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Sample records for instance geometry approximation

  1. A practical approximation algorithm for solving massive instances of hybridization number

    Iersel, van L.J.J.; Kelk, S.M.; Lekic, N.; Scornavacca, C.; Raphael, B.; Tang, J.

    2012-01-01

    Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. In practice, exact solvers struggle to solve instances with

  2. Padé approximations and diophantine geometry.

    Chudnovsky, D V; Chudnovsky, G V

    1985-04-01

    Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves.

  3. A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees.

    van Iersel, Leo; Kelk, Steven; Lekić, Nela; Scornavacca, Celine

    2014-05-05

    Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. Even for binary trees, exact solvers struggle to solve instances with reticulation number larger than 40-50. Here we present CycleKiller and NonbinaryCycleKiller, the first methods to produce solutions verifiably close to optimality for instances with hundreds or even thousands of reticulations. Using simulations, we demonstrate that these algorithms run quickly for large and difficult instances, producing solutions that are very close to optimality. As a spin-off from our simulations we also present TerminusEst, which is the fastest exact method currently available that can handle nonbinary trees: this is used to measure the accuracy of the NonbinaryCycleKiller algorithm. All three methods are based on extensions of previous theoretical work (SIDMA 26(4):1635-1656, TCBB 10(1):18-25, SIDMA 28(1):49-66) and are publicly available. We also apply our methods to real data.

  4. Sums over geometries and improvements on the mean field approximation

    Sacksteder, Vincent E. IV

    2007-01-01

    The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean-field approximations to D-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally treelike, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels

  5. Analytic Approximation to Radiation Fields from Line Source Geometry

    Michieli, I.

    2000-01-01

    Line sources with slab shields represent typical source-shield configuration in gamma-ray attenuation problems. Such shielding problems often lead to the generalized Secant integrals of the specific form. Besides numerical integration approach, various expansions and rational approximations with limited applicability are in use for computing the value of such integral functions. Lately, the author developed rapidly convergent infinite series representation of generalized Secant Integrals involving incomplete Gamma functions. Validity of such representation was established for zero and positive values of integral parameter a (a=0). In this paper recurrence relations for generalized Secant Integrals are derived allowing us simple approximate analytic calculation of the integral for arbitrary a values. It is demonstrated how truncated series representation can be used, as the basis for such calculations, when possibly negative a values are encountered. (author)

  6. Specific features of time-dependent Psub(N) approximations in spherical geometry

    Peltzer, P.; Pucker, N.

    1979-01-01

    Approximations to the time-dependent linear transport equation can result in more serious distortions in the description of the actual physical situation than in the stationary problem. This is demonstrated in detail for the case of a neutron pulse in spherical geometry, treated within a P 1 approximation. One has to pay special attention to the singularity at r = 0 and to the effect of the boundary conditions. Effects similar to those shown here are also to be expected in connection with Psub(N) approximations of higher order. (Auth.)

  7. Approximations to the non-adiabatic particle response in toroidal geometry

    Schep, T.J.; Braams, B.J.

    1981-08-01

    The non-adiabatic part of the particle response to low-frequency electromagnetic modes with long parallel wavelengths is discussed. Analytic approximations to the kernels of the integrals that relate the amplitudes of the perturbed potentials to the non-adiabatic part of the perturbed density in an axisymmetric toroidal configuration are presented and the results are compared with numerical calculations. It is shown that both in the plane slab and in toroidal geometry the kernel contains a logarithmic singularity. This singularity is associated with particles with vanishing parallel velocity so that, in toroidal geometry, it is related with the behaviour of trapped particles near their turning points. In contrast to the plane slab, in toroidal geometry this logarithmic singularity is mainly real and associated with non-resonant particles. Apart from this logarithmic term, the kernel contains a complex regular part arising from resonant as well as from non-resonant particles. The analytic approximations that will be presented make the dispersion relation of drift-type modes in toroidal geometry amenable to analytic as well as to simpler numerical calculation of the growth rate and of the spatial mode structure

  8. Solution of the kinetic equation in the P3-approximation in a plane geometry

    Vlasov, Yu.A.

    1975-01-01

    A method and a program are described for solving single-velocity kinetic equations of neutron transfer for the plane geometry in the finite-difference approximation. A difference high-accuracy scheme and a matrix factorization method are used for the differential-difference equation systems. The program is written in the ALGOL-60 language and is adapted for M-20, M-220, M-222 and BESM-4 computers

  9. Approximate albedo boundary conditions for energy multigroup X,Y-geometry discrete ordinates nuclear global calculations

    Silva, Davi J.M.; Nunes, Carlos E.A.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: davijmsilva@yahoo.com.br, E-mail: ceanunes@yahoo.com.br, E-mail: rcbarros@pq.cnpq.br [Secretaria Municipal de Educacao de Itaborai, RJ (Brazil); Universidade Estacio de Sa (UNESA), Rio de Janeiro, RJ (Brazil); Universidade do Estado do Rio de Janeiro (UERJ), Novra Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional

    2017-11-01

    Discussed here is the accuracy of approximate albedo boundary conditions for energy multigroup discrete ordinates (S{sub N}) eigenvalue problems in two-dimensional rectangular geometry for criticality calculations in neutron fission reacting systems, such as nuclear reactors. The multigroup (S{sub N}) albedo matrix substitutes approximately the non-multiplying media around the core, e.g., baffle and reflector, as we neglect the transverse leakage terms within these non-multiplying regions. Numerical results to a typical model problem are given to illustrate the accuracy versus the computer running time. (author)

  10. Effect of cosine current approximation in lattice cell calculations in cylindrical geometry

    Mohanakrishnan, P.

    1978-01-01

    It is found that one-dimensional cylindrical geometry reactor lattice cell calculations using cosine angular current approximation at spatial mesh interfaces give results surprisingly close to the results of accurate neutron transport calculations as well as experimental measurements. This is especially true for tight light water moderated lattices. Reasons for this close agreement are investigated here. By re-examining the effects of reflective and white cell boundary conditions in these calculations it is concluded that one major reason is the use of white boundary condition necessitated by the approximation of the two-dimensional reactor lattice cell by a one-dimensional one. (orig.) [de

  11. Rational function approximation method for discrete ordinates problems in slab geometry

    Leal, Andre Luiz do C.; Barros, Ricardo C.

    2009-01-01

    In this work we use rational function approaches to obtain the transfer functions that appear in the spectral Green's function (SGF) auxiliary equations for one-speed isotropic scattering SN equations in one-dimensional Cartesian geometry. For this task we use the computation of the Pade approximants to compare the results with the standard SGF method's applied to deep penetration problems in homogeneous domains. This work is a preliminary investigation of a new proposal for handling leakage terms that appear in the two transverse integrated one-dimensional SN equations in the exponential SGF method (SGF-ExpN). Numerical results are presented to illustrate the rational function approximation accuracy. (author)

  12. SHADOK-3-6, Transport Equation with Anisotropic Diffusion in P1 Approximation for Spherical and Cylindrical Geometry

    Ligou, J.; Thomi, P.A.

    1973-01-01

    1 - Nature of physical problem solved: Integral transport equation, anisotropy of diffusion in P1 approximation. SHADOK3 - cylindrical geometry; direct solution of the linear system. SHADOK4 - cylindrical geometry; Thermalization iteration; solution of the linear system with inverse matrix calculation. SHADOK5 - like SHADOK3 for spherical geometry. SHADOK6 - like SHADOK4 for spherical geometry. 2 - Method of solution: Analysis in terms of annuli for each of which polynomial approximation is applied. Dynamic allocation (for formulas see report TM(10)). 3 - Restrictions on the complexity of the problem: Relative accuracy of the Bickley functions about 1.0E-13

  13. Variational P1 approximations of general-geometry multigroup transport problems

    Rulko, R.P.; Tomasevic, D.; Larsen, E.W.

    1995-01-01

    A variational approximation is developed for general-geometry multigroup transport problems with arbitrary anisotropic scattering. The variational principle is based on a functional that approximates a reaction rate in a subdomain of the system. In principle, approximations that result from this functional ''optimally'' determine such reaction rates. The functional contains an arbitrary parameter α and requires the approximate solutions of a forward and an adjoint transport problem. If the basis functions for the forward and adjoint solutions are chosen to be linear functions of the angular variable Ω, the functional yields the familiar multigroup P 1 equations for all values of α. However, the boundary conditions that result from the functional depend on α. In particular, for problems with vacuum boundaries, one obtains the conventional mixed boundary condition, but with an extrapolation distance that depends continuously on α. The choice α = 0 yields a generalization of boundary conditions derived earlier by Federighi and Pomraning for a more limited class of problems. The choice α = 1 yields a generalization of boundary conditions derived previously by Davis for monoenergetic problems. Other boundary conditions are obtained by choosing different values of α. The authors discuss this indeterminancy of α in conjunction with numerical experiments

  14. Dose uncertainties for large solar particle events: Input spectra variability and human geometry approximations

    Townsend, Lawrence W.; Zapp, E. Neal

    1999-01-01

    The true uncertainties in estimates of body organ absorbed dose and dose equivalent, from exposures of interplanetary astronauts to large solar particle events (SPEs), are essentially unknown. Variations in models used to parameterize SPE proton spectra for input into space radiation transport and shielding computer codes can result in uncertainty about the reliability of dose predictions for these events. Also, different radiation transport codes and their input databases can yield significant differences in dose predictions, even for the same input spectra. Different results may also be obtained for the same input spectra and transport codes if different spacecraft and body self-shielding distributions are assumed. Heretofore there have been no systematic investigations of the variations in dose and dose equivalent resulting from these assumptions and models. In this work we present a study of the variability in predictions of organ dose and dose equivalent arising from the use of different parameters to represent the same incident SPE proton data and from the use of equivalent sphere approximations to represent human body geometry. The study uses the BRYNTRN space radiation transport code to calculate dose and dose equivalent for the skin, ocular lens and bone marrow using the October 1989 SPE as a model event. Comparisons of organ dose and dose equivalent, obtained with a realistic human geometry model and with the oft-used equivalent sphere approximation, are also made. It is demonstrated that variations of 30-40% in organ dose and dose equivalent are obtained for slight variations in spectral fitting parameters obtained when various data points are included or excluded from the fitting procedure. It is further demonstrated that extrapolating spectra from low energy (≤30 MeV) proton fluence measurements, rather than using fluence data extending out to 100 MeV results in dose and dose equivalent predictions that are underestimated by factors as large as 2

  15. Geometries

    Sossinsky, A B

    2012-01-01

    The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...

  16. Geometry

    . In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...

  17. Approximation methods in loop quantum cosmology: from Gowdy cosmologies to inhomogeneous models in Friedmann–Robertson–Walker geometries

    Martín-Benito, Mercedes; Martín-de Blas, Daniel; Marugán, Guillermo A Mena

    2014-01-01

    We develop approximation methods in the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field, for the case of three-torus spatial topology. The loop quantization of the homogeneous gravitational sector of the Gowdy model (according to the improved dynamics prescription) and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical results calls for the introduction of well justified approximations. We first show how to approximate the homogeneous part of the Hamiltonian constraint, corresponding to Bianchi I geometries, as if it described a Friedmann–Robertson–Walker (FRW) model corrected with anisotropies. This approximation is valid in the sector of high energies of the FRW geometry (concerning its contribution to the constraint) and for anisotropy profiles that are sufficiently smooth. In addition, for certain families of states related to regimes of physical interest, with negligible quantum effects of the anisotropies and small inhomogeneities, one can approximate the Hamiltonian constraint of the inhomogeneous system by that of an FRW geometry with a relatively simple matter content, and then obtain its solutions. (paper)

  18. Geometry

    Prasolov, V V

    2015-01-01

    This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

  19. Program for photon shielding calculations. Examination of approximations on irradiation geometries

    Isozumi, Yasuhito; Ishizuka, Fumihiko; Miyatake, Hideo; Kato, Takahisa; Tosaki, Mitsuo

    2004-01-01

    Penetration factors and related numerical data in 'Manual of Practical Shield Calculation of Radiation Facilities (2000)', which correspond to the irradiation geometries of point isotropic source in infinite thick material (PI), point isotropic source in finite thick material (PF) and vertical incident to finite thick material (VF), have been carefully examined. The shield calculation based on the PI geometry is usually performed with effective dose penetration factors of radioisotopes given in the 'manual'. The present work cleary shows that such a calculation may lead to an overestimate more than twice larger, especially for thick shield of concrete and water. Employing the numerical data in the 'manual', we have fabricated a simple computer program for the estimation of penetration factors and effective doses of radioisotopes in the different irradiation geometries, i.e., PI, PF and VF. The program is also available to calculate the effective dose from a set of radioisotopes in the different positions, which is necessary for the γ-ray shielding of radioisotope facilities. (author)

  20. Diffusion Coefficient Calculations With Low Order Legendre Polynomial and Chebyshev Polynomial Approximation for the Transport Equation in Spherical Geometry

    Yasa, F.; Anli, F.; Guengoer, S.

    2007-01-01

    We present analytical calculations of spherically symmetric radioactive transfer and neutron transport using a hypothesis of P1 and T1 low order polynomial approximation for diffusion coefficient D. Transport equation in spherical geometry is considered as the pseudo slab equation. The validity of polynomial expansionion in transport theory is investigated through a comparison with classic diffusion theory. It is found that for causes when the fluctuation of the scattering cross section dominates, the quantitative difference between the polynomial approximation and diffusion results was physically acceptable in general

  1. Neutron diffusion approximation solution for the the three layer borehole cylindrical geometry. Pt. 1. Theoretical description

    Czubek, J.A.; Woznicka, U.

    1997-01-01

    A solution of the neutron diffusion equation is given for a three layer cylindrical coaxial geometry. The calculation is performed in two neutron-energy groups which distinguish the thermal and epithermal neutron fluxes in the media irradiated by the fast point neutron source. The aim of the calculation is to define the neutron slowing down and migration lengths which are observed at a given point of the system. Generally, the slowing down and migration lengths are defined for an infinite homogenous medium (irradiated by the point neutron source) as a quotient of the neutron flux moment of the (2n + 2)-order to the moment of the 2n-order. Czubek(1992) introduced in the same manner the apparent neutron slowing down length and the apparent migration length for a given multi-region cylindrical geometry. The solutions in the present paper are applied to the method of semi-empirical calibration of neutron well-logging tools. The three-region cylindrical geometry corresponds to the borehole of radius R 1 surrounded by the intermediate region (e.g. mud cake) of thickness (R 2 -R 1 ) and finally surrounded by the geological formation which spreads from R 2 up to infinity. The cylinders of an infinite length are considered. The paper gives detailed solutions for the 0-th, 2-nd and 4-th neutron moments of the neutron fluxes for each neutron energy group and in each cylindrical layer. A comprehensive list of the solutions for integrals containing Bessel functions or their derivatives, which are absent in common tables of integrals, is also included. (author)

  2. Neutron diffusion approximation solution for the the three layer borehole cylindrical geometry. Pt. 1. Theoretical description

    Czubek, J.A.; Woznicka, U. [The H. Niewodniczanski Inst. of Nuclear Physics, Cracow (Poland)

    1997-12-31

    A solution of the neutron diffusion equation is given for a three layer cylindrical coaxial geometry. The calculation is performed in two neutron-energy groups which distinguish the thermal and epithermal neutron fluxes in the media irradiated by the fast point neutron source. The aim of the calculation is to define the neutron slowing down and migration lengths which are observed at a given point of the system. Generally, the slowing down and migration lengths are defined for an infinite homogenous medium (irradiated by the point neutron source) as a quotient of the neutron flux moment of the (2n{sup +}2)-order to the moment of the 2n-order. Czubek(1992) introduced in the same manner the apparent neutron slowing down length and the apparent migration length for a given multi-region cylindrical geometry. The solutions in the present paper are applied to the method of semi-empirical calibration of neutron well-logging tools. The three-region cylindrical geometry corresponds to the borehole of radius R{sub 1} surrounded by the intermediate region (e.g. mud cake) of thickness (R{sub 2}-R{sub 1}) and finally surrounded by the geological formation which spreads from R{sub 2} up to infinity. The cylinders of an infinite length are considered. The paper gives detailed solutions for the 0-th, 2-nd and 4-th neutron moments of the neutron fluxes for each neutron energy group and in each cylindrical layer. A comprehensive list of the solutions for integrals containing Bessel functions or their derivatives, which are absent in common tables of integrals, is also included. (author) 6 refs, 2 figs

  3. Development of a discrete-ordinate approximation of the neutron transport equation for coupled xy-R-geometry

    Maertens, H.D.

    1982-01-01

    The inhomogenious structure of modern heavy water reactor fuel elements result in a strong spacial dependence of the neutron flux. The flux distribution can be calculated in detail by numerical methods, which describe exactly the geometrical heterogeniety and take into account the neutron flux anisotropy by higher transport theoretical approximations. Starting from the discrete ordinate method an approximation of the neutron transport equation has been developed, allowing for a cylindrical representation of the fuel-elements in a rectangular array of rods. The discretisation of the space variables, is based on the finite-difference approximation, defining a rectangular lattice in a two-dimensional cartesian coordinate system, which can be cut and replaced by circular mesh elements of a partially one-dimensional cylindrical coordinate system at arbitrary space points. To couple the two spacial regions the outer circle line of a cylindrical geometry is approximated in the cartesian system by a polygon with n >= 8. A cylindrical geometry is approximated in the cartesian system by a polygon with n>=8. A cylindrical geometry is thus enclosed by a system of two-dimensional rectangular, triangular and trapezoid mesh elements. The directional distribution of the neutron flux is conserved when switching from the xy-system to the cylindrical coordinate system. The angle discretisation by balanced sets of squares (EQsub(n)) allows a simple definition of transfer-coefficients for the redistribution of the neutron flux due to coordinate transformations. The procedure is verified and tested by selected problems. Possible applications and limits are discussed. (orig.) [de

  4. Floating-point geometry: toward guaranteed geometric computations with approximate arithmetics

    Bajard, Jean-Claude; Langlois, Philippe; Michelucci, Dominique; Morin, Géraldine; Revol, Nathalie

    2008-08-01

    Geometric computations can fail because of inconsistencies due to floating-point inaccuracy. For instance, the computed intersection point between two curves does not lie on the curves: it is unavoidable when the intersection point coordinates are non rational, and thus not representable using floating-point arithmetic. A popular heuristic approach tests equalities and nullities up to a tolerance ɛ. But transitivity of equality is lost: we can have A approx B and B approx C, but A not approx C (where A approx B means ||A - B|| < ɛ for A,B two floating-point values). Interval arithmetic is another, self-validated, alternative; the difficulty is to limit the swell of the width of intervals with computations. Unfortunately interval arithmetic cannot decide equality nor nullity, even in cases where it is decidable by other means. A new approach, developed in this paper, consists in modifying the geometric problems and algorithms, to account for the undecidability of the equality test and unavoidable inaccuracy. In particular, all curves come with a non-zero thickness, so two curves (generically) cut in a region with non-zero area, an inner and outer representation of which is computable. This last approach no more assumes that an equality or nullity test is available. The question which arises is: which geometric problems can still be solved with this last approach, and which cannot? This paper begins with the description of some cases where every known arithmetic fails in practice. Then, for each arithmetic, some properties of the problems they can solve are given. We end this work by proposing the bases of a new approach which aims to fulfill the geometric computations requirements.

  5. Geometry

    Pedoe, Dan

    1988-01-01

    ""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he

  6. Approximate inverse for the common offset acquisition geometry in 2D seismic imaging

    Grathwohl, Christine; Kunstmann, Peer; Quinto, Eric Todd; Rieder, Andreas

    2018-01-01

    We explore how the concept of approximate inverse can be used and implemented to recover singularities in the sound speed from common offset measurements in two space dimensions. Numerical experiments demonstrate the performance of the method. We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173. Quinto additionally thanks the Otto Mønsteds Fond and U.S. National Science Foundation (under grants DMS 1311558 and DMS 1712207) for their support. He thanks colleagues at DTU and KIT for their warm hospitality while this research was being done.

  7. Higher-order meshing of implicit geometries, Part II: Approximations on manifolds

    Fries, T. P.; Schöllhammer, D.

    2017-11-01

    A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it enables a completely automatic workflow from the geometric description to the numerical analysis without any user-intervention. A master level-set function defines the shape of the manifold through its zero-isosurface which is then restricted to a finite domain by additional level-set functions. It is ensured that the surface elements are sufficiently continuous and shape regular which is achieved by manipulating the background mesh. The numerical results show that optimal convergence rates are obtained with a moderate increase in the condition number compared to handcrafted surface meshes.

  8. January: IBM 7094 programme for the resolution of cell problems in planar, spherical and cylindrical geometry using the double Pn approximation

    Amouyal, A.; Tariel, H.

    1966-01-01

    Code name: January 1 st SCEA 011S. 2) Computer: IBM 7094; Programme system: Fortran II, 2 nd version. 3) Nature of the problem: resolution of cell problems with one space variable (planar, spherical and cylindrical geometries) and with one energy group, with isotropic sources in the double P n approximation (DP 1 and DP 3 approximation in planar and spherical geometries, DP 1 and DP 2 in cylindrical geometry). 4) Method used: the differential equations with limiting conditions are transformed into differential system with initial conditions which are integrated by a separate-step method. 5) Restrictions: number of physical media [fr

  9. January: IBM 7094 programme for the resolution of cell problems in planar, spherical and cylindrical geometry using the double P{sub n} approximation; Janvier: programme de resolution sur IBM 7094 des problemes de cellules en geometrie plane, spherique et cylindrique dans l'approximation double P{sub n}

    Amouyal, A; Tariel, H [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1966-07-01

    Code name: January 1{sup st} SCEA 011S. 2) Computer: IBM 7094; Programme system: Fortran II, 2{sup nd} version. 3) Nature of the problem: resolution of cell problems with one space variable (planar, spherical and cylindrical geometries) and with one energy group, with isotropic sources in the double P{sub n} approximation (DP 1 and DP 3 approximation in planar and spherical geometries, DP 1 and DP 2 in cylindrical geometry). 4) Method used: the differential equations with limiting conditions are transformed into differential system with initial conditions which are integrated by a separate-step method. 5) Restrictions: number of physical media < 100, number of geometrical regions < 100, number of points < 1000. 6) Physical approximations: limiting conditions for reflection, black body or grey body (restrictions for spherical and cylindrical geometries). The diffusion can include an isotropy term in cylindrical geometry, 2 terms in the other geometries. Taking into account of macroscopic data. 7) Duration: calculation time for a network of 100 points: planar and spherical geometry: double P 1 1 second, D P 3 = 4 seconds; cylindrical geometry: double P 1 2 seconds, D P 2 = 4 seconds. To these times should be added the 3 seconds required for the output. 8) State of the programme under production. (authors) [French] 1) Nom du Code: Janvier 1 SCEA 011S. 2) Calculateur: IBM 7094; Systeme de programmation: Fortran II version-2. 3) Nature du probleme: resolution des problemes de cellule a une variable d'espace (geometries plane, spherique et cylindrique) et un groupe d'energie, avec sources isotropes, dans l'approxirnation double P{sub n} (Approximations DP 1 et DP 3 en geometrie plane et spherique, approximations DP 1 et DP 2 en geometrie cylindrique). Methode employee: les equations differentielles avec conditions aux limites sont transformees en systemes differentiels avec conditions initiales que l'on integre par une methode a pas separes. 5) Restrictions: nombre de

  10. Instance annotation for multi-instance multi-label learning

    F. Briggs; X.Z. Fern; R. Raich; Q. Lou

    2013-01-01

    Multi-instance multi-label learning (MIML) is a framework for supervised classification where the objects to be classified are bags of instances associated with multiple labels. For example, an image can be represented as a bag of segments and associated with a list of objects it contains. Prior work on MIML has focused on predicting label sets for previously unseen...

  11. Cellular neural network to the spherical harmonics approximation of neutron transport equation in x–y geometry

    Pirouzmand, Ahmad; Hadad, Kamal

    2012-01-01

    Highlights: ► This paper describes the solution of time-dependent neutron transport equation. ► We use a novel method based on cellular neural networks (CNNs) coupled with the spherical harmonics method. ► We apply the CNN model to simulate step and ramp perturbation transients in a core. ► The accuracy and capabilities of the CNN model are examined for x–y geometry. - Abstract: In an earlier paper we utilized a novel method using cellular neural networks (CNNs) coupled with spherical harmonics method to solve the steady state neutron transport equation in x–y geometry. Here, the previous work is extended to the study of time-dependent neutron transport equation. To achieve this goal, an equivalent electrical circuit based on a second-order form of time-dependent neutron transport equation and one equivalent group of neutron precursor density is obtained by the CNN method. The CNN model is used to simulate step and ramp perturbation transients in a typical 2D core.

  12. Cellular neural networks (CNN) simulation for the TN approximation of the time dependent neutron transport equation in slab geometry

    Hadad, Kamal; Pirouzmand, Ahmad; Ayoobian, Navid

    2008-01-01

    This paper describes the application of a multilayer cellular neural network (CNN) to model and solve the time dependent one-speed neutron transport equation in slab geometry. We use a neutron angular flux in terms of the Chebyshev polynomials (T N ) of the first kind and then we attempt to implement the equations in an equivalent electrical circuit. We apply this equivalent circuit to analyze the T N moments equation in a uniform finite slab using Marshak type vacuum boundary condition. The validity of the CNN results is evaluated with numerical solution of the steady state T N moments equations by MATLAB. Steady state, as well as transient simulations, shows a very good comparison between the two methods. We used our CNN model to simulate space-time response of total flux and its moments for various c (where c is the mean number of secondary neutrons per collision). The complete algorithm could be implemented using very large-scale integrated circuit (VLSI) circuitry. The efficiency of the calculation method makes it useful for neutron transport calculations

  13. Applicability of the successive approximation methods in the control elements treatment in nuclear systems with irregular geometry

    El Maftoum, W.R.

