Strong-field ionization of polar molecules: Stark-shift-corrected strong-field approximation
DEFF Research Database (Denmark)
Dimitrovski, Darko; Martiny, Christian P. J.; Madsen, Lars Bojer
2010-01-01
We extend the molecular strong-field approximation for ionization, in the tunneling limit, to include systematically the linear and quadratic static Stark shifts of the ionizing molecular orbital. This approach, simple to implement, is capable of describing the essential physics of the process of...
Approximation for a Coulomb-Volkov solution in strong fields
Reiss, H. R.; Krainov, V. P.
1994-08-01
A simple analytical approximation is found for the wave function of an electron simultaneously exposed to a strong, circularly polarized plane-wave field and an atomic Coulomb potential. The approximation is valid when α0>>1, where α0 is the classical radius of motion of a free electron in the plane-wave field. This constraint is sufficiently mild at low frequencies that it makes possible a major extension of the lower bound of laser intensities for which Volkov-solution-based approximations are useful.
Strong field approximation within a Faddeev-like formalism for laser-matter interactions
International Nuclear Information System (INIS)
Popov, Y.; Galstyan, A.; Piraux, B.; Mota-Furtado, F.; O'Mahony, P.F.
2017-01-01
We consider the interaction of atomic hydrogen with an intense laser field within the strong-field approximation (SFA). By using a Faddeev-like formalism, we introduce a new perturbative series in the binding potential of the atom. As a first test of this new approach, we calculate the electron energy spectrum in the very simple case of a photon energy higher than the ionisation potential. We show that by contrast to the standard perturbative series in the binding potential obtained within the strong field approximation, the first terms of the new series converge rapidly towards the results we get by solving the corresponding time-dependent Schroedinger equation. (authors)
International Nuclear Information System (INIS)
Arbo, D.G.; Toekesi, K.; Miraglia, J.E.; FCEN, University of Buenos Aires
2008-01-01
Complete text of publication follows. We presented a theoretical study of the ionization of hydrogen atoms as a result of the interaction with an ultrashort external electric field. Doubly-differential momentum distributions and angular momentum distributions of ejected electrons calculated in the framework of the Coulomb-Volkov and strong field approximations, as well as classical calculations are compared with the exact solution of the time dependent Schroedinger equation. We have shown that the Coulomb-Volkov approximation (CVA) describes the quantum atomic ionization probabilities exactly when the external field is described by a sudden momentum transfer [1]. The velocity distribution of emitted electrons right after ionization by a sudden momentum transfer is given through the strong field approximation (SFA) within both the CVA and CTMC methods. In this case, the classical and quantum time dependent evolutions of an atom subject to a sudden momentum transfer are identical. The difference between the classical and quantum final momentum distributions resides in the time evolution of the escaping electron under the subsequent action of the Coulomb field. Furthermore, classical mechanics is incapable of reproducing the quantum angular momentum distribution due to the improper initial radial distribution used in the CTMC calculations, i.e., the microcanonical ensemble. We find that in the limit of high momentum transfer, based on the SFA, there is a direct relation between the cylindrical radial distribution dP/dρ and the final angular momentum distribution dP/dL. This leads to a close analytical expression for the partial wave populations (dP/dL) SFA-Q given by dP SFA-Q / dL = 4Z 3 L 2 / (Δp) 3 K 1 (2ZL/Δp) which, together with the prescription L = l + 1/2, reproduces quite accurately the quantum (CVA) results. Considering the inverse problem, knowing the final angular momentum distribution can lead to the inference of the initial probability distribution
Rydberg atoms in strong fields
International Nuclear Information System (INIS)
Kleppner, D.; Tsimmerman, M.
1985-01-01
Experimental and theoretical achievements in studying Rydberg atoms in external fields are considered. Only static (or quasistatic) fields and ''one-electron'' atoms, i.e. atoms that are well described by one-electron states, are discussed. Mainly behaviour of alkali metal atoms in electric field is considered. The state of theoretical investigations for hydrogen atom in magnetic field is described, but experimental data for atoms of alkali metals are presented as an illustration. Results of the latest experimental and theoretical investigations into the structure of Rydberg atoms in strong fields are presented
Quantum electrodynamics of strong fields
International Nuclear Information System (INIS)
Greiner, W.
1983-01-01
Quantum Electrodynamics of Strong Fields provides a broad survey of the theoretical and experimental work accomplished, presenting papers by a group of international researchers who have made significant contributions to this developing area. Exploring the quantum theory of strong fields, the volume focuses on the phase transition to a charged vacuum in strong electric fields. The contributors also discuss such related topics as QED at short distances, precision tests of QED, nonperturbative QCD and confinement, pion condensation, and strong gravitational fields In addition, the volume features a historical paper on the roots of quantum field theory in the history of quantum physics by noted researcher Friedrich Hund
Tao, Wanghai; Wang, Quanjiu; Lin, Henry
2018-03-01
Soil and water loss from farmland causes land degradation and water pollution, thus continued efforts are needed to establish mathematical model for quantitative analysis of relevant processes and mechanisms. In this study, an approximate analytical solution has been developed for overland flow model and sediment transport model, offering a simple and effective means to predict overland flow and erosion under natural rainfall conditions. In the overland flow model, the flow regime was considered to be transitional with the value of parameter β (in the kinematic wave model) approximately two. The change rate of unit discharge with distance was assumed to be constant and equal to the runoff rate at the outlet of the plane. The excess rainfall was considered to be constant under uniform rainfall conditions. The overland flow model developed can be further applied to natural rainfall conditions by treating excess rainfall intensity as constant over a small time interval. For the sediment model, the recommended values of the runoff erosion calibration constant (cr) and the splash erosion calibration constant (cf) have been given in this study so that it is easier to use the model. These recommended values are 0.15 and 0.12, respectively. Comparisons with observed results were carried out to validate the proposed analytical solution. The results showed that the approximate analytical solution developed in this paper closely matches the observed data, thus providing an alternative method of predicting runoff generation and sediment yield, and offering a more convenient method of analyzing the quantitative relationships between variables. Furthermore, the model developed in this study can be used as a theoretical basis for developing runoff and erosion control methods.
Quantum theory of strong-field frustrated tunneling
Popruzhenko, S. V.
2018-01-01
We show how the strong-field approximation, widely used for description of multiphoton and tunneling ionization, can be extended to analyse the excitation of bound states in intense low-frequency laser pulses. The proposed theory is based on the formalism of quantum trajectories and fills the gap between the numerical solution of the time-dependent Schrödinger equation and classical simulations. In particular, it allows identifying non-adiabatic and interference effects in strong-field excitation of Rydberg states.
Vibrational Excitation of Diatomic Molecular Ions in Strong Field Ionization of Diatomic Molecules
International Nuclear Information System (INIS)
Kjeldsen, Thomas K.; Madsen, Lars Bojer
2005-01-01
A model based on the strong-field and Born-Oppenheimer approximations qualitatively describes the distribution over vibrational states formed in a diatomic molecular ion following ionization of the neutral molecule by intense laser pulses. Good agreement is found with a recent experiment [X. Urbain et al., Phys. Rev. Lett. 92, 163004 (2004)]. In particular, the observed deviation from a Franck-Condon-like distribution is reproduced. Additionally, we demonstrate control of the vibrational distribution by a variation of the peak intensity or a change of frequency of the laser pulse
Perlt, Eva; Ray, Promit; Hansen, Andreas; Malberg, Friedrich; Grimme, Stefan; Kirchner, Barbara
2018-05-01
Ionic liquids raise interesting but complicated questions for theoretical investigations due to the fact that a number of different inter-molecular interactions, e.g., hydrogen bonding, long-range Coulomb interactions, and dispersion interactions, need to be described properly. Here, we present a detailed study on the ionic liquids ethylammonium nitrate and 1-ethyl-3-methylimidazolium acetate, in which we compare different dispersion corrected density functional approximations to accurate local coupled cluster data in static calculations on ionic liquid clusters. The efficient new composite method B97-3c is tested and has been implemented in CP2K for future studies. Furthermore, tight-binding based approaches which may be used in large scale simulations are assessed. Subsequently, ab initio as well as classical molecular dynamics simulations are conducted and structural analyses are presented in order to shed light on the different short- and long-range structural patterns depending on the method and the system size considered in the simulation. Our results indicate the presence of strong hydrogen bonds in ionic liquids as well as the aggregation of alkyl side chains due to dispersion interactions.
Altajskij, M V; Erokhin, N S; Zolnikova, N N; Mikhajlovskaya, L A; Moiseev, S S
2002-01-01
The approximation formulae for modeling the interaction of the fast alpha-particles and superthermal electrons with the solid-state plasma of the emitter films of the secondary emission radioisotope current source are developed. The evaluations of the interactions characteristic parameters, including the effective breaking efficiency of the emitter composite medium and the alpha-particles run, the emitter optimal thickness and maximum number of the current binary cells are accomplished on their basis. The obtained results may be used for optimizing the parameters of the experimental sample of such source and for the analysis of the problems, connected with its operation
Strong-field relativistic processes in highly charged ions
Energy Technology Data Exchange (ETDEWEB)
Postavaru, Octavian
2010-12-08
In this thesis we investigate strong-field relativistic processes in highly charged ions. In the first part, we study resonance fluorescence of laser-driven highly charged ions in the relativistic regime by solving the time-dependent master equation in a multi-level model. Our ab initio approach based on the Dirac equation allows for investigating highly relativistic ions, and, consequently, provides a sensitive means to test correlated relativistic dynamics, bound-state quantum electrodynamic phenomena and nuclear effects by applying coherent light with x-ray frequencies. Atomic dipole or multipole moments may be determined to unprecedented accuracy by measuring the interference-narrowed fluorescence spectrum. Furthermore, we investigate the level structure of heavy hydrogenlike ions in laser beams. Interaction with the light field leads to dynamic shifts of the electronic energy levels, which is relevant for spectroscopic experiments. We apply a fully relativistic description of the electronic states by means of the Dirac equation. Our formalism goes beyond the dipole approximation and takes into account non-dipole effects of retardation and interaction with the magnetic field components of the laser beam. We predicted cross sections for the inter-shell trielectronic recombination (TR) and quadruelectronic recombination processes which have been experimentally confirmed in electron beam ion trap measurements, mainly for C-like ions, of Ar, Fe and Kr. For Kr{sup 30}+, inter-shell TR contributions of nearly 6% to the total resonant photorecombination rate were found. (orig.)
Probing Strong-field General Relativity with Gravitational Waves
Pretorius, Frans
We are on the verge of a new era in astrophysics as a world-wide effort to observe the universe with gravitational waves takes hold---ground based laser interferometers (Hz to kHz), pulsar timing (micro to nano Hz), measurements of polarization of the cosmic microwave background (sub-nano Hz), and the planned NASA/ESA mission LISA (.1 mHz to .1 Hz). This project will study the theoretical nature of gravitational waves (GWs) emitted by two sources in the LISA band, namely supermassive-black-hole (SMBH) binary mergers, and extreme-mass-ratio-inspirals (EMRI's)---the merger of a stellar mass black hole, neutron star, or white dwarf with a SMBH. The primary goal will be to ascertain how well LISA, by observing these sources, could answer the following related questions about the fundamental nature of strong-field gravity: Does Einstein's theory of general relativity (GR) describe the geometry of black holes in the universe? What constraints can GW observations of SMBH mergers and EMRIs place on alternative theories of gravity? If there are deviations from GR, are there statistics that could give indications of a deviation if sources are detected using a search strategy based solely on GR waveforms? The primary reasons for focusing on LISA sources to answer these questions are (a) binary SMBH mergers could be detected by LISA with exquisitely high signal-to- noise, allowing enough parameters of the system to be accurately extracted to perform consistency checks of the underlying theory, (b) EMRIs will spend numerous orbits close to the central black hole, and thus will be quite sensitive to even small near-horizon deviations from GR. One approach to develop the requisite knowledge and tools to answer these questions is to study a concrete, theoretically viable alternative to GR. We will focus on the dynamical variant of Chern-Simons modified gravity (CSMG), which is interesting for several reasons, chief among which are (1) that CSMG generically arises in both string
Strong-field short-pulse nondipole dynamics
DEFF Research Database (Denmark)
Dimitrovski, Darko; Førre, Morten; Madsen, Lars Bojer
2009-01-01
We present a quantitative investigation of strong-field short-pulse nondipole dynamics in laser-matter interactions. We find excellent agreement between ab initio numerical and analytic results obtained using the Magnus expansion. We show that in the short-pulse limit, ultrafast transfer and cont......We present a quantitative investigation of strong-field short-pulse nondipole dynamics in laser-matter interactions. We find excellent agreement between ab initio numerical and analytic results obtained using the Magnus expansion. We show that in the short-pulse limit, ultrafast transfer...... and control of population can be achieved using nondipole effects. The relative importance of nondipole to dipole effects depends on the displacement imparted to a free classical electron....
Colloquium: Strong-field phenomena in periodic systems
Kruchinin, Stanislav Yu.; Krausz, Ferenc; Yakovlev, Vladislav S.
2018-04-01
The advent of visible-infrared laser pulses carrying a substantial fraction of their energy in a single field oscillation cycle has opened a new era in the experimental investigation of ultrafast processes in semiconductors and dielectrics (bulk as well as nanostructured), motivated by the quest for the ultimate frontiers of electron-based signal metrology and processing. Exploring ways to approach those frontiers requires insight into the physics underlying the interaction of strong high-frequency (optical) fields with electrons moving in periodic potentials. This Colloquium aims at providing this insight. Introduction to the foundations of strong-field phenomena defines and compares regimes of field-matter interaction in periodic systems, including (perfect) crystals as well as optical and semiconductor superlattices, followed by a review of recent experimental advances in the study of strong-field dynamics in crystals and nanostructures. Avenues toward measuring and controlling electronic processes up to petahertz frequencies are discussed.
Computational strong-field quantum dynamics intense light-matter interactions
2017-01-01
This graduate textbook introduces the computational techniques to study ultra-fast quantum dynamics of matter exposed to strong laser fields. Coverage includes methods to propagate wavefunctions according to the time-dependent Schrödinger, Klein-Gordon or Dirac equation, the calculation of typical observables, time-dependent density functional theory, multi-configurational time-dependent Hartree-Fock, time-dependent configuration interaction singles, the strong-field approximation, and the microscopic particle-in-cell approach.
Computational strong-field quantum dynamics. Intense light-matter interactions
Energy Technology Data Exchange (ETDEWEB)
Bauer, Dieter (ed.) [Rostock Univ. (Germany). Inst. fuer Physik
2017-09-01
This graduate textbook introduces the computational techniques to study ultra-fast quantum dynamics of matter exposed to strong laser fields. Coverage includes methods to propagate wavefunctions according to the time dependent Schroedinger, Klein-Gordon or Dirac equation, the calculation of typical observables, time-dependent density functional theory, multi configurational time-dependent Hartree-Fock, time-dependent configuration interaction singles, the strong-field approximation, and the microscopic particle-in-cell approach.
NATO Advanced Study Institute on Atoms in Strong Fields
Clark, Charles; Nayfeh, Munir
1990-01-01
This book collects the lectures given at the NATO Advanced Study Institute on "Atoms in Strong Fields", which took place on the island of Kos, Greece, during the two weeks of October 9-21,1988. The designation "strong field" applies here to an external electromagnetic field that is sufficiently strong to cause highly nonlinear alterations in atomic or molecular struc ture and dynamics. The specific topics treated in this volume fall into two general cater gories, which are those for which strong field effects can be studied in detail in terrestrial laboratories: the dynamics of excited states in static or quasi-static electric and magnetic fields; and the interaction of atoms and molecules with intense laser radiation. In both areas there exist promising opportunities for research of a fundamental nature. An electric field of even a few volts per centimeter can be very strong on the atom ic scale, if it acts upon a weakly bound state. The study of Rydberg states with high reso lution laser spectroscop...
DEFF Research Database (Denmark)
Etches, Adam; Madsen, Christian Bruun; Madsen, Lars Bojer
A correction term is introduced in the stationary-point analysis on high-order harmonic generation (HHG) from aligned molecules. Arising from a multi-centre expansion of the electron wave function, this term brings our numerical calculations of the Lewenstein model into qualitative agreement...
Strong-field control landscapes of coherent electronic excitation
Bayer, Tim; Wollenhaupt, Matthias; Baumert, Thomas
2008-04-01
We report on physical mechanisms behind resonant strong-field coherent control. To this end, we study multi-photon ionization of potassium atoms using intense shaped femtosecond laser pulses. The measured photoelectron spectra are discussed in terms of selective population of dressed states (SPODS). A physically motivated pulse parameterization is introduced which opens up two-dimensional parameter spaces comprising pulse sequences as well as chirped pulses. The control topologies of these subspaces are mapped out experimentally and are presented in the form of strong-field control landscapes (SFCLs). In the SFCLs, complementary realizations of SPODS via photon locking and rapid adiabatic passage are observed. Moreover, the combined effect, termed Multi-RAP, arises when both mechanisms are at play simultaneously. In order to better understand the performance of adaptive optimization procedures, we experimentally study their capability to find optimal solutions on a given parameter space. The evolution of different optimization procedures is visualized by means of control trajectories on the surface of the measured SFCL.
Virtual detector theory for strong-field atomic ionization
Wang, Xu; Tian, Justin; Eberly, J. H.
2018-04-01
A virtual detector (VD) is an imaginary device located at a fixed position in space that extracts information from the wave packet passing through it. By recording the particle momentum and the corresponding probability current at each time, the VDs can accumulate and build the differential momentum distribution of the particle, in a way that resembles real experiments. A mathematical proof is given for the equivalence of the differential momentum distribution obtained by the VD method and by Fourier transforming the wave function. In addition to being a tool for reducing the computational load, VDs have also been found useful in interpreting the ultrafast strong-field ionization process, especially the controversial quantum tunneling process.
The ESRg matrix for strong field d5 systems
Directory of Open Access Journals (Sweden)
McGarvey Bruce R.
1998-01-01
Full Text Available This review has tried to collect and correlate all the various equations for the g matrix of strong field d5 systems obtained from different basis sets using full electron and hole formalism calculations. It has corrected mistakes found in the literature and shown how the failure to properly take in symmetry boundary conditions has produced a variety of apparently inconsistent equations in the literature. The review has reexamined the problem of spin-orbit interaction with excited t4e states and finds that the earlier reports that it is zero in octahedral symmetry is not correct. It has shown how redefining what x, y, and z are in the principal coordinate system simplifies, compared to previous methods, the analysis of experimental g values with the equations.
Probing strong-field general relativity near black holes
CERN. Geneva; Alvarez-Gaumé, Luís
2005-01-01
Nature has sprinkled black holes of various sizes throughout the universe, from stellar mass black holes in X-ray sources to supermassive black holes of billions of solar masses in quasars. Astronomers today are probing the spacetime near black holes using X-rays, and gravitational waves will open a different view in the near future. These tools give us an unprecedented opportunity to test ultra-strong-field general relativity, including the fundamental theorem of the uniqueness of the Kerr metric and Roger Penrose's cosmic censorship conjecture. Already, fascinating studies of spectral lines are showing the extreme gravitational lensing effects near black holes and allowing crude measurements of black hole spin. When the ESA-NASA gravitational wave detector LISA begins its observations in about 10 years, it will make measurements of dynamical spacetimes near black holes with an accuracy greater even than that which theoreticians can reach with their computations today. Most importantly, when gravitational wa...
Tian, Justin; Wang, Xu; Eberly, J. H.
2017-05-01
The lack of analytical solutions for the exit momentum in the laser-driven tunneling theory is a well-recognized problem in strong field physics. Theoretical studies of electron momentum distributions in the neighborhood of the tunneling exit depend heavily on ad hoc assumptions. In this Letter, we apply a new numerical method to study the exiting electron's longitudinal momentum distribution under intense short-pulse laser excitation. We present the first realizations of the dynamic behavior of an electron near the so-called tunneling exit region without adopting a tunneling approximation.
DEFF Research Database (Denmark)
Hansen, Jonas Lerche; Stapelfeldt, Henrik; Dimitrovski, Darko
2011-01-01
A nanosecond laser pulse confines the spatial orientation of naphthalene in 1D or 3D while a femtosecond kick pulse initiates rotation of the molecular plane around the fixed long axis. Time-dependent photoelectron angular distributions (PADs), resulting from ionization by an intense femtosecond...... probe pulse, exhibit pronounced changes as the molecular plane rotates. Enhanced 3D alignment, occurring shortly after the kick pulse, provides strongly improved contrast in molecular-frame PADs. Calculations in the strong-field approximation show that the striking structures observed in the PADs...
Matter in strong fields: from molecules to living cells
International Nuclear Information System (INIS)
Mathur, D
2007-01-01
Strong optical fields induce multiple ionization in irradiated molecules. The ionization dynamics are governed by optical-field-induced distortions of molecular potential energy surfaces and molecular dissociation is the expected by-product. Recent experiments have even shown, quite counter-intuitively, that strong optical fields may even induce bond formation processes in molecules. All such processes are all manifestations of how intense light affects matter. In turn, matter also affects intense light. A visually dramatic manifestation of matter affecting light is obtained when ultrashort pulses of intense light propagate though condensed matter. The temporal and spatial properties of the incident light pulse are modified, and such modifications manifest themselves in an enlarged optical frequency sweep, resulting in the generation of broadband radiation (white light) known as supercontinuum production. Although the physics that governs supercontinuum generation is not properly understood, some recent progress is summarized. Novel applications of strong field phenomena are reported that are of relevance in the biomedical and life sciences
Towards strong field tests of beyond Horndeski gravity theories
Sakstein, Jeremy; Babichev, Eugeny; Koyama, Kazuya; Langlois, David; Saito, Ryo
2017-03-01
Theories of gravity in the beyond Horndeski class encompass a wide range of scalar-tensor theories that will be tested on cosmological scales over the coming decade. In this work, we investigate the possibility of testing them in the strong field regime by looking at the properties of compact objects—neutron, hyperon, and quark stars—embedded in an asymptotically de Sitter space-time, for a specific subclass of theories. We extend previous works to include slow rotation and find a relation between the dimensionless moment of inertia (I ¯ =I c2/GNM3 ) and the compactness C =GNM /R c2 (an I ¯-C relation), independent of the equation of state, that is reminiscent of but distinct from the general relativity prediction. Several of our equations of state contain hyperons and free quarks, allowing us to revisit the hyperon puzzle. We find that the maximum mass of hyperon stars can be larger than 2 M⊙ for small values of the beyond Horndeski parameter, thus providing a resolution of the hyperon puzzle based on modified gravity. Moreover, stable quark stars exist when hyperonic stars are unstable, which means that the phase transition from hyperon to quark stars is predicted just as in general relativity (GR), albeit with larger quark star masses. Two important and potentially observable consequences of some of the theories we consider are the existence of neutron stars in a range of masses significantly higher than in GR and I ¯-C relations that differ from their GR counterparts. In the former case, we find objects that, if observed, could not be accounted for in GR because they violate the usual GR causality condition. We end by discussing several difficult technical issues that remain to be addressed in order to reach more realistic predictions that may be tested using gravitational wave searches or neutron star observations.
Relativistic quantum dynamics in strong fields: Photon emission from heavy, few-electron ions
International Nuclear Information System (INIS)
Fritzsche, S.; Stoehlker, T.
2005-03-01
Recent progress in the study of the photon emission from highly-charged heavy ions is reviewed. These investigations show that high-Z ions provide a unique tool for improving the understanding of the electron-electron and electron-photon interaction in the presence of strong fields. Apart from the bound-state transitions, which are accurately described in the framework of quantum electrodynamics, much information has been obtained also from the radiative capture of (quasi-) free electrons by high-Z ions. Many features in the observed spectra hereby confirm the inherently relativistic behavior of even the simplest compound quantum systems in nature. (orig.)
Influence of the initial angular distribution on strong-field molecular dissociation
Yu, Youliang; Zeng, Shuo; Hernández, J. V.; Wang, Yujun; Esry, B. D.
2016-08-01
We study few-cycle, strong-field dissociation of aligned H2+ by solving the time-dependent Schrödinger equation including rotation. We examine the dependence of the final angular distribution, the kinetic energy release spectrum, and the total dissociation yield on the initial nuclear angular distribution. In particular, we look at the dependence on the relative angle θ0 between the laser polarization and the symmetry axis of a well-aligned initial distribution, as well as the dependence on the delay between the "pump" pulse that prepares the alignment and the few-cycle probe pulse. Surprisingly, we find the dissociation probability for θ0=90∘ can be appreciable even though the transitions involved are purely parallel. We therefore address the limits of the commonly held "ball-and-stick" picture for molecules in intense fields as well as the validity of the axial recoil approximation.
Morishita, Toru; Tolstikhin, Oleg I.
2017-11-01
We present a comprehensive treatise on the derivation of the factorization formula describing strong-field photoelectron momentum distributions near the outermost backward rescattering caustic within the adiabatic theory and its validation by calculations. The formula derived holds for ionization by linearly polarized laser pulses of sufficiently low frequency and becomes exact as the frequency tends to zero for a fixed pulse amplitude. The convergence of the results obtained from the formula to accurate photoelectron momentum distributions obtained by solving the time-dependent Schrödinger equation is demonstrated. The formula is shown to work quantitatively in both tunneling and over-the-barrier regimes of ionization for finite-range potentials as well as potentials with a Coulomb tail. This paves the way for future applications of the present theory in strong-field physics. In particular, the explicit analytical form of the returning photoelectron wave packet given here enables one to extract differential cross sections for elastic scattering of a photoelectron on the parent ion from experimental photoelectron momentum distributions.
Strong-field QED processes in short laser pulses. One- and two-photon Compton scattering
Energy Technology Data Exchange (ETDEWEB)
Seipt, Daniel
2012-12-20
The purpose of this thesis is to advance the understanding of strong-field QED processes in short laser pulses. The processes of non-linear one-photon and two-photon Compton scattering are studied, that is the scattering of photons in the interaction of relativistic electrons with ultra-short high-intensity laser pulses. These investigations are done in view of the present and next generation of ultra-high intensity optical lasers which are supposed to achieve unprecedented intensities of the order of 10{sup 24} W/cm{sup 2} and beyond, with pulse lengths in the order of some femtoseconds. The ultra-high laser intensity requires a non-perturbative description of the interaction of charged particles with the laser field to allow for multi-photon interactions, which is beyond the usual perturbative expansion of QED organized in powers of the fine structure constant. This is achieved in strong-field QED by employing the Furry picture and non-perturbative solutions of the Dirac equation in the presence of a background laser field as initial and final state wave functions, as well as the laser dressed Dirac-Volkov propagator. The primary objective is a realistic description of scattering processes with regard to the finite laser pulse duration beyond the common approximation of infinite plane waves, which is made necessary by the ultra-short pulse length of modern high-intensity lasers. Non-linear finite size effects are identified, which are a result of the interplay between the ultra-high intensity and the ultra-short pulse length. In particular, the frequency spectra and azimuthal photon emission spectra are studied emphasizing the differences between pulsed and infinite laser fields. The proper description of the finite temporal duration of the laser pulse leads to a regularization of unphysical infinities (due to the infinite plane-wave description) of the laser-dressed Dirac-Volkov propagator and in the second-order strong-field process of two-photon Compton
Strong-field QED processes in short laser pulses. One- and two-photon Compton scattering
International Nuclear Information System (INIS)
Seipt, Daniel
2012-01-01
The purpose of this thesis is to advance the understanding of strong-field QED processes in short laser pulses. The processes of non-linear one-photon and two-photon Compton scattering are studied, that is the scattering of photons in the interaction of relativistic electrons with ultra-short high-intensity laser pulses. These investigations are done in view of the present and next generation of ultra-high intensity optical lasers which are supposed to achieve unprecedented intensities of the order of 10 24 W/cm 2 and beyond, with pulse lengths in the order of some femtoseconds. The ultra-high laser intensity requires a non-perturbative description of the interaction of charged particles with the laser field to allow for multi-photon interactions, which is beyond the usual perturbative expansion of QED organized in powers of the fine structure constant. This is achieved in strong-field QED by employing the Furry picture and non-perturbative solutions of the Dirac equation in the presence of a background laser field as initial and final state wave functions, as well as the laser dressed Dirac-Volkov propagator. The primary objective is a realistic description of scattering processes with regard to the finite laser pulse duration beyond the common approximation of infinite plane waves, which is made necessary by the ultra-short pulse length of modern high-intensity lasers. Non-linear finite size effects are identified, which are a result of the interplay between the ultra-high intensity and the ultra-short pulse length. In particular, the frequency spectra and azimuthal photon emission spectra are studied emphasizing the differences between pulsed and infinite laser fields. The proper description of the finite temporal duration of the laser pulse leads to a regularization of unphysical infinities (due to the infinite plane-wave description) of the laser-dressed Dirac-Volkov propagator and in the second-order strong-field process of two-photon Compton scattering. An
Zhang, C.; Feng, T.; Raabe, N.; Rottke, H.
2018-02-01
Strong-field ionization (SFI) of the homonuclear noble gas dimer Xe2 is investigated and compared with SFI of the Xe atom and of the ArXe heteronuclear dimer by using ultrashort Ti:sapphire laser pulses and photoelectron momentum spectroscopy. The large separation of the two nuclei of the dimer allows the study of two-equivalent-center interference effects on the photoelectron momentum distribution. Comparing the experimental results with a new model calculation, which is based on the strong-field approximation, actually reveals the influence of interference. Moreover, the comparison indicates that the presence of closely spaced gerade and ungerade electronic state pairs of the Xe2 + ion at the Xe2 ionization threshold, which are strongly dipole coupled, affects the photoelectron momentum distribution.
Quantum-orbit theory of high-order atomic processes in strong fields
International Nuclear Information System (INIS)
Milosevic, D.B.
2005-01-01
Full text: Atoms submitted to strong laser fields can emit electrons and photons of very high energies. These processes find a highly intuitive and also quantitative explanation in terms of Feynman's path integral and the concept of quantum orbits. The quantum-orbit formalism is particularly useful for high-order atomic processes in strong laser fields. For such multi-step processes there is an intermediate step during which the electron is approximately under the influence of the laser field only and can absorb energy from the field. This leads to the appearance of the plateau structures in the emitted electron or photon spectra. Usual examples of such processes are high-order harmonic generation (HHG) and high-order above threshold ionization (HATI). These structures were also observed in high-order above-threshold detachment, laser-assisted x-ray-atom scattering, laser-assisted electron-ion recombination, and electron-atom scattering. We will present high-order strong-field approximation (SFA) and show how the quantum-orbit formalism follows from it. This will be done for various above-mentioned processes. For HHG a classification of quantum orbits will be given [10) and generalized to the presence of a static field. The low-energy part of the HHG spectra and the enhancement of HHG near the channel closings can be explained taking into account a large number of quantum orbits. For HATI we will concentrate on the case of few-cycle laser pulse. The influence of the carrier-envelope relative phase on the HATI spectrum can easily be explained in terms of quantum orbits. The SFA and the quantum-orbit results will be compared with the results obtained by Dieter Bauer using ab initio solutions of the time-dependent Schroedinger equation. It will be shown that the Coulomb effects are important for low-energy electron spectra. Refs. 11 (author)
Shvetsov-Shilovski, N. I.; Lein, M.
2018-01-01
Using the semiclassical two-step model for strong-field ionization we investigate the interference structures emerging in strong-field photoelectron holography, taking into account the Coulomb potential of the atomic core. For every kind of the interference pattern predicted by the three-step model, we calculate the corresponding structure in the presence of the Coulomb field, showing that the Coulomb potential modifies the interference patterns significantly.
High energy heavy ion collisions from the view point of the 'strong field physics'
International Nuclear Information System (INIS)
Itakura, Kazunori
2012-01-01
In the high energy heavy ion collisions at the facilities like RHIC and LHC, two strongest fields in the present universe are generated. First of all, a very strong electromagnetic field is generated, though its duration is very short due to the very high speed collisions of nuclei and the large electric charges. On the other hand, the nuclei are described as the high density saturation gluon state just before the moment of the collision and the high density gluon is released by the collision. A very strong color electromagnetic field is generated. The color glass condensate (CGC) is a reasonable picture. In this text, dynamics of the GLASMA (Glass + plasma), the new physics brought about by those 'strong fields', are introduced and are explained how the yet unsolved problems of the heavy ion collisions are going to be investigated on the new view point. The mechanism of the apparitions of the strong electromagnetic field and the strong color electromagnetic field are explained at first. The heavy ion collisions can be described as the process CGC to develop into QGP. As the phenomena under the strong electromagnetic field and the heavy ion collisions, their synchrotron radiations, the photon birefringence, the photon decay, the splitting of photons and the chiral phase transitions under high field are picked up. Concerning the strong color electromagnetic field dynamics and the heavy ion collisions, the plasma flux tube dynamics, the color magnetic flux tube, the color electric flux tube and the coexisting case of the color electric field and magnetic field are presented. (S. Funahashi)
Sissay, Adonay; Abanador, Paul; Mauger, François; Gaarde, Mette; Schafer, Kenneth J; Lopata, Kenneth
2016-09-07
Strong-field ionization and the resulting electronic dynamics are important for a range of processes such as high harmonic generation, photodamage, charge resonance enhanced ionization, and ionization-triggered charge migration. Modeling ionization dynamics in molecular systems from first-principles can be challenging due to the large spatial extent of the wavefunction which stresses the accuracy of basis sets, and the intense fields which require non-perturbative time-dependent electronic structure methods. In this paper, we develop a time-dependent density functional theory approach which uses a Gaussian-type orbital (GTO) basis set to capture strong-field ionization rates and dynamics in atoms and small molecules. This involves propagating the electronic density matrix in time with a time-dependent laser potential and a spatial non-Hermitian complex absorbing potential which is projected onto an atom-centered basis set to remove ionized charge from the simulation. For the density functional theory (DFT) functional we use a tuned range-separated functional LC-PBE*, which has the correct asymptotic 1/r form of the potential and a reduced delocalization error compared to traditional DFT functionals. Ionization rates are computed for hydrogen, molecular nitrogen, and iodoacetylene under various field frequencies, intensities, and polarizations (angle-dependent ionization), and the results are shown to quantitatively agree with time-dependent Schrödinger equation and strong-field approximation calculations. This tuned DFT with GTO method opens the door to predictive all-electron time-dependent density functional theory simulations of ionization and ionization-triggered dynamics in molecular systems using tuned range-separated hybrid functionals.
Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering
Walt, Samuel G.; Bhargava Ram, Niraghatam; Atala, Marcos; Shvetsov-Shilovski, Nikolay I; von Conta, Aaron; Baykusheva, Denitsa; Lein, Manfred; Wörner, Hans Jakob
2017-01-01
Strong-field photoelectron holography and laser-induced electron diffraction (LIED) are two powerful emerging methods for probing the ultrafast dynamics of molecules. However, both of them have remained restricted to static systems and to nuclear dynamics induced by strong-field ionization. Here we extend these promising methods to image purely electronic valence-shell dynamics in molecules using photoelectron holography. In the same experiment, we use LIED and photoelectron holography simultaneously, to observe coupled electronic-rotational dynamics taking place on similar timescales. These results offer perspectives for imaging ultrafast dynamics of molecules on femtosecond to attosecond timescales. PMID:28643771
Ehrenfest's theorem and the validity of the two-step model for strong-field ionization
DEFF Research Database (Denmark)
Shvetsov-Shilovskiy, Nikolay; Dimitrovski, Darko; Madsen, Lars Bojer
By comparison with the solution of the time-dependent Schrodinger equation we explore the validity of the two-step semiclassical model for strong-field ionization in elliptically polarized laser pulses. We find that the discrepancy between the two-step model and the quantum theory correlates...
Lackner, Florian; Chatterley, Adam S.; Pemmaraju, C. D.; Closser, Kristina D.; Prendergast, David; Neumark, Daniel M.; Leone, Stephen R.; Gessner, Oliver
2016-12-01
Femtosecond extreme ultraviolet transient absorption spectroscopy is used to explore strong-field ionization induced dynamics in selenophene (C4H4Se). The dynamics are monitored in real-time from the viewpoint of the Se atom by recording the temporal evolution of element-specific spectral features near the Se 3d inner-shell absorption edge (˜58 eV). The interpretation of the experimental results is supported by first-principles time-dependent density functional theory calculations. The experiments simultaneously capture the instantaneous population of stable molecular ions, the emergence and decay of excited cation states, and the appearance of atomic fragments. The experiments reveal, in particular, insight into the strong-field induced ring-opening dynamics in the selenophene cation, which are traced by the emergence of non-cyclic molecules as well as the liberation of Se+ ions within an overall time scale of approximately 170 fs. We propose that both products may be associated with dynamics on the same electronic surfaces but with different degrees of vibrational excitation. The time-dependent inner-shell absorption features provide direct evidence for a complex relaxation mechanism that may be approximated by a two-step model, whereby the initially prepared, excited cyclic cation decays within τ1 = 80 ± 30 fs into a transient molecular species, which then gives rise to the emergence of bare Se+ and ring-open cations within an additional τ2 = 80 ± 30 fs. The combined experimental and theoretical results suggest a close relationship between σ* excited cation states and the observed ring-opening reactions. The findings demonstrate that the combination of femtosecond time-resolved core-level spectroscopy with ab initio estimates of spectroscopic signatures provide new insights into complex, ultrafast photochemical reactions such as ring-opening dynamics in organic molecules in real-time and with simultaneous sensitivity for electronic and structural
Fritz, Sean; Hernandez-Castillo, Alicia O.; Abeysekera, Chamara; Zwier, Timothy S.
