Phase diagrams of the ternary alloy with a single-ion anisotropy in the mean-field approximation
International Nuclear Information System (INIS)
Dely, J.; Bobak, A.
2006-01-01
The phase diagram of the AB p C 1-p ternary alloy consisting of Ising spins S A =32, S B =2, and S C =52 is investigated by the use of a mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. The effect of the single-ion anisotropy on the phase diagrams is discussed by changing values of the parameters in the model Hamiltonian and comparison is made with the recently reported finite-temperature phase diagrams for the ternary alloy having spin S B =1
Dentate Gyrus circuitry features improve performance of sparse approximation algorithms.
Directory of Open Access Journals (Sweden)
Panagiotis C Petrantonakis
Full Text Available Memory-related activity in the Dentate Gyrus (DG is characterized by sparsity. Memory representations are seen as activated neuronal populations of granule cells, the main encoding cells in DG, which are estimated to engage 2-4% of the total population. This sparsity is assumed to enhance the ability of DG to perform pattern separation, one of the most valuable contributions of DG during memory formation. In this work, we investigate how features of the DG such as its excitatory and inhibitory connectivity diagram can be used to develop theoretical algorithms performing Sparse Approximation, a widely used strategy in the Signal Processing field. Sparse approximation stands for the algorithmic identification of few components from a dictionary that approximate a certain signal. The ability of DG to achieve pattern separation by sparsifing its representations is exploited here to improve the performance of the state of the art sparse approximation algorithm "Iterative Soft Thresholding" (IST by adding new algorithmic features inspired by the DG circuitry. Lateral inhibition of granule cells, either direct or indirect, via mossy cells, is shown to enhance the performance of the IST. Apart from revealing the potential of DG-inspired theoretical algorithms, this work presents new insights regarding the function of particular cell types in the pattern separation task of the DG.
Single-ion irradiation: physics, technology and applications
International Nuclear Information System (INIS)
Ohdomari, Iwao
2008-01-01
Among the various radiation effects which involve the study of radiation environments, responses of materials and devices to radiation, radiation testing and radiation hardening of devices and equipment, this review mainly considers the radiation effects induced by alpha particles and other ions used in semiconductor technology on Si crystals and Si devices. We first describe the single-ion microprobe that enables the study of the site dependence of radiation hardness in a semiconductor device. Next, we describe single-ion implantation as a tool for suppressing fluctuation in device function induced by the discrete number and random position of dopant atoms. Finally, we describe the common features associated with both 'probing' and 'modification' in terms of the nature and behaviour of defect clusters induced by single-ion irradiation. A special feature of the review is that the radiation effects discussed here are induced by 'single' particles, and not by particle beams. Although there is a great amount of accumulated data on radiation effects, they are discussed in the conventional terms of 'dose' or 'fluence,' whose unit is cm -2 . Therefore, this review provides complementary information on radiation effects. (topical review)
Directory of Open Access Journals (Sweden)
Hui Huang
2017-01-01
Full Text Available According to the pros and cons of contourlet transform and multimodality medical imaging, here we propose a novel image fusion algorithm that combines nonlinear approximation of contourlet transform with image regional features. The most important coefficient bands of the contourlet sparse matrix are retained by nonlinear approximation. Low-frequency and high-frequency regional features are also elaborated to fuse medical images. The results strongly suggested that the proposed algorithm could improve the visual effects of medical image fusion and image quality, image denoising, and enhancement.
Liu, Yongbin; He, Bing; Liu, Fang; Lu, Siliang; Zhao, Yilei
2016-12-01
Fault pattern identification is a crucial step for the intelligent fault diagnosis of real-time health conditions in monitoring a mechanical system. However, many challenges exist in extracting the effective feature from vibration signals for fault recognition. A new feature fusion method is proposed in this study to extract new features using kernel joint approximate diagonalization of eigen-matrices (KJADE). In the method, the input space that is composed of original features is mapped into a high-dimensional feature space by nonlinear mapping. Then, the new features can be estimated through the eigen-decomposition of the fourth-order cumulative kernel matrix obtained from the feature space. Therefore, the proposed method could be used to reduce data redundancy because it extracts the inherent pattern structure of different fault classes as it is nonlinear by nature. The integration evaluation factor of between-class and within-class scatters (SS) is employed to depict the clustering performance quantitatively, and the new feature subset extracted by the proposed method is fed into a multi-class support vector machine for fault pattern identification. Finally, the effectiveness of the proposed method is verified by experimental vibration signals with different bearing fault types and severities. Results of several cases show that the KJADE algorithm is efficient in feature fusion for bearing fault identification.
Directory of Open Access Journals (Sweden)
Jarosław Rudy
2015-01-01
Full Text Available In this paper the job shop scheduling problem (JSP with minimizing two criteria simultaneously is considered. JSP is frequently used model in real world applications of combinatorial optimization. Multi-objective job shop problems (MOJSP were rarely studied. We implement and compare two multi-agent nature-based methods, namely ant colony optimization (ACO and genetic algorithm (GA for MOJSP. Both of those methods employ certain technique, taken from the multi-criteria decision analysis in order to establish ranking of solutions. ACO and GA differ in a method of keeping information about previously found solutions and their quality, which affects the course of the search. In result, new features of Pareto approximations provided by said algorithms are observed: aside from the slight superiority of the ACO method the Pareto frontier approximations provided by both methods are disjoint sets. Thus, both methods can be used to search mutually exclusive areas of the Pareto frontier.
Tian, Fuyang; Cao, Dong; Dong, Xiaoning; Zhao, Xinqiang; Li, Fade; Wang, Zhonghua
2017-06-01
Behavioral features recognition was an important effect to detect oestrus and sickness in dairy herds and there is a need for heat detection aid. The detection method was based on the measure of the individual behavioural activity, standing time, and temperature of dairy using vibrational sensor and temperature sensor in this paper. The data of behavioural activity index, standing time, lying time and walking time were sent to computer by lower power consumption wireless communication system. The fast approximate K-means algorithm (FAKM) was proposed to deal the data of the sensor for behavioral features recognition. As a result of technical progress in monitoring cows using computers, automatic oestrus detection has become possible.
Improved single ion cyclotron resonance mass spectroscopy
International Nuclear Information System (INIS)
Boyce, K.R.
1993-01-01
The author has improved the state of the art for precision mass spectroscopy of a mass doublet to below one part in 10 10 . By alternately loading single ions into a Penning trap, the author has determined the mass ratio M(CO + )/M(N + 2 ) = 0.999 598 887 74(11), an accuracy of 1 x 10 -10 . This is a factor of 4 improvement over previous measurements, and a factor of 10 better than the 1985 atomic mass table adjustment [WAA85a]. Much of the author's apparatus has been rebuilt, increasing the signal-to-noise ratio and improving the reliability of the machine. The typical time needed to make and cool a single ion has been reduced from about half an hour to under 5 minutes. This was done by a combination of faster ion-making and a much faster procedure for driving out ions of the wrong species. The improved S/N, in combination with a much better signal processing algorithm to extract the ion phase and frequency from the author's data, has substantially reduced the time required for the actual measurements. This is important now that the measurement time is a substantial fraction of the cycle time (the time to make a new ion and measure it). The improvements allow over 30 comparisons in one night, compared to 2 per night previously. This not only improves the statistics, but eliminates the possibility of large non-Gaussian errors due to sudden magnetic field shifts
Specific features of time-dependent Psub(N) approximations in spherical geometry
International Nuclear Information System (INIS)
Peltzer, P.; Pucker, N.
1979-01-01
Approximations to the time-dependent linear transport equation can result in more serious distortions in the description of the actual physical situation than in the stationary problem. This is demonstrated in detail for the case of a neutron pulse in spherical geometry, treated within a P 1 approximation. One has to pay special attention to the singularity at r = 0 and to the effect of the boundary conditions. Effects similar to those shown here are also to be expected in connection with Psub(N) approximations of higher order. (Auth.)
Improvement of the Energy Stability of the Single Ion Microbeam
International Nuclear Information System (INIS)
Zhan Furu; Qi Xuehong; Xu Mingliang; Chen Lianyun; Yu Zengliang
2008-01-01
Energy instability strongly affects the state and the beam size of the single ion microbeam. A facility based on the Generating Voltmeter was developed to improve the energy stability of the CAS-LIBB (Chinese Academy of Sciences, key laboratory of ion beam bioengineering) single ion microbeam. This paper presents the analysis of the energy instability of the single ion microbeam. A simplified theoretical model is set up to calculate the relationship between the energy instability and the beam spot size. By using this technique, the energy instability is adjusted to about 1%. Stable run-time is over 6 hours. The radius of the single ion beam is reduced by 10% compared to the previous one.
Development of pulsation technique for single ion hit system
Energy Technology Data Exchange (ETDEWEB)
Sakai, Takuro; Hamano, Tsuyoshi; Hirao, Toshio; Kamiya, Tomihiro [Japan Atomic Energy Research Inst., Takasaki, Gunma (Japan). Takasaki Radiation Chemistry Research Establishment
1996-12-01
When a high energy heavy ion enters into a substance, high density of ionization and excitement occurrs along its flying trace. Especially, when such an ion enters into a semiconductor cell, a bit inversion called single event is occurred or a phenomenon destroyed element itself on case of the worst is formed. The present semiconductor cell is made in a size of some micron square, as different from its accumulated degree. In order to analyze the single event phenomenon formed by entering ion into such fine region in detail, a technique possible enter heavy ion beam with space resolution under 1 micron to each sample is necessary. In order to develop this technique, a static type high speed beam switch for control of entering a beam into a sample and a single ion detector for detecting entrance of ion into the sample were installed to heavy ion microbeam forming apparatus. The single ion hit system in Takasaki Radiation Chemistry Research Establishment, JAERI succeeded in detection and control technique of the single ion and control of noise due to pulsization and finished development of basic technique of the single ion hit, since now. After today, it is planned to hit actually the single ion onto the sample and evaluate its accuracy. (G.K.)
Development of a keV single-ion-implanter for nanofabrication
International Nuclear Information System (INIS)
Yang, C.; Jamieson, D.N.; Hopf, T.; Tamanyan, G.; Spizziri, P.; Pakes, C.; Andresen, S.E.; Hudson, F.; Gauja, E.; Dzurak, A.; Clark, R.G.
2005-01-01
Traditional methods of doping semiconductors have a difficulty meeting the demand for high precision doping due to large statistical fluctuations in the numbers of dopant atoms introduced in the ever shrinking volume in micro- and nano-electronics devices, especially when the fabrication process approaches the nanometre scale. The statistical fluctuations in doping semiconductors for the fabrication of devices with a very small feature size may lead to inconsistent and unreliable performance. This paper describes the adaptation of a commercial ion implanter into a single-ion-implantation system for the accurate delivery of dopants into a nanometre or micrometre area in a silicon substrate. All the implanted ions can be accurately counted with near 100% certainty through online detection using the silicon substrate itself as an ion detector. A variety of ion species including B + , N + , P + at the energy range of 10-15 keV can be delivered in the single ion implantation system. (author). 6 refs., 6 figs
Single Ion Trapping for the Enriched Xenon Observatory
Energy Technology Data Exchange (ETDEWEB)
Waldman, Samuel J.; /Stanford U., Phys. Dept. /SLAC
2006-03-28
In the last decade, a variety of neutrino oscillation experiments have established that there is a mass difference between neutrino flavors, without determining the absolute neutrino mass scale. The Enriched Xenon Observatory for neutrinoless double beta decay (EXO) will search for the rare decays of xenon to determine the absolute value of the neutrino mass. The experiment uses a novel technique to minimize backgrounds, identifying the decay daughter product in real time using single ion spectroscopy. Here, we describe single ion trapping and spectroscopy compatible with the EXO detector. We extend the technique of single ion trapping in ultrahigh vacuum to trapping in xenon gas. With this technique, EXO will achieve a neutrino mass sensitivity of
International Nuclear Information System (INIS)
Oshtrakh, M. I.; Semionkin, V. A.
2004-01-01
Moessbauer spectra of hemoglobins have some features in the range of liquid nitrogen temperature: a non-Lorentzian asymmetric line shape for oxyhemoglobins and symmetric Lorentzian line shape for deoxyhemoglobins. A comparison of the approximation of the hemoglobin Moessbauer spectra by a superposition of two quadrupole doublets and by a distribution of the quadrupole splitting demonstrates that a superposition of two quadrupole doublets is more reliable and may reflect the non-equivalent iron electronic structure and the stereochemistry in the α- and β-subunits of hemoglobin tetramers.
Single ion counting with a MCP (microchannel plate) detector
Energy Technology Data Exchange (ETDEWEB)
Tawara, Hiroko; Sasaki, Shinichi; Miyajima, Mitsuhiro [National Lab. for High Energy Physics, Tsukuba, Ibaraki (Japan); Shibamura, Eido
1996-07-01
In this study, a single-ion-counting method using alpha-particle-impact ionization of Ar atoms is demonstrated and the preliminary {epsilon}{sub mcp} for Ar ions with incident energies of 3 to 4.7 keV is determined. The single-ion counting by the MCP is aimed to be performed under experimental conditions as follows: (1) A signal from the MCP is reasonably identified as incidence of single Ar-ion. (2) The counting rate of Ar ions is less than 1 s{sup -1}. (3) The incident Ar ions are not focused on a small part of an active area of the MCP, namely, {epsilon}{sub mcp} is determined with respect to the whole active area of the MCP. So far, any absolute detection efficiency has not been reported under these conditions. (J.P.N.)
Quantum Heisenberg antiferromagnetic chains with exchange and single-ion anisotropies
International Nuclear Information System (INIS)
Peters, D; Selke, W; McCulloch, I P
2010-01-01
Using density matrix renormalization group calculations, ground state properties of the spin-1 Heisenberg chain with exchange and quadratic single-ion anisotropies in an external field are studied, for special choices of the two kinds of anisotropies. In particular, the phase diagram includes antiferromagnetic, spin-liquid (or spin-flop), IS2, and supersolid (or biconical) phases. Especially, new features of the spin-liquid and supersolid phases are discussed. Properties of the quantum chains are compared to those of corresponding classical spin chains.