    1983-01-01

    The solution of the steady-state wave equation was found by a Fourier series expansion in an arbitrarily shaped n-dimensional domain. This solution, subject to a homogeneous boundary condition (Dirichlet), was applied to a reactor with partially inserted control rods. A Fortran IV program was developed which solves the equation for two media. Criticality calculations were carried out and the worth of partially inserted rod was determined for several problems with an accuracy comparable with that in the existing literature. As a further consequence the technique, associated with the method of sucessive approximations, allowed to derive perturbative formulas for the eigenvalues of the wave equation and related equations. (Author) [pt

  14. Cellular neural network to the spherical harmonics approximation of neutron transport equation in x-y geometry. Part I: Modeling and verification for time-independent solution

    Pirouzmand, Ahmad; Hadad, Kamal

    2011-01-01

    Highlights: → This paper describes the solution of time-independent neutron transport equation. → Using a novel method based on cellular neural networks (CNNs) coupled with P N method. → Utilize the CNN model to simulate spatial scalar flux distribution in steady state. → The accuracy, stability, and capabilities of CNN model are examined in x-y geometry. - Abstract: This paper describes a novel method based on using cellular neural networks (CNN) coupled with spherical harmonics method (P N ) to solve the time-independent neutron transport equation in x-y geometry. To achieve this, an equivalent electrical circuit based on second-order form of neutron transport equation and relevant boundary conditions is obtained using CNN method. We use the CNN model to simulate spatial response of scalar flux distribution in the steady state condition for different order of spherical harmonics approximations. The accuracy, stability, and capabilities of CNN model are examined in 2D Cartesian geometry for fixed source and criticality problems.

  15. First-row diatomics: Calculation of the geometry and energetics using self-consistent gradient-functional approximations

    Kutzler, F.W.; Painter, G.S.

    1992-01-01

    A fully self-consistent series of nonlocal (gradient) density-functional calculations has been carried out using the augmented-Gaussian-orbital method to determine the magnitude of gradient corrections to the potential-energy curves of the first-row diatomics, Li 2 through F 2 . Both the Langreth-Mehl-Hu and the Perdew-Wang gradient-density functionals were used in calculations of the binding energy, bond length, and vibrational frequency for each dimer. Comparison with results obtained in the local-spin-density approximation (LSDA) using the Vosko-Wilk-Nusair functional, and with experiment, reveals that bond lengths and vibrational frequencies are rather insensitive to details of the gradient functionals, including self-consistency effects, but the gradient corrections reduce the overbinding commonly observed in the LSDA calculations of first-row diatomics (with the exception of Li 2 , the gradient-functional binding-energy error is only 50--12 % of the LSDA error). The improved binding energies result from a large differential energy lowering, which occurs in open-shell atoms relative to the diatomics. The stabilization of the atom arises from the use of nonspherical charge and spin densities in the gradient-functional calculations. This stabilization is negligibly small in LSDA calculations performed with nonspherical densities

  16. Instance-specific algorithm configuration

    Malitsky, Yuri

    2014-01-01

    This book presents a modular and expandable technique in the rapidly emerging research area of automatic configuration and selection of the best algorithm for the instance at hand. The author presents the basic model behind ISAC and then details a number of modifications and practical applications. In particular, he addresses automated feature generation, offline algorithm configuration for portfolio generation, algorithm selection, adaptive solvers, online tuning, and parallelization.    The author's related thesis was honorably mentioned (runner-up) for the ACP Dissertation Award in 2014,

  17. Information geometry

    Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz

    2017-01-01

    The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...

  18. Multi-instance learning based on instance consistency for image retrieval

    Zhang, Miao; Wu, Zhize; Wan, Shouhong; Yue, Lihua; Yin, Bangjie

    2017-07-01

    Multiple-instance learning (MIL) has been successfully utilized in image retrieval. Existing approaches cannot select positive instances correctly from positive bags which may result in a low accuracy. In this paper, we propose a new image retrieval approach called multiple instance learning based on instance-consistency (MILIC) to mitigate such issue. First, we select potential positive instances effectively in each positive bag by ranking instance-consistency (IC) values of instances. Then, we design a feature representation scheme, which can represent the relationship among bags and instances, based on potential positive instances to convert a bag into a single instance. Finally, we can use a standard single-instance learning strategy, such as the support vector machine, for performing object-based image retrieval. Experimental results on two challenging data sets show the effectiveness of our proposal in terms of accuracy and run time.

  19. Development of a geometry-compensated neutron time-of-flight detector for ICF applications with approximately 200 ps time response

    Murphy, T.J.; Lerche, R.A.

    1992-01-01

    Current-mode neutron time-of-flight detectors are used on Nova for neutron yield, ion temperature, and neutron emission time measurements. Currently used detectors are limited by the time response of the microchannel plate photomultiplier tubes used with the scintillators, scintillator decay time, scintillator thickness, and oscilloscope response time. A change in the geometry of the scintillator allows one to take advantage of the increased time resolution made possible by more advanced transient recorders and microchannel plate photomultiplier tubes. A prototype detector has been designed to incorporate these changes, and could potentially yield time resolution of less than 150 ps. Experimental results are presented demonstrating an ion temperature measurement of a direct-drive DT implosion on Nova

  20. Learning concept mappings from instance similarity

    Wang, S.; Englebienne, G.; Schlobach, S.

    2008-01-01

    Finding mappings between compatible ontologies is an important but difficult open problem. Instance-based methods for solving this problem have the advantage of focusing on the most active parts of the ontologies and reflect concept semantics as they are actually being used. However such methods

  1. Spinning geometry = Twisted geometry

    Freidel, Laurent; Ziprick, Jonathan

    2014-01-01

    It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)

  2. An instance theory of associative learning.

    Jamieson, Randall K; Crump, Matthew J C; Hannah, Samuel D

    2012-03-01

    We present and test an instance model of associative learning. The model, Minerva-AL, treats associative learning as cued recall. Memory preserves the events of individual trials in separate traces. A probe presented to memory contacts all traces in parallel and retrieves a weighted sum of the traces, a structure called the echo. Learning of a cue-outcome relationship is measured by the cue's ability to retrieve a target outcome. The theory predicts a number of associative learning phenomena, including acquisition, extinction, reacquisition, conditioned inhibition, external inhibition, latent inhibition, discrimination, generalization, blocking, overshadowing, overexpectation, superconditioning, recovery from blocking, recovery from overshadowing, recovery from overexpectation, backward blocking, backward conditioned inhibition, and second-order retrospective revaluation. We argue that associative learning is consistent with an instance-based approach to learning and memory.

  3. Dissimilarity-based multiple instance learning

    Sørensen, Lauge; Loog, Marco; Tax, David M. J.

    2010-01-01

    In this paper, we propose to solve multiple instance learning problems using a dissimilarity representation of the objects. Once the dissimilarity space has been constructed, the problem is turned into a standard supervised learning problem that can be solved with a general purpose supervised cla...... between distributions of within- and between set point distances, thereby taking relations within and between sets into account. Experiments on five publicly available data sets show competitive performance in terms of classification accuracy compared to previously published results....

  4. Basics of XBRL Instance for Financial Reporting

    Mihaela Enachi

    2011-10-01

    Full Text Available The development of XBRL (eXtensible Business Reporting Language for financial reporting has significantly changed the way which financial statements are presented to differentusers and implicitly the quantity and quality of information provided through such a modern format. Following a standard structure, but adaptable to the regulations from different countriesor regions of the world, we can communicate and process financial accounting information more efficient and effective. This paper tries to clarify the manner of preparation and presentation ofthe financial statements if using XBRL as reporting tool.Keywords: XML, XBRL, financial reporting, specification, taxonomy, instance

  5. Object instance recognition using motion cues and instance specific appearance models

    Schumann, Arne

    2014-03-01

    In this paper we present an object instance retrieval approach. The baseline approach consists of a pool of image features which are computed on the bounding boxes of a query object track and compared to a database of tracks in order to find additional appearances of the same object instance. We improve over this simple baseline approach in multiple ways: 1) we include motion cues to achieve improved robustness to viewpoint and rotation changes, 2) we include operator feedback to iteratively re-rank the resulting retrieval lists and 3) we use operator feedback and location constraints to train classifiers and learn an instance specific appearance model. We use these classifiers to further improve the retrieval results. The approach is evaluated on two popular public datasets for two different applications. We evaluate person re-identification on the CAVIAR shopping mall surveillance dataset and vehicle instance recognition on the VIVID aerial dataset and achieve significant improvements over our baseline results.

  6. A critique of medicalisation: three instances.

    Ryang, Sonia

    2017-12-01

    By briefly exploring three different examples where the existence of mental illness and developmental delay has been presumed, this paper sheds light on the way what Foucault calls the emergence of a regime of truth, i.e. where something that does not exist is made to exist through the construction of a system of truth around it. The first example concerns the direct marketing of pharmaceutical products to consumers in the US, the second the use of psychology in semi-post-Cold War Korea, and the third the persisting authority of psychology in the treatment of the developmentally delayed. While these instances are not innately connected, looking at these as part of the process by which the authoritative knowledge is established will help us understand, albeit partially, the mechanism by which mental illness penetrates our lives as truth, and how this regime of truth is supported by the authority of psychology, psychiatry and psychoanalysis, what Foucault calls the 'psy-function,' reinforcing the medicalisation of our lives.

  7. Multiple-instance learning as a classifier combining problem

    Li, Yan; Tax, David M. J.; Duin, Robert P. W.

    2013-01-01

    In multiple-instance learning (MIL), an object is represented as a bag consisting of a set of feature vectors called instances. In the training set, the labels of bags are given, while the uncertainty comes from the unknown labels of instances in the bags. In this paper, we study MIL with the ass...

  8. Hyperbolic geometry

    Iversen, Birger

    1992-01-01

    Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics

  9. Introduction to combinatorial geometry

    Gabriel, T.A.; Emmett, M.B.

    1985-01-01

    The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity

  10. Twistor geometry

    van den Broek, P.M.

    1984-01-01

    The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.

  11. Coarse-Grain QoS-Aware Dynamic Instance Provisioning for Interactive Workload in the Cloud

    Jianxiong Wan

    2014-01-01

    Full Text Available Cloud computing paradigm renders the Internet service providers (ISPs with a new approach to deliver their service with less cost. ISPs can rent virtual machines from the Infrastructure-as-a-Service (IaaS provided by the cloud rather than purchasing them. In addition, commercial cloud providers (CPs offer diverse VM instance rental services in various time granularities, which provide another opportunity for ISPs to reduce cost. We investigate a Coarse-grain QoS-aware Dynamic Instance Provisioning (CDIP problem for interactive workload in the cloud from the perspective of ISPs. We formulate the CDIP problem as an optimization problem where the objective is to minimize the VM instance rental cost and the constraint is the percentile delay bound. Since the Internet traffic shows a strong self-similar property, it is hard to get an analytical form of the percentile delay constraint. To address this issue, we purpose a lookup table structure together with a learning algorithm to estimate the performance of the instance provisioning policy. This approach is further extended with two function approximations to enhance the scalability of the learning algorithm. We also present an efficient dynamic instance provisioning algorithm, which takes full advantage of the rental service diversity, to determine the instance rental policy. Extensive simulations are conducted to validate the effectiveness of the proposed algorithms.

  12. Experimental Matching of Instances to Heuristics for Constraint Satisfaction Problems.

    Moreno-Scott, Jorge Humberto; Ortiz-Bayliss, José Carlos; Terashima-Marín, Hugo; Conant-Pablos, Santiago Enrique

    2016-01-01

    Constraint satisfaction problems are of special interest for the artificial intelligence and operations research community due to their many applications. Although heuristics involved in solving these problems have largely been studied in the past, little is known about the relation between instances and the respective performance of the heuristics used to solve them. This paper focuses on both the exploration of the instance space to identify relations between instances and good performing heuristics and how to use such relations to improve the search. Firstly, the document describes a methodology to explore the instance space of constraint satisfaction problems and evaluate the corresponding performance of six variable ordering heuristics for such instances in order to find regions on the instance space where some heuristics outperform the others. Analyzing such regions favors the understanding of how these heuristics work and contribute to their improvement. Secondly, we use the information gathered from the first stage to predict the most suitable heuristic to use according to the features of the instance currently being solved. This approach proved to be competitive when compared against the heuristics applied in isolation on both randomly generated and structured instances of constraint satisfaction problems.

  13. Multi-instance dictionary learning via multivariate performance measure optimization

    Wang, Jim Jing-Yan

    2016-12-29

    The multi-instance dictionary plays a critical role in multi-instance data representation. Meanwhile, different multi-instance learning applications are evaluated by specific multivariate performance measures. For example, multi-instance ranking reports the precision and recall. It is not difficult to see that to obtain different optimal performance measures, different dictionaries are needed. This observation motives us to learn performance-optimal dictionaries for this problem. In this paper, we propose a novel joint framework for learning the multi-instance dictionary and the classifier to optimize a given multivariate performance measure, such as the F1 score and precision at rank k. We propose to represent the bags as bag-level features via the bag-instance similarity, and learn a classifier in the bag-level feature space to optimize the given performance measure. We propose to minimize the upper bound of a multivariate loss corresponding to the performance measure, the complexity of the classifier, and the complexity of the dictionary, simultaneously, with regard to both the dictionary and the classifier parameters. In this way, the dictionary learning is regularized by the performance optimization, and a performance-optimal dictionary is obtained. We develop an iterative algorithm to solve this minimization problem efficiently using a cutting-plane algorithm and a coordinate descent method. Experiments on multi-instance benchmark data sets show its advantage over both traditional multi-instance learning and performance optimization methods.

  14. Multi-instance dictionary learning via multivariate performance measure optimization

    Wang, Jim Jing-Yan; Tsang, Ivor Wai-Hung; Cui, Xuefeng; Lu, Zhiwu; Gao, Xin

    2016-01-01

    The multi-instance dictionary plays a critical role in multi-instance data representation. Meanwhile, different multi-instance learning applications are evaluated by specific multivariate performance measures. For example, multi-instance ranking reports the precision and recall. It is not difficult to see that to obtain different optimal performance measures, different dictionaries are needed. This observation motives us to learn performance-optimal dictionaries for this problem. In this paper, we propose a novel joint framework for learning the multi-instance dictionary and the classifier to optimize a given multivariate performance measure, such as the F1 score and precision at rank k. We propose to represent the bags as bag-level features via the bag-instance similarity, and learn a classifier in the bag-level feature space to optimize the given performance measure. We propose to minimize the upper bound of a multivariate loss corresponding to the performance measure, the complexity of the classifier, and the complexity of the dictionary, simultaneously, with regard to both the dictionary and the classifier parameters. In this way, the dictionary learning is regularized by the performance optimization, and a performance-optimal dictionary is obtained. We develop an iterative algorithm to solve this minimization problem efficiently using a cutting-plane algorithm and a coordinate descent method. Experiments on multi-instance benchmark data sets show its advantage over both traditional multi-instance learning and performance optimization methods.

  15. Comparative analysis of instance selection algorithms for instance-based classifiers in the context of medical decision support

    Mazurowski, Maciej A; Tourassi, Georgia D; Malof, Jordan M

    2011-01-01

    When constructing a pattern classifier, it is important to make best use of the instances (a.k.a. cases, examples, patterns or prototypes) available for its development. In this paper we present an extensive comparative analysis of algorithms that, given a pool of previously acquired instances, attempt to select those that will be the most effective to construct an instance-based classifier in terms of classification performance, time efficiency and storage requirements. We evaluate seven previously proposed instance selection algorithms and compare their performance to simple random selection of instances. We perform the evaluation using k-nearest neighbor classifier and three classification problems: one with simulated Gaussian data and two based on clinical databases for breast cancer detection and diagnosis, respectively. Finally, we evaluate the impact of the number of instances available for selection on the performance of the selection algorithms and conduct initial analysis of the selected instances. The experiments show that for all investigated classification problems, it was possible to reduce the size of the original development dataset to less than 3% of its initial size while maintaining or improving the classification performance. Random mutation hill climbing emerges as the superior selection algorithm. Furthermore, we show that some previously proposed algorithms perform worse than random selection. Regarding the impact of the number of instances available for the classifier development on the performance of the selection algorithms, we confirm that the selection algorithms are generally more effective as the pool of available instances increases. In conclusion, instance selection is generally beneficial for instance-based classifiers as it can improve their performance, reduce their storage requirements and improve their response time. However, choosing the right selection algorithm is crucial.

  16. Molecular geometry

    Rodger, Alison

    1995-01-01

    Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans

  17. Geometric approximation algorithms

    Har-Peled, Sariel

    2011-01-01

    Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

  18. Optical geometry

    Robinson, I.; Trautman, A.

    1988-01-01

    The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem

  19. Multimodality and children's participation in classrooms: Instances of ...

    Multimodality and children's participation in classrooms: Instances of research. ... deficit models of children, drawing on their everyday experiences and their existing ... It outlines the theoretical framework supporting the pedagogical approach, ...

  20. Memory for Instances and Categories in Children and Adults

    Tighe, Thomas J.; And Others

    1975-01-01

    Two studies of 7-year-olds and college students tested the hypothesis of a developmental difference in the degree to which subjects' memory performance was controlled by categorical properties vs. specific instance properties of test items. (GO)

  1. Architectural geometry

    Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes

    2014-01-01

    Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

  2. Architectural geometry

    Pottmann, Helmut

    2014-11-26

    Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

  3. Beautiful geometry

    Maor, Eli

    2014-01-01

    If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur

  4. Analytische Geometrie

    Kemnitz, Arnfried

    Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.

  5. Algebraic geometry

    Lefschetz, Solomon

    2005-01-01

    An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

  6. International Conference Approximation Theory XV

    Schumaker, Larry

    2017-01-01

    These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...

  7. Resource Planning for Massive Number of Process Instances

    Xu, Jiajie; Liu, Chengfei; Zhao, Xiaohui

    Resource allocation has been recognised as an important topic for business process execution. In this paper, we focus on planning resources for a massive number of process instances to meet the process requirements and cater for rational utilisation of resources before execution. After a motivating example, we present a model for planning resources for process instances. Then we design a set of heuristic rules that take both optimised planning at build time and instance dependencies at run time into account. Based on these rules we propose two strategies, one is called holistic and the other is called batched, for resource planning. Both strategies target a lower cost, however, the holistic strategy can achieve an earlier deadline while the batched strategy aims at rational use of resources. We discuss how to find balance between them in the paper with a comprehensive experimental study on these two approaches.

  8. Boosting instance prototypes to detect local dermoscopic features.

    Situ, Ning; Yuan, Xiaojing; Zouridakis, George

    2010-01-01

    Local dermoscopic features are useful in many dermoscopic criteria for skin cancer detection. We address the problem of detecting local dermoscopic features from epiluminescence (ELM) microscopy skin lesion images. We formulate the recognition of local dermoscopic features as a multi-instance learning (MIL) problem. We employ the method of diverse density (DD) and evidence confidence (EC) function to convert MIL to a single-instance learning (SIL) problem. We apply Adaboost to improve the classification performance with support vector machines (SVMs) as the base classifier. We also propose to boost the selection of instance prototypes through changing the data weights in the DD function. We validate the methods on detecting ten local dermoscopic features from a dataset with 360 images. We compare the performance of the MIL approach, its boosting version, and a baseline method without using MIL. Our results show that boosting can provide performance improvement compared to the other two methods.

  9. Time and activity sequence prediction of business process instances

    Polato, Mirko; Sperduti, Alessandro; Burattin, Andrea

    2018-01-01

    The ability to know in advance the trend of running process instances, with respect to different features, such as the expected completion time, would allow business managers to timely counteract to undesired situations, in order to prevent losses. Therefore, the ability to accurately predict...... future features of running business process instances would be a very helpful aid when managing processes, especially under service level agreement constraints. However, making such accurate forecasts is not easy: many factors may influence the predicted features. Many approaches have been proposed...

  10. Spatial geometry and special relativity

    Kneubil, Fabiana Botelho

    2016-01-01

    In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame......-dependent and frame-independent entities. We depart from a subject well known by students, which is the three-dimensional geometric space in order to compare, afterwards, with the treatment of four-dimensional space in the special relativity. The differences and similarities between these two subjects are also...

  11. Approximate Likelihood

    CERN. Geneva

    2015-01-01

    Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...

  12. Diophantine approximation

    Schmidt, Wolfgang M

    1980-01-01

    "In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)

  13. Analytic geometry

    Burdette, A C

    1971-01-01

    Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st

  14. Geometry Revealed

    Berger, Marcel

    2010-01-01

    Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,

  15. Vector geometry

    Robinson, Gilbert de B

    2011-01-01

    This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom

  16. Noncommutative geometry

    Connes, Alain

    1994-01-01

    This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat

  17. TNO at TRECVID 2013: Multimedia Event Detection and Instance Search

    Bouma, H.; Azzopardi, G.; Spitters, M.M.; Wit, J.J. de; Versloot, C.A.; Zon, R.W.L. van der; Eendebak, P.T.; Baan, J.; Hove, R.J.M. ten; Eekeren, A.W.M. van; Haar, F.B. ter; Hollander, R.J.M. den; Huis, R.J. van; Boer, M.H.T. de; Antwerpen, G. van; Broekhuijsen, B.J.; Daniele, L.M.; Brandt, P.; Schavemaker, J.G.M.; Kraaij, W.; Schutte, K.

    2013-01-01

    We describe the TNO system and the evaluation results for TRECVID 2013 Multimedia Event Detection (MED) and instance search (INS) tasks. The MED system consists of a bag-of-word (BOW) approach with spatial tiling that uses low-level static and dynamic visual features, an audio feature and high-level

  18. Locality in Generic Instance Search from One Example

    Tao, R.; Gavves, E.; Snoek, C.G.M.; Smeulders, A.W.M.

    2014-01-01

    This paper aims for generic instance search from a single example. Where the state-of-the-art relies on global image representation for the search, we proceed by including locality at all steps of the method. As the first novelty, we consider many boxes per database image as candidate targets to

  19. Data-aware remaining time prediction of business process instances

    Polato, M.; Sperduti, A.; Burattin, A.; Leoni, de M.

    2014-01-01

    Accurate prediction of the completion time of a business process instance would constitute a valuable tool when managing processes under service level agreement constraints. Such prediction, however, is a very challenging task. A wide variety of factors could influence the trend of a process

  20. Projective Geometry

    mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.

  1. Geometry -----------~--------------RESONANCE

    Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.

  2. The quasilocalized charge approximation

    Kalman, G J; Golden, K I; Donko, Z; Hartmann, P

    2005-01-01

    The quasilocalized charge approximation (QLCA) has been used for some time as a formalism for the calculation of the dielectric response and for determining the collective mode dispersion in strongly coupled Coulomb and Yukawa liquids. The approach is based on a microscopic model in which the charges are quasilocalized on a short-time scale in local potential fluctuations. We review the conceptual basis and theoretical structure of the QLC approach and together with recent results from molecular dynamics simulations that corroborate and quantify the theoretical concepts. We also summarize the major applications of the QLCA to various physical systems, combined with the corresponding results of the molecular dynamics simulations and point out the general agreement and instances of disagreement between the two

  3. First instance competence of the Higher Administrative Court

    Anon.

    1988-01-01

    (1) An interlocutory judgement can determine the admissibility of a legal action, also with regard to single procedural prerequisites (following BVerwG decision 14, 273). (2) The first instance competence for disputes about the dismantling of a decommissioned nuclear installation lies with the administrative courts and not with the higher administrative courts. Federal Administrative Court, decision of May 19, 1988 - 7 C 43.88 - (VGH Munich). (orig.) [de

  4. Riemannian geometry

    Petersen, Peter

    2016-01-01

    Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...

  5. Special geometry

    Strominger, A.

    1990-01-01

    A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)

  6. SIFT Meets CNN: A Decade Survey of Instance Retrieval.

    Zheng, Liang; Yang, Yi; Tian, Qi

    2018-05-01

    In the early days, content-based image retrieval (CBIR) was studied with global features. Since 2003, image retrieval based on local descriptors (de facto SIFT) has been extensively studied for over a decade due to the advantage of SIFT in dealing with image transformations. Recently, image representations based on the convolutional neural network (CNN) have attracted increasing interest in the community and demonstrated impressive performance. Given this time of rapid evolution, this article provides a comprehensive survey of instance retrieval over the last decade. Two broad categories, SIFT-based and CNN-based methods, are presented. For the former, according to the codebook size, we organize the literature into using large/medium-sized/small codebooks. For the latter, we discuss three lines of methods, i.e., using pre-trained or fine-tuned CNN models, and hybrid methods. The first two perform a single-pass of an image to the network, while the last category employs a patch-based feature extraction scheme. This survey presents milestones in modern instance retrieval, reviews a broad selection of previous works in different categories, and provides insights on the connection between SIFT and CNN-based methods. After analyzing and comparing retrieval performance of different categories on several datasets, we discuss promising directions towards generic and specialized instance retrieval.

  7. Domain Adaptation for Machine Translation with Instance Selection

    Biçici Ergun

    2015-04-01

    Full Text Available Domain adaptation for machine translation (MT can be achieved by selecting training instances close to the test set from a larger set of instances. We consider 7 different domain adaptation strategies and answer 7 research questions, which give us a recipe for domain adaptation in MT. We perform English to German statistical MT (SMT experiments in a setting where test and training sentences can come from different corpora and one of our goals is to learn the parameters of the sampling process. Domain adaptation with training instance selection can obtain 22% increase in target 2-gram recall and can gain up to 3:55 BLEU points compared with random selection. Domain adaptation with feature decay algorithm (FDA not only achieves the highest target 2-gram recall and BLEU performance but also perfectly learns the test sample distribution parameter with correlation 0:99. Moses SMT systems built with FDA selected 10K training sentences is able to obtain F1 results as good as the baselines that use up to 2M sentences. Moses SMT systems built with FDA selected 50K training sentences is able to obtain F1 point better results than the baselines.

  8. Instance Selection for Classifier Performance Estimation in Meta Learning

    Marcin Blachnik

    2017-11-01

    Full Text Available Building an accurate prediction model is challenging and requires appropriate model selection. This process is very time consuming but can be accelerated with meta-learning–automatic model recommendation by estimating the performances of given prediction models without training them. Meta-learning utilizes metadata extracted from the dataset to effectively estimate the accuracy of the model in question. To achieve that goal, metadata descriptors must be gathered efficiently and must be informative to allow the precise estimation of prediction accuracy. In this paper, a new type of metadata descriptors is analyzed. These descriptors are based on the compression level obtained from the instance selection methods at the data-preprocessing stage. To verify their suitability, two types of experiments on real-world datasets have been conducted. In the first one, 11 instance selection methods were examined in order to validate the compression–accuracy relation for three classifiers: k-nearest neighbors (kNN, support vector machine (SVM, and random forest. From this analysis, two methods are recommended (instance-based learning type 2 (IB2, and edited nearest neighbor (ENN which are then compared with the state-of-the-art metaset descriptors. The obtained results confirm that the two suggested compression-based meta-features help to predict accuracy of the base model much more accurately than the state-of-the-art solution.