2017-06-01
The 8-18 GHz conformer specific rotational spectrum of gauche- and anti-3-phenylpropionitrile (C6H5-CH2-CH2-CN) conformers has been recorded using the strong field coherence breaking (SFCB) technique [1] with a modified line picking scheme for multiple selective excitations (MSE). As the recombination product of benzyl and cyanomethyl resonance-stabilized radicals, 3-phenylpropionitrile is a likely component of the complex organics in Titan's atmosphere, motivating its structural characterization. Details of the modified line picking scheme, hyperfine constants and relative population ratios of the two conformers will be presented. [1] A.O Hernandez-Castillo, Chamara Abeysekera, Brian M. Hays, Timothy S. Zwier, "Broadband Multi-Resonant Strong Field Coherence Breaking as a Tool for Single Isomer Microwave Spectroscopy." J. Chem. Phys. 145, 114203 (2016).
Null Geodesics and Strong Field Gravitational Lensing of Black Hole with Global Monopole
International Nuclear Information System (INIS)
Iftikhar, Sehrish; Sharif, M.
2015-01-01
We study two interesting features of a black hole with an ordinary as well as phantom global monopole. Firstly, we investigate null geodesics which imply unstable orbital motion of particles for both cases. Secondly, we evaluate deflection angle in strong field regime. We then find Einstein rings, magnifications, and observables of the relativistic images for supermassive black hole at the center of galaxy NGC4486B. We also examine time delays for different galaxies and present our results numerically. It is found that the deflection angle for ordinary/phantom global monopole is greater/smaller than that of Schwarzschild black hole. In strong field limit, the remaining properties of these black holes are quite different from the Schwarzschild black hole
Role of high-order dispersion on strong-field laser-molecule interactions
Dantus, Marcos; Nairat, Muath
2016-05-01
Strong-field (1012- 1016 W/ cm2) laser-matter interactions are characterized by the extent of fragmentation and charge of the resulting ions as a function of peak intensity and pulse duration. Interactions are influenced by high-order dispersion, which is difficult to characterize and compress. Fourth-order dispersion (FOD) causes a time-symmetric pedestal, while third-order dispersion (TOD) causes a leading (negative) or following (positive) pedestal. Here, we report on strong-field interactions with pentane and toluene molecules, tracking the molecular ion and the doubly charged carbon ion C2+ yields as a function of TOD and FOD for otherwise transform-limited (TL) 35fs pulses. We find TL pulses enhance molecular ion yield and suppress C2+ yield, while FOD reverses this trend. Interestingly, the leading pedestal in negative TOD enhances C2+ yield compared to positive TOD. Pulse pedestals are of particular importance in strong-field science because target ionization or alignment can be induced well before the main pulse arrives. A pedestal following an intense laser pulse can cause sequential ionization or accelerate electrons causing cascaded ionization. Control of high-order dispersion allows us to provide strong-field measurements that can help address the mechanisms responsible for different product ions in the presence and absence of pedestals. Financial support of this work comes from the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy, DOE SISGR (DE-SC0002325)
Gonoskov, I A; Tsatrafyllis, N; Kominis, I K; Tzallas, P
2016-09-07
We analytically describe the strong-field light-electron interaction using a quantized coherent laser state with arbitrary photon number. We obtain a light-electron wave function which is a closed-form solution of the time-dependent Schrödinger equation (TDSE). This wave function provides information about the quantum optical features of the interaction not accessible by semi-classical theories. With this approach we can reveal the quantum optical properties of high harmonic generation (HHG) process in gases by measuring the photon statistics of the transmitted infrared (IR) laser radiation. This work can lead to novel experiments in high-resolution spectroscopy in extreme-ultraviolet (XUV) and attosecond science without the need to measure the XUV light, while it can pave the way for the development of intense non-classical light sources.
Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum
Directory of Open Access Journals (Sweden)
Psaltis Dimitrios
2008-11-01
Full Text Available Neutron stars and black holes are the astrophysical systems with the strongest gravitational fields in the universe. In this article, I review the prospect of using observations of such compact objects to probe some of the most intriguing general relativistic predictions in the strong-field regime: the absence of stable circular orbits near a compact object and the presence of event horizons around black-hole singularities. I discuss the need for a theoretical framework, within which future experiments will provide detailed, quantitative tests of gravity theories. Finally, I summarize the constraints imposed by current observations of neutron stars on potential deviations from general relativity.
Ehrenfest's theorem and the validity of the two-step model for strong-field ionization
DEFF Research Database (Denmark)
Shvetsov-Shilovskiy, Nikolay; Dimitrovski, Darko; Madsen, Lars Bojer
2013-01-01
with situations where the ensemble average of the force deviates considerably from the force calculated at the average position of the trajectories of the ensemble. We identify the general trends for the applicability of the semiclassical model in terms of intensity, ellipticity, and wavelength of the laser pulse......By comparison with the solution of the time-dependent Schrödinger equation we explore the validity of the two-step semiclassical model for strong-field ionization in elliptically polarized laser pulses. We find that the discrepancy between the two-step model and the quantum theory correlates...
High precision hyperfine measurements in Bismuth challenge bound-state strong-field QED.
Ullmann, Johannes; Andelkovic, Zoran; Brandau, Carsten; Dax, Andreas; Geithner, Wolfgang; Geppert, Christopher; Gorges, Christian; Hammen, Michael; Hannen, Volker; Kaufmann, Simon; König, Kristian; Litvinov, Yuri A; Lochmann, Matthias; Maaß, Bernhard; Meisner, Johann; Murböck, Tobias; Sánchez, Rodolfo; Schmidt, Matthias; Schmidt, Stefan; Steck, Markus; Stöhlker, Thomas; Thompson, Richard C; Trageser, Christian; Vollbrecht, Jonas; Weinheimer, Christian; Nörtershäuser, Wilfried
2017-05-16
Electrons bound in highly charged heavy ions such as hydrogen-like bismuth 209 Bi 82+ experience electromagnetic fields that are a million times stronger than in light atoms. Measuring the wavelength of light emitted and absorbed by these ions is therefore a sensitive testing ground for quantum electrodynamical (QED) effects and especially the electron-nucleus interaction under such extreme conditions. However, insufficient knowledge of the nuclear structure has prevented a rigorous test of strong-field QED. Here we present a measurement of the so-called specific difference between the hyperfine splittings in hydrogen-like and lithium-like bismuth 209 Bi 82+,80+ with a precision that is improved by more than an order of magnitude. Even though this quantity is believed to be largely insensitive to nuclear structure and therefore the most decisive test of QED in the strong magnetic field regime, we find a 7-σ discrepancy compared with the theoretical prediction.
Willingham, D; Brenes, D A; Winograd, N; Wucher, A
2011-01-01
Molecular depth profiles of model organic thin films were performed using a 40 keV C 60 + cluster ion source in concert with TOF-SIMS. Strong-field photoionization of intact neutral molecules sputtered by 40 keV C 60 + primary ions was used to analyze changes in the chemical environment of the guanine thin films as a function of ion fluence. Direct comparison of the secondary ion and neutral components of the molecular depth profiles yields valuable information about chemical damage accumulation as well as changes in the molecular ionization probability. An analytical protocol based on the erosion dynamics model is developed and evaluated using guanine and trehalose molecular secondary ion signals with and without comparable laser photoionization data.
Spatial characterization of Bessel-like beams for strong-field physics.
Summers, Adam M; Yu, Xiaoming; Wang, Xinya; Raoul, Maxime; Nelson, Josh; Todd, Daniel; Zigo, Stefan; Lei, Shuting; Trallero-Herrero, Carlos A
2017-02-06
We present a compact, simple design for the generation and tuning of both the spot size and effective focal length of Bessel-like beams. In particular, this setup provides an important tool for the use of Bessel-like beams with high-power, femtosecond laser systems. Using a shallow angle axicon in conjunction with a spherical lens, we show that it is possible to focus Bessel-like modes to comparable focal spot sizes to sharp axicons while maintaining a long effective focal length. The resulting focal profiles are characterized in detail using an accurate high dynamic range imaging technique. Quantitatively, we introduce a metric (R0.8) which defines the spot-size containing 80% of the total energy. Our setup overcomes the typical compromise between long working distances and small spot sizes. This is particularly relevant for strong-field physics where most experiments must operate in vacuum.
Combined visible and near-infrared OPA for wavelength scaling experiments in strong-field physics
Lloyd, David T.; O'Keeffe, Kevin; Wyatt, Adam S.; Anderson, Patrick N.; Treacher, Daniel; Hooker, Simon M.
2017-02-01
We report the operation of an optical parametric amplifier (OPA) capable of producing gigawatt peak-power laser pulses with tunable wavelength in either the visible or near-infrared spectrum. The OPA has two distinct operation modes (i) generation of > 350 μJ, sub 100 fs pulses, tunable between 1250 - 1550 nm; (ii) generation of > 170 μJ, sub 150 fs pulses tunable between 490 - 530 nm. We have recorded high-order harmonic spectra over a wide range of driving wavelengths. This flexible source of femtosecond pulses presents a useful tool for exploring the wavelength-dependence of strong-field phenomena, in both the multi-photon and tunnel ionization regimes.
Probing strong-field electron-nuclear dynamics of polyatomic molecules using proton motion
International Nuclear Information System (INIS)
Markevitch, Alexei N.; Smith, Stanley M.; Levis, Robert J.; Romanov, Dmitri A.
2007-01-01
Proton ejection during Coulomb explosion is studied for several structure-related organic molecules (anthracene, anthraquinone, and octahydroanthracene) subjected to 800 nm, 60 fs laser pulses at intensities from 0.50 to 4.0x10 14 W cm -2 . The proton kinetic energy distributions are found to be markedly structure specific. The distributions are bimodal for anthracene and octahydroanthracene and trimodal for anthraquinone. Maximum (cutoff) energies of the distributions range from 50 eV for anthracene to 83 eV for anthraquinone. The low-energy mode (∼10 eV) is most pronounced in octahydroanthracene. The dependence of the characteristic features of the distributions on the laser intensity provides insights into molecular specificity of such strong-field phenomena as (i) nonadiabatic charge localization and (ii) field-mediated restructuring of polyatomic molecules polarized by a strong laser field
Strong-field effects in Rabi oscillations between a single state and a superposition of states
International Nuclear Information System (INIS)
Zhdanovich, S.; Milner, V.; Hepburn, J. W.
2011-01-01
Rabi oscillations of quantum population are known to occur in two-level systems driven by spectrally narrow laser fields. In this work we study Rabi oscillations induced by shaped broadband femtosecond laser pulses. Due to the broad spectral width of the driving field, the oscillations are initiated between a ground state and a coherent superposition of excited states, or a ''wave packet,'' rather than a single excited state. Our experiments reveal an intricate dependence of the wave-packet phase on the intensity of the laser field. We confirm numerically that the effect is associated with the strong-field nature of the interaction and provide a qualitative picture by invoking a simple theoretical model.
Direct Visualization of Valence Electron Motion Using Strong-Field Photoelectron Holography
He, Mingrui; Li, Yang; Zhou, Yueming; Li, Min; Cao, Wei; Lu, Peixiang
2018-03-01
Watching the valence electron move in molecules on its intrinsic timescale has been one of the central goals of attosecond science and it requires measurements with subatomic spatial and attosecond temporal resolutions. The time-resolved photoelectron holography in strong-field tunneling ionization holds the promise to access this realm. However, it remains to be a challenging task hitherto. Here we reveal how the information of valence electron motion is encoded in the hologram of the photoelectron momentum distribution (PEMD) and develop a novel approach of retrieval. As a demonstration, applying it to the PEMDs obtained by solving the time-dependent Schrödinger equation for the prototypical molecule H2+ , the attosecond charge migration is directly visualized with picometer spatial and attosecond temporal resolutions. Our method represents a general approach for monitoring attosecond charge migration in more complex polyatomic and biological molecules, which is one of the central tasks in the newly emerging attosecond chemistry.
STRONG FIELD EFFECTS ON EMISSION LINE PROFILES: KERR BLACK HOLES AND WARPED ACCRETION DISKS
International Nuclear Information System (INIS)
Wang Yan; Li Xiangdong
2012-01-01
If an accretion disk around a black hole is illuminated by hard X-rays from non-thermal coronae, fluorescent iron lines will be emitted from the inner region of the accretion disk. The emission line profiles will show a variety of strong field effects, which may be used as a probe of the spin parameter of the black hole and the structure of the accretion disk. In this paper, we generalize the previous relativistic line profile models by including both the black hole spinning effects and the non-axisymmetries of warped accretion disks. Our results show different features from the conventional calculations for either a flat disk around a Kerr black hole or a warped disk around a Schwarzschild black hole by presenting, at the same time, multiple peaks, rather long red tails, and time variations of line profiles with the precession of the disk. We show disk images as seen by a distant observer, which are distorted by the strong gravity. Although we are primarily concerned with the iron K-shell lines in this paper, the calculation is general and is valid for any emission lines produced from a warped accretion disk around a black hole.
Channel-closing effects in strong-field ionization by a bicircular field
Milošević, D. B.; Becker, W.
2018-03-01
Channel-closing effects, such as threshold anomalies and resonantlike intensity-dependent enhancements in strong-field ionization by a bicircular laser field are analyzed. A bicircular field consists of two coplanar corotating or counter-rotating circularly polarized fields having different frequencies. For the total detachment rate of a negative ion by a bicircular field we observe threshold anomalies and explain them using the Wigner threshold law and energy and angular momentum conservation. For the corotating bicircular case, these effects are negligible, while for the counter-rotating case they are pronounced and their position depends on the magnetic quantum number of the initial state. For high-order above-threshold ionization of rare-gas atoms by a counter-rotating bicircular laser field we observe very pronounced intensity-dependent enhancements. We find all four types of threshold anomalies known from collision theory. Contrary to the case of linear polarization, channel-closing effects for a bicircular field are visible also in the cutoff region of the electron energy spectrum, which is explained using quantum-orbit theory.
Control and identification of strong field dissociative channels in CO2+ via molecular alignment
International Nuclear Information System (INIS)
Oppermann, M; Weber, S J; Marangos, J P; Morales, F; Richter, M; Patchkovskii, S; Ivanov, M; Smirnova, O; Csehi, A; Vibók, Á
2014-01-01
The dissociative excitation of CO 2 + was studied in the molecular frame as a function of probe laser intensity, ellipticity and polarization with respect to the molecular bond at laser wavelengths of 800 nm and 1350 nm. This allowed the identification of the main excitation pathway consisting of tunnel ionization from HOMO-2 followed by a parallel dipole transition from the second excited state B to the predissociating, third excited state C. Recollision excitation was shown to play a negligible role. Using laser induced impulsive alignment, the strong field induced coupling at 800 nm and 1350 nm of the ionic states B and C could thus be controlled by the laser polarization. This leads to a suppression of the fragmentation yield of up to 70% when the laser polarization was perpendicular to the molecular axis compared to parallel polarization. We have performed simulations of various ionization channels of CO 2 . Our simulations reflect the experimental findings and show that dissociation of CO 2 + is induced by tunnelling from deeper molecular orbitals HOMO-1, HOMO-2, HOMO-3, followed by laser driven hole dynamics in the ion. (paper)
2016-04-15
AFRL-AFOSR-VA-TR-2016-0166 Phase-Sensitive Control Of Molecular Dissociation Through Attosecond Pump/Strong-Field Mid- IR Probe Spectroscopy Jeffery...Pump/Strong- Field Mid- IR Probe Spectroscopy 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-12-1-0080 5c. PROGRAM ELEMENT NUMBER 61102F 6. AUTHOR(S...sequentially controlling ionization and dissociation steps in the H2+ molecule using tightly synchronized few-fs EUV and few-cycle mid- IR pulses. We
Ionization, photoelectron dynamics and elastic scattering in relativistic, ultra-strong field
Luo, Sui
Ultrastrong laser-matter interaction has direct bearing to next generation technologies including plasma acceleration, laser fusion and attosecond X-ray generation. The commonly known physics in strong field becomes different as one progress to ultrastrong field. The works presented in this dissertation theoretically study the influence of relativistic effect and magnetic component of the laser field on the ionization, photoelectron dynamics and elastic scattering processes. The influence of magnetic component (B laser) of circularly polarized (CP) ultrastrong fields (up to3 x 1022 W/cm2) on atomic bound state dynamics is investigated. The Poincare plots are used to find the changes in trajectory energies are on the order of a few percent for intensities up to1 x 1022 W/cm2. It is found that at intensities where ionization approaches 50% for the bound state, the small changes from Blaser of the circular polarized light can actually result in a several-fold decrease in ionization probability. The force on the bound electron exerted by the Lorentz force from B laser is perpendicular to the rotating plane of the circular polarized light, and this nature makes those trajectories which are aligned away from the minimum in the potential barrier stabilized against tunneling ionization. Our results provide a classical understanding for ionization in ultrastrong fields and indicate that relativistic effects in ultrastrong field ionization may most easily be seen with CP fields. The photoelectron energy spectra from elastic rescattering in ultrastrong laser fields (up to 2x1019 W/cm2) is studied by using a relativistic adaption of a semi-classical three-step recollision model. The Hartree-Fock scattering potentials are used in calculating the elastic rescattering for both hydrogenlike and noble gas species. It is found that there is a reduction in elastic rescattering for intensities beyond 6 x 1016 W/cm2 when the laser Lorentz deflection of the photoelectron exceeds its
Witte, S.; Hickstein, D.D.; Ranitovic, P.; Tong, X.-M.; Huismans, Y.; Arpin, P.; Zhou, X.; Keister, K.E.; Hogle, C.W.; Zhang, B.; Ding, C.; Johnsson, P.; Toshima, N.; Vrakking, M.J.J.; Murnane, M.M.; Kapteyn, H.C.
2012-01-01
Using a simple model of strong-field ionization of atoms that generalizes the well-known 3-step model from 1D to 3D, we show that the experimental photoelectron angular distributions resulting from laser ionization of xenon and argon display prominent structures that correspond to electrons that
Attosecond counter-rotating-wave effect in xenon driven by strong fields
Anand, M.; Pabst, Stefan; Kwon, Ojoon; Kim, Dong Eon
2017-05-01
We investigate the subfemtosecond dynamics of a highly excited xenon atom coherently driven by a strong control field at which the Rabi frequency of the system is comparable to the frequency of a driving laser. The widely used rotating-wave approximation breaks down at such fields, resulting in features such as the counter-rotating-wave (CRW) effect. We present a time-resolved observation of the CRW effect in the highly excited 4 d-1n p xenon using attosecond transient absorption spectroscopy. Time-dependent many-body theory confirms the observation and explains the various features of the absorption spectrum seen in experiment.
DEFF Research Database (Denmark)
Etches, Adam; Madsen, Lars Bojer
2010-01-01
Polar molecules such as CO are interesting target systems for high-order harmonic generation (HHG) as they can be oriented with current laser techniques, thus allowing the study of systems without inversion symmetry. However, the asymmetry of the molecule also means that the molecular orbitals...... (enhanced) every other half-cycle. We show that the Stark shift weakens the strength of system-induced gating and also determines the relative contribution from opposite orientations in field-induced gating. Finally, we propose a novel scheme for extending the high-order harmonic cutoff by letting the two...
Energy Technology Data Exchange (ETDEWEB)
Bucksbaum, Philip H
2011-04-13
The term "molecular movie" has come to describe efforts to track and record Angstrom-scale coherent atomic and electronic motion in a molecule. The relevant time scales for this range cover several orders of magnitude, from sub-femtosecond motion associated with electron-electron correlations, to 100-fs internal vibrations, to multi-picosecond motion associated with the dispersion and quantum revivals of molecular reorientation. Conventional methods of cinematography do not work well in this ultrafast and ultrasmall regime, but stroboscopic "pump and probe" techniques can reveal this motion with high fidelity. This talk will describe some of the methods and recent progress in exciting and controlling this motion, using both laboratory lasers and the SLAC Linac Coherent Light Source x-ray free electron laser, and will further try to relate the date to the goal of molecular movies.
Indian Academy of Sciences (India)
IAS Admin
V S Borkar is the Institute. Chair Professor of. Electrical Engineering at. IIT Bombay. His research interests are stochastic optimization, theory, algorithms and applica- tions. 1 'Markov Chain Monte Carlo' is another one (see [1]), not to mention schemes that combine both. Stochastic approximation is one of the unsung.
2008-01-01
Since the invention of the laser in the 1960s, people have strived to reach higher intensities and shorter pulse durations. High intensities and ultrashort pulse durations are intimately related. Recent developments have shown that high intensity lasers also open the way to realize pulses with the shortest durations to date, giving birth to the field of attosecond science (1 asec = 10-18s). This book is about high-intensity lasers and their applications. The goal is to give an up to date introduction to the technology behind these laser systems and to the broad range of intense laser applications. These applications include AMO (atomic molecular and optical) physics, x-ray science, attosecond science, plasma physics and particle acceleration, condensed matter science and laser micromachining, and finally even high-energy physics.
Chatterley, A. S.; Lackner, F.; Neumark, D. M.; Leone, S. R.; Gessner, O.
2016-05-01
Strong field induced dissociation dynamics of the small haloalkane 1,2-dibromoethane (DBE) have been explored using femtosecond XUV transient absorption spectroscopy. Dynamics are initiated by a near IR pump pulse with intensities between 75 and 220 TW cm-2, and are probed by the atomic site specific XUV absorption of the Br 3d levels. Immediately upon ionization, the spectral signatures of molecular ions appear. These molecular peaks decay in tandem with the appearance of atomic Br peaks in charge states of 0, + 1 and + 2, which are all monitored simultaneously. Neutral Br atoms are eliminated in 300 fs, presumably from statistical dissociation of vibrationally hot DBE+ ions, Br+ ions are eliminated in 70 fs from a more energetic dissociative ionization pathway, and Br++ ions are eliminated within the duration of the 35 fs pump pulse. The simultaneous recording of multiple parent molecule and fragment ion traces enables new insight into predominant dissociation pathways induced by strong field ionization of organic molecules.
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...
Jarnac, Amélie; Brizuela, Fernando; Heyl, Christoph M.; Rudawski, Piotr; Campi, Filippo; Kim, Byunghoon; Rading, Linnea; Johnsson, Per; Mysyrowicz, André; L'Huillier, Anne; Houard, Aurélien; Arnold, Cord L.
2014-12-01
We demonstrate pulse post-compression of a TW class chirped pulse amplification laser employing a gas-filled planar hollow waveguide. A waveguide throughput of 80% is achieved for 50 mJ input pulse energy. Good focusability is found and after compression with chirped mirrors a pulse duration of sub-15 fs is measured in the beam center. Whereas a total energy efficiency of ≈70% should be achievable, our post-compressor currently delivers 20 mJ output pulse energy (≈40% efficiency), mostly limited by apertures of chirped mirrors and vacuum windows. The viability of the planar hollow waveguide compression scheme for applications in strong-field physics is demonstrated by generating high-order harmonics in a pulsed Ar gas cell. Contribution to the Topical Issue "X-ray Generation from Ultrafast Lasers", edited by Germán J. de Valcárcel, Luis Roso and Amelle Zaïr.
Strong-field Breit–Wheeler pair production in two consecutive laser pulses with variable time delay
Energy Technology Data Exchange (ETDEWEB)
Jansen, Martin J.A.; Müller, Carsten, E-mail: c.mueller@tp1.uni-duesseldorf.de
2017-03-10
Photoproduction of electron–positron pairs by the strong-field Breit–Wheeler process in an intense laser field is studied. The laser field is assumed to consist of two consecutive short pulses, with a variable time delay in between. By numerical calculations within the framework of scalar quantum electrodynamics, we demonstrate that the time delay exerts a strong impact on the pair-creation probability. For the case when both pulses are identical, the effect is traced back to the relative quantum phase of the interfering S-matrix amplitudes and explained within a simplified analytical model. Conversely, when the two laser pulses differ from each other, the pair-creation probability depends not only on the time delay but, in general, also on the temporal order of the pulses.
How Mathematics Describes Life
Teklu, Abraham
2017-01-01
The circle of life is something we have all heard of from somewhere, but we don't usually try to calculate it. For some time we have been working on analyzing a predator-prey model to better understand how mathematics can describe life, in particular the interaction between two different species. The model we are analyzing is called the Holling-Tanner model, and it cannot be solved analytically. The Holling-Tanner model is a very common model in population dynamics because it is a simple descriptor of how predators and prey interact. The model is a system of two differential equations. The model is not specific to any particular set of species and so it can describe predator-prey species ranging from lions and zebras to white blood cells and infections. One thing all these systems have in common are critical points. A critical point is a value for both populations that keeps both populations constant. It is important because at this point the differential equations are equal to zero. For this model there are two critical points, a predator free critical point and a coexistence critical point. Most of the analysis we did is on the coexistence critical point because the predator free critical point is always unstable and frankly less interesting than the coexistence critical point. What we did is consider two regimes for the differential equations, large B and small B. B, A, and C are parameters in the differential equations that control the system where B measures how responsive the predators are to change in the population, A represents predation of the prey, and C represents the satiation point of the prey population. For the large B case we were able to approximate the system of differential equations by a single scalar equation. For the small B case we were able to predict the limit cycle. The limit cycle is a process of the predator and prey populations growing and shrinking periodically. This model has a limit cycle in the regime of small B, that we solved for
Pyak, P. E.; Usachenko, V. I.
2018-03-01
The phenomenon of pronounced peak structure(s) of longitudinal momentum distributions as well as a spike-like structure of low-energy spectra of photoelectrons emitted from laser-irradiated Ar and Ne atoms in a single ionization process is theoretically studied in the tunneling and multiphoton regimes of ionization. The problem is addressed assuming only the direct above-threshold ionization (ATI) as a physical mechanism underlying the phenomenon under consideration (viz. solely contributing to observed photoelectron momentum distributions (PMD)) and using the Coulomb-Volkov (CV) ansatz within the frame of conventional strong-field approximation (SFA) applied in the length-gauge formulation. The developed CV-SFA approach also incorporates the density functional theory essentially exploited for numerical composition of initial (laser-free) atomic state(s) constructed from atomic orbitals of Gaussian type. Our presented CV-SFA based (and laser focal-volume averaged) calculation results proved to be well reproducing both the pronounced double-peak and/or ATI-like multi-peak structure(s) experimentally observed in longitudinal PMD under conditions of tunneling and/or multiphoton regime, respectively. In addition, our CV-SFA results presented for tunneling regime also suggest and remarkably reproduce a pronounced structure observed in relevant experiments as a ‘spike-like’ enhanced maximum arising in low-energy region (around the value of about 1 eV) of photoelectron spectra. The latter consistency allows to identify and interpret these results as the so-called low-energy structure (LES) since the phenomenon proved to appear as the most prominent if the influence of Coulomb potential on photoelectron continuum states is maximally taken into account under calculations (viz. if the parameter Z in CV’s functions is put equal to 1). Moreover, the calculated LES proved to correspond (viz., established as closely related) to the mentioned double-peak structure arising
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
Energy Technology Data Exchange (ETDEWEB)
Chan, Chi-kwan; Psaltis, Dimitrios; Özel, Feryal; Marrone, Daniel [Steward Observatory and Department of Astronomy, University of Arizona, 933 N. Cherry Avenue, Tucson, AZ 85721 (United States); Medeiros, Lia [Department of Physics, Broida Hall, University of California, Santa Barbara, Santa Barbara, CA 93106 (United States); Sadowski, Aleksander [MIT Kavli Institute for Astrophysics and Space Research, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Narayan, Ramesh, E-mail: chanc@email.arizona.edu [Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
2015-10-20
We explore the variability properties of long, high-cadence general relativistic magnetohydrodynamic (GRMHD) simulations across the electromagnetic spectrum using an efficient, GPU-based radiative transfer algorithm. We focus on both standard and normal evolution (SANE) and magnetically arrested disk (MAD) simulations with parameters that successfully reproduce the time-averaged spectral properties of Sgr A* and the size of its image at 1.3 mm. We find that the SANE models produce short-timescale variability with amplitudes and power spectra that closely resemble those inferred observationally. In contrast, MAD models generate only slow variability at lower flux levels. Neither set of models shows any X-ray flares, which most likely indicates that additional physics, such as particle acceleration mechanisms, need to be incorporated into the GRMHD simulations to account for them. The SANE models show strong, short-lived millimeter/infrared (IR) flares, with short (≲1 hr) time lags between the millimeter and IR wavelengths, that arise from the combination of short-lived magnetic flux tubes and strong-field gravitational lensing near the horizon. Such events provide a natural explanation for the observed IR flares with no X-ray counterparts.
Hori, K.; Teed, R. J.; Jones, C. A.
2018-03-01
We investigate slow magnetic Rossby waves in convection-driven dynamos in rotating spherical shells. Quasi-geostrophic waves riding on a mean zonal flow may account for some of the geomagnetic westward drifts and have the potential to allow the toroidal field strength within the planetary fluid core to be estimated. We extend the work of Hori et al. (2015) to include a wider range of models, and perform a detailed analysis of the results. We find that a predicted dispersion relation matches well with the longitudinal drifts observed in our strong-field dynamos. We discuss the validity of our linear theory, since we also find that the nonlinear Lorentz terms influence the observed waveforms. These wave motions are excited by convective instability, which determines the preferred azimuthal wavenumbers. Studies of linear rotating magnetoconvection have suggested that slow magnetic Rossby modes emerge in the magnetostrophic regime, in which the Lorentz and Coriolis forces are in balance in the vorticity equation. We confirm this to be predominant balance for the slow waves we have detected in nonlinear dynamo systems. We also show that a completely different wave regime emerges if the magnetic field is not present. Finally we report the corresponding radial magnetic field variations observed at the surface of the shell in our simulations and discuss the detectability of these waves in the geomagnetic secular variation.
International Nuclear Information System (INIS)
Silaev, A.A.; Ryabikin, M.Yu.; Vvedenskii, N.V.
2010-01-01
Complete text of publication follows. The development of theoretical approaches to the description of strong-field phenomena caused by ultrashort laser pulses is optical for studying the interaction of atoms and molecules with intense laser fields. In this work, we address two phenomena which attract much attention and can be observed under similar experimental conditions, namely, when a gas is ionized by ultrashort laser pulse. The first phenomenon is the excitation of high-order harmonics of the driving field frequency in the electron current, which leads to the generation of vacuum ultraviolet and soft X-ray radiation, as well as the attosecond pulse production. The second phenomenon is the excitation of a quasi-dc residual current in the laser-produced plasma, which results in the generation of radiation having a frequency below the laser one, e.g., terahertz waves. We present new one-dimensional (1D) and two-dimensional (2D) quantum-mechanical models for the description of such phenomena for the case a hydrogen (H) atom, and the generalization of these models to the case of various noble-gas atoms. The shape of the electrostatic potential produced by an atomic ion is shown to influence significantly the rates of the processes in the dynamics of atomic electron, and even more, the rates of the tunneling and above-barrier ionization, which is of utmost importance for the considered phenomena. The results of solving the time-dependent Schroedinger equation with the 1D and 2D potentials, which we propose, are compared with the results of the ab initio three-dimensional calculations for the H atom. We find the regions of laser pulse parameters, where the results obtained with proposed models have much better accuracy than the results provided by the models used earlier. Acknowledgements. This work was supported by the Russian Foundation for Basic Research, the Presidential Council on Grants of the Russian Federation, the Ministry of Education and Science of the
Energy Technology Data Exchange (ETDEWEB)
Ali, Ahmed; Blaschke, David; Issadykov, Aidos; Ivanov, Mikhail (eds.)
2017-04-15
The Helmholtz International Summer School (HISS) entitled ''Quantum Field Theory at the Limits: from Strong Fields to Heavy Quarks (SF→HQ)'', was held in the period July 18-30, 2016 at the Bogolyubov Laboratory of Theoretical Physics (BLTP) of the Joint Institute for Nuclear Research (JINR) in Dubna, Russia, as part of the activities of the Dubna International Advanced School of Theoretical Physics (DIAS-TH). It was co-organized by Ahmed Ali (DESY Hamburg), David Blaschke (JINR Dubna, MEPhI and Univ. Wroclaw), Holger Gies (HI Jena), and Mikhail Ivanov (JINR Dubna), and was attended by 82 participants (faculty+students), not counting the JINR physicists who attended some lectures as non-registered participants. The school (SF→HQ) continued the workshops and schools of the HISS series held earlier in Dubna (1993, 1996, 2000, 2005, 2008, 2013), Bad Honnef (1994) and Rostock (1997). The scientific program of the school consisted of five regular (one-hour long) lectures in the morning and afternoon sessions, with typically two contributed talks given by younger participants (students and postdocs), each half-hour long, in the late afternoons. Altogether, we had sixty lectures by the faculty and participants. In addition, black-board exercises were held in the post-lunch periods on selected aspects of strong fields and field theory. The HISS series of schools has played an important role in bringing together an international faculty and young physicists (Ph.D. and postdocs), mostly from Russia and Germany, but increasingly also from other countries, including those affiliated to JINR Dubna. They participate in two-week long intense scientific discourse, mainly dedicated lectures on selected topics covering the foundation and the frontiers of high energy physics and cosmology. The novelty of this year's school was its bifocal interest, which brought together two different physical science communities - particle and laser physicists. There were
International Nuclear Information System (INIS)
Ali, Ahmed; Blaschke, David; Issadykov, Aidos; Ivanov, Mikhail
2017-04-01
The Helmholtz International Summer School (HISS) entitled ''Quantum Field Theory at the Limits: from Strong Fields to Heavy Quarks (SF→HQ)'', was held in the period July 18-30, 2016 at the Bogolyubov Laboratory of Theoretical Physics (BLTP) of the Joint Institute for Nuclear Research (JINR) in Dubna, Russia, as part of the activities of the Dubna International Advanced School of Theoretical Physics (DIAS-TH). It was co-organized by Ahmed Ali (DESY Hamburg), David Blaschke (JINR Dubna, MEPhI and Univ. Wroclaw), Holger Gies (HI Jena), and Mikhail Ivanov (JINR Dubna), and was attended by 82 participants (faculty+students), not counting the JINR physicists who attended some lectures as non-registered participants. The school (SF→HQ) continued the workshops and schools of the HISS series held earlier in Dubna (1993, 1996, 2000, 2005, 2008, 2013), Bad Honnef (1994) and Rostock (1997). The scientific program of the school consisted of five regular (one-hour long) lectures in the morning and afternoon sessions, with typically two contributed talks given by younger participants (students and postdocs), each half-hour long, in the late afternoons. Altogether, we had sixty lectures by the faculty and participants. In addition, black-board exercises were held in the post-lunch periods on selected aspects of strong fields and field theory. The HISS series of schools has played an important role in bringing together an international faculty and young physicists (Ph.D. and postdocs), mostly from Russia and Germany, but increasingly also from other countries, including those affiliated to JINR Dubna. They participate in two-week long intense scientific discourse, mainly dedicated lectures on selected topics covering the foundation and the frontiers of high energy physics and cosmology. The novelty of this year's school was its bifocal interest, which brought together two different physical science communities - particle and laser physicists. There were
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.
Pharmacobezoars described and demystified.
Simpson, Serge-Emile
2011-02-01
A bezoar is a concretion of foreign material that forms and persists in the gastrointestinal tract. Bezoars are classified by their material origins. Phytobezoars contain plant material, trichobezoars contain hair, lactobezoars contain milk proteins, and pharmacobezoars contain pharmaceutical products. Tablets, suspensions, and even insoluble drug delivery vehicles can, on rare occasions, and sometimes under specific circumstances, form pharmacobezoars. The goal of this review is to catalog and examine all of the available reports in the English language medical literature that convincingly describe the formation and management of pharmacobezoars. Articles included in this review were identified by performing searches using the terms "bezoar," "pharmacobezoar," and "concretion" in the following databases: OVID MEDLINE, PubMed, and JSTOR. The complete MEDLINE and JSTOR holdings were included in the search without date ranges. The results were limited to English language publications. Articles that described nonmedication bezoars were not included in the review. Articles describing phytobezoars, food bezoars, fecal impactions, illicit drug packet ingestions, enteral feeding material bezoars, and hygroscopic diet aid bezoars were excluded. The bibliographic references within the articles already accumulated were then examined in order to gather additional pharmacobezoar cases. The cases are grouped by pharmaceutical agent that formed the bezoar, and groupings are arranged in alphabetical order. Discussions and conclusions specific to each pharmaceutical agent are included in that agent's subheading. Patterns and themes that emerged in the review of the assembled case reports are reviewed and presented in a more concise format. Pharmacobezoars form under a wide variety of circumstances and in a wide variety of patients. They are difficult to diagnose reliably. Rules for suspecting, diagnosing, and properly managing a pharmacobezoar are highly dependent on the
[Deep mycoses rarely described].
Charles, D
1986-01-01
Beside deep mycoses very well known: histoplasmosis, candidosis, cryptococcosis, there are other mycoses less frequently described. Some of them are endemic in some countries: South American blastomycosis in Brazil, coccidioidomycosis in California; some others are cosmopolitan and may affect everyone: sporotrichosis, or may affect only immunodeficient persons: mucormycosis. They do not spare Africa, we may encounter basidiobolomycosis, rhinophycomycosis, dermatophytosis, sporotrichosis and, more recently reported, rhinosporidiosis. Important therapeutic progresses have been accomplished with amphotericin B and with antifungus imidazole compounds (miconazole and ketoconazole). Surgical intervention is sometime recommended in chromomycosis and rhinosporidiosis.
Ivanov, I. A.
2015-12-01
We study the origin of the cusp structure in the transverse or lateral electron momentum distribution (TEMD) for the process of tunneling ionization driven by a linearly polarized laser pulse. We show that the appearance of the cusp in the TEMD can be explained as follows. Projection on the set of the Coulomb scattering states leads to the appearance of elementary cusps which have a simple structure as functions of the lateral momentum. This structure is independent of the detailed dynamics of the ionization process and can be described analytically. These elementary cusps can be used to describe the cusp structure in TEMD.