Energy Technology Data Exchange (ETDEWEB)
Yokoyama, Akihito, E-mail: yokoyama.akihito@jaea.go.jp [Graduate School of Science and Technology, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma 376-8515 (Japan); Takasaki Advanced Radiation Research Institute (TARRI), Japan Atomic Energy Agency (JAEA), 1233 Watanuki-machi, Takasaki, Gunma 370-1292 (Japan); Kada, Wataru [Graduate School of Science and Technology, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma 376-8515 (Japan); Satoh, Takahiro; Koka, Masashi [Takasaki Advanced Radiation Research Institute (TARRI), Japan Atomic Energy Agency (JAEA), 1233 Watanuki-machi, Takasaki, Gunma 370-1292 (Japan); Shimada, Keisuke; Yokoata, Yuya; Miura, Kenta; Hanaizumi, Osamu [Graduate School of Science and Technology, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma 376-8515 (Japan)
2016-03-15
In this paper, we propose and test a real-time detection system for single-ion hits using mega-electronvolt (MeV)-heavy ions. The system was constructed using G2000 and G9 glass scintillators, as well as an electron-multiplying charge-coupled device (EMCCD) camera combined with an inverted microscope with a 10× objective lens. Commercially available G2000 and G9 glass scintillators, which have been reported to exhibit strong photoluminescence at 489, 543, 585, and 622 nm as a result of the Tb{sup 3+} f–f transition, were employed for highly accurate ionized particle detection. The EMCCD camera had a resolution of 512 × 512 pixels, each with a size of 16 μm × 16 μm, and a maximum linear gain of 8 × 10{sup 5} electrons. For 260-MeV Ne, 3 ion hits/s were detected by our system. The intensity of the ionoluminescence (IL) peak induced by the heavy ions was 140 times the noise intensity. In contrast, the luminous diameter at the full width at half maximum (FWHM) in both the horizontal and vertical directions was calculated to be approximately 4.5 μm. These results suggest that our detection system can accurately detect single-ion hits with a diameter of the order of 1 μm.
Plastic flow produced by single ion impacts on metals
International Nuclear Information System (INIS)
Birtcher, R. C.
1998-01-01
Single ion impacts have been observed using in situ transmission electron microscopy and video recording with a time resolution of 33 milliseconds. Gold was irradiated at 50 K and room temperature. Single ion impacts produce holes, modify existing holes, and extrude material into the initial specimen hole and holes formed by other ion impacts. The same behavior is observed at both temperatures. At both temperatures, ion impacts result in craters and ejected material. Ion impacts produce more small craters than large ones for all ion masses, while heavier mass ions produce more and larger craters than lighter mass ions. This comparison is affected by the ion energy. As the energy of an ion is increased, the probability for deposition near the surface decreases and fewer craters are formed. For a given ion mass, crater production depends on the probability for displacement cascade production in the near surface region. Crater and holes are stable at room temperature, however, ion impacts near an existing crater may cause flow of material into the crater either reshaping or annihilating it. Holes and craters result from the explosive outflow of material from the molten zone of near-surface cascades. The outflow may take the form of molten material, a solid lid or an ejected particle. The surface is a major perturbation on displacement cascades resulting from ion impacts
Plastic Flow Induced by Single Ion Impacts on Gold
International Nuclear Information System (INIS)
Birtcher, R.C.; Donnelly, S.E.
1996-01-01
The formation of holes in thin gold foils as a result of single ion impacts by 200keV Xe ions has been followed using transmission electron microscopy. Video recording provided details of microstructure evolution with a time resolution of 1/30th sec. Hole formation involves the movement by plastic flow of massive amounts of material, on the order of tens of thousands of Au atoms per ion impact. Plastic flow, as a consequence of individual ion impacts, results in a continual filling of both holes and craters as well as a thickening of the gold foil. Changes in morphology during irradiation is attributed to a localized, thermal-spike induced melting, coupled with plastic flow of effected material under the influence of surface forces. copyright 1996 The American Physical Society
Single-ion and single-chain magnetism in triangular spin-chain oxides
Seikh, Md. Motin; Caignaert, Vincent; Perez, Olivier; Raveau, Bernard; Hardy, Vincent
2017-05-01
S r4 -xC axM n2Co O9 oxides (x =0 and x =2 ) are found to exhibit magnetic responses typical of single-chain magnets (SCMs) and single-ion magnets (SIMs), two features generally investigated in coordination polymers or complexes. The compound x =0 appears to be a genuine SCM, in that blocking effects associated with slow spin dynamics yield remanence and coercivity in the absence of long-range ordering (LRO). In addition, SIM signatures of nearly identical nature are detected in both compounds, coexisting with SCM in x =0 and with LRO in x =2 . It is also observed that a SCM response can be recovered in x =2 after application of magnetic field. These results suggest that purely inorganic systems could play a valuable role in the topical issue of the interplay among SIM, SCM, and LRO phenomena in low-dimensional magnetism.
Design of a single ion facility and its applications
Energy Technology Data Exchange (ETDEWEB)
Cholewa, M.; Saint, A.; Legge, G.J.F. [Melbourne Univ., Parkville, VIC (Australia). School of Physics
1996-12-31
The use of micro-irradiation techniques in radiobiology is not new; however, the current techniques take advantage of recent developments in particle delivery, focussing detection, image processing, cell recognition and computer control. These developments have generally come from other fields, for example microbeam elemental analysis techniques and single-event upset testing of semiconductor devices. Also in radiation biology there have been important advances in developments of individual cell assays, which allow a wide range of endpoints to be studied with good accuracy at low doses. Many of the studies that are planned involve following the responses of individual cells after a programmed exposure to charged-particle traversals. To probe the radiation sensitivity of a single cell and/or its constituents with a submicron resolution several developments are needed. The essential parameters of the proposed system can be summarised as follows: a focussed beam of ions of 300nm or less at the cell; a reliable (close to 100%) single ion detection; a fast beam switch to prevent second hits; a target holder adapted for the irradiation of wet cells and a fully automated system for cell recognition and single hits. 1 fig.
Design of a single ion facility and its applications
Energy Technology Data Exchange (ETDEWEB)
Cholewa, M; Saint, A; Legge, G J.F. [Melbourne Univ., Parkville, VIC (Australia). School of Physics
1997-12-31
The use of micro-irradiation techniques in radiobiology is not new; however, the current techniques take advantage of recent developments in particle delivery, focussing detection, image processing, cell recognition and computer control. These developments have generally come from other fields, for example microbeam elemental analysis techniques and single-event upset testing of semiconductor devices. Also in radiation biology there have been important advances in developments of individual cell assays, which allow a wide range of endpoints to be studied with good accuracy at low doses. Many of the studies that are planned involve following the responses of individual cells after a programmed exposure to charged-particle traversals. To probe the radiation sensitivity of a single cell and/or its constituents with a submicron resolution several developments are needed. The essential parameters of the proposed system can be summarised as follows: a focussed beam of ions of 300nm or less at the cell; a reliable (close to 100%) single ion detection; a fast beam switch to prevent second hits; a target holder adapted for the irradiation of wet cells and a fully automated system for cell recognition and single hits. 1 fig.
Conduction Mechanisms and Structure of Ionomeric Single-Ion Conductors
Energy Technology Data Exchange (ETDEWEB)
Colby, Ralph H. [Pennsylvania State Univ., University Park, PA (United States); Maranas, Janna K. [Pennsylvania State Univ., University Park, PA (United States); Mueller, Karl T. [Pennsylvania State Univ., University Park, PA (United States); Runt, James [Pennsylvania State Univ., University Park, PA (United States); Winey, Karen I. [Univ. of Pennsylvania, Philadelphia, PA (United States)
2015-03-01
Our team has designed using DFT (Gaussian) and synthesized low glass transition temperature single-ion conductors that are either polyanions that conduct small cations Li^{+}, Na^{+}, Cs^{+} or polycations that conduct small anions F^{-}, OH^{-}, Br^{-}. We utilize a wide range of complimentary experimental materials characterization tools to understand ion transport; differential scanning calorimetry, dielectric relaxation spectroscopy, infrared spectroscopy, nuclear magnetic resonance spectroscopy, linear viscoelasticity, X-ray scattering and molecular dynamics simulations. The glass transition temperature T_{g} needs to be as low as possible to facilitate ion transport, so the nonionic parts of the polymer need to be polar, flexible and have strong solvation interactions with the ions. The lowest T_{g} we have managed for polyanions conducting Li^{+} is -60 °C. In contrast, polysiloxanes with PEO side chains and tetrabutylphosphonium cationic side groups have T_{g} ≈ -75 °C that barely increases with ion content, as anticipated by DFT. A survey of all polyanions in the literature suggests that T_{g} < -80 °C is needed to achieve the 10^{-4} S/cm conductivity needed for battery separators.
Pajevic, Sinisa; Aldroubi, Akram; Basser, Peter J
2002-01-01
The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.
Single ion impact detection and scanning probe aligned ion implantation for quantum bit formation
International Nuclear Information System (INIS)
Weis, Christoph D.
2011-01-01
Quantum computing and quantum information processing is a promising path to replace classical information processing via conventional computers which are approaching fundamental physical limits. Instead of classical bits, quantum bits (qubits) are utilized for computing operations. Due to quantum mechanical phenomena such as superposition and entanglement, a completely different way of information processing is achieved, enabling enhanced performance for certain problem sets. Various proposals exist on how to realize a quantum bit. Among them are electron or nuclear spins of defect centers in solid state systems. Two such candidates with spin degree of freedom are single donor atoms in silicon and nitrogen vacancy (NV) defect centers in diamond. Both qubit candidates possess extraordinary qualities which makes them promising building blocks. Besides certain advantages, the qubits share the necessity to be placed precisely in their host materials and device structures. A commonly used method is to introduce the donor atoms into the substrate materials via ion implantation. For this, focused ion beam systems can be used, or collimation techniques as in this work. A broad ion beam hits the back of a scanning probe microscope (SPM) cantilever with incorporated apertures. The high resolution imaging capabilities of the SPM allows the non destructive location of device areas and the alignment of the cantilever and thus collimated ion beam spot to the desired implant locations. In this work, this technique is explored, applied and pushed forward to meet necessary precision requirements. The alignment of the ion beam to surface features, which are sensitive to ion impacts and thus act as detectors, is demonstrated. The technique is also used to create NV center arrays in diamond substrates. Further, single ion impacts into silicon device structures are detected which enables deliberate single ion doping.
Single ion impact detection and scanning probe aligned ion implantation for quantum bit formation
Energy Technology Data Exchange (ETDEWEB)
Weis, Christoph D.
2011-10-04
Quantum computing and quantum information processing is a promising path to replace classical information processing via conventional computers which are approaching fundamental physical limits. Instead of classical bits, quantum bits (qubits) are utilized for computing operations. Due to quantum mechanical phenomena such as superposition and entanglement, a completely different way of information processing is achieved, enabling enhanced performance for certain problem sets. Various proposals exist on how to realize a quantum bit. Among them are electron or nuclear spins of defect centers in solid state systems. Two such candidates with spin degree of freedom are single donor atoms in silicon and nitrogen vacancy (NV) defect centers in diamond. Both qubit candidates possess extraordinary qualities which makes them promising building blocks. Besides certain advantages, the qubits share the necessity to be placed precisely in their host materials and device structures. A commonly used method is to introduce the donor atoms into the substrate materials via ion implantation. For this, focused ion beam systems can be used, or collimation techniques as in this work. A broad ion beam hits the back of a scanning probe microscope (SPM) cantilever with incorporated apertures. The high resolution imaging capabilities of the SPM allows the non destructive location of device areas and the alignment of the cantilever and thus collimated ion beam spot to the desired implant locations. In this work, this technique is explored, applied and pushed forward to meet necessary precision requirements. The alignment of the ion beam to surface features, which are sensitive to ion impacts and thus act as detectors, is demonstrated. The technique is also used to create NV center arrays in diamond substrates. Further, single ion impacts into silicon device structures are detected which enables deliberate single ion doping.
DEFF Research Database (Denmark)
Sloth, Peter
1993-01-01
The grand canonical ensemble has been used to study the evaluation of single ion activity coefficients in homogeneous ionic fluids. In this work, the Coulombic interactions are truncated according to the minimum image approximation, and the ions are assumed to be placed in a structureless......, homogeneous dielectric continuum. Grand canonical ensemble Monte Carlo calculation results for two primitive model electrolyte solutions are presented. Also, a formula involving the second moments of the total correlation functions is derived from fluctuation theory, which applies for the derivatives...... of the individual ionic activity coefficients with respect to the total ionic concentration. This formula has previously been proposed on the basis of somewhat different considerations....
Single-Ion Implantation for the Development of Si-Based MOSFET Devices with Quantum Functionalities
Directory of Open Access Journals (Sweden)
Jeffrey C. McCallum
2012-01-01
Full Text Available Interest in single-ion implantation is driven in part by research into development of solid-state devices that exhibit quantum behaviour in their electronic or optical characteristics. Here, we provide an overview of international research work on single ion implantation and single ion detection for development of electronic devices for quantum computing. The scope of international research into single ion implantation is presented in the context of our own research in the Centre for Quantum Computation and Communication Technology in Australia. Various single ion detection schemes are presented, and limitations on dopant placement accuracy due to ion straggling are discussed together with pathways for scale-up to multiple quantum devices on the one chip. Possible future directions for ion implantation in quantum computing and communications are also discussed.
An automated single ion hit at JAERI heavy ion microbeam to observe individual radiation damage
International Nuclear Information System (INIS)
Kamiya, Tomihiro; Sakai, Takuro; Naitoh, Yutaka; Hamano, Tsuyoshi; Hirao, Toshio
1999-01-01
Microbeam scanning and a single ion hit technique have been combined to establish an automated beam positioning and single ion hit system at the JAERI Takasaki heavy ion microbeam system. Single ion irradiation on preset points of a sample in various patterns can be performed automatically in a short period. The reliability of the system was demonstrated using CR-39 nuclear track detectors. Single ion hit patterns were achieved with a positioning accuracy of 2 μm or less. In measurement of single event transient current using this system, the reduction of the pulse height by accumulation of radiation damages was observed by single ion injection to the same local areas. This technique showed a possibility to get some quantitative information about the lateral displacement of an individual radiation effect in silicon PIN photodiodes. This paper will give details of the irradiation system and present results from several experiments
Development of the IFJ single ion hit facility for cells irradiation
International Nuclear Information System (INIS)
Veselov, O.; Polak, W.; Ugenskiene, R.; Hajduk, R.; Lebed, K.; Lekki, J.; Horwacik, T.; Dutkiewicz, E.M.; Maranda, S.; Pieprzyca, T.; Sarnecki, C.; Stachura, Z.; Szklarz, Z.; Styczen, J.