  9. General Geometry and Geometry of Electromagnetism

    Shahverdiyev, Shervgi S.

    2002-01-01

    It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...

  10. Differential geometry

    Ciarlet, Philippe G

    2007-01-01

    This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and

  11. Le contentieux camerounais devant les instances sportives internationales

    Dikoume François Claude

    2016-01-01

    Les acteurs du sport depuis lors, utilisent donc les voies de recours au niveau international soit vers les fédérations sportives internationales ou encore et surtout vers le TAS qui s'occupe des litiges de toutes les disciplines sportives. Il est question ici de faire un inventaire casuistique descriptif non exhaustif des requêtes contentieuses camerounaises portées devant les diverses instances sportives internationales ; ceci permettra de questionner l'esprit processuel et la qualité technique de leurs réclamations juridiques en matière sportive.

  12. Clustering with Instance and Attribute Level Side Information

    Jinlong Wang

    2010-12-01

    Full Text Available Selecting a suitable proximity measure is one of the fundamental tasks in clustering. How to effectively utilize all available side information, including the instance level information in the form of pair-wise constraints, and the attribute level information in the form of attribute order preferences, is an essential problem in metric learning. In this paper, we propose a learning framework in which both the pair-wise constraints and the attribute order preferences can be incorporated simultaneously. The theory behind it and the related parameter adjusting technique have been described in details. Experimental results on benchmark data sets demonstrate the effectiveness of proposed method.

  13. Dual-Layer Density Estimation for Multiple Object Instance Detection

    Qiang Zhang

    2016-01-01

    Full Text Available This paper introduces a dual-layer density estimation-based architecture for multiple object instance detection in robot inventory management applications. The approach consists of raw scale-invariant feature transform (SIFT feature matching and key point projection. The dominant scale ratio and a reference clustering threshold are estimated using the first layer of the density estimation. A cascade of filters is applied after feature template reconstruction and refined feature matching to eliminate false matches. Before the second layer of density estimation, the adaptive threshold is finalized by multiplying an empirical coefficient for the reference value. The coefficient is identified experimentally. Adaptive threshold-based grid voting is applied to find all candidate object instances. Error detection is eliminated using final geometric verification in accordance with Random Sample Consensus (RANSAC. The detection results of the proposed approach are evaluated on a self-built dataset collected in a supermarket. The results demonstrate that the approach provides high robustness and low latency for inventory management application.

  14. Kernel Methods for Mining Instance Data in Ontologies

    Bloehdorn, Stephan; Sure, York

    The amount of ontologies and meta data available on the Web is constantly growing. The successful application of machine learning techniques for learning of ontologies from textual data, i.e. mining for the Semantic Web, contributes to this trend. However, no principal approaches exist so far for mining from the Semantic Web. We investigate how machine learning algorithms can be made amenable for directly taking advantage of the rich knowledge expressed in ontologies and associated instance data. Kernel methods have been successfully employed in various learning tasks and provide a clean framework for interfacing between non-vectorial data and machine learning algorithms. In this spirit, we express the problem of mining instances in ontologies as the problem of defining valid corresponding kernels. We present a principled framework for designing such kernels by means of decomposing the kernel computation into specialized kernels for selected characteristics of an ontology which can be flexibly assembled and tuned. Initial experiments on real world Semantic Web data enjoy promising results and show the usefulness of our approach.

  15. Breaking Newton’s third law: electromagnetic instances

    Kneubil, Fabiana B

    2016-01-01

    In this work, three instances are discussed within electromagnetism which highlight failures in the validity of Newton’s third law, all of them related to moving charged particles. It is well known that electromagnetic theory paved the way for relativity and that it disclosed new phenomena which were not compatible with the laws of mechanics. However, even if widely known in its generality, this issue is not clearly approached in introductory textbooks and it is difficult for students to perceive by themselves. Three explicit concrete situations involving the breaking of Newton’s third law are presented in this paper, together with a didactical procedure to construct graphically the configurations of electric field lines, which allow pictures produced by interactive radiation simulators available in websites to be better understood. (paper)

  16. Image annotation based on positive-negative instances learning

    Zhang, Kai; Hu, Jiwei; Liu, Quan; Lou, Ping

    2017-07-01

    Automatic image annotation is now a tough task in computer vision, the main sense of this tech is to deal with managing the massive image on the Internet and assisting intelligent retrieval. This paper designs a new image annotation model based on visual bag of words, using the low level features like color and texture information as well as mid-level feature as SIFT, and mixture the pic2pic, label2pic and label2label correlation to measure the correlation degree of labels and images. We aim to prune the specific features for each single label and formalize the annotation task as a learning process base on Positive-Negative Instances Learning. Experiments are performed using the Corel5K Dataset, and provide a quite promising result when comparing with other existing methods.

  17. Geometry of physical dispersion relations

    Raetzel, Dennis; Rivera, Sergio; Schuller, Frederic P.

    2011-01-01

    To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.

  18. Multiple instance learning tracking method with local sparse representation

    Xie, Chengjun

    2013-10-01

    When objects undergo large pose change, illumination variation or partial occlusion, most existed visual tracking algorithms tend to drift away from targets and even fail in tracking them. To address this issue, in this study, the authors propose an online algorithm by combining multiple instance learning (MIL) and local sparse representation for tracking an object in a video system. The key idea in our method is to model the appearance of an object by local sparse codes that can be formed as training data for the MIL framework. First, local image patches of a target object are represented as sparse codes with an overcomplete dictionary, where the adaptive representation can be helpful in overcoming partial occlusion in object tracking. Then MIL learns the sparse codes by a classifier to discriminate the target from the background. Finally, results from the trained classifier are input into a particle filter framework to sequentially estimate the target state over time in visual tracking. In addition, to decrease the visual drift because of the accumulative errors when updating the dictionary and classifier, a two-step object tracking method combining a static MIL classifier with a dynamical MIL classifier is proposed. Experiments on some publicly available benchmarks of video sequences show that our proposed tracker is more robust and effective than others. © The Institution of Engineering and Technology 2013.

  19. Parallel multiple instance learning for extremely large histopathology image analysis.

    Xu, Yan; Li, Yeshu; Shen, Zhengyang; Wu, Ziwei; Gao, Teng; Fan, Yubo; Lai, Maode; Chang, Eric I-Chao

    2017-08-03

    Histopathology images are critical for medical diagnosis, e.g., cancer and its treatment. A standard histopathology slice can be easily scanned at a high resolution of, say, 200,000×200,000 pixels. These high resolution images can make most existing imaging processing tools infeasible or less effective when operated on a single machine with limited memory, disk space and computing power. In this paper, we propose an algorithm tackling this new emerging "big data" problem utilizing parallel computing on High-Performance-Computing (HPC) clusters. Experimental results on a large-scale data set (1318 images at a scale of 10 billion pixels each) demonstrate the efficiency and effectiveness of the proposed algorithm for low-latency real-time applications. The framework proposed an effective and efficient system for extremely large histopathology image analysis. It is based on the multiple instance learning formulation for weakly-supervised learning for image classification, segmentation and clustering. When a max-margin concept is adopted for different clusters, we obtain further improvement in clustering performance.

  20. Diophantine approximation and badly approximable sets

    Kristensen, S.; Thorn, R.; Velani, S.

    2006-01-01

    . The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...

  1. Marx, Materialism and the Brain: Determination in the Last Instance?

    Joss Hands

    2018-05-01

    Full Text Available It is well acknowledged that there is not one but many Marxes, and one area where this has been most evident is in the question of technological and economic determinism. This article traces some key moments in this debate and attempts to locate their most recent iteration in disagreements over the place of the human brain in both historical agency and value creation in so called ‘cognitive’ or ‘post-Fordist’ capitalism. Of significant interest in the current configuration – or rather composition – of capital is the place of the digitisation of the labour process and its relation to, and integration with, human cognition and volition. Arguments over the attention economy and the power of post-Fordist capitalism to distract and direct is a significant variation of the question of ideology and the latest variation of the base/superstructure debate. This article will unpack the aforesaid issues to offer an articulated perspective in order to make the argument that taking a balanced view of determination will allow us to acknowledge that – drawing on the argument of determination in the last instance – we can hold both of these ‘Marxes’ to be simultaneously valid. Here, a revisiting of Marx’s concept of General Intellect will be undertaken, wherein the productive capacity of living labour is employed in both active agency and the capture of value, in which the plasticity of the living brain becomes the pivot point for both exploitation by, and resistance to, capital.

  2. Complex analysis and geometry

    Silva, Alessandro

    1993-01-01

    The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.

  3. Non-Riemannian geometry

    Eisenhart, Luther Pfahler

    2005-01-01

    This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.

  4. Geometry of the Universe

    Gurevich, L.Eh.; Gliner, Eh.B.

    1978-01-01

    Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding

  5. An approach for management of geometry data

    Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.

    1980-01-01

    The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.

  6. Product forms in Gabor analysis for a quincunx-type sampling geometry

    Bastiaans, M.J.; Leest, van A.J.; Veen, J.P.

    1998-01-01

    Recently a new sampling lattice - the quincunx lattice - has been introduced [1] as a sampling geometry in the Gabor scheme, which geometry is different from the traditional rectangular sampling geometry. In this paper we will show how results that hold for rectangular sampling (see, for instance,

  7. An Efficient Metric of Automatic Weight Generation for Properties in Instance Matching Technique

    Seddiqui, Md. Hanif; Nath, Rudra Pratap Deb; Aono, Masaki

    2015-01-01

    The proliferation of heterogeneous data sources of semantic knowledge base intensifies the need of an automatic instance matching technique. However, the efficiency of instance matching is often influenced by the weight of a property associated to instances. Automatic weight generation is a non-trivial, however an important task in instance matching technique. Therefore, identifying an appropriate metric for generating weight for a property automatically is nevertheless a formidab...

  8. Stochastic Learning of Multi-Instance Dictionary for Earth Mover's Distance based Histogram Comparison

    Fan, Jihong; Liang, Ru-Ze

    2016-01-01

    Dictionary plays an important role in multi-instance data representation. It maps bags of instances to histograms. Earth mover's distance (EMD) is the most effective histogram distance metric for the application of multi-instance retrieval. However, up to now, there is no existing multi-instance dictionary learning methods designed for EMD based histogram comparison. To fill this gap, we develop the first EMD-optimal dictionary learning method using stochastic optimization method. In the stoc...

  9. 28 CFR 51.46 - Reconsideration of objection at the instance of the Attorney General.

    2010-07-01

    ... instance of the Attorney General. 51.46 Section 51.46 Judicial Administration DEPARTMENT OF JUSTICE... Processing of Submissions § 51.46 Reconsideration of objection at the instance of the Attorney General. (a... may be reconsidered, if it is deemed appropriate, at the instance of the Attorney General. (b) Notice...

  10. Riemannian geometry and geometric analysis

    Jost, Jürgen

    2017-01-01

    This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research.  The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...

  11. DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS

    BERG, J.S.; JOHNSTONE, C.; SUMMERS, D.

    2001-01-01

    Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective

  12. From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks

    Jupri, Al

    2017-04-01

    In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems - considered as tasks inviting the use of problem solving and reasoning skills - theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instance, are intended for assessing student problem solving and reasoning skills.

  13. Geometry and its applications

    Meyer, Walter J

    2006-01-01

    Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...

  14. Algebraic geometry in India

    algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.

  15. Spinorial Geometry and Branes

    Sloane, Peter

    2007-01-01

    We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

  16. Spinorial Geometry and Branes

    Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)

    2007-09-15

    We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

  17. Time efficient optimization of instance based problems with application to tone onset detection

    Bauer, Nadja; Friedrichs, Klaus; Weihs, Claus

    2016-01-01

    A time efficient optimization technique for instance based problems is proposed, where for each parameter setting the target function has to be evaluated on a large set of problem instances. Computational time is reduced by beginning with a performance estimation based on the evaluation of a representative subset of instances. Subsequently, only promising settings are evaluated on the whole data set. As application a comprehensive music onset detection algorithm is introduce...

  18. Approximations for Markovian multi-class queues with preemptive priorities

    van der Heijden, Matthijs C.; van Harten, Aart; Sleptchenko, Andrei

    2004-01-01

    We discuss the approximation of performance measures in multi-class M/M/k queues with preemptive priorities for large problem instances (many classes and servers) using class aggregation and server reduction. We compared our approximations to exact and simulation results and found that our approach

  19. Casimir forces and geometry

    Buescher, R.

    2005-01-01

    Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the

  20. Faster and Simpler Approximation of Stable Matchings

    Katarzyna Paluch

    2014-04-01

    Full Text Available We give a 3 2 -approximation algorithm for finding stable matchings that runs in O(m time. The previous most well-known algorithm, by McDermid, has the same approximation ratio but runs in O(n3/2m time, where n denotes the number of people andm is the total length of the preference lists in a given instance. In addition, the algorithm and the analysis are much simpler. We also give the extension of the algorithm for computing stable many-to-many matchings.

  1. Geometry essentials for dummies

    Ryan, Mark

    2011-01-01

    Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque

  2. Modulated Pade approximant

    Ginsburg, C.A.

    1980-01-01

    In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)

  3. Arithmetic noncommutative geometry

    Marcolli, Matilde

    2005-01-01

    Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

  4. Configuring Airspace Sectors with Approximate Dynamic Programming

    Bloem, Michael; Gupta, Pramod

    2010-01-01

    In response to changing traffic and staffing conditions, supervisors dynamically configure airspace sectors by assigning them to control positions. A finite horizon airspace sector configuration problem models this supervisor decision. The problem is to select an airspace configuration at each time step while considering a workload cost, a reconfiguration cost, and a constraint on the number of control positions at each time step. Three algorithms for this problem are proposed and evaluated: a myopic heuristic, an exact dynamic programming algorithm, and a rollouts approximate dynamic programming algorithm. On problem instances from current operations with only dozens of possible configurations, an exact dynamic programming solution gives the optimal cost value. The rollouts algorithm achieves costs within 2% of optimal for these instances, on average. For larger problem instances that are representative of future operations and have thousands of possible configurations, excessive computation time prohibits the use of exact dynamic programming. On such problem instances, the rollouts algorithm reduces the cost achieved by the heuristic by more than 15% on average with an acceptable computation time.

  5. Scheduling jobs in the cloud using on-demand and reserved instances

    Shen, S.; Deng, K.; Iosup, A.; Epema, D.H.J.; Wolf, F.; Mohr, B.; Mey, an D.

    2013-01-01

    Deploying applications in leased cloud infrastructure is increasingly considered by a variety of business and service integrators. However, the challenge of selecting the leasing strategy — larger or faster instances? on-demand or reserved instances? etc.— and to configure the leasing strategy with

  6. Stochastic learning of multi-instance dictionary for earth mover’s distance-based histogram comparison

    Fan, Jihong; Liang, Ru-Ze

    2016-01-01

    Dictionary plays an important role in multi-instance data representation. It maps bags of instances to histograms. Earth mover’s distance (EMD) is the most effective histogram distance metric for the application of multi-instance retrieval. However

  7. Sparse approximation with bases

    2015-01-01

    This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications.  The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

  8. Multijet final states: exact results and the leading pole approximation

    Ellis, R.K.; Owens, J.F.

    1984-09-01

    Exact results for the process gg → ggg are compared with those obtained using the leading pole approximation. Regions of phase space where the approximation breaks down are discussed. A specific example relevant for background estimates to W boson production is presented. It is concluded that in this instance the leading pole approximation may underestimate the standard QCD background by more than a factor of two in certain kinematic regions of physical interest

  9. Approximate symmetries of Hamiltonians

    Chubb, Christopher T.; Flammia, Steven T.

    2017-08-01

    We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

  10. The Geometry Conference

    Bárány, Imre; Vilcu, Costin

    2016-01-01

    This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.

  11. Approximating distributions from moments

    Pawula, R. F.

    1987-11-01

    A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.

  12. CONTRIBUTIONS TO RATIONAL APPROXIMATION,

    Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

  13. THE EXECUTION INSTANCE OF THE JUDICIAL JUDGEMENTS SENTENCED IN THE LITIGATIONS OF ADMINISTRATIVE CONTENTIOUS

    ADRIANA ELENA BELU

    2012-05-01

    Full Text Available The instance which solved the fund of the litigation rising from an administrative contract differs depending on the material competence sanctioned by law, in contrast to the subject of the commercial law where the execution instance is the court. In this matter the High Court stated in a decision1 that in a first case the competence of solving the legal contest against the proper forced execution and of the legal contest that has in view the explanation of the meaning of spreading and applying the enforceable title which does not proceed from a jurisdiction organ is in the authority of the court. The Law of the Administrative Contentious no 554/2004 defines in Article 2 paragraph 1 letter t the notion of execution instance, providing that this is the instance which solved the fund of the litigation of administrative contentious, so even in the case of the administrative contracts the execution instance is the one which solved the litigation rising from the contract. Corroborating this disposal with the ones existing in articles 22 and 25 in the Law, it can be shown that no matter the instance which decision is an enforceable title, the execution of the law will be done by the instance which solved the fund of the litigation regarding the administrative contentious.

  14. Approximation techniques for engineers

    Komzsik, Louis

    2006-01-01

    Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.

  15. Algorithms in Algebraic Geometry

    Dickenstein, Alicia; Sommese, Andrew J

    2008-01-01

    In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

  16. Revolutions of Geometry

    O'Leary, Michael

    2010-01-01

    Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull

  17. Fundamental concepts of geometry

    Meserve, Bruce E

    1983-01-01

    Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

  18. Developments in special geometry

    Mohaupt, Thomas; Vaughan, Owen

    2012-01-01

    We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.

  19. Expectation Consistent Approximate Inference

    Opper, Manfred; Winther, Ole

    2005-01-01

    We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...

  20. Ordered cones and approximation

    Keimel, Klaus

    1992-01-01

    This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

  1. Geometry of multihadron production

    Bjorken, J.D.

    1994-10-01

    This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.

  2. Designs and finite geometries

    1996-01-01

    Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.

  3. Geometry of multihadron production

    Bjorken, J.D.

    1994-10-01

    This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions

  4. The Beauty of Geometry

    Morris, Barbara H.

    2004-01-01

    This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…

  5. A Lorentzian quantum geometry

    Grotz, Andreas

    2011-10-07

    In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

  6. Methods of information geometry

    Amari, Shun-Ichi

    2000-01-01

    Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...

  7. A Lorentzian quantum geometry

    Grotz, Andreas

    2011-01-01

    In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

  8. Approximate and renormgroup symmetries

    Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling

    2009-07-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  9. Approximate and renormgroup symmetries

    Ibragimov, Nail H.; Kovalev, Vladimir F.

    2009-01-01

    ''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)

  10. Approximations of Fuzzy Systems

    Vinai K. Singh

    2013-03-01

    Full Text Available A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems, with product inference, centroid defuzzification and Gaussian functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions

  11. General Rytov approximation.

    Potvin, Guy

    2015-10-01

    We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.

  12. Geometry on the space of geometries

    Christodoulakis, T.; Zanelli, J.

    1988-06-01

    We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs

  13. INTOR cost approximation

    Knobloch, A.F.

    1980-01-01

    A simplified cost approximation for INTOR parameter sets in a narrow parameter range is shown. Plausible constraints permit the evaluation of the consequences of parameter variations on overall cost. (orig.) [de

  14. Approximation and Computation

    Gautschi, Walter; Rassias, Themistocles M

    2011-01-01

    Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg

  15. Approximate kernel competitive learning.

    Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang

    2015-03-01

    Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.

  16. Quantification of Porcine Vocal Fold Geometry.

    Stevens, Kimberly A; Thomson, Scott L; Jetté, Marie E; Thibeault, Susan L

    2016-07-01

    The aim of this study was to quantify porcine vocal fold medial surface geometry and three-dimensional geometric distortion induced by freezing the larynx, especially in the region of the vocal folds. The medial surface geometries of five excised porcine larynges were quantified and reported. Five porcine larynges were imaged in a micro-CT scanner, frozen, and rescanned. Segmentations and three-dimensional reconstructions were used to quantify and characterize geometric features. Comparisons were made with geometry data previously obtained using canine and human vocal folds as well as geometries of selected synthetic vocal fold models. Freezing induced an overall expansion of approximately 5% in the transverse plane and comparable levels of nonuniform distortion in sagittal and coronal planes. The medial surface of the porcine vocal folds was found to compare reasonably well with other geometries, although the compared geometries exhibited a notable discrepancy with one set of published human female vocal fold geometry. Porcine vocal folds are qualitatively geometrically similar to data available for canine and human vocal folds, as well as commonly used models. Freezing of tissue in the larynx causes distortion of around 5%. The data can provide direction in estimating uncertainty due to bulk distortion of tissue caused by freezing, as well as quantitative geometric data that can be directly used in developing vocal fold models. Copyright © 2016 The Voice Foundation. Published by Elsevier Inc. All rights reserved.

  17. Semiclassical approximation in Batalin-Vilkovisky formalism

    Schwarz, A.

    1993-01-01

    The geometry of supermanifolds provided with a Q-structure (i.e. with an odd vector field Q satisfying {Q, Q}=0), a P-structure (odd symplectic structure) and an S-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of the Batalin-Vilkovisky approach to the quantization of gauge theories. In particular the semiclassical approximation in this approach is expressed in terms of Reidemeister torsion. (orig.)

  18. Complex and symplectic geometry

    Medori, Costantino; Tomassini, Adriano

    2017-01-01

    This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

  19. Non-Euclidean geometry

    Kulczycki, Stefan

    2008-01-01

    This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff

  20. Multiple Time-Instances Features of Degraded Speech for Single Ended Quality Measurement

    Rajesh Kumar Dubey

    2017-01-01

    Full Text Available The use of single time-instance features, where entire speech utterance is used for feature computation, is not accurate and adequate in capturing the time localized information of short-time transient distortions and their distinction from plosive sounds of speech, particularly degraded by impulsive noise. Hence, the importance of estimating features at multiple time-instances is sought. In this, only active speech segments of degraded speech are used for features computation at multiple time-instances on per frame basis. Here, active speech means both voiced and unvoiced frames except silence. The features of different combinations of multiple contiguous active speech segments are computed and called multiple time-instances features. The joint GMM training has been done using these features along with the subjective MOS of the corresponding speech utterance to obtain the parameters of GMM. These parameters of GMM and multiple time-instances features of test speech are used to compute the objective MOS values of different combinations of multiple contiguous active speech segments. The overall objective MOS of the test speech utterance is obtained by assigning equal weight to the objective MOS values of the different combinations of multiple contiguous active speech segments. This algorithm outperforms the Recommendation ITU-T P.563 and recently published algorithms.

  1. Lectures on coarse geometry

    Roe, John

    2003-01-01

    Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...

  2. Lectures on Symplectic Geometry

    Silva, Ana Cannas

    2001-01-01

    The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...

  3. Complex algebraic geometry

    Kollár, János

    1997-01-01

    This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

  4. Geometry and Combinatorics

    Kokkendorff, Simon Lyngby

    2002-01-01

    The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...

  5. The geometry of geodesics

    Busemann, Herbert

    2005-01-01

    A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.

  6. Geometry and billiards

    Tabachnikov, Serge

    2005-01-01

    Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...

  7. Introduction to tropical geometry

    Maclagan, Diane

    2015-01-01

    Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...

  8. Rudiments of algebraic geometry

    Jenner, WE

    2017-01-01

    Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.

  9. Implosions and hypertoric geometry

    Dancer, A.; Kirwan, F.; Swann, A.

    2013-01-01

    The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....

  10. Intermediate algebra & analytic geometry

    Gondin, William R

    1967-01-01

    Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system

  11. d-geometries revisited

    Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio

    2013-01-01

    We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.

  12. CMS geometry through 2020

    Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J

    2014-01-01

    CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.

  13. Software Geometry in Simulations

    Alion, Tyler; Viren, Brett; Junk, Tom

    2015-04-01

    The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).

  14. On Covering Approximation Subspaces

    Xun Ge

    2009-06-01

    Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

  15. Discrete quantum geometries and their effective dimension

    Thuerigen, Johannes

    2015-01-01

    In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.

  16. Improving Multi-Instance Multi-Label Learning by Extreme Learning Machine

    Ying Yin

    2016-05-01

    Full Text Available Multi-instance multi-label learning is a learning framework, where every object is represented by a bag of instances and associated with multiple labels simultaneously. The existing degeneration strategy-based methods often suffer from some common drawbacks: (1 the user-specific parameter for the number of clusters may incur the effective problem; (2 SVM may bring a high computational cost when utilized as the classifier builder. In this paper, we propose an algorithm, namely multi-instance multi-label (MIML-extreme learning machine (ELM, to address the problems. To our best knowledge, we are the first to utilize ELM in the MIML problem and to conduct the comparison of ELM and SVM on MIML. Extensive experiments have been conducted on real datasets and synthetic datasets. The results show that MIMLELM tends to achieve better generalization performance at a higher learning speed.

  17. Sparse Representation Based Multi-Instance Learning for Breast Ultrasound Image Classification.

    Bing, Lu; Wang, Wei

    2017-01-01

    We propose a novel method based on sparse representation for breast ultrasound image classification under the framework of multi-instance learning (MIL). After image enhancement and segmentation, concentric circle is used to extract the global and local features for improving the accuracy in diagnosis and prediction. The classification problem of ultrasound image is converted to sparse representation based MIL problem. Each instance of a bag is represented as a sparse linear combination of all basis vectors in the dictionary, and then the bag is represented by one feature vector which is obtained via sparse representations of all instances within the bag. The sparse and MIL problem is further converted to a conventional learning problem that is solved by relevance vector machine (RVM). Results of single classifiers are combined to be used for classification. Experimental results on the breast cancer datasets demonstrate the superiority of the proposed method in terms of classification accuracy as compared with state-of-the-art MIL methods.

  18. Simplified discrete ordinates method in spherical geometry

    Elsawi, M.A.; Abdurrahman, N.M.; Yavuz, M.