Hara, Takuya; Luhmann, Janet G.; Halekas, Jasper S.; Espley, Jared R.; Seki, Kanako; Brain, David A.; Hasegawa, Hiroshi; McFadden, James P.; Mitchell, David L.; Mazelle, Christian;
2016-01-01
We present initial results of strong field amplitude flux ropes observed by Mars Atmosphere and Volatile EvolutioN (MAVEN) mission around Mars during the interplanetary coronal mass ejection (ICME) passage on 8 March 2015. The observed durations were shorter than 5 s and the magnetic field magnitudes peaked above 80 nT, which is a few times stronger than those usually seen in the magnetosheath barrier. These are the first unique observations that MAVEN detected such flux ropes with a strong field at high altitudes (greater than 5000 km). Across these structures, MAVEN coincidentally measured planetary heavy ions with energies higher than a few keV. The spatial properties inferred from the Grad-Shafranov equation suggest that the speed of the structure can be estimated at least an order of magnitude faster than those previously reported quiet-time counterparts. Hence, the space weather event like the ICME passage can be responsible for generating the observed strong field, fast-traveling flux ropes.
Time- and frequency-resolved detection of atomic coherence in the regime of strong-field interaction with intense femtosecond laser pulses
International Nuclear Information System (INIS)
Konorov, S. O.; Hepburn, J. W.; Milner, V.
2011-01-01
Understanding the effect of strong laser pulses on the evolution of an atomic or molecular wave function is important in the context of coherent control in the strong-field regime, when power broadening and dynamic Stark shifts become comparable with or bigger than the bandwidth of the control field. We experimentally demonstrate the method of complete characterization of a complex-valued amplitude of a quantum state driven by a strong two-photon field. The method is based on coherent scattering of a weak probe pulse from the strong-field-induced atomic coherence, followed by the detection of the time- and frequency-resolved parametric four-wave-mixing signal. We show that the proposed technique corresponds to a cross-correlation frequency-resolved optical gating (XFROG) of the highly perturbed evolution of an atomic quantum state. Utilizing the XFROG retrieval algorithm, we determine both the amplitude and phase of an atomic wave function at any time moment throughout the interaction with the driving field. The direct retrieval of the time-dependent phase of the wave function, rather than the population dynamics only, enables us to observe the strong-field effects with arbitrary time and frequency resolution.
Observation and quantification of the quantum dynamics of a strong-field excited multi-level system.
Liu, Zuoye; Wang, Quanjun; Ding, Jingjie; Cavaletto, Stefano M; Pfeifer, Thomas; Hu, Bitao
2017-01-04
The quantum dynamics of a V-type three-level system, whose two resonances are first excited by a weak probe pulse and subsequently modified by another strong one, is studied. The quantum dynamics of the multi-level system is closely related to the absorption spectrum of the transmitted probe pulse and its modification manifests itself as a modulation of the absorption line shape. Applying the dipole-control model, the modulation induced by the second strong pulse to the system's dynamics is quantified by eight intensity-dependent parameters, describing the self and inter-state contributions. The present study opens the route to control the quantum dynamics of multi-level systems and to quantify the quantum-control process.
International Nuclear Information System (INIS)
Petrovic, Vladimir S.; Kim, Jaehee; Schorb, Sebastian; White, James; Cryan, James P.; Zipp, Lucas; Glownia, J. Michael; Broege, Douglas; Miyabe, Shungo; Tao, Hongli; Martinez, Todd; Bucksbaum, Philip H.
2013-01-01
Nonradiative energy dissipation in electronically excited polyatomic molecules proceeds through conical intersections, loci of degeneracy between electronic states. We observe a marked enhancement of laser-induced double ionization in the vicinity of a conical intersection during a non-radiative transition. We measured double ionization by detecting the kinetic energy of ions released by laser-induced strong-field fragmentation during the ring-opening transition between 1,3-cyclohexadiene and 1,3,5-hexatriene. The enhancement of the double ionization correlates with the conical intersection between the HOMO and LUMO orbitals
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X. The clas......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... 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...
Dissipative Strong-Field Electrodynamics
Gruzinov, Andrei
2007-01-01
A dissipative Lorentz-covariant Ohm's law which uses only the electromagnetic degrees of freedom is proposed. For large conductivity, Maxwell equations equipped with this Ohm's law reduce to the equations of Force-Free Electrodynamics (FFE) with small dissipative corrections, but only in the regions where the ideal FFE 4-current is space-like. This might indicate that the pulsar emission comes primarily from the magnetic separartrix.
Directory of Open Access Journals (Sweden)
Anna G. Ciriolo
2017-03-01
Full Text Available Over the last few decades, the investigation of ultrafast phenomena occurring in atoms, molecules and solid-state systems under a strong-field regime of light-matter interaction has attracted great attention. The increasing request for a suitable optical technology is significantly boosting the development of powerful ultrafast laser sources. In this framework, Optical Parametric Amplification (OPA is currently becoming a leading solution for applications in high-power ultra-broadband light burst generation. The main advantage provided by the OPA scheme consists of the possibility of exploring spectral ranges that are inaccessible by other laser technologies, as the InfraRed (IR window. In this paper, we will give an overview on recent progress in the development of high-power few-optical-cycle parametric amplifiers in the near-IR and in the mid-IR spectral domain. In particular, the design of the most advanced OPA implementations is provided, containing a discussion on the key technical aspects. In addition, a review on their application to the study of strong-field ultrafast physical processes is reported.
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.
International Nuclear Information System (INIS)
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)
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Meidam, Jeroen; Tsang, Ka Wa; Goldstein, Janna; Agathos, Michalis; Ghosh, Archisman; Haster, Carl-Johan; Raymond, Vivien; Samajdar, Anuradha; Schmidt, Patricia; Smith, Rory; Blackburn, Kent; Del Pozzo, Walter; Field, Scott E.; Li, Tjonnie; Pürrer, Michael; Van Den Broeck, Chris; Veitch, John; Vitale, Salvatore
2018-02-01
Thanks to the recent discoveries of gravitational wave signals from binary black hole mergers by Advanced Laser Interferometer Gravitational Wave Observatory and Advanced Virgo, the genuinely strong-field dynamics of spacetime can now be probed, allowing for stringent tests of general relativity (GR). One set of tests consists of allowing for parametrized deformations away from GR in the template waveform models and then constraining the size of the deviations, as was done for the detected signals in previous work. In this paper, we construct reduced-order quadratures so as to speed up likelihood calculations for parameter estimation on future events. Next, we explicitly demonstrate the robustness of the parametrized tests by showing that they will correctly indicate consistency with GR if the theory is valid. We also check to what extent deviations from GR can be constrained as information from an increasing number of detections is combined. Finally, we evaluate the sensitivity of the method to possible violations of GR.
Loh, Zhi-Heng; Khalil, Munira; Correa, Raoul E; Santra, Robin; Buth, Christian; Leone, Stephen R
2007-04-06
Femtosecond high-order harmonic transient absorption spectroscopy is used to resolve the complete |j,m quantum state distribution of Xe+ produced by optical strong-field ionization of Xe atoms at 800 nm. Probing at the Xe N4/5 edge yields a population distribution rhoj,|m| of rho3/2,1/2ratiorho1/2,1/2ratiorho3/2,3/2=75+/-6 :12+/-3 :13+/-6%. The result is compared to a tunnel ionization calculation with the inclusion of spin-orbit coupling, revealing nonadiabatic ionization behavior. The sub-50-fs time resolution paves the way for tabletop extreme ultraviolet absorption probing of ultrafast dynamics.
Directory of Open Access Journals (Sweden)
Lijing Shao
2017-10-01
Full Text Available Pulsar timing and laser-interferometer gravitational-wave (GW detectors are superb laboratories to study gravity theories in the strong-field regime. Here, we combine these tools to test the mono-scalar-tensor theory of Damour and Esposito-Farèse (DEF, which predicts nonperturbative scalarization phenomena for neutron stars (NSs. First, applying Markov-chain Monte Carlo techniques, we use the absence of dipolar radiation in the pulsar-timing observations of five binary systems composed of a NS and a white dwarf, and eleven equations of state (EOSs for NSs, to derive the most stringent constraints on the two free parameters of the DEF scalar-tensor theory. Since the binary-pulsar bounds depend on the NS mass and the EOS, we find that current pulsar-timing observations leave scalarization windows, i.e., regions of parameter space where scalarization can still be prominent. Then, we investigate if these scalarization windows could be closed and if pulsar-timing constraints could be improved by laser-interferometer GW detectors, when spontaneous (or dynamical scalarization sets in during the early (or late stages of a binary NS (BNS evolution. For the early inspiral of a BNS carrying constant scalar charge, we employ a Fisher-matrix analysis to show that Advanced LIGO can improve pulsar-timing constraints for some EOSs, and next-generation detectors, such as the Cosmic Explorer and Einstein Telescope, will be able to improve those bounds for all eleven EOSs. Using the late inspiral of a BNS, we estimate that for some of the EOSs under consideration, the onset of dynamical scalarization can happen early enough to improve the constraints on the DEF parameters obtained by combining the five binary pulsars. Thus, in the near future, the complementarity of pulsar timing and direct observations of GWs on the ground will be extremely valuable in probing gravity theories in the strong-field regime.
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...
Topological approximations of multisets
Directory of Open Access Journals (Sweden)
El-Sayed A. Abo-Tabl
2013-07-01
Full Text Available Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we define and investigate three types of lower and upper multiset approximations of any multiset. These types based on the multiset base of multiset topology induced by a multiset relation. Moreover, the relationships between generalized rough msets and mset topologies are given. In addition, an illustrative example is given to illustrate the relationships between different types of generalized definitions of rough multiset approximations.
Expectation Consistent Approximate Inference
DEFF Research Database (Denmark)
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...
The nuclear magnetic moment of 208Bi and its relevance for a test of bound-state strong-field QED
Schmidt, S.; Billowes, J.; Bissell, M. L.; Blaum, K.; Garcia Ruiz, R. F.; Heylen, H.; Malbrunot-Ettenauer, S.; Neyens, G.; Nörtershäuser, W.; Plunien, G.; Sailer, S.; Shabaev, V. M.; Skripnikov, L. V.; Tupitsyn, I. I.; Volotka, A. V.; Yang, X. F.
2018-04-01
The hyperfine structure splitting in the 6p3 3/2 4S → 6p2 7 s 1/2 4P transition at 307 nm in atomic 208Bi was measured with collinear laser spectroscopy at ISOLDE, CERN. The hyperfine A and B factors of both states were determined with an order of magnitude improved accuracy. Based on these measurements, theoretical input for the hyperfine structure anomaly, and results from hyperfine measurements on hydrogen-like and lithium-like 209Bi80+,82+, the nuclear magnetic moment of 208Bi has been determined to μ (208Bi) = + 4.570 (10)μN. Using this value, the transition energy of the ground-state hyperfine splitting in hydrogen-like and lithium-like 208Bi80+,82+ and their specific difference of -67.491(5)(148) meV are predicted. This provides a means for an experimental confirmation of the cancellation of nuclear structure effects in the specific difference in order to exclude such contributions as the cause of the hyperfine puzzle, the recently reported 7-σ discrepancy between experiment and bound-state strong-field QED calculations of the specific difference in the hyperfine structure splitting of 209Bi80+,82+.
Approximations of Fuzzy Systems
Directory of Open Access Journals (Sweden)
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
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. Loose-cluster approximation. Continuous curve Our Theory. Dashed curve Our Simulation. Loose cluster approx. not only. captures -the anomalous. qualitative features but is also,. quantitatively, quite accurate. Notes:
Bosma, Wieb
1990-01-01
The distribution is determined of some sequences that measure how well a number is approximated by its mediants (or intermediate continued fraction convergents). The connection with a theorem of Fatou, as well as a new proof of this, is given.
International Nuclear Information System (INIS)
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
Approximation Behooves Calibration
DEFF Research Database (Denmark)
da Silva Ribeiro, André Manuel; Poulsen, Rolf
2013-01-01
Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009.......Calibration based on an expansion approximation for option prices in the Heston stochastic volatility model gives stable, accurate, and fast results for S&P500-index option data over the period 2005–2009....
Five Describing Factors of Dyslexia
Tamboer, Peter; Vorst, Harrie C. M.; Oort, Frans J.
2016-01-01
Two subtypes of dyslexia (phonological, visual) have been under debate in various studies. However, the number of symptoms of dyslexia described in the literature exceeds the number of subtypes, and underlying relations remain unclear. We investigated underlying cognitive features of dyslexia with exploratory and confirmatory factor analyses. A…
The Post-Newtonian Approximation for Relativistic Compact Binaries
Directory of Open Access Journals (Sweden)
Futamase Toshifumi
2007-03-01
Full Text Available We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive post-Newtonian equations of motion for relativistic compact binaries based on a surface integral approach and the strong field point particle limit. As an application we derive third post-Newtonian equations of motion for relativistic compact binaries which respect the Lorentz invariance in the post-Newtonian perturbative sense, admit a conserved energy, and are free from any ambiguity.
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
Improved Approximation Algorithm for
Byrka, Jaroslaw; Li, S.; Rybicki, Bartosz
2014-01-01
We study the k-level uncapacitated facility location problem (k-level UFL) in which clients need to be connected with paths crossing open facilities of k types (levels). In this paper we first propose an approximation algorithm that for any constant k, in polynomial time, delivers solutions of
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.
Generalized Approximate Message Passing
DEFF Research Database (Denmark)
Oxvig, Christian Schou; Arildsen, Thomas; Larsen, Torben
2017-01-01
This tech report details a collection of results related to the Generalised Approximate Message Passing (GAMP) algorithm. It is a summary of the results that the authors have found critical in understanding the GAMP algorithm. In particular, emphasis is on the details that are crucial in implemen...
Wolff, Hans
This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic…
DEFF Research Database (Denmark)
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...
Procedure to describe clavicular motion.
Gutierrez Delgado, Guivey; De Beule, Matthieu; Ortega Cardentey, Dolgis R; Segers, Patrick; Iznaga Benítez, Arsenio M; Rodríguez Moliner, Tania; Verhegghe, Benedict; Palmans, Tanneke; Van Hoof, Tom; Van Tongel, Alexander
2017-03-01
For many years, researchers have attempted to describe shoulder motions by using different mathematical methods. The aim of this study was to describe a procedure to quantify clavicular motion. The procedure proposed for the kinematic analysis consists of 4 main processes: 3 transcortical pins in the clavicle, motion capture, obtaining 3-dimensional bone models, and data processing. Clavicular motion by abduction (30° to 150°) and flexion (55° to 165°) were characterized by an increment of retraction of 27° to 33°, elevation of 25° to 28°, and posterior rotation of 14° to 15°, respectively. In circumduction, clavicular movement described an ellipse, which was reflected by retraction and elevation. Kinematic analysis shows that the articular surfaces move by simultaneously rolling and sliding on the convex surface of the sternum for the 3 movements of abduction, flexion, and circumduction. The use of 3 body landmarks in the clavicle and the direct measurement of bone allowed description of the osteokinematic and arthrokinematic movement of the clavicle. Copyright © 2017 Journal of Shoulder and Elbow Surgery Board of Trustees. Published by Elsevier Inc. All rights reserved.
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.
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...
Fragments of approximate counting
Czech Academy of Sciences Publication Activity Database
Buss, S.R.; Kolodziejczyk, L. A.; Thapen, Neil
2014-01-01
Roč. 79, č. 2 (2014), s. 496-525 ISSN 0022-4812 R&D Projects: GA AV ČR IAA100190902 Institutional support: RVO:67985840 Keywords : approximate counting * bounded arithmetic * ordering principle Subject RIV: BA - General Mathematics Impact factor: 0.541, year: 2014 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9287274&fileId=S0022481213000376
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.
Approximate Bayesian recursive estimation
Czech Academy of Sciences Publication Activity Database
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
Topics in Metric Approximation
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
Completely Described Undirected Graph Structure
Directory of Open Access Journals (Sweden)
G. S. Ivanova
2016-01-01
, approximated by the quadratic function, which is consistent with the theoretical estimates. The experimental results of studies, in general, prove those of theoretical estimates.
Persistence Statements: Describing Digital Stickiness
Directory of Open Access Journals (Sweden)
John Kunze
2017-08-01
Full Text Available In this paper we present a draft vocabulary for making “persistence statements.” These are simple tools for pragmatically addressing the concern that anyone feels upon experiencing a broken web link. Scholars increasingly use scientific and cultural assets in digital form, but choosing which among many objects to cite for the long term can be difficult. There are few well-defined terms to describe the various kinds and qualities of persistence that object repositories and identifier resolvers do or don’t provide. Given an object’s identifier, one should be able to query a provider to retrieve human- and machine-readable information to help judge the level of service to expect and help gauge whether the identifier is durable enough, as a sort of long-term bet, to include in a citation. The vocabulary should enable providers to articulate persistence policies and set user expectations.
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
International Nuclear Information System (INIS)
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)
Cyclic approximation to stasis
Directory of Open Access Journals (Sweden)
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.
Approximate Euclidean Ramsey theorems
Directory of Open Access Journals (Sweden)
Adrian Dumitrescu
2011-04-01
Full Text Available According to a classical result of Szemerédi, every dense subset of 1,2,…,N contains an arbitrary long arithmetic progression, if N is large enough. Its analogue in higher dimensions due to Fürstenberg and Katznelson says that every dense subset of {1,2,…,N}d contains an arbitrary large grid, if N is large enough. Here we generalize these results for separated point sets on the line and respectively in the Euclidean space: (i every dense separated set of points in some interval [0,L] on the line contains an arbitrary long approximate arithmetic progression, if L is large enough. (ii every dense separated set of points in the d-dimensional cube [0,L]d in Rd contains an arbitrary large approximate grid, if L is large enough. A further generalization for any finite pattern in Rd is also established. The separation condition is shown to be necessary for such results to hold. In the end we show that every sufficiently large point set in Rd contains an arbitrarily large subset of almost collinear points. No separation condition is needed in this case.
Approximate Bayesian computation.
Directory of Open Access Journals (Sweden)
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.
The quasilocalized charge approximation
International Nuclear Information System (INIS)
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
(Approximate) Uncertain Skylines
DEFF Research Database (Denmark)
Afshani, Peyman; Agarwal, Pankaj K.; Arge, Lars Allan
2011-01-01
Given a set of points with uncertain locations, we consider the problem of computing the probability of each point lying on the skyline, that is, the probability that it is not dominated by any other input point. If each point’s uncertainty is described as a probability distribution over a discre...
(Approximate) Uncertain Skylines
DEFF Research Database (Denmark)
Afshani, Peyman; Agarwal, Pankaj K.; Arge, Lars
2013-01-01
Given a set of points with uncertain locations, we consider the problem of computing the probability of each point lying on the skyline, that is, the probability that it is not dominated by any other input point. If each point’s uncertainty is described as a probability distribution over a discre...
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...
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.
Improved Dutch Roll Approximation for Hypersonic Vehicle
Directory of Open Access Journals (Sweden)
Liang-Liang Yin
2014-06-01
Full Text Available An improved dutch roll approximation for hypersonic vehicle is presented. From the new approximations, the dutch roll frequency is shown to be a function of the stability axis yaw stability and the dutch roll damping is mainly effected by the roll damping ratio. In additional, an important parameter called roll-to-yaw ratio is obtained to describe the dutch roll mode. Solution shows that large-roll-to-yaw ratio is the generate character of hypersonic vehicle, which results the large error for the practical approximation. Predictions from the literal approximations derived in this paper are compared with actual numerical values for s example hypersonic vehicle, results show the approximations work well and the error is below 10 %.
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
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...
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.
Comparative Study of Approximate Multipliers
Masadeh, Mahmoud; Hasan, Osman; Tahar, Sofiene
2018-01-01
Approximate multipliers are widely being advocated for energy-efficient computing in applications that exhibit an inherent tolerance to inaccuracy. However, the inclusion of accuracy as a key design parameter, besides the performance, area and power, makes the identification of the most suitable approximate multiplier quite challenging. In this paper, we identify three major decision making factors for the selection of an approximate multipliers circuit: (1) the type of approximate full adder...
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.
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
Low Rank Approximation Algorithms, Implementation, Applications
Markovsky, Ivan
2012-01-01
Matrix low-rank approximation is intimately related to data modelling; a problem that arises frequently in many different fields. Low Rank Approximation: Algorithms, Implementation, Applications is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory. Applications described include: system and control theory: approximate realization, model reduction, output error, and errors-in-variables identification; signal processing: harmonic retrieval, sum-of-damped exponentials, finite impulse response modeling, and array processing; machine learning: multidimensional scaling and recommender system; computer vision: algebraic curve fitting and fundamental matrix estimation; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; ...
Quasilinear theory without the random phase approximation
International Nuclear Information System (INIS)
Weibel, E.S.; Vaclavik, J.
1980-08-01
The system of quasilinear equations is derived without making use of the random phase approximation. The fluctuating quantities are described by the autocorrelation function of the electric field using the techniques of Fourier analysis. The resulting equations posses the necessary conservation properties, but comprise new terms which hitherto have been lost in the conventional derivations
GAS LASERS FOR STRONG-FIELD APPLICATIONS.
Energy Technology Data Exchange (ETDEWEB)
POGORELSKY,I.V.
2004-09-15
Atomic-, molecular- and excimer-gas lasers employ variety of pumping schemes including electric discharge, optical, or chemical reactions and cover a broad spectral range from UV to far-IR. Several types of gas lasers can produce multi-kilojoule pulses and kilowatts of average power. Among them, excimer- and high-pressure molecular lasers have sufficient bandwidth for generating pico- and femtosecond pulses. Projects are underway and prospects are opening up to bring ultrafast gas laser technology to the front lines of advanced accelerator applications.
Experimental investigation of strong field trident production
Esberg, J.; Kirsebom, K.; Knudsen, H.; Thomsen, H.D.; Uggerhøj, E.; Uggerhøj, U.I.; Sona, P.; Mangiarotti, A.; Ketel, T.J.; Ditzdar, A.; Dalton, M.M.; Ballestrero, S.; Connell, S.H.
2010-01-01
We show by experiment that an electron impinging on an electric field that is of critical magnitude in its rest frame, may produce an electron-positron pair. Our measurements address higher-order QED, using the strong electric fields obtainable along particular crystallographic directions in single
Experimental investigation of strong field trident production
Esberg, J; Knudsen, H; Thomsen, H D; Uggerhøj, E; Uggerhøj, U I; Sona, P; Mangiarotti, A; Ketel, T J; Dizdar, A; Dalton, M M; Ballestrero, S; Connell, S H
2010-01-01
We show by experiment that an electron impinging on an electric field that is of critical magnitude in its rest frame, may produce an electron-positron pair. Our measurements address higher-order QED, using the strong electric fields obtainable along particular crystallographic directions in single crystals. For the amorphous material our data are in good agreement with theory, whereas a discrepancy with theory on the magnitude of the trident enhancement is found in the precisely aligned case where the strong electric field acts.
Approximation by planar elastic curves
DEFF Research Database (Denmark)
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...
Anytime classification by ontology approximation
Schlobach, S.; Blaauw, E.; El Kebir, M.; Ten Teije, A.; Van Harmelen, F.; Bortoli, S.; Hobbelman, M.C.; Millian, K.; Ren, Y.; Stam, S.; Thomassen, P.; Van Het Schip, R.; Van Willigem, W.
2007-01-01
Reasoning with large or complex ontologies is one of the bottle-necks of the Semantic Web. In this paper we present an anytime algorithm for classification based on approximate subsumption. We give the formal definitions for approximate subsumption, and show its monotonicity and soundness; we show
Some results in Diophantine approximation
DEFF Research Database (Denmark)
Pedersen, Steffen Højris
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...... 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...... in the formal Laurent series over F3. The first paper is on intrinsic Diophantine approximation in the Cantor set in the formal Laurent series over F3. The summary contains a short motivation, the results of the paper and sketches of the proofs, mainly focusing on the ideas involved. The details of the proofs...
On the dipole approximation with error estimates
Boßmann, Lea; Grummt, Robert; Kolb, Martin
2018-01-01
The dipole approximation is employed to describe interactions between atoms and radiation. It essentially consists of neglecting the spatial variation of the external field over the atom. Heuristically, this is justified by arguing that the wavelength is considerably larger than the atomic length scale, which holds under usual experimental conditions. We prove the dipole approximation in the limit of infinite wavelengths compared to the atomic length scale and estimate the rate of convergence. Our results include N-body Coulomb potentials and experimentally relevant electromagnetic fields such as plane waves and laser pulses.
Approximate Implicitization Using Linear Algebra
Directory of Open Access Journals (Sweden)
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.
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
Shearlets and Optimally Sparse Approximations
DEFF Research Database (Denmark)
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
2012-01-01
of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model class, and approximation properties were measured by considering the decay rate of the $L^2$ error of the best $N$-term approximation. Shearlet systems are to date the only representation system, which provide...... 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....
Mathematical algorithms for approximate reasoning
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
The Grammar of Approximating Number Pairs
Eriksson, Kimmo; Bailey, Drew H.; Geary, David C.
2009-01-01
We studied approximating pairs of numbers (a, b) used to estimate quantity in a single phrase (“two, three years ago”). Pollmann and Jansen (1996) found that only a few of the many possible pairs are actually used, suggesting an interaction between the ways in which people estimate quantity and their use of quantitative phrases in colloquial speech. They proposed a set of rules that describe which approximating pairs are used in Dutch phrases. We revisit this issue in an analysis of Swedish and American language corpora and in a series of three experiments in which Swedish and American adults rated the acceptability of various approximating pairs, and created approximating pairs of their own in response to various estimation tasks. We find evidence for Pollmann’s and Jansen’s rules in both Swedish and English phrases, but also identify additional rules and substantial individual and cross-language variation. We discuss implications for the origin of this loose “grammar” of approximating pairs. PMID:20234023
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.
The grammar of approximating number pairs.
Eriksson, Kimmo; Bailey, Drew H; Geary, David C
2010-04-01
In the present article, we studied approximating pairs of numbers (a, b) that were used to estimate quantity in a single phrase ("two, three years ago"). Pollmann and Jansen (1996) found that only a few of the many possible pairs are actually used, suggesting an interaction between the ways in which people estimate quantity and their use of quantitative phrases in colloquial speech. They proposed a set of rules that describe which approximating pairs are used in Dutch phrases. We revisited this issue in an analysis of Swedish and American language corpora and in a series of three experiments in which Swedish and American adults rated the acceptability of various approximating pairs and created approximating pairs of their own in response to various estimation tasks. We found evidence for Pollmann and Jansen's rules in both Swedish and English phrases, but we also identified additional rules and substantial individual and cross-language variation. We will discuss implications for the origin of this loose "grammar" of approximating pairs.
Traveltime approximations for inhomogeneous HTI media
Alkhalifah, Tariq Ali
2011-01-01
Traveltimes information is convenient for parameter estimation especially if the medium is described by an anisotropic set of parameters. This is especially true if we could relate traveltimes analytically to these medium parameters, which is generally hard to do in inhomogeneous media. As a result, I develop traveltimes approximations for horizontaly transversely isotropic (HTI) media as simplified and even linear functions of the anisotropic parameters. This is accomplished by perturbing the solution of the HTI eikonal equation with respect to η and the azimuthal symmetry direction (usually used to describe the fracture direction) from a generally inhomogeneous elliptically anisotropic background medium. The resulting approximations can provide accurate analytical description of the traveltime in a homogenous background compared to other published moveout equations out there. These equations will allow us to readily extend the inhomogenous background elliptical anisotropic model to an HTI with a variable, but smoothly varying, η and horizontal symmetry direction values. © 2011 Society of Exploration Geophysicists.
Stochastic Oscillations of General Relativistic Disks Described
Indian Academy of Sciences (India)
4
Reply 3: According to the referee's suggestion we have added an Appendix, where we present the several definitions of fractional derivatives, and obtain the differential approximation for Caputo derivative. 4) A brief description of the numerical algorithm used to integrate the fractional differential equation is also necessary ...
Optical pulse propagation with minimal approximations
Kinsler, Paul
2008-01-01
Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations -- including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first order propagation equation using a minimum of approximations and a straightforward "factorization" mathematical scheme. The approach generates exact coupled bi-directional equations, after which it is clear that the description can be reduced to a singl...
Approximate number sense theory or approximate theory of magnitude?
Content, Alain; Velde, Michael Vande; Adriano, Andrea
2017-01-01
Leibovich et al. argue that the evidence in favor of a perceptual mechanism devoted to the extraction of numerosity from visual collections is unsatisfactory and propose to replace it with an unspecific mechanism capturing approximate magnitudes from continuous dimensions. We argue that their representation of the evidence is incomplete and that their theoretical proposal is too vague to be useful.
Approximate Matching of Hierarchial Data
DEFF Research Database (Denmark)
Augsten, Nikolaus
The goal of this thesis is to design, develop, and evaluate new methods for the approximate matching of hierarchical data represented as labeled trees. In approximate matching scenarios two items should be matched if they are similar. Computing the similarity between labeled trees is hard...... formally proof that the pq-gram index can be incrementally updated based on the log of edit operations without reconstructing intermediate tree versions. The incremental update is independent of the data size and scales to a large number of changes in the data. We introduce windowed pq...... as in addition to the data values also the structure must be considered. A well-known measure for comparing trees is the tree edit distance. It is computationally expensive and leads to a prohibitively high run time. Our solution for the approximate matching of hierarchical data are pq-grams. The pq...
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.
Face Recognition using Approximate Arithmetic
DEFF Research Database (Denmark)
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...... as possible. The use of diﬀerent approaches such as neural networks and machine learning can lead to fast and eﬃcient solutions however, these solutions are expensive in terms of hardware resources and power consumption. A possible solution to this problem can be use of approximate arithmetic. In many image...... 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....
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...
Approximate reasoning in physical systems
International Nuclear Information System (INIS)
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)
Improved approximate inspirals of test bodies into Kerr black holes
International Nuclear Information System (INIS)
Gair, Jonathan R; Glampedakis, Kostas
2006-01-01
We present an improved version of the approximate scheme for generating inspirals of test bodies into a Kerr black hole recently developed by Glampedakis, Hughes and Kennefick. Their original 'hybrid' scheme was based on combining exact relativistic expressions for the evolution of the orbital elements (the semilatus rectum p and eccentricity e) with an approximate, weak-field, formula for the energy and angular momentum fluxes, amended by the assumption of constant inclination angle ι during the inspiral. Despite the fact that the resulting inspirals were overall well behaved, certain pathologies remained for orbits in the strong-field regime and for orbits which are nearly circular and/or nearly polar. In this paper we eliminate these problems by incorporating an array of improvements in the approximate fluxes. First, we add certain corrections which ensure the correct behavior of the fluxes in the limit of vanishing eccentricity and/or 90 deg. inclination. Second, we use higher order post-Newtonian formulas, adapted for generic orbits. Third, we drop the assumption of constant inclination. Instead, we first evolve the Carter constant by means of an approximate post-Newtonian expression and subsequently extract the evolution of ι. Finally, we improve the evolution of circular orbits by using fits to the angular momentum and inclination evolution determined by Teukolsky-based calculations. As an application of our improved scheme, we provide a sample of generic Kerr inspirals which we expect to be the most accurate to date, and for the specific case of nearly circular orbits we locate the critical radius where orbits begin to decircularize under radiation reaction. These easy-to-generate inspirals should become a useful tool for exploring LISA data analysis issues and may ultimately play a role in the detection of inspiral signals in the LISA data
Approximations to the Newton potential
International Nuclear Information System (INIS)
Warburton, A.E.A.; Hatfield, R.W.
1977-01-01
Explicit expressions are obtained for Newton's (Newton, R.G., J. Math. Phys., 3:75-82 (1962)) solution to the inverse scattering problem in the approximations where up to two phase shifts are treated exactly and the rest to first order. (author)
Approximation properties of haplotype tagging
Directory of Open Access Journals (Sweden)
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.
Approximate Reanalysis in Topology Optimization
DEFF Research Database (Denmark)
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...
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
APPROXIMATE MODELS FOR FLOOD ROUTING
African Journals Online (AJOL)
kinematic model and a nonlinear convection-diffusion model are extracted from a normalized form of the St. Venant equations, and applied to ... normal ﬂow condition is moderate. Keywords: approximate models, nonlinear kinematic ... The concern here is with the movement of an abnormal amount of water along a river or ...
On badly approximable complex numbers
DEFF Research Database (Denmark)
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...
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.
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
Approximate Reasoning with Fuzzy Booleans
van den Broek, P.M.; Noppen, J.A.R.
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp
An approximate classical unimolecular reaction rate theory
Zhao, Meishan; Rice, Stuart A.
1992-05-01
We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying approximations. These approximations concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration-rotation state dependent separatrix, which approximation is similar to but extends and improves the approximations for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is calculated with an analytic representation instead of a stroboscopic mapping. The rate of unimolecular reaction is identified with the net rate at which phase points escape from the region of quasiperiodic bounded motion to the region of free fragment motion by consecutively crossing the dividing surfaces for intramolecular energy exchange and the separatrix. This new theory generates predictions of the rates of predissociation of the van der Waals molecules HeI2, NeI2 and ArI2 which are in very good agreement with available experimental data.
Children describe life after Hurricane Andrew.
Coffman, S
1994-01-01
Hurricane Andrew, which devastated the south Florida coast in August 1992, left over 250,000 people homeless with multiple health and social problems. This nursing study explored the experiences of 17 children, ages 5 through 12, who lived in the geographic area of storm damage. Common experiences described by the children included remembering the storm, dealing with after-effects, and reestablishing a new life. In general, children described a sense of strangeness, articulated as "life is weird" after the hurricane. In addition to stressful responses, many positive reactions were described by children in the study, revealing that the disaster also had a maturing effect.
Simplified stock markets described by number operators
Bagarello, F.
2009-06-01
In this paper we continue our systematic analysis of the operatorial approach previously proposed in an economical context and we discuss a mixed toy model of a simplified stock market, i.e. a model in which the price of the shares is given as an input. We deduce the time evolution of the portfolio of the various traders of the market, as well as of other observable quantities. As in a previous paper, we solve the equations of motion by means of a fixed point like approximation.
Disposition of recently described species of Penicillium
Frisvad, Jens C.; Samson, Robert A.; Stolk, Amelia C.
1990-01-01
Hundred and twenty-two species, varieties, and new combinations of Penicillium, Eupenicillium, and Talaromyces described since 1977 have been studied taxonomically and screened for mycotoxin production. Only 48 taxa could be accepted: Eupenicillium angustiporcatum, E. cryptum, E. lineolatum, E.
Describing content in middle school science curricula
Schwarz-Ballard, Jennifer A.
As researchers and designers, we intuitively recognize differences between curricula and describe them in terms of design strategy: project-based, laboratory-based, modular, traditional, and textbook, among others. We assume that practitioners recognize the differences in how each requires that students use knowledge, however these intuitive differences have not been captured or systematically described by the existing languages for describing learning goals. In this dissertation I argue that we need new ways of capturing relationships among elements of content, and propose a theory that describes some of the important differences in how students reason in differently designed curricula and activities. Educational researchers and curriculum designers have taken a variety of approaches to laying out learning goals for science. Through an analysis of existing descriptions of learning goals I argue that to describe differences in the understanding students come away with, they need to (1) be specific about the form of knowledge, (2) incorporate both the processes through which knowledge is used and its form, and (3) capture content development across a curriculum. To show the value of inquiry curricula, learning goals need to incorporate distinctions among the variety of ways we ask students to use knowledge. Here I propose the Epistemic Structures Framework as one way to describe differences in students reasoning that are not captured by existing descriptions of learning goals. The usefulness of the Epistemic Structures framework is demonstrated in the four curriculum case study examples in Part II of this work. The curricula in the case studies represent a range of content coverage, curriculum structure, and design rationale. They serve both to illustrate the Epistemic Structures analysis process and make the case that it does in fact describe learning goals in a way that captures important differences in students reasoning in differently designed curricula
Hydrogen: Beyond the Classic Approximation
International Nuclear Information System (INIS)
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
Hydrogen Beyond the Classic Approximation
Scivetti, I
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
Good points for diophantine approximation
Indian Academy of Sciences (India)
n=1 of real numbers in the interval [0, 1) and a sequence. (δn)∞ n=1 of positive numbers tending to zero, we consider the size of the set of numbers in [0, 1] which can be 'well approximated' by terms of the first sequence, namely, those y ∈ [0, 1] for which the inequality |y − xn| < δn holds for infinitely many positive integers n ...
Dimensionality Reduction with Adaptive Approximation
Kokiopoulou, Effrosyni; Frossard, Pascal
2007-01-01
In this paper, we propose the use of (adaptive) nonlinear approximation for dimensionality reduction. In particular, we propose a dimensionality reduction method for learning a parts based representation of signals using redundant dictionaries. A redundant dictionary is an overcomplete set of basis vectors that spans the signal space. The signals are jointly represented in a common subspace extracted from the redundant dictionary, using greedy pursuit algorithms for simultaneous sparse approx...
Ultrafast approximation for phylogenetic bootstrap.
Minh, Bui Quang; Nguyen, Minh Anh Thi; von Haeseler, Arndt
2013-05-01
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 the Shimodaira-Hasegawa-like approximate likelihood ratio test have been introduced to speed up the bootstrap. Here, we suggest an ultrafast bootstrap approximation approach (UFBoot) to compute the support of phylogenetic groups in maximum likelihood (ML) based trees. To achieve this, we combine the resampling estimated log-likelihood method with a simple but effective collection scheme of candidate trees. We also propose a stopping rule that assesses the convergence of branch support values to automatically determine when to stop collecting candidate trees. UFBoot achieves a median speed up of 3.1 (range: 0.66-33.3) to 10.2 (range: 1.32-41.4) compared with RAxML RBS for real DNA and amino acid alignments, respectively. Moreover, our extensive simulations show that UFBoot is robust against moderate model violations and the support values obtained appear to be relatively unbiased compared with the conservative standard bootstrap. This provides a more direct interpretation of the bootstrap support. We offer an efficient and easy-to-use software (available at http://www.cibiv.at/software/iqtree) to perform the UFBoot analysis with ML tree inference.
Initially Approximated Quasi Equilibrium Manifold
International Nuclear Information System (INIS)
Shahzad, M.; Arif, H.; Gulistan, M.; Sajid, M.