2005-12-01
In recent years a single ion hit facility (SIHF) has been constructed at the IFJ ion microprobe. The setup is used for the precise irradiations of living cells by a controlled number of ions. The facility allows investigations in various aspects of biomedical research, such as adaptive response, bystander effect, inverse dose-rate effect, low-dose hypersensitivity, etc. Those investigations have two very important requirements: (i) cells must be examined in their natural state and environment, i.e. without previously being killed, and preferentially, neither fixed nor stained, and (ii) a possibility of automatic irradiation of large number of cells with a computer recognition of their positions must be provided. This work presents some of the crucial features of the off-line and on-line optical systems, including self-developed software responsible for the automatic cell recognition. We also show several tests carried out to determine the efficiency of the whole setup and some segments. In conclusion, the results of our first irradiation measurements performed with living cells are demonstrated. (author)
Porcarelli, Luca; Aboudzadeh, M. Ali; Rubatat, Laurent; Nair, Jijeesh R.; Shaplov, Alexander S.; Gerbaldi, Claudio; Mecerreyes, David
2017-10-01
Single-ion conducting polymer electrolytes represent the ideal solution to reduce concentration polarization in lithium metal batteries (LMBs). This paper reports on the synthesis and characterization of single-ion ABA triblock copolymer electrolytes comprising PEO and poly(lithium 1-[3-(methacryloyloxy)propylsulfonyl]-1-(trifluoromethylsulfonyl)imide) blocks, poly(LiMTFSI). Block copolymers are prepared by reversible addition-fragmentation chain transfer polymerization, showing low glass transition temperature (-55 to 7 °C) and degree of crystallinity (51-0%). Comparatively high values of ionic conductivity are obtained (up to ≈ 10-4 S cm-1 at 70 °C), combined with a lithium-ion transference number close to unity (tLi+ ≈ 0.91) and a 4 V electrochemical stability window. In addition to these promising features, solid polymer electrolytes are successfully tested in lithium metal cells at 70 °C providing long lifetime up to 300 cycles, and stable charge/discharge cycling at C/2 (≈100 mAh g-1).
Energy Technology Data Exchange (ETDEWEB)
Lee, Jinhong; Song, Jongchan; Lee, Hongkyung; Noh, Hyungjun; Kim, Yun-Jung; Kwon, Sung Hyun; Lee, Seung Geol; Kim, Hee-Tak
2017-04-19
Formation of soluble polysulfide (PS), which is a key feature of lithium sulfur (Li–S) batteries, provides a fast redox kinetic based on a liquid–solid mechanism; however, it imposes the critical problem of PS shuttle. Here, we address the dilemma by exploiting a solvent-swollen polymeric single-ion conductor (SPSIC) as the electrolyte medium of the Li–S battery. The SPSIC consisting of a polymeric single-ion conductor and lithium salt-free organic solvents provides Li ion hopping by forming a nanoscale conducting channel and suppresses PS shuttle according to the Donnan exclusion principle when being employed for Li–S batteries. The organic solvents at the interface of the sulfur/carbon composite and SPSIC eliminate the poor interfacial contact and function as a soluble PS reservoir for maintaining the liquid–solid mechanism. Furthermore, the quasi-solid-state SPSIC allows the fabrication of a bipolar-type stack, which promises the realization of a high-voltage and energy-dense Li–S battery.
Ferrimagnetic Properties of Bond Dilution Mixed Blume-Capel Model with Random Single-Ion Anisotropy
International Nuclear Information System (INIS)
Liu Lei; Yan Shilei
2005-01-01
We study the ferrimagnetic properties of spin 1/2 and spin-1 systems by means of the effective field theory. The system is considered in the framework of bond dilution mixed Blume-Capel model (BCM) with random single-ion anisotropy. The investigation of phase diagrams and magnetization curves indicates the existence of induced magnetic ordering and single or multi-compensation points. Special emphasis is placed on the influence of bond dilution and random single-ion anisotropy on normal or induced magnetic ordering states and single or multi-compensation points. Normal magnetic ordering states take on new phase diagrams with increasing randomness (bond and anisotropy), while anisotropy induced magnetic ordering states are always occurrence no matter whether concentration of anisotropy is large or small. Existence and disappearance of compensation points rely strongly on bond dilution and random single-ion anisotropy. Some results have not been revealed in previous papers and predicted by Neel theory of ferrimagnetism.
Single ion implantation for single donor devices using Geiger mode detectors
International Nuclear Information System (INIS)
Bielejec, E; Seamons, J A; Carroll, M S
2010-01-01
Electronic devices that are designed to use the properties of single atoms such as donors or defects have become a reality with recent demonstrations of donor spectroscopy, single photon emission sources, and magnetic imaging using defect centers in diamond. Ion implantation, an industry standard for atom placement in materials, requires augmentation for single ion capability including a method for detecting a single ion arrival. Integrating single ion detection techniques with the single donor device construction region allows single ion arrival to be assured. Improving detector sensitivity is linked to improving control over the straggle of the ion as well as providing more flexibility in lay-out integration with the active region of the single donor device construction zone by allowing ion sensing at potentially greater distances. Using a remotely located passively gated single ion Geiger mode avalanche diode (SIGMA) detector we have demonstrated 100% detection efficiency at a distance of >75 μm from the center of the collecting junction. This detection efficiency is achieved with sensitivity to ∼600 or fewer electron-hole pairs produced by the implanted ion. Ion detectors with this sensitivity and integrated with a thin dielectric, for example a 5 nm gate oxide, using low energy Sb implantation would have an end of range straggle of -1 and 10 -4 for operation temperatures of ∼300 K and ∼77 K, respectively. Low temperature operation and reduced false, 'dark', counts are critical to achieving high confidence in single ion arrival. For the device performance in this work, the confidence is calculated as a probability of >98% for counting one and only one ion for a false count probability of 10 -4 at an average ion number per gated window of 0.015.
DEFF Research Database (Denmark)
Dreiser, Jan; Wäckerlin, Christian; Ali, Md. Ehesan
2014-01-01
We present a comprehensive study of Er(trensal) single-ion magnets deposited in ultrahigh vacuum onto metallic surfaces. X-ray photoelectron spectroscopy reveals that the molecular structure is preserved after sublimation, and that the molecules are physisorbed on Au(111) while they are chemisorbed...... on a Ni thin film on Cu(100) single-crystalline surfaces. X-ray magnetic circular dichroism (XMCD) measurements performed on Au(111) samples covered with molecular monolayers held at temperatures down to 4 K suggest that the easy axes of the strongly anisotropic molecules are randomly oriented...... pathways toward optical addressing of surface-deposited single-ion magnets....
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...
Single-ion conducting diblock terpolymers for lithium-ion batteries
Morris, Melody; Epps, Thomas H., III
Block polymer (BP) electrolytes provide an attractive route to overcome the competing constraints of high conductivity and mechanical/thermal stability in lithium-ion batteries through nanoscale self-assembly. For example, macromolecules can be engineered such that one domain conducts lithium ions and the other prevents lithium dendrite formation. Herein, we report on the behavior of a single-ion conducting BP electrolyte that was designed to facilitate the transport of lithium ions. These polymers differ from traditional salt-doped BP electrolytes, which require the addition of a lithium salt to bestow conductivity and typically suffer from substantial counterion motion that reduces efficiency. New single-ion BPs were synthesized, and the nanoscale morphologies were determined using small angle X-ray scattering and transmission electron microscopy. Electrolyte performance was measured using AC impedance spectroscopy and DC polarization, and the results were correlated to nanoscale morphology and ion content. Enhanced physical understanding of single-ion BPs was gained by connecting the ion mobility to the chemistry, chain structure, and ion content of the single-ion BP. These studies can be applied to other charged-neutral block polymers to elucidate the effects of ion content on self-assembly and macroscopic properties.
On the single-ion Magnetic Anisotropy of the Rare-Earth Metals
DEFF Research Database (Denmark)
Kolmakova, N.P.; Tishin, A.M.; Bohr, Jakob
1996-01-01
The temperature dependences of the single-ion magnetic anisotropy constants for Tb and Dy metals are calculated in terms of the multipole moments of the rare-earth ions utilizing the available crystal-field parameters. The results are compared with the existing experimental data....
A simple and rapid method for high-resolution visualization of single-ion tracks
Directory of Open Access Journals (Sweden)
Masaaki Omichi
2014-11-01
Full Text Available Prompt determination of spatial points of single-ion tracks plays a key role in high-energy particle induced-cancer therapy and gene/plant mutations. In this study, a simple method for the high-resolution visualization of single-ion tracks without etching was developed through the use of polyacrylic acid (PAA-N, N’-methylene bisacrylamide (MBAAm blend films. One of the steps of the proposed method includes exposure of the irradiated films to water vapor for several minutes. Water vapor was found to promote the cross-linking reaction of PAA and MBAAm to form a bulky cross-linked structure; the ion-track scars were detectable at a nanometer scale by atomic force microscopy. This study demonstrated that each scar is easily distinguishable, and the amount of generated radicals of the ion tracks can be estimated by measuring the height of the scars, even in highly dense ion tracks. This method is suitable for the visualization of the penumbra region in a single-ion track with a high spatial resolution of 50 nm, which is sufficiently small to confirm that a single ion hits a cell nucleus with a size ranging between 5 and 20 μm.
A simple and rapid method for high-resolution visualization of single-ion tracks
Energy Technology Data Exchange (ETDEWEB)
Omichi, Masaaki [Department of Applied Chemistry, Graduate School of Engineering, Osaka University, Osaka 565-0871 (Japan); Center for Collaborative Research, Anan National College of Technology, Anan, Tokushima 774-0017 (Japan); Choi, Wookjin; Sakamaki, Daisuke; Seki, Shu, E-mail: seki@chem.eng.osaka-u.ac.jp [Department of Applied Chemistry, Graduate School of Engineering, Osaka University, Osaka 565-0871 (Japan); Tsukuda, Satoshi [Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai, Miyagi 980-8577 (Japan); Sugimoto, Masaki [Japan Atomic Energy Agency, Takasaki Advanced Radiation Research Institute, Gunma, Gunma 370-1292 (Japan)
2014-11-15
Prompt determination of spatial points of single-ion tracks plays a key role in high-energy particle induced-cancer therapy and gene/plant mutations. In this study, a simple method for the high-resolution visualization of single-ion tracks without etching was developed through the use of polyacrylic acid (PAA)-N, N’-methylene bisacrylamide (MBAAm) blend films. One of the steps of the proposed method includes exposure of the irradiated films to water vapor for several minutes. Water vapor was found to promote the cross-linking reaction of PAA and MBAAm to form a bulky cross-linked structure; the ion-track scars were detectable at a nanometer scale by atomic force microscopy. This study demonstrated that each scar is easily distinguishable, and the amount of generated radicals of the ion tracks can be estimated by measuring the height of the scars, even in highly dense ion tracks. This method is suitable for the visualization of the penumbra region in a single-ion track with a high spatial resolution of 50 nm, which is sufficiently small to confirm that a single ion hits a cell nucleus with a size ranging between 5 and 20 μm.
Pollard, Travis P.; Beck, Thomas L.
2018-06-01
Attempts to establish an absolute single-ion hydration free energy scale have followed multiple strategies. Two central themes consist of (1) employing bulk pair thermodynamic data and an underlying interfacial-potential-free model to partition the hydration free energy into individual contributions [Marcus, Latimer, and tetraphenyl-arsonium/tetraphenyl-borate (TATB) methods] or (2) utilizing bulk thermodynamic and cluster data to estimate the free energy to insert a proton into water, including in principle an interfacial potential contribution [the cluster pair approximation (CPA)]. While the results for the hydration free energy of the proton agree remarkably well between the three approaches in the first category, the value differs from the CPA result by roughly +10 kcal/mol, implying a value for the effective electrochemical surface potential of water of -0.4 V. This paper provides a computational re-analysis of the TATB method for single-ion free energies using quasichemical theory. A previous study indicated a significant discrepancy between the free energies of hydration for the TA cation and the TB anion. We show that the main contribution to this large computed difference is an electrostatic artifact arising from modeling interactions in periodic boundaries. No attempt is made here to develop more accurate models for the local ion/solvent interactions that may lead to further small free energy differences between the TA and TB ions, but the results clarify the primary importance of interfacial potential effects for analysis of the various free energy scales. Results are also presented, related to the TATB assumption in the organic solvents dimethyl sulfoxide and 1,2-dichloroethane.
The single-ion anisotropy effects in the mixed-spin ternary-alloy
Albayrak, Erhan
2018-04-01
The effect of single-ion anisotropy on the thermal properties of the ternary-alloy in the form of ABpC1-p is investigated on the Bethe lattice (BL) in terms of exact recursion relations. The simulation on the BL consists of placing A atoms (spin-1/2) on the odd shells and randomly placing B (spin-3/2) or C (spin-5/2) atoms with concentrations p and 1 - p, respectively, on the even shells. The phase diagrams are calculated in possible planes spanned by the system parameters: temperature, single-ion anisotropy, concentration and ratio of the bilinear interaction parameters for z = 3 corresponding to the honeycomb lattice. It is found that the crystal field drives the system to the lowest possible state therefore reducing the temperatures of the critical lines in agreement with the literature.
Quantum phase transitions in spin-1 X X Z chains with rhombic single-ion anisotropy
Ren, Jie; Wang, Yimin; You, Wen-Long
2018-04-01
We explore numerically the inverse participation ratios in the ground state of one-dimensional spin-1 X X Z chains with the rhombic single-ion anisotropy. By employing the techniques of density-matrix renormalization group, effects of the rhombic single-ion anisotropy on various information theoretical measures are investigated, such as the fidelity susceptibility, the quantum coherence, and the entanglement entropy. Their relations with the quantum phase transitions are also analyzed. The phase transitions from the Y -Néel phase to the large-Ex or the Haldane phase can be well characterized by the fidelity susceptibility. The second-order derivative of the ground-state energy indicates all the transitions are of second order. We also find that the quantum coherence, the entanglement entropy, the Schmidt gap, and the inverse participation ratios can be used to detect the critical points of quantum phase transitions. Results drawn from these quantum information observables agree well with each other. Finally we provide a ground-state phase diagram as functions of the exchange anisotropy Δ and the rhombic single-ion anisotropy E .
Tu, Zhengyuan; Choudhury, Snehashis; Zachman, Michael J.; Wei, Shuya; Zhang, Kaihang; Kourkoutis, Lena F.; Archer, Lynden A.
2017-01-01
energy storage technologies. In lithium-ion batteries, electrolytes with single- or near-single-ion conductivity reduce losses caused by ion polarization. In emergent lithium or sodium metal batteries, they maintain high conductivity at the anode
Subattoampere current induced by single ions in silicon oxide layers of nonvolatile memory cells
International Nuclear Information System (INIS)
Cellere, G.; Paccagnella, A.; Larcher, L.; Visconti, A.; Bonanomi, M.
2006-01-01
A single ion impinging on a thin silicon dioxide layer generates a number of electron/hole pairs proportional to its linear energy transfer coefficient. Defects generated by recombination can act as a conductive path for electrons that cross the oxide barrier, thanks to a multitrap-assisted mechanism. We present data on the dependence of this phenomenon on the oxide thickness by using floating gate memory arrays. The tiny number of excess electrons stored in these devices allows for extremely high sensitivity, impossible with any direct measurement of oxide leakage current. Results are of particular interest for next generation devices
Heisenberg magnetic chain with single-ion easy-plane anisotropy: Hubbard operators approach
International Nuclear Information System (INIS)
Spirin, D.V.; Fridman, Y.A.