    1999-01-01

    The authors extend the method of simplified discrete ordinates (SS N ) to spherical geometry. The motivation for such an extension is that the appearance of the angular derivative (redistribution) term in the spherical geometry transport equation makes it difficult to decide which differencing scheme best approximates this term. In the present method, the angular derivative term is treated implicitly and thus avoids the need for the approximation of such term. This method can be considered to be analytic in nature with the advantage of being free from spatial truncation errors from which most of the existing transport codes suffer. In addition, it treats the angular redistribution term implicitly with the advantage of avoiding approximations to that term. The method also can handle scattering in a very general manner with the advantage of spending almost the same computational effort for all scattering modes. Moreover, the methods can easily be applied to higher-order S N calculations

  19. On Convex Quadratic Approximation

    den Hertog, D.; de Klerk, E.; Roos, J.

    2000-01-01

    In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

  20. Prestack wavefield approximations

    Alkhalifah, Tariq

    2013-01-01

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

  1. Approximating The DCM

    Madsen, Rasmus Elsborg

    2005-01-01

    The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM...

  2. Approximation by Cylinder Surfaces

    Randrup, Thomas

    1997-01-01

    We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...

  3. Prestack wavefield approximations

    Alkhalifah, Tariq

    2013-09-01

    The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.

  4. Global aspects of complex geometry

    Catanese, Fabrizio; Huckleberry, Alan T

    2006-01-01

    Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.

  5. Exact solution of the neutron transport equation in spherical geometry

    Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters

    2017-03-15

    Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.

  6. Approximate Bayesian evaluations of measurement uncertainty

    Possolo, Antonio; Bodnar, Olha

    2018-04-01

    The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

  7. Instance-optimality in probability with an instance" xmlns="http://www.e

    DeVore, Ronald

    2009-11-01

    Let Φ (ω), ω ∈ Ω, be a family of n × N random matrices whose entries φ{symbol}i, j are independent realizations of a symmetric, real random variable η with expectation E η = 0 and variance E η2 = 1 / n. Such matrices are used in compressed sensing to encode a vector x ∈ RN by y = Φ x. The information y holds about x is extracted by using a decoder Δ : Rn → RN. The most prominent decoder is the ℓ1-minimization decoder Δ which gives for a given y ∈ Rn the element Δ (y) ∈ RN which has minimal ℓ1-norm among all z ∈ RN with Φ z = y. This paper is interested in properties of the random family Φ (ω) which guarantee that the vector over(x, ̄) : = Δ (Φ x) will with high probability approximate x in ℓ2 N to an accuracy comparable with the best k-term error of approximation in ℓ2 N for the range k ≤ a n / log2 (N / n). This means that for the above range of k, for each signal x ∈ RN, the vector over(x, ̄) : = Δ (Φ x) satisfies{norm of matrix} x - over(x, ̄) {norm of matrix}ℓ2N ≤ C under(inf, z ∈ Σk) {norm of matrix} x - z {norm of matrix}ℓ2N with high probability on the draw of Φ. Here, Σk consists of all vectors with at most k nonzero coordinates. The first result of this type was proved by Wojtaszczyk [P. Wojtaszczyk, Stability and instance optimality for Gaussian measurements in compressed sensing, Found. Comput. Math., in press] who showed this property when η is a normalized Gaussian random variable. We extend this property to more general random variables, including the particular case where η is the Bernoulli random variable which takes the values ± 1 / sqrt(n) with equal probability. The proofs of our results use geometric mapping properties of such random matrices some of which were recently obtained in [A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, Smallest singular value of random matrices and geometry of random polytopes, Adv. Math. 195 (2005) 491-523]. © 2009 Elsevier Inc. All rights

  8. A variational solution of transport equation based on spherical geometry

    Liu Hui; Zhang Ben'ai

    2002-01-01

    A variational method with differential forms gives better precision for numerical solution of transport critical problem based on spherical geometry, and its computation seems simple than other approximate methods

  9. Sources of hyperbolic geometry

    Stillwell, John

    1996-01-01

    This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...

  10. Generalizing optical geometry

    Jonsson, Rickard; Westman, Hans

    2006-01-01

    We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity

  11. The approximation gap for the metric facility location problem is not yet closed

    Byrka, J.; Aardal, K.I.

    2007-01-01

    We consider the 1.52-approximation algorithm of Mahdian et al. for the metric uncapacitated facility location problem. We show that their algorithm does not close the gap with the lower bound on approximability, 1.463, by providing a construction of instances for which its approximation ratio is not

  12. An improved saddlepoint approximation.

    Gillespie, Colin S; Renshaw, Eric

    2007-08-01

    Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents. However, it suffers from the problem of not always yielding full support, and whilst [S. Wang, General saddlepoint approximations in the bootstrap, Prob. Stat. Lett. 27 (1992) 61.] neat scaling approach provides a solution to this hurdle, it leads to potentially inaccurate and aberrant results. We therefore propose several new ways of surmounting such difficulties, including: extending the inversion of the cumulant generating function to second-order; selecting an appropriate probability structure for higher-order cumulants (the standard moment closure procedure takes them to be zero); and, making subtle changes to the target cumulants and then optimising via the simplex algorithm.

  13. Prestack traveltime approximations

    Alkhalifah, Tariq Ali

    2011-01-01

    Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.

  14. Topology, calculus and approximation

    Komornik, Vilmos

    2017-01-01

    Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...

  15. Approximate Bayesian recursive estimation

    Kárný, Miroslav

    2014-01-01

    Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf

  16. Approximating Preemptive Stochastic Scheduling

    Megow Nicole; Vredeveld Tjark

    2009-01-01

    We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...

  17. Optimization and approximation

    Pedregal, Pablo

    2017-01-01

    This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

  18. Feature Subset Selection and Instance Filtering for Cross-project Defect Prediction - Classification and Ranking

    Faimison Porto

    2016-12-01

    Full Text Available The defect prediction models can be a good tool on organizing the project's test resources. The models can be constructed with two main goals: 1 to classify the software parts - defective or not; or 2 to rank the most defective parts in a decreasing order. However, not all companies maintain an appropriate set of historical defect data. In this case, a company can build an appropriate dataset from known external projects - called Cross-project Defect Prediction (CPDP. The CPDP models, however, present low prediction performances due to the heterogeneity of data. Recently, Instance Filtering methods were proposed in order to reduce this heterogeneity by selecting the most similar instances from the training dataset. Originally, the similarity is calculated based on all the available dataset features (or independent variables. We propose that using only the most relevant features on the similarity calculation can result in more accurate filtered datasets and better prediction performances. In this study we extend our previous work. We analyse both prediction goals - Classification and Ranking. We present an empirical evaluation of 41 different methods by associating Instance Filtering methods with Feature Selection methods. We used 36 versions of 11 open source projects on experiments. The results show similar evidences for both prediction goals. First, the defect prediction performance of CPDP models can be improved by associating Feature Selection and Instance Filtering. Second, no evaluated method presented general better performances. Indeed, the most appropriate method can vary according to the characteristics of the project being predicted.

  19. Instances or Sequences? Improving the State of the Art of Qualitative Research

    David Silverman

    2005-09-01

    Full Text Available Numbers apparently talk. With few numbers, qualitative researchers appear to rely on examples or instances to support their analysis. Hence research reports routinely display data extracts which serve as telling instances of some claimed phenomenon. However, the use of such an evidential base rightly provokes the charge of (possible anecdotalism, i.e. choosing just those extracts which support your argument. I suggest that this methodological problem is best addressed by returning to those features of our theoretical roots which tend to distinguish what we do from the work of quantitative social scientists. Although SAUSSURE is most cited in linguistics and structural anthropology, he provides a simple rule that applies to us all. In a rebuke to our reli­ance on instances, SAUSSURE tells us "no mean­ing exists in a single item". Everything depends upon how single items (elements are articulated. One everyday activity in which the social world is articulated is through the construction of se­quences. Just as participants attend to the se­quential placing of interactional "events", so should social scientists. Using examples drawn from focus groups, fieldnotes and audiotapes, I argue that the identification of such sequences rather than the citing of instances should constitute a prime test for the adequacy of any claim about qualitative data. URN: urn:nbn:de:0114-fqs0503301

  20. Anaphoric Reference to Instances, Instantiated and Non-Instantiated Categories: A Reading Time Study.

    Garnham, Alan

    1981-01-01

    Experiments using memory paradigms have shown that general terms receive context-dependent encodings. This experiment investigates the encoding of category and instance nouns. The results indicate that representations set up during reading are the product of both the linguistic input and of general knowledge. (Author/KC)

  1. Microsoft and the Court of First Instance: What Does it All Mean?

    Renata Hesse

    2007-01-01

    As someone who has spent a considerable portion of the last five years working on issues involving Microsoft’s conduct and the competition laws, I read with interest the commentary that followed the issuance of the Court of First Instance’s decision on September 17.

  2. Feature selection is the ReliefF for multiple instance learning

    Zafra, A.; Pechenizkiy, M.; Ventura, S.

    2010-01-01

    Dimensionality reduction and feature selection in particular are known to be of a great help for making supervised learning more effective and efficient. Many different feature selection techniques have been proposed for the traditional settings, where each instance is expected to have a label. In

  3. HyDR-MI : A hybrid algorithm to reduce dimensionality in multiple instance learning

    Zafra, A.; Pechenizkiy, M.; Ventura, S.

    2013-01-01

    Feature selection techniques have been successfully applied in many applications for making supervised learning more effective and efficient. These techniques have been widely used and studied in traditional supervised learning settings, where each instance is expected to have a label. In multiple

  4. Increasing the detection of minority class instances in financial statement fraud

    Moepya, Stephen

    2017-04-01

    Full Text Available -1 Asian Conference on Intelligent Information and Database Systems, 3-5 April 2017, Kanazawa, Japan Increasing the detection of minority class instances in financial statement fraud Stephen Obakeng Moepya1,2(B), Fulufhelo V. Nelwamondo1...

  5. On Combining Multiple-Instance Learning and Active Learning for Computer-Aided Detection of Tuberculosis

    Melendez Rodriguez, J.C.; Ginneken, B. van; Maduskar, P.; Philipsen, R.H.H.M.; Ayles, H.; Sanchez, C.I.

    2016-01-01

    The major advantage of multiple-instance learning (MIL) applied to a computer-aided detection (CAD) system is that it allows optimizing the latter with case-level labels instead of accurate lesion outlines as traditionally required for a supervised approach. As shown in previous work, a MIL-based

  6. Intrinsic and extrinsic geometries of a tidally deformed black hole

    Vega, Ian; Poisson, Eric; Massey, Ryan

    2011-01-01

    A description of the event horizon of a perturbed Schwarzschild black hole is provided in terms of the intrinsic and extrinsic geometries of the null hypersurface. This description relies on a Gauss-Codazzi theory of null hypersurfaces embedded in spacetime, which extends the standard theory of spacelike and timelike hypersurfaces involving the first and second fundamental forms. We show that the intrinsic geometry of the event horizon is invariant under a reparameterization of the null generators, and that the extrinsic geometry depends on the parameterization. Stated differently, we show that while the extrinsic geometry depends on the choice of gauge, the intrinsic geometry is gauge invariant. We apply the formalism to solutions to the vacuum field equations that describe a tidally deformed black hole. In a first instance, we consider a slowly varying, quadrupolar tidal field imposed on the black hole, and in a second instance, we examine the tide raised during a close parabolic encounter between the black hole and a small orbiting body.

  7. Computational synthetic geometry

    Bokowski, Jürgen

    1989-01-01

    Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...

  8. Discrete and computational geometry

    Devadoss, Satyan L

    2011-01-01

    Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...

  9. Geometry and Cloaking Devices

    Ochiai, T.; Nacher, J. C.

    2011-09-01

    Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.

  10. Lectures on discrete geometry

    2002-01-01

    Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...

  11. Complex differential geometry

    Zheng, Fangyang

    2002-01-01

    The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...

  12. Solving large instances of the quadratic cost of partition problem on dense graphs by data correcting algorithms

    Goldengorin, Boris; Vink, Marius de

    1999-01-01

    The Data-Correcting Algorithm (DCA) corrects the data of a hard problem instance in such a way that we obtain an instance of a well solvable special case. For a given prescribed accuracy of the solution, the DCA uses a branch and bound scheme to make sure that the solution of the corrected instance

  13. Geometry and symmetry

    Yale, Paul B

    2012-01-01

    This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi

  14. Cyclic approximation to stasis

    Stewart D. Johnson

    2009-06-01

    Full Text Available Neighborhoods of points in $mathbb{R}^n$ where a positive linear combination of $C^1$ vector fields sum to zero contain, generically, cyclic trajectories that switch between the vector fields. Such points are called stasis points, and the approximating switching cycle can be chosen so that the timing of the switches exactly matches the positive linear weighting. In the case of two vector fields, the stasis points form one-dimensional $C^1$ manifolds containing nearby families of two-cycles. The generic case of two flows in $mathbb{R}^3$ can be diffeomorphed to a standard form with cubic curves as trajectories.

  15. On the WKBJ approximation

    El Sawi, M.

    1983-07-01

    A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution. The method is also extended for the solution of inhomogeneous equations. (author)

  16. The relaxation time approximation

    Gairola, R.P.; Indu, B.D.

    1991-01-01

    A plausible approximation has been made to estimate the relaxation time from a knowledge of the transition probability of phonons from one state (r vector, q vector) to other state (r' vector, q' vector), as a result of collision. The relaxation time, thus obtained, shows a strong dependence on temperature and weak dependence on the wave vector. In view of this dependence, relaxation time has been expressed in terms of a temperature Taylor's series in the first Brillouin zone. Consequently, a simple model for estimating the thermal conductivity is suggested. the calculations become much easier than the Callaway model. (author). 14 refs

  17. Polynomial approximation on polytopes

    Totik, Vilmos

    2014-01-01

    Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.

  18. Finite elements and approximation

    Zienkiewicz, O C

    2006-01-01

    A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

  19.  Higher Order Improvements for Approximate Estimators

    Kristensen, Dennis; Salanié, Bernard

    Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties of such appr......Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties...... of such approximate estimators at a low computational cost. The first two methods correct the objective function so as to remove the leading term of the bias due to the approximation. One variant provides an analytical bias adjustment, but it only works for estimators based on stochastic approximators......, such as simulation-based estimators. Our second bias correction is based on ideas from the resampling literature; it eliminates the leading bias term for non-stochastic as well as stochastic approximators. Finally, we propose an iterative procedure where we use Newton-Raphson (NR) iterations based on a much finer...

  20. Towards relativistic quantum geometry

    Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)

    2015-12-17

    We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.

  1. Multiplicity in difference geometry

    Tomasic, Ivan

    2011-01-01

    We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.

  2. Spacetime and Euclidean geometry

    Brill, Dieter; Jacobson, Ted

    2006-04-01

    Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.

  3. Physics and geometry

    Konopleva, N.P.

    2009-01-01

    The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered

  4. Origami, Geometry and Art

    Wares, Arsalan; Elstak, Iwan

    2017-01-01

    The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…

  5. Gravity is Geometry.

    MacKeown, P. K.

    1984-01-01

    Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)

  6. Towards a Nano Geometry?

    Booss-Bavnbek, Bernhelm

    2011-01-01

    This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...

  7. Diophantine geometry an introduction

    Hindry, Marc

    2000-01-01

    This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

  8. Sliding vane geometry turbines

    Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R

    2014-12-30

    Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.

  9. History of analytic geometry

    Boyer, Carl B

    2012-01-01

    Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.

  10. Non-euclidean geometry

    Coxeter, HSM

    1965-01-01

    This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.

  11. Topics in Riemannian geometry

    Ezin, J.P.

    1988-08-01

    The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs

  12. Geometry Euclid and beyond

    Hartshorne, Robin

    2000-01-01

    In recent years, I have been teaching a junior-senior-level course on the classi­ cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa­ rately. The remainder of the book is an exploration of questions that arise natu­ rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...

  13. Approximate Bayesian computation.

    Mikael Sunnåker

    Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.

  14. Flexible intuitions of Euclidean geometry in an Amazonian indigene group

    Izard, Véronique; Pica, Pierre; Spelke, Elizabeth S.; Dehaene, Stanislas

    2011-01-01

    Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. PMID:21606377

  15. The random phase approximation

    Schuck, P.

    1985-01-01

    RPA is the adequate theory to describe vibrations of the nucleus of very small amplitudes. These vibrations can either be forced by an external electromagnetic field or can be eigenmodes of the nucleus. In a one dimensional analogue the potential corresponding to such eigenmodes of very small amplitude should be rather stiff otherwise the motion risks to be a large amplitude one and to enter a region where the approximation is not valid. This means that nuclei which are supposedly well described by RPA must have a very stable groundstate configuration (must e.g. be very stiff against deformation). This is usually the case for doubly magic nuclei or close to magic nuclei which are in the middle of proton and neutron shells which develop a very stable groundstate deformation; we take the deformation as an example but there are many other possible degrees of freedom as, for example, compression modes, isovector degrees of freedom, spin degrees of freedom, and many more

  16. Multi-Instance Quotation System (SaaS) Based on Docker Containerizing Platform

    Shekhamis, Anass

    2016-01-01

    This thesis covers the development of a quotation system that is built as a multi-instance SaaS. Quotation systems usually come as part of customer relationship management systems, but not necessarily included. They also tend to have invoicing alongside the original functionality; creating quotations for customers. The system uses Microservices Architecture were each service is a replaceable and upgradeable component that achieve certain functionality and easily integrate with other third-par...

  17. FCNN-MR: A Parallel Instance Selection Method Based on Fast Condensed Nearest Neighbor Rule

    Lu Si; Jie Yu; Shasha Li; Jun Ma; Lei Luo; Qingbo Wu; Yongqi Ma; Zhengji Liu

    2017-01-01

    Instance selection (IS) technique is used to reduce the data size to improve the performance of data mining methods. Recently, to process very large data set, several proposed methods divide the training set into some disjoint subsets and apply IS algorithms independently to each subset. In this paper, we analyze the limitation of these methods and give our viewpoint about how to divide and conquer in IS procedure. Then, based on fast condensed nearest neighbor (FCNN) rul...

  18. Extension of instance search technique by geometric coding and quantization error compensation

    García Del Molino, Ana

    2013-01-01

    [ANGLÈS] This PFC analyzes two ways of improving the video retrieval techniques for instance search problem. In one hand, "Pairing Interest Points for a better Signature using Sparse Detector's Spatial Information", allows the Bag-of-Words model to keep some spatial information. In the other, "Study of the Hamming Embedding Signature Symmetry in Video Retrieval" provides binary signatures that refine the matching based on visual words, and aims to find the best way of matching taking into acc...

  19. Instances of Use of United States Armed Forces Abroad, 1798-2014

    2014-09-15

    Garcia, and Thomas J. Nicola . Instances of Use of United States Armed Forces Abroad, 1798-2014 Congressional Research Service Contents...landing zones near the U.S. Embassy in Saigon and the Tan Son Nhut Airfield. Mayaguez incident. On May 15, 1975, President Ford reported he had ordered...Report R41989, Congressional Authority to Limit Military Operations, by Jennifer K. Elsea, Michael John Garcia and Thomas J. Nicola . CRS Report R43344

  20. Hermeticity of three cryogenic calorimeter geometries

    Strovink, M.; Wormersley, W.J.; Forden, G.E.

    1989-04-01

    We calculate the effect of cracks and dead material on resolution in three simplified cryogenic calorimeter geometries, using a crude approximation that neglects transverse shower spreading and considers only a small set of incident angles. For each dead region, we estimate the average unseen energy using a shower parametrization, and relate it to resolution broadening using a simple approximation that agrees with experimental data. Making reasonable and consistent assumptions on cryostat wall thicknesses, we find that the effects of cracks and dead material dominate the expected resolution in the region where separate ''barrel'' and ''end'' cryostats meet. This is particularly true for one geometry in which the end calorimeter caps the barrel and also protrudes into the hole within it. We also find that carefully designed auxiliary ''crack filler'' detectors can substantially reduce the loss of resolution in these areas. 6 figs

  1. A Hybrid Instance Selection Using Nearest-Neighbor for Cross-Project Defect Prediction

    Duksan Ryu; Jong-In Jang; Jongmoon Baik; Member; ACM; IEEE

    2015-01-01

    Software defect prediction (SDP) is an active research field in software engineering to identify defect-prone modules. Thanks to SDP, limited testing resources can be effectively allocated to defect-prone modules. Although SDP requires suffcient local data within a company, there are cases where local data are not available, e.g., pilot projects. Companies without local data can employ cross-project defect prediction (CPDP) using external data to build classifiers. The major challenge of CPDP is different distributions between training and test data. To tackle this, instances of source data similar to target data are selected to build classifiers. Software datasets have a class imbalance problem meaning the ratio of defective class to clean class is far low. It usually lowers the performance of classifiers. We propose a Hybrid Instance Selection Using Nearest-Neighbor (HISNN) method that performs a hybrid classification selectively learning local knowledge (via k-nearest neighbor) and global knowledge (via na¨ıve Bayes). Instances having strong local knowledge are identified via nearest-neighbors with the same class label. Previous studies showed low PD (probability of detection) or high PF (probability of false alarm) which is impractical to use. The experimental results show that HISNN produces high overall performance as well as high PD and low PF.

  2. A medley of meanings: Insights from an instance of gameplay in League of Legends

    Max Watson

    2015-06-01

    Full Text Available This article engages with the notion of insightful gameplay. It recounts debates about what, if anything, makes play meaningful. Through these, it contends that while some games are explicitly designed to foster insightful gameplay, most are not and many might even be considered utterly meaningless. It notes how discussions about what makes playing games meaningful raise concomitant questions about what playing means. It then strives to reconcile these two interrelated questions by offering the notion of a medley of meanings. A medley of meanings is the notion that each player brings their own subjective disposition to playing to a particular instance of gameplay; no participant to gameplay should be considered as in a state that is “not playing”. Because these subjective dispositions to playing can be quite divergent, players can and often do clash in instances of gameplay. This article then contends that these clashes can in turn render the most seemingly meaningless games potential hotbeds of insightful gameplay. The second half of this article discusses the ethnographic example of an instance of gameplay in the digital game League of Legends in order to explicate the notion of a medley of meanings.

  3. Instance selection in digital soil mapping: a study case in Rio Grande do Sul, Brazil

    Elvio Giasson

    2015-09-01

    Full Text Available A critical issue in digital soil mapping (DSM is the selection of data sampling method for model training. One emerging approach applies instance selection to reduce the size of the dataset by drawing only relevant samples in order to obtain a representative subset that is still large enough to preserve relevant information, but small enough to be easily handled by learning algorithms. Although there are suggestions to distribute data sampling as a function of the soil map unit (MU boundaries location, there are still contradictions among research recommendations for locating samples either closer or more distant from soil MU boundaries. A study was conducted to evaluate instance selection methods based on spatially-explicit data collection using location in relation to soil MU boundaries as the main criterion. Decision tree analysis was performed for modeling digital soil class mapping using two different sampling schemes: a selecting sampling points located outside buffers near soil MU boundaries, and b selecting sampling points located within buffers near soil MU boundaries. Data was prepared for generating classification trees to include only data points located within or outside buffers with widths of 60, 120, 240, 360, 480, and 600m near MU boundaries. Instance selection methods using both spatial selection of methods was effective for reduced size of the dataset used for calibrating classification tree models, but failed to provide advantages to digital soil mapping because of potential reduction in the accuracy of classification tree models.

  4. Sparse Representation Based Multi-Instance Learning for Breast Ultrasound Image Classification

    Lu Bing

    2017-01-01

    Full Text Available We propose a novel method based on sparse representation for breast ultrasound image classification under the framework of multi-instance learning (MIL. After image enhancement and segmentation, concentric circle is used to extract the global and local features for improving the accuracy in diagnosis and prediction. The classification problem of ultrasound image is converted to sparse representation based MIL problem. Each instance of a bag is represented as a sparse linear combination of all basis vectors in the dictionary, and then the bag is represented by one feature vector which is obtained via sparse representations of all instances within the bag. The sparse and MIL problem is further converted to a conventional learning problem that is solved by relevance vector machine (RVM. Results of single classifiers are combined to be used for classification. Experimental results on the breast cancer datasets demonstrate the superiority of the proposed method in terms of classification accuracy as compared with state-of-the-art MIL methods.

  5. Multivariate calculus and geometry

    Dineen, Seán

    2014-01-01

    Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

  6. Transformational plane geometry

    Umble, Ronald N

    2014-01-01

    Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...

  7. Multilevel geometry optimization

    Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.

    2000-02-01

    Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.

  8. Multilevel geometry optimization

    Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)

    2000-02-15

    Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.

  9. Finite quantum physics and noncommutative geometry

    Balachandran, A.P.; Ercolessi, E.; Landi, G.; Teotonio-Sobrinho, P.; Lizzi, F.; Sparano, G.

    1994-04-01

    Conventional discrete approximations of a manifold do not preserve its nontrivial topological features. In this article we describe an approximation scheme due to Sorkin which reproduces physically important aspects of manifold topology with striking fidelity. The approximating topological spaces in this scheme are partially ordered sets (posets). Now, in ordinary quantum physics on a manifold M, continuous probability densities generate the commutative C * -algebra C(M) of continuous functions on M. It has a fundamental physical significance, containing the information to reconstruct the topology of M, and serving to specify the domains of observables like the Hamiltonian. For a poset, the role of this algebra is assumed by a noncommutative C * -algebra A. As noncommutative geometries are based on noncommutative C * -algebra, we therefore have a remarkable connection between finite approximations to quantum physics and noncommutative geometries. Varies methods for doing quantum physics using A are explored. Particular attention is paid to developing numerically viable approximation schemes which at the same time preserve important topological features of continuum physics. (author). 21 refs, 13 figs

  10. Geometry as an aspect of dynamics

    Videira, A.L.L.; Barros, A.L.R.; Fernandes, N.C.

    1982-07-01

    Contrary to the predominant way of doing physics, it is shown that the geometric structure of a general differentiable space-time manifold can be determined by means of the introduction in that manifold of a minimal set of fundamental dynamical quantities associated to a free particle endowed with the fundamental property of momentum. Thus, general relativistic physics implies a general pseudo-Riemannian geometry, whereas the physics of the special theory of relativity is tied up with Minkowski space-time, and Newtonian dynamics is bound to Newtonian space-time. While in the relativistic instance, the Riemannian character of the manifold is basically fixed by means only of the Hamiltonian state function of the free particle (its kynetic energy), in the latter case, it has to resort, perhaps not unexpectedly, to the two dynamical entities mass and energy, separately. (Author) [pt

  11. Geometry as an aspect of dynamics

    Videira, A.L.L.; Barros, A.L.R.; Fernandes, N.C.