2015-01-01
Most commonly, kinetics model reduction techniques are based on exploiting time scale separation into fast and slow reaction processes. Then, a researcher approximates the system dynamically with dimension reduction for slow ones eliminating the fast modes. The main idea behind the construction of the lower dimension manifold is based on finding its initial approximation using Quasi Equilibrium Manifold (QEM). Here, we provide an efficient numerical method, which allow us to calculate low dimensional manifolds of chemical reaction systems. This computation technique is not restricted to our specific complex problem, but it can also be applied to other reacting flows or dynamic systems provided with the condition that a large number of extra (decaying) components can be eliminated from the system. Through computational approach, we approximate low dimensional manifold for a mechanism of six chemical species to simplify complex chemical kinetics. A reduced descriptive form of slow invariant manifold is obtained from dissipative system. This method is applicable for higher dimensions and is applied over an oxidation of CO/Pt. (author)
International Nuclear Information System (INIS)
Roy, Amlan K.; Chu, Shih-I
2002-01-01
We explore the feasibility of extending the quantum-fluid dynamics (QFD) approach for quantitative investigation of nonlinear optical processes of many-electron quantum systems in intense laser fields. Through the amalgamation of the QFD and density-functional theory (DFT), a single time-dependent hydrodynamical equation of motion can be derived. This equation has the form of a generalized nonlinear Schroedinger equation (GNLSE) but includes the many-body effects through a local time-dependent exchange-correlation potential. The time-dependent generalized pseudospectral method is extended to the solution of the GNLSE in spherical coordinates, allowing nonuniform spatial discretization and efficient, accurate solution of the hydrodynamical density and wave function in space and time. The procedure is applied to the study of multiphoton ionization (MPI) and high-order harmonic generation (HHG) of He and Ne atoms in intense laser fields. Excellent agreement with other recent self-interaction-free time-dependent DFT calculations is obtained for He, while for Ne, good agreement is achieved. Four different exchange-correlation energy functionals are used in the study with an aim to explore the roles of exchange and correlation on MPI/HHG processes in details. The method offers a conceptually appealing and computationally practical approach for nonperturbative treatment of strong-field processes of many-electron systems beyond the time-dependent Hartree-Fock level
Roy, Amlan K.; Chu, Shih-I.
2002-04-01
We explore the feasibility of extending the quantum-fluid dynamics (QFD) approach for quantitative investigation of nonlinear optical processes of many-electron quantum systems in intense laser fields. Through the amalgamation of the QFD and density-functional theory (DFT), a single time-dependent hydrodynamical equation of motion can be derived. This equation has the form of a generalized nonlinear Schrödinger equation (GNLSE) but includes the many-body effects through a local time-dependent exchange-correlation potential. The time-dependent generalized pseudospectral method is extended to the solution of the GNLSE in spherical coordinates, allowing nonuniform spatial discretization and efficient, accurate solution of the hydrodynamical density and wave function in space and time. The procedure is applied to the study of multiphoton ionization (MPI) and high-order harmonic generation (HHG) of He and Ne atoms in intense laser fields. Excellent agreement with other recent self-interaction-free time-dependent DFT calculations is obtained for He, while for Ne, good agreement is achieved. Four different exchange-correlation energy functionals are used in the study with an aim to explore the roles of exchange and correlation on MPI/HHG processes in details. The method offers a conceptually appealing and computationally practical approach for nonperturbative treatment of strong-field processes of many-electron systems beyond the time-dependent Hartree-Fock level.
Approximate Inference for Wireless Communications
DEFF Research Database (Denmark)
Hansen, Morten
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......-phase and all-pass filters. This enables us to view Sphere Detection (SD) as an adaptive variant of minimum-phase prefiltered reduced-state sequence estimation. Thus, a novel way of computing the minimum-phase filter and its associated all-pass filter using the numerically stable QL-factorization is suggested...
Generalized Gradient Approximation Made Simple
International Nuclear Information System (INIS)
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
Statistical Methods for Describing Developmental Patterns.
Burchinal, Margaret R.
1999-01-01
Describes a variety of analytic tools available to address questions about development, including growth-curve methods, hierarchical regressions, and both primary and secondary data analysis of project and extant data. Demonstrates some of these techniques using extant data from two projects to examine questions about treatment efficacy and…
Did goethe describe attention deficit hyperactivity disorder?
Bonazza, Sara; Scaglione, Cesa; Poppi, Massimo; Rizzo, Giovanni
2011-01-01
As early as 1846, the typical symptoms of attention deficit hyperactivity disorder (ADHD) were described by Heinrich Hoffmann (1809-1894). However, in Goethe's masterpiece Faust (1832), the character of Euphorion strongly suggests ADHD diagnosis. Copyright © 2011 S. Karger AG, Basel.
Frameworks for understanding and describing business models
DEFF Research Database (Denmark)
Nielsen, Christian; Roslender, Robin
2014-01-01
This chapter provides in a chronological fashion an introduction to six frameworks that one can apply to describing, understanding and also potentially innovating business models. These six frameworks have been chosen carefully as they represent six very different perspectives on business models ...... Maps (2001) • Intellectual Capital Statements (2003) • Chesbrough’s framework for Open Business Models (2006) • Business Model Canvas (2008)...
Modeling Approaches for Describing Microbial Population Heterogeneity
DEFF Research Database (Denmark)
Lencastre Fernandes, Rita
in a computational (CFD) fluid dynamic model. The anaerobic Growth of a budding yeast population in a continuously run microbioreactor was used as example. The proposed integrated model describes the fluid flow, the local cell size and cell cycle position distributions, as well as the local concentrations of glucose...
Phenomenological approach to describe logistic growth and ...
Indian Academy of Sciences (India)
2016-10-18
Oct 18, 2016 ... to describe temporal evolution of systems occurring in physics, biology, statistics and economics. .... may be considered to define a new class whose growth is affected by environmental constraints like ... The growth processes may be endogenous or exoge- nous by nature. These natures do not depend on ...
Analytical Solutions To Describe Juxtaposed Sands | Adeniji ...
African Journals Online (AJOL)
Mathematical (linear diffusion) equations are presented for two pseudoreservoir regions intersected by fault that describe the effects of partial communicating fault on pressure transient behaviour for each fault block. Green's and source function technique solve these equations. A two-well system is considered for the ...
A simple approximation method for dilute Ising systems
International Nuclear Information System (INIS)
Saber, M.
1996-10-01
We describe a simple approximate method to analyze dilute Ising systems. The method takes into consideration the fluctuations of the effective field, and is based on a probability distribution of random variables which correctly accounts for all the single site kinematic relations. It is shown that the simplest approximation gives satisfactory results when compared with other methods. (author). 12 refs, 2 tabs
The second Born approximation of electron–argon elastic scattering ...
Indian Academy of Sciences (India)
We study the elastic scattering of atomic argon by electron in the presence of a bichromatic laser ﬁeld in the second Born approximation. The target atom is approximated by a simple screening potential and the continuum states of the impinging and emitting electrons are described as Volkov states. We evaluate the S-matrix ...
The second Born approximation of electron–argon elastic scattering ...
Indian Academy of Sciences (India)
Abstract. We study the elastic scattering of atomic argon by electron in the presence of a bichro- matic laser field in the second Born approximation. The target atom is approximated by a simple screening potential and the continuum states of the impinging and emitting electrons are described as Volkov states. We evaluate ...
Wavelet Approximation in Data Assimilation
Tangborn, Andrew; Atlas, Robert (Technical Monitor)
2002-01-01
Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.
Plasma Physics Approximations in Ares
International Nuclear Information System (INIS)
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.
Parameters Describing Earth Observing Remote Sensing Systems
Zanoni, Vicki; Ryan, Robert E.; Pagnutti, Mary; Davis, Bruce; Markham, Brian; Storey, Jim
2003-01-01
The Earth science community needs to generate consistent and standard definitions for spatial, spectral, radiometric, and geometric properties describing passive electro-optical Earth observing sensors and their products. The parameters used to describe sensors and to describe their products are often confused. In some cases, parameters for a sensor and for its products are identical; in other cases, these parameters vary widely. Sensor parameters are bound by the fundamental performance of a system, while product parameters describe what is available to the end user. Products are often resampled, edge sharpened, pan-sharpened, or compressed, and can differ drastically from the intrinsic data acquired by the sensor. Because detailed sensor performance information may not be readily available to an international science community, standardization of product parameters is of primary performance. Spatial product parameters described include Modulation Transfer Function (MTF), point spread function, line spread function, edge response, stray light, edge sharpening, aliasing, ringing, and compression effects. Spectral product parameters discussed include full width half maximum, ripple, slope edge, and out-of-band rejection. Radiometric product properties discussed include relative and absolute radiometry, noise equivalent spectral radiance, noise equivalent temperature diffenence, and signal-to-noise ratio. Geometric product properties discussed include geopositional accuracy expressed as CE90, LE90, and root mean square error. Correlated properties discussed include such parameters as band-to-band registration, which is both a spectral and a spatial property. In addition, the proliferation of staring and pushbroom sensor architectures requires new parameters to describe artifacts that are different from traditional cross-track system artifacts. A better understanding of how various system parameters affect product performance is also needed to better ascertain the
High-order finite element approximations of the Maxwell equations
Sarmany, D.
2010-01-01
This thesis discusses numerical approximations of electromagnetic wave propagation, which is mathematically described by the Maxwell equations. These equations are typically either formulated as integral equations or as (partial) differential equations. Throughout this thesis, the numerical
Generating and Describing Affective Eye Behaviors
Mao, Xia; Li, Zheng
The manner of a person's eye movement conveys much about nonverbal information and emotional intent beyond speech. This paper describes work on expressing emotion through eye behaviors in virtual agents based on the parameters selected from the AU-Coded facial expression database and real-time eye movement data (pupil size, blink rate and saccade). A rule-based approach to generate primary (joyful, sad, angry, afraid, disgusted and surprise) and intermediate emotions (emotions that can be represented as the mixture of two primary emotions) utilized the MPEG4 FAPs (facial animation parameters) is introduced. Meanwhile, based on our research, a scripting tool, named EEMML (Emotional Eye Movement Markup Language) that enables authors to describe and generate emotional eye movement of virtual agents, is proposed.
Describing Spirituality at the End of Life.
Stephenson, Pam Shockey; Berry, Devon M
2015-09-01
Spirituality is salient to persons nearing the end of life (EOL). Unfortunately, researchers have not been able to agree on a universal definition of spirituality reducing the effectiveness of spiritual research. To advance spiritual knowledge and build an evidence base, researchers must develop creative ways to describe spirituality as it cannot be explicitly defined. A literature review was conducted to determine the common attributes that comprise the essence of spirituality, thereby creating a common ground on which to base spiritual research. Forty original research articles (2002 to 2012) focusing on EOL and including spiritual definitions/descriptions were reviewed. Analysis identified five attributes that most commonly described the essence of spirituality, including meaning, beliefs, connecting, self-transcendence, and value. © The Author(s) 2014.
Approximate particle number projection in hot nuclei
International Nuclear Information System (INIS)
Kosov, D.S.; Vdovin, A.I.
1995-01-01
Heated finite systems like, e.g., hot atomic nuclei have to be described by the canonical partition function. But this is a quite difficult technical problem and, as a rule, the grand canonical partition function is used in the studies. As a result, some shortcomings of the theoretical description appear because of the thermal fluctuations of the number of particles. Moreover, in nuclei with pairing correlations the quantum number fluctuations are introduced by some approximate methods (e.g., by the standard BCS method). The exact particle number projection is very cumbersome and an approximate number projection method for T ≠ 0 basing on the formalism of thermo field dynamics is proposed. The idea of the Lipkin-Nogami method to perform any operator as a series in the number operator powers is used. The system of equations for the coefficients of this expansion is written and the solution of the system in the next approximation after the BCS one is obtained. The method which is of the 'projection after variation' type is applied to a degenerate single j-shell model. 14 refs., 1 tab
Impulse approximation versus elementary particle method
International Nuclear Information System (INIS)
Klieb, L.
1982-01-01
Calculations are made for radiative muon capture in 3 He, both in impulse approximation and with the elementary particle method, and results are compared. It is argued that a diagrammatic method which takes a selected set of Feynman diagrams into account only provides insufficient warrant that effects not included are small. Therefore low-energy theorems are employed, as first given by Adler and Dothan, to determine the amplitude up to and including all terms linear in photon momentum and momentum transfer at the weak vertex. This amplitude is applied to radiative muon capture with the elementary particle method (EPM). The various form factors needed are discussed. It is shown that the results are particularly sensitive to the π- 3 He- 3 H coupling constant of which many contradictory determinations have been described in the literature. The classification of the nuclear wave function employed in the impulse approximation (IA) is summarized. The ν-decay of 3 H and (radiative muon capture in 3 He is treated and numerical results are given. Next, pion photoproduction and radiative pion capture are considered. IA and EPM for radiative muon capture are compared more closely. It is concluded that two-step processes are inherently difficult; the elementary particle method has convergence problems, and unknown parameters are present. In the impulse approximation, which is perhaps conceptually more difficult, the two-step interaction for the nucleon is considered as effectively point-like with small non-local corrections. (Auth.)
LiveDescribe: Can Amateur Describers Create High-Quality Audio Description?
Branje, Carmen J.; Fels, Deborah I.
2012-01-01
Introduction: The study presented here evaluated the usability of the audio description software LiveDescribe and explored the acceptance rates of audio description created by amateur describers who used LiveDescribe to facilitate the creation of their descriptions. Methods: Twelve amateur describers with little or no previous experience with…
How do consumers describe wine astringency?
Vidal, Leticia; Giménez, Ana; Medina, Karina; Boido, Eduardo; Ares, Gastón
2015-12-01
Astringency is one of the most important sensory characteristics of red wine. Although a hierarchically structured vocabulary to describe the mouthfeel sensations of red wine has been proposed, research on consumers' astringency vocabulary is lacking. In this context, the aim of this work was to gain an insight on the vocabulary used by wine consumers to describe the astringency of red wine and to evaluate the influence of wine involvement on consumers' vocabulary. One hundred and twenty-five wine consumers completed and on-line survey with five tasks: an open-ended question about the definition of wine astringency, free listing the sensations perceived when drinking an astringent wine, free listing the words they would use to describe the astringency of a red wine, a CATA question with 44 terms used in the literature to describe astringency, and a wine involvement questionnaire. When thinking about wine astringency consumers freely elicited terms included in the Mouth-feel Wheel, such as dryness and harsh. The majority of the specific sub-qualities of the Mouth-feel Wheel were not included in consumer responses. Also, terms not classified as astringency descriptors were elicited (e.g. acid and bitter). Only 17 out of the 31 terms from the Mouth-feel Wheel were used by more than 10% of participants when answering the CATA question. There were no large differences in the responses of consumer segments with different wine involvement. Results from the present work suggest that most of the terms of the Mouth-feel Wheel might not be adequate to communicate the astringency characteristics of red wine to consumers. Copyright © 2015 Elsevier Ltd. All rights reserved.
Adiabatically describing rare earths using microscopic deformations
Nobre, Gustavo; Dupuis, Marc; Herman, Michal; Brown, David
2017-09-01
Recent works showed that reactions on well-deformed nuclei in the rare-earth region are very well described by an adiabatic method. This assumes a spherical optical potential (OP) accounting for non-rotational degrees of freedom while the deformed configuration is described by couplings to states of the g.s. rotational band. This method has, apart from the global OP, only the deformation parameters as inputs, with no additional fit- ted variables. For this reason, it has only been applied to nuclei with well-measured deformations. With the new computational capabilities, microscopic large-scale calculations of deformation parameters within the HFB method based on the D1S Gogny force are available in the literature. We propose to use such microscopic deformations in our adi- abatic method, allowing us to reproduce the cross sections agreements observed in stable nuclei, and to reliably extend this description to nuclei far from stability, describing the whole rare-earth region. Since all cross sections, such as capture and charge exchange, strongly depend on the correct calculation of absorption from the incident channel (from direct reaction mechanisms), this approach significantly improves the accuracy of cross sections and transitions relevant to astrophysical studies. The work at BNL was sponsored by the Office of Nuclear Physics, Office of Science of the US Department of Energy, under Contract No. DE-AC02-98CH10886 with Brookhaven Science Associates, LLC.
Approximation by double Walsh polynomials
Directory of Open Access Journals (Sweden)
Ferenc Móricz
1992-01-01
Full Text Available We study the rate of approximation by rectangular partial sums, Cesàro means, and de la Vallée Poussin means of double Walsh-Fourier series of a function in a homogeneous Banach space X. In particular, X may be Lp(I2, where 1≦p<∞ and I2=[0,1×[0,1, or CW(I2, the latter being the collection of uniformly W-continuous functions on I2. We extend the results by Watari, Fine, Yano, Jastrebova, Bljumin, Esfahanizadeh and Siddiqi from univariate to multivariate cases. As by-products, we deduce sufficient conditions for convergence in Lp(I2-norm and uniform convergence on I2 as well as characterizations of Lipschitz classes of functions. At the end, we raise three problems.
Approximating the minimum cycle mean
Directory of Open Access Journals (Sweden)
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.
Nonlinear higher quasiparticle random phase approximation
Smetana, Adam; Šimkovic, Fedor; Štefánik, Dušan; Krivoruchenko, Mikhail
2017-10-01
We develop a new approach to describe nuclear states of multiphonon origin, motivated by the necessity for a more accurate description of matrix elements of neutrinoless double-beta decay. Our approach is an extension of the Quasiparticle Random Phase Approximation (QRPA), in which nonlinear phonon operators play an essential role. Before applying the nonlinear higher QRPA (nhQRPA) to realistic problems, we test its efficiency with exactly solvable models. The first considered model is equivalent to a harmonic oscillator. The nhQRPA solutions follow from the standard QRPA equation, but for nonlinear phonon operators defined for each individual excited state separately. The second exactly solvable model is the proton-neutron Lipkin model that describes successfully not only energy spectrum of nuclei, but also beta-decay transitions. Again, we reproduce exactly the numerical solutions in the nhQRPA framework. We show in particular that truncation of the nonlinear phonon operators leads to an approximation similar to the self-consistent second QRPA, given the phonon operators are defined with a constant term. The test results demonstrate that the proposed nhQRPA is a promising tool for a realistic calculation of energy spectra and nuclear transitions.
Using fundamental equations to describe basic phenomena
DEFF Research Database (Denmark)
Jakobsen, Arne; Rasmussen, Bjarne D.
1999-01-01
When the fundamental thermodynamic balance equations (mass, energy, and momentum) are used to describe the processes in a simple refrigeration system, then one finds that the resulting equation system will have a degree of freedom equal to one. Further investigations reveal that it is the equation...... and subcooling are introduced. Since the degree of freedom was equal to one, using both the superheat and subcooling require that one of the fundamental equations must be omitted from the equation system.The main purpose of the paper is to clarify the relation between the fundamental balance equations...
Nonlinear approximation with dictionaries I. Direct estimates
DEFF Research Database (Denmark)
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...
On Redundancy in Describing Linguistic Systems
Directory of Open Access Journals (Sweden)
Vladimir Borissov Pericliev
2015-12-01
Full Text Available On Redundancy in Describing Linguistic Systems The notion of system of linguistic elements figures prominently in most post-Saussurian linguistics up to the present. A “system” is the network of the contrastive (or, distinctive features each element in the system bears to the remaining elements. The meaning (valeur of each element in the system is the set of features that are necessary and jointly sufficient to distinguish this element from all others. The paper addresses the problems of “redundancy”, i.e. the occurrence of features that are not strictly necessary in describing an element in a system. Redundancy is shown to smuggle into the description of linguistic systems, this infelicitous practice illustrated with some examples from the literature (e.g. the classical phonemic analysis of Russian by Cherry, Halle, and Jakobson, 1953. The logic and psychology of the occurrence of redundancy are briefly sketched and it is shown that, in addition to some other problems, redundancy leads to a huge and unresolvable ambiguity of descriptions of linguistic systems (the Buridan’s ass problem.
Describing the learning curve for bulbar urethroplasty.
Spilotros, Marco; Malde, Sachin; Greenwell, Tamsin J
2017-12-01
Learning curves have been described for a number of urological procedures including radical prostatectomy and laparoscopic nephrectomy but rarely for urethroplasty. We describe the learning curve for bulbar urethroplasty in a single surgeon series. A retrospective case note review was performed of 91 consecutive men median age 32 years (range, 15-66 years) having bulbar urethroplasty performed by a single surgeon. Data was collected on type of urethroplasty, restricture rate (as defined by urethrogram and/or flow rate) and duration of follow up. The restricture rates were compared by quartiles and statistical analysis was by ¦Ö 2 between the first and fourth quartiles. The 91 men had 42 dorsal onlay buccal mucosal graft (Dorsal BMG), 20 BMG augmented bulbobulbar anastomotic (Augmented Rooftop) and 29 bulbobulbar anastomotic (BBA) urethroplasties performed. Median follow up was 39 months for the first quartile, 42 months for the second, 36 months for the third, and 35 months for the fourth. The restricture rate was 17% in the first quartile, 8.7% in the second and third quartiles and 4.5% in the fourth quartile. There were no restrictures noted after 24 months. There were 4 restrictures in the first quartile and 1 restricture in the fourth quartile (¦Ö 2 Plearning curve for bulbar urethroplasty with a reduced restricture rate each quartile and it may take as many as 90 cases to reach optimum restricture rates.
Is an eclipse described in the Odyssey?
Baikouzis, Constantino; Magnasco, Marcelo O
2008-07-01
Plutarch and Heraclitus believed a certain passage in the 20th book of the Odyssey ("Theoclymenus's prophecy") to be a poetic description of a total solar eclipse. In the late 1920s, Schoch and Neugebauer computed that the solar eclipse of 16 April 1178 B.C.E. was total over the Ionian Islands and was the only suitable eclipse in more than a century to agree with classical estimates of the decade-earlier sack of Troy around 1192-1184 B.C.E. However, much skepticism remains about whether the verses refer to this, or any, eclipse. To contribute to the issue independently of the disputed eclipse reference, we analyze other astronomical references in the Epic, without assuming the existence of an eclipse, and search for dates matching the astronomical phenomena we believe they describe. We use three overt astronomical references in the epic: to Boötes and the Pleiades, Venus, and the New Moon; we supplement them with a conjectural identification of Hermes's trip to Ogygia as relating to the motion of planet Mercury. Performing an exhaustive search of all possible dates in the span 1250-1115 B.C., we looked to match these phenomena in the order and manner that the text describes. In that period, a single date closely matches our references: 16 April 1178 B.C.E. We speculate that these references, plus the disputed eclipse reference, may refer to that specific eclipse.
Stimulated recall interviews for describing pragmatic epistemology
Shubert, Christopher W.; Meredith, Dawn C.
2015-12-01
Students' epistemologies affect how and what they learn: do they believe physics is a list of equations, or a coherent and sensible description of the physical world? In order to study these epistemologies as part of curricular assessment, we adopt the resources framework, which posits that students have many productive epistemological resources that can be brought to bear as they learn physics. In previous studies, these epistemologies have been either inferred from behavior in learning contexts or probed through surveys or interviews outside of the learning context. We argue that stimulated recall interviews provide a contextually and interpretively valid method to access students' epistemologies that complement existing methods. We develop a stimulated recall interview methodology to assess a curricular intervention and find evidence that epistemological resources aptly describe student epistemologies.
Does Guru Granth Sahib describe depression?
Kalra, Gurvinder; Bhui, Kamaldeep; Bhugra, Dinesh
2013-01-01
Sikhism is a relatively young religion, with Guru Granth Sahib as its key religious text. This text describes emotions in everyday life, such as happiness, sadness, anger, hatred, and also more serious mental health issues such as depression and psychosis. There are references to the causation of these emotional disturbances and also ways to get out of them. We studied both the Gurumukhi version and the English translation of the Guru Granth Sahib to understand what it had to say about depression, its henomenology, and religious prescriptions for recovery. We discuss these descriptions in this paper and understand its meaning within the context of clinical depression. Such knowledge is important as explicit descriptions about depression and sadness can help encourage culturally appropriate assessment and treatment, as well as promote public health through education.
Describing chaotic attractors: Regular and perpetual points
Dudkowski, Dawid; Prasad, Awadhesh; Kapitaniak, Tomasz
2018-03-01
We study the concepts of regular and perpetual points for describing the behavior of chaotic attractors in dynamical systems. The idea of these points, which have been recently introduced to theoretical investigations, is thoroughly discussed and extended into new types of models. We analyze the correlation between regular and perpetual points, as well as their relation with phase space, showing the potential usefulness of both types of points in the qualitative description of co-existing states. The ability of perpetual points in finding attractors is indicated, along with its potential cause. The location of chaotic trajectories and sets of considered points is investigated and the study on the stability of systems is shown. The statistical analysis of the observing desired states is performed. We focus on various types of dynamical systems, i.e., chaotic flows with self-excited and hidden attractors, forced mechanical models, and semiconductor superlattices, exhibiting the universality of appearance of the observed patterns and relations.
Plans should abstractly describe intended behavior
Energy Technology Data Exchange (ETDEWEB)
Pfleger, K.; Hayes-Roth, B. [Stanford Univ., CA (United States)
1996-12-31
Planning is the process of formulating a potential course of action. How courses of action (plans) produced by a planning module are represented and how they are used by execution-oriented modules of a complex agent to influence or dictate behavior are critical architectural issues. In contrast to the traditional model of plans as executable programs that dictate precise behaviors, we claim that autonomous agents inhabiting dynamic, unpredictable environments can make better use of plans that only abstractly describe their intended behavior. Such plans only influence or constrain behavior, rather than dictating it. This idea has been discussed in a variety of contexts, but it is seldom incorporated into working complex agents. Experiments involving instantiations of our Adaptive Intelligent Systems architecture in a variety of domains have demonstrated the generality and usefulness of the approach, even with our currently simple plan representation and mechanisms for plan following. The behavioral benefits include (1) robust improvisation of goal-directed behavior in response to dynamic situations, (2) ready exploitation of dynamically acquired knowledge or behavioral capabilities, and (3) adaptation based on dynamic aspects of coordinating diverse behaviors to achieve multiple goals. In addition to these run-time advantages, the approach has useful implications for the design and configuration of agents. Indeed, the core ideas of the approach are natural extensions of fundamental ideas in software engineering.
Biofilm carrier migration model describes reactor performance.
Boltz, Joshua P; Johnson, Bruce R; Takács, Imre; Daigger, Glen T; Morgenroth, Eberhard; Brockmann, Doris; Kovács, Róbert; Calhoun, Jason M; Choubert, Jean-Marc; Derlon, Nicolas
2017-06-01
The accuracy of a biofilm reactor model depends on the extent to which physical system conditions (particularly bulk-liquid hydrodynamics and their influence on biofilm dynamics) deviate from the ideal conditions upon which the model is based. It follows that an improved capacity to model a biofilm reactor does not necessarily rely on an improved biofilm model, but does rely on an improved mathematical description of the biofilm reactor and its components. Existing biofilm reactor models typically include a one-dimensional biofilm model, a process (biokinetic and stoichiometric) model, and a continuous flow stirred tank reactor (CFSTR) mass balance that [when organizing CFSTRs in series] creates a pseudo two-dimensional (2-D) model of bulk-liquid hydrodynamics approaching plug flow. In such a biofilm reactor model, the user-defined biofilm area is specified for each CFSTR; thereby, X carrier does not exit the boundaries of the CFSTR to which they are assigned or exchange boundaries with other CFSTRs in the series. The error introduced by this pseudo 2-D biofilm reactor modeling approach may adversely affect model results and limit model-user capacity to accurately calibrate a model. This paper presents a new sub-model that describes the migration of X carrier and associated biofilms, and evaluates the impact that X carrier migration and axial dispersion has on simulated system performance. Relevance of the new biofilm reactor model to engineering situations is discussed by applying it to known biofilm reactor types and operational conditions.
Time operators, innovations and approximations
Suchanecki, Z
2003-01-01
We present a new approach to the spectral analysis and prediction of such complex systems for which the time evolution is described by a semigroup of operators. This approach is based on an extended concept of time operator and can be interpreted as a shift representation of dynamical systems. The time operator method includes the multiresolution analysis of wavelets as a particular case but can also be applied for a substantially larger class of dynamical systems. Among the examples where shift representation have been explicitly derived are exact endomorphisms, the diffusion equation, generalized shifts associated with the Haar or Faber-Schauder basis and some classes of stochastic processes.
Describing pediatric dysphonia with nonlinear dynamic parameters
Meredith, Morgan L.; Theis, Shannon M.; McMurray, J. Scott; Zhang, Yu; Jiang, Jack J.
2008-01-01
Objective Nonlinear dynamic analysis has emerged as a reliable and objective tool for assessing voice disorders. However, it has only been tested on adult populations. In the present study, nonlinear dynamic analysis was applied to normal and dysphonic pediatric populations with the goal of collecting normative data. Jitter analysis was also applied in order to compare nonlinear dynamic and perturbation measures. This study’s findings will be useful in creating standards for the use of nonlinear dynamic analysis as a tool to describe dysphonia in the pediatric population. Methods The study included 38 pediatric subjects (23 children with dysphonia and 15 without). Recordings of sustained vowels were obtained from each subject and underwent nonlinear dynamic analysis and percent jitter analysis. The resulting correlation dimension (D2) and percent jitter values were compared across the two groups using t-tests set at a significance level of p = 0.05. Results It was shown that D2 values covary with the presence of pathology in children. D2 values were significantly higher in dysphonic children than in normal children (p = 0.002). Standard deviations indicated a higher level of variation in normal children’s D2 values than in dysphonic children’s D2 values. Jitter analysis showed markedly higher percent jitter in dysphonic children than in normal children (p = 0.025) and large standard deviations for both groups. Conclusion This study indicates that nonlinear dynamic analysis could be a viable tool for the detection and assessment of dysphonia in children. Further investigations and more normative data are needed to create standards for using nonlinear dynamic parameters for the clinical evaluation of pediatric dysphonia. PMID:18947887
Analytical approximations for stick-slip vibration amplitudes
DEFF Research Database (Denmark)
Thomsen, Jon Juel; Fidlin, A.
2003-01-01
The classical "mass-on-moving-belt" model for describing friction-induced vibrations is considered, with a friction law describing friction forces that first decreases and then increases smoothly with relative interface speed. Approximate analytical expressions are derived for the conditions...
Improving the wide resonance approximation
International Nuclear Information System (INIS)
Aboustta, Mohamed A.; Martinez, Aquilino S.
1999-01-01
A resonance is considered wide if its practical width, in energy, exceeds the average energy loss per collision, E(1-α A )/2, of the absorbing material. When the mass number, A, is taken infinite, the scattering produces only a change in the direction of motion of the neutron and not in its energy. Based on this assumption, the integral in the slowing-down equation describing the contribution of the resonant absorber is evaluated by taking its limit when α A →1. This work questions the necessity to take such a limit and shows that it is still possible to obtain a simple and more accurate expression for the integral without taking such limit
Improving the wide resonance approximation
Energy Technology Data Exchange (ETDEWEB)
Aboustta, Mohamed A.; Martinez, Aquilino S
1999-03-01
A resonance is considered wide if its practical width, in energy, exceeds the average energy loss per collision, E(1-{alpha}{sub A})/2, of the absorbing material. When the mass number, A, is taken infinite, the scattering produces only a change in the direction of motion of the neutron and not in its energy. Based on this assumption, the integral in the slowing-down equation describing the contribution of the resonant absorber is evaluated by taking its limit when {alpha}{sub A}{yields}1. This work questions the necessity to take such a limit and shows that it is still possible to obtain a simple and more accurate expression for the integral without taking such limit.
Regularity and approximability of electronic wave functions
Yserentant, Harry
2010-01-01
The electronic Schrödinger equation describes the motion of N-electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, with three spatial dimensions for each electron. Approximating these solutions is thus inordinately challenging, and it is generally believed that a reduction to simplified models, such as those of the Hartree-Fock method or density functional theory, is the only tenable approach. This book seeks to show readers that this conventional wisdom need not be ironclad: the regularity of the solutions, which increases with the number of electrons, the decay behavior of their mixed derivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allow these functions to be approximated with an order of complexity which comes arbitrarily close to that for a system of one or two electrons. The text is accessible to a mathematical audience at the beginning graduate level as...
The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes
Blas, Diego; Tram, Thomas
2011-01-01
Boltzmann codes are used extensively by several groups for constraining cosmological parameters with Cosmic Microwave Background and Large Scale Structure data. This activity is computationally expensive, since a typical project requires from 10'000 to 100'000 Boltzmann code executions. The newly released code CLASS (Cosmic Linear Anisotropy Solving System) incorporates improved approximation schemes leading to a simultaneous gain in speed and precision. We describe here the three approximations used by CLASS for basic LambdaCDM models, namely: a baryon-photon tight-coupling approximation which can be set to first order, second order or to a compromise between the two; an ultra-relativistic fluid approximation which had not been implemented in public distributions before; and finally a radiation streaming approximation taking reionisation into account.
Turbulent Evolution of a Plasma Described Through Classical Mechanics Only
Escande, D. F.; Elskens, Y.
2003-06-01
For the first time an old dream of the XIXth century comes true: the non trivial evolution of a macroscopic many-body system is described through classical mechanics only. This is done for the relaxation of a warm electron beam in a plasma, which results in the generation of Langmuir turbulence and in the formation of a plateau in the velocity distribution function of the electrons. Our derivation starts from the hamiltonian describing the one-dimensional N-body system corresponding to the beam and plasma bulk electrons in electrostatic interaction. For such a system, the dynamics can be reduced to the resonant interaction of M Langmuir waves with N'(≪ N) beam particles. The rigorous analytical calculation of a quasilinear diffusion coefficient is performed for the chaotic motion of a particle in a quite general set of prescribed longitudinal waves with random phases and large amplitudes. This result proves to be extendable within controllable approximations to the self-consistent evolution of M ≫ 1 Langmuir waves with N' ≫ 1 beam particles. This yields the proof of the classical quasilinear equations describing the coupled evolution of the wave spectrum and of the beam velocity distribution function in the strongly nonlinear regime where their validity is the matter of a longstanding controversy.
ESCAPE DYNAMICS AS A WAY TO DESCRIBE ECONOMIC PHENOMENA
Directory of Open Access Journals (Sweden)
Bogomolova A. S.
2017-06-01
Full Text Available This paper presents the review of issues and approaches to the analysis of escape dynamics in economic models with constant gain adaptive learning which is used to model and describe the behavior of various (macroeconomic as well as microeconomic variables in diverse economic phenomena such as currency crises, inflation episodes, endogenous collusion in oligopoly, and cycles of economic activity. This review considers and contrasts two currently existing approaches to the analysis of escape dynamics: the discrete-time approach employed, for example, by Cho, Williams and Sargent (2002, and the continuous-time approach proposed by Kasa (2004 and extended recently by Kolyuzhnov, Bogomolova and Slobodyan (2014, stressing the advantages of the latter. The continuous-time approach is based on the application of the results of the continuous-time version of the large deviations theory to the diffusion approximation of the original discrete-time dynamics under learning. Escape dynamics is characterized by analytically deriving the most probable escape point and mean escape time. The paper provides an example of the continuous-time approach applied to the Phelps problem of a government controlling inflation while adaptively learning the approximate Phillips curve.
Error bounds for approximations with deep ReLU networks.
Yarotsky, Dmitry
2017-10-01
We study expressive power of shallow and deep neural networks with piece-wise linear activation functions. We establish new rigorous upper and lower bounds for the network complexity in the setting of approximations in Sobolev spaces. In particular, we prove that deep ReLU networks more efficiently approximate smooth functions than shallow networks. In the case of approximations of 1D Lipschitz functions we describe adaptive depth-6 network architectures more efficient than the standard shallow architecture. Copyright © 2017 Elsevier Ltd. All rights reserved.
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
is called the metric invariant translation approximation property for a countable dis- crete metric space. Moreover ... Uniform Roe algebras; fine hyperbolic graph; metric invariant translation approximation property. ..... ate Studies in Mathematics, Volume 88 (2008) (Rhode Island: American Mathematical. Society Providence).
Approximate Uniqueness Estimates for Singular Correlation Matrices.
Finkbeiner, C. T.; Tucker, L. R.
1982-01-01
The residual variance is often used as an approximation to the uniqueness in factor analysis. An upper bound approximation to the residual variance is presented for the case when the correlation matrix is singular. (Author/JKS)
Reduction of Linear Programming to Linear Approximation
Vaserstein, Leonid N.
2006-01-01
It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.
HE11 radiation patterns and gaussian approximations
International Nuclear Information System (INIS)
Rebuffi, L.; Crenn, J.P.
1986-12-01
The possibility of approximating the HE11 radiation pattern with a Gaussian distribution is presented. A numerical comparison between HE11 far-field theoretical patterns and Abrams and Crenn approximations permits an evaluation of the validity of these two approximations. A new numerically optimized HE11 Gaussian approximation for the far-field, extended to great part of the near field, has been found. In particular, the value given for the beam radius at the waist, has been demonstrated to give the best HE11 Gaussian approximation in the far-field. The Crenn approximation is found to be very close to this optimal approximation, while the Abrams approximation is shown to be less precise. Universal curves for intensity, amplitude and power distribution are given for the HE11 radiated mode. These results are of interest for laser waveguide applications and for plasma ECRH transmission systems
Analytical approximations of Chandrasekhar's H-Function
International Nuclear Information System (INIS)
Simovic, R.; Vukanic, J.
1995-01-01
Analytical approximations of Chandrasekhar's H-function are derived in this paper by using ordinary and modified DPN methods. The accuracy of the approximations is discussed and the energy dependent albedo problem is treated. (author)
Study of quarkonium spectroscopy through the approximated variational method
International Nuclear Information System (INIS)
Brandao, H.J.A.; Kimel, I.