2003-01-01
We investigate the gap in excitation spectrum of one-dimensional S=1 ferro- and antiferromagnets with easy-plane single-ion anisotropy. The self-consistent modification of Hubbard operators approach which enables to account single-site term exactly is used. For antiferromagnetic model we found Haldane phase that exists up to point D=4J (where D is anisotropy parameter, J is exchange coupling), while quadrupolar phase realizes at larger values of anisotropy. Our results specify those of Golinelli et al. (Phys. Rev. B. 45 (1992) 9798), where similar model was studied. Besides the method gives gap value closer to numerical estimations than usual spin-wave theories
Feasibility of Observing and Characterizing Single Ion Strikes in Microelectronic Components
International Nuclear Information System (INIS)
Dingreville, Remi Philippe Michel; Hattar, Khalid Mikhiel; Bufford, Daniel Charles
2015-01-01
The transient degradation of semiconductor device performance under irradiation has long been an issue of concern. A single high-energy charged particle can degrade or permanently destroy the microelectronic component, potentially altering the course or function of the systems. Disruption of the the crystalline structure through the introduction of quasi-stable defect structures can change properties from semiconductor to conductor. Typically, the initial defect formation phase is followed by a recovery phase in which defect-defect or defect-dopant interactions modify the characteristics of the damaged structure. In this LDRD Express, in-situ ion irradiation transmission microscopy (TEM) in-situ TEM experiments combined with atomistic simulations have been conducted to determine the feasibility of imaging and characterizing the defect structure resulting from a single cascade in silicon. In-situ TEM experiments have been conducted to demonstrate that a single ion strike can be observed in Si thin films with nanometer resolution in real time using the in-situ ion irradiation transmission electron microscope (I 3 TEM). Parallel to this experimental effort, ion implantation has been numerically simulated using Molecular Dynamics (MD). This numerical framework provides detailed predictions of the damage and follow the evolution of the damage during the first nanoseconds. The experimental results demonstrate that single ion strike can be observed in prototypical semiconductors.
A reliable method for the counting and control of single ions for single-dopant controlled devices
International Nuclear Information System (INIS)
Shinada, T; Kurosawa, T; Nakayama, H; Zhu, Y; Hori, M; Ohdomari, I
2008-01-01
By 2016, transistor device size will be just 10 nm. However, a transistor that is doped at a typical concentration of 10 18 atoms cm -3 has only one dopant atom in the active channel region. Therefore, it can be predicted that conventional doping methods such as ion implantation and thermal diffusion will not be available ten years from now. We have been developing a single-ion implantation (SII) method that enables us to implant dopant ions one-by-one into semiconductors until the desired number is reached. Here we report a simple but reliable method to control the number of single-dopant atoms by detecting the change in drain current induced by single-ion implantation. The drain current decreases in a stepwise fashion as a result of the clusters of displaced Si atoms created by every single-ion incidence. This result indicates that the single-ion detection method we have developed is capable of detecting single-ion incidence with 100% efficiency. Our method potentially could pave the way to future single-atom devices, including a solid-state quantum computer
A fast online hit verification method for the single ion hit system at GSI
International Nuclear Information System (INIS)
Du, G.; Fischer, B.; Barberet, P.; Heiss, M.
2006-01-01
For a single ion hit facility built to irradiate specific targets inside biological cells, it is necessary to prove that the ions hit the selected targets reliably because the ion hits usually cannot be seen. That ability is traditionally tested either indirectly by aiming at pre-etched tracks in a nuclear track detector or directly by making the ion tracks inside cells visible using a stain coupled to special proteins produced in response to ion hits. However, both methods are time consuming and hits can be verified only after the experiment. This means that targeting errors in the experiment cannot be corrected during the experiment. Therefore, we have developed a fast online hit verification method that measures the targeting accuracy electronically with a spatial resolution of ±1 μm before cell irradiation takes place. (authors)
Single Ion transient-IBIC analyses of semiconductor devices using a cryogenic temperature stage
International Nuclear Information System (INIS)
Laird, J.S.; Bardos, R.; Legge, G.J.F.; Jagadish, C.
1998-01-01
A new Transient - IBIC data acquisition and analysis system at MARC is described. A discussion on the need for single ion control and temperature control is also given. The recorded signal is used as the trigger for beam pulsing. The new cryostatic temperature control stage is introduced. Data is presented on line profiles across the edge of a Au-Si junction collected over the temperature range of 25-300K using a developed C-V and I-V variable temperature stage incorporating a liquid helium cryostat. It demonstrates the potential improvements in spatial resolution in materials of long lifetime by mapping on timing windows around the prompt charge component in the charge transient
Dynamics of a single ion in a perturbed Penning trap: Octupolar perturbation
International Nuclear Information System (INIS)
Lara, Martin; Salas, J. Pablo
2004-01-01
Imperfections in the design or implementation of Penning traps may give rise to electrostatic perturbations that introduce nonlinearities in the dynamics. In this paper we investigate, from the point of view of classical mechanics, the dynamics of a single ion trapped in a Penning trap perturbed by an octupolar perturbation. Because of the axial symmetry of the problem, the system has two degrees of freedom. Hence, this model is ideal to be managed by numerical techniques like continuation of families of periodic orbits and Poincare surfaces of section. We find that, through the variation of the two parameters controlling the dynamics, several periodic orbits emanate from two fundamental periodic orbits. This process produces important changes (bifurcations) in the phase space structure leading to chaotic behavior
Soles, Christopher; Peng, Hua-Gen; Page, Kirt; Snyder, Chad; Pandy, Ashoutosh; Jeong, Youmi; Runt, James; NIST Collaboration; Pennsylvania Collaboration
2011-03-01
The application of solid polymer electrolytes in rechargeable batteries has not been fully realized after decades of research due to its low conductivity. Dramatic increases of the ion conductivity are needed and this progress requires the understanding of conduction mechanism. We address this topic in two fronts, namely, the effect of plasticizer additives and geometric confinement on the charge transfer mechanism. To this end, we combine broadband dielectric spectroscopy (BDS) to characterize the ion mobility and quasi-elastic neutron scattering (QENS) to quantify segmental motion on a single-ion model polymer electrolyte. Deuterated small molecules were used as plasticizers so that the segmental motion of the polymer electrolyte could be monitored by QENS to understand the mechanism behind the increased conductivity. Anodic aluminum oxide (AAO) membranes with well defined channel sizes are used as the matrix to study the transport of ions solvated in a 1D polymer electrolyte.
Development of noise-suppressed detector for single ion hit system
Energy Technology Data Exchange (ETDEWEB)
Sakai, Takuro; Hamano, Tsuyoshi; Suda, Tamotsu; Hirao, Toshio; Kamiya, Tomihiro [Japan Atomic Energy Research Inst., Takasaki, Gunma (Japan). Takasaki Radiation Chemistry Research Establishment
1997-03-01
A noise-suppressed detector for single ion detection has been developed, and combined with the heavy ion microbeam apparatus. This detector consists of a pair of micro channel plates (MCP`s) and a very thin carbon foil. The detection signal is formed by the coincidence of the signals from these MCP`s, so that this detector and the coincidence measurement unit can reduce miscounting in the circuit. The detection efficiency for 15 MeV heavy ions was evaluated to be comparable to that of a silicon surface-barrier detector (SSD) and the miscounting rate was 4 orders lower than the noise rate of a single MCP. The rise time of the detection signal was also estimated. (author)
Guegan, K; Stals, K; Day, M; Turnpenny, P; Ellard, S
2012-07-01
Alagille syndrome is a multisystem disorder characterized by highly variable expressivity, most frequently caused by heterozygous JAG1 gene mutations. Classic diagnostic criteria combine the presence of bile duct paucity on liver biopsy with three of five systems affected; liver, heart, skeleton, eye and dysmorphic facies. The aim of this study was to determine the prevalence and distribution of JAG1 mutations in patients referred for routine clinical diagnostic testing. Clinical data were available for 241 patients from 135 families. The index cases were grouped according to the number of systems affected (heart, liver, skeletal, eye and facies) and the mutation frequency calculated for each group. JAG1 mutations were identified in 59/135 (44%) probands. The highest mutation detection rates were observed in patients with the most frequent presenting features of Alagille syndrome; ranging from 20% (one system) to 86% (five systems). The overall mutation pick-up rate in a clinical diagnostic setting was lower than in previous research studies. Identification of a JAG1 gene mutation is particularly useful for those patients with atypical or mild Alagille syndrome who do not meet classic diagnostic criteria as it provides a definite molecular diagnosis and allows accurate genetic counselling for the family. © 2011 John Wiley & Sons A/S.
Influence of strong single-ion anisotropy on phase states of 3D and 2D frustrated magnets
International Nuclear Information System (INIS)
Fridman, Yu.A.; Kosmachev, O.A.; Matunin, D.A.; Gorelikov, G.A.; Klevets, Ph.N.
2010-01-01
We investigated the influence of strong single-ion anisotropy, exceeding exchange interaction, and frustrated exchange interaction on spin-wave excitation spectra and phase states using the Hubbard operators' technique, allowing the exact account of single-ion anisotropy. The results show that both the homogeneous phases (ferromagnetic and quadrupolar) and the spatially inhomogeneous phase (spiral structure) are possible in the 3D magnetic crystal. The region of existence of the spiral structure is considerably smaller than that in the analogues system, but with weak single-ion anisotropy. The situation is more complex in the 2D system; another spatially inhomogeneous state (the domain structure) can be realized in addition to the spiral magnetic structure. The phase diagrams for both the 3D and 2D systems were plotted.
Schmidt, Wolfgang M
1980-01-01
"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)
Single ion hit detection set-up for the Zagreb ion microprobe
Smith, R. W.; Karlušić, M.; Jakšić, M.
2012-04-01
Irradiation of materials by heavy ions accelerated in MV tandem accelerators may lead to the production of latent ion tracks in many insulators and semiconductors. If irradiation is performed in a high resolution microprobe facility, ion tracks can be ordered by submicrometer positioning precision. However, full control of the ion track positioning can only be achieved by a reliable ion hit detection system that should provide a trigger signal irrespectively of the type and thickness of the material being irradiated. The most useful process that can be utilised for this purpose is emission of secondary electrons from the sample surface that follows the ion impact. The status report of the set-up presented here is based on the use of a channel electron multiplier (CEM) detector mounted on an interchangable sample holder that is inserted into the chamber in a close geometry along with the sample to be irradiated. The set-up has been tested at the Zagreb ion microprobe for different ions and energies, as well as different geometrical arrangements. For energies of heavy ions below 1 MeV/amu, results show that efficient (100%) control of ion impact can be achieved only for ions heavier than silicon. The successful use of the set-up is demonstrated by production of ordered single ion tracks in a polycarbonate film and by monitoring fluence during ion microbeam patterning of Foturan glass.
Diode-like single-ion track membrane prepared by electro-stopping
International Nuclear Information System (INIS)
Apel, P.Yu.; Korchev, Yu.E.; Siwy, Z.; Spohr, R.; Yoshida, M.
2001-01-01
The preparation of an asymmetric membrane in poly(ethylene terephthalate) (PET) is described, using a combination of chemical and electro-stopping. For this purpose, a single-ion-irradiated PET film is inserted into an electrolytic cell and etched from one side in 9 M sodium hydroxide while bathing the other side in a mixture of 2 M KCl and 2 M HCOOH (1:1 by volume), electrically retracting the OH - ions from the tip of the etch pit during pore break-through. When a preset current has been reached, the etch process is interrupted by replacing the etching solution with acidic 1 M potassium chloride solution. After etching, the current-voltage (I-V) characteristic is determined under symmetric bathing conditions, immersing both sides of the membrane in KCl solutions of identical concentration (0.01-1 M) and pH (3-8). The I-V characteristic is strongly non-linear, comparable to that of an electrical diode. If the polarity during etching is reversed, pushing the OH - ions into the tip of the etch pit, the resulting pores are larger and the degree of asymmetry smaller. The importance of electro-stopping is compared with chemical stopping
Luminescent single-ion magnets from Lanthanoid(III) complexes with monodentate ketone ligands
Energy Technology Data Exchange (ETDEWEB)
Kanetomo, Takuya; Ishida, Takayuki, E-mail: takayuki.ishida@uec.ac.jp [Department of Engineering Science, The University of Electro-Communications, Tokyo (Japan)
2016-02-01
We synthesized [Ln{sup III}(hfac){sub 3}(H{sub 2}O)(L)] (abbreviated as Ln-L; Ln = Gd, Tb, Eu; L = DTBK (di-t-butyl ketone), BP (benzophenone)), in which the carbonyl oxygen atom was coordinated to the Ln ion center, despite of such bulky substituents. Their crystal structures were determined by means of X-ray diffraction study. Gd-DTBK is completely isomorphous to the di-t-butyl nitroxide derivative and accordingly can be regarded as a model with the ligand spin masked. The ac magnetic susceptibility measurements on Tb-DTBK and -BP showed frequency dependence, characteristic of single-ion magnets. They also displayed photoluminescence in the solid state at room temperature. The quantum yields of the luminescence of Tb-DTBK and -BP (λ{sub ex} = 360 nm) were improved to 57 and 35%, respectively, from that of the starting material [TbI{sup III}(hfac){sub 3}(H{sub 2}O){sub 2}] (28% at λ{sub ex} = 370 nm). Similarly, the quantum yields for Eu-DTBK and -BP were 8 and 15%, respectively, with λ{sub ex} = 400 nm, while that of the starting material [EuI{sup III}(hfac){sub 3}(H{sub 2}O){sub 2}] was 4% at λ{sub ex}=400 nm.
Comb-shaped single ion conductors based on polyacrylate ethers and lithium alkyl sulfonate
International Nuclear Information System (INIS)
Sun Xiaoguang; Hou Jun; Kerr, John B.
2005-01-01
Comb-shaped single ion conductors have been synthesized by (1) sulfonation of small molecule chloroethyleneglycols, which, after ion exchange to the Li + salt were then converted to the acrylate by reaction with acryloyl chloride and copolymerized with polyethylene glycol monomethyl ether acrylate (Mn = 454, n = 8) (PAE 8 -co-E 3 SO 3 Li); (2) sulfonation of chloride end groups grafted on to prepolymers of polyacrylate ethers (PAE 8 -g-E n SO 3 Li, n = 2, 3). The highest conductivity at 25 deg. C of 2.0 x 10 -7 S cm -1 was obtained for the PAE 8 -co-E 3 SO 3 Li with a salt concentration of EO/Li = 40. The conductivity of PAE 8 -g-E 3 SO 3 Li is lower than that of PAE 8 -co-E 3 SO 3 Li at similar salt concentrations, which is related to the incomplete sulfonation of the grafted polymer that leads to a lower concentration of Li + . The addition of 50 wt.% of plasticizer, PC/EMC (1/1, v/v), to PAE 8 -g-E 2 SO 3 Li increases the ambient conductivity by three orders of magnitude, which is due to the increased ion mobility in a micro-liquid environment and an increase concentration of free ions as a result of the higher dielectric constant of the solvent. A symmetrical Li/Li cell with an electrolyte membrane consisting of 75 wt.% PC/EMC (1/1, v/v) was cycled at a current density of 100 μA cm -2 at 85 deg. C. The cycling profile showed no concentration polarization after a break-in period during the first few cycles, which was apparently due to reaction of the solvent at the lithium metal surface that reacted with lithium metal to form a stable SEI layer
Self-similar factor approximants
International Nuclear Information System (INIS)
Gluzman, S.; Yukalov, V.I.; Sornette, D.