    1983-12-01

    Contrary to the predominant way of doing physics, it is shown that the geometric structure of a general differentiable space-time manifold can be determined by means of the introduction in that manifold of a minimal set of fundamental dynamical quantities associated to a particle endowed with the fundamental property of covariant momentum. Thus, general relativistic physics implies a general pseudo-Riemannian geometry, whereas the physics of the special theory of relativity is tied up with Minkowski space-time, and Newtonian dynamics is bound to Newtonian space-time. While in the relativistic instance, the Riemannian character of the manifold is basically fixed by means only of the Hamiltonian state function of the particle (its energy), in the latter case, one have to resort, perhaps not unexpectedly, to the two dynamical entities mass energy, separately. (Author) [pt

  12. Geometry and Destiny

    Krauss, Lawrence M.; Turner, Michael S.

    1999-01-01

    The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.

  13. Complex geometries in wood

    Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob

    2009-01-01

    The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....

  14. Electroweak vacuum geometry

    Lepora, N.; Kibble, T.

    1999-01-01

    We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)

  15. W-geometry

    Hull, C.M.

    1993-01-01

    The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)

  16. Integral geometry and valuations

    Solanes, Gil

    2014-01-01

    Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...

  17. CBM RICH geometry optimization

    Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration

    2016-07-01

    The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.

  18. Perturbative stability of the approximate Killing field eigenvalue problem

    Beetle, Christopher; Wilder, Shawn

    2014-01-01

    An approximate Killing field may be defined on a compact, Riemannian geometry by solving an eigenvalue problem for a certain elliptic operator. This paper studies the effect of small perturbations in the Riemannian metric on the resulting vector field. It shows that small metric perturbations, as measured using a Sobolev-type supremum norm on the space of Riemannian geometries on a fixed manifold, yield small perturbations in the approximate Killing field, as measured using a Hilbert-type square integral norm. It also discusses applications to the problem of computing the spin of a generic black hole in general relativity. (paper)

  19. Approximate quantum Markov chains

    Sutter, David

    2018-01-01

    This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...

  20. Prestack traveltime approximations

    Alkhalifah, Tariq Ali

    2012-05-01

    Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.

  1. Introducing geometry concept based on history of Islamic geometry

    Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

    2018-01-01

    Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

  2. Blind sensor calibration using approximate message passing

    Schülke, Christophe; Caltagirone, Francesco; Zdeborová, Lenka

    2015-01-01

    The ubiquity of approximately sparse data has led a variety of communities to take great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying them to real data can be problematic if imperfect sensing devices introduce deviations from this ideal signal acquisition process, caused by sensor decalibration or failure. We propose a message passing algorithm called calibration approximate message passing (Cal-AMP) that can treat a variety of such sensor-induced imperfections. In addition to deriving the general form of the algorithm, we numerically investigate two particular settings. In the first, a fraction of the sensors is faulty, giving readings unrelated to the signal. In the second, sensors are decalibrated and each one introduces a different multiplicative gain to the measurements. Cal-AMP shares the scalability of approximate message passing, allowing us to treat large sized instances of these problems, and experimentally exhibits a phase transition between domains of success and failure. (paper)

  3. Two lectures on D-geometry and noncommutative geometry

    Douglas, M.R.

    1999-01-01

    This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)

  4. Calculus and Geometry

    IAS Admin

    time when Archimedes (287 BC{212 BC) was computing volumes and .... will look like a right circular cylinder. We know how ... approximations have been made that may lead to wrong ... compute volume and surface area, we use these tech-.

  5. Approximate determination of efficiency for activity measurements of cylindrical samples

    Helbig, W [Nuclear Engineering and Analytics Rossendorf, Inc. (VKTA), Dresden (Germany); Bothe, M [Nuclear Engineering and Analytics Rossendorf, Inc. (VKTA), Dresden (Germany)

    1997-03-01

    Some calibration samples are necessary with the same geometrical parameters but of different materials, containing known activities A homogeniously distributed. Their densities are measured, their mass absorption coefficients may be unknown. These calibration samples are positioned in the counting geometry, for instance directly on the detector. The efficiency function {epsilon}(E) for each sample is gained by measuring the gamma spectra and evaluating all usable gamma energy peaks. From these {epsilon}(E) the common valid {epsilon}{sub geom}(E) will be deduced. For this purpose the functions {epsilon}{sub mu}(E) for these samples have to be established. (orig.)

  6. Synergistic Instance-Level Subspace Alignment for Fine-Grained Sketch-Based Image Retrieval.

    Li, Ke; Pang, Kaiyue; Song, Yi-Zhe; Hospedales, Timothy M; Xiang, Tao; Zhang, Honggang

    2017-08-25

    We study the problem of fine-grained sketch-based image retrieval. By performing instance-level (rather than category-level) retrieval, it embodies a timely and practical application, particularly with the ubiquitous availability of touchscreens. Three factors contribute to the challenging nature of the problem: (i) free-hand sketches are inherently abstract and iconic, making visual comparisons with photos difficult, (ii) sketches and photos are in two different visual domains, i.e. black and white lines vs. color pixels, and (iii) fine-grained distinctions are especially challenging when executed across domain and abstraction-level. To address these challenges, we propose to bridge the image-sketch gap both at the high-level via parts and attributes, as well as at the low-level, via introducing a new domain alignment method. More specifically, (i) we contribute a dataset with 304 photos and 912 sketches, where each sketch and image is annotated with its semantic parts and associated part-level attributes. With the help of this dataset, we investigate (ii) how strongly-supervised deformable part-based models can be learned that subsequently enable automatic detection of part-level attributes, and provide pose-aligned sketch-image comparisons. To reduce the sketch-image gap when comparing low-level features, we also (iii) propose a novel method for instance-level domain-alignment, that exploits both subspace and instance-level cues to better align the domains. Finally (iv) these are combined in a matching framework integrating aligned low-level features, mid-level geometric structure and high-level semantic attributes. Extensive experiments conducted on our new dataset demonstrate effectiveness of the proposed method.

  7. On the instance of misuse of unprofitable energy prices under cartel law

    Schoening, M.

    1993-01-01

    The practice of fixing prices which do not cover the costs can on principle not be considered an instance of misuse pursuant to Articles 22 Section 4 Clause 2 No. 2, 103 Section 5 Clause 2 No. 2 of the GWB (cartel laws). If the authority for the supervision of cartels takes action against companies operating with unprofitable prices, this constitutes a violation not only of cartel law, but also of the constitution. The cartel authorities have no right to dismiss a dominating company's referral to poor business prospects on the ground that its business report is theoretically manipulable. Rather, the burden of proof of concealment is on the authorities. (orig.) [de

  8. Automatic provisioning, deployment and orchestration for load-balancing THREDDS instances

    Cofino, A. S.; Fernández-Tejería, S.; Kershaw, P.; Cimadevilla, E.; Petri, R.; Pryor, M.; Stephens, A.; Herrera, S.

    2017-12-01

    THREDDS is a widely used web server to provide to different scientific communities with data access and discovery. Due to THREDDS's lack of horizontal scalability and automatic configuration management and deployment, this service usually deals with service downtimes and time consuming configuration tasks, mainly when an intensive use is done as is usual within the scientific community (e.g. climate). Instead of the typical installation and configuration of a single or multiple independent THREDDS servers, manually configured, this work presents an automatic provisioning, deployment and orchestration cluster of THREDDS servers. This solution it's based on Ansible playbooks, used to control automatically the deployment and configuration setup on a infrastructure and to manage the datasets available in THREDDS instances. The playbooks are based on modules (or roles) of different backends and frontends load-balancing setups and solutions. The frontend load-balancing system enables horizontal scalability by delegating requests to backend workers, consisting in a variable number of instances for the THREDDS server. This implementation allows to configure different infrastructure and deployment scenario setups, as more workers are easily added to the cluster by simply declaring them as Ansible variables and executing the playbooks, and also provides fault-tolerance and better reliability since if any of the workers fail another instance of the cluster can take over it. In order to test the solution proposed, two real scenarios are analyzed in this contribution: The JASMIN Group Workspaces at CEDA and the User Data Gateway (UDG) at the Data Climate Service from the University of Cantabria. On the one hand, the proposed configuration has provided CEDA with a higher level and more scalable Group Workspaces (GWS) service than the previous one based on Unix permissions, improving also the data discovery and data access experience. On the other hand, the UDG has improved its

  9. Self-similar factor approximants

    Gluzman, S.; Yukalov, V.I.; Sornette, D.

    2003-01-01

    The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties

  10. Geometry of Quantum States

    Hook, D W

    2008-01-01

    A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric framework, and

  11. Functional integration over geometries

    Mottola, E.

    1995-01-01

    The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted

  12. Kinematic geometry of gearing

    Dooner, David B

    2012-01-01

    Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat

  13. From geometry to topology

    Flegg, H Graham

    2001-01-01

    This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.

  14. Torsional heterotic geometries

    Becker, Katrin; Sethi, Savdeep

    2009-01-01

    We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.

  15. Geometrie verstehen: statisch - kinematisch

    Kroll, Ekkehard

    Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.

  16. Elementary algebraic geometry

    Kendig, Keith

    2015-01-01

    Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th

  17. Local analytic geometry

    Abhyankar, Shreeram Shankar

    1964-01-01

    This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from

  18. Geometry of conics

    Akopyan, A V

    2007-01-01

    The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca

  19. Geometry and trigonometry

    2015-01-01

    This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent

  20. Geometry I essentials

    REA, The Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric

  1. Graded geometry and Poisson reduction

    Cattaneo, A S; Zambon, M

    2009-01-01

    The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics

  2. Automatic analysis of online image data for law enforcement agencies by concept detection and instance search

    de Boer, Maaike H. T.; Bouma, Henri; Kruithof, Maarten C.; ter Haar, Frank B.; Fischer, Noëlle M.; Hagendoorn, Laurens K.; Joosten, Bart; Raaijmakers, Stephan

    2017-10-01

    The information available on-line and off-line, from open as well as from private sources, is growing at an exponential rate and places an increasing demand on the limited resources of Law Enforcement Agencies (LEAs). The absence of appropriate tools and techniques to collect, process, and analyze the volumes of complex and heterogeneous data has created a severe information overload. If a solution is not found, the impact on law enforcement will be dramatic, e.g. because important evidence is missed or the investigation time is too long. Furthermore, there is an uneven level of capabilities to deal with the large volumes of complex and heterogeneous data that come from multiple open and private sources at national level across the EU, which hinders cooperation and information sharing. Consequently, there is a pertinent need to develop tools, systems and processes which expedite online investigations. In this paper, we describe a suite of analysis tools to identify and localize generic concepts, instances of objects and logos in images, which constitutes a significant portion of everyday law enforcement data. We describe how incremental learning based on only a few examples and large-scale indexing are addressed in both concept detection and instance search. Our search technology allows querying of the database by visual examples and by keywords. Our tools are packaged in a Docker container to guarantee easy deployment on a system and our tools exploit possibilities provided by open source toolboxes, contributing to the technical autonomy of LEAs.

  3. Entropy-Weighted Instance Matching Between Different Sourcing Points of Interest

    Lin Li

    2016-01-01

    Full Text Available The crucial problem for integrating geospatial data is finding the corresponding objects (the counterpart from different sources. Most current studies focus on object matching with individual attributes such as spatial, name, or other attributes, which avoids the difficulty of integrating those attributes, but at the cost of an ineffective matching. In this study, we propose an approach for matching instances by integrating heterogeneous attributes with the allocation of suitable attribute weights via information entropy. First, a normalized similarity formula is developed, which can simplify the calculation of spatial attribute similarity. Second, sound-based and word segmentation-based methods are adopted to eliminate the semantic ambiguity when there is a lack of a normative coding standard in geospatial data to express the name attribute. Third, category mapping is established to address the heterogeneity among different classifications. Finally, to address the non-linear characteristic of attribute similarity, the weights of the attributes are calculated by the entropy of the attributes. Experiments demonstrate that the Entropy-Weighted Approach (EWA has good performance both in terms of precision and recall for instance matching from different data sets.

  4. Towards a new procreation ethic: the exemplary instance of cleft lip and palate.

    Le Dref, Gaëlle; Grollemund, Bruno; Danion-Grilliat, Anne; Weber, Jean-Christophe

    2013-08-01

    The improvement of ultrasound scan techniques is enabling ever earlier prenatal diagnosis of developmental anomalies. In France, apart from cases where the mother's life is endangered, the detection of "particularly serious" conditions, and conditions that are "incurable at the time of diagnosis" are the only instances in which a therapeutic abortion can be performed, this applying up to the 9th month of pregnancy. Thus numerous conditions, despite the fact that they cause distress or pain or are socially disabling, do not qualify for therapeutic abortion, despite sometimes pressing demands from parents aware of the difficulties in store for their child and themselves, in a society that is not very favourable towards the integration and self-fulfilment of people with a disability. Cleft lip and palate (CLP), although it can be completely treated, is one of the conditions that considerably complicates the lives of child and parents. Nevertheless, the recent scope for making very early diagnosis of CLP, before the deadline for legal voluntary abortion, has not led to any wave of abortions. CLP in France has the benefit of a exceptional care plan, targeting both the health and the integration of the individuals affected. This article sets out, via the emblematic instance of CLP, to show how present fears of an emerging "domestic" or liberal eugenic trend could become redundant if disability is addressed politically and medically, so that individuals with a disability have the same social rights as any other citizen.

  5. Reversing Kristeva's first instance of abjection: the formation of self reconsidered.

    McCabe, Janet L; Holmes, Dave

    2011-03-01

    Psychoanalyst Julia Kristeva defines the theoretical concept of abjection as an unconscious defence mechanism used to protect the self against threats to one's subjectivity. Kristeva suggests that the first instance of abjection in an individual's life occurs when the child abjects the mother. However, the instance of abjection addressed within this paper is the reverse of this: the abjection of the child, with a disability, by the parent, and more broadly society. Using the contemporary example of prenatal testing, the authors explore how parents of children with disabilities may be influenced in abjecting the child. The implications of abjection of the child are then used to explore normalization, routinization of care and the development of standardized care practices within health-care. Prenatal screening practices and standardized care permeate medical obstetric care and social discourses regarding pregnancy and childbirth, thereby affecting not only healthcare professionals but also parents in their position as consumers of health-care. In a time when the focus of health-care is increasingly placed on disease prevention and broader medical and social discourses glorify normalcy and consistency, the unconscious abjection of those that do not fit within these standards must be identified and addressed. © 2011 Blackwell Publishing Ltd.

  6. Seeing is believing: video classification for computed tomographic colonography using multiple-instance learning.

    Wang, Shijun; McKenna, Matthew T; Nguyen, Tan B; Burns, Joseph E; Petrick, Nicholas; Sahiner, Berkman; Summers, Ronald M

    2012-05-01

    In this paper, we present development and testing results for a novel colonic polyp classification method for use as part of a computed tomographic colonography (CTC) computer-aided detection (CAD) system. Inspired by the interpretative methodology of radiologists using 3-D fly-through mode in CTC reading, we have developed an algorithm which utilizes sequences of images (referred to here as videos) for classification of CAD marks. For each CAD mark, we created a video composed of a series of intraluminal, volume-rendered images visualizing the detection from multiple viewpoints. We then framed the video classification question as a multiple-instance learning (MIL) problem. Since a positive (negative) bag may contain negative (positive) instances, which in our case depends on the viewing angles and camera distance to the target, we developed a novel MIL paradigm to accommodate this class of problems. We solved the new MIL problem by maximizing a L2-norm soft margin using semidefinite programming, which can optimize relevant parameters automatically. We tested our method by analyzing a CTC data set obtained from 50 patients from three medical centers. Our proposed method showed significantly better performance compared with several traditional MIL methods.

  7. Emancipation trough the Artistic Experience and the Meaning of Handicap as Instance of Otherness

    Robi Kroflič

    2014-03-01

    Full Text Available The key hypothesis of the article is that successful inter-mediation of art to vulnerable groups of people (including children depends on the correct identification of the nature of an artistic act and on the meaning that handicap—as an instance of otherness—has in the life of artists and spectators. A just access to the artistic experience is basically not the question of the distribution of artistic production (since if artistic object is principally accessible to all people, it will not reach vulnerable groups of spectators, but of ensuring artistic creativity and presentation. This presupposes a spectator as a competent being who is able to interact with the artistic object without our interpretative explanation and who is sensible to the instance of otherness (handicap is merely a specific form of otherness. The theory of emancipation from J. Ranciere, the theory of recognition from A. Honneth, and the theory of narration from P. Ricoeur and R. Kearney, as well as our experiences with a comprehensive inductive approach and artistic experience as one of its basic educational methods offer us a theoretical framework for such a model of art inter-mediation.

  8. Monoenergetic approximation of a polyenergetic beam: a theoretical approach

    Robinson, D.M.; Scrimger, J.W.

    1991-01-01

    There exist numerous occasions in which it is desirable to approximate the polyenergetic beams employed in radiation therapy by a beam of photons of a single energy. In some instances, commonly used rules of thumb for the selection of an appropriate energy may be valid. A more accurate approximate energy, however, may be determined by an analysis which takes into account both the spectral qualities of the beam and the material through which it passes. The theoretical basis of this method of analysis is presented in this paper. Experimental agreement with theory for a range of materials and beam qualities is also presented and demonstrates the validity of the theoretical approach taken. (author)

  9. From combinatorial optimization to real algebraic geometry and back

    Janez Povh

    2014-12-01

    Full Text Available In this paper, we explain the relations between combinatorial optimization and real algebraic geometry with a special focus to the quadratic assignment problem. We demonstrate how to write a quadratic optimization problem over discrete feasible set as a linear optimization problem over the cone of completely positive matrices. The latter formulation enables a hierarchy of approximations which rely on results from polynomial optimization, a sub-eld of real algebraic geometry.

  10. Hierarchical low-rank approximation for high dimensional approximation

    Nouy, Anthony

    2016-01-01

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  11. Hierarchical low-rank approximation for high dimensional approximation

    Nouy, Anthony

    2016-01-07

    Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

  12. Real algebraic geometry

    Bochnak, Jacek; Roy, Marie-Françoise

    1998-01-01

    This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.

  13. Critique of information geometry

    Skilling, John

    2014-01-01

    As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples

  14. Geometry from Gauge Theory

    Correa, Diego H.; Silva, Guillermo A.

    2008-01-01

    We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents

  15. Emergent geometry of membranes

    Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)

    2015-11-13

    In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.

  16. Iatrogenic alterations in the biodistribution of radiotracers as a result of drug therapy: Reported instances

    Hladik, W.B. III; Ponto, J.A.; Lentle, B.C.; Laven, D.L.

    1987-01-01

    This chapter is a compilation of reported instances in which the biodistribution of a radiopharmaceutical has been (or could be) modified by the administration of a therapeutic nonradioactive drug or contrast agent in such a way as to potentially interfere with the interpretation of the nuclear medicine study in question. This type of phenomenon is commonly referred to as a drug-radiopharmaceutical interaction. In this chapter, interactions are arranged according to the radiopharmaceutical involved; each interaction is characterized by use of the following descriptors: 1. Interfering drug: the interfering nonradioactive drug that alters the kinetics of the radiopharmaceutical and thus changes the resulting diagnostic data obtained from the study. 2. Nuclear medicine study affected: the nuclear medicine study in which the interaction is likely to occur. 3. Effect on image: the appearance of the image (or the effect on diagnostic data) which results from the interaction. 4. Significance: the potential clinical significance of the interaction

  17. Prediction of Ionizing Radiation Resistance in Bacteria Using a Multiple Instance Learning Model.

    Aridhi, Sabeur; Sghaier, Haïtham; Zoghlami, Manel; Maddouri, Mondher; Nguifo, Engelbert Mephu

    2016-01-01

    Ionizing-radiation-resistant bacteria (IRRB) are important in biotechnology. In this context, in silico methods of phenotypic prediction and genotype-phenotype relationship discovery are limited. In this work, we analyzed basal DNA repair proteins of most known proteome sequences of IRRB and ionizing-radiation-sensitive bacteria (IRSB) in order to learn a classifier that correctly predicts this bacterial phenotype. We formulated the problem of predicting bacterial ionizing radiation resistance (IRR) as a multiple-instance learning (MIL) problem, and we proposed a novel approach for this purpose. We provide a MIL-based prediction system that classifies a bacterium to either IRRB or IRSB. The experimental results of the proposed system are satisfactory with 91.5% of successful predictions.

  18. Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.

    Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V

    2016-01-01

    Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.

  19. The Impact of Culture On Smart Community Technology: The Case of 13 Wikipedia Instances

    Zinayida Petrushyna

    2014-11-01

    Full Text Available Smart communities provide technologies for monitoring social behaviors inside communities. The technologies that support knowledge building should consider the cultural background of community members. The studies of the influence of the culture on knowledge building is limited. Just a few works consider digital traces of individuals that they explain using cultural values and beliefs. In this work, we analyze 13 Wikipedia instances where users with different cultural background build knowledge in different ways. We compare edits of users. Using social network analysis we build and analyze co- authorship networks and watch the networks evolution. We explain the differences we have found using Hofstede dimensions and Schwartz cultural values and discuss implications for the design of smart community technologies. Our findings provide insights in requirements for technologies used for smart communities in different cultures.

  20. Retrieving clinically relevant diabetic retinopathy images using a multi-class multiple-instance framework

    Chandakkar, Parag S.; Venkatesan, Ragav; Li, Baoxin

    2013-02-01

    Diabetic retinopathy (DR) is a vision-threatening complication from diabetes mellitus, a medical condition that is rising globally. Unfortunately, many patients are unaware of this complication because of absence of symptoms. Regular screening of DR is necessary to detect the condition for timely treatment. Content-based image retrieval, using archived and diagnosed fundus (retinal) camera DR images can improve screening efficiency of DR. This content-based image retrieval study focuses on two DR clinical findings, microaneurysm and neovascularization, which are clinical signs of non-proliferative and proliferative diabetic retinopathy. The authors propose a multi-class multiple-instance image retrieval framework which deploys a modified color correlogram and statistics of steerable Gaussian Filter responses, for retrieving clinically relevant images from a database of DR fundus image database.

  1. An anomaly detection and isolation scheme with instance-based learning and sequential analysis

    Yoo, T. S.; Garcia, H. E.

    2006-01-01

    This paper presents an online anomaly detection and isolation (FDI) technique using an instance-based learning method combined with a sequential change detection and isolation algorithm. The proposed method uses kernel density estimation techniques to build statistical models of the given empirical data (null hypothesis). The null hypothesis is associated with the set of alternative hypotheses modeling the abnormalities of the systems. A decision procedure involves a sequential change detection and isolation algorithm. Notably, the proposed method enjoys asymptotic optimality as the applied change detection and isolation algorithm is optimal in minimizing the worst mean detection/isolation delay for a given mean time before a false alarm or a false isolation. Applicability of this methodology is illustrated with redundant sensor data set and its performance. (authors)

  2. Interpreting Black-Box Classifiers Using Instance-Level Visual Explanations

    Tamagnini, Paolo; Krause, Josua W.; Dasgupta, Aritra; Bertini, Enrico

    2017-05-14

    To realize the full potential of machine learning in diverse real- world domains, it is necessary for model predictions to be readily interpretable and actionable for the human in the loop. Analysts, who are the users but not the developers of machine learning models, often do not trust a model because of the lack of transparency in associating predictions with the underlying data space. To address this problem, we propose Rivelo, a visual analytic interface that enables analysts to understand the causes behind predictions of binary classifiers by interactively exploring a set of instance-level explanations. These explanations are model-agnostic, treating a model as a black box, and they help analysts in interactively probing the high-dimensional binary data space for detecting features relevant to predictions. We demonstrate the utility of the interface with a case study analyzing a random forest model on the sentiment of Yelp reviews about doctors.

  3. Automated detection of age-related macular degeneration in OCT images using multiple instance learning

    Sun, Weiwei; Liu, Xiaoming; Yang, Zhou

    2017-07-01

    Age-related Macular Degeneration (AMD) is a kind of macular disease which mostly occurs in old people,and it may cause decreased vision or even lead to permanent blindness. Drusen is an important clinical indicator for AMD which can help doctor diagnose disease and decide the strategy of treatment. Optical Coherence Tomography (OCT) is widely used in the diagnosis of ophthalmic diseases, include AMD. In this paper, we propose a classification method based on Multiple Instance Learning (MIL) to detect AMD. Drusen can exist in a few slices of OCT images, and MIL is utilized in our method. We divided the method into two phases: training phase and testing phase. We train the initial features and clustered to create a codebook, and employ the trained classifier in the test set. Experiment results show that our method achieved high accuracy and effectiveness.

  4. Geometry through history Euclidean, hyperbolic, and projective geometries

    Dillon, Meighan I

    2018-01-01

    Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...

  5. Forms of Approximate Radiation Transport

    Brunner, G

    2002-01-01

    Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.

  6. Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. I. Semi-infinite slab approximations

    Berkel, van M.; Zwart, Heiko J.; Tamura, N.; Hogeweij, G.M.D.; Inagaki, S.; de Baar, M.R.; Ida, K.

    2014-01-01

    In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The

  7. Approximation by planar elastic curves

    Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge

    2016-01-01

    We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....

  8. Stages as models of scene geometry.

    Nedović, Vladimir; Smeulders, Arnold W M; Redert, André; Geusebroek, Jan-Mark

    2010-09-01

    Reconstruction of 3D scene geometry is an important element for scene understanding, autonomous vehicle and robot navigation, image retrieval, and 3D television. We propose accounting for the inherent structure of the visual world when trying to solve the scene reconstruction problem. Consequently, we identify geometric scene categorization as the first step toward robust and efficient depth estimation from single images. We introduce 15 typical 3D scene geometries called stages, each with a unique depth profile, which roughly correspond to a large majority of broadcast video frames. Stage information serves as a first approximation of global depth, narrowing down the search space in depth estimation and object localization. We propose different sets of low-level features for depth estimation, and perform stage classification on two diverse data sets of television broadcasts. Classification results demonstrate that stages can often be efficiently learned from low-dimensional image representations.