1982-01-01
The spectroscopy of the qq sup(-) bound states in a non-relativistic approximation using a approximate variational method is studied. Because of its similarity to positronium, a wave function of the hidrogen atom, is used. The 'coulomb-logaritmic-linear' was the potential used to described it. The fitting is done, and relevant coupling constant due to a logaritmic piece is found. All states described in this way furnishes v 2 3 P are reasonably explained and it no occurs with the mass diference between psi and eta sub(c). (Author) [pt
Axiomatic Characterizations of IVF Rough Approximation Operators
Directory of Open Access Journals (Sweden)
Guangji Yu
2014-01-01
Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.
Truth Approximation, Social Epistemology, and Opinion Dynamics
Douven, Igor; Kelp, Christoph
This paper highlights some connections between work on truth approximation and work in social epistemology, in particular work on peer disagreement. In some of the literature on truth approximation, questions have been addressed concerning the efficiency of research strategies for approximating the
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
Approximate Nearest Neighbor Queries among Parallel Segments
DEFF Research Database (Denmark)
Emiris, Ioannis Z.; Malamatos, Theocharis; Tsigaridas, Elias
2010-01-01
We develop a data structure for answering efficiently approximate nearest neighbor queries over a set of parallel segments in three dimensions. We connect this problem to approximate nearest neighbor searching under weight constraints and approximate nearest neighbor searching on historical data...
Nonlinear approximation with dictionaries I. Direct estimates
DEFF Research Database (Denmark)
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...... with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove...... that assuming a certain structure of the dictionary is sufficient and (almost) necessary to obtain stronger results. We give examples of classical dictionaries in L^p spaces and modulation spaces where our results recover some known Jackson type estimates, and discuss som new estimates they provide....
Nonlinear approximation with dictionaries, I: Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
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 with algorithmic constraints: thresholding and Chebychev approximation classes are studied respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space......, and we prove that assuming a certain structure of the dictionary is sufficient and (almost) necessary to obtain stronger results. We give examples of classical dictionaries in $L^p$ spaces and modulation spaces where our results recover some known Jackson type estimates, and discuss som new estimates...
Bounded-Degree Approximations of Stochastic Networks
Energy Technology Data Exchange (ETDEWEB)
Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar
2017-06-01
We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.
Mapping moveout approximations in TI media
Stovas, Alexey
2013-11-21
Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.
Bond selective chemistry beyond the adiabatic approximation
Energy Technology Data Exchange (ETDEWEB)
Butler, L.J. [Univ. of Chicago, IL (United States)
1993-12-01
One of the most important challenges in chemistry is to develop predictive ability for the branching between energetically allowed chemical reaction pathways. Such predictive capability, coupled with a fundamental understanding of the important molecular interactions, is essential to the development and utilization of new fuels and the design of efficient combustion processes. Existing transition state and exact quantum theories successfully predict the branching between available product channels for systems in which each reaction coordinate can be adequately described by different paths along a single adiabatic potential energy surface. In particular, unimolecular dissociation following thermal, infrared multiphoton, or overtone excitation in the ground state yields a branching between energetically allowed product channels which can be successfully predicted by the application of statistical theories, i.e. the weakest bond breaks. (The predictions are particularly good for competing reactions in which when there is no saddle point along the reaction coordinates, as in simple bond fission reactions.) The predicted lack of bond selectivity results from the assumption of rapid internal vibrational energy redistribution and the implicit use of a single adiabatic Born-Oppenheimer potential energy surface for the reaction. However, the adiabatic approximation is not valid for the reaction of a wide variety of energetic materials and organic fuels; coupling between the electronic states of the reacting species play a a key role in determining the selectivity of the chemical reactions induced. The work described below investigated the central role played by coupling between electronic states in polyatomic molecules in determining the selective branching between energetically allowed fragmentation pathways in two key systems.
Approximation with positive linear operators and linear combinations
Gupta, Vijay
2017-01-01
This book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian–Ivanov for linear combinations of Bernstein and Bernstein–Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as we...
Approximate models for broken clouds in stochastic radiative transfer theory
International Nuclear Information System (INIS)
Doicu, Adrian; Efremenko, Dmitry S.; Loyola, Diego; Trautmann, Thomas
2014-01-01
This paper presents approximate models in stochastic radiative transfer theory. The independent column approximation and its modified version with a solar source computed in a full three-dimensional atmosphere are formulated in a stochastic framework and for arbitrary cloud statistics. The nth-order stochastic models describing the independent column approximations are equivalent to the nth-order stochastic models for the original radiance fields in which the gradient vectors are neglected. Fast approximate models are further derived on the basis of zeroth-order stochastic models and the independent column approximation. The so-called “internal mixing” models assume a combination of the optical properties of the cloud and the clear sky, while the “external mixing” models assume a combination of the radiances corresponding to completely overcast and clear skies. A consistent treatment of internal and external mixing models is provided, and a new parameterization of the closure coefficient in the effective thickness approximation is given. An efficient computation of the closure coefficient for internal mixing models, using a previously derived vector stochastic model as a reference, is also presented. Equipped with appropriate look-up tables for the closure coefficient, these models can easily be integrated into operational trace gas retrieval systems that exploit absorption features in the near-IR solar spectrum. - Highlights: • Independent column approximation in a stochastic setting. • Fast internal and external mixing models for total and diffuse radiances. • Efficient optimization of internal mixing models to match reference models
Dynamic flow-driven erosion - An improved approximate solution
Yu, Bofu; Guo, Dawei; Rose, Calvin W.
2017-09-01
Rose et al. (2007) published an approximate solution of dynamic sediment concentration for steady and uniform flows, and this approximate solution shows a peak sediment concentration at the early stage of a runoff event, which can be used to describe and explain the first flush effect, a commonly observed phenomenon, especially in the urban environment. However the approximate solution does not converge to the steady state solution that is known exactly. The purpose of the note is to improve the approximate solution of Rose et al. (2007) by maintaining its functional form while forcing its steady state behaviour for sediment concentration to converge to the known steady state solution. The quality of the new approximate solution was assessed by comparing the new approximate solution with an exact solution for the single size class case, and with the numerical solution for the multiple size classes. It was found that 1) the relative error, or discrepancy, decreases as the stream power increases for all three soils considered; 2) the largest discrepancy occurs for the peak sediment concentration, and the average discrepancy in the peak concentration is less than 10% for the three soils considered; 3) for the majority of the 27 slope-flow combinations and for the three soils considered, the new approximate solution modestly underestimates the peak sediment concentration.
Interatomic forces in the electron-gas approximation
International Nuclear Information System (INIS)
Harker, A.H.
1980-09-01
This report describes the approximations involved in calculating the separate kinetic, coulomb, exchange and correlation contributions to the non-bonded interaction energy between closed-shell atoms. The basis of the method is an electron-gas model. The resulting potentials may be used in solid-state physics calculations or molecular dynamics simulations. Instructions are included for running three computer programs, HERSKILL, EXPAND and WEDEPOHL, which use the method described. (author)
Cost versus precision for approximate typing for Python
Fritz, Levin; Hage, J.
2017-01-01
In this paper we describe a variation of monotone frameworks that enables us to perform approximate typing of Python, in particular for dealing with some of its more dynamic features such as first-class functions and Python's dynamic class system. We additionally introduce a substantial number of
Calculating Resonance Positions and Widths Using the Siegert Approximation Method
Rapedius, Kevin
2011-01-01
Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear…
Cost versus Precision for Approximate Typing for Python
Fritz, Levin; Hage, J
2014-01-01
In this paper we describe a variation of monotone frameworks that enables us to perform approximate typing of Python, in particular for dealing with some of its more dynamic features such as first-class functions and Python’s dynamic class system. We additionally introduce a substantial number of
New approximating results for data with errors in both variables
Bogdanova, N.; Todorov, S.
2015-05-01
We introduce new data from mineral water probe Lenovo Bulgaria, measured with errors in both variables. We apply our Orthonormal Polynomial Expansion Method (OPEM), based on Forsythe recurrence formula to describe the data in the new error corridor. The development of OPEM gives the approximating curves and their derivatives in optimal orthonormal and usual expansions including the errors in both variables with special criteria.
Multilevel Monte Carlo in Approximate Bayesian Computation
Jasra, Ajay
2017-02-13
In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.
Approximate unitary equivalence of normaloid type operators
Zhu, Sen
2015-01-01
In this paper, we explore approximate unitary equivalence of normaloid operators and classify several normaloid type operators including transaloid operators, polynomial-normaloid operators and von Neumann operators up to approximate unitary equivalence. As an application, we explore approximation of transaloid operators with closed numerical ranges. Among other things, it is proved that those transaloid operators with closed numerical ranges are norm dense in the class of transaloid operators.
Uniform analytic approximation of Wigner rotation matrices
Hoffmann, Scott E.
2018-02-01
We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.
A Note on Generalized Approximation Property
Directory of Open Access Journals (Sweden)
Antara Bhar
2013-01-01
Full Text Available We introduce a notion of generalized approximation property, which we refer to as --AP possessed by a Banach space , corresponding to an arbitrary Banach sequence space and a convex subset of , the class of bounded linear operators on . This property includes approximation property studied by Grothendieck, -approximation property considered by Sinha and Karn and Delgado et al., and also approximation property studied by Lissitsin et al. We characterize a Banach space having --AP with the help of -compact operators, -nuclear operators, and quasi--nuclear operators. A particular case for ( has also been characterized.
Local density approximations for relativistic exchange energies
International Nuclear Information System (INIS)
MacDonald, A.H.
1986-01-01
The use of local density approximations to approximate exchange interactions in relativistic electron systems is reviewed. Particular attention is paid to the physical content of these exchange energies by discussing results for the uniform relativistic electron gas from a new point of view. Work on applying these local density approximations in atoms and solids is reviewed and it is concluded that good accuracy is usually possible provided self-interaction corrections are applied. The local density approximations necessary for spin-polarized relativistic systems are discussed and some new results are presented
Approximate maximum parsimony and ancestral maximum likelihood.
Alon, Noga; Chor, Benny; Pardi, Fabio; Rapoport, Anat
2010-01-01
We explore the maximum parsimony (MP) and ancestral maximum likelihood (AML) criteria in phylogenetic tree reconstruction. Both problems are NP-hard, so we seek approximate solutions. We formulate the two problems as Steiner tree problems under appropriate distances. The gist of our approach is the succinct characterization of Steiner trees for a small number of leaves for the two distances. This enables the use of known Steiner tree approximation algorithms. The approach leads to a 16/9 approximation ratio for AML and asymptotically to a 1.55 approximation ratio for MP.
Inference of random walk models to describe leukocyte migration
Jones, Phoebe J. M.; Sim, Aaron; Taylor, Harriet B.; Bugeon, Laurence; Dallman, Magaret J.; Pereira, Bernard; Stumpf, Michael P. H.; Liepe, Juliane
2015-12-01
While the majority of cells in an organism are static and remain relatively immobile in their tissue, migrating cells occur commonly during developmental processes and are crucial for a functioning immune response. The mode of migration has been described in terms of various types of random walks. To understand the details of the migratory behaviour we rely on mathematical models and their calibration to experimental data. Here we propose an approximate Bayesian inference scheme to calibrate a class of random walk models characterized by a specific, parametric particle re-orientation mechanism to observed trajectory data. We elaborate the concept of transition matrices (TMs) to detect random walk patterns and determine a statistic to quantify these TM to make them applicable for inference schemes. We apply the developed pipeline to in vivo trajectory data of macrophages and neutrophils, extracted from zebrafish that had undergone tail transection. We find that macrophage and neutrophils exhibit very distinct biased persistent random walk patterns, where the strengths of the persistence and bias are spatio-temporally regulated. Furthermore, the movement of macrophages is far less persistent than that of neutrophils in response to wounding.
Kinetic isotope effects and how to describe them
Directory of Open Access Journals (Sweden)
Konstantin Karandashev
2017-11-01
Full Text Available We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H2 and ⋅H + CH4 reactions. The absolute rate constants computed with the semiclassical instanton method both using on-the-fly electronic structure calculations and fitted potential-energy surfaces are also compared directly with exact quantum dynamics results. The error inherent in the instanton approximation is found to be relatively small and similar in magnitude to that introduced by using fitted surfaces. The kinetic isotope effect computed by the quantum instanton is even more accurate, and although it is computationally more expensive, the efficiency can be improved by path-integral acceleration techniques. We also test a simple approach for designing potential-energy surfaces for the example of proton transfer in malonaldehyde. The tunneling splittings are computed, and although they are found to deviate from experimental results, the ratio of the splitting to that of an isotopically substituted form is in much better agreement. We discuss the strengths and limitations of the potential-energy surface and based on our findings suggest ways in which it can be improved.
INCAS: an analytical model to describe displacement cascades
International Nuclear Information System (INIS)
Jumel, Stephanie; Claude Van-Duysen, Jean
2004-01-01
REVE (REactor for Virtual Experiments) is an international project aimed at developing tools to simulate neutron irradiation effects in Light Water Reactor materials (Fe, Ni or Zr-based alloys). One of the important steps of the project is to characterise the displacement cascades induced by neutrons. Accordingly, the Department of Material Studies of Electricite de France developed an analytical model based on the binary collision approximation. This model, called INCAS (INtegration of CAScades), was devised to be applied on pure elements; however, it can also be used on diluted alloys (reactor pressure vessel steels, etc.) or alloys composed of atoms with close atomic numbers (stainless steels, etc.). INCAS describes displacement cascades by taking into account the nuclear collisions and electronic interactions undergone by the moving atoms. In particular, it enables to determine the mean number of sub-cascades induced by a PKA (depending on its energy) as well as the mean energy dissipated in each of them. The experimental validation of INCAS requires a large effort and could not be carried out in the framework of the study. However, it was verified that INCAS results are in conformity with those obtained from other approaches. As a first application, INCAS was applied to determine the sub-cascade spectrum induced in iron by the neutron spectrum corresponding to the central channel of the High Flux Irradiation Reactor of Oak Ridge National Laboratory
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-06-23
We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.
Diagonal Pade approximations for initial value problems
International Nuclear Information System (INIS)
Reusch, M.F.; Ratzan, L.; Pomphrey, N.; Park, W.
1987-06-01
Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab
Simultaneous approximation in scales of Banach spaces
International Nuclear Information System (INIS)
Bramble, J.H.; Scott, R.
1978-01-01
The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... In this paper, we propose a definition of approximation property which is called the metric invariant translation approximation property for a countable discrete metric space. Moreover, we use ... Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209, People's Republic of China ...
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...
Quirks of Stirling's Approximation
Macrae, Roderick M.; Allgeier, Benjamin M.
2013-01-01
Stirling's approximation to ln "n"! is typically introduced to physical chemistry students as a step in the derivation of the statistical expression for the entropy. However, naive application of this approximation leads to incorrect conclusions. In this article, the problem is first illustrated using a familiar "toy…
On approximating multi-criteria TSP
Manthey, Bodo; Albers, S.; Marion, J.-Y.
2009-01-01
We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP), whose performances are independent of the number $k$ of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present randomized
On approximating multi-criteria TSP
Manthey, Bodo
We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multicriteria maximum traveling salesman problems (Max-TSP). For multicriteria Max-STSP where the edge weights have to be
Boundary Value Problems and Approximate Solutions ...
African Journals Online (AJOL)
In this paper, we discuss about some basic things of boundary value problems. Secondly, we study boundary conditions involving derivatives and obtain finite difference approximations of partial derivatives of boundary value problems. The last section is devoted to determine an approximate solution for boundary value ...
Polynomial approximation approach to transient heat conduction ...
African Journals Online (AJOL)
This work reports polynomial approximation approach to transient heat conduction in a long slab, long cylinder and sphere with linear internal heat generation. It has been shown that the polynomial approximation method is able to calculate average temperature as a function of time for higher value of Biot numbers.
Approximation algorithms for guarding holey polygons ...
African Journals Online (AJOL)
Guarding edges of polygons is a version of art gallery problem.The goal is finding the minimum number of guards to cover the edges of a polygon. This problem is NP-hard, and to our knowledge there are approximation algorithms just for simple polygons. In this paper we present two approximation algorithms for guarding ...
Similarity based approximate reasoning: fuzzy control
Raha, S.; Hossain, A.; Ghosh, S.
2008-01-01
This paper presents an approach to similarity based approximate reasoning that elucidates the connection between similarity and existing approaches to inference in approximate reasoning methodology. A set of axioms is proposed to get a reasonable measure of similarity between two fuzzy sets. The
Hydration thermodynamics beyond the linear response approximation.
Raineri, Fernando O
2016-10-19
The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, [Formula: see text] and [Formula: see text], with the solvent environment. Throughout the A [Formula: see text] B transformation of the solute, the solvation system is described by a Hamiltonian [Formula: see text] that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density [Formula: see text] that the dimensionless perturbational solute-solvent interaction energy [Formula: see text] has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both [Formula: see text] and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density [Formula: see text]. The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute
Approximations of kidney models and compartmental kidney models
International Nuclear Information System (INIS)
Nahorski, Z.
1996-01-01
Compartmental models were proposed in sixties to model the flow of isotopes through the kidney. These models were then criticized to not conform to the physiology of the kidney flow of isotopes. That is why they were abandoned, even thought their fits to the measured data were usually good. In this paper it is shown that some approximations of a physiological model proposed earlier by the present author can be interpreted as equations describing compartmental models. Their parameters have, however, different interpretation than the rates of intercompartmental flows. Diagrams of the time variations of the isotope content in the kidney are compared for the exact and approximate model using computer simulation technique
Slab-diffusion approximation from time-constant-like calculations
Energy Technology Data Exchange (ETDEWEB)
Johnson, R. W.
1976-12-01
Two equations were derived which describe the quantity and any fluid diffused from a slab as a function of time. One equation is applicable to the initial stage of the process; the other to the final stage. Accuracy is 0.2 percent at the one point where both approximations apply and where accuracy of either approximation is the poorest. Characterizing other rate processes might be facilitated by the use of the concept of NOLOR (normal of the logarithm of the rate) and its time dependence. (auth)
Slab-diffusion approximation from time-constant-like calculations
International Nuclear Information System (INIS)
Johnson, R.W.
1976-12-01
Two equations were derived which describe the quantity and any fluid diffused from a slab as a function of time. One equation is applicable to the initial stage of the process; the other to the final stage. Accuracy is 0.2 percent at the one point where both approximations apply and where accuracy of either approximation is the poorest. Characterizing other rate processes might be facilitated by the use of the concept of NOLOR (normal of the logarithm of the rate) and its time dependence
Fourier-Jacobi harmonic analysis and approximation of functions
International Nuclear Information System (INIS)
Platonov, S S
2014-01-01
We use the methods of Fourier-Jacobi harmonic analysis to study problems of the approximation of functions by algebraic polynomials in weighted function spaces on [−1,1]. We prove analogues of Jackson's direct theorem for the moduli of smoothness of all orders constructed on the basis of Jacobi generalized translations. The moduli of smoothness are shown to be equivalent to K-functionals constructed from Sobolev-type spaces. We define Nikol'skii-Besov spaces for the Jacobi generalized translation and describe them in terms of best approximations. We also prove analogues of some inverse theorems of Stechkin
The tendon approximator device in traumatic injuries.
Forootan, Kamal S; Karimi, Hamid; Forootan, Nazilla-Sadat S
2015-01-01
Precise and tension-free approximation of two tendon endings is the key predictor of outcomes following tendon lacerations and repairs. We evaluate the efficacy of a new tendon approximator device in tendon laceration repairs. In a comparative study, we used our new tendon approximator device in 99 consecutive patients with laceration of 266 tendons who attend a university hospital and evaluated the operative time to repair the tendons, surgeons' satisfaction as well as patient's outcomes in a long-term follow-up. Data were compared with the data of control patients undergoing tendon repair by conventional method. Totally 266 tendons were repaired by approximator device and 199 tendons by conventional technique. 78.7% of patients in first group were male and 21.2% were female. In approximator group 38% of patients had secondary repair of cut tendons and 62% had primary repair. Patients were followed for a mean period of 3years (14-60 months). Time required for repair of each tendon was significantly reduced with the approximator device (2 min vs. 5.5 min, ptendon repair were identical in the two groups and were not significantly different. 1% of tendons in group A and 1.2% in group B had rupture that was not significantly different. The new nerve approximator device is cheap, feasible to use and reduces the time of tendon repair with sustained outcomes comparable to the conventional methods.
Hardness and Approximation for Network Flow Interdiction
Chestnut, Stephen R.; Zenklusen, Rico
2015-01-01
In the Network Flow Interdiction problem an adversary attacks a network in order to minimize the maximum s-t-flow. Very little is known about the approximatibility of this problem despite decades of interest in it. We present the first approximation hardness, showing that Network Flow Interdiction and several of its variants cannot be much easier to approximate than Densest k-Subgraph. In particular, any $n^{o(1)}$-approximation algorithm for Network Flow Interdiction would imply an $n^{o(1)}...
Regression with Sparse Approximations of Data
DEFF Research Database (Denmark)
Noorzad, Pardis; Sturm, Bob L.
2012-01-01
We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...
Approximately Liner Phase IIR Digital Filter Banks
Directory of Open Access Journals (Sweden)
J. D. Ćertić
2013-11-01
Full Text Available In this paper, uniform and nonuniform digital filter banks based on approximately linear phase IIR filters and frequency response masking technique (FRM are presented. Both filter banks are realized as a connection of an interpolated half-band approximately linear phase IIR filter as a first stage of the FRM design and an appropriate number of masking filters. The masking filters are half-band IIR filters with an approximately linear phase. The resulting IIR filter banks are compared with linear-phase FIR filter banks exhibiting similar magnitude responses. The effects of coefficient quantization are analyzed.
Mathematical analysis, approximation theory and their applications
Gupta, Vijay
2016-01-01
Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
Approximation of the semi-infinite interval
Directory of Open Access Journals (Sweden)
A. McD. Mercer
1980-01-01
Full Text Available The approximation of a function f∈C[a,b] by Bernstein polynomials is well-known. It is based on the binomial distribution. O. Szasz has shown that there are analogous approximations on the interval [0,∞ based on the Poisson distribution. Recently R. Mohapatra has generalized Szasz' result to the case in which the approximating function is αe−ux∑k=N∞(uxkα+β−1Γ(kα+βf(kαuThe present note shows that these results are special cases of a Tauberian theorem for certain infinite series having positive coefficients.
Directory of Open Access Journals (Sweden)
Jie Shen
2015-01-01
Full Text Available We describe an extension of the redistributed technique form classical proximal bundle method to the inexact situation for minimizing nonsmooth nonconvex functions. The cutting-planes model we construct is not the approximation to the whole nonconvex function, but to the local convexification of the approximate objective function, and this kind of local convexification is modified dynamically in order to always yield nonnegative linearization errors. Since we only employ the approximate function values and approximate subgradients, theoretical convergence analysis shows that an approximate stationary point or some double approximate stationary point can be obtained under some mild conditions.
Nuclear data processing, analysis, transformation and storage with Pade-approximants
International Nuclear Information System (INIS)
Badikov, S.A.; Gay, E.V.; Guseynov, M.A.; Rabotnov, N.S.
1992-01-01
A method is described to generate rational approximants of high order with applications to neutron data handling. The problems considered are: The approximations of neutron cross-sections in resonance region producing the parameters for Adler-Adler type formulae; calculations of resulting rational approximants' errors given in analytical form allowing to compute the error at any energy point inside the interval of approximation; calculations of the correlation coefficient of error values in two arbitrary points provided that experimental errors are independent and normally distributed; a method of simultaneous generation of a few rational approximants with identical set of poles; functionals other than LSM; two-dimensional approximation. (orig.)
Integral approximants for functions of higher monodromic dimension
Energy Technology Data Exchange (ETDEWEB)
Baker, G.A. Jr.
1987-01-01
In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.
Approximate models for the analysis of laser velocimetry correlation functions
International Nuclear Information System (INIS)
Robinson, D.P.
1981-01-01
Velocity distributions in the subchannels of an eleven pin test section representing a slice through a Fast Reactor sub-assembly were measured with a dual beam laser velocimeter system using a Malvern K 7023 digital photon correlator for signal processing. Two techniques were used for data reduction of the correlation function to obtain velocity and turbulence values. Whilst both techniques were in excellent agreement on the velocity, marked discrepancies were apparent in the turbulence levels. As a consequence of this the turbulence data were not reported. Subsequent investigation has shown that the approximate technique used as the basis of Malvern's Data Processor 7023V is restricted in its range of application. In this note alternative approximate models are described and evaluated. The objective of this investigation was to develop an approximate model which could be used for on-line determination of the turbulence level. (author)
Pion-nucleus cross sections approximation
International Nuclear Information System (INIS)
Barashenkov, V.S.; Polanski, A.; Sosnin, A.N.
1990-01-01
Analytical approximation of pion-nucleus elastic and inelastic interaction cross-section is suggested, with could be applied in the energy range exceeding several dozens of MeV for nuclei heavier than beryllium. 3 refs.; 4 tabs
Square well approximation to the optical potential
International Nuclear Information System (INIS)
Jain, A.K.; Gupta, M.C.; Marwadi, P.R.
1976-01-01
Approximations for obtaining T-matrix elements for a sum of several potentials in terms of T-matrices for individual potentials are studied. Based on model calculations for S-wave for a sum of two separable non-local potentials of Yukawa type form factors and a sum of two delta function potentials, it is shown that the T-matrix for a sum of several potentials can be approximated satisfactorily over all the energy regions by the sum of T-matrices for individual potentials. Based on this, an approximate method for finding T-matrix for any local potential by approximating it by a sum of suitable number of square wells is presented. This provides an interesting way to calculate the T-matrix for any arbitary potential in terms of Bessel functions to a good degree of accuracy. The method is applied to the Saxon-Wood potentials and good agreement with exact results is found. (author)
Seismic wave extrapolation using lowrank symbol approximation
Fomel, Sergey
2012-04-30
We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.
Steepest descent approximations for accretive operator equations
International Nuclear Information System (INIS)
Chidume, C.E.
1993-03-01
A necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi-accretive operators defined on a uniformly smooth Banach space. (author). 49 refs
Degree of Approximation and Green Potential
Directory of Open Access Journals (Sweden)
M. Simkani
2009-03-01
Full Text Available We will relate the degree of rational approximation of a meromorphic function f to the minimum value, on the natural boundary of f, of Green potential of the weak∗ limit of the normalized pole-counting measures
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
APPROXIMATE DEVELOPMENTS FOR SURFACES OF REVOLUTION
Directory of Open Access Journals (Sweden)
Mădălina Roxana Buneci
2016-12-01
Full Text Available The purpose of this paper is provide a set of Maple procedures to construct approximate developments of a general surface of revolution generalizing the well-known gore method for sphere
An overview on Approximate Bayesian computation*
Directory of Open Access Journals (Sweden)
Baragatti Meïli
2014-01-01
Full Text Available Approximate Bayesian computation techniques, also called likelihood-free methods, are one of the most satisfactory approach to intractable likelihood problems. This overview presents recent results since its introduction about ten years ago in population genetics.
Approximation for the adjoint neutron spectrum
International Nuclear Information System (INIS)
Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da
2002-01-01
The proposal of this work is the determination of an analytical approximation which is capable to reproduce the adjoint neutron flux for the energy range of the narrow resonances (NR). In a previous work we developed a method for the calculation of the adjoint spectrum which was calculated from the adjoint neutron balance equations, that were obtained by the collision probabilities method, this method involved a considerable quantity of numerical calculation. In the analytical method some approximations were done, like the multiplication of the escape probability in the fuel by the adjoint flux in the moderator, and after these approximations, taking into account the case of the narrow resonances, were substituted in the adjoint neutron balance equation for the fuel, resulting in an analytical approximation for the adjoint flux. The results obtained in this work were compared to the results generated with the reference method, which demonstrated a good and precise results for the adjoint neutron flux for the narrow resonances. (author)
TMB: Automatic differentiation and laplace approximation
DEFF Research Database (Denmark)
Kristensen, Kasper; Nielsen, Anders; Berg, Casper Willestofte
2016-01-01
are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (approximate to 10(6)) and parameters (approximate to 10...... computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects......(3)). Computation times using ADMB and TMB are compared on a suite of examples ranging from simple models to large spatial models where the random effects are a Gaussian random field. Speedups ranging from 1.5 to about 100 are obtained with increasing gains for large problems...
Approximations of Stochastic Partial Differential Equations
Di Nunno, Giulia; Zhang, Tusheng
2014-01-01
In this paper we show that solutions of stochastic partial differ- ential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic Burgers equations are discussed.
Saddlepoint approximation methods in financial engineering
Kwok, Yue Kuen
2018-01-01
This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables. The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quanti...
Hugon, Cedric; Aubert, Guy; Sakellariou, Dimitris
2012-01-01
Mapping (or plotting) the magnetic field has a critical importance for the achievement of the homogeneous magnetic field necessary to standard MR experiments. A powerful tool for this purpose is the Spherical Harmonic Expansion (SHE), which provides a simple way to describe the spatial variations of a field in free space. Well-controlled non-zero spatial variations of the field are critical to MRI. The resolution of the image is directly related to the strength of the gradient used to encode space. As a result, it is desirable to have strong variations of the field. In that case, the SHE cannot be used as is, because the field modulus variations are affected by the variations of all components of the field. In this paper, we propose a method based on the SHE to characterize such variations, theoretically and experimentally, in the limit of an axisymmetric magnetic field. Practical applications of this method are proposed through the examples of single-sided magnet design and characterization, along with Stray-Field Imaging (STRAFI). Copyright © 2011 Elsevier Inc. All rights reserved.
Approximative solutions of stochastic optimization problem
Czech Academy of Sciences Publication Activity Database
Lachout, Petr
2010-01-01
Roč. 46, č. 3 (2010), s. 513-523 ISSN 0023-5954 R&D Projects: GA ČR GA201/08/0539 Institutional research plan: CEZ:AV0Z10750506 Keywords : Stochastic optimization problem * sensitivity * approximative solution Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/lachout-approximative solutions of stochastic optimization problem.pdf
Nonlinear approximation with nonstationary Gabor frames
DEFF Research Database (Denmark)
Ottosen, Emil Solsbæk; Nielsen, Morten
2018-01-01
We consider sparseness properties of adaptive time-frequency representations obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical Gabor frames by allowing for adaptivity in either time or frequency. It is known that the concept of painless nonorthogonal expansions...... resolution. Based on this characterization we prove an upper bound on the approximation error occurring when thresholding the coefficients of the corresponding frame expansions. We complement the theoretical results with numerical experiments, estimating the rate of approximation obtained from thresholding...
Lattice quantum chromodynamics with approximately chiral fermions
Energy Technology Data Exchange (ETDEWEB)
Hierl, Dieter
2008-05-15
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, s.
1999-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G(1) surface consisting of pieces of cones or cylinders of revolution or a G(r) NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produ...... robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding. (C) 1999 Academic Press....
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, S.
1998-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G_1 surface consisting of pieces of cones or cylinders of revolution or a G_r NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...... robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in shipbuilding....
Lattice quantum chromodynamics with approximately chiral fermions
International Nuclear Information System (INIS)
Hierl, Dieter
2008-05-01
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the Θ + pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
Nonlinear Stochastic PDEs: Analysis and Approximations
2016-05-23
Approximation to Nonlinear SPDEs with Discrete Random Variables , SIAM J Scientific Computing, (08 2015): 1872. doi: R. Mikulevicius, B. Rozovskii. On...multiplicative discrete random variables , ( ) S. Lototsky, B. Rozovsky. Stochastic Partial Differential Equations, (09 2015) B. Rozovsky, R...B. Rozovsky and G.E. Karniadakis, "Adaptive Wick-Malliavin approximation to nonlinear SPDEs with discrete random variables ," SIAM J. Sci. Comput., 37
Polynomial approximation of functions in Sobolev spaces
International Nuclear Information System (INIS)
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces
Approximation properties ofλ-Bernstein operators.
Cai, Qing-Bo; Lian, Bo-Yong; Zhou, Guorong
2018-01-01
In this paper, we introduce a new type λ -Bernstein operators with parameter [Formula: see text], we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Finally, we give some graphs and numerical examples to show the convergence of [Formula: see text] to [Formula: see text], and we see that in some cases the errors are smaller than [Formula: see text] to f .
Rough Sets Approximations for Learning Outcomes
Encheva, Sylvia; Tumin, Sharil
Discovering dependencies between students' responses and their level of mastering of a particular skill is very important in the process of developing intelligent tutoring systems. This work is an approach to attain a higher level of certainty while following students' learning progress. Rough sets approximations are applied for assessing students understanding of a concept. Consecutive responses from each individual learner to automated tests are placed in corresponding rough sets approximations. The resulting path provides strong indication about the current level of learning outcomes.
Approximations for the Erlang Loss Function
DEFF Research Database (Denmark)
Mejlbro, Leif
1998-01-01
Theoretically, at least three formulae are needed for arbitrarily good approximates of the Erlang Loss Function. In the paper, for convenience five formulae are presented guaranteeing a relative error <1E-2, and methods are indicated for improving this bound.......Theoretically, at least three formulae are needed for arbitrarily good approximates of the Erlang Loss Function. In the paper, for convenience five formulae are presented guaranteeing a relative error
Approximating centrality in evolving graphs: toward sublinearity
Priest, Benjamin W.; Cybenko, George
2017-05-01
The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.
VLSI design of universal approximator neuro-fuzzy systems
Baturone, I.; Sánchez-Solano, Santiago; Barriga, Angel; Jiménez Fernández, Carlos Jesús; Senhadji, Raouf; López, D. R.
2001-01-01
Neuro-fuzzy systems can theoretically solve any problem since they are universal approximators. Besides, they combine the advantages of the neuro and fuzzy paradigms. This paper describes and compares the different strategies that can be adopted to implement the learning and inference mechanisms involved in a neuro-fuzzy system. CAD tools, most of them integrated into the fuzzy system development environment Xfuzzy 2.0, have been developed to assist the designer in the implementation of neuro...
The failure rate in reliability: approximations and bounds
Directory of Open Access Journals (Sweden)
Christiane Cocozza-Thivent
1996-01-01
Full Text Available We consider models typical to the area of reliability, and a failure rate function for processes describing the dynamics of these models. Various approximations of the failure rate function are proposed and their accuracies are investigated. The basic case studied in the paper is a regenerative model. Some interesting particular cases (Markov, semi-Markov, etc. are considered. All proposed estimates are stated in a tractable analytic form.
Analytical approximation formulae for hydrogen diffusion in a metal slab
International Nuclear Information System (INIS)
Pohl, F.; Bohdansky, J.
1984-12-01
This report treats hydrogen diffusion in the first wall of a fusion machine (INTOR, reactor, etc.), taking the thermal load into account. Analytical approximation formulae are given for the concentration and flux density of hydrogen diffusing through a plane metal slab. The re-emission flux, particularly during the dwell time(s) of machine operation, is also described with analytical formulae. The analytical formulae are compared with numerical calculations for steel as first wall material. (orig.)
'LTE-diffusion approximation' for arc calculations
International Nuclear Information System (INIS)
Lowke, J J; Tanaka, M
2006-01-01
This paper proposes the use of the 'LTE-diffusion approximation' for predicting the properties of electric arcs. Under this approximation, local thermodynamic equilibrium (LTE) is assumed, with a particular mesh size near the electrodes chosen to be equal to the 'diffusion length', based on D e /W, where D e is the electron diffusion coefficient and W is the electron drift velocity. This approximation overcomes the problem that the equilibrium electrical conductivity in the arc near the electrodes is almost zero, which makes accurate calculations using LTE impossible in the limit of small mesh size, as then voltages would tend towards infinity. Use of the LTE-diffusion approximation for a 200 A arc with a thermionic cathode gives predictions of total arc voltage, electrode temperatures, arc temperatures and radial profiles of heat flux density and current density at the anode that are in approximate agreement with more accurate calculations which include an account of the diffusion of electric charges to the electrodes, and also with experimental results. Calculations, which include diffusion of charges, agree with experimental results of current and heat flux density as a function of radius if the Milne boundary condition is used at the anode surface rather than imposing zero charge density at the anode
Semiclassical initial value approximation for Green's function.
Kay, Kenneth G
2010-06-28
A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincare surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-10-01
The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400-407]. After five decades of continual development, it has developed into an important area in systems control and optimization, and it has also served as a prototype for the development of adaptive algorithms for on-line estimation and control of stochastic systems. Recently, it has been used in statistics with Markov chain Monte Carlo for solving maximum likelihood estimation problems and for general simulation and optimizations. In this paper, we first show that the trajectory averaging estimator is asymptotically efficient for the stochastic approximation MCMC (SAMCMC) algorithm under mild conditions, and then apply this result to the stochastic approximation Monte Carlo algorithm [Liang, Liu and Carroll J. Amer. Statist. Assoc. 102 (2007) 305-320]. The application of the trajectory averaging estimator to other stochastic approximationMCMC algorithms, for example, a stochastic approximation MLE algorithm for missing data problems, is also considered in the paper. © Institute of Mathematical Statistics, 2010.
Multilevel weighted least squares polynomial approximation
Haji-Ali, Abdul-Lateef
2017-06-30
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.
Analytical approximations for stick-slip vibration amplitudes
DEFF Research Database (Denmark)
Thomsen, Jon Juel; Fidlin, A.
2003-01-01
The classical "mass-on-moving-belt" model for describing friction-induced vibrations is considered, with a friction law describing friction forces that first decreases and then increases smoothly with relative interface speed. Approximate analytical expressions are derived for the conditions...... and periodicity. The results are illustrated and tested by time-series, phase plots and amplitude response diagrams, which compare very favorably with results obtained by numerical simulation of the equation of motion, as long as the difference in static and kinetic friction is not too large....
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
A Three-Compartment Model Describing Temperature Changes in Tethered Flying Blowflies
Stavenga, D.G.; Schwering, P.B.W.; Tinbergen, J.