2003-01-01
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties
International Nuclear Information System (INIS)
Pu Qiurong; Chen Yuan
2013-01-01
Green's function method is applied to investigate the two-dimensional spin-1 ferromagnetic Heisenberg model with the exchange and single-ion anisotropies. In the presence of the magnetic field, the effects of the anisotropies and field on the thermodynamic properties are obtained within the random phase approximation combining with Anderson-Callen approximation. The field-induced laws are found for the thermodynamic properties. Field dependences of heights of the susceptibility maximum and specific heat maximum fit well to power laws. The linear increase at high fields is shown for positions of the susceptibility maximum and specific heat maximum. A power law at low fields occurs for the position of the susceptibility maximum. At the positions of the maxima, the magnetization and internal energy display the power-law increase and linear decrease with the field, respectively. The exponents of the power laws are dependent of the anisotropies, as well as the slopes of the linear laws. Our results do not support the 2/3 power law which was obtained by the Landau theory.
International Nuclear Information System (INIS)
Tosaki, M.; Nakamura, M.; Hirose, M.; Matsumoto, H.
2011-01-01
A heavy-ion microbeam system for cell irradiation has been developed using an accelerator at Kyoto University. We have successfully developed proton-, carbon-, fluorine- and silicon-beams in order to irradiate a micro-meter sized area with ion counting, especially single ion irradiation. In the heavy-ion microbeam system, an imaging plate (IP) was utilized for beam diagnostics on the irradiation. The IP is widely used for radiography studies in biology. However, there are a few studies on the low linear energy transfer (LET) by single ions, i.e., low-intensity exposure. Thus we have investigated the energy response for the IP, which can be utilized for microbeam diagnostics.
Quantum phase transitions driven by rhombic-type single-ion anisotropy in the S =1 Haldane chain
Tzeng, Yu-Chin; Onishi, Hiroaki; Okubo, Tsuyoshi; Kao, Ying-Jer
2017-08-01
The spin-1 Haldane chain is an example of the symmetry-protected-topological (SPT) phase in one dimension. Experimental realization of the spin chain materials usually involves both the uniaxial-type, D (Sz)2 , and the rhombic-type, E [(Sx)2-(Sy)2] , single-ion anisotropies. Here, we provide a precise ground-state phase diagram for a spin-1 Haldane chain with these single-ion anisotropies. Using quantum numbers, we find that the Z2 symmetry breaking phase can be characterized by double degeneracy in the entanglement spectrum. Topological quantum phase transitions take place on particular paths in the phase diagram, from the Haldane phase to the large-Ex, large-Ey, or large-D phases. The topological critical points are determined by the level spectroscopy method with a newly developed parity technique in the density matrix renormalization group [Phys. Rev. B 86, 024403 (2012), 10.1103/PhysRevB.86.024403], and the Haldane-large-D critical point is obtained with an unprecedented precision, (D/J ) c=0.9684713 (1 ) . Close to this critical point, a small rhombic single-ion anisotropy |E |/J ≪1 can destroy the Haldane phase and bring the system into a y -Néel phase. We propose that the compound [Ni (HF2) (3-Clpy ) 4] BF4 is a candidate system to search for the y -Néel phase.
Tu, Zhengyuan
2017-09-21
Substrates able to rectify transport of ions based on charge and/or size are ubiquitous in biological systems. Electrolytes and interphases that selectively transport electrochemically active ions are likewise of broad interest in all electrical energy storage technologies. In lithium-ion batteries, electrolytes with single- or near-single-ion conductivity reduce losses caused by ion polarization. In emergent lithium or sodium metal batteries, they maintain high conductivity at the anode and stabilize metal deposition by fundamental mechanisms. We report that 20- to 300-nm-thick, single-ion-conducting membranes deposited at the anode enable electrolytes with the highest combination of cation transference number, ionic conductivity, and electrochemical stability reported. By means of direct visualization we find that single-ion membranes also reduce dendritic deposition of Li in liquids. Galvanostatic measurements further show that the electrolytes facilitate long (3 mAh) recharge of full Li/LiNi0.8Co0.15Al0.05O2 (NCA) cells with high cathode loadings (3 mAh cm−2/19.9 mg cm−2) and at high current densities (3 mA cm−2).
Spin dynamics in the single-ion magnet [Er(W5O18) 2 ] 9 -
Mariani, M.; Borsa, F.; Graf, M. J.; Sanna, S.; Filibian, M.; Orlando, T.; Sabareesh, K. P. V.; Cardona-Serra, S.; Coronado, E.; Lascialfari, A.
2018-04-01
In this work we present a detailed NMR and μ+SR investigation of the spin dynamics in the new hydrated sodium salt containing the single-ion magnet [Er(W5O18) 2 ] 9 -. The 1HNMR absorption spectra at various applied magnetic fields present a line broadening on decreasing temperature which indicates a progressive spin freezing of the single-molecule magnetic moments. The onset of quasistatic local magnetic fields, due to spin freezing, is observed also in the muon relaxation curves at low temperature. Both techniques yield a local field distribution of the order of 0.1-0.2 T, which appears to be of dipolar origin. On decreasing the temperature, a gradual loss of the 1HNMR signal intensity is observed, a phenomenon known as wipe-out effect. The effect is analyzed quantitatively on the basis of a simple model which relies on the enhancement of the NMR spin-spin, T2-1, relaxation rate due to the slowing down of the magnetic fluctuations. Measurements of spin-lattice relaxation rate T1-1 for 1HNMR and of the muon longitudinal relaxation rate λ show an increase as the temperature is lowered. However, while for the NMR case the signal is lost before reaching the very slow fluctuation region, the muon spin-lattice relaxation λ can be followed until very low temperatures and the characteristic maximum, reached when the electronic spin fluctuation frequency becomes of the order of the muon Larmor frequency, can be observed. At high temperatures, the data can be well reproduced with a simple model based on a single correlation time τ =τ0exp (Δ /T ) for the magnetic fluctuations. However, to fit the relaxation data for both NMR and μ+SR over the whole temperature and magnetic field range, one has to use a more detailed model that takes into account spin-phonon transitions among the E r3 + magnetic sublevels. A good agreement for both proton NMR and μ+SR relaxation is obtained, which confirms the validity of the energy level scheme previously calculated from an
Measuring kinetics of complex single ion channel data using mean-variance histograms.
Patlak, J B
1993-07-01
The measurement of single ion channel kinetics is difficult when those channels exhibit subconductance events. When the kinetics are fast, and when the current magnitudes are small, as is the case for Na+, Ca2+, and some K+ channels, these difficulties can lead to serious errors in the estimation of channel kinetics. I present here a method, based on the construction and analysis of mean-variance histograms, that can overcome these problems. A mean-variance histogram is constructed by calculating the mean current and the current variance within a brief "window" (a set of N consecutive data samples) superimposed on the digitized raw channel data. Systematic movement of this window over the data produces large numbers of mean-variance pairs which can be assembled into a two-dimensional histogram. Defined current levels (open, closed, or sublevel) appear in such plots as low variance regions. The total number of events in such low variance regions is estimated by curve fitting and plotted as a function of window width. This function decreases with the same time constants as the original dwell time probability distribution for each of the regions. The method can therefore be used: 1) to present a qualitative summary of the single channel data from which the signal-to-noise ratio, open channel noise, steadiness of the baseline, and number of conductance levels can be quickly determined; 2) to quantify the dwell time distribution in each of the levels exhibited. In this paper I present the analysis of a Na+ channel recording that had a number of complexities. The signal-to-noise ratio was only about 8 for the main open state, open channel noise, and fast flickers to other states were present, as were a substantial number of subconductance states. "Standard" half-amplitude threshold analysis of these data produce open and closed time histograms that were well fitted by the sum of two exponentials, but with apparently erroneous time constants, whereas the mean
International Nuclear Information System (INIS)
Tonegawa, T; Okamoto, K; Sakai, T; Kaburagi, M
2009-01-01
Employing various numerical methods, we determine the ground-state phase diagram of an (S, S') = (1, 2) spin-alternating chain with antiferromagnetic nearest-neighboring exchange interactions and uniaxial single-ion anisotropies. The resulting phase diagram consists of eight kinds of phases including two phases which accompany the spontaneous breaking of the translational symmetry and a ferrimagnetic phase in which the ground-state magnetization varies continuously with the uniaxial single-ion anisotropy constants for the S=1 and S =2 spins. The appearance of these three phases is attributed to the competition between the uniaxial single-ion anisotropies of both spins.
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
. The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
Pereira, J. R. V.; Tunes, T. M.; de Arruda, A. S.; Godoy, M.
2018-06-01
In this work, we have performed Monte Carlo simulations to study a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on a square lattice with two different random single-ion anisotropies. This lattice is divided in two interpenetrating sublattices with spins SA = 1 in the sublattice A and SB = 3 / 2 in the sublattice B. The exchange interaction between the spins on the sublattices is antiferromagnetic (J single-ion anisotropies, DiA and DjB , on the sublattices A and B, respectively. We have determined the phase diagram of the model in the critical temperature Tc versus strength of the random single-ion anisotropy D plane and we shown that it exhibits only second-order phase transition lines. We also shown that this system displays compensation temperatures for some cases of the random single-ion distribution.
Network type sp3 boron-based single-ion conducting polymer electrolytes for lithium ion batteries
Deng, Kuirong; Wang, Shuanjin; Ren, Shan; Han, Dongmei; Xiao, Min; Meng, Yuezhong
2017-08-01
Electrolytes play a vital role in modulating lithium ion battery performance. An outstanding electrolyte should possess both high ionic conductivity and unity lithium ion transference number. Here, we present a facile method to fabricate a network type sp3 boron-based single-ion conducting polymer electrolyte (SIPE) with high ionic conductivity and lithium ion transference number approaching unity. The SIPE was synthesized by coupling of lithium bis(allylmalonato)borate (LiBAMB) and pentaerythritol tetrakis(2-mercaptoacetate) (PETMP) via one-step photoinitiated in situ thiol-ene click reaction in plasticizers. Influence of kinds and content of plasticizers was investigated and the optimized electrolytes show both outstanding ionic conductivity (1.47 × 10-3 S cm-1 at 25 °C) and high lithium transference number of 0.89. This ionic conductivity is among the highest ionic conductivity exhibited by SIPEs reported to date. Its electrochemical stability window is up to 5.2 V. More importantly, Li/LiFePO4 cells with the prepared single-ion conducting electrolytes as the electrolyte as well as the separator display highly reversible capacity and excellent rate capacity under room temperature. It also demonstrates excellent long-term stability and reliability as it maintains capacity of 124 mA h g-1 at 1 C rate even after 500 cycles without obvious decay.
Chen, Yan-Cong; Liu, Jun-Liang; Wernsdorfer, Wolfgang; Liu, Dan; Chibotaru, Liviu F; Chen, Xiao-Ming; Tong, Ming-Liang
2017-04-24
An extremely rare non-Kramers holmium(III) single-ion magnet (SIM) is reported to be stabilized in the pentagonal-bipyramidal geometry by a phosphine oxide with a high energy barrier of 237(4) cm -1 . The suppression of the quantum tunneling of magnetization (QTM) at zero field and the hyperfine structures originating from field-induced QTMs can be observed even from the field-dependent alternating-current magnetic susceptibility in addition to single-crystal hysteresis loops. These dramatic dynamics were attributed to the combination of the favorable crystal-field environment and the hyperfine interactions arising from 165 Ho (I=7/2) with a natural abundance of 100 %. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Energy Technology Data Exchange (ETDEWEB)
Chen, Yan-Cong; Liu, Jun-Liang; Chen, Xiao-Ming; Tong, Ming-Liang [Key Lab. of Bioinorganic and Synthetic Chemistry of Ministry of Education, School of Chemistry, Sun Yat-Sen Univ., Guangzhou (China); Wernsdorfer, Wolfgang [Institut Neel, CNRS and Universite Joseph Fournier, Grenoble (France); Institute of Nanotechnology, Karlsruhe Institute of Technology (Germany); Physikalisches Institut, Karlsruhe Institute of Technology (Germany); Liu, Dan; Chibotaru, Liviu F. [Theory of Nanomaterials Group and INPAC-Institute of Nanoscale Physics and Chemistry, Katholieke Universiteit Leuven (Belgium)
2017-04-24
An extremely rare non-Kramers holmium(III) single-ion magnet (SIM) is reported to be stabilized in the pentagonal-bipyramidal geometry by a phosphine oxide with a high energy barrier of 237(4) cm{sup -1}. The suppression of the quantum tunneling of magnetization (QTM) at zero field and the hyperfine structures originating from field-induced QTMs can be observed even from the field-dependent alternating-current magnetic susceptibility in addition to single-crystal hysteresis loops. These dramatic dynamics were attributed to the combination of the favorable crystal-field environment and the hyperfine interactions arising from {sup 165}Ho (I=7/2) with a natural abundance of 100 %. (copyright 2017 Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim)
Cai, Weiwei; Zhang, Yunfeng; Li, Jing; Sun, Yubao; Cheng, Hansong
2014-04-01
Conductive processes involving lithium ions are analyzed in detail from a mechanistic perspective, and demonstrate that single ion polymeric electrolyte (SIPE) membranes can be used in lithium-ion batteries with a wide operating temperature range (25-80 °C) through systematic optimization of electrodes and electrode/electrolyte interfaces, in sharp contrast to other batteries equipped with SIPE membranes that display appreciable operability only at elevated temperatures (>60 °C). The performance is comparable to that of batteries using liquid electrolyte of inorganic salt, and the batteries exhibit excellent cycle life and rate performance. This significant widening of battery operation temperatures coupled with the inherent flexibility and robustness of the SIPE membranes makes it possible to develop thin and flexible Li-ion batteries for a broad range of applications. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Finite-temperature dynamic structure factor of the spin-1 XXZ chain with single-ion anisotropy
Lange, Florian; Ejima, Satoshi; Fehske, Holger
2018-02-01
Improving matrix-product state techniques based on the purification of the density matrix, we are able to accurately calculate the finite-temperature dynamic response of the infinite spin-1 XXZ chain with single-ion anisotropy in the Haldane, large-D , and antiferromagnetic phases. Distinct thermally activated scattering processes make a significant contribution to the spectral weight in all cases. In the Haldane phase, intraband magnon scattering is prominent, and the on-site anisotropy causes the magnon to split into singlet and doublet branches. In the large-D phase response, the intraband signal is separated from an exciton-antiexciton continuum. In the antiferromagnetic phase, holons are the lowest-lying excitations, with a gap that closes at the transition to the Haldane state. At finite temperatures, scattering between domain-wall excitations becomes especially important and strongly enhances the spectral weight for momentum transfer π .