  9. On organizing principles of discrete differential geometry. Geometry of spheres

    Bobenko, Alexander I; Suris, Yury B

    2007-01-01

    Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.

  10. Higher geometry an introduction to advanced methods in analytic geometry

    Woods, Frederick S

    2005-01-01

    For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study

  11. Exact constants in approximation theory

    Korneichuk, N

    1991-01-01

    This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base

  12. International Conference Approximation Theory XIV

    Schumaker, Larry

    2014-01-01

    This volume developed from papers presented at the international conference Approximation Theory XIV,  held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.

  13. Stochastic learning of multi-instance dictionary for earth mover’s distance-based histogram comparison

    Fan, Jihong

    2016-09-17

    Dictionary plays an important role in multi-instance data representation. It maps bags of instances to histograms. Earth mover’s distance (EMD) is the most effective histogram distance metric for the application of multi-instance retrieval. However, up to now, there is no existing multi-instance dictionary learning methods designed for EMD-based histogram comparison. To fill this gap, we develop the first EMD-optimal dictionary learning method using stochastic optimization method. In the stochastic learning framework, we have one triplet of bags, including one basic bag, one positive bag, and one negative bag. These bags are mapped to histograms using a multi-instance dictionary. We argue that the EMD between the basic histogram and the positive histogram should be smaller than that between the basic histogram and the negative histogram. Base on this condition, we design a hinge loss. By minimizing this hinge loss and some regularization terms of the dictionary, we update the dictionary instances. The experiments over multi-instance retrieval applications shows its effectiveness when compared to other dictionary learning methods over the problems of medical image retrieval and natural language relation classification. © 2016 The Natural Computing Applications Forum

  14. An Origami Approximation to the Cosmic Web

    Neyrinck, Mark C.

    2016-10-01

    The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in `polygonal' or `polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls to be more easily understood, and may aid in understanding spin correlations between nearby galaxies. This contribution explores kinematic origami-approximation models giving velocity fields for the first time.

  15. An introduction to incidence geometry

    De Bruyn, Bart

    2016-01-01

    This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...

  16. Planetary Image Geometry Library

    Deen, Robert C.; Pariser, Oleg

    2010-01-01

    The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A

  17. Initiation to global Finslerian geometry

    Akbar-Zadeh, Hassan

    2006-01-01

    After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p

  18. Ostrich eggs geometry

    Šárka Nedomová

    2013-01-01

    Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.

  19. Nonperturbative quantum geometries

    Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara

    1988-01-01

    Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)

  20. Matrix Information Geometry

    Bhatia, Rajendra

    2013-01-01

    This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR).  During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented  are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.  

  1. Landmark-based deep multi-instance learning for brain disease diagnosis.

    Liu, Mingxia; Zhang, Jun; Adeli, Ehsan; Shen, Dinggang

    2018-01-01

    In conventional Magnetic Resonance (MR) image based methods, two stages are often involved to capture brain structural information for disease diagnosis, i.e., 1) manually partitioning each MR image into a number of regions-of-interest (ROIs), and 2) extracting pre-defined features from each ROI for diagnosis with a certain classifier. However, these pre-defined features often limit the performance of the diagnosis, due to challenges in 1) defining the ROIs and 2) extracting effective disease-related features. In this paper, we propose a landmark-based deep multi-instance learning (LDMIL) framework for brain disease diagnosis. Specifically, we first adopt a data-driven learning approach to discover disease-related anatomical landmarks in the brain MR images, along with their nearby image patches. Then, our LDMIL framework learns an end-to-end MR image classifier for capturing both the local structural information conveyed by image patches located by landmarks and the global structural information derived from all detected landmarks. We have evaluated our proposed framework on 1526 subjects from three public datasets (i.e., ADNI-1, ADNI-2, and MIRIAD), and the experimental results show that our framework can achieve superior performance over state-of-the-art approaches. Copyright © 2017 Elsevier B.V. All rights reserved.

  2. Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.

    Nadia Said

    Full Text Available Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.

  3. When palliative treatment achieves more than palliation: Instances of long-term survival after palliative radiotherapy

    Madhup Rastogi

    2012-01-01

    Full Text Available Context: Palliative radiotherapy aims at symptom alleviation and improvement of quality of life. It may be effective in conferring a reasonable quantum of local control, as well as possibly prolonging survival on the short term. However, there can be rare instances where long-term survival, or even cure, results from palliative radiotherapy, which mostly uses sub-therapeutic doses. Aim: To categorize and characterize the patients with long-term survival and/or cure after palliative radiotherapy. Materials and Methods: This study is a retrospective analysis of hospital records of patients treated with palliative radiotherapy from 2001 to 2006 at the Regional Cancer Centre, Shimla. Results: Of the analyzed 963 patients who received palliative radiotherapy, 2.4% (n = 23 survived at least 5 years, with a large majority of these surviving patients (73.9%, n = 17 being free of disease. Conclusions: In addition to providing valuable symptom relief, palliative radiotherapy utilizing sub-therapeutic doses may, in a small proportion of patients, bestow long-term survival, and possibly cure. Rationally, such a favorable, but rare outcome cannot be expected with supportive care alone.

  4. Mass detection in digital breast tomosynthesis data using convolutional neural networks and multiple instance learning.

    Yousefi, Mina; Krzyżak, Adam; Suen, Ching Y

    2018-05-01

    Digital breast tomosynthesis (DBT) was developed in the field of breast cancer screening as a new tomographic technique to minimize the limitations of conventional digital mammography breast screening methods. A computer-aided detection (CAD) framework for mass detection in DBT has been developed and is described in this paper. The proposed framework operates on a set of two-dimensional (2D) slices. With plane-to-plane analysis on corresponding 2D slices from each DBT, it automatically learns complex patterns of 2D slices through a deep convolutional neural network (DCNN). It then applies multiple instance learning (MIL) with a randomized trees approach to classify DBT images based on extracted information from 2D slices. This CAD framework was developed and evaluated using 5040 2D image slices derived from 87 DBT volumes. The empirical results demonstrate that this proposed CAD framework achieves much better performance than CAD systems that use hand-crafted features and deep cardinality-restricted Bolzmann machines to detect masses in DBTs. Copyright © 2018 Elsevier Ltd. All rights reserved.

  5. Horror Image Recognition Based on Context-Aware Multi-Instance Learning.

    Li, Bing; Xiong, Weihua; Wu, Ou; Hu, Weiming; Maybank, Stephen; Yan, Shuicheng

    2015-12-01

    Horror content sharing on the Web is a growing phenomenon that can interfere with our daily life and affect the mental health of those involved. As an important form of expression, horror images have their own characteristics that can evoke extreme emotions. In this paper, we present a novel context-aware multi-instance learning (CMIL) algorithm for horror image recognition. The CMIL algorithm identifies horror images and picks out the regions that cause the sensation of horror in these horror images. It obtains contextual cues among adjacent regions in an image using a random walk on a contextual graph. Borrowing the strength of the fuzzy support vector machine (FSVM), we define a heuristic optimization procedure based on the FSVM to search for the optimal classifier for the CMIL. To improve the initialization of the CMIL, we propose a novel visual saliency model based on the tensor analysis. The average saliency value of each segmented region is set as its initial fuzzy membership in the CMIL. The advantage of the tensor-based visual saliency model is that it not only adaptively selects features, but also dynamically determines fusion weights for saliency value combination from different feature subspaces. The effectiveness of the proposed CMIL model is demonstrated by its use in horror image recognition on two large-scale image sets collected from the Internet.

  6. The role of inertia in modeling decisions from experience with instance-based learning.

    Dutt, Varun; Gonzalez, Cleotilde

    2012-01-01

    One form of inertia is the tendency to repeat the last decision irrespective of the obtained outcomes while making decisions from experience (DFE). A number of computational models based upon the Instance-Based Learning Theory, a theory of DFE, have included different inertia implementations and have shown to simultaneously account for both risk-taking and alternations between alternatives. The role that inertia plays in these models, however, is unclear as the same model without inertia is also able to account for observed risk-taking quite well. This paper demonstrates the predictive benefits of incorporating one particular implementation of inertia in an existing IBL model. We use two large datasets, estimation and competition, from the Technion Prediction Tournament involving a repeated binary-choice task to show that incorporating an inertia mechanism in an IBL model enables it to account for the observed average risk-taking and alternations. Including inertia, however, does not help the model to account for the trends in risk-taking and alternations over trials compared to the IBL model without the inertia mechanism. We generalize the two IBL models, with and without inertia, to the competition set by using the parameters determined in the estimation set. The generalization process demonstrates both the advantages and disadvantages of including inertia in an IBL model.

  7. A Fisher Kernel Approach for Multiple Instance Based Object Retrieval in Video Surveillance

    MIRONICA, I.

    2015-11-01

    Full Text Available This paper presents an automated surveillance system that exploits the Fisher Kernel representation in the context of multiple-instance object retrieval task. The proposed algorithm has the main purpose of tracking a list of persons in several video sources, using only few training examples. In the first step, the Fisher Kernel representation describes a set of features as the derivative with respect to the log-likelihood of the generative probability distribution that models the feature distribution. Then, we learn the generative probability distribution over all features extracted from a reduced set of relevant frames. The proposed approach shows significant improvements and we demonstrate that Fisher kernels are well suited for this task. We demonstrate the generality of our approach in terms of features by conducting an extensive evaluation with a broad range of keypoints features. Also, we evaluate our method on two standard video surveillance datasets attaining superior results comparing to state-of-the-art object recognition algorithms.

  8. The boundaries of instance-based learning theory for explaining decisions from experience.

    Gonzalez, Cleotilde

    2013-01-01

    Most demonstrations of how people make decisions in risky situations rely on decisions from description, where outcomes and their probabilities are explicitly stated. But recently, more attention has been given to decisions from experience where people discover these outcomes and probabilities through exploration. More importantly, risky behavior depends on how decisions are made (from description or experience), and although prospect theory explains decisions from description, a comprehensive model of decisions from experience is yet to be found. Instance-based learning theory (IBLT) explains how decisions are made from experience through interactions with dynamic environments (Gonzalez et al., 2003). The theory has shown robust explanations of behavior across multiple tasks and contexts, but it is becoming unclear what the theory is able to explain and what it does not. The goal of this chapter is to start addressing this problem. I will introduce IBLT and a recent cognitive model based on this theory: the IBL model of repeated binary choice; then I will discuss the phenomena that the IBL model explains and those that the model does not. The argument is for the theory's robustness but also for clarity in terms of concrete effects that the theory can or cannot account for. Copyright © 2013 Elsevier B.V. All rights reserved.

  9. Multiple-instance learning for computer-aided detection of tuberculosis

    Melendez, J.; Sánchez, C. I.; Philipsen, R. H. H. M.; Maduskar, P.; van Ginneken, B.

    2014-03-01

    Detection of tuberculosis (TB) on chest radiographs (CXRs) is a hard problem. Therefore, to help radiologists or even take their place when they are not available, computer-aided detection (CAD) systems are being developed. In order to reach a performance comparable to that of human experts, the pattern recognition algorithms of these systems are typically trained on large CXR databases that have been manually annotated to indicate the abnormal lung regions. However, manually outlining those regions constitutes a time-consuming process that, besides, is prone to inconsistencies and errors introduced by interobserver variability and the absence of an external reference standard. In this paper, we investigate an alternative pattern classi cation method, namely multiple-instance learning (MIL), that does not require such detailed information for a CAD system to be trained. We have applied this alternative approach to a CAD system aimed at detecting textural lesions associated with TB. Only the case (or image) condition (normal or abnormal) was provided in the training stage. We compared the resulting performance with those achieved by several variations of a conventional system trained with detailed annotations. A database of 917 CXRs was constructed for experimentation. It was divided into two roughly equal parts that were used as training and test sets. The area under the receiver operating characteristic curve was utilized as a performance measure. Our experiments show that, by applying the investigated MIL approach, comparable results as with the aforementioned conventional systems are obtained in most cases, without requiring condition information at the lesion level.

  10. Event recognition in personal photo collections via multiple instance learning-based classification of multiple images

    Ahmad, Kashif; Conci, Nicola; Boato, Giulia; De Natale, Francesco G. B.

    2017-11-01

    Over the last few years, a rapid growth has been witnessed in the number of digital photos produced per year. This rapid process poses challenges in the organization and management of multimedia collections, and one viable solution consists of arranging the media on the basis of the underlying events. However, album-level annotation and the presence of irrelevant pictures in photo collections make event-based organization of personal photo albums a more challenging task. To tackle these challenges, in contrast to conventional approaches relying on supervised learning, we propose a pipeline for event recognition in personal photo collections relying on a multiple instance-learning (MIL) strategy. MIL is a modified form of supervised learning and fits well for such applications with weakly labeled data. The experimental evaluation of the proposed approach is carried out on two large-scale datasets including a self-collected and a benchmark dataset. On both, our approach significantly outperforms the existing state-of-the-art.

  11. Some results in Diophantine approximation

    Pedersen, Steffen Højris

    the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered......This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...

  12. Limitations of shallow nets approximation.

    Lin, Shao-Bo

    2017-10-01

    In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.

  13. A new numerical approximation of the fractal ordinary differential equation

    Atangana, Abdon; Jain, Sonal

    2018-02-01

    The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.

  14. GPS: Geometry, Probability, and Statistics

    Field, Mike

    2012-01-01

    It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

  15. Surrogate Modeling for Geometry Optimization

    Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie

    2009-01-01

    A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....

  16. Kaehler geometry and SUSY mechanics

    Bellucci, Stefano; Nersessian, Armen

    2001-01-01

    We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed

  17. A prediction for bubbling geometries

    Okuda, Takuya

    2007-01-01

    We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.

  18. Molecular motion in restricted geometries

    Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...

  19. Control of nonholonomic systems from sub-Riemannian geometry to motion planning

    Jean, Frédéric

    2014-01-01

    Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems. In particular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry. The aim of these notes is to present these notions of approximation and their application to the motion planning problem for nonholonomic systems.

  20. Photonic crystal geometry for organic solar cells.

    Ko, Doo-Hyun; Tumbleston, John R; Zhang, Lei; Williams, Stuart; DeSimone, Joseph M; Lopez, Rene; Samulski, Edward T

    2009-07-01

    We report organic solar cells with a photonic crystal nanostructure embossed in the photoactive bulk heterojunction layer, a topography that exhibits a 3-fold enhancement of the absorption in specific regions of the solar spectrum in part through multiple excitation resonances. The photonic crystal geometry is fabricated using a materials-agnostic process called PRINT wherein highly ordered arrays of nanoscale features are readily made in a single processing step over wide areas (approximately 4 cm(2)) that is scalable. We show efficiency improvements of approximately 70% that result not only from greater absorption, but also from electrical enhancements. The methodology is generally applicable to organic solar cells and the experimental findings reported in our manuscript corroborate theoretical expectations.

  1. Basic algebraic geometry, v.2

    Shafarevich, Igor Rostislavovich

    1994-01-01

    Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...

  2. Optical geometry across the horizon

    Jonsson, Rickard

    2006-01-01

    In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework

  3. Holographic free energy and thermodynamic geometry

    Ghorai, Debabrata; Gangopadhyay, Sunandan

    2016-12-01

    We obtain the free energy and thermodynamic geometry of holographic superconductors in 2+1 dimensions. The gravitational theory in the bulk dual to this 2+1-dimensional strongly coupled theory lives in the 3+1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method.

  4. Holographic free energy and thermodynamic geometry

    Ghorai, Debabrata; Gangopadhyay, Sunandan

    2016-01-01

    We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)

  5. Holographic free energy and thermodynamic geometry

    Ghorai, Debabrata [S.N. Bose National Centre for Basic Sciences, Kolkata (India); Gangopadhyay, Sunandan [Indian Institute of Science Education and Research, Kolkata, Nadia (India); West Bengal State University, Department of Physics, Barasat (India); Inter University Centre for Astronomy and Astrophysics, Pune (India)

    2016-12-15

    We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)

  6. Spherical Approximation on Unit Sphere

    Eman Samir Bhaya

    2018-01-01

    Full Text Available In this paper we introduce a Jackson type theorem for functions in LP spaces on sphere And study on best approximation of  functions in  spaces defined on unit sphere. our central problem is to describe the approximation behavior of functions in    spaces for  by modulus of smoothness of functions.

  7. MaMiCo: Transient multi-instance molecular-continuum flow simulation on supercomputers

    Neumann, Philipp; Bian, Xin

    2017-11-01

    We present extensions of the macro-micro-coupling tool MaMiCo, which was designed to couple continuum fluid dynamics solvers with discrete particle dynamics. To enable local extraction of smooth flow field quantities especially on rather short time scales, sampling over an ensemble of molecular dynamics simulations is introduced. We provide details on these extensions including the transient coupling algorithm, open boundary forcing, and multi-instance sampling. Furthermore, we validate the coupling in Couette flow using different particle simulation software packages and particle models, i.e. molecular dynamics and dissipative particle dynamics. Finally, we demonstrate the parallel scalability of the molecular-continuum simulations by using up to 65 536 compute cores of the supercomputer Shaheen II located at KAUST. Program Files doi:http://dx.doi.org/10.17632/w7rgdrhb85.1 Licensing provisions: BSD 3-clause Programming language: C, C++ External routines/libraries: For compiling: SCons, MPI (optional) Subprograms used: ESPResSo, LAMMPS, ls1 mardyn, waLBerla For installation procedures of the MaMiCo interfaces, see the README files in the respective code directories located in coupling/interface/impl. Journal reference of previous version: P. Neumann, H. Flohr, R. Arora, P. Jarmatz, N. Tchipev, H.-J. Bungartz. MaMiCo: Software design for parallel molecular-continuum flow simulations, Computer Physics Communications 200: 324-335, 2016 Does the new version supersede the previous version?: Yes. The functionality of the previous version is completely retained in the new version. Nature of problem: Coupled molecular-continuum simulation for multi-resolution fluid dynamics: parts of the domain are resolved by molecular dynamics or another particle-based solver whereas large parts are covered by a mesh-based CFD solver, e.g. a lattice Boltzmann automaton. Solution method: We couple existing MD and CFD solvers via MaMiCo (macro-micro coupling tool). Data exchange and

  8. Approximate circuits for increased reliability

    Hamlet, Jason R.; Mayo, Jackson R.

    2015-08-18

    Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.

  9. Salience Assignment for Multiple-Instance Data and Its Application to Crop Yield Prediction

    Wagstaff, Kiri L.; Lane, Terran

    2010-01-01

    An algorithm was developed to generate crop yield predictions from orbital remote sensing observations, by analyzing thousands of pixels per county and the associated historical crop yield data for those counties. The algorithm determines which pixels contain which crop. Since each known yield value is associated with thousands of individual pixels, this is a multiple instance learning problem. Because individual crop growth is related to the resulting yield, this relationship has been leveraged to identify pixels that are individually related to corn, wheat, cotton, and soybean yield. Those that have the strongest relationship to a given crop s yield values are most likely to contain fields with that crop. Remote sensing time series data (a new observation every 8 days) was examined for each pixel, which contains information for that pixel s growth curve, peak greenness, and other relevant features. An alternating-projection (AP) technique was used to first estimate the "salience" of each pixel, with respect to the given target (crop yield), and then those estimates were used to build a regression model that relates input data (remote sensing observations) to the target. This is achieved by constructing an exemplar for each crop in each county that is a weighted average of all the pixels within the county; the pixels are weighted according to the salience values. The new regression model estimate then informs the next estimate of the salience values. By iterating between these two steps, the algorithm converges to a stable estimate of both the salience of each pixel and the regression model. The salience values indicate which pixels are most relevant to each crop under consideration.

  10. Cyber situation awareness: modeling detection of cyber attacks with instance-based learning theory.

    Dutt, Varun; Ahn, Young-Suk; Gonzalez, Cleotilde

    2013-06-01

    To determine the effects of an adversary's behavior on the defender's accurate and timely detection of network threats. Cyber attacks cause major work disruption. It is important to understand how a defender's behavior (experience and tolerance to threats), as well as adversarial behavior (attack strategy), might impact the detection of threats. In this article, we use cognitive modeling to make predictions regarding these factors. Different model types representing a defender, based on Instance-Based Learning Theory (IBLT), faced different adversarial behaviors. A defender's model was defined by experience of threats: threat-prone (90% threats and 10% nonthreats) and nonthreat-prone (10% threats and 90% nonthreats); and different tolerance levels to threats: risk-averse (model declares a cyber attack after perceiving one threat out of eight total) and risk-seeking (model declares a cyber attack after perceiving seven threats out of eight total). Adversarial behavior is simulated by considering different attack strategies: patient (threats occur late) and impatient (threats occur early). For an impatient strategy, risk-averse models with threat-prone experiences show improved detection compared with risk-seeking models with nonthreat-prone experiences; however, the same is not true for a patient strategy. Based upon model predictions, a defender's prior threat experiences and his or her tolerance to threats are likely to predict detection accuracy; but considering the nature of adversarial behavior is also important. Decision-support tools that consider the role of a defender's experience and tolerance to threats along with the nature of adversarial behavior are likely to improve a defender's overall threat detection.

  11. Instance-based Policy Learning by Real-coded Genetic Algorithms and Its Application to Control of Nonholonomic Systems

    Miyamae, Atsushi; Sakuma, Jun; Ono, Isao; Kobayashi, Shigenobu

    The stabilization control of nonholonomic systems have been extensively studied because it is essential for nonholonomic robot control problems. The difficulty in this problem is that the theoretical derivation of control policy is not necessarily guaranteed achievable. In this paper, we present a reinforcement learning (RL) method with instance-based policy (IBP) representation, in which control policies for this class are optimized with respect to user-defined cost functions. Direct policy search (DPS) is an approach for RL; the policy is represented by parametric models and the model parameters are directly searched by optimization techniques including genetic algorithms (GAs). In IBP representation an instance consists of a state and an action pair; a policy consists of a set of instances. Several DPSs with IBP have been previously proposed. In these methods, sometimes fail to obtain optimal control policies when state-action variables are continuous. In this paper, we present a real-coded GA for DPSs with IBP. Our method is specifically designed for continuous domains. Optimization of IBP has three difficulties; high-dimensionality, epistasis, and multi-modality. Our solution is designed for overcoming these difficulties. The policy search with IBP representation appears to be high-dimensional optimization; however, instances which can improve the fitness are often limited to active instances (instances used for the evaluation). In fact, the number of active instances is small. Therefore, we treat the search problem as a low dimensional problem by restricting search variables only to active instances. It has been commonly known that functions with epistasis can be efficiently optimized with crossovers which satisfy the inheritance of statistics. For efficient search of IBP, we propose extended crossover-like mutation (extended XLM) which generates a new instance around an instance with satisfying the inheritance of statistics. For overcoming multi-modality, we

  12. Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

    Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E

    2018-06-01

    An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.

  13. Approximating Markov Chains: What and why

    Pincus, S.

    1996-01-01

    Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to open-quote open-quote solve,close-quote close-quote or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the attractor, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. copyright 1996 American Institute of Physics

  14. Complex analysis and CR geometry

    Zampieri, Giuseppe

    2008-01-01

    Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...

  15. The geometry description markup language

    Chytracek, R.

    2001-01-01

    Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML

  16. Parametric excitation of drift waves in a sheared slab geometry

    Vranjes, J.; Weiland, J.

    1992-01-01

    The threshold for parametric excitation of drift waves in a sheared slab geometry is calculated for a pump wave that is a standing wave along the magnetic field, using the Hasegawa-Mima nonlinearity. The shear damping is counteracted by the parametric coupling and the eigenvalue problem is solved analytically using Taylor's strong coupling approximation. (au)

  17. The efficiency of Flory approximation

    Obukhov, S.P.

    1984-01-01

    The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)

  18. Head First 2D Geometry

    Fallow), Stray

    2009-01-01

    Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and

  19. A first course in geometry

    Walsh, Edward T

    2014-01-01

    This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl

  20. Differential geometry curves, surfaces, manifolds

    Kohnel, Wolfgang

    2002-01-01

    This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.

  1. A Novel Geometry for Shear Test Using Axial Tensile Setup

    Sibo Yuan

    2018-05-01

    Full Text Available This paper studies a novel geometry for the in-plane shear test performed with an axial electromechanical testing machine. In order to investigate the influence of the triaxiality rate on the mechanical behavior, different tests will be performed on the studied material: simple tensile tests, large tensile tests and shear tests. For the whole campaign, a common equipment should be employed to minimize the impact of the testing device. As a consequence, for the shear tests, the geometry of the specimen must be carefully designed in order to adapt the force value and make it comparable to the one obtained for the tensile tests. Like most of the existing shear-included tensile test specimens, the axial loading is converted to shear loading at a particular region through the effect of geometry. A symmetric shape is generally preferred, since it can restrict the in-plane rotation of the shear section, keep shear increasing in a more monotonic path and double the force level thanks to the two shear zones. Due to the specific experimental conditions, such as dimensions of the furnace and the clamping system, the position of the extensometer or the restriction of sheet thickness (related to the further studies of size effect at mesoscale and hot temperature, several geometries were brought up and evaluated in an iterative procedure via finite element simulations. Both the numerical and experimental results reveal that the final geometry ensures some advantages. For instance, a relatively low triaxiality in the shear zone, limited in-plane rotation and no necking are observed. Moreover, it also prevents any out-of-plane displacement of the specimen which seems to be highly sensitive to the geometry, and presents a very limited influence of the material and the thickness.

  2. Approximate Implicitization Using Linear Algebra

    Oliver J. D. Barrowclough

    2012-01-01

    Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.

  3. Rollout sampling approximate policy iteration

    Dimitrakakis, C.; Lagoudakis, M.G.

    2008-01-01

    Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a

  4. Weighted approximation with varying weight

    Totik, Vilmos

    1994-01-01

    A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

  5. Framework for sequential approximate optimization

    Jacobs, J.H.; Etman, L.F.P.; Keulen, van F.; Rooda, J.E.

    2004-01-01

    An object-oriented framework for Sequential Approximate Optimization (SAO) isproposed. The framework aims to provide an open environment for thespecification and implementation of SAO strategies. The framework is based onthe Python programming language and contains a toolbox of Python

  6. Approximate analytical solutions in the analysis of elastic structures of complex geometry

    Goloskokov, Dmitriy P.; Matrosov, Alexander V.

