes
NASA Astrophysics Data System (ADS)
Lochan, Kinjalk; Chakraborty, Sumanta
2016-04-01
The quantum genesis of Hawking radiation is a long-standing puzzle in black hole physics. Semi-classically one can argue that the spectrum of radiation emitted by a black hole look very much sparse unlike what is expected from a thermal object. It was demonstrated through a simple quantum model that a quantum black hole will retain a discrete profile, at least in the weak energy regime. However, it was suggested that this discreteness might be an artifact of the simplicity of eigen-spectrum of the model considered. Different quantum theories can, in principle, give rise to different complicated spectra and make the radiation from black hole dense enough in transition lines, to make them look continuous in profile. We show that such a hope from a geometry-quantized black hole is not realized as long as large enough black holes are dubbed with a classical mass area relation in any gravity theory ranging from GR, Lanczos-Lovelock to f(R) gravity. We show that the smallest frequency of emission from black hole in any quantum description, is bounded from below, to be of the order of its inverse mass. That leaves the emission with only two possibilities. It can either be non-thermal, or it can be thermal only with the temperature being much larger than 1/M.
Analysis of discretization errors in LES
NASA Technical Reports Server (NTRS)
Ghosal, Sandip
1995-01-01
All numerical simulations of turbulence (DNS or LES) involve some discretization errors. The integrity of such simulations therefore depend on our ability to quantify and control such errors. In the classical literature on analysis of errors in partial differential equations, one typically studies simple linear equations (such as the wave equation or Laplace's equation). The qualitative insight gained from studying such simple situations is then used to design numerical methods for more complex problems such as the Navier-Stokes equations. Though such an approach may seem reasonable as a first approximation, it should be recognized that strongly nonlinear problems, such as turbulence, have a feature that is absent in linear problems. This feature is the simultaneous presence of a continuum of space and time scales. Thus, in an analysis of errors in the one dimensional wave equation, one may, without loss of generality, rescale the equations so that the dependent variable is always of order unity. This is not possible in the turbulence problem since the amplitudes of the Fourier modes of the velocity field have a continuous distribution. The objective of the present research is to provide some quantitative measures of numerical errors in such situations. Though the focus of this work is LES, the methods introduced here can be just as easily applied to DNS. Errors due to discretization of the time-variable are neglected for the purpose of this analysis.
Compressor Stability Enhancement Using Discrete Tip Injection
NASA Technical Reports Server (NTRS)
Suder, Kenneth L.; Hathaway, Michael D.; Thorp, Scott A.; Strazisar, Anthony J.; Bright, Michelle B.
2001-01-01
Mass injection upstream of the tip of a high-speed axial compressor rotor is a stability enhancement approach known to be effective in suppressing small in tip-critical rotors. This process is examined in a transonic axial compressor rotor through experiments and time-averaged Navier-Stokes CFD simulations. Measurements and simulations for discrete injection are presented for a range of injection rates and distributions of injectors around the annulus. The simulations indicate that tip injection increases stability by unloading the rotor tip and that increasing injection velocity improves the effectiveness of tip injection. For the tested rotor, experimental results demonstrate that at 70 percent speed the stalling flow coefficient can be reduced by 30 percent using an injected mass- flow equivalent to 1 percent of the annulus flow. At design speed, the stalling flow coefficient was reduced by 6 percent using an injected mass-fiow equivalent to 2 percent of the annulus flow. The experiments show that stability enhancement is related to the mass-averaged axial velocity at the tip. For a given injected mass-flow, the mass-averaged axial velocity at the tip is increased by injecting flow over discrete portions of the circumference as opposed to full-annular injection. The implications of these results on the design of recirculating casing treatments and other methods to enhance stability will be discussed.
Discrete Bubble Modeling for Cavitation Bubbles
NASA Astrophysics Data System (ADS)
Choi, Jin-Keun; Chahine, Georges; Hsiao, Chao-Tsung
2007-03-01
Dynaflow, Inc. has conducted extensive studies on non-spherical bubble dynamics and interactions with solid and free boundaries, vortical flow structures, and other bubbles. From these studies, emerged a simplified Surface Averaged Pressure (SAP) spherical bubble dynamics model and a Lagrangian bubble tracking scheme. In this SAP scheme, the pressure and velocity of the surrounding flow field are averaged on the bubble surface, and then used for the bubble motion and volume dynamics calculations. This model is implemented using the Fluent User Defined Function (UDF) as Discrete Bubble Model (DBM). The Bubble dynamics portion can be solved using an incompressible liquid modified Rayleigh-Plesset equation or a compressible liquid modified Gilmore equation. The Discrete Bubble Model is a very suitable tool for the studies on cavitation inception of foils and turbo machinery, bubble nuclei effects, noise from the bubbles, and can be used in many practical problems in industrial and naval applications associated with flows in pipes, jets, pumps, propellers, ships, and the ocean. Applications to propeller cavitation, wake signatures of waterjet propelled ships, bubble-wake interactions, modeling of cavitating jets, and bubble entrainments around a ship will be presented.