1993-01-01
A three-compartment model is presented that describes temperature measurements of tethered flying blowflies, obtained by thermal imaging. During rest, the body temperature is approximately equal to the ambient temperature. At the start of flight, the thorax temperature increases exponentially with a
Numerical approximation of partial differential equations
Bartels, Sören
2016-01-01
Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular ...
Fast wavelet based sparse approximate inverse preconditioner
Energy Technology Data Exchange (ETDEWEB)
Wan, W.L. [Univ. of California, Los Angeles, CA (United States)
1996-12-31
Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.
Piecewise-Cubic Approximation in Autotracking Mode
Dikoussar, N D
2004-01-01
A method for piecewise-cubic approximation within the frame of four-point transforms is proposed. The knots of the segments are detected in autotracking mode using a digitized curve. A three-point cubic parametric spline (TPS) is used as a model of a local approximant. A free parameter $\\theta$ (a coefficient at $x^{3}$) is found in a line following mode, using step-by-step averaging. A formula for expression of the free parameter via a length of the segment and values of a function and derivatives in joining points is received. The $C^{1}$-smoothness depends on the accuracy of the $\\theta$-estimate. The stability of the method w.r.t. input errors is shown as well. The key parameters of the approximation are: the parameters of the basic functions, the variance of the input errors, and a sampling step. The efficiency of the method is shown by numerical calculations on test examples.
On transparent potentials: a Born approximation study
International Nuclear Information System (INIS)
Coudray, C.
1980-01-01
In the frame of the scattering inverse problem at fixed energy, a class of potentials transparent in Born approximation is obtained. All these potentials are spherically symmetric and are oscillating functions of the reduced radial variable. Amongst them, the Born approximation of the transparent potential of the Newton-Sabatier method is found. In the same class, quasi-transparent potentials are exhibited. Very general features of potentials transparent in Born approximation are then stated. And bounds are given for the exact scattering amplitudes corresponding to most of the potentials previously exhibited. These bounds, obtained at fixed energy, and for large values of the angular momentum, are found to be independent on the energy
The adiabatic approximation in multichannel scattering
International Nuclear Information System (INIS)
Schulte, A.M.
1978-01-01
Using two-dimensional models, an attempt has been made to get an impression of the conditions of validity of the adiabatic approximation. For a nucleon bound to a rotating nucleus the Coriolis coupling is neglected and the relation between this nuclear Coriolis coupling and the classical Coriolis force has been examined. The approximation for particle scattering from an axially symmetric rotating nucleus based on a short duration of the collision, has been combined with an approximation based on the limitation of angular momentum transfer between particle and nucleus. Numerical calculations demonstrate the validity of the new combined method. The concept of time duration for quantum mechanical collisions has also been studied, as has the collective description of permanently deformed nuclei. (C.F.)
The binary collision approximation: Background and introduction
International Nuclear Information System (INIS)
Robinson, M.T.
1992-08-01
The binary collision approximation (BCA) has long been used in computer simulations of the interactions of energetic atoms with solid targets, as well as being the basis of most analytical theory in this area. While mainly a high-energy approximation, the BCA retains qualitative significance at low energies and, with proper formulation, gives useful quantitative information as well. Moreover, computer simulations based on the BCA can achieve good statistics in many situations where those based on full classical dynamical models require the most advanced computer hardware or are even impracticable. The foundations of the BCA in classical scattering are reviewed, including methods of evaluating the scattering integrals, interaction potentials, and electron excitation effects. The explicit evaluation of time at significant points on particle trajectories is discussed, as are scheduling algorithms for ordering the collisions in a developing cascade. An approximate treatment of nearly simultaneous collisions is outlined and the searching algorithms used in MARLOWE are presented
Minimal entropy approximation for cellular automata
International Nuclear Information System (INIS)
Fukś, Henryk
2014-01-01
We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim. (paper)
APPROXIMATE INTEGRATION OF HIGHLY OSCILLATING FUNCTIONS
Directory of Open Access Journals (Sweden)
I. N. Melashko
2017-01-01
Full Text Available Elementary approximate formulae for numerical integration of functions containing oscillating factors of a special form with a parameter have been proposed in the paper. In this case general quadrature formulae can be used only at sufficiently small values of the parameter. Therefore, it is necessary to consider in advance presence of strongly oscillating factors in order to obtain formulae for numerical integration which are suitable in the case when the parameter is changing within wide limits. This can be done by taking into account such factors as weighting functions. Moreover, since the parameter can take values which cannot always be predicted in advance, approximate formulae for calculation of such integrals should be constructed in such a way that they contain this parameter in a letter format and they are suitable for calculation at any and particularly large values of the parameter. Computational rules with such properties are generally obtained by dividing an interval of integration into elementary while making successive approximation of the integral density at each elementary interval with polynomials of the first, second and third degrees and taking the oscillating factors as weighting functions. The paper considers the variant when density of the integrals at each elementary interval is approximated by a polynomial of zero degree that is a constant which is equal to the value of density in the middle of the interval. At the same time one approximate formula for calculation of an improper integral with infinite interval of the function with oscillating factor of a special type has been constructed in the paper. In this case it has been assumed that density of the improper integral rather quickly goes to zero when an argument module is increasing indefinitely. In other words it is considered as small to negligible outside some finite interval. Uniforms in parameter used for evaluation of errors in approximate formulae have been
Stopping Rules for Linear Stochastic Approximation
Wada, Takayuki; Itani, Takamitsu; Fujisaki, Yasumasa
Stopping rules are developed for stochastic approximation which is an iterative method for solving an unknown equation based on its consecutive residuals corrupted by additive random noise. It is assumed that the equation is linear and the noise is independent and identically distributed random vectors with zero mean and a bounded covariance. Then, the number of iterations for achieving a given probabilistic accuracy of the resultant solution is derived, which gives a rigorous stopping rule for the stochastic approximation. This number is polynomial of the problem size.
Computational topology for approximations of knots
Directory of Open Access Journals (Sweden)
Ji Li
2014-10-01
• a sum of total curvature and derivative. High degree Bézier curves are often used as smooth representations, where computational efficiency is a practical concern. Subdivision can produce PL approximations for a given B\\'ezier curve, fulfilling the above two conditions. The primary contributions are: (i a priori bounds on the number of subdivision iterations sufficient to achieve a PL approximation that is ambient isotopic to the original B\\'ezier curve, and (ii improved iteration bounds over those previously established.
Static correlation beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian Sommer
2014-01-01
derived from Hedin's equations (Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), Bethe-Salpeter equation (BSE), and Time-Dependent GW) all reproduce the correct dissociation limit. We also show that the BSE improves the correlation energies obtained within RPA and TDHF significantly...... for intermediate binding distances. A Hubbard model for the dimer allows us to obtain exact analytical results for the various approximations, which is readily compared with the exact diagonalization of the model. Moreover, the model is shown to reproduce all the qualitative results from the ab initio calculations...
Faster and Simpler Approximation of Stable Matchings
Directory of Open Access Journals (Sweden)
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.
An approximate analytical approach to resampling averages
DEFF Research Database (Denmark)
Malzahn, Dorthe; Opper, M.
2004-01-01
Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach for appr......Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach...
APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING MODELS
Directory of Open Access Journals (Sweden)
T. I. Aliev
2013-03-01
Full Text Available For probability distributions with variation coefficient, not equal to unity, mathematical dependences for approximating distributions on the basis of first two moments are derived by making use of multi exponential distributions. It is proposed to approximate distributions with coefficient of variation less than unity by using hypoexponential distribution, which makes it possible to generate random variables with coefficient of variation, taking any value in a range (0; 1, as opposed to Erlang distribution, having only discrete values of coefficient of variation.
Approximate Controllability of Fractional Integrodifferential Evolution Equations
Directory of Open Access Journals (Sweden)
R. Ganesh
2013-01-01
Full Text Available This paper addresses the issue of approximate controllability for a class of control system which is represented by nonlinear fractional integrodifferential equations with nonlocal conditions. By using semigroup theory, p-mean continuity and fractional calculations, a set of sufficient conditions, are formulated and proved for the nonlinear fractional control systems. More precisely, the results are established under the assumption that the corresponding linear system is approximately controllable and functions satisfy non-Lipschitz conditions. The results generalize and improve some known results.
Approximated Fractional Order Chebyshev Lowpass Filters
Directory of Open Access Journals (Sweden)
Todd Freeborn
2015-01-01
Full Text Available We propose the use of nonlinear least squares optimization to approximate the passband ripple characteristics of traditional Chebyshev lowpass filters with fractional order steps in the stopband. MATLAB simulations of (1+α, (2+α, and (3+α order lowpass filters with fractional steps from α = 0.1 to α = 0.9 are given as examples. SPICE simulations of 1.2, 1.5, and 1.8 order lowpass filters using approximated fractional order capacitors in a Tow-Thomas biquad circuit validate the implementation of these filter circuits.
Approximate Inference and Deep Generative Models
CERN. Geneva
2018-01-01
Advances in deep generative models are at the forefront of deep learning research because of the promise they offer for allowing data-efficient learning, and for model-based reinforcement learning. In this talk I'll review a few standard methods for approximate inference and introduce modern approximations which allow for efficient large-scale training of a wide variety of generative models. Finally, I'll demonstrate several important application of these models to density estimation, missing data imputation, data compression and planning.
Approximation result toward nearest neighbor heuristic
Directory of Open Access Journals (Sweden)
Monnot Jér"me
2002-01-01
Full Text Available In this paper, we revisit the famous heuristic called nearest neighbor (N N for the traveling salesman problem under maximization and minimization goal. We deal with variants where the edge costs belong to interval Ša;taĆ for a>0 and t>1, which certainly corresponds to practical cases of these problems. We prove that NN is a (t+1/2t-approximation for maxTSPŠa;taĆ and a 2/(t+1-approximation for minTSPŠa;taĆ under the standard performance ratio. Moreover, we show that these ratios are tight for some instances.
Radiation forces in the discrete dipole approximation
Hoekstra, A.G.; Frijlink, M.O.; Waters, L.B.F.M.; Sloot, P.M.A.
2001-01-01
The theory of the discrete-dipole approximation (DDA) for light scattering is extended to allow for the calculation of radiation forces on each dipole in the DDA model. Starting with the theory of Draine and Weingartner [Astrophys. J. 470, 551 (1996)] we derive an expression for the radiation force
Perturbation of operators and approximation of spectrum
Indian Academy of Sciences (India)
The pure linear algebraic approach is the main advantage of the results here. Keywords. Operator .... The paper is organized as follows. In §2, the approximation results are extended to the case of a one-parameter norm continuous family of operators. In §3, the spectral gap prediction results are proved with some examples.
Isotopic Approximation of Implicit Curves and Surfaces
Plantinga, Simon; Vegter, Gert
2004-01-01
Implicit surfaces are defined as the zero set of a function F: R3 → R. Although several algorithms exist for generating piecewise linear approximations, most of them are based on a user-defined stepsize or bounds to indicate the precision, and therefore cannot guarantee topological correctness.
A rational approximation of the effectiveness factor
DEFF Research Database (Denmark)
Wedel, Stig; Luss, Dan
1980-01-01
A fast, approximate method of calculating the effectiveness factor for arbitrary rate expressions is presented. The method does not require any iterative or interpolative calculations. It utilizes the well known asymptotic behavior for small and large Thiele moduli to derive a rational function w...
An approximate analytical approach to resampling averages
DEFF Research Database (Denmark)
Malzahn, Dorthe; Opper, M.
2004-01-01
Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach for appr...
Approximate solutions to variational inequalities and applications
Directory of Open Access Journals (Sweden)
M. Beatrice Lignola
1994-11-01
Full Text Available The aim of this paper is to investigate two concepts of approximate solutions to parametric variational inequalities in topological vector spaces for which the corresponding solution map is closed graph and/or lower semicontinuous and to apply the results to the stability of optimization problems with variational inequality constrains.
Nanostructures: Scattering beyond the Born approximation
Grigoriev, S.V.; Syromyatnikov, A. V.; Chumakov, A. P.; Grigoryeva, N.A.; Napolskii, K.S.; Roslyakov, I. V.; Eliseev, A.A.; Petukhov, A.V.; Eckerlebe, H.
2010-01-01
The neutron scattering on a two-dimensional ordered nanostructure with the third nonperiodic dimension can go beyond the Born approximation. In our model supported by the exact theoretical solution a well-correlated hexagonal porous structure of anodic aluminum oxide films acts as a peculiar
Large hierarchies from approximate R symmetries
International Nuclear Information System (INIS)
Kappl, Rolf; Ratz, Michael; Vaudrevange, Patrick K.S.
2008-12-01
We show that hierarchically small vacuum expectation values of the superpotential in supersymmetric theories can be a consequence of an approximate R symmetry. We briefly discuss the role of such small constants in moduli stabilization and understanding the huge hierarchy between the Planck and electroweak scales. (orig.)
Approximability and Parameterized Complexity of Minmax Values
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Hansen, Thomas Dueholm; Miltersen, Peter Bro
2008-01-01
We consider approximating the minmax value of a multi player game in strategic form. Tightening recent bounds by Borgs et al., we observe that approximating the value with a precision of ε log n digits (for any constant ε > 0) is NP-hard, where n is the size of the game. On the other hand......, approximating the value with a precision of c log log n digits (for any constant c ≥ 1) can be done in quasi-polynomial time. We consider the parameterized complexity of the problem, with the parameter being the number of pure strategies k of the player for which the minmax value is computed. We show...... that if there are three players, k = 2 and there are only two possible rational payoffs, the minmax value is a rational number and can be computed exactly in linear time. In the general case, we show that the value can be approximated wigh any polynomial number of digits of accuracy in time n^O(k) . On the other hand, we...
An Approximate Bayesian Fundamental Frequency Estimator
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt
2012-01-01
Joint fundamental frequency and model order estimation is an important problem in several applications such as speech and music processing. In this paper, we develop an approximate estimation algorithm of these quantities using Bayesian inference. The inference about the fundamental frequency...
Pade approximant calculations for neutron escape probability
International Nuclear Information System (INIS)
El Wakil, S.A.; Saad, E.A.; Hendi, A.A.
1984-07-01
The neutron escape probability from a non-multiplying slab containing internal source is defined in terms of a functional relation for the scattering function for the diffuse reflection problem. The Pade approximant technique is used to get numerical results which compare with exact results. (author)
Uniform semiclassical approximation for absorptive scattering systems
International Nuclear Information System (INIS)
Hussein, M.S.; Pato, M.P.
1987-07-01
The uniform semiclassical approximation of the elastic scattering amplitude is generalized to absorptive systems. An integral equation is derived which connects the absorption modified amplitude to the absorption free one. Division of the amplitude into a diffractive and refractive components is then made possible. (Author) [pt
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-11-30
We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.
Nonlinear approximation with dictionaries. II. Inverse Estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2006-01-01
In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block...
Nonlinear approximation with dictionaries,.. II: Inverse estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
In this paper we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for separated decomposable dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually...
Generalized Lower and Upper Approximations in Quantales
Directory of Open Access Journals (Sweden)
Qimei Xiao
2012-01-01
Full Text Available We introduce the concepts of set-valued homomorphism and strong set-valued homomorphism of a quantale which are the extended notions of congruence and complete congruence, respectively. The properties of generalized lower and upper approximations, constructed by a set-valued mapping, are discussed.
Uncertainty relations for approximation and estimation
Energy Technology Data Exchange (ETDEWEB)
Lee, Jaeha, E-mail: jlee@post.kek.jp [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Tsutsui, Izumi, E-mail: izumi.tsutsui@kek.jp [Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)
2016-05-27
We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for proxy functions used for the approximation is given by Aharonov's weak value, which also determines the classical Fisher information in parameter estimation, turning our inequality into the genuine Cramér–Rao inequality. Since the standard form of the uncertainty relation arises as a special case of our inequality, and since the parameter estimation is available as well, our inequality can treat both the position–momentum and the time–energy relations in one framework albeit handled differently. - Highlights: • Several inequalities interpreted as uncertainty relations for approximation/estimation are derived from a single ‘versatile inequality’. • The ‘versatile inequality’ sets a limit on the approximation of an observable and/or the estimation of a parameter by another observable. • The ‘versatile inequality’ turns into an elaboration of the Robertson–Kennard (Schrödinger) inequality and the Cramér–Rao inequality. • Both the position–momentum and the time–energy relation are treated in one framework. • In every case, Aharonov's weak value arises as a key geometrical ingredient, deciding the optimal choice for the proxy functions.
Markov operators, positive semigroups and approximation processes
Altomare, Francesco; Leonessa, Vita; Rasa, Ioan
2015-01-01
In recent years several investigations have been devoted to the study of large classes of (mainly degenerate) initial-boundary value evolution problems in connection with the possibility to obtain a constructive approximation of the associated positive C_0-semigroups. In this research monograph we present the main lines of a theory which finds its root in the above-mentioned research field.
Orthorhombic rational approximants for decagonal quasicrystals
Indian Academy of Sciences (India)
Unknown
An important exercise in the study of rational approximants is to derive their metric, especially in relation to the corresponding quasicrystal or the underlying clusters. Kuo's model has ..... the smaller diagonal of the fat rhombus in the Penrose tiling. This length scale is obtained by a section along a1 in the Penrose tiling and ...
Uncertainty relations for approximation and estimation
International Nuclear Information System (INIS)
Lee, Jaeha; Tsutsui, Izumi
2016-01-01
We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for proxy functions used for the approximation is given by Aharonov's weak value, which also determines the classical Fisher information in parameter estimation, turning our inequality into the genuine Cramér–Rao inequality. Since the standard form of the uncertainty relation arises as a special case of our inequality, and since the parameter estimation is available as well, our inequality can treat both the position–momentum and the time–energy relations in one framework albeit handled differently. - Highlights: • Several inequalities interpreted as uncertainty relations for approximation/estimation are derived from a single ‘versatile inequality’. • The ‘versatile inequality’ sets a limit on the approximation of an observable and/or the estimation of a parameter by another observable. • The ‘versatile inequality’ turns into an elaboration of the Robertson–Kennard (Schrödinger) inequality and the Cramér–Rao inequality. • Both the position–momentum and the time–energy relation are treated in one framework. • In every case, Aharonov's weak value arises as a key geometrical ingredient, deciding the optimal choice for the proxy functions.
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
groups have invariant translation approximation property (ITAP, see Definition 2.2). He also pointed out that there was no serious difficulty in extending the main theorem to fine hyperbolic graphs, but he did not outline the proof. So in this paper, we first give a proof for this extension, see Theorem 1.1 below. Then we define ...
Approximate Dynamic Programming by Practical Examples
Mes, Martijn R.K.; Perez Rivera, Arturo Eduardo; Boucherie, Richard; van Dijk, Nico M.
2017-01-01
Computing the exact solution of an MDP model is generally difficult and possibly intractable for realistically sized problem instances. A powerful technique to solve the large scale discrete time multistage stochastic control processes is Approximate Dynamic Programming (ADP). Although ADP is used
Approximation Algorithms for Model-Based Diagnosis
Feldman, A.B.
2010-01-01
Model-based diagnosis is an area of abductive inference that uses a system model, together with observations about system behavior, to isolate sets of faulty components (diagnoses) that explain the observed behavior, according to some minimality criterion. This thesis presents greedy approximation
Statistical model semiquantitatively approximates arabinoxylooligosaccharides' structural diversity
DEFF Research Database (Denmark)
Dotsenko, Gleb; Nielsen, Michael Krogsgaard; Lange, Lene
2016-01-01
(wheat flour arabinoxylan (arabinose/xylose, A/X = 0.47); grass arabinoxylan (A/X = 0.24); wheat straw arabinoxylan (A/X = 0.15); and hydrothermally pretreated wheat straw arabinoxylan (A/X = 0.05)), is semiquantitatively approximated using the proposed model. The suggested approach can be applied...
Upper Bounds on Numerical Approximation Errors
DEFF Research Database (Denmark)
Raahauge, Peter
2004-01-01
This paper suggests a method for determining rigorous upper bounds on approximationerrors of numerical solutions to infinite horizon dynamic programming models.Bounds are provided for approximations of the value function and the policyfunction as well as the derivatives of the value function...
Multi-Interpretation Operators and Approximate Classification
Engelfriet, J.; Treur, J.
2003-01-01
In this paper non-classical logical techniques are introduced to formalize the analysis of multi-interpretable observation information, in particular in approximate classification processes where information on attributes of an object is to be inferred on the basis of observable properties of the
Approximate Furthest Neighbor in High Dimensions
DEFF Research Database (Denmark)
Pagh, Rasmus; Silvestri, Francesco; Sivertsen, Johan von Tangen
2015-01-01
-dimensional Euclidean space. We build on the technique of Indyk (SODA 2003), storing random projections to provide sublinear query time for AFN. However, we introduce a different query algorithm, improving on Indyk’s approximation factor and reducing the running time by a logarithmic factor. We also present a variation...
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.
tt in the soft-gluon approximation
Indian Academy of Sciences (India)
April 2002 physics pp. 575–590. QCD corrections to decay-lepton polar and azimuthal angular distributions in ee+ee- t t in the soft-gluon approximation. SAURABH D RINDANI ... accurate determination of its couplings will have to await the construction of a linear e ·e collider. ..... is the azimuthal angle of the l· momentum.
Stability of approximate factorization with $ heta $-methods
W. Hundsdorfer (Willem)
1997-01-01
textabstractApproximate factorization seems for certain problems a viable alternative to time splitting. Since a splitting error is avoided, accuracy will in general be favourable compared to time splitting methods. However, it is not clear to what extent stability is affected by factorization.
Decision-theoretic troubleshooting: Hardness of approximation
Czech Academy of Sciences Publication Activity Database
Lín, Václav
2014-01-01
Roč. 55, č. 4 (2014), s. 977-988 ISSN 0888-613X R&D Projects: GA ČR GA13-20012S Institutional support: RVO:67985556 Keywords : Decision-theoretic troubleshooting * Hardness of approximation * NP-completeness Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.451, year: 2014
Comparison of Two Approaches to Approximated Reasoning
van den Broek, P.M.; Wagenknecht, Michael; Hampel, Rainer
A comparison is made of two approaches to approximate reasoning: Mamdani's interpolation method and the implication method. Both approaches are variants of Zadeh's compositional rule of inference. It is shown that the approaches are not equivalent. A correspondence between the approaches is
Lognormal Approximations of Fault Tree Uncertainty Distributions.
El-Shanawany, Ashraf Ben; Ardron, Keith H; Walker, Simon P
2018-01-26
Fault trees are used in reliability modeling to create logical models of fault combinations that can lead to undesirable events. The output of a fault tree analysis (the top event probability) is expressed in terms of the failure probabilities of basic events that are input to the model. Typically, the basic event probabilities are not known exactly, but are modeled as probability distributions: therefore, the top event probability is also represented as an uncertainty distribution. Monte Carlo methods are generally used for evaluating the uncertainty distribution, but such calculations are computationally intensive and do not readily reveal the dominant contributors to the uncertainty. In this article, a closed-form approximation for the fault tree top event uncertainty distribution is developed, which is applicable when the uncertainties in the basic events of the model are lognormally distributed. The results of the approximate method are compared with results from two sampling-based methods: namely, the Monte Carlo method and the Wilks method based on order statistics. It is shown that the closed-form expression can provide a reasonable approximation to results obtained by Monte Carlo sampling, without incurring the computational expense. The Wilks method is found to be a useful means of providing an upper bound for the percentiles of the uncertainty distribution while being computationally inexpensive compared with full Monte Carlo sampling. The lognormal approximation method and Wilks's method appear attractive, practical alternatives for the evaluation of uncertainty in the output of fault trees and similar multilinear models. © 2018 Society for Risk Analysis.
Counting independent sets using the Bethe approximation
Energy Technology Data Exchange (ETDEWEB)
Chertkov, Michael [Los Alamos National Laboratory; Chandrasekaran, V [MIT; Gamarmik, D [MIT; Shah, D [MIT; Sin, J [MIT
2009-01-01
The authors consider the problem of counting the number of independent sets or the partition function of a hard-core model in a graph. The problem in general is computationally hard (P hard). They study the quality of the approximation provided by the Bethe free energy. Belief propagation (BP) is a message-passing algorithm can be used to compute fixed points of the Bethe approximation; however, BP is not always guarantee to converge. As the first result, they propose a simple message-passing algorithm that converges to a BP fixed pont for any grapy. They find that their algorithm converges within a multiplicative error 1 + {var_epsilon} of a fixed point in {Omicron}(n{sup 2}E{sup -4} log{sup 3}(nE{sup -1})) iterations for any bounded degree graph of n nodes. In a nutshell, the algorithm can be thought of as a modification of BP with 'time-varying' message-passing. Next, they analyze the resulting error to the number of independent sets provided by such a fixed point of the Bethe approximation. Using the recently developed loop calculus approach by Vhertkov and Chernyak, they establish that for any bounded graph with large enough girth, the error is {Omicron}(n{sup -{gamma}}) for some {gamma} > 0. As an application, they find that for random 3-regular graph, Bethe approximation of log-partition function (log of the number of independent sets) is within o(1) of corret log-partition - this is quite surprising as previous physics-based predictions were expecting an error of o(n). In sum, their results provide a systematic way to find Bethe fixed points for any graph quickly and allow for estimating error in Bethe approximation using novel combinatorial techniques.
Eccentric binaries of compact objects in strong-field gravity
International Nuclear Information System (INIS)
Gold, Roman
2011-01-01
In this thesis we study the dynamics as well as the resulting gravitational radiation from eccentric binaries of compact objects in the non-linear regime of General Relativity. For this purpose we solve Einstein's field equation numerically in a 3+1 decomposition using the moving-puncture technique. We focus our study on very particular orbits, arising as a purely relativistic phenomenon of the two-body problem in General Relativity, which are associated with unstable circular orbits. They are governed by a fast, nearly circular revolution at a short distance followed by a slow, radial motion on a nearly elliptic trajectory. Due to the unique features of their orbital trajectories they are called zoom-whirl orbits. We analyze how the peculiar dynamics manifests itself in the emitted gravitational radiation and to which extent one can infer the orbital properties from observations of the gravitational waves. In the first part, we consider black hole binaries. We perform a comprehensive parameter study by varying the initial eccentricity, computing and characterizing the resulting gravitational waveforms. We address aspects, which can only be obtained from non-perturbative methods, and which are crucial to the astrophysical relevance of these orbits. In particular, our results imply a fairly low amount of fine-tuning necessary to spot zoom-whirl effects. We find whirl orbits for values of the eccentricities, which fall in disjunct intervals extending to rather low values. Furthermore, we show that whirl effects just before merger cause a signal with significant amplitude. In the second part, we investigate neutron star binaries on eccentric orbits in full General Relativity, which has not been studied so far. We explore their phenomenology and study the consequences for the matter after the neutron stars have merged. In these evolutions the merged neutron stars sooner or later collapse to form a black hole. During the collapse most of the matter is accreted on to the black hole, but in general a non-negligible amount may form an accretion disk around the merger remnant. Depending on the initial eccentricity, we find that a disk of substantial mass is left behind. We give strong evidence that the disk masses for a considerable range of eccentricities are generically large enough to power a short gamma-ray burst. Furthermore we find strong tidal interactions, when the neutron stars orbit close to each other, exerting a strong perturbation on the internal dynamics of the stars. We demonstrate that this effect modifies the gravitational waveform in a characteristic way. Our results emphasize the potential of gravitational waves from eccentric neutron star binaries to constrain models for the unknown equation of state of the neutron star material.
Interference Effects in Strong-Field Dissociative Ionization
DEFF Research Database (Denmark)
Yue, Lun; Madsen, Lars Bojer
2015-01-01
with simple energy conservation arguments. We explain the structures as interferences between wave packets released during different optical cycles, and during the same optical cycle, respectively. Both inter- and intracycle interference structures are clearly visible in the joint energy spectra. The shapes...
Strong field transient manipulation of electronic states and bands
Directory of Open Access Journals (Sweden)
I. Crassee
2017-11-01
Full Text Available In the present review, laser fields are so strong that they become part of the electronic potential, and sometimes even dominate the Coulomb contribution. This manipulation of atomic potentials and of the associated states and bands finds fascinating applications in gases and solids, both in the bulk and at the surface. We present some recent spectacular examples obtained within the NCCR MUST in Switzerland.
Modeling strong-field above-threshold ionization
International Nuclear Information System (INIS)
Sundaram, B.; Armstrong, L. Jr.
1990-01-01
Above-threshold ionization (ATI) by intense, short-pulse lasers is studied numerically, using the stretched hydrogen atom Hamiltonian. Within our model system, we isolate several mechanisms that contribute to the ATI process. These mechanisms, which involve both excited bound states and continuum states, all invoke intermediate, off-energy shell transitions. In particular, the importance of excited bound states and off-energy shell bound-free processes to the ionization mechanism are shown to relate to a simple physical criterion. These processes point to importance differences in the interpretation of ionization characteristics for short pulses from that for longer pulses. Our analysis concludes that although components of ATI admit of simple, few-state modeling, the ultimate synthesis points to a highly complex mechanism
Spin effects in strong-field laser-electron interactions
International Nuclear Information System (INIS)
Ahrens, S; Bauke, H; Müller, T-O; Villalba-Chávez, S; Müller, C
2013-01-01
The electron spin degree of freedom can play a significant role in relativistic scattering processes involving intense laser fields. In this contribution we discuss the influence of the electron spin on (i) Kapitza-Dirac scattering in an x-ray laser field of high intensity, (ii) photo-induced electron-positron pair production in a strong laser wave and (iii) multiphoton electron-positron pair production on an atomic nucleus. We show that in all cases under consideration the electron spin can have a characteristic impact on the process properties and their total probabilities. To this end, spin-resolved calculations based on the Dirac equation in the presence of an intense laser field are performed. The predictions from Dirac theory are also compared with the corresponding results from the Klein-Gordon equation.
Strong-field physics with singular light beams
Zürch, M.; Kern, C.; Hansinger, P.; Dreischuh, A.; Spielmann, Ch.
2012-10-01
Light beams carrying a point singularity with a screw-type phase distribution are associated with an optical vortex. The corresponding momentum flow leads to an orbital angular momentum of the photons. The study of optical vortices has led to applications such as particle micro-manipulation, imaging, interferometry, quantum information and high-resolution microscopy and lithography. Recent analyses showed that transitions forbidden by selection rules seem to be allowed when using optical vortex beams. To exploit these intriguing new applications, it is often necessary to shorten the wavelength by nonlinear frequency conversion. However, during the conversion the optical vortices tend to break up. Here we show that optical vortices can be generated in the extreme ultraviolet (XUV) region using high-harmonic generation. The singularity impressed on the fundamental beam survives the highly nonlinear process. Vortices in the XUV region have the same phase distribution as the driving field, which is in contradiction to previous findings, where multiplication of the momentum by the harmonic order is expected. This approach opens the way for several applications based on vortex beams in the XUV region.
Probing strong field ionization of solids with a Thomson parabola ...
Indian Academy of Sciences (India)
2014-01-11
Jan 11, 2014 ... large electric field drives the electrons to a very high energy. These hot electrons quickly move out of the solid surface, long before the ions move and the electron drift creates a strong quasistatic charge separation sheath electric field. Ions are then accelerated in this sheath field preferentially along the ...
Eccentric binaries of compact objects in strong-field gravity
Energy Technology Data Exchange (ETDEWEB)
Gold, Roman
2011-09-27
In this thesis we study the dynamics as well as the resulting gravitational radiation from eccentric binaries of compact objects in the non-linear regime of General Relativity. For this purpose we solve Einstein's field equation numerically in a 3+1 decomposition using the moving-puncture technique. We focus our study on very particular orbits, arising as a purely relativistic phenomenon of the two-body problem in General Relativity, which are associated with unstable circular orbits. They are governed by a fast, nearly circular revolution at a short distance followed by a slow, radial motion on a nearly elliptic trajectory. Due to the unique features of their orbital trajectories they are called zoom-whirl orbits. We analyze how the peculiar dynamics manifests itself in the emitted gravitational radiation and to which extent one can infer the orbital properties from observations of the gravitational waves. In the first part, we consider black hole binaries. We perform a comprehensive parameter study by varying the initial eccentricity, computing and characterizing the resulting gravitational waveforms. We address aspects, which can only be obtained from non-perturbative methods, and which are crucial to the astrophysical relevance of these orbits. In particular, our results imply a fairly low amount of fine-tuning necessary to spot zoom-whirl effects. We find whirl orbits for values of the eccentricities, which fall in disjunct intervals extending to rather low values. Furthermore, we show that whirl effects just before merger cause a signal with significant amplitude. In the second part, we investigate neutron star binaries on eccentric orbits in full General Relativity, which has not been studied so far. We explore their phenomenology and study the consequences for the matter after the neutron stars have merged. In these evolutions the merged neutron stars sooner or later collapse to form a black hole. During the collapse most of the matter is accreted on to the black hole, but in general a non-negligible amount may form an accretion disk around the merger remnant. Depending on the initial eccentricity, we find that a disk of substantial mass is left behind. We give strong evidence that the disk masses for a considerable range of eccentricities are generically large enough to power a short gamma-ray burst. Furthermore we find strong tidal interactions, when the neutron stars orbit close to each other, exerting a strong perturbation on the internal dynamics of the stars. We demonstrate that this effect modifies the gravitational waveform in a characteristic way. Our results emphasize the potential of gravitational waves from eccentric neutron star binaries to constrain models for the unknown equation of state of the neutron star material.
Strong-field-ionization suppression by light-field control
DEFF Research Database (Denmark)
Räsänen, Esa; Madsen, Lars Bojer
2012-01-01
in the intensity and thus preventing tunneling. In contrast, at high frequencies in the extreme ultraviolet regime the optimized pulses strongly couple with the (de)-excitations of the system, which leads to different pulse characteristics. Finally, we show that the applied target functional works, to some extent...
Probing strong field ionization of solids with a Thomson parabola ...
Indian Academy of Sciences (India)
2014-01-11
Jan 11, 2014 ... Ion spectrometry from laser–plasma is convolved with multiple atomic systems, several charge states and a broad energy spread. Conventional mass spectrometric techniques have serious limitations to probe this ionization dynamics. We have developed an imaging ion spectrometer that measures ...
Probing strong field ionization of solids with a Thomson parabola ...
Indian Academy of Sciences (India)
2014-01-11
Jan 11, 2014 ... spectrometry from laser–plasma is convolved with multiple atomic systems, several charge states and a broad energy spread. Conventional mass spectrometric techniques have serious limitations to probe this ionization dynamics. We have developed an imaging ion spectrometer that measures.
Theory of strong-field attosecond transient absorption
International Nuclear Information System (INIS)
Wu, Mengxi; Chen, Shaohao; Camp, Seth; Schafer, Kenneth J; Gaarde, Mette B
2016-01-01
Attosecond transient absorption is one of the promising new techniques being developed to exploit the availability of sub-femtosecond extreme ultraviolet (XUV) pulses to study the dynamics of the electron on its natural time scale. The temporal resolution in a transient absorption setup comes from the control of the relative delay and coherence between pump and probe pulses, while the spectral resolution comes from the characteristic width of the features that are being probed. In this review we focus on transient absorption scenarios where an attosecond pulse of XUV radiation creates a broadband excitation that is subsequently probed by a few cycle infrared (IR) laser. Because the attosecond XUV pulses are locked to the IR field cycle, the exchange of energy in the laser–matter interaction can be studied with unprecedented precision. We focus on the transient absorption by helium atoms of XUV radiation around the first ionization threshold, where we can simultaneoulsy solve the time-dependent Schrödinger equation for the single atom response and the Maxwell wave equation for the collective response of the nonlinear medium. We use a time-domain method that allows us to treat on an equal footing all the different linear and nonlinear processes by which the medium can exchange energy with the fields. We present several simple models, based on a few-level system interacting with a strong IR field, to explain many of the novel features found in attosecond transient absorption spectrograms. These include the presence of light-induced states, which demonstrate the ability to probe the dressed states of the atom. We also present a time-domain interpretation of the resonant pulse propagation features that appear in absorption spectra in dense, macroscopic media. We close by reviewing several recent experimental results that can be explained in terms of the models we discuss. Our aim is to present a road map for understanding future attosecond transient absorption experiments in more complex systems. (topical review)
Spin and Angular Momentum in Strong-Field Ionization
Trabert, D.; Hartung, A.; Eckart, S.; Trinter, F.; Kalinin, A.; Schöffler, M.; Schmidt, L. Ph. H.; Jahnke, T.; Kunitski, M.; Dörner, R.
2018-01-01
The spin polarization of electrons from multiphoton ionization of Xe by 395 nm circularly polarized laser pulses at 6 ×1013 W /cm2 has been measured. At this photon energy of 3.14 eV the above-threshold ionization peaks connected to Xe+ ions in the ground state (J =3 /2 , ionization potential Ip=12.1 eV ) and the first excited state (J =1 /2 , Ip=13.4 eV ) are clearly separated in the electron energy distribution. These two combs of above-threshold ionization peaks show opposite spin polarizations. The magnitude of the spin polarization is a factor of 2 higher for the J =1 /2 than for the J =3 /2 final ionic state. In turn, the data show that the ionization probability is strongly dependent on the sign of the magnetic quantum number.