    2018-05-01

    A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method.

  7. Advances in discrete differential geometry

    2016-01-01

    This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...

  8. Hyperbolic Metamaterials with Complex Geometry

    Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei

    2016-01-01

    We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...

  9. An introduction to differential geometry

    Willmore, T J

    2012-01-01

    This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

  10. Symplectic geometry and Fourier analysis

    Wallach, Nolan R

    2018-01-01

    Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.

  11. A Galerkin approximation for linear elastic shallow shells

    Figueiredo, I. N.; Trabucho, L.

    1992-03-01

    This work is a generalization to shallow shell models of previous results for plates by B. Miara (1989). Using the same basis functions as in the plate case, we construct a Galerkin approximation of the three-dimensional linearized elasticity problem, and establish some error estimates as a function of the thickness, the curvature, the geometry of the shell, the forces and the Lamé costants.

  12. Topology and geometry for physicists

    Nash, Charles

    1983-01-01

    Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr

  13. Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations

    Giraldi, Loic; Nouy, Anthony

    2017-01-01

    This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only requires evaluations of the residual of the parameter-dependent equation and of a preconditioner (such as the differential of the residual) for instances of the parameters independently. The algorithm provides an approximation of the set of solutions associated with a possibly large number of instances of the parameters, with a computational complexity which can be orders of magnitude lower than when using the same Newton-like solver for all instances of the parameters. The reduction of complexity requires efficient strategies for obtaining low-rank approximations of the residual, of the preconditioner, and of the increment at each iteration of the algorithm. For the approximation of the residual and the preconditioner, weakly intrusive variants of the empirical interpolation method are introduced, which require evaluations of entries of the residual and the preconditioner. Then, an approximation of the increment is obtained by using a greedy algorithm for low-rank approximation, and a low-rank approximation of the iterate is finally obtained by using a truncated singular value decomposition. When the preconditioner is the differential of the residual, the proposed algorithm is interpreted as an inexact Newton solver for which a detailed convergence analysis is provided. Numerical examples illustrate the efficiency of the method.

  14. Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations

    Giraldi, Loic

    2017-06-30

    This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only requires evaluations of the residual of the parameter-dependent equation and of a preconditioner (such as the differential of the residual) for instances of the parameters independently. The algorithm provides an approximation of the set of solutions associated with a possibly large number of instances of the parameters, with a computational complexity which can be orders of magnitude lower than when using the same Newton-like solver for all instances of the parameters. The reduction of complexity requires efficient strategies for obtaining low-rank approximations of the residual, of the preconditioner, and of the increment at each iteration of the algorithm. For the approximation of the residual and the preconditioner, weakly intrusive variants of the empirical interpolation method are introduced, which require evaluations of entries of the residual and the preconditioner. Then, an approximation of the increment is obtained by using a greedy algorithm for low-rank approximation, and a low-rank approximation of the iterate is finally obtained by using a truncated singular value decomposition. When the preconditioner is the differential of the residual, the proposed algorithm is interpreted as an inexact Newton solver for which a detailed convergence analysis is provided. Numerical examples illustrate the efficiency of the method.

  15. Improvement of Tone's method with two-term rational approximation

    Yamamoto, Akio; Endo, Tomohiro; Chiba, Go

    2011-01-01

    An improvement of Tone's method, which is a resonance calculation method based on the equivalence theory, is proposed. In order to increase calculation accuracy, the two-term rational approximation is incorporated for the representation of neutron flux. Furthermore, some theoretical aspects of Tone's method, i.e., its inherent approximation and choice of adequate multigroup cross section for collision probability estimation, are also discussed. The validity of improved Tone's method is confirmed through a verification calculation in an irregular lattice geometry, which represents part of an LWR fuel assembly. The calculation result clarifies the validity of the present method. (author)

  16. Gaussian Multiple Instance Learning Approach for Mapping the Slums of the World Using Very High Resolution Imagery

    Vatsavai, Raju [ORNL

    2013-01-01

    In this paper, we present a computationally efficient algo- rithm based on multiple instance learning for mapping infor- mal settlements (slums) using very high-resolution remote sensing imagery. From remote sensing perspective, infor- mal settlements share unique spatial characteristics that dis- tinguish them from other urban structures like industrial, commercial, and formal residential settlements. However, regular pattern recognition and machine learning methods, which are predominantly single-instance or per-pixel classi- fiers, often fail to accurately map the informal settlements as they do not capture the complex spatial patterns. To overcome these limitations we employed a multiple instance based machine learning approach, where groups of contigu- ous pixels (image patches) are modeled as generated by a Gaussian distribution. We have conducted several experi- ments on very high-resolution satellite imagery, represent- ing four unique geographic regions across the world. Our method showed consistent improvement in accurately iden- tifying informal settlements.

  17. Spectral dimension of quantum geometries

    Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

    2014-01-01

    The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)

  18. Computer-optimized γ-NDA geometries for uranium enrichment verification of gaseous UF6

    Wichers, V.A.; Aaldijk, J.K.; Betue, P.A.C. de; Harry, R.J.S.

    1993-05-01

    An improved collimator pair of novel design tailored for deposit independent enrichment verification of gaseous UF 6 at low pressures in cascade-to-header pipes of small diameters in centrifuge enrichment plants is presented. The designs are adapted for use in a dual-geometry arrangement for simultaneous measurements with both detection geometries. The average measurement time with the dual-geometry arrangement is approximately half an hour for deposit-to-gas activity ratios as high as 20. (orig.)

  19. A new experiment-independent mechanism to persistify and serve the detector geometry of ATLAS

    Bianchi, Riccardo Maria; Boudreau, Joseph; Vukotic, Ilija

    2017-10-01

    The complex geometry of the whole detector of the ATLAS experiment at LHC is currently stored only in custom online databases, from which it is built on-the-fly on request. Accessing the online geometry guarantees accessing the latest version of the detector description, but requires the setup of the full ATLAS software framework “Athena”, which provides the online services and the tools to retrieve the data from the database. This operation is cumbersome and slows down the applications that need to access the geometry. Moreover, all applications that need to access the detector geometry need to be built and run on the same platform as the ATLAS framework, preventing the usage of the actual detector geometry in stand-alone applications. Here we propose a new mechanism to persistify (in software development in general, and in HEP computing in particular, persistifying means taking an object which lives in memory only - for example because it was built on-the-fly while processing the experimental data, - serializing it and storing it on disk as a persistent object) and serve the geometry of HEP experiments. The new mechanism is composed by a new file format and the modules to make use of it. The new file format allows to store the whole detector description locally in a file, and it is especially optimized to describe large complex detectors with the minimum file size, making use of shared instances and storing compressed representations of geometry transformations. Then, the detector description can be read back in, to fully restore the in-memory geometry tree. Moreover, a dedicated REST API is being designed and developed to serve the geometry in standard exchange formats like JSON, to let users and applications download specific partial geometry information. With this new geometry persistification a new generation of applications could be developed, which can use the actual detector geometry while being platform-independent and experiment-independent.

  20. Nuclear Hartree-Fock approximation testing and other related approximations

    Cohenca, J.M.

    1970-01-01

    Hartree-Fock, and Tamm-Dancoff approximations are tested for angular momentum of even-even nuclei. Wave functions, energy levels and momenta are comparatively evaluated. Quadripole interactions are studied following the Elliott model. Results are applied to Ne 20 [pt

  1. Electroencephalography in ellipsoidal geometry with fourth-order harmonics.

    Alcocer-Sosa, M; Gutierrez, D

    2016-08-01

    We present a solution to the electroencephalographs (EEG) forward problem of computing the scalp electric potentials for the case when the head's geometry is modeled using a four-shell ellipsoidal geometry and the brain sources with an equivalent current dipole (ECD). The proposed solution includes terms up to the fourth-order ellipsoidal harmonics and we compare this new approximation against those that only considered up to second- and third-order harmonics. Our comparisons use as reference a solution in which a tessellated volume approximates the head and the forward problem is solved through the boundary element method (BEM). We also assess the solution to the inverse problem of estimating the magnitude of an ECD through different harmonic approximations. Our results show that the fourth-order solution provides a better estimate of the ECD in comparison to lesser order ones.

  2. Shearlets and Optimally Sparse Approximations

    Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q

    2012-01-01

    Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....

  3. Diophantine approximation and Dirichlet series

    Queffélec, Hervé

    2013-01-01

    This self-contained book will benefit beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given. Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of anal...

  4. Approximations to camera sensor noise

    Jin, Xiaodan; Hirakawa, Keigo

    2013-02-01

    Noise is present in all image sensor data. Poisson distribution is said to model the stochastic nature of the photon arrival process, while it is common to approximate readout/thermal noise by additive white Gaussian noise (AWGN). Other sources of signal-dependent noise such as Fano and quantization also contribute to the overall noise profile. Question remains, however, about how best to model the combined sensor noise. Though additive Gaussian noise with signal-dependent noise variance (SD-AWGN) and Poisson corruption are two widely used models to approximate the actual sensor noise distribution, the justification given to these types of models are based on limited evidence. The goal of this paper is to provide a more comprehensive characterization of random noise. We concluded by presenting concrete evidence that Poisson model is a better approximation to real camera model than SD-AWGN. We suggest further modification to Poisson that may improve the noise model.

  5. Rational approximations for tomographic reconstructions

    Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas

    2013-01-01

    We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp–Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image. (paper)

  6. Approximation methods in probability theory

    Čekanavičius, Vydas

    2016-01-01

    This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.

  7. Approximate reasoning in physical systems

    Mutihac, R.

    1991-01-01

    The theory of fuzzy sets provides excellent ground to deal with fuzzy observations (uncertain or imprecise signals, wavelengths, temperatures,etc.) fuzzy functions (spectra and depth profiles) and fuzzy logic and approximate reasoning. First, the basic ideas of fuzzy set theory are briefly presented. Secondly, stress is put on application of simple fuzzy set operations for matching candidate reference spectra of a spectral library to an unknown sample spectrum (e.g. IR spectroscopy). Thirdly, approximate reasoning is applied to infer an unknown property from information available in a database (e.g. crystal systems). Finally, multi-dimensional fuzzy reasoning techniques are suggested. (Author)

  8. Face Recognition using Approximate Arithmetic

    Marso, Karol

    Face recognition is image processing technique which aims to identify human faces and found its use in various different fields for example in security. Throughout the years this field evolved and there are many approaches and many different algorithms which aim to make the face recognition as effective...... processing applications the results do not need to be completely precise and use of the approximate arithmetic can lead to reduction in terms of delay, space and power consumption. In this paper we examine possible use of approximate arithmetic in face recognition using Eigenfaces algorithm....

  9. Independent instances of "souvenir" Asian skulls from the Tampa Bay area.

    Wienker, C W; Wood, J E; Diggs, C A

    1990-05-01

    In the summer of 1984, police in Pinellas County, Florida, confiscated six identically colored imported Asian skulls (in a shipping case) from a private citizen. In May 1988, in nearby Hillsborough County, police confiscated a very similar skull from another private citizen, who allegedly had found it in an abandoned house. Aside from slight color differences between the six found in Pinellas County and the one found in Hillsborough County, the skulls are virtually identical in their osteological characteristics and condition and in the vital statistics derived from each. Each skull is as clean and dry as those typically sold by commercial scientific supply outlets in the United States. Each is edentulous (primarily premortem), between approximately 20 and 60 years of age at death, and morphologically Asian. Five of the seven are morphologically male, one is morphologically female, and one is a mosaic with respect to gender-related features. Police, medical examiners, coroners, and forensic anthropologists should be aware of such "souvenir" specimens, in the event that they encounter similar skulls. Discriminant function analyses for race and sex yield considerably conflicting results, which underscores the need for using extreme caution when interpreting forensic science estimates based on such techniques.

  10. A Pareto-based Ensemble with Feature and Instance Selection for Learning from Multi-Class Imbalanced Datasets.

    Fernández, Alberto; Carmona, Cristobal José; José Del Jesus, María; Herrera, Francisco

    2017-09-01

    Imbalanced classification is related to those problems that have an uneven distribution among classes. In addition to the former, when instances are located into the overlapped areas, the correct modeling of the problem becomes harder. Current solutions for both issues are often focused on the binary case study, as multi-class datasets require an additional effort to be addressed. In this research, we overcome these problems by carrying out a combination between feature and instance selections. Feature selection will allow simplifying the overlapping areas easing the generation of rules to distinguish among the classes. Selection of instances from all classes will address the imbalance itself by finding the most appropriate class distribution for the learning task, as well as possibly removing noise and difficult borderline examples. For the sake of obtaining an optimal joint set of features and instances, we embedded the searching for both parameters in a Multi-Objective Evolutionary Algorithm, using the C4.5 decision tree as baseline classifier in this wrapper approach. The multi-objective scheme allows taking a double advantage: the search space becomes broader, and we may provide a set of different solutions in order to build an ensemble of classifiers. This proposal has been contrasted versus several state-of-the-art solutions on imbalanced classification showing excellent results in both binary and multi-class problems.

  11. Guide en matière d'évaluation à l'intention des instances qui ...

    Les évaluations sont un élément clé de la recherche pour le développement, puisqu'elles ... Comprendre le rôle des instances qui commandent des évaluations ... Avec l'aide du CRDI, l'Instituto de la Salud, Medio Ambiente, Economia y ...

  12. Approximate Reanalysis in Topology Optimization

    Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole

    2009-01-01

    In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...

  13. Approximate Matching of Hierarchial Data

    Augsten, Nikolaus

    -grams of a tree are all its subtrees of a particular shape. Intuitively, two trees are similar if they have many pq-grams in common. The pq-gram distance is an efficient and effective approximation of the tree edit distance. We analyze the properties of the pq-gram distance and compare it with the tree edit...

  14. Approximation of Surfaces by Cylinders

    Randrup, Thomas

    1998-01-01

    We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...

  15. Approximation properties of haplotype tagging

    Dreiseitl Stephan

    2006-01-01

    Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.

  16. All-Norm Approximation Algorithms

    Azar, Yossi; Epstein, Leah; Richter, Yossi; Woeginger, Gerhard J.; Penttonen, Martti; Meineche Schmidt, Erik

    2002-01-01

    A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different ℓ p norms. We address this problem by introducing the concept of an All-norm ρ-approximation

  17. Truthful approximations to range voting

    Filos-Ratsika, Aris; Miltersen, Peter Bro

    We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare...

  18. On badly approximable complex numbers

    Esdahl-Schou, Rune; Kristensen, S.

    We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...

  19. Approximate reasoning in decision analysis

    Gupta, M M; Sanchez, E

    1982-01-01

    The volume aims to incorporate the recent advances in both theory and applications. It contains 44 articles by 74 contributors from 17 different countries. The topics considered include: membership functions; composite fuzzy relations; fuzzy logic and inference; classifications and similarity measures; expert systems and medical diagnosis; psychological measurements and human behaviour; approximate reasoning and decision analysis; and fuzzy clustering algorithms.

  20. Rational approximation of vertical segments

    Salazar Celis, Oliver; Cuyt, Annie; Verdonk, Brigitte

    2007-08-01

    In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.

  1. Pythagorean Approximations and Continued Fractions

    Peralta, Javier

    2008-01-01

    In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…

  2. Ultrafast Approximation for Phylogenetic Bootstrap

    Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt

    Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and

  3. Variable geometry Darrieus wind machine

    Pytlinski, J. T.; Serrano, D.

    1983-08-01

    A variable geometry Darrieus wind machine is proposed. The lower attachment of the blades to the rotor can move freely up and down the axle allowing the blades of change shape during rotation. Experimental data for a 17 m. diameter Darrieus rotor and a theoretical model for multiple streamtube performance prediction were used to develop a computer simulation program for studying parameters that affect the machine's performance. This new variable geometry concept is described and interrelated with multiple streamtube theory through aerodynamic parameters. The computer simulation study shows that governor behavior of a Darrieus turbine can not be attained by a standard turbine operating within normally occurring rotational velocity limits. A second generation variable geometry Darrieus wind turbine which uses a telescopic blade is proposed as a potential improvement on the studied concept.

  4. Flux compactifications and generalized geometries

    Grana, Mariana

    2006-01-01

    Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry

  5. Flux compactifications and generalized geometries

    Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)

    2006-11-07

    Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.

  6. Euclidean geometry and its subgeometries

    Specht, Edward John; Calkins, Keith G; Rhoads, Donald H

    2015-01-01

    In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...

  7. Guide to Computational Geometry Processing

    Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François

    be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...

  8. Electrodynamics and Spacetime Geometry: Foundations

    Cabral, Francisco; Lobo, Francisco S. N.

    2017-02-01

    We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.

  9. Dayside merging and cusp geometry

    Crooker, N.U.

    1979-01-01

    Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle

  10. Geometric Transformations in Engineering Geometry

    I. F. Borovikov

    2015-01-01

    Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry

  11. Classical geometry from the quantum Liouville theory

    Hadasz, Leszek; Jaskólski, Zbigniew; Piaţek, Marcin

    2005-09-01

    Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.

  12. Classical geometry from the quantum Liouville theory

    Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Cracow (Poland)]. E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: jask@ift.uni.wroc.pl; Piatek, Marcin [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: piatek@ift.uni.wroc.pl

    2005-09-26

    Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.

  13. Classical geometry from the quantum Liouville theory

    Hadasz, Leszek; Jaskolski, Zbigniew; Piatek, Marcin

    2005-01-01

    Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere

  14. Magnetic response of certain curved graphitic geometries

    Wang, L.; Davids, P.S.; Saxena, A.; Bishop, A.R.

    1992-01-01

    The quasi-particle energy spectra associated with some members of buckyfamily (curved graphitic geometries), in particular C 50 , C 60 , C 70 and related fullerenes as well as coaxial helical microtubules of graphite, are obtained analytically within the mean-field approximation. These energy spectra are then used to calculate various response functions. Specifically, we calculate the specific heat, magnetization and magnetic susceptibility in the presence of an external magnetic field at low temperatures. For a single microtubule an extra peak superimposed on the first de Haas van Alphen (dHvA) oscillation in magnetic susceptibility is found in the 50--170 Tesla range depending on the radius which is possibly accessible in special (explosive flux compression) experiments. Finally, we point to important potential applications of these novel mesoscopic structures in nanotechnology

  15. Nonlinear poisson brackets geometry and quantization

    Karasev, M V

    2012-01-01

    This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.

  16. On the convergence of multigroup discrete-ordinates approximations

    Victory, H.D. Jr.; Allen, E.J.; Ganguly, K.

    1987-01-01

    Our analysis is divided into two distinct parts which we label for convenience as Part A and Part B. In Part A, we demonstrate that the multigroup discrete-ordinates approximations are well-defined and converge to the exact transport solution in any subcritical setting. For the most part, we focus on transport in two-dimensional Cartesian geometry. A Nystroem technique is used to extend the discrete ordinates multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ collectively compact operator theory to deduce stability and convergence of the approximates. In Part B, we perform a thorough convergence analysis for the multigroup discrete-ordinates method for an anisotropically-scattering subcritical medium in slab geometry. The diamond-difference and step-characteristic spatial approximation methods are each studied. The multigroup neutron fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution. This is the first thorough convergence analysis for the fully-discretized multigroup neutron transport equations

  17. The P1approximation in the transport of beta rays

    Legarda, F.; Idoeta, R.; Herranz, M.

    1994-01-01

    A validation test for the p1 approximation to the linear transport of electrons in planar geometry has been performed. The p1 approximation is shown to be a good option for the description of the transport of beta rays with endpoint energies between 400kev and 3.5Mev through aluminium foils . This approximation together with the use of only elastic interactions of electrons with atoms has found good agreement with experimental results . A calculation has been made of the fraction of transmitted electrons through foils, solving the transport equation for planar geometry in the p1 approximation and assuming that only elastic scattering processes take place. The boundary condition at the entrance of the foil was a collimated beta source, while at the end of the foil has been adopted a vaccum boundary condition.Sources considered are those for which experimental and calculated spectrum shapes are known to agree. The calculated fractional transmission through different absorber thicknesses is found to have an exponential shape . Besides this fact the attenuation coefficients found ,when compared with those empirically obtained, agree to within 5%. 1 fig.; 4 refs. (author)

  18. KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI

    Irkham Ulil Albab

    2014-10-01

    Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews

  19. Graphical debugging of combinational geometry

    Burns, T.J.; Smith, M.S.

    1992-01-01

    A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development

  20. Lectures on Algebraic Geometry I

    Harder, Gunter

    2012-01-01

    This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho

  1. Combinatorial geometry in the plane

    Hadwiger, Hugo; Klee, Victor

    2014-01-01

    Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa

  2. Modern differential geometry for physicists

    Isham, C J

    1989-01-01

    These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields

  3. Comparison theorems in Riemannian geometry

    Cheeger, Jeff

    2008-01-01

    The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re

  4. Geometry, topology, and string theory

    Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)

    2003-01-01

    A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

  5. Stochastic geometry and its applications

    Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph

    2013-01-01

    An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a

  6. Introduction to topology and geometry

    Stahl, Saul

    2014-01-01

    An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele

  7. Algebraic geometry and theta functions

    Coble, Arthur B

    1929-01-01

    This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and

  8. Geometry, topology, and string theory

    Varadarajan, Uday

    2003-01-01

    A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated

  9. Mass transfer in supercritical fluids instancing selected fluids in supercritical carbon dioxide

    Hu, Miao; Benning, Rainer; Delgado, Antonio; Ertunc, Oezguer

    discussed. As the thermodynamic properties of a fluid are strongly dependent on the dimensions and the conditions in which the process is taken place, the models are limited to the hardware designed for this experiment setup. In order to evolve other applications, they need to be generalized and adjusted to fit the situations accordingly. As usual, the experiment data are to be submitted to these calculations to complete the models, and also to test and to proof if they satisfy some general properties of the systems that are already known. This leads to another very important part of the work -the experiments. Because of the sophistication of the behavior of fluids around their critical points, throughout the literature the theoretical description of the phase transition as well as other processes taken place under this circumstance, still depends largely on the empirical analysis. No matter how well considered a model can be, it represents only a partial and a simplified picture of the whole process. So the experimental part is of great importance not only as a support to the theoretical solution, but also as a means to get first hand data especially for the processes under investigation in this work. As solvent supercritical carbon dioxide was chosen considering its unique economical and ecological effects. As solutes DL-α-tocopherol and n-hexane were cho-sen. Two fundamental mass transfer processes are observed, namely diffusion and nucleation, both in laboratory as well as under compensated gravity (The experiment are to be performed in parabolic flight this March 2010). Both phenomena are obtained under isothermal condition through adjustments of the pressure inside a high pressure container. The container was spe-cially designed for this case. It has a cylindrical geometry with two pistons as movable walls on both sides to control the solvent volume. For diffusion a droplet of sample is fixed between two wetting barriers in the middle of the container with filled

  10. Beyond the random phase approximation

    Olsen, Thomas; Thygesen, Kristian S.

    2013-01-01

    We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...... functional theory and the adiabatic connection fluctuation-dissipation theorem and contains no fitted parameters. The new kernel is shown to preserve the accurate description of dispersive interactions from RPA while significantly improving the description of short-range correlation in molecules, insulators......, and metals. For molecular atomization energies, the rALDA is a factor of 7 better than RPA and a factor of 4 better than the Perdew-Burke-Ernzerhof (PBE) functional when compared to experiments, and a factor of 3 (1.5) better than RPA (PBE) for cohesive energies of solids. For transition metals...

  11. Hydrogen: Beyond the Classic Approximation

    Scivetti, Ivan

    2003-01-01

    The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position

  12. Orienteering in Knowledge Spaces: The Hyperbolic Geometry of Wikipedia Mathematics

    Leibon, Gregory; Rockmore, Daniel N.

    2013-01-01

    In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example of the pages of Wikipedia devoted to Mathematics, or “The MathWiki.” The applicability of these ideas extends beyond Wikipedia to provide a natural framework for visual search and to prescribe a natural mode of navigation for any kind of “knowledge space” in which higher order concepts aggregate various instances of information. Other examples would include genre or author organization of cultural objects such as books, movies, documents or even merchandise in an online store. PMID:23844017

  13. Orienteering in knowledge spaces: the hyperbolic geometry of Wikipedia Mathematics.

    Gregory Leibon

    Full Text Available In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example of the pages of Wikipedia devoted to Mathematics, or "The MathWiki." The applicability of these ideas extends beyond Wikipedia to provide a natural framework for visual search and to prescribe a natural mode of navigation for any kind of "knowledge space" in which higher order concepts aggregate various instances of information. Other examples would include genre or author organization of cultural objects such as books, movies, documents or even merchandise in an online store.

  14. Moritz enhancements for visualization of complicated geometry models

    Van Riper, K. A.

    2009-01-01

    We describe new features implemented in the Moritz geometry editing and visualization program to enhance the accuracy and efficiency of viewing complex geometry models. The 3D display is based on OpenGL and requires conversion of the combinatorial surface and solid body geometry used by MCNP and other transport codes to a set of polygons. Calculation of those polygons can take many minutes for complex models. Once calculated, the polygons can be saved to a file and reused when the same or a derivative model is loaded; the file can be read and processed in under a second. A cell can be filled with a collection of other cells constituting a universe. A new option bypasses use of the filled cell's boundaries when calculating the polygons for the filling universe. This option, when applicable, speeds processing, improves the 3D image, and permits reuse of the universe's polygons when other cells are filled with transformed instances of the universe. Surfaces and solid bodies used in a cell description must be converted to polygons before calculating the polygonal representation of a cell; this conversion requires truncation of infinite surfaces. A new method for truncating transformed surfaces ensures the finite surface intersects the entire model. When a surface or solid body is processed in a cell description, an optional test detects when that object does not contribute additional polygons; if so, that object May be extraneous for the cell description. (authors)

  15. Approximation errors during variance propagation

    Dinsmore, Stephen

    1986-01-01

    Risk and reliability analyses are often performed by constructing and quantifying large fault trees. The inputs to these models are component failure events whose probability of occuring are best represented as random variables. This paper examines the errors inherent in two approximation techniques used to calculate the top event's variance from the inputs' variance. Two sample fault trees are evaluated and several three dimensional plots illustrating the magnitude of the error over a wide range of input means and variances are given

  16. WKB approximation in atomic physics

    Karnakov, Boris Mikhailovich

    2013-01-01

    Provides extensive coverage of the Wentzel-Kramers-Brillouin approximation and its applications. Presented as a sequence of problems with highly detailed solutions. Gives a concise introduction for calculating Rydberg states, potential barriers and quasistationary systems. This book has evolved from lectures devoted to applications of the Wentzel-Kramers-Brillouin- (WKB or quasi-classical) approximation and of the method of 1/N -expansion for solving various problems in atomic and nuclear physics. The intent of this book is to help students and investigators in this field to extend their knowledge of these important calculation methods in quantum mechanics. Much material is contained herein that is not to be found elsewhere. WKB approximation, while constituting a fundamental area in atomic physics, has not been the focus of many books. A novel method has been adopted for the presentation of the subject matter, the material is presented as a succession of problems, followed by a detailed way of solving them. The methods introduced are then used to calculate Rydberg states in atomic systems and to evaluate potential barriers and quasistationary states. Finally, adiabatic transition and ionization of quantum systems are covered.