Monte Carlo prediction of crater formation by single ion impact on solid surface
International Nuclear Information System (INIS)
Perez-Martin, A.M.C.; Dominguez-Vazquez, J.; Jimenez-Rodriguez, J.J.; Collins, R.; Gras-Marti, A.
1994-01-01
A method is presented for predicting the topography changes following the impact of one energetic ion on the plane surface of a monatomic amorphous solid. This is done in two stages. The first is a Monte Carlo calculation of the sputter yield and interior distribution relocated atoms, with no compensation for local departures from equilibrium density. In the second stage there is a systematic relaxation of the solid, in which the density returns to its previous constant value and a crater develops in the surface. Two alternative methods of carrying out stage two are compared. In the first the solid is subdivided into cells within which relaxation is carried out normal to the surface, as in previous one-dimensional studies. The second method treats the solid as a 3-dimensional incompressible medium. Both seem to reproduce quite well the main features found experimentally. (orig.)
Pliego, Josefredo R.
2017-07-01
The cluster expansion method has been used in the imperfect gas theory for several decades. This paper proposes a cluster expansion of the solvation free energy difference. This difference, which results from a change in the solute-solvent potential energy, can be written as the logarithm of a finite series. Similar to the Mayer function, the terms in the series are related to configurational integrals, which makes the integrand relevant only for configurations of the solvent molecules close to the solute. In addition, the terms involve interaction of solute with one, two, and so on solvent molecules. The approach could be used for hybrid quantum mechanical and molecular mechanics methods or mixed cluster-continuum approximation. A simple form of the theory was applied for prediction of pKa in methanol; the results indicated that three explicit methanol molecules and the dielectric continuum lead to a root of mean squared error (RMSE) of only 1.3 pKa units, whereas the pure continuum solvation model based on density method leads to a RMSE of 6.6 pKa units.
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)
Exactly solved mixed spin-(1,1/2) Ising–Heisenberg diamond chain with a single-ion anisotropy
International Nuclear Information System (INIS)
Lisnyi, Bohdan; Strečka, Jozef
2015-01-01
The mixed spin-(1,1/2) Ising–Heisenberg diamond chain with a single-ion anisotropy is exactly solved through the generalized decoration–iteration transformation and the transfer-matrix method. The decoration–iteration transformation is first used for establishing a rigorous mapping equivalence with the corresponding spin-1 Blume–Emery–Griffiths chain, which is subsequently exactly treated within the transfer-matrix technique. Apart from three classical ground states the model exhibits three striking quantum ground states in which a singlet-dimer state of the interstitial Heisenberg spins is accompanied either with a frustrated state or a polarized state or a non-magnetic state of the nodal Ising spins. It is evidenced that two magnetization plateaus at zero and/or one-half of the saturation magnetization may appear in low-temperature magnetization curves. The specific heat may display remarkable temperature dependences with up to three and four distinct round maxima in a zero and non-zero magnetic field, respectively. - Highlights: • Mixed spin-(1,1/2) Ising–Heisenberg diamond chain is exactly solved. • Quantum ground states with a singlet-dimer state of the Heisenberg spins are found. • Magnetization curve displays intermediate plateaus at zero and half of full magnetization. • Thermal dependences of specific heat may display up to four distinct peaks
U/Th dating by SHRIMP RG ion-microprobe mass spectrometry using single ion-exchange beads
Bischoff, J.L.; Wooden, J.; Murphy, F.; Williams, Ross W.
2005-01-01
We present a new analytical method for U-series isotopes using the SHRIMP RG (Sensitive High mass Resolution Ion MicroProbe) mass spectrometer that utilizes the preconcentration of the U-series isotopes from a sample onto a single ion-exchange bead. Ion-microprobe mass spectrometry is capable of producing Th ionization efficiencies in excess of 2%. Analytical precision is typically better than alpha spectroscopy, but not as good as thermal ionization mass spectroscopy (TIMS) and inductively coupled plasma multicollector mass spectrometry (ICP-MS). Like TIMS and ICP-MS the method allows analysis of small samples sizes, but also adds the advantage of rapidity of analysis. A major advantage of ion-microprobe analysis is that U and Th isotopes are analyzed in the same bead, simplifying the process of chemical separation. Analytical time on the instrument is ???60 min per sample, and a single instrument-loading can accommodate 15-20 samples to be analyzed in a 24-h day. An additional advantage is that the method allows multiple reanalyses of the same bead and that samples can be archived for reanalysis at a later time. Because the ion beam excavates a pit only a few ??m deep, the mount can later be repolished and reanalyzed numerous times. The method described of preconcentrating a low concentration sample onto a small conductive substrate to allow ion-microprobe mass spectrometry is potentially applicable to many other systems. Copyright ?? 2005 Elsevier Ltd.
Energy Technology Data Exchange (ETDEWEB)
Prakrajang, K. [Plasma and Beam Physics Research Facility, Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai 50200 (Thailand); Faculty of Science, Maejo University, Chiang Mai 50290 (Thailand); Jeynes, J.C.G.; Merchant, M.J.; Kirkby, K.; Kirkby, N. [Surrey Ion Beam Center, Faculty of Engineering and Physical Science, University of Surrey, Guildford Surrey, GU2 7XH (United Kingdom); Thopan, P. [Plasma and Beam Physics Research Facility, Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai 50200 (Thailand); Yu, L.D., E-mail: yuld@fnrf.science.cmu.ac.th [Plasma and Beam Physics Research Facility, Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai 50200 (Thailand); Thailand Center of Excellence in Physics, Commission on Higher Education, 328 Si Ayutthaya Road, Bangkok 10400 (Thailand)
2013-07-15
Highlights: •Recently completed nanobeam at the Surrey Ion Beam Centre was used. •3.8-MeV single and broad proton beams irradiated Chinese hamster cells. •Cell survival curves were measured and compared with 300-kV X-ray irradiation. •Single ion irradiation had a lower survival part at ultra-low dose. •It implies hypersensitivity, bystander effect and cell cycle phase of cell death. -- Abstract: As a part of a systematic study on mechanisms involved in physical cancer therapies, this work investigated response of mammalian cells to ultra-low-dose ion beam irradiation. The ion beam irradiation was performed using the recently completed nanobeam facility at the Surrey Ion Beam Centre. A scanning focused vertical ion nano-beam was applied to irradiate Chinese hamster V79 cells. The V79 cells were irradiated in two different beam modes, namely, focused single ion beam and defocused scanning broad ion beam of 3.8-MeV protons. The single ion beam was capable of irradiating a single cell with a precisely controlled number of the ions to extremely low doses. After irradiation and cell incubation, the number of surviving colonies as a function of the number of the irradiating ions was measured for the cell survival fraction curve. A lower survival for the single ion beam irradiation than that of the broad beam case implied the hypersensitivity and bystander effect. The ion-beam-induced cell survival curves were compared with that from 300-kV X-ray irradiation. Theoretical studies indicated that the cell death in single ion irradiation mainly occurred in the cell cycle phases of cell division and intervals between the cell division and the DNA replication. The success in the experiment demonstrated the Surrey vertical nanobeam successfully completed.
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...
Shearlets and Optimally Sparse Approximations
DEFF Research Database (Denmark)
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
2012-01-01
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....
Approximate symmetries of Hamiltonians
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
Approximating distributions from moments
Pawula, R. F.
1987-11-01
A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.
CONTRIBUTIONS TO RATIONAL APPROXIMATION,
Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)
Approximation techniques for engineers
Komzsik, Louis
2006-01-01
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
International Nuclear Information System (INIS)
Bobak, Andrej; Dely, Jan; Pokorny, Vladislav
2010-01-01
The effects of both an exchange anisotropy and a single-ion anisotropy on the magnetic susceptibility of the mixed spin-1 and spin- 1/2 Heisenberg model are investigated by the use of an Oguchi approximation. Particular emphasis is given to the simple cubic lattice with coordination number z = 6 for which the magnetic susceptibility is determined numerically. Anomalous behaviour in the thermal variation of the magnetic susceptibility in the low-temperature region is found due to the applied negative single-ion anisotropy field strength. Also, the difference between the behaviours of the magnetic susceptibility of the Heisenberg and Ising models is discussed.
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 dis...
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
Approximate and renormgroup symmetries
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Approximate and renormgroup symmetries
International Nuclear Information System (INIS)
Ibragimov, Nail H.; Kovalev, Vladimir F.
2009-01-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
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
Potvin, Guy
2015-10-01
We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.
Geometric approximation algorithms
Har-Peled, Sariel
2011-01-01
Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.
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
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
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Zarubin, Dmitri P., E-mail: dmitri.zarubin@mtu-net.ru [Department of Physical and Collod Chemistry, Moscow State University of Technology and Management, 73 Zemlyanoi Val, Moscow 109803 (Russian Federation)
2011-08-15
Highlights: > Problem of ionic activity coefficients, determined by potentiometry, is reconsidered. > They are found to be functions of mean activity coefficients and transport numbers of ions. > The finding is verified by calculations and comparing the results with reported data. > Calculations are performed for systems with single electrolytes and binary mixtures. - Abstract: Potentiometric measurements on cells with liquid junctions are sometimes used for calculations of single-ion activity coefficients in electrolyte solutions, the incidence of this being increased recently. As surmised by Guggenheim in the 1930s, such coefficients (of ions i), {gamma}{sub i}, are actually complicated functions of mean ionic activity coefficients, {gamma}{sub {+-}}, and transport numbers of ions, t{sub i}. In the present paper specific functions {gamma}{sub i}({gamma}{sub {+-}}, t{sub i}) are derived for a number of cell types with an arbitrary mixture of strong electrolytes in a one-component solvent in the liquid-junction system. The cell types include cells with (i) identical electrodes, (ii) dissimilar electrodes reversible to the same ions, (iii) dissimilar electrodes reversible to ions of opposite charge signs, (iv) dissimilar electrodes reversible to different ions of the same charge sign, and (v) identical reference electrodes and an ion-selective membrane permeable to ions of only one type. Pairs of functions for oppositely charged ions are found to be consistent with the mean ionic activity coefficients as would be expected for pairs of the proper {gamma}{sub i} quantities by definition of {gamma}{sub {+-}}. The functions are tested numerically on some of the reported {gamma}{sub i} datasets that are the more tractable. A generally good agreement is found with data reported for cells with single electrolytes HCl and KCl in solutions, and with binary mixtures in the liquid-junction systems of KCl from the reference solutions and NaCl and HCl from the test solutions. It
International Nuclear Information System (INIS)
Shu Seki; Satoshi Tsukuda, Yoichi Yoshida; Seiichi Tagawa; Masaki Sugimoto; Shigeru Tanaka
2002-01-01
1-D nano-sized materials such as carbon nanotubes have attracted much attention as ideal quantum wires for future manufacturing techniques of nano-scaled opto-electronic devices. However it is still difficult to control the sizes, spatial distributions, or positions of nanotubes by conventional synthetic techniques to date. The MeV order heavy ion beams causes ultra-high density energy deposition which can not be realized by any other techniques (lasers, H, etc), and penetrate the polymer target straighforward as long as 1∼100 m depth. the energy deposited area produces non-homogeneous field can be controlled by changing the energy deposition rate of incident ions (LET: linear energy transfer, eV/nm). We found that cross-linking reaction of polysilane derivatives was predominantly caused and gave nano-gel in the chemical core, unlike main chain scission occurring at the outside of the area. high density energy deposition by ion beams causes non-homogeneous crosslinking reaction of polysilane derivatives within a nano-sized cylindrical area along an ion trajectory, and gives -SiC based nano-wires of which sizes (length, thickness) and number densities are completely under control by changing the parameters of incident ion beams and molecular sizes of target polymers. based on the concept pf the single track gelation, the present study demonstrates the formation of cross-linked polysilane nano-wires with the fairly controlled sizes. Recently the techniques of position-selective single ion hitting have been developed for MeV order ion beams, however it is not sufficient to control precisely the positions of the nano-wires on the substrates within sub- m area. in the present study, we report the selective adhesion of anno-wires on Si substrates by the surface treatments before coating, which enables the patterning of planted nano-wires on substrates and/or electrodes as candidates for nano-sized field emissive cathodes or electro-luminescent devices. Some examples of
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
International Nuclear Information System (INIS)
Sun, Xiao-Guang; Kerr, John B.
2004-01-01
Network single ion conductors (NSICs) based on comb-branch polyepoxide ethers and lithium bis(allylmalonato) borate have been synthesized and thoroughly characterized by means of ionic conductivity measurements, electrochemical impedance and by dynamic mechanical analysis (DMA). The materials have been tested as battery electrolytes by cycling in symmetrical Li/Li half cells and in Li/V 6 O 13 full cells in which the NSIC was used as both binder and electrolyte in the cathode electrode and as the electrolyte separator membrane,. The substitution of the trimethylene oxide (TMO) unit into the side chains in place of ethylene oxide (EO) units increased the polymerion mobility (lower glass transition temperature). However, the ionic conductivity was nearly one and half orders of magnitude lower than the corresponding pure EO based single ion conductor at the same salt concentration. This effect may be ascribed to the lower dielectric constant of the TMO side chains that result in a lower concentration of free conducting lithium cations. For a highly cross-linked system (EO/Li=20), only 47 wt% plasticizing solvent (ethylene carbonate (EC)/ethyl methyl carbonate (EMC), 1/1 by wt) could be taken up and the ionic conductivity was only increased by one order of magnitude over the dry polyelectrolyte while for a less densely crosslinked system (EO/Li=80), up to 75 wt% plasticizer could be taken up and the ionic conductivity was increased by nearly two orders of magnitude. A Li/Li symmetric cell that was cycled at 85 C at a current density of 25(micro)Acm -2 showed no concentration polarization or diffusional relaxation, consistent with a lithium ion transference number of one. However, both the bulk and interfacial impedances increased after 20 cycles, apparently due to continued cross-linking reactions within the membrane and on the surface of the lithium electrodes. A Li/V 6 O 13 full cell constructed using a single ion conductor gel (propylene carbonate (PC)/EMC, 1/1 in
On Covering Approximation Subspaces
Directory of Open Access Journals (Sweden)
Xun Ge
2009-06-01
Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.
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
Prestack wavefield approximations
Alkhalifah, Tariq
2013-01-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
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...
Approximation by Cylinder Surfaces
DEFF Research Database (Denmark)
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...
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.
An improved saddlepoint approximation.