Numerical Hydrodynamics in Strong-Field General Relativity
East, William Edward
In this thesis we develop and test methods for numerically evolving hydrodynamics coupled to the Einstein field equations, and then apply them to several problems in gravitational physics and astrophysics. The hydrodynamics scheme utilizes high-resolution shock-capturing techniques with flux corrections while the Einstein equations are evolved in the generalized harmonic formulation using finite difference methods. We construct initial data by solving the constraint equations using a multigrid algorithm with free data chosen based on superposing isolated compact objects. One application we consider is the merger of black hole-neutron star and neutron star-neutron star binaries that form through dynamical capture, as may occur in globular clusters or galactic nuclei. These systems can merge with non-negligible orbital eccentricity and display significant variability in dynamics and outcome as a function of initial impact parameter. We study the electromagnetic and gravitational-wave transients that these mergers may produce and their prospects for being detected with upcoming observations. We also introduce a numerical technique that allows solutions to the full Einstein equations to be obtained for extreme-mass-ratio systems where the spacetime is dominated by a known background solution. This technique is based on using the knowledge of a background solution to subtract off its contribution to the truncation error. We use this to study the tidal effects and gravitational radiation from a solar-type star falling into a supermassive black hole. Finally, we utilize general-relativistic hydrodynamics to study ultrarelativistic black hole formation. We study the head-on collision of fluid particles well within the kinetic energy dominated regime (Lorentz factors of 8-12). We find that black hole formation does occur at energies a factor of a few below simple hoop conjecture estimates. We also find that near the threshold for black hole formation, the collision leads to two separate apparent horizons which then merge. Both of these phenomena can be understood in terms of a gravitational focusing effect.
Linear approximation of Rayleigh-Brillouin scattering spectra.
Binietoglou, Ioannis; Giampouras, Paris; Belegante, Livio
2016-09-20
Rayleigh-Brillouin scattering is the basis of many remote sensing techniques, including high spectral resolution lidar measurements of aerosols and wind. Rayleigh-Brillouin spectra can be accurately estimated using physics-based models like the so-called Tenti's S6 and Pan's S7 models. Unfortunately, these are computationally expensive and can be the bottleneck for real-time lidar processing and iterative parameter estimation problems. This short article describes a very efficient linear approximation of the Rayleigh-Brillouin spectra based on Principal Component Analysis (PCA). Using PCA, the outputs of the above models can be approximated with very high accuracy using a single matrix multiplication. The described method can be applied to the output of any detailed scattering model, thus it can be used for a wide range of problems, e.g., for scattering from different gases (Air, N2, O2,…) and for different ranges of temperature and pressure. The precision of the approximation can be adapted to the requirements of the studied problem, and can easily exceed the actual accuracy of the reference models.
Computational analysis of the model describing HIV infection of CD4+T Cells.
Atangana, Abdon; Doungmo Goufo, Emile Franc
2014-01-01
An analysis of the model underpinning the description of the spread of HIV infection of CD4(+)T cells is examined in detail in this work. Investigations of the disease free and endemic equilibrium are done using the method of Jacobian matrix. An iteration technique, namely, the homotopy decomposition method (HDM), is implemented to give an approximate solution of nonlinear ordinary differential equation systems. The technique is described and illustrated with numerical examples. The approximated solution obtained via HDM is compared with those obtained via other methods to prove the trustworthiness of HDM. Moreover, the lessening and simplicity in calculations furnish HDM with a broader applicability.
Analytical Ballistic Trajectories with Approximately Linear Drag
Directory of Open Access Journals (Sweden)
Giliam J. P. de Carpentier
2014-01-01
Full Text Available This paper introduces a practical analytical approximation of projectile trajectories in 2D and 3D roughly based on a linear drag model and explores a variety of different planning algorithms for these trajectories. Although the trajectories are only approximate, they still capture many of the characteristics of a real projectile in free fall under the influence of an invariant wind, gravitational pull, and terminal velocity, while the required math for these trajectories and planners is still simple enough to efficiently run on almost all modern hardware devices. Together, these properties make the proposed approach particularly useful for real-time applications where accuracy and performance need to be carefully balanced, such as in computer games.
Analysing organic transistors based on interface approximation
International Nuclear Information System (INIS)
Akiyama, Yuto; Mori, Takehiko
2014-01-01
Temperature-dependent characteristics of organic transistors are analysed thoroughly using interface approximation. In contrast to amorphous silicon transistors, it is characteristic of organic transistors that the accumulation layer is concentrated on the first monolayer, and it is appropriate to consider interface charge rather than band bending. On the basis of this model, observed characteristics of hexamethylenetetrathiafulvalene (HMTTF) and dibenzotetrathiafulvalene (DBTTF) transistors with various surface treatments are analysed, and the trap distribution is extracted. In turn, starting from a simple exponential distribution, we can reproduce the temperature-dependent transistor characteristics as well as the gate voltage dependence of the activation energy, so we can investigate various aspects of organic transistors self-consistently under the interface approximation. Small deviation from such an ideal transistor operation is discussed assuming the presence of an energetically discrete trap level, which leads to a hump in the transfer characteristics. The contact resistance is estimated by measuring the transfer characteristics up to the linear region
Nonlinear analysis approximation theory, optimization and applications
2014-01-01
Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.
Simple Lie groups without the approximation property
DEFF Research Database (Denmark)
Haagerup, Uffe; de Laat, Tim
2013-01-01
For a locally compact group G, let A(G) denote its Fourier algebra, and let M0A(G) denote the space of completely bounded Fourier multipliers on G. The group G is said to have the Approximation Property (AP) if the constant function 1 can be approximated by a net in A(G) in the weak-∗ topology...... on the space M0A(G). Recently, Lafforgue and de la Salle proved that SL(3,R) does not have the AP, implying the first example of an exact discrete group without it, namely, SL(3,Z). In this paper we prove that Sp(2,R) does not have the AP. It follows that all connected simple Lie groups with finite center...... and real rank greater than or equal to two do not have the AP. This naturally gives rise to many examples of exact discrete groups without the AP....
The optimal XFEM approximation for fracture analysis
International Nuclear Information System (INIS)
Jiang Shouyan; Du Chengbin; Ying Zongquan
2010-01-01
The extended finite element method (XFEM) provides an effective tool for analyzing fracture mechanics problems. A XFEM approximation consists of standard finite elements which are used in the major part of the domain and enriched elements in the enriched sub-domain for capturing special solution properties such as discontinuities and singularities. However, two issues in the standard XFEM should specially be concerned: efficient numerical integration methods and an appropriate construction of the blending elements. In the paper, an optimal XFEM approximation is proposed to overcome the disadvantage mentioned above in the standard XFEM. The modified enrichment functions are presented that can reproduced exactly everywhere in the domain. The corresponding FORTRAN program is developed for fracture analysis. A classic problem of fracture mechanics is used to benchmark the program. The results indicate that the optimal XFEM can alleviate the errors and improve numerical precision.
Approximated solutions to Born-Infeld dynamics
Energy Technology Data Exchange (ETDEWEB)
Ferraro, Rafael [Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA),Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina); Nigro, Mauro [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina)
2016-02-01
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.
Incomplete Sparse Approximate Inverses for Parallel Preconditioning
International Nuclear Information System (INIS)
Anzt, Hartwig; University of Tennessee, Knoxville, TN; Huckle, Thomas K.; Bräckle, Jürgen; Dongarra, Jack
2017-01-01
In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as an attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.
Approximate Solutions in Planted 3-SAT
Hsu, Benjamin; Laumann, Christopher; Moessner, Roderich; Sondhi, Shivaji
2013-03-01
In many computational settings, there exists many instances where finding a solution requires a computing time that grows exponentially in the number of variables. Concrete examples occur in combinatorial optimization problems and cryptography in computer science or glassy systems in physics. However, while exact solutions are often known to require exponential time, a related and important question is the running time required to find approximate solutions. Treating this problem as a problem in statistical physics at finite temperature, we examine the computational running time in finding approximate solutions in 3-satisfiability for randomly generated 3-SAT instances which are guaranteed to have a solution. Analytic predictions are corroborated by numerical evidence using stochastic local search algorithms. A first order transition is found in the running time of these algorithms.
Time Stamps for Fixed-Point Approximation
DEFF Research Database (Denmark)
Damian, Daniela
2001-01-01
Time stamps were introduced in Shivers's PhD thesis for approximating the result of a control-flow analysis. We show them to be suitable for computing program analyses where the space of results (e.g., control-flow graphs) is large. We formalize time-stamping as a top-down, fixed-point approximat......Time stamps were introduced in Shivers's PhD thesis for approximating the result of a control-flow analysis. We show them to be suitable for computing program analyses where the space of results (e.g., control-flow graphs) is large. We formalize time-stamping as a top-down, fixed...
The approximability of the String Barcoding problem
Directory of Open Access Journals (Sweden)
Rizzi Romeo
2006-08-01
Full Text Available Abstract The String Barcoding (SBC problem, introduced by Rash and Gusfield (RECOMB, 2002, consists in finding a minimum set of substrings that can be used to distinguish between all members of a set of given strings. In a computational biology context, the given strings represent a set of known viruses, while the substrings can be used as probes for an hybridization experiment via microarray. Eventually, one aims at the classification of new strings (unknown viruses through the result of the hybridization experiment. In this paper we show that SBC is as hard to approximate as Set Cover. Furthermore, we show that the constrained version of SBC (with probes of bounded length is also hard to approximate. These negative results are tight.
Approximations in the PE-method
DEFF Research Database (Denmark)
Arranz, Marta Galindo
1996-01-01
Two differenct sources of errors may occur in the implementation of the PE methods; a phase error introduced in the approximation of a pseudo-differential operator and an amplitude error generated from the starting field. First, the inherent phase errors introduced in the solution are analyzed...... for a case where the normal mode solution to the wave equation is valid, when the sound is propagated in a downward refracting atmosphere. The angular limitations for the different parabolic approximations are deduced, and calculations showing shifts in the starter as the second source of error...... is investigated. Numerical and analytical starters are compared for source locations close to the ground. The spectral properties of several starters are presented....
A Varifold Approach to Surface Approximation
Buet, Blanche; Leonardi, Gian Paolo; Masnou, Simon
2017-11-01
We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we introduce the notion of approximate mean curvature and show various convergence results that hold, in particular, for sequences of discrete varifolds associated with point clouds or pixel/voxel-type discretizations of d-surfaces in the Euclidean n-space, without restrictions on dimension and codimension. The variational nature of the approach also allows us to consider surfaces with singularities, and in that case the approximate mean curvature is consistent with the generalized mean curvature of the limit surface. A series of numerical tests are provided in order to illustrate the effectiveness and generality of the method.
Approximations and Solution Estimates in Optimization
2016-04-06
for applications in machine learning and stochastic optimization . In this paper, we quantify the error in optimal values, optimal solutions, near...problem from that of another rather different problem is especially important in stochastic optimization , optimal control, and semi-infinite...approximate solutions to convex stochastic programs. SIAM J. Optimization , 18(3):961–979, 2007. [26] J. O. Royset and R. J-B Wets. From data to
Finite element approximation of the Isaacs equation
Salgado, Abner J.; Zhang, Wujun
2015-01-01
We propose and analyze a two-scale finite element method for the Isaacs equation. The fine scale is given by the mesh size $h$ whereas the coarse scale $\\varepsilon$ is dictated by an integro-differential approximation of the partial differential equation. We show that the method satisfies the discrete maximum principle provided that the mesh is weakly acute. This, in conjunction with weak operator consistency of the finite element method, allows us to establish convergence of the numerical s...
Mean-field approximation minimizes relative entropy
International Nuclear Information System (INIS)
Bilbro, G.L.; Snyder, W.E.; Mann, R.C.
1991-01-01
The authors derive the mean-field approximation from the information-theoretic principle of minimum relative entropy instead of by minimizing Peierls's inequality for the Weiss free energy of statistical physics theory. They show that information theory leads to the statistical mechanics procedure. As an example, they consider a problem in binary image restoration. They find that mean-field annealing compares favorably with the stochastic approach
Fast Approximate Joint Diagonalization Incorporating Weight Matrices
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Yeredor, A.
2009-01-01
Roč. 57, č. 3 (2009), s. 878-891 ISSN 1053-587X R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : autoregressive processes * blind source separation * nonstationary random processes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.212, year: 2009 http://library.utia.cas.cz/separaty/2009/SI/tichavsky-fast approximate joint diagonalization incorporating weight matrices.pdf
Fast approximate convex decomposition using relative concavity
Ghosh, Mukulika
2013-02-01
Approximate convex decomposition (ACD) is a technique that partitions an input object into approximately convex components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can also generate a more manageable number of components. It can be used as a basis of divide-and-conquer algorithms for applications such as collision detection, skeleton extraction and mesh generation. In this paper, we propose a new method called Fast Approximate Convex Decomposition (FACD) that improves the quality of the decomposition and reduces the cost of computing it for both 2D and 3D models. In particular, we propose a new strategy for evaluating potential cuts that aims to reduce the relative concavity, rather than absolute concavity. As shown in our results, this leads to more natural and smaller decompositions that include components for small but important features such as toes or fingers while not decomposing larger components, such as the torso, that may have concavities due to surface texture. Second, instead of decomposing a component into two pieces at each step, as in the original ACD, we propose a new strategy that uses a dynamic programming approach to select a set of n c non-crossing (independent) cuts that can be simultaneously applied to decompose the component into n c+1 components. This reduces the depth of recursion and, together with a more efficient method for computing the concavity measure, leads to significant gains in efficiency. We provide comparative results for 2D and 3D models illustrating the improvements obtained by FACD over ACD and we compare with the segmentation methods in the Princeton Shape Benchmark by Chen et al. (2009) [31]. © 2012 Elsevier Ltd. All rights reserved.
Approximations of Two-Attribute Utility Functions
1976-09-01
06320 i Technology Cambridge, Massachusetts 02139 Dr. Jack R. Borsting, Chairman Dept. of Operations Research and Professor Oskar Morgenstern ... Morgenstern utility functions u defined on two attributes from the viewpoint of mathematical --roxi-n’tion theory.r It focuses on approximations v of u that...von Neumann and Morgenstern (1947) or an equivalent system (Herstein and Milnor, 1953; Fishburn, 1970) so that there exists u: T + Re such that P - Q
Approximate Inverse Preconditioners with Adaptive Dropping
Czech Academy of Sciences Publication Activity Database
Kopal, J.; Rozložník, Miroslav; Tůma, Miroslav
2015-01-01
Roč. 84, June (2015), s. 13-20 ISSN 0965-9978 R&D Projects: GA ČR(CZ) GAP108/11/0853; GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : approximate inverse * Gram-Schmidt orthogonalization * incomplete decomposition * preconditioned conjugate gradient method * algebraic preconditioning * pivoting Subject RIV: BA - General Mathematics Impact factor: 1.673, year: 2015
Solving Math Problems Approximately: A Developmental Perspective.
Directory of Open Access Journals (Sweden)
Dana Ganor-Stern
Full Text Available Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults' ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger than the exact answer and when it was far (vs. close from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-07
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(n log n). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and optimal design
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander
2015-01-05
We approximate large non-structured covariance matrices in the H-matrix format with a log-linear computational cost and storage O(nlogn). We compute inverse, Cholesky decomposition and determinant in H-format. As an example we consider the class of Matern covariance functions, which are very popular in spatial statistics, geostatistics, machine learning and image analysis. Applications are: kriging and op- timal design.
Solving Math Problems Approximately: A Developmental Perspective.
Ganor-Stern, Dana
2016-01-01
Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults' ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner.
Markdown Optimization via Approximate Dynamic Programming
Directory of Open Access Journals (Sweden)
Cos?gun
2013-02-01
Full Text Available We consider the markdown optimization problem faced by the leading apparel retail chain. Because of substitution among products the markdown policy of one product affects the sales of other products. Therefore, markdown policies for product groups having a significant crossprice elasticity among each other should be jointly determined. Since the state space of the problem is very huge, we use Approximate Dynamic Programming. Finally, we provide insights on the behavior of how each product price affects the markdown policy.
Factorized Approximate Inverses With Adaptive Dropping
Czech Academy of Sciences Publication Activity Database
Kopal, Jiří; Rozložník, Miroslav; Tůma, Miroslav
2016-01-01
Roč. 38, č. 3 (2016), A1807-A1820 ISSN 1064-8275 R&D Projects: GA ČR GA13-06684S Grant - others:GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : approximate inverses * incomplete factorization * Gram–Schmidt orthogonalization * preconditioned iterative methods Subject RIV: BA - General Mathematics Impact factor: 2.195, year: 2016
An analytical approximation for resonance integral
International Nuclear Information System (INIS)
Magalhaes, C.G. de; Martinez, A.S.
1985-01-01
It is developed a method which allows to obtain an analytical solution for the resonance integral. The problem formulation is completely theoretical and based in concepts of physics of general character. The analytical expression for integral does not involve any empiric correlation or parameter. Results of approximation are compared with pattern values for each individual resonance and for sum of all resonances. (M.C.K.) [pt
Fast algorithms for approximate circular string matching.
Barton, Carl; Iliopoulos, Costas S; Pissis, Solon P
2014-03-22
Circular string matching is a problem which naturally arises in many biological contexts. It consists in finding all occurrences of the rotations of a pattern of length m in a text of length n. There exist optimal average-case algorithms for exact circular string matching. Approximate circular string matching is a rather undeveloped area. In this article, we present a suboptimal average-case algorithm for exact circular string matching requiring time O(n). Based on our solution for the exact case, we present two fast average-case algorithms for approximate circular string matching with k-mismatches, under the Hamming distance model, requiring time O(n) for moderate values of k, that is k=O(m/logm). We show how the same results can be easily obtained under the edit distance model. The presented algorithms are also implemented as library functions. Experimental results demonstrate that the functions provided in this library accelerate the computations by more than three orders of magnitude compared to a naïve approach. We present two fast average-case algorithms for approximate circular string matching with k-mismatches; and show that they also perform very well in practice. The importance of our contribution is underlined by the fact that the provided functions may be seamlessly integrated into any biological pipeline. The source code of the library is freely available at http://www.inf.kcl.ac.uk/research/projects/asmf/.
Feedforward Approximations to Dynamic Recurrent Network Architectures.
Muir, Dylan R
2018-02-01
Recurrent neural network architectures can have useful computational properties, with complex temporal dynamics and input-sensitive attractor states. However, evaluation of recurrent dynamic architectures requires solving systems of differential equations, and the number of evaluations required to determine their response to a given input can vary with the input or can be indeterminate altogether in the case of oscillations or instability. In feedforward networks, by contrast, only a single pass through the network is needed to determine the response to a given input. Modern machine learning systems are designed to operate efficiently on feedforward architectures. We hypothesized that two-layer feedforward architectures with simple, deterministic dynamics could approximate the responses of single-layer recurrent network architectures. By identifying the fixed-point responses of a given recurrent network, we trained two-layer networks to directly approximate the fixed-point response to a given input. These feedforward networks then embodied useful computations, including competitive interactions, information transformations, and noise rejection. Our approach was able to find useful approximations to recurrent networks, which can then be evaluated in linear and deterministic time complexity.
Ranking Support Vector Machine with Kernel Approximation
Directory of Open Access Journals (Sweden)
Kai Chen
2017-01-01
Full Text Available Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels can give higher accuracy than linear RankSVM (RankSVM with a linear kernel for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.
CMB-lensing beyond the Born approximation
International Nuclear Information System (INIS)
Marozzi, Giovanni; Fanizza, Giuseppe; Durrer, Ruth; Dio, Enea Di
2016-01-01
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles ℓ ∼< 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.
Function approximation of tasks by neural networks
International Nuclear Information System (INIS)
Gougam, L.A.; Chikhi, A.; Mekideche-Chafa, F.
2008-01-01
For several years now, neural network models have enjoyed wide popularity, being applied to problems of regression, classification and time series analysis. Neural networks have been recently seen as attractive tools for developing efficient solutions for many real world problems in function approximation. The latter is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. In a previous contribution, we have used a well known simplified architecture to show that it provides a reasonably efficient, practical and robust, multi-frequency analysis. We have investigated the universal approximation theory of neural networks whose transfer functions are: sigmoid (because of biological relevance), Gaussian and two specified families of wavelets. The latter have been found to be more appropriate to use. The aim of the present contribution is therefore to use a m exican hat wavelet a s transfer function to approximate different tasks relevant and inherent to various applications in physics. The results complement and provide new insights into previously published results on this problem
Simultaneous perturbation stochastic approximation for tidal models
Altaf, M.U.
2011-05-12
The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.
Quasielastic electron-deuteron scattering in the weak binding approximation
Energy Technology Data Exchange (ETDEWEB)
Ethier, Jacob J. [William and Mary College, JLAB; Doshi, Nidhi P. [Carnegie Mellon University; Malace, Simona P. [JLAB; Melnitchouk, Wally [JLAB
2014-06-01
We perform a global analysis of all available electron-deuteron quasielastic scattering data using Q^2-dependent smearing functions that describe inclusive inelastic e-d scattering within the weak binding approximation. We study the dependence of the cross sections on the deuteron wave function and the off-shell extrapolation of the elastic electron-nucleon cross section, which show particular sensitivity at x >> 1. The excellent overall agreement with data over a large range of Q^2 and x suggest a limited need for effects beyond the impulse approximation, with the exception of the very high-x or very low-Q^2 regions, where short-distance effects in the deuteron become more relevant.
Shape Approximation Based on Higher-Degree Polynomials
Dikusar, Nikolay
2018-02-01
The planar shape (contour) of an object is a fundamental source of information in a pattern recognition problem. Obtaining the relevant information set rests on difficult procedures and is a key problem in pattern recognition. A method is proposed for the segmentation of contours with a complex geometrical form. It is based on a parametric piecewise approximation of 12th order spanned by a polynomial model defined by basic elements. Higher-order polynomial approximation allows to optimize the number of segments on the contour and to obtain analytically the dependence of the curvature for more exact calculation of informative signs that are invariant to geometrical transformations. The algorithm based on this method as well as specific examples are described in detail.
Approximate scaling properties of RNA free energy landscapes
Baskaran, S.; Stadler, P. F.; Schuster, P.
1996-01-01
RNA free energy landscapes are analysed by means of "time-series" that are obtained from random walks restricted to excursion sets. The power spectra, the scaling of the jump size distribution, and the scaling of the curve length measured with different yard stick lengths are used to describe the structure of these "time series". Although they are stationary by construction, we find that their local behavior is consistent with both AR(1) and self-affine processes. Random walks confined to excursion sets (i.e., with the restriction that the fitness value exceeds a certain threshold at each step) exhibit essentially the same statistics as free random walks. We find that an AR(1) time series is in general approximately self-affine on timescales up to approximately the correlation length. We present an empirical relation between the correlation parameter rho of the AR(1) model and the exponents characterizing self-affinity.
Quasi-planar elemental clusters in pair interactions approximation
Directory of Open Access Journals (Sweden)
Chkhartishvili Levan
2016-01-01
Full Text Available The pair-interactions approximation, when applied to describe elemental clusters, only takes into account bonding between neighboring atoms. According to this approach, isomers of wrapped forms of 2D clusters – nanotubular and fullerene-like structures – and truly 3D clusters, are generally expected to be more stable than their quasi-planar counterparts. This is because quasi-planar clusters contain more peripheral atoms with dangling bonds and, correspondingly, fewer atoms with saturated bonds. However, the differences in coordination numbers between central and peripheral atoms lead to the polarization of bonds. The related corrections to the molar binding energy can make small, quasi-planar clusters more stable than their 2D wrapped allotropes and 3D isomers. The present work provides a general theoretical frame for studying the relative stability of small elemental clusters within the pair interactions approximation.
Background approximation in automatic qualitative X-ray-fluorescent analysis
International Nuclear Information System (INIS)
Jordanov, J.; Tsanov, T.; Stefanov, R.; Jordanov, N.; Paunov, M.
1982-01-01
An empirical method of finding the dependence of the background intensity (Isub(bg) on the wavelength is proposed, based on the approximation of the experimentally found values for the background in the course of an automatic qualitative X-ray fluorescent analysis with pre-set curve. It is assumed that the dependence I(lambda) will be well approximated by a curve of the type Isub(bg)=(lambda-lambda sub(o)sup(fsub(1)(lambda))exp[fsub(2)(lambda)] where fsub(1) (lambda) and f 2 (lambda) are linear functions with respect to the sought parameters. This assumption was checked out on a ''pure'' starch background, in which it is not known beforehand which points belong to the background. It was assumed that the dependence I(lambda) can be found from all minima in the spectrum. Three types of minima has been distinguished: 1. the lowest point between two well-solved X-ray lines; 2. a minimum obtained as a result of statistical fluctuations of the measured signal; 3. the lowest point between two overlapped lines. The minima strongly deviating from the background are removed from the obtained set. The sum-total of the remaining minima serves as a base for the approximation of the dependence I(lambda). The unknown parameters are determined by means of the LSM. The approximated curve obtained by this method is closer to the real background than the background determined by the method described by Kigaki Denki, as the effect of all recorded minima is taken into account. As an example the PbTe spectrum recorded with crystal LiF 220 is shown graphically. The curve well describes the background of the spectrum even in the regions in which there are no minima belonging to the background. (authors)
Approximate waveforms for extreme-mass-ratio inspirals in modified gravity spacetimes
International Nuclear Information System (INIS)
Gair, Jonathan; Yunes, Nicolas
2011-01-01
Extreme mass-ratio inspirals, in which a stellar-mass compact object spirals into a supermassive black hole, are prime candidates for detection with space-borne milliHertz gravitational wave detectors, similar to the Laser Interferometer Space Antenna. The gravitational waves generated during such inspirals encode information about the background in which the small object is moving, providing a tracer of the spacetime geometry and a probe of strong-field physics. In this paper, we construct approximate, ''analytic-kludge'' waveforms for such inspirals with parametrized post-Einsteinian corrections that allow for generic, model-independent deformations of the supermassive black hole background away from the Kerr metric. These approximate waveforms include all of the qualitative features of true waveforms for generic inspirals, including orbital eccentricity and relativistic precession. The deformations of the Kerr metric are modeled using a recently proposed, modified gravity bumpy metric, which parametrically deforms the Kerr spacetime while ensuring that three approximate constants of the motion remain for geodesic orbits: a conserved energy, azimuthal angular momentum and Carter constant. The deformations represent modified gravity effects and have been analytically mapped to several modified gravity black hole solutions in four dimensions. In the analytic kludge waveforms, the conservative motion is modeled by a post-Newtonian expansion of the geodesic equations in the deformed spacetimes, which in turn induce modifications to the radiation-reaction force. These analytic-kludge waveforms serve as a first step toward complete and model-independent tests of general relativity with extreme mass-ratio inspirals.
Low-frequency approximation for high-order harmonic generation by a bicircular laser field
Milošević, D. B.
2018-01-01
We present low-frequency approximation (LFA) for high-order harmonic generation (HHG) process. LFA represents the lowest-order term of an expansion of the final-state interaction matrix element in powers of the laser-field frequency ω . In this approximation the plane-wave recombination matrix element which appears in the strong-field approximation is replaced by the exact laser-free recombination matrix element calculated for the laser-field dressed electron momenta. First, we have shown that the HHG spectra obtained using the LFA agree with those obtained solving the time-dependent Schrödinger equation. Next, we have applied this LFA to calculate the HHG rate for inert gases exposed to a bicircular field. The bicircular field, which consists of two coplanar counter-rotating fields having different frequencies (usually ω and 2 ω ), is presently an important subject of scientific research since it enables efficient generation of circularly polarized high-order harmonics (coherent soft x rays). Analyzing the photorecombination matrix element we have found that the HHG rate can efficiently be calculated using the angular momentum basis with the states oriented in the direction of the bicircular field components. Our numerical results show that the HHG rate for atoms having p ground state, for higher high-order harmonic energies, is larger for circularly polarized harmonics having the helicity -1 . For lower energies the harmonics having helicity +1 prevails. The transition between these two harmonic energy regions can appear near the Cooper minimum, which, in the case of Ar atoms, makes the selection of high-order harmonics having the same helicity much easier. This is important for applications (for example, for generation of attosecond pulse trains of circularly polarized harmonics).
Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin
2016-01-01
What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright
Photoelectron spectroscopy and the dipole approximation
Energy Technology Data Exchange (ETDEWEB)
Hemmers, O.; Hansen, D.L.; Wang, H. [Univ. of Nevada, Las Vegas, NV (United States)] [and others
1997-04-01
Photoelectron spectroscopy is a powerful technique because it directly probes, via the measurement of photoelectron kinetic energies, orbital and band structure in valence and core levels in a wide variety of samples. The technique becomes even more powerful when it is performed in an angle-resolved mode, where photoelectrons are distinguished not only by their kinetic energy, but by their direction of emission as well. Determining the probability of electron ejection as a function of angle probes the different quantum-mechanical channels available to a photoemission process, because it is sensitive to phase differences among the channels. As a result, angle-resolved photoemission has been used successfully for many years to provide stringent tests of the understanding of basic physical processes underlying gas-phase and solid-state interactions with radiation. One mainstay in the application of angle-resolved photoelectron spectroscopy is the well-known electric-dipole approximation for photon interactions. In this simplification, all higher-order terms, such as those due to electric-quadrupole and magnetic-dipole interactions, are neglected. As the photon energy increases, however, effects beyond the dipole approximation become important. To best determine the range of validity of the dipole approximation, photoemission measurements on a simple atomic system, neon, where extra-atomic effects cannot play a role, were performed at BL 8.0. The measurements show that deviations from {open_quotes}dipole{close_quotes} expectations in angle-resolved valence photoemission are observable for photon energies down to at least 0.25 keV, and are quite significant at energies around 1 keV. From these results, it is clear that non-dipole angular-distribution effects may need to be considered in any application of angle-resolved photoelectron spectroscopy that uses x-ray photons of energies as low as a few hundred eV.
Product-State Approximations to Quantum States
Brandão, Fernando G. S. L.; Harrow, Aram W.
2016-02-01
We show that for any many-body quantum state there exists an unentangled quantum state such that most of the two-body reduced density matrices are close to those of the original state. This is a statement about the monogamy of entanglement, which cannot be shared without limit in the same way as classical correlation. Our main application is to Hamiltonians that are sums of two-body terms. For such Hamiltonians we show that there exist product states with energy that is close to the ground-state energy whenever the interaction graph of the Hamiltonian has high degree. This proves the validity of mean-field theory and gives an explicitly bounded approximation error. If we allow states that are entangled within small clusters of systems but product across clusters then good approximations exist when the Hamiltonian satisfies one or more of the following properties: (1) high degree, (2) small expansion, or (3) a ground state where the blocks in the partition have sublinear entanglement. Previously this was known only in the case of small expansion or in the regime where the entanglement was close to zero. Our approximations allow an extensive error in energy, which is the scale considered by the quantum PCP (probabilistically checkable proof) and NLTS (no low-energy trivial-state) conjectures. Thus our results put restrictions on the possible Hamiltonians that could be used for a possible proof of the qPCP or NLTS conjectures. By contrast the classical PCP constructions are often based on constraint graphs with high degree. Likewise we show that the parallel repetition that is possible with classical constraint satisfaction problems cannot also be possible for quantum Hamiltonians, unless qPCP is false. The main technical tool behind our results is a collection of new classical and quantum de Finetti theorems which do not make any symmetry assumptions on the underlying states.
Dynamic system evolution and markov chain approximation
Directory of Open Access Journals (Sweden)
Roderick V. Nicholas Melnik
1998-01-01
Full Text Available In this paper computational aspects of the mathematical modelling of dynamic system evolution have been considered as a problem in information theory. The construction of mathematical models is treated as a decision making process with limited available information.The solution of the problem is associated with a computational model based on heuristics of a Markov Chain in a discrete space–time of events. A stable approximation of the chain has been derived and the limiting cases are discussed. An intrinsic interconnection of constructive, sequential, and evolutionary approaches in related optimization problems provides new challenges for future work.
The EH Interpolation Spline and Its Approximation
Directory of Open Access Journals (Sweden)
Jin Xie
2014-01-01
Full Text Available A new interpolation spline with two parameters, called EH interpolation spline, is presented in this paper, which is the extension of the standard cubic Hermite interpolation spline, and inherits the same properties of the standard cubic Hermite interpolation spline. Given the fixed interpolation conditions, the shape of the proposed splines can be adjusted by changing the values of the parameters. Also, the introduced spline could approximate to the interpolated function better than the standard cubic Hermite interpolation spline and the quartic Hermite interpolation splines with single parameter by a new algorithm.
On one approximation in quantum chromodynamics
International Nuclear Information System (INIS)
Alekseev, A.I.; Bajkov, V.A.; Boos, Eh.Eh.
1982-01-01
Form of a complete fermion propagator near the mass shell is investigated. Considered is a nodel of quantum chromodynamics (MQC) where in the fermion section the Block-Nordsic approximation has been made, i. e. u-numbers are substituted for ν matrices. The model was investigated by means of the Schwinger-Dyson equation for a quark propagator in the infrared region. The Schwinger-Dyson equation was managed to reduce to a differential equation which is easily solved. At that, the Green function is suitable to represent as integral transformation
Topics in multivariate approximation and interpolation
Jetter, Kurt
2005-01-01
This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for gr
Shape theory categorical methods of approximation
Cordier, J M
2008-01-01
This in-depth treatment uses shape theory as a ""case study"" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras.A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and
Mean field approximation to QCD, 1
International Nuclear Information System (INIS)
Tezuka, Hirokazu.
1987-09-01
We apply mean field approximation to the gluon field in the equations of motion derived from the QCD lagrangian. The gluon mean field is restricted to the time-independent 0th component, and color exchange components are ignored. The equation of motion for the gluon mean field turns into a Poisson equation, and that for the quark field into a Dirac equation with a potential term. For example, assuming spherical symmetric box-like distribution and Gauss-like distribution to quarks, we try to solve these two equations simultaneously. (author)
Dislocation kinetics and the acoustic-wave approximation for liquids
International Nuclear Information System (INIS)
Stout, R.B.
1983-03-01
A dislocation-dependent model for liquids describes the lattice deformation and the fluidity deformation as additive deformations. The lattice deformation represents distortions of an atom's potential energy structure and is a recoverable deformation response. The fluidity deformation represents discontinuous repositioning of atoms by dislocation kinetics in the lattice structure and is a nonrecoverable deformation response. From this model, one concludes that in liquids the acoustic-wave approximation is a description of a recoverable oscillation deformation that has dissipation because of dislocation kinetics. Other more-complex waves may exist, but such waves would rapidly disappear because of the small thermodynamic potential for dislocation kinetics in liquids
Fuzzy Universal Model Approximator for Distributed Solar Collector Field Control
Elmetennani, Shahrazed
2014-07-01
This paper deals with the control of concentrating parabolic solar collectors by forcing the outlet oil temperature to track a set reference. A fuzzy universal approximate model is introduced in order to accurately reproduce the behavior of the system dynamics. The proposed model is a low order state space representation derived from the partial differential equation describing the oil temperature evolution using fuzzy transform theory. The resulting set of ordinary differential equations simplifies the system analysis and the control law design and is suitable for real time control implementation. Simulation results show good performance of the proposed model.
Lattice approximation of gauge theories with Dirac Kaehler fermions
International Nuclear Information System (INIS)
Joos, H.
1988-01-01
A program which tries to overcome the systematic difficulties caused by the lattice fermion problem by the consideration of models which describe Dirac fields by differential forms is reported. In the first lecture the formalism is developped and applied to the formulation of geometric QCD and of a Geometric Standard Model. The second lecture treats the characteristic symmetry problems which appear in the lattice approximation of geometric field theories. In the last lecture strong coupling dynamics of geometric QCD are considered with the final aim of a derivation of the quark model for the hadron spectrum. (author) [pt
Manifolds in random media: beyond the variational approximation
Goldschmidt, Yadin Y.
1994-01-01
In this paper we give a closed form expression for the 1/d corrections to the selfenergy characterizing the correlation function of a manifold in random media. This amounts to the first confection beyond the variational approximation. At this time we were able to evaluate these corrections in the high temperature "phase" of the notorious toy-model describing a classical particle subject to the influence of both a harmonic potential and a random potential. Although in this phase the correct solution is replica symmetric the calculation is non-trivial. The outcome is compared with previous analytical and numerical results. The corrections diverge at the "transition" temperature.
Nodal approximations in space and time for neutron kinetics
International Nuclear Information System (INIS)
Grossman, L.M.; Hennart, J.P.
2005-01-01
A general formalism is described of the nodal type in time and space for the neutron kinetics equations. In space, several nodal methods are given of the Raviart-Thomas type (RT0 and RT1), of the Brezzi-Douglas-Marini type (BDM0 and BDM1) and of the Brezzi-Douglas-Fortin-Marini type (BDFM 1). In time, polynomial and analytical approximations are derived. In the analytical case, they are based on the inclusion of an exponential term in the basis function. They can be continuous or discontinuous in time, leading in particular to the well-known Crank-Nicolson, Backward Euler and θ schemes
Phase diagram of charged dumbbells: a random phase approximation approach.
Kudlay, Alexander; Ermoshkin, Alexander V; de la Cruz, Monica Olvera
2004-08-01
The phase diagram of the charged hard dumbbell system (hard spheres of opposite unit charge fixed at contact) is obtained with the use of the random phase approximation (RPA). The effect of the impenetrability of charged spheres on charge-charge fluctuations is described by introduction of a modified electrostatic potential. The correlations of ions in a pair are included via a correlation function in the RPA. The coexistence curve is in good agreement with Monte Carlo simulations. The relevance of the theory to the restricted primitive model is discussed.
Approximating perfection a mathematician's journey into the world of mechanics
Lebedev, Leonid P
2004-01-01
This is a book for those who enjoy thinking about how and why Nature can be described using mathematical tools. Approximating Perfection considers the background behind mechanics as well as the mathematical ideas that play key roles in mechanical applications. Concentrating on the models of applied mechanics, the book engages the reader in the types of nuts-and-bolts considerations that are normally avoided in formal engineering courses: how and why models remain imperfect, and the factors that motivated their development. The opening chapter reviews and reconsiders the basics of c
Nodal approximations in space and time for neutron kinetics
Energy Technology Data Exchange (ETDEWEB)
Grossman, L.M. [Department of Nuclear Engineering, University of California, Berkeley, CA 94720 (United States); Hennart, J.P. [Department of Mathematical and Numerical Methods, Institute for Research in Applied Mathematics and Systems, National Autonomous University of Mexico, A.P. 20-726, 01000 Mexico D.F. (Mexico)
2005-07-01
A general formalism is described of the nodal type in time and space for the neutron kinetics equations. In space, several nodal methods are given of the Raviart-Thomas type (RT0 and RT1), of the Brezzi-Douglas-Marini type (BDM0 and BDM1) and of the Brezzi-Douglas-Fortin-Marini type (BDFM 1). In time, polynomial and analytical approximations are derived. In the analytical case, they are based on the inclusion of an exponential term in the basis function. They can be continuous or discontinuous in time, leading in particular to the well-known Crank-Nicolson, Backward Euler and {theta} schemes.