  17. The Idea of Order at Geometry Class.

    Rishel, Thomas

    The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…

  18. Teaching Spatial Geometry in a Virtual World

    Förster, Klaus-Tycho

    2017-01-01

    Spatial geometry is one of the fundamental mathematical building blocks of any engineering education. However, it is overshadowed by planar geometry in the curriculum between playful early primary education and later analytical geometry, leaving a multi-year gap where spatial geometry is absent...

  19. Approximate solution to neutron transport equation with linear anisotropic scattering

    Coppa, G.; Ravetto, P.; Sumini, M.

    1983-01-01

    A method to obtain an approximate solution to the transport equation, when both sources and collisions show a linearly anisotropic behavior, is outlined and the possible implications for numerical calculations in applied neutronics as well as shielding evaluations are investigated. The form of the differential system of equations taken by the method is quite handy and looks simpler and more manageable than any other today available technique. To go deeper into the efficiency of the method, some typical calculations concerning critical dimension of multiplying systems are then performed and the results are compared with the ones coming from the classical Ssub(N) approximations. The outcome of such calculations leads us to think of interesting developments of the method which could be quite useful in alternative to other today widespread approximate procedures, for any geometry, but especially for curved ones. (author)

  20. Analogical Reasoning in Geometry Education

    Magdas, Ioana

    2015-01-01

    The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…

  1. Normal forms in Poisson geometry

    Marcut, I.T.

    2013-01-01

    The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric

  2. Exploring Bundling Theory with Geometry

    Eckalbar, John C.

    2006-01-01

    The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…

  3. Stochastic Modelling of River Geometry

    Sørensen, John Dalsgaard; Schaarup-Jensen, K.

    1996-01-01

    Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....

  4. Matter in toy dynamical geometries

    Konopka, T.J.

    2009-01-01

    One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect

  5. Let??s teach geometry

    Ca??adas, Mar??a C.; Molina, Marta; Gallardo, Sandra; Mart??nez-Santaolalla, Manuel J.; Pe??as, Mar??a

    2010-01-01

    In this work we present an activity for High School students in which various mathematical concepts of plane and spatial geometry are involved. The final objective of the proposed tasks is constructing a particular polyhedron, the cube, by using a modality of origami called modular origami.

  6. Granular flows in constrained geometries

    Murthy, Tejas; Viswanathan, Koushik

    Confined geometries are widespread in granular processing applications. The deformation and flow fields in such a geometry, with non-trivial boundary conditions, determine the resultant mechanical properties of the material (local porosity, density, residual stresses etc.). We present experimental studies of deformation and plastic flow of a prototypical granular medium in different nontrivial geometries- flat-punch compression, Couette-shear flow and a rigid body sliding past a granular half-space. These geometries represent simplified scaled-down versions of common industrial configurations such as compaction and dredging. The corresponding granular flows show a rich variety of flow features, representing the entire gamut of material types, from elastic solids (beam buckling) to fluids (vortex-formation, boundary layers) and even plastically deforming metals (dead material zone, pile-up). The effect of changing particle-level properties (e.g., shape, size, density) on the observed flows is also explicitly demonstrated. Non-smooth contact dynamics particle simulations are shown to reproduce some of the observed flow features quantitatively. These results showcase some central challenges facing continuum-scale constitutive theories for dynamic granular flows.

  7. General Relativity: Geometry Meets Physics

    Thomsen, Dietrick E.

    1975-01-01

    Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…

  8. Learners engaging with transformation geometry

    participants engaged in investigative semi-structured interviews with the resear- chers. ... Keywords: analysis; conversions; transformation geometry; transformations; treatments .... semiotic systems of representation is not only to designate mathematical objects or to com- municate but also to ... Research design. We believe ...

  9. Multivariable calculus and differential geometry

    Walschap, Gerard

    2015-01-01

    This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.

  10. College geometry a unified development

    Kay, David C

    2011-01-01

    ""The book is a comprehensive textbook on basic geometry. … Key features of the book include numerous figures and many problems, more than half of which come with hints or even complete solutions. Frequent historical comments add to making the reading a pleasant one.""-Michael Joswig, Zentralblatt MATH 1273

  11. Open problems in the geometry and analysis of Banach spaces

    Guirao, Antonio J; Zizler, Václav

    2016-01-01

    This is a collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help convince young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems presented herein are longstanding open problems, some are recent, some are more important and some are only "local" problems. Some would ...

  12. Measurement of proton momentum distributions using a direct geometry instrument

    Senesi, R; Andreani, C; Kolesnikov, A I

    2014-01-01

    We report the results of inelastic neutron scattering measurements on bulk water and ice using the direct geometry SEQUOIA chopper spectrometer at the Spallation Neutron Source (USA), with incident energy E i = 6 eV. In this set up the measurements allow to access the Deep Inelastic Neutron Scattering regime. The scattering is centred at the proton recoil energy given by the impulse approximation, and the shape of the recoil peak conveys information on the proton momentum distribution in the system. The comparison with the performance of inverse geometry instruments, such as VESUVIO at the ISIS source (UK), shows that complementary information can be accessed by the use of direct and inverse geometry instruments. Analysis of the neutron Compton profiles shows that the proton kinetic energy in ice at 271 K is larger than in room temperature liquid water, in agreement with previous measurements on VESUVIO

  13. Nonlinear Methods in Riemannian and Kählerian Geometry

    Jost, Jürgen

    1991-01-01

    In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps ...

  14. Geometry.

    Mahaffey, Michael L.

    One of a series of experimental units for children at the preschool level, this booklet deals with geometric concepts. A unit on volume and a unit on linear measurement are covered; for each unit a discussion of mathematical objectives, a list of materials needed, and a sequence of learning activities are provided. Directions are specified for the…

  15. Geometri

    Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...

  16. Cuckoo Search Algorithm with Lévy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering

    Andrés Iglesias

    2018-03-01

    Full Text Available This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction. In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications. Given a set of measured data points, the approximation is formulated as a nonlinear continuous least-squares optimization problem. Then, a recent metaheuristics called Cuckoo Search Algorithm (CSA is applied to compute all relevant free variables of this minimization problem (namely, the data parameters and the surface poles. The method includes the iterative generation of new solutions by using the Lévy flights to promote the diversity of solutions and prevent stagnation. A critical advantage of this method is its simplicity: the CSA requires only two parameters, many fewer than any other metaheuristic approach, so the parameter tuning becomes a very easy task. The method is also simple to understand and easy to implement. Our approach has been applied to a benchmark of three illustrative sets of noisy data points corresponding to surfaces exhibiting several challenging features. Our experimental results show that the method performs very well even for the cases of noisy and unorganized data points. Therefore, the method can be directly used for real-world applications for reverse engineering without further pre/post-processing. Comparative work with the most classical mathematical techniques for this problem as well as a recent modification of the CSA called Improved CSA (ICSA is also reported. Two nonparametric statistical tests show that our method outperforms the classical mathematical techniques and provides equivalent results to ICSA

  17. Discrete differential geometry. Consistency as integrability

    Bobenko, Alexander I.; Suris, Yuri B.

    2005-01-01

    A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

  18. Instance Analysis for the Error of Three-pivot Pressure Transducer Static Balancing Method for Hydraulic Turbine Runner

    Weng, Hanli; Li, Youping

    2017-04-01

    The working principle, process device and test procedure of runner static balancing test method by weighting with three-pivot pressure transducers are introduced in this paper. Based on an actual instance of a V hydraulic turbine runner, the error and sensitivity of the three-pivot pressure transducer static balancing method are analysed. Suggestions about improving the accuracy and the application of the method are also proposed.

  19. Approximate solutions to Mathieu's equation

    Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

    2018-06-01

    Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

  20. Approximate Inference for Wireless Communications

    Hansen, Morten

    This thesis investigates signal processing techniques for wireless communication receivers. The aim is to improve the performance or reduce the computationally complexity of these, where the primary focus area is cellular systems such as Global System for Mobile communications (GSM) (and extensions...... to the optimal one, which usually requires an unacceptable high complexity. Some of the treated approximate methods are based on QL-factorization of the channel matrix. In the work presented in this thesis it is proven how the QL-factorization of frequency-selective channels asymptotically provides the minimum...

  1. Quantum tunneling beyond semiclassical approximation

    Banerjee, Rabin; Majhi, Bibhas Ranjan

    2008-01-01

    Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.

  2. Generalized Gradient Approximation Made Simple

    Perdew, J.P.; Burke, K.; Ernzerhof, M.

    1996-01-01

    Generalized gradient approximations (GGA close-quote s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. copyright 1996 The American Physical Society

  3. Numerically robust geometry engine for compound solid geometries

    Vlachoudis, V.; Sinuela-Pastor, D.

    2013-01-01

    Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)

  4. Correspondence of Concept Hierarchies in Semantic Web Based upon Global Instances and its Application to Facility Management Database

    Takahashi, Hiroki; Nishi, Yuusuke; Gion, Tomohiro; Minami, Shinichi; Fukunaga, Tatsuya; Ogata, Jiro; Yoshie, Osamu

    Semantic Web is the technology which determines the relevance of data over the Web using meta-data and which enables advanced search of global information. It is now desired to develop and apply this technology to many situations of facility management. In facility management, vocabulary should be unified to share the database of facilities for generating optimal maintenance schedule and so on. Under such situations, ontology databases are usually used to describe composition or hierarchy of facility parts. However, these vocabularies used in databases are not unified even between factories of same company, and this situation causes communication hazard between them. Moreover, concept involved in the hierarchy cannot be corresponded each other. There are some methods to correspond concepts of different hierarchy. But these methods have some defects, because they only attend target hierarchy itself and the number of instances. We propose improved method for corresponding concepts between different concepts' hierarchies, which uses other hierarchies all over the world of Web and the distance of instances to identify their relations. Our method can work even if the sets of instances belonging to the concepts are not identical.

  5. Multi-View Multi-Instance Learning Based on Joint Sparse Representation and Multi-View Dictionary Learning.

    Li, Bing; Yuan, Chunfeng; Xiong, Weihua; Hu, Weiming; Peng, Houwen; Ding, Xinmiao; Maybank, Steve

    2017-12-01

    In multi-instance learning (MIL), the relations among instances in a bag convey important contextual information in many applications. Previous studies on MIL either ignore such relations or simply model them with a fixed graph structure so that the overall performance inevitably degrades in complex environments. To address this problem, this paper proposes a novel multi-view multi-instance learning algorithm (MIL) that combines multiple context structures in a bag into a unified framework. The novel aspects are: (i) we propose a sparse -graph model that can generate different graphs with different parameters to represent various context relations in a bag, (ii) we propose a multi-view joint sparse representation that integrates these graphs into a unified framework for bag classification, and (iii) we propose a multi-view dictionary learning algorithm to obtain a multi-view graph dictionary that considers cues from all views simultaneously to improve the discrimination of the MIL. Experiments and analyses in many practical applications prove the effectiveness of the M IL.

  6. Impulse approximation in solid helium

    Glyde, H.R.

    1985-01-01

    The incoherent dynamic form factor S/sub i/(Q, ω) is evaluated in solid helium for comparison with the impulse approximation (IA). The purpose is to determine the Q values for which the IA is valid for systems such a helium where the atoms interact via a potential having a steeply repulsive but not infinite hard core. For 3 He, S/sub i/(Q, ω) is evaluated from first principles, beginning with the pair potential. The density of states g(ω) is evaluated using the self-consistent phonon theory and S/sub i/(Q,ω) is expressed in terms of g(ω). For solid 4 He resonable models of g(ω) using observed input parameters are used to evaluate S/sub i/(Q,ω). In both cases S/sub i/(Q, ω) is found to approach the impulse approximation S/sub IA/(Q, ω) closely for wave vector transfers Q> or approx. =20 A -1 . The difference between S/sub i/ and S/sub IA/, which is due to final state interactions of the scattering atom with the remainder of the atoms in the solid, is also predominantly antisymmetric in (ω-ω/sub R/), where ω/sub R/ is the recoil frequency. This suggests that the symmetrization procedure proposed by Sears to eliminate final state contributions should work well in solid helium

  7. Finite approximations in fluid mechanics

    Hirschel, E.H.

    1986-01-01

    This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for the Euler equations, etc. Applications are made to channel flows, gas dynamical problems, large eddy simulation of turbulence, non-Newtonian flow, turbomachine flow, zonal solutions for viscous flow problems, etc. The contents include: multigrid methods for problems from fluid dynamics, development of a 2D-Transonic Potential Flow Solver; a boundary element spectral method for nonstationary viscous flows in 3 dimensions; navier-stokes computations of two-dimensional laminar flows in a channel with a backward facing step; calculations and experimental investigations of the laminar unsteady flow in a pipe expansion; calculation of the flow-field caused by shock wave and deflagration interaction; a multi-level discretization and solution method for potential flow problems in three dimensions; solutions of the conservation equations with the approximate factorization method; inviscid and viscous flow through rotating meridional contours; zonal solutions for viscous flow problems

  8. Plasma Physics Approximations in Ares

    Managan, R. A.

    2015-01-01

    Lee & More derived analytic forms for the transport properties of a plasma. Many hydro-codes use their formulae for electrical and thermal conductivity. The coefficients are complex functions of Fermi-Dirac integrals, Fn( μ/θ ), the chemical potential, μ or ζ = ln(1+e μ/θ ), and the temperature, θ = kT. Since these formulae are expensive to compute, rational function approximations were fit to them. Approximations are also used to find the chemical potential, either μ or ζ . The fits use ζ as the independent variable instead of μ/θ . New fits are provided for A α (ζ ),A β (ζ ), ζ, f(ζ ) = (1 + e -μ/θ )F 1/2 (μ/θ), F 1/2 '/F 1/2 , F c α , and F c β . In each case the relative error of the fit is minimized since the functions can vary by many orders of magnitude. The new fits are designed to exactly preserve the limiting values in the non-degenerate and highly degenerate limits or as ζ→ 0 or ∞. The original fits due to Lee & More and George Zimmerman are presented for comparison.

  9. Power deposition in a cylindrical geometry using B-10 coatings

    Chung, A.K.; Prelas, M.A.

    1983-01-01

    The transport of charged particles produced by 10 B (n, α) Li and 235 U (n, νn) ff nuclear reactions in a two region cylindrical geometry is predicted. We employed a mean-range straight-flight approximation to calculate the power deposition by the charged particles in a gaseous medium. Our model demonstrated some features in a cylindrical experiment which were suspected but not proven. In the common slab model used by Guyot et al 1 and Romero 2 , the spatial distribution of power deposition is much flatter than it would be in a cylindrical model. A steeper gradient in the power deposition is expected in a cylindrical geometry than in a slab geometry. We also found that for a standard thickness of Boron-10 coating (1.73 μm) used in NPLs, the expected efficiency of a cylindrical geometry (7.5%) is much lower than the 12% efficiency predicted by the slab model. Indeed the use of slab geometry in modeling current NPL experimental devices is not accurate

  10. Slab2 - Updated Subduction Zone Geometries and Modeling Tools

    Moore, G.; Hayes, G. P.; Portner, D. E.; Furtney, M.; Flamme, H. E.; Hearne, M. G.

    2017-12-01

    The U.S. Geological Survey database of global subduction zone geometries (Slab1.0), is a highly utilized dataset that has been applied to a wide range of geophysical problems. In 2017, these models have been improved and expanded upon as part of the Slab2 modeling effort. With a new data driven approach that can be applied to a broader range of tectonic settings and geophysical data sets, we have generated a model set that will serve as a more comprehensive, reliable, and reproducible resource for three-dimensional slab geometries at all of the world's convergent margins. The newly developed framework of Slab2 is guided by: (1) a large integrated dataset, consisting of a variety of geophysical sources (e.g., earthquake hypocenters, moment tensors, active-source seismic survey images of the shallow slab, tomography models, receiver functions, bathymetry, trench ages, and sediment thickness information); (2) a dynamic filtering scheme aimed at constraining incorporated seismicity to only slab related events; (3) a 3-D data interpolation approach which captures both high resolution shallow geometries and instances of slab rollback and overlap at depth; and (4) an algorithm which incorporates uncertainties of contributing datasets to identify the most probable surface depth over the extent of each subduction zone. Further layers will also be added to the base geometry dataset, such as historic moment release, earthquake tectonic providence, and interface coupling. Along with access to several queryable data formats, all components have been wrapped into an open source library in Python, such that suites of updated models can be released as further data becomes available. This presentation will discuss the extent of Slab2 development, as well as the current availability of the model and modeling tools.

  11. Code subspaces for LLM geometries

    Berenstein, David; Miller, Alexandra

    2018-03-01

    We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.

  12. Euclidean distance geometry an introduction

    Liberti, Leo

    2017-01-01

    This textbook, the first of its kind, presents the fundamentals of distance geometry:  theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several.  Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.

  13. Fractal geometry and computer graphics

    Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele

    1992-01-01

    Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...

  14. The geometry of celestial mechanics

    Geiges, Hansjörg

    2016-01-01

    Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.

  15. Differential geometry and mathematical physics

    Rudolph, Gerd

    Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...

  16. Grassmannian geometry of scattering amplitudes

    Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav

    2016-01-01

    Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...

  17. Foliation theory in algebraic geometry

    McKernan, James; Pereira, Jorge

    2016-01-01

    Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013.  Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...

  18. Groups and Geometries : Siena Conference

    Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria

    1998-01-01

    On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi­ tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...

  19. Needle decompositions in Riemannian geometry

    Klartag, Bo'az

    2017-01-01

    The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.

  20. Systematics of IIB spinorial geometry

    Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.

    2005-01-01

    We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hep-th/0503046] to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of...

  1. Geometry Dependence of Stellarator Turbulence

    Mynick, H.E.; Xanthopoulos, P.; Boozer, A.H.

    2009-01-01

    Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes

  2. Superbanana orbits in stellarator geometries

    Derr, J.A.; Shohet, J.L.

    1979-04-01

    The presence of superbanana orbit types localized to either the interior or the exterior of stellarators and torsatrons is numerically investigated for 3.5 MeV alpha particles. The absence of the interior superbanana in both geometries is found to be due to non-conservation of the action. Exterior superbananas are found in the stellarator only, as a consequence of the existence of closed helical magnetic wells. No superbananas of either type are found in the torsatron

  3. Turtle geometry the Python way

    Battle, S.

    2014-01-01

    An introduction to coding using Python’s on-screen ‘turtle’ that can be commanded with a few simple instructions including forward, backward, left and right. The turtle leaves a trace that can be used to draw geometric figures. This workshop is aimed at beginners of all ages. The aim is to learn a smattering of programming and a little bit of geometry in a fun way.

  4. Topics in modern differential geometry

    Verstraelen, Leopold

    2017-01-01

    A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

  5. Approximating the minimum cycle mean

    Krishnendu Chatterjee

    2013-07-01

    Full Text Available We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1 First we show that the algorithmic question is reducible in O(n^2 time to the problem of a logarithmic number of min-plus matrix multiplications of n-by-n matrices, where n is the number of vertices of the graph. (2 Second, when the weights are nonnegative, we present the first (1 + ε-approximation algorithm for the problem and the running time of our algorithm is ilde(O(n^ω log^3(nW/ε / ε, where O(n^ω is the time required for the classic n-by-n matrix multiplication and W is the maximum value of the weights.

  6. Computational geometry for reactor applications

    Brown, F.B.; Bischoff, F.G.

    1988-01-01

    Monte Carlo codes for simulating particle transport involve three basic computational sections: a geometry package for locating particles and computing distances to regional boundaries, a physics package for analyzing interactions between particles and problem materials, and an editing package for determining event statistics and overall results. This paper describes the computational geometry methods in RACER, a vectorized Monte Carlo code used for reactor physics analysis, so that comparisons may be made with techniques used in other codes. The principal applications for RACER are eigenvalue calculations and power distributions associated with reactor core physics analysis. Successive batches of neutrons are run until convergence and acceptable confidence intervals are obtained, with typical problems involving >10 6 histories. As such, the development of computational geometry methods has emphasized two basic needs: a flexible but compact geometric representation that permits accurate modeling of reactor core details and efficient geometric computation to permit very large numbers of histories to be run. The current geometric capabilities meet these needs effectively, supporting a variety of very large and demanding applications

  7. Number theory III Diophantine geometry

    1991-01-01

    From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...

  8. Donaldson invariants in algebraic geometry

    Goettsche, L.

    2000-01-01

    In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)

  9. Aspects of differential geometry II

    Gilkey, Peter

    2015-01-01

    Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups an...

  10. Nonlinear approximation with dictionaries I. Direct estimates

    Gribonval, Rémi; Nielsen, Morten

    2004-01-01

    We study various approximation classes associated with m-term approximation by elements from a (possibly) redundant dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation w...

  11. Approximate cohomology in Banach algebras | Pourabbas ...

    We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate cohomologies. As a special case, approximate Hochschild cohomology is ...

  12. The C{sub n} method for approximation of the Boltzmann equation; La methode C{sub n} d'approximation de l'equation de Boltzmann

    Benoist, P; Kavenoky, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1968-01-15

    In a new method of approximation of the Boltzmann equation, one starts from a particular form of the equation which involves only the angular flux at the boundary of the considered medium and where the space variable does not appear explicitly. Expanding in orthogonal polynomials the angular flux of neutrons leaking from the medium and making no assumption about the angular flux within the medium, very good approximations to several classical plane geometry problems, i.e. the albedo of slabs and the transmission by slabs, the extrapolation length of the Milne problem, the spectrum of neutrons reflected by a semi-infinite slowing down medium. The method can be extended to other geometries. (authors) [French] On etablit une nouvelle methode d'approximation pour l'equation de Boltzmann en partant d'une forme particuliere de cette equation qui n'implique que le flux angulaire a la frontiere du milieu et ou les variables d'espace n'apparaissent pas explicitement. Par un developpement en polynomes orthogonaux du flux angulaire sortant du milieu et sans faire d'hypothese sur le flux angulaire a l'interieur du milieu, on obtient de tres bonnes approximations pour plusieurs problemes classiques en geometrie plane: l'albedo et le facteur de transmission des plaques, la longueur d'extrapolation du probleme de Milne, le spectre des neutrons reflechis par un milieu semi-infini ralentisseur. La methode se generalise a d'autres geometries. (auteurs)

  13. Algebraic Geometry and Number Theory Summer School

    Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk

    2017-01-01

    This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

  14. Geometry success in 20 minutes a day

    LLC, LearningExpress

    2014-01-01

    Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr

  15. Spectral nodal method for one-speed X,Y-geometry Eigenvalue diffusion problems

    Dominguez, Dany S.; Lorenzo, Daniel M.; Hernandez, Carlos G.; Barros, Ricardo C.; Silva, Fernando C. da

    2001-01-01

    Presented here is a new numerical nodal method for steady-state multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the transverse-integrated nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X and Y directions, and then considering flat approximations for the transverse leakage terms. These flat approximations are the only approximations that we consider in this method; as a result the numerical solutions are completely free from truncation errors in slab geometry. We show numerical results to illustrate the method's accuracy for coarse mesh calculations in a heterogeneous medium. (author)

  16. An approximate methods approach to probabilistic structural analysis

    Mcclung, R. C.; Millwater, H. R.; Wu, Y.-T.; Thacker, B. H.; Burnside, O. H.

    1989-01-01

    A probabilistic structural analysis method (PSAM) is described which makes an approximate calculation of the structural response of a system, including the associated probabilistic distributions, with minimal computation time and cost, based on a simplified representation of the geometry, loads, and material. The method employs the fast probability integration (FPI) algorithm of Wu and Wirsching. Typical solution strategies are illustrated by formulations for a representative critical component chosen from the Space Shuttle Main Engine (SSME) as part of a major NASA-sponsored program on PSAM. Typical results are presented to demonstrate the role of the methodology in engineering design and analysis.

  17. Network geometry with flavor: From complexity to quantum geometry

    Bianconi, Ginestra; Rahmede, Christoph

    2016-03-01

    Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but

  18. Multiple Instance Fuzzy Inference

    2015-12-02

    Fashion models 5.19 14 Sunset scenes 3.52 15 Cars 4.93 16 Waterfalls 2.56 17 Antique furniture 2.30 18 Battle ships 4.32 19 Skiing 3.34 20 Desserts ...1000, in addition 10% of the Desserts category images were confused with Beach and 20.9% of Mountains and glaciers images were misclassified as

  19. Eurochemic: failure or instance

    Busekist, O. von

    1982-01-01

    In this article, the author draws up a balance sheet of twenty-three years of good and bad luck of the European venture Eurochemic. It turns out that an important number of errors of judgement are the source of the present difficult situation of the European market for the nuclear reprocessing. (AF)

  20. Theory, For Instance

    Balle, Søren Hattesen

    This paper takes its starting point in a short poem by Wallace Stevens from 1917, which incidentally bears the title “Theory”. The poem can be read as a parable of theory, i.e., as something literally ’thrown beside’ theory (cf. OED: “...“). In the philosophical tradition this is also how the style of theory has been figured, that is to say: as something that is incidental to it or just happens to be around as so much paraphernalia. In my reading of Stevens’ poem I shall argue that this is exactly the position from which Stevens takes off when he assumes...... the task of writing a personified portrait of theory. Theory emerges as always beside(s) itself in what constitutes its style, but the poem also suggests that theory’s style is what gives theory both its power and its contingency. Figured as a duchess Theoria is only capable of retaining her power...