Gillespie, Colin S; Renshaw, Eric
2007-08-01
Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents. However, it suffers from the problem of not always yielding full support, and whilst [S. Wang, General saddlepoint approximations in the bootstrap, Prob. Stat. Lett. 27 (1992) 61.] neat scaling approach provides a solution to this hurdle, it leads to potentially inaccurate and aberrant results. We therefore propose several new ways of surmounting such difficulties, including: extending the inversion of the cumulant generating function to second-order; selecting an appropriate probability structure for higher-order cumulants (the standard moment closure procedure takes them to be zero); and, making subtle changes to the target cumulants and then optimising via the simplex algorithm.
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...
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
Approximating Preemptive Stochastic Scheduling
Megow Nicole; Vredeveld Tjark
2009-01-01
We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...
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.
International Nuclear Information System (INIS)
Bobak, A.; Dely, J.
2007-01-01
The effect of a single-ion anisotropy on the phase diagram of the mixed spin-32 and spin-2 Ising system is investigated by the use of a mean-field theory based on the Bogoliubov inequality for the free energy. Topologically different kinds of phase diagrams are achieved by changing values of the parameter in the model Hamiltonian. Besides second-order transitions, lines of first-order transitions terminating either at a tricritical point or an isolated critical point, are found
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.
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)
The relaxation time approximation
International Nuclear Information System (INIS)
Gairola, R.P.; Indu, B.D.
1991-01-01
A plausible approximation has been made to estimate the relaxation time from a knowledge of the transition probability of phonons from one state (r vector, q vector) to other state (r' vector, q' vector), as a result of collision. The relaxation time, thus obtained, shows a strong dependence on temperature and weak dependence on the wave vector. In view of this dependence, relaxation time has been expressed in terms of a temperature Taylor's series in the first Brillouin zone. Consequently, a simple model for estimating the thermal conductivity is suggested. the calculations become much easier than the Callaway model. (author). 14 refs
Polynomial approximation on polytopes
Totik, Vilmos
2014-01-01
Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.
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
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.
Duignan, Timothy T.; Baer, Marcel D.; Mundy, Christopher J.
2018-06-01
The tetra-phenyl arsonium and tetra-phenyl borate (TATB) assumption is a commonly used extra-thermodynamic assumption that allows single ion free energies to be split into cationic and anionic contributions. The assumption is that the values for the TATB salt can be divided equally. This is justified by arguing that these large hydrophobic ions will cause a symmetric response in water. Experimental and classical simulation work has raised potential flaws with this assumption, indicating that hydrogen bonding with the phenyl ring may favor the solvation of the TB- anion. Here, we perform ab initio molecular dynamics simulations of these ions in bulk water demonstrating that there are significant structural differences. We quantify our findings by reproducing the experimentally observed vibrational shift for the TB- anion and confirm that this is associated with hydrogen bonding with the phenyl rings. Finally, we demonstrate that this results in a substantial energetic preference of the water to solvate the anion. Our results suggest that the validity of the TATB assumption, which is still widely used today, should be reconsidered experimentally in order to properly reference single ion solvation free energy, enthalpy, and entropy.
The random phase approximation
International Nuclear Information System (INIS)
Schuck, P.
1985-01-01
RPA is the adequate theory to describe vibrations of the nucleus of very small amplitudes. These vibrations can either be forced by an external electromagnetic field or can be eigenmodes of the nucleus. In a one dimensional analogue the potential corresponding to such eigenmodes of very small amplitude should be rather stiff otherwise the motion risks to be a large amplitude one and to enter a region where the approximation is not valid. This means that nuclei which are supposedly well described by RPA must have a very stable groundstate configuration (must e.g. be very stiff against deformation). This is usually the case for doubly magic nuclei or close to magic nuclei which are in the middle of proton and neutron shells which develop a very stable groundstate deformation; we take the deformation as an example but there are many other possible degrees of freedom as, for example, compression modes, isovector degrees of freedom, spin degrees of freedom, and many more
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 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.
Tension and Approximation in Poetic Translation
Al-Shabab, Omar A. S.; Baka, Farida H.
2015-01-01
Simple observation reveals that each language and each culture enjoys specific linguistic features and rhetorical traditions. In poetry translation difference and the resultant linguistic tension create a gap between Source Language and Target language, a gap that needs to be bridged by creating an approximation processed through the translator's…
Radtke, Valentin; Ermantraut, Andreas; Himmel, Daniel; Koslowski, Thorsten; Leito, Ivo; Krossing, Ingo
2018-02-23
Described is a procedure for the thermodynamically rigorous, experimental determination of the Gibbs energy of transfer of single ions between solvents. The method is based on potential difference measurements between two electrochemical half cells with different solvents connected by an ideal ionic liquid salt bridge (ILSB). Discussed are the specific requirements for the IL with regard to the procedure, thus ensuring that the liquid junction potentials (LJP) at both ends of the ILSB are mostly canceled. The remaining parts of the LJPs can be determined by separate electromotive force measurements. No extra-thermodynamic assumptions are necessary for this procedure. The accuracy of the measurements depends, amongst others, on the ideality of the IL used, as shown in our companion paper Part II. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Pliego, Josefredo R; Miguel, Elizabeth L M
2013-05-02
Absolute solvation free energy of the lithium cation in methanol was calculated by the cluster-continuum quasichemical theory of solvation. Clusters with up to five methanol molecules were investigated using X3LYP, MP2, and MP4 methods with DZVP, 6-311+G(2df,2p), TZVPP+diff, and QZVPP+diff basis sets and including the cluster solvation through the PCM and SMD continuum models. Our calculations have determined a value of -118.1 kcal mol(-1) for the solvation free energy of the lithium, in close agreement with a value of -116.6 kcal mol(-1) consistent with the TATB assumption. Using data of solvation and transfer free energy of a pair of ions, electrode potentials and pKa, we have obtained the solvation free energy of 25 ions in methanol. Our analysis leads to a value of -253.6 kcal mol(-1) for the solvation free energy of the proton, which can be compared with the value of -263.5 kcal mol(-1) obtained by Kelly et al. using the cluster pair approximation. Considering that this difference is due to the methanol surface potential, we have estimated that it corresponds to -0.429 V.
Milne, R K; Yeo, G F; Edeson, R O; Madsen, B W
1988-04-22
Stochastic models of ion channels have been based largely on Markov theory where individual states and transition rates must be specified, and sojourn-time densities for each state are constrained to be exponential. This study presents an approach based on random-sum methods and alternating-renewal theory, allowing individual states to be grouped into classes provided the successive sojourn times in a given class are independent and identically distributed. Under these conditions Markov models form a special case. The utility of the approach is illustrated by considering the effects of limited time resolution (modelled by using a discrete detection limit, xi) on the properties of observable events, with emphasis on the observed open-time (xi-open-time). The cumulants and Laplace transform for a xi-open-time are derived for a range of Markov and non-Markov models; several useful approximations to the xi-open-time density function are presented. Numerical studies show that the effects of limited time resolution can be extreme, and also highlight the relative importance of the various model parameters. The theory could form a basis for future inferential studies in which parameter estimation takes account of limited time resolution in single channel records. Appendixes include relevant results concerning random sums and a discussion of the role of exponential distributions in Markov models.
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
2016-01-01
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
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.
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.
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 optimization is then used to find the approximating elastic curve....
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
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.
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
Understanding Legacy Features with Featureous
DEFF Research Database (Denmark)
Olszak, Andrzej; Jørgensen, Bo Nørregaard
2011-01-01
Java programs called Featureous that addresses this issue. Featureous allows a programmer to easily establish feature-code traceability links and to analyze their characteristics using a number of visualizations. Featureous is an extension to the NetBeans IDE, and can itself be extended by third...
Some results in Diophantine approximation
DEFF Research Database (Denmark)
Pedersen, Steffen Højris
the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered......This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...
Limitations of shallow nets approximation.
Lin, Shao-Bo
2017-10-01
In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.
Hamid, Arian Zad
2016-12-01
We analytically investigate Multiple Quantum (MQ) NMR dynamics in a mixed-three-spin (1/2,1,1/2) system with XXX Heisenberg model at the front of an external homogeneous magnetic field B. A single-ion anisotropy property ζ is considered for the spin-1. The intensities dependence of MQ NMR coherences on their orders (zeroth and second orders) for two pairs of spins (1,1/2) and (1/2,1/2) of the favorite tripartite system are obtained. It is also investigated dynamics of the pairwise quantum entanglement for the bipartite (sub)systems (1,1/2) and (1/2,1/2) permanently coupled by, respectively, coupling constants J}1 and J}2, by means of concurrence and fidelity. Then, some straightforward comparisons are done between these quantities and the intensities of MQ NMR coherences and ultimately some interesting results are reported. We also show that the time evolution of MQ coherences based on the reduced density matrix of the pair spins (1,1/2) is closely connected with the dynamics of the pairwise entanglement. Finally, we prove that one can introduce MQ coherence of the zeroth order corresponds to the pair spins (1,1/2) as an entanglement witness at some special time intervals.
Spherical Approximation on Unit Sphere
Directory of Open Access Journals (Sweden)
Eman Samir Bhaya
2018-01-01
Full Text Available In this paper we introduce a Jackson type theorem for functions in LP spaces on sphere And study on best approximation of functions in spaces defined on unit sphere. our central problem is to describe the approximation behavior of functions in spaces for by modulus of smoothness of functions.
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.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education. Feature Article. Articles in Resonance – Journal of Science Education. Volume 1 Issue 1 January 1996 pp 80-85 Feature Article. What's New in Computers Windows 95 · Vijnan Shastri · More Details Fulltext PDF. Volume 1 Issue 1 January 1996 pp 86-89 Feature ...
Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.
Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E
2018-06-01
An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.
The efficiency of Flory approximation
International Nuclear Information System (INIS)
Obukhov, S.P.
1984-01-01
The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)
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
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Framework for sequential approximate optimization
Jacobs, J.H.; Etman, L.F.P.; Keulen, van F.; Rooda, J.E.
2004-01-01
An object-oriented framework for Sequential Approximate Optimization (SAO) isproposed. The framework aims to provide an open environment for thespecification and implementation of SAO strategies. The framework is based onthe Python programming language and contains a toolbox of Python
Wilson, A.; Lawrence, J.; Yang, E.-C.; Nakano, M.; Hendrickson, D. N.; Hill, S.
2006-10-01
Electron paramagnetic resonance (EPR) studies of a Ni4 single-molecule magnet (SMM) yield the zero-field-splitting (ZFS) parameters D , B40 , and B44 , based on the giant spin approximation (GSA) with S=4 ; B44 is responsible for the magnetization tunneling in this SMM. Experiments on an isostructural Ni-doped Zn4 crystal establish the NiII ion ZFS parameters. The fourth-order ZFS parameters in the GSA arise from the interplay between the Heisenberg interaction Jŝ1•ŝ2 and the second-order single-ion anisotropy, giving rise to mixing of higher-lying S≠4 states into the S=4 state. Consequently, J directly influences the ZFS in the ground state, enabling its determination by EPR.
Nuclear Hartree-Fock approximation testing and other related approximations
International Nuclear Information System (INIS)
Cohenca, J.M.
1970-01-01
Hartree-Fock, and Tamm-Dancoff approximations are tested for angular momentum of even-even nuclei. Wave functions, energy levels and momenta are comparatively evaluated. Quadripole interactions are studied following the Elliott model. Results are applied to Ne 20 [pt
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...
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.
Rational approximations for tomographic reconstructions
International Nuclear Information System (INIS)
Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas
2013-01-01
We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp–Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image. (paper)
Approximation methods in probability theory
Čekanavičius, Vydas
2016-01-01
This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.
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)
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...... 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....
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...
Approximate Matching of Hierarchial Data
DEFF Research Database (Denmark)
Augsten, Nikolaus
-grams of a tree are all its subtrees of a particular shape. Intuitively, two trees are similar if they have many pq-grams in common. The pq-gram distance is an efficient and effective approximation of the tree edit distance. We analyze the properties of the pq-gram distance and compare it with the tree edit...
Approximation of Surfaces by Cylinders
DEFF Research Database (Denmark)
Randrup, Thomas
1998-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...
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.
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
Truthful approximations to range voting
DEFF Research Database (Denmark)
Filos-Ratsika, Aris; Miltersen, Peter Bro
We consider the fundamental mechanism design problem of approximate social welfare maximization under general cardinal preferences on a finite number of alternatives and without money. The well-known range voting scheme can be thought of as a non-truthful mechanism for exact social welfare...
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...
Approximate reasoning in decision analysis
Energy Technology Data Exchange (ETDEWEB)
Gupta, M M; Sanchez, E
1982-01-01
The volume aims to incorporate the recent advances in both theory and applications. It contains 44 articles by 74 contributors from 17 different countries. The topics considered include: membership functions; composite fuzzy relations; fuzzy logic and inference; classifications and similarity measures; expert systems and medical diagnosis; psychological measurements and human behaviour; approximate reasoning and decision analysis; and fuzzy clustering algorithms.
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.
Pythagorean Approximations and Continued Fractions
Peralta, Javier
2008-01-01
In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…
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
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.
Ranking Support Vector Machine with Kernel Approximation.
Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi
2017-01-01
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.
CERN. Geneva
2015-01-01
Feature selection and reduction are key to robust multivariate analyses. In this talk I will focus on pros and cons of various variable selection methods and focus on those that are most relevant in the context of HEP.
National Oceanic and Atmospheric Administration, Department of Commerce — Collection includes a variety of solar feature datasets contributed by a number of national and private solar observatories located worldwide.
U.S. Environmental Protection Agency — This dataset consists of various site features from multiple Superfund sites in U.S. EPA Region 8. These data were acquired from multiple sources at different times...
Beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...... functional theory and the adiabatic connection fluctuation-dissipation theorem and contains no fitted parameters. The new kernel is shown to preserve the accurate description of dispersive interactions from RPA while significantly improving the description of short-range correlation in molecules, insulators......, and metals. For molecular atomization energies, the rALDA is a factor of 7 better than RPA and a factor of 4 better than the Perdew-Burke-Ernzerhof (PBE) functional when compared to experiments, and a factor of 3 (1.5) better than RPA (PBE) for cohesive energies of solids. For transition metals...
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
Fast approximate convex decomposition using relative concavity
Ghosh, Mukulika; Amato, Nancy M.; Lu, Yanyan; Lien, Jyh-Ming
2013-01-01
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.
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.