Delta-function Approximation SSC Model in 3C 273 S. J. Kang1 ...
Indian Academy of Sciences (India)
Abstract. We obtain an approximate analytical solution using δ approximate calculation on the traditional one-zone synchrotron self-. Compton (SSC) model. In this model, we describe the electron energy distribution by a broken power-law function with a sharp cut-off, and non- thermal photons are produced by both ...
Fast approximate hierarchical clustering using similarity heuristics
Directory of Open Access Journals (Sweden)
Kull Meelis
2008-09-01
Full Text Available Abstract Background Agglomerative hierarchical clustering (AHC is a common unsupervised data analysis technique used in several biological applications. Standard AHC methods require that all pairwise distances between data objects must be known. With ever-increasing data sizes this quadratic complexity poses problems that cannot be overcome by simply waiting for faster computers. Results We propose an approximate AHC algorithm HappieClust which can output a biologically meaningful clustering of a large dataset more than an order of magnitude faster than full AHC algorithms. The key to the algorithm is to limit the number of calculated pairwise distances to a carefully chosen subset of all possible distances. We choose distances using a similarity heuristic based on a small set of pivot objects. The heuristic efficiently finds pairs of similar objects and these help to mimic the greedy choices of full AHC. Quality of approximate AHC as compared to full AHC is studied with three measures. The first measure evaluates the global quality of the achieved clustering, while the second compares biological relevance using enrichment of biological functions in every subtree of the clusterings. The third measure studies how well the contents of subtrees are conserved between the clusterings. Conclusion The HappieClust algorithm is well suited for large-scale gene expression visualization and analysis both on personal computers as well as public online web applications. The software is available from the URL http://www.quretec.com/HappieClust
Traveling cluster approximation for uncorrelated amorphous systems
International Nuclear Information System (INIS)
Kaplan, T.; Sen, A.K.; Gray, L.J.; Mills, R.
1985-01-01
In this paper, the authors apply the TCA concepts to spatially disordered, uncorrelated systems (e.g., fluids or amorphous metals without short-range order). This is the first approximation scheme for amorphous systems that takes cluster effects into account while preserving the Herglotz property for any amount of disorder. They have performed some computer calculations for the pair TCA, for the model case of delta-function potentials on a one-dimensional random chain. These results are compared with exact calculations (which, in principle, taken into account all cluster effects) and with the CPA, which is the single-site TCA. The density of states for the pair TCA clearly shows some improvement over the CPA, and yet, apparently, the pair approximation distorts some of the features of the exact results. They conclude that the effects of large clusters are much more important in an uncorrelated liquid metal than in a substitutional alloy. As a result, the pair TCA, which does quite a nice job for alloys, is not adequate for the liquid. Larger clusters must be treated exactly, and therefore an n-TCA with n > 2 must be used
APPROXIMATING INNOVATION POTENTIAL WITH NEUROFUZZY ROBUST MODEL
Directory of Open Access Journals (Sweden)
Kasa, Richard
2015-01-01
Full Text Available In a remarkably short time, economic globalisation has changed the world’s economic order, bringing new challenges and opportunities to SMEs. These processes pushed the need to measure innovation capability, which has become a crucial issue for today’s economic and political decision makers. Companies cannot compete in this new environment unless they become more innovative and respond more effectively to consumers’ needs and preferences – as mentioned in the EU’s innovation strategy. Decision makers cannot make accurate and efficient decisions without knowing the capability for innovation of companies in a sector or a region. This need is forcing economists to develop an integrated, unified and complete method of measuring, approximating and even forecasting the innovation performance not only on a macro but also a micro level. In this recent article a critical analysis of the literature on innovation potential approximation and prediction is given, showing their weaknesses and a possible alternative that eliminates the limitations and disadvantages of classical measuring and predictive methods.
Analytic approximate radiation effects due to Bremsstrahlung
Energy Technology Data Exchange (ETDEWEB)
Ben-Zvi I.
2012-02-01
The purpose of this note is to provide analytic approximate expressions that can provide quick estimates of the various effects of the Bremsstrahlung radiation produced relatively low energy electrons, such as the dumping of the beam into the beam stop at the ERL or field emission in superconducting cavities. The purpose of this work is not to replace a dependable calculation or, better yet, a measurement under real conditions, but to provide a quick but approximate estimate for guidance purposes only. These effects include dose to personnel, ozone generation in the air volume exposed to the radiation, hydrogen generation in the beam dump water cooling system and radiation damage to near-by magnets. These expressions can be used for other purposes, but one should note that the electron beam energy range is limited. In these calculations the good range is from about 0.5 MeV to 10 MeV. To help in the application of this note, calculations are presented as a worked out example for the beam dump of the R&D Energy Recovery Linac.
Approximate reversal of quantum Gaussian dynamics
Lami, Ludovico; Das, Siddhartha; Wilde, Mark M.
2018-03-01
Recently, there has been focus on determining the conditions under which the data processing inequality for quantum relative entropy is satisfied with approximate equality. The solution of the exact equality case is due to Petz, who showed that the quantum relative entropy between two quantum states stays the same after the action of a quantum channel if and only if there is a reversal channel that recovers the original states after the channel acts. Furthermore, this reversal channel can be constructed explicitly and is now called the Petz recovery map. Recent developments have shown that a variation of the Petz recovery map works well for recovery in the case of approximate equality of the data processing inequality. Our main contribution here is a proof that bosonic Gaussian states and channels possess a particular closure property, namely, that the Petz recovery map associated to a bosonic Gaussian state σ and a bosonic Gaussian channel N is itself a bosonic Gaussian channel. We furthermore give an explicit construction of the Petz recovery map in this case, in terms of the mean vector and covariance matrix of the state σ and the Gaussian specification of the channel N .
Approximating Markov Chains: What and why
International Nuclear Information System (INIS)
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
Analytic approximate radiation effects due to Bremsstrahlung
International Nuclear Information System (INIS)
Ben-Zvi, I.
2012-01-01
The purpose of this note is to provide analytic approximate expressions that can provide quick estimates of the various effects of the Bremsstrahlung radiation produced relatively low energy electrons, such as the dumping of the beam into the beam stop at the ERL or field emission in superconducting cavities. The purpose of this work is not to replace a dependable calculation or, better yet, a measurement under real conditions, but to provide a quick but approximate estimate for guidance purposes only. These effects include dose to personnel, ozone generation in the air volume exposed to the radiation, hydrogen generation in the beam dump water cooling system and radiation damage to near-by magnets. These expressions can be used for other purposes, but one should note that the electron beam energy range is limited. In these calculations the good range is from about 0.5 MeV to 10 MeV. To help in the application of this note, calculations are presented as a worked out example for the beam dump of the R and D Energy Recovery Linac.
On some applications of diophantine approximations.
Chudnovsky, G V
1984-03-01
Siegel's results [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1] on the transcendence and algebraic independence of values of E-functions are refined to obtain the best possible bound for the measures of irrationality and linear independence of values of arbitrary E-functions at rational points. Our results show that values of E-functions at rational points have measures of diophantine approximations typical to "almost all" numbers. In particular, any such number has the "2 + epsilon" exponent of irrationality: Theta - p/q > q(-2-epsilon) for relatively prime rational integers p,q, with q >/= q(0) (Theta, epsilon). These results answer some problems posed by Lang. The methods used here are based on the introduction of graded Padé approximations to systems of functions satisfying linear differential equations with rational function coefficients. The constructions and proofs of this paper were used in the functional (nonarithmetic case) in a previous paper [Chudnovsky, D. V. & Chudnovsky, G. V. (1983) Proc. Natl. Acad. Sci. USA 80, 5158-5162].
Adaptive and Approximate Orthogonal Range Counting
DEFF Research Database (Denmark)
Chan, Timothy M.; Wilkinson, Bryan Thomas
2013-01-01
-case optimal query time O(log_w n). We give an O(n loglog n)-space adaptive data structure that improves the query time to O(loglog n + log_w k), where k is the output count. When k=O(1), our bounds match the state of the art for the 2-D orthogonal range emptiness problem [Chan, Larsen, and Pătraşcu, SoCG 2011......]. •We give an O(n loglog n)-space data structure for approximate 2-D orthogonal range counting that can compute a (1+δ)-factor approximation to the count in O(loglog n) time for any fixed constant δ>0. Again, our bounds match the state of the art for the 2-D orthogonal range emptiness problem. •Lastly......Close Abstract We present three new results on one of the most basic problems in geometric data structures, 2-D orthogonal range counting. All the results are in the w-bit word RAM model. •It is well known that there are linear-space data structures for 2-D orthogonal range counting with worst...
Aluminium and Alzheimer's disease: the science that describes the link
National Research Council Canada - National Science Library
Exley, Christopher
2001-01-01
... that has been encircled is the gene for the amyloid precursor protein. (Thanks to Walter Lukiw for supplying this information.) Aluminium and Alzheimer's Disease: The Science that Describes the LinkAluminium and Alzheimer's Disease The Science that Describes the Link Edited by Christopher Exley Birchall Centre for Inorganic Chemistry and Materials Scienc...
Approximate maximum likelihood estimation for population genetic inference.
Bertl, Johanna; Ewing, Gregory; Kosiol, Carolin; Futschik, Andreas
2017-11-27
In many population genetic problems, parameter estimation is obstructed by an intractable likelihood function. Therefore, approximate estimation methods have been developed, and with growing computational power, sampling-based methods became popular. However, these methods such as Approximate Bayesian Computation (ABC) can be inefficient in high-dimensional problems. This led to the development of more sophisticated iterative estimation methods like particle filters. Here, we propose an alternative approach that is based on stochastic approximation. By moving along a simulated gradient or ascent direction, the algorithm produces a sequence of estimates that eventually converges to the maximum likelihood estimate, given a set of observed summary statistics. This strategy does not sample much from low-likelihood regions of the parameter space, and is fast, even when many summary statistics are involved. We put considerable efforts into providing tuning guidelines that improve the robustness and lead to good performance on problems with high-dimensional summary statistics and a low signal-to-noise ratio. We then investigate the performance of our resulting approach and study its properties in simulations. Finally, we re-estimate parameters describing the demographic history of Bornean and Sumatran orang-utans.
Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets
Litvinenko, Alexander
2017-11-01
The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Matérn covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\\\H$-) matrix format with computational cost $\\\\mathcal{O}(k^2n \\\\log^2 n/p)$ and storage $\\\\mathcal{O}(kn \\\\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.
Pade approximants, NN scattering, and hard core repulsions
International Nuclear Information System (INIS)
Hartt, K.
1980-01-01
Pade approximants to the scattering function F=k cot(delta 0 ) are studied in terms of the variable x=k 2 , using four examples of potential models which possess features of the np 1 S 0 state. Strategies are thereby developed for analytically continuing F when only approximate partial knowledge of F is available. Results are characterized by high accuracy of interpolation. It is suggested that a physically realistic inverse scattering problem begins with such an analytically continued F. When it exists, the solution of this problem in terms of the Marchenko equation is a local potential of the Bargmann type. Some strategies for carrying out this program lead to a stably defined potential, while others do not. With hard core repulsions present, low-order Pade approximants accurately describe F for E/sub c.m./< or =300 MeV. However, since the condition Δ(infinity)-delta(0)=0 is not satisfied in any of our examples containing hard core repulsions, the Marchenko method does not have a solution for them. A possible physical consequence of this result is discussed. Another inverse scattering method is proposed for application to hard core problems
Multiple Scattering Model for Optical Coherence Tomography with Rytov Approximation
Li, Muxingzi
2017-04-24
Optical Coherence Tomography (OCT) is a coherence-gated, micrometer-resolution imaging technique that focuses a broadband near-infrared laser beam to penetrate into optical scattering media, e.g. biological tissues. The OCT resolution is split into two parts, with the axial resolution defined by half the coherence length, and the depth-dependent lateral resolution determined by the beam geometry, which is well described by a Gaussian beam model. The depth dependence of lateral resolution directly results in the defocusing effect outside the confocal region and restricts current OCT probes to small numerical aperture (NA) at the expense of lateral resolution near the focus. Another limitation on OCT development is the presence of a mixture of speckles due to multiple scatterers within the coherence length, and other random noise. Motivated by the above two challenges, a multiple scattering model based on Rytov approximation and Gaussian beam optics is proposed for the OCT setup. Some previous papers have adopted the first Born approximation with the assumption of small perturbation of the incident field in inhomogeneous media. The Rytov method of the same order with smooth phase perturbation assumption benefits from a wider spatial range of validity. A deconvolution method for solving the inverse problem associated with the first Rytov approximation is developed, significantly reducing the defocusing effect through depth and therefore extending the feasible range of NA.
DEFF Research Database (Denmark)
Sadegh, Payman
1997-01-01
This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...... of the optimization parameters. It is shown that, under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point, The procedure is illustrated by a numerical example, (C) 1997 Elsevier Science Ltd....
Thermal properties of composite materials: a complex systems approximation
Carrillo, J. L.; Bonilla, Beatriz; Reyes, J. J.; Dossetti, Victor
We propose an effective media approximation to describe the thermal diffusivity of composite samples made of polyester resin and magnetite inclusions. By means of photoacoustic spectroscopy, the thermal diffusivity of the samples were experimentally measured. The volume fraction of the inclusions was systematically varied in order to study the changes in the effective thermal diffusivity of the composites. For some samples, a static magnetic field was applied during the polymerization process, resulting in anisotropic inclusion distributions. Our results show a significant difference in the thermal properties of the anisotropic samples, compared to the isotropic randomly distributed. We correlate some measures of the complexity of the inclusion structure with the observed thermal response through a multifractal analysis. In this way, we are able to describe, and at some extent predict, the behavior of the thermal diffusivity in terms of the lacunarity and other measures of the complexity of these samples Partial Financial Support by CONACyT México and VIEP-BUAP.
Barlow, Nathaniel S; Schultz, Andrew J; Weinstein, Steven J; Kofke, David A
2015-08-21
The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.
International Nuclear Information System (INIS)
Weissbach, F.; Hencken, K.; Rohe, D.; Sick, I.; Trautmann, D.
2006-01-01
Analyzing (e,e ' p) experimental data involves corrections for radiative effects which change the interaction kinematics and which have to be carefully considered in order to obtain the desired accuracy. Missing momentum and energy due to bremsstrahlung have so far often been incorporated into the simulations and the experimental analyses using the peaking approximation. It assumes that all bremsstrahlung is emitted in the direction of the radiating particle. In this article we introduce a full angular Monte Carlo simulation method which overcomes this approximation. As a test, the angular distribution of the bremsstrahlung photons is reconstructed from H(e,e ' p) data. Its width is found to be underestimated by the peaking approximation and described much better by the approach developed in this work. The impact of the soft-photon approximation on the photon angular distribution is found to be minor as compared to the impact of the peaking approximation. (orig.)
Hydromagnetic turbulence in the direct interaction approximation
International Nuclear Information System (INIS)
Nagarajan, S.
1975-01-01
The dissertation is concerned with the nature of turbulence in a medium with large electrical conductivity. Three distinct though inter-related questions are asked. Firstly, the evolution of a weak, random initial magnetic field in a highly conducting, isotropically turbulent fluid is discussed. This was first discussed in the paper 'Growth of Turbulent Magnetic Fields' by Kraichnan and Nagargian. The Physics of Fluids, volume 10, number 4, 1967. Secondly, the direct interaction approximation for hydromagnetic turbulence maintained by stationary, isotropic, random stirring forces is formulated in the wave-number-frequency domain. Thirdly, the dynamical evolution of a weak, random, magnetic excitation in a turbulent electrically conducting fluid is examined under varying kinematic conditions. (G.T.H.)
Discrete Spectrum Reconstruction Using Integral Approximation Algorithm.
Sizikov, Valery; Sidorov, Denis
2017-07-01
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of linear-nonlinear equations (SLNE) with respect to intensities and frequencies of the discrete spectral lines. The SLNE is linear with respect to lines' intensities and nonlinear with respect to the lines' frequencies. The integral approximation algorithm is proposed for the solution of this SLNE. The algorithm combines solution of linear integral equations with solution of a system of linear algebraic equations and avoids nonlinear equations. Numerical examples of the application of the technique, both to synthetic and experimental spectra, demonstrate the efficacy of the proposed approach in enabling an effective enhancement of the spectrometer's resolution.
Nanostructures: Scattering beyond the Born approximation
Grigoriev, S. V.; Syromyatnikov, A. V.; Chumakov, A. P.; Grigoryeva, N. A.; Napolskii, K. S.; Roslyakov, I. V.; Eliseev, A. A.; Petukhov, A. V.; Eckerlebe, H.
2010-03-01
The neutron scattering on a two-dimensional ordered nanostructure with the third nonperiodic dimension can go beyond the Born approximation. In our model supported by the exact theoretical solution a well-correlated hexagonal porous structure of anodic aluminum oxide films acts as a peculiar two-dimensional grating for the coherent neutron wave. The thickness of the film L (length of pores) plays important role in the transition from the weak to the strong scattering regimes. It is shown that the coherency of the standard small-angle neutron scattering setups suits to the geometry of the studied objects and often affects the intensity of scattering. The proposed theoretical solution can be applied in the small-angle neutron diffraction experiments with flux lines in superconductors, periodic arrays of magnetic or superconducting nanowires, as well as in small-angle diffraction experiments on synchrotron radiation.
UFBoot2: Improving the Ultrafast Bootstrap Approximation.
Hoang, Diep Thi; Chernomor, Olga; von Haeseler, Arndt; Minh, Bui Quang; Vinh, Le Sy
2018-02-01
The standard bootstrap (SBS), despite being computationally intensive, is widely used in maximum likelihood phylogenetic analyses. We recently proposed the ultrafast bootstrap approximation (UFBoot) to reduce computing time while achieving more unbiased branch supports than SBS under mild model violations. UFBoot has been steadily adopted as an efficient alternative to SBS and other bootstrap approaches. Here, we present UFBoot2, which substantially accelerates UFBoot and reduces the risk of overestimating branch supports due to polytomies or severe model violations. Additionally, UFBoot2 provides suitable bootstrap resampling strategies for phylogenomic data. UFBoot2 is 778 times (median) faster than SBS and 8.4 times (median) faster than RAxML rapid bootstrap on tested data sets. UFBoot2 is implemented in the IQ-TREE software package version 1.6 and freely available at http://www.iqtree.org. © The Author 2017. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.
Approximation by max-product type operators
Bede, Barnabás; Gal, Sorin G
2016-01-01
This monograph presents a broad treatment of developments in an area of constructive approximation involving the so-called "max-product" type operators. The exposition highlights the max-product operators as those which allow one to obtain, in many cases, more valuable estimates than those obtained by classical approaches. The text considers a wide variety of operators which are studied for a number of interesting problems such as quantitative estimates, convergence, saturation results, localization, to name several. Additionally, the book discusses the perfect analogies between the probabilistic approaches of the classical Bernstein type operators and of the classical convolution operators (non-periodic and periodic cases), and the possibilistic approaches of the max-product variants of these operators. These approaches allow for two natural interpretations of the max-product Bernstein type operators and convolution type operators: firstly, as possibilistic expectations of some fuzzy variables, and secondly,...
PROX: Approximated Summarization of Data Provenance.
Ainy, Eleanor; Bourhis, Pierre; Davidson, Susan B; Deutch, Daniel; Milo, Tova
2016-03-01
Many modern applications involve collecting large amounts of data from multiple sources, and then aggregating and manipulating it in intricate ways. The complexity of such applications, combined with the size of the collected data, makes it difficult to understand the application logic and how information was derived. Data provenance has been proven helpful in this respect in different contexts; however, maintaining and presenting the full and exact provenance may be infeasible, due to its size and complex structure. For that reason, we introduce the notion of approximated summarized provenance, where we seek a compact representation of the provenance at the possible cost of information loss. Based on this notion, we have developed PROX, a system for the management, presentation and use of data provenance for complex applications. We propose to demonstrate PROX in the context of a movies rating crowd-sourcing system, letting participants view provenance summarization and use it to gain insights on the application and its underlying data.
Exact and Approximate Probabilistic Symbolic Execution
Luckow, Kasper; Pasareanu, Corina S.; Dwyer, Matthew B.; Filieri, Antonio; Visser, Willem
2014-01-01
Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.
Approximate analytical modeling of leptospirosis infection
Ismail, Nur Atikah; Azmi, Amirah; Yusof, Fauzi Mohamed; Ismail, Ahmad Izani
2017-11-01
Leptospirosis is an infectious disease carried by rodents which can cause death in humans. The disease spreads directly through contact with feces, urine or through bites of infected rodents and indirectly via water contaminated with urine and droppings from them. Significant increase in the number of leptospirosis cases in Malaysia caused by the recent severe floods were recorded during heavy rainfall season. Therefore, to understand the dynamics of leptospirosis infection, a mathematical model based on fractional differential equations have been developed and analyzed. In this paper an approximate analytical method, the multi-step Laplace Adomian decomposition method, has been used to conduct numerical simulations so as to gain insight on the spread of leptospirosis infection.
Analytical approximations for wide and narrow resonances
International Nuclear Information System (INIS)
Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da
2005-01-01
This paper aims at developing analytical expressions for the adjoint neutron spectrum in the resonance energy region, taking into account both narrow and wide resonance approximations, in order to reduce the numerical computations involved. These analytical expressions, besides reducing computing time, are very simple from a mathematical point of view. The results obtained with this analytical formulation were compared to a reference solution obtained with a numerical method previously developed to solve the neutron balance adjoint equations. Narrow and wide resonances of U 238 were treated and the analytical procedure gave satisfactory results as compared with the reference solution, for the resonance energy range. The adjoint neutron spectrum is useful to determine the neutron resonance absorption, so that multigroup adjoint cross sections used by the adjoint diffusion equation can be obtained. (author)
Analytical approximations for wide and narrow resonances
Energy Technology Data Exchange (ETDEWEB)
Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]. E-mail: aquilino@lmp.ufrj.br
2005-07-01
This paper aims at developing analytical expressions for the adjoint neutron spectrum in the resonance energy region, taking into account both narrow and wide resonance approximations, in order to reduce the numerical computations involved. These analytical expressions, besides reducing computing time, are very simple from a mathematical point of view. The results obtained with this analytical formulation were compared to a reference solution obtained with a numerical method previously developed to solve the neutron balance adjoint equations. Narrow and wide resonances of U{sup 238} were treated and the analytical procedure gave satisfactory results as compared with the reference solution, for the resonance energy range. The adjoint neutron spectrum is useful to determine the neutron resonance absorption, so that multigroup adjoint cross sections used by the adjoint diffusion equation can be obtained. (author)
Evaluating methods for approximating stochastic differential equations.
Brown, Scott D; Ratcliff, Roger; Smith, Philip L
2006-08-01
Models of decision making and response time (RT) are often formulated using stochastic differential equations (SDEs). Researchers often investigate these models using a simple Monte Carlo method based on Euler's method for solving ordinary differential equations. The accuracy of Euler's method is investigated and compared to the performance of more complex simulation methods. The more complex methods for solving SDEs yielded no improvement in accuracy over the Euler method. However, the matrix method proposed by Diederich and Busemeyer (2003) yielded significant improvements. The accuracy of all methods depended critically on the size of the approximating time step. The large (∼10 ms) step sizes often used by psychological researchers resulted in large and systematic errors in evaluating RT distributions.
Efficient Approximate OLAP Querying Over Time Series
DEFF Research Database (Denmark)
Perera, Kasun Baruhupolage Don Kasun Sanjeewa; Hahmann, Martin; Lehner, Wolfgang
2016-01-01
The ongoing trend for data gathering not only produces larger volumes of data, but also increases the variety of recorded data types. Out of these, especially time series, e.g. various sensor readings, have attracted attention in the domains of business intelligence and decision making. As OLAP...... queries play a major role in these domains, it is desirable to also execute them on time series data. While this is not a problem on the conceptual level, it can become a bottleneck with regards to query run-time. In general, processing OLAP queries gets more computationally intensive as the volume...... are either costly or require continuous maintenance. In this paper we propose an approach for approximate OLAP querying of time series that offers constant latency and is maintenance-free. To achieve this, we identify similarities between aggregation cuboids and propose algorithms that eliminate...
Approximate truncation robust computed tomography—ATRACT
International Nuclear Information System (INIS)
Dennerlein, Frank; Maier, Andreas
2013-01-01
We present an approximate truncation robust algorithm to compute tomographic images (ATRACT). This algorithm targets at reconstructing volumetric images from cone-beam projections in scenarios where these projections are highly truncated in each dimension. It thus facilitates reconstructions of small subvolumes of interest, without involving prior knowledge about the object. Our method is readily applicable to medical C-arm imaging, where it may contribute to new clinical workflows together with a considerable reduction of x-ray dose. We give a detailed derivation of ATRACT that starts from the conventional Feldkamp filtered-backprojection algorithm and that involves, as one component, a novel original formula for the inversion of the two-dimensional Radon transform. Discretization and numerical implementation are discussed and reconstruction results from both, simulated projections and first clinical data sets are presented. (paper)
Approximate Sensory Data Collection: A Survey
Directory of Open Access Journals (Sweden)
Siyao Cheng
2017-03-01
Full Text Available With the rapid development of the Internet of Things (IoTs, wireless sensor networks (WSNs and related techniques, the amount of sensory data manifests an explosive growth. In some applications of IoTs and WSNs, the size of sensory data has already exceeded several petabytes annually, which brings too many troubles and challenges for the data collection, which is a primary operation in IoTs and WSNs. Since the exact data collection is not affordable for many WSN and IoT systems due to the limitations on bandwidth and energy, many approximate data collection algorithms have been proposed in the last decade. This survey reviews the state of the art of approximatedatacollectionalgorithms. Weclassifythemintothreecategories: themodel-basedones, the compressive sensing based ones, and the query-driven ones. For each category of algorithms, the advantages and disadvantages are elaborated, some challenges and unsolved problems are pointed out, and the research prospects are forecasted.
Approximate Sensory Data Collection: A Survey.
Cheng, Siyao; Cai, Zhipeng; Li, Jianzhong
2017-03-10
With the rapid development of the Internet of Things (IoTs), wireless sensor networks (WSNs) and related techniques, the amount of sensory data manifests an explosive growth. In some applications of IoTs and WSNs, the size of sensory data has already exceeded several petabytes annually, which brings too many troubles and challenges for the data collection, which is a primary operation in IoTs and WSNs. Since the exact data collection is not affordable for many WSN and IoT systems due to the limitations on bandwidth and energy, many approximate data collection algorithms have been proposed in the last decade. This survey reviews the state of the art of approximatedatacollectionalgorithms. Weclassifythemintothreecategories: themodel-basedones, the compressive sensing based ones, and the query-driven ones. For each category of algorithms, the advantages and disadvantages are elaborated, some challenges and unsolved problems are pointed out, and the research prospects are forecasted.
The Bloch Approximation in Periodically Perforated Media
International Nuclear Information System (INIS)
Conca, C.; Gomez, D.; Lobo, M.; Perez, E.
2005-01-01
We consider a periodically heterogeneous and perforated medium filling an open domain Ω of R N . Assuming that the size of the periodicity of the structure and of the holes is O(ε),we study the asymptotic behavior, as ε → 0, of the solution of an elliptic boundary value problem with strongly oscillating coefficients posed in Ω ε (Ω ε being Ω minus the holes) with a Neumann condition on the boundary of the holes. We use Bloch wave decomposition to introduce an approximation of the solution in the energy norm which can be computed from the homogenized solution and the first Bloch eigenfunction. We first consider the case where Ωis R N and then localize the problem for abounded domain Ω, considering a homogeneous Dirichlet condition on the boundary of Ω
Coated sphere scattering by geometric optics approximation.
Mengran, Zhai; Qieni, Lü; Hongxia, Zhang; Yinxin, Zhang
2014-10-01
A new geometric optics model has been developed for the calculation of light scattering by a coated sphere, and the analytic expression for scattering is presented according to whether rays hit the core or not. The ray of various geometric optics approximation (GOA) terms is parameterized by the number of reflections in the coating/core interface, the coating/medium interface, and the number of chords in the core, with the degeneracy path and repeated path terms considered for the rays striking the core, which simplifies the calculation. For the ray missing the core, the various GOA terms are dealt with by a homogeneous sphere. The scattering intensity of coated particles are calculated and then compared with those of Debye series and Aden-Kerker theory. The consistency of the results proves the validity of the method proposed in this work.
Describing Simple Data Access Services Version 1.1
Plante, Ray; Demleitner, Markus; Plante, Raymond; Delago, Jesus; Harrison, Paul; Tody, Doug; Plante, Ray; Demleitner, Markus
2017-05-01
An application that queries or consumes descriptions of VO resources must be able to recognize a resource's support for standard IVOA protocols. This specification describes how to describe a service that supports any of the four typed data access protocols - Simple Cone Search (SCS), Simple Image Access (SIA), Simple Spectral Access (SSA), Simple Line Access (SLA) - using the VOResource XML encoding standard. A key part of this specification is the set of VOResource XML extension schemas that define new metadata that are specific to those protocols. This document describes rules for describing such services within the context of IVOA Registries and data discovery as well as the VO Support Interfaces (VOSI) and service self-description. In particular, this document spells out the essential mark-up needed to identify support for a standard protocol and the base URL required to access the interface that supports that protocol.
Chikungunya means 'that which bends up', and describes the ...
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. CHIK virus was first isolated from patients during an epidemic in Tanzania in 1952-53. Chikungunya means 'that which bends up', and describes the symptoms caused by the severe joint pains.
Propositions that describe the intended meaning of Enterprise Architecture
CSIR Research Space (South Africa)
Mentz, JC
2014-09-01
Full Text Available In scientific inquiry definitions serves the purpose of describing what something is in terms that are concise, precise and allows for clear communication. Since the start of the enterprise architecture (EA) research field the issue...
Approximate formulas for elasticity of the Tornquist functions and some their advantages
Issin, Meyram
2017-09-01
In this article functions of demand for prime necessity, second necessity and luxury goods depending on the income are considered. These functions are called Tornquist functions. By means of the return model the demand for prime necessity goods and second necessity goods are approximately described. Then on the basis of a method of the smallest squares approximate formulas for elasticity of these Tornquist functions are received. To receive an approximate formula for elasticity of function of demand for luxury goods, the linear asymptotic formula is constructed for this function. Some benefits of approximate formulas for elasticity of Tornquist functions are specified.
Zulma Ageitos de Castellanos: Publications and status of described taxa.
Signorelli, Javier H; Urteaga, Diego; Teso, Valeria
2015-10-28
Zulma Ageitos de Castellanos was an Argentinian malacologist working in the "Facultad de Ciencias Naturales y Museo" at La Plata University where she taught invertebrate zoology between 1947 and 1990. Her scientific publications are listed in chronological order. Described genus-group and species-group taxa are listed. Information about the type locality and type material, and taxonomic remarks are also provided. Finally, type material of all described taxa was requested and, when located, illustrated.
Layered recognition networks that pre-process, classify, and describe
Uhr, L.
1971-01-01
A brief overview is presented of six types of pattern recognition programs that: (1) preprocess, then characterize; (2) preprocess and characterize together; (3) preprocess and characterize into a recognition cone; (4) describe as well as name; (5) compose interrelated descriptions; and (6) converse. A computer program (of types 3 through 6) is presented that transforms and characterizes the input scene through the successive layers of a recognition cone, and then engages in a stylized conversation to describe the scene.
System reliability assessment with an approximate reasoning model
Energy Technology Data Exchange (ETDEWEB)
Eisenhawer, S.W.; Bott, T.F.; Helm, T.M.; Boerigter, S.T.
1998-12-31
The projected service life of weapons in the US nuclear stockpile will exceed the original design life of their critical components. Interim metrics are needed to describe weapon states for use in simulation models of the nuclear weapons complex. The authors present an approach to this problem based upon the theory of approximate reasoning (AR) that allows meaningful assessments to be made in an environment where reliability models are incomplete. AR models are designed to emulate the inference process used by subject matter experts. The emulation is based upon a formal logic structure that relates evidence about components. This evidence is translated using natural language expressions into linguistic variables that describe membership in fuzzy sets. The authors introduce a metric that measures the acceptability of a weapon to nuclear deterrence planners. Implication rule bases are used to draw a series of forward chaining inferences about the acceptability of components, subsystems and individual weapons. They describe each component in the AR model in some detail and illustrate its behavior with a small example. The integration of the acceptability metric into a prototype model to simulate the weapons complex is also described.
DEFF Research Database (Denmark)
Sadegh, Payman; Spall, J. C.
1998-01-01
The simultaneous perturbation stochastic approximation (SPSA) algorithm has attracted considerable attention for challenging optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient...... simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...... process. The objective is to minimize the mean square error of the estimate. The authors also consider maximization of the likelihood that the estimate be confined within a bounded symmetric region of the true parameter. The optimal distribution for the components of the simultaneous perturbation vector...
DEFF Research Database (Denmark)
Sadegh, Payman; Spall, J. C.
1997-01-01
The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient...... simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...... process. The objective is to minimize the mean square error of the estimate. We also consider maximization of the likelihood that the estimate be confined within a bounded symmetric region of the true parameter. The optimal distribution for the components of the simultaneous perturbation vector is found...
Some properties of dual and approximate dual of fusion frames
Arefijamaal, Ali Akbar; Neyshaburi, Fahimeh Arabyani
2016-01-01
In this paper we extend the notion of approximate dual to fusion frames and present some approaches to obtain dual and approximate alternate dual fusion frames. Also, we study the stability of dual and approximate alternate dual fusion frames.
Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.
Wei, Qinglai; Li, Benkai; Song, Ruizhuo
2018-04-01
In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.
Approximate Model for Turbulent Stagnation Point Flow.
Energy Technology Data Exchange (ETDEWEB)
Dechant, Lawrence [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
Here we derive an approximate turbulent self-similar model for a class of favorable pressure gradient wedge-like flows, focusing on the stagnation point limit. While the self-similar model provides a useful gross flow field estimate this approach must be combined with a near wall model is to determine skin friction and by Reynolds analogy the heat transfer coefficient. The combined approach is developed in detail for the stagnation point flow problem where turbulent skin friction and Nusselt number results are obtained. Comparison to the classical Van Driest (1958) result suggests overall reasonable agreement. Though the model is only valid near the stagnation region of cylinders and spheres it nonetheless provides a reasonable model for overall cylinder and sphere heat transfer. The enhancement effect of free stream turbulence upon the laminar flow is used to derive a similar expression which is valid for turbulent flow. Examination of free stream enhanced laminar flow suggests that the rather than enhancement of a laminar flow behavior free stream disturbance results in early transition to turbulent stagnation point behavior. Excellent agreement is shown between enhanced laminar flow and turbulent flow behavior for high levels, e.g. 5% of free stream turbulence. Finally the blunt body turbulent stagnation results are shown to provide realistic heat transfer results for turbulent jet impingement problems.
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.
Adaptive approximation of higher order posterior statistics
Lee, Wonjung
2014-02-01
Filtering is an approach for incorporating observed data into time-evolving systems. Instead of a family of Dirac delta masses that is widely used in Monte Carlo methods, we here use the Wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem. The Wiener chaos expansion is not the best method for uncertainty propagation without observations. Nevertheless, the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the Wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification, but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution. The aim of the present paper is to investigate this hypothesis. We answer in the affirmative for the (stochastic) Lorenz-63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by Brownian motion and the near-Gaussianity of the measure to be updated, respectively. © 2013 Elsevier Inc.
Rainbows: Mie computations and the Airy approximation.
Wang, R T; van de Hulst, H C
1991-01-01
Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to 6 mm. We present a method for evaluating the Mie coefficients from the ratios between Riccati-Bessel and Neumann functions of successive order. We probe the applicability of the Airy approximation, which we generalize to rainbows of arbitrary p (number of internal reflections = p - 1), by comparing the Mie and Airy intensity patterns. Millimeter size water drops show a match in all details, including the position and intensity of the supernumerary maxima and the polarization. A fairly good match is still seen for drops of 0.1 mm. A small spread in sizes helps to smooth out irrelevant detail. The dark band between the rainbows is used to test more subtle features. We conclude that this band contains not only externally reflected light (p = 0) but also a sizable contribution f rom the p = 6 and p = 7 rainbows, which shift rapidly with wavelength. The higher the refractive index, the closer both theories agree on the first primary rainbow (p = 2) peak for drop diameters as small as 0.02 mm. This may be useful in supporting experimental work.
Approximate von Neumann entropy for directed graphs.
Ye, Cheng; Wilson, Richard C; Comin, César H; Costa, Luciano da F; Hancock, Edwin R
2014-05-01
In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks.
Turbulent Evolution of a Plasma Described Through Classical Mechanics Only
International Nuclear Information System (INIS)
Escande, D.F.; Elskens, Y.
2003-01-01
For the first time an old dream of the XIXth century comes true: the non trivial evolution of a macroscopic many-body system is described through classical mechanics only. This is done for the relaxation of a warm electron beam in a plasma, which results in the generation of Langmuir turbulence and in the formation of a plateau in the velocity distribution function of the electrons. Our derivation starts from the hamiltonian describing the one-dimensional N-body system corresponding to the beam and plasma bulk electrons in electrostatic interaction. For such a system, the dynamics can be reduced to the resonant interaction of M Langmuir waves with N'( > 1 Langmuir waves with N' >> 1 beam particles. This yields the proof of the classical quasilinear equations describing the coupled evolution of the wave spectrum and of the beam velocity distribution function in the strongly nonlinear regime where their validity is the matter of a longstanding controversy