Approximation errors during variance propagation
International Nuclear Information System (INIS)
Dinsmore, Stephen
1986-01-01
Risk and reliability analyses are often performed by constructing and quantifying large fault trees. The inputs to these models are component failure events whose probability of occuring are best represented as random variables. This paper examines the errors inherent in two approximation techniques used to calculate the top event's variance from the inputs' variance. Two sample fault trees are evaluated and several three dimensional plots illustrating the magnitude of the error over a wide range of input means and variances are given
WKB approximation in atomic physics
International Nuclear Information System (INIS)
Karnakov, Boris Mikhailovich
2013-01-01
Provides extensive coverage of the Wentzel-Kramers-Brillouin approximation and its applications. Presented as a sequence of problems with highly detailed solutions. Gives a concise introduction for calculating Rydberg states, potential barriers and quasistationary systems. This book has evolved from lectures devoted to applications of the Wentzel-Kramers-Brillouin- (WKB or quasi-classical) approximation and of the method of 1/N -expansion for solving various problems in atomic and nuclear physics. The intent of this book is to help students and investigators in this field to extend their knowledge of these important calculation methods in quantum mechanics. Much material is contained herein that is not to be found elsewhere. WKB approximation, while constituting a fundamental area in atomic physics, has not been the focus of many books. A novel method has been adopted for the presentation of the subject matter, the material is presented as a succession of problems, followed by a detailed way of solving them. The methods introduced are then used to calculate Rydberg states in atomic systems and to evaluate potential barriers and quasistationary states. Finally, adiabatic transition and ionization of quantum systems are covered.
Approximate solutions to Mathieu's equation
Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.
2018-06-01
Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.
Approximate Inference for Wireless Communications
DEFF Research Database (Denmark)
Hansen, Morten
This thesis investigates signal processing techniques for wireless communication receivers. The aim is to improve the performance or reduce the computationally complexity of these, where the primary focus area is cellular systems such as Global System for Mobile communications (GSM) (and extensions...... to the optimal one, which usually requires an unacceptable high complexity. Some of the treated approximate methods are based on QL-factorization of the channel matrix. In the work presented in this thesis it is proven how the QL-factorization of frequency-selective channels asymptotically provides the minimum...
Quantum tunneling beyond semiclassical approximation
International Nuclear Information System (INIS)
Banerjee, Rabin; Majhi, Bibhas Ranjan
2008-01-01
Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.
Approximate Method for Solving the Linear Fuzzy Delay Differential Equations
Directory of Open Access Journals (Sweden)
S. Narayanamoorthy
2015-01-01
Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.
Discussion of CoSA: Clustering of Sparse Approximations
Energy Technology Data Exchange (ETDEWEB)
Armstrong, Derek Elswick [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-03-07
The purpose of this talk is to discuss the possible applications of CoSA (Clustering of Sparse Approximations) to the exploitation of HSI (HyperSpectral Imagery) data. CoSA is presented by Moody et al. in the Journal of Applied Remote Sensing (“Land cover classification in multispectral imagery using clustering of sparse approximations over learned feature dictionaries”, Vol. 8, 2014) and is based on machine learning techniques.
Vortex sheet approximation of boundary layers
International Nuclear Information System (INIS)
Chorin, A.J.
1978-01-01
a grid free method for approximating incomprssible boundary layers is introduced. The computational elements are segments of vortex sheets. The method is related to the earlier vortex method; simplicity is achieved at the cost of replacing the Navier-Stokes equations by the Prandtl boundary layer equations. A new method for generating vorticity at boundaries is also presented; it can be used with the earlier voartex method. The applications presented include (i) flat plate problems, and (ii) a flow problem in a model cylinder- piston assembly, where the new method is used near walls and an improved version of the random choice method is used in the interior. One of the attractive features of the new method is the ease with which it can be incorporated into hybrid algorithms
Impulse approximation in solid helium
International Nuclear Information System (INIS)
Glyde, H.R.
1985-01-01
The incoherent dynamic form factor S/sub i/(Q, ω) is evaluated in solid helium for comparison with the impulse approximation (IA). The purpose is to determine the Q values for which the IA is valid for systems such a helium where the atoms interact via a potential having a steeply repulsive but not infinite hard core. For 3 He, S/sub i/(Q, ω) is evaluated from first principles, beginning with the pair potential. The density of states g(ω) is evaluated using the self-consistent phonon theory and S/sub i/(Q,ω) is expressed in terms of g(ω). For solid 4 He resonable models of g(ω) using observed input parameters are used to evaluate S/sub i/(Q,ω). In both cases S/sub i/(Q, ω) is found to approach the impulse approximation S/sub IA/(Q, ω) closely for wave vector transfers Q> or approx. =20 A -1 . The difference between S/sub i/ and S/sub IA/, which is due to final state interactions of the scattering atom with the remainder of the atoms in the solid, is also predominantly antisymmetric in (ω-ω/sub R/), where ω/sub R/ is the recoil frequency. This suggests that the symmetrization procedure proposed by Sears to eliminate final state contributions should work well in solid helium
Finite approximations in fluid mechanics
International Nuclear Information System (INIS)
Hirschel, E.H.
1986-01-01
This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for the Euler equations, etc. Applications are made to channel flows, gas dynamical problems, large eddy simulation of turbulence, non-Newtonian flow, turbomachine flow, zonal solutions for viscous flow problems, etc. The contents include: multigrid methods for problems from fluid dynamics, development of a 2D-Transonic Potential Flow Solver; a boundary element spectral method for nonstationary viscous flows in 3 dimensions; navier-stokes computations of two-dimensional laminar flows in a channel with a backward facing step; calculations and experimental investigations of the laminar unsteady flow in a pipe expansion; calculation of the flow-field caused by shock wave and deflagration interaction; a multi-level discretization and solution method for potential flow problems in three dimensions; solutions of the conservation equations with the approximate factorization method; inviscid and viscous flow through rotating meridional contours; zonal solutions for viscous flow problems
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.
Kim, SungKun; Lee, Hunpyo
2017-06-01
Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.
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 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 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...
Approximate cohomology in Banach algebras | Pourabbas ...
African Journals Online (AJOL)
We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate cohomologies. As a special case, approximate Hochschild cohomology is ...
Lunar ash flows - Isothermal approximation.
Pai, S. I.; Hsieh, T.; O'Keefe, J. A.
1972-01-01
Suggestion of the ash flow mechanism as one of the major processes required to account for some features of lunar soil. First the observational background and the gardening hypothesis are reviewed, and the shortcomings of the gardening hypothesis are shown. Then a general description of the lunar ash flow is given, and a simple mathematical model of the isothermal lunar ash flow is worked out with numerical examples to show the differences between the lunar and the terrestrial ash flow. The important parameters of the ash flow process are isolated and analyzed. It appears that the lunar surface layer in the maria is not a residual mantle rock (regolith) but a series of ash flows due, at least in part, to great meteorite impacts. The possibility of a volcanic contribution is not excluded. Some further analytic research on lunar ash flows is recommended.
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
The dilute random field Ising model by finite cluster approximation
International Nuclear Information System (INIS)
Benyoussef, A.; Saber, M.
1987-09-01
Using the finite cluster approximation, phase diagrams of bond and site diluted three-dimensional simple cubic Ising models with a random field have been determined. The resulting phase diagrams have the same general features for both bond and site dilution. (author). 7 refs, 4 figs
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
Fondo, Matilde; Corredoira-Vázquez, Julio; Herrera-Lanzós, Antía; García-Deibe, Ana M; Sanmartín-Matalobos, Jesús; Herrera, Juan Manuel; Colacio, Enrique; Nuñez, Cristina
2017-12-12
Mononuclear complexes of stoichiometry [Ln(H 3 L)(H 2 O)(NO 3 )](NO 3 ) 2 (Ln = Tb, 1; Dy, 2, Er, 3), which crystallise with different solvates, and the heterotrinuclear compound [Zn 2 Dy(L)(NO 3 ) 3 (OH)] (4) can be obtained with the same H 3 L compartmental ligand. The single X-ray crystal structure of the mononuclear complexes shows a LnO 9 core with a muffin-like disposition while the geometry of the DyO 9 core in 4 seems to be closer to spherical capped square antiprism. The analysis of the magnetic properties of all the complexes demonstrates that the mononuclear lanthanide compounds do not show slow relaxation of the magnetization, even when the samples are diluted with a diamagnetic matrix and subjected to a dc applied field of 1000 Oe. Nevertheless, the heterotrinuclear dysprosium complex 4·3H 2 O is a field-induced single ion magnet, with an estimated U eff barrier of 59 K. The luminescence characterisation of all the metal complexes in methanol solution at 298 K also shows a notable increase in the fluorescence emission of the heterotrinuclear complex with respect to the mononuclear ones, in such a way that 4 can be defined as a fluorescent single ion magnet.
Directory of Open Access Journals (Sweden)
Elizabeth Ritter
2015-01-01
Full Text Available Algonquian languages are famous for their animacy-based grammatical properties—an animacy based noun classification system and direct/inverse system which gives rise to animacy hierarchy effects in the determination of verb agreement. In this paper I provide new evidence for the proposal that the distinctive properties of these languages is due to the use of participant-based features, rather than spatio-temporal ones, for both nominal and verbal functional categories (Ritter & Wiltschko 2009, 2014. Building on Wiltschko (2012, I develop a formal treatment of the Blackfoot aspectual system that assumes a category Inner Aspect (cf. MacDonald 2008, Travis 1991, 2010. Focusing on lexical aspect in Blackfoot, I demonstrate that the classification of both nouns (Seinsarten and verbs (Aktionsarten is based on animacy, rather than boundedness, resulting in a strikingly different aspectual system for both categories.
Data approximation using a blending type spline construction
International Nuclear Information System (INIS)
Dalmo, Rune; Bratlie, Jostein
2014-01-01
Generalized expo-rational B-splines (GERBS) is a blending type spline construction where local functions at each knot are blended together by C k -smooth basis functions. One way of approximating discrete regular data using GERBS is by partitioning the data set into subsets and fit a local function to each subset. Partitioning and fitting strategies can be devised such that important or interesting data points are interpolated in order to preserve certain features. We present a method for fitting discrete data using a tensor product GERBS construction. The method is based on detection of feature points using differential geometry. Derivatives, which are necessary for feature point detection and used to construct local surface patches, are approximated from the discrete data using finite differences
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
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.
Dynamical Vertex Approximation for the Hubbard Model
Toschi, Alessandro
A full understanding of correlated electron systems in the physically relevant situations of three and two dimensions represents a challenge for the contemporary condensed matter theory. However, in the last years considerable progress has been achieved by means of increasingly more powerful quantum many-body algorithms, applied to the basic model for correlated electrons, the Hubbard Hamiltonian. Here, I will review the physics emerging from studies performed with the dynamical vertex approximation, which includes diagrammatic corrections to the local description of the dynamical mean field theory (DMFT). In particular, I will first discuss the phase diagram in three dimensions with a special focus on the commensurate and incommensurate magnetic phases, their (quantum) critical properties, and the impact of fluctuations on electronic lifetimes and spectral functions. In two dimensions, the effects of non-local fluctuations beyond DMFT grow enormously, determining the appearance of a low-temperature insulating behavior for all values of the interaction in the unfrustrated model: Here the prototypical features of the Mott-Hubbard metal-insulator transition, as well as the existence of magnetically ordered phases, are completely overwhelmed by antiferromagnetic fluctuations of exponentially large extension, in accordance with the Mermin-Wagner theorem. Eventually, by a fluctuation diagnostics analysis of cluster DMFT self-energies, the same magnetic fluctuations are identified as responsible for the pseudogap regime in the holed-doped frustrated case, with important implications for the theoretical modeling of the cuprate physics.
On the approximation of crack shapes found during inservice inspection
International Nuclear Information System (INIS)
Bhate, S.R.; Chawla, D.S.; Kushwaha, H.S.
1997-01-01
This paper addresses the characterization of axial internal flaw found during inservice inspection of a pipe. J-integral distribution for various flaw shapes is obtained using line spring finite, element method. The peak J-value and its distribution across the crack is found to be characteristic feature of each shape. The triangular shape yields peak J-value away from the center, the point of depth. The elliptic approximation results in large overestimate of J-value for unsymmetric flaws. Triangular approximation is recommended for such flaws so that further service can be obtained from the component
On the approximation of crack shapes found during inservice inspection
Energy Technology Data Exchange (ETDEWEB)
Bhate, S.R.; Chawla, D.S.; Kushwaha, H.S. [Bhabha Atomic Research Centre, Bombay (India)] [and others
1997-04-01
This paper addresses the characterization of axial internal flaw found during inservice inspection of a pipe. J-integral distribution for various flaw shapes is obtained using line spring finite, element method. The peak J-value and its distribution across the crack is found to be characteristic feature of each shape. The triangular shape yields peak J-value away from the center, the point of depth. The elliptic approximation results in large overestimate of J-value for unsymmetric flaws. Triangular approximation is recommended for such flaws so that further service can be obtained from the component.
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-01-01
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
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.
Mercaldo, M. T.; Rabuffo, I.; De Cesare, L.; Caramico D'Auria, A.
2016-04-01
In this work we study the quantum phase transition, the phase diagram and the quantum criticality induced by the easy-plane single-ion anisotropy in a d-dimensional quantum spin-1 XY model in absence of an external longitudinal magnetic field. We employ the two-time Green function method by avoiding the Anderson-Callen decoupling of spin operators at the same sites which is of doubtful accuracy. Following the original Devlin procedure we treat exactly the higher order single-site anisotropy Green functions and use Tyablikov-like decouplings for the exchange higher order ones. The related self-consistent equations appear suitable for an analysis of the thermodynamic properties at and around second order phase transition points. Remarkably, the equivalence between the microscopic spin model and the continuous O(2) -vector model with transverse-Ising model (TIM)-like dynamics, characterized by a dynamic critical exponent z=1, emerges at low temperatures close to the quantum critical point with the single-ion anisotropy parameter D as the non-thermal control parameter. The zero-temperature critic anisotropy parameter Dc is obtained for dimensionalities d > 1 as a function of the microscopic exchange coupling parameter and the related numerical data for different lattices are found to be in reasonable agreement with those obtained by means of alternative analytical and numerical methods. For d > 2, and in particular for d=3, we determine the finite-temperature critical line ending in the quantum critical point and the related TIM-like shift exponent, consistently with recent renormalization group predictions. The main crossover lines between different asymptotic regimes around the quantum critical point are also estimated providing a global phase diagram and a quantum criticality very similar to the conventional ones.
Some relations between entropy and approximation numbers
Institute of Scientific and Technical Information of China (English)
郑志明
1999-01-01
A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.
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.
An approximation for kanban controlled assembly systems
Topan, E.; Avsar, Z.M.
2011-01-01
An approximation is proposed to evaluate the steady-state performance of kanban controlled two-stage assembly systems. The development of the approximation is as follows. The considered continuous-time Markov chain is aggregated keeping the model exact, and this aggregate model is approximated
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.
Analysis of corrections to the eikonal approximation
Hebborn, C.; Capel, P.
2017-11-01
Various corrections to the eikonal approximations are studied for two- and three-body nuclear collisions with the goal to extend the range of validity of this approximation to beam energies of 10 MeV/nucleon. Wallace's correction does not improve much the elastic-scattering cross sections obtained at the usual eikonal approximation. On the contrary, a semiclassical approximation that substitutes the impact parameter by a complex distance of closest approach computed with the projectile-target optical potential efficiently corrects the eikonal approximation. This opens the possibility to analyze data measured down to 10 MeV/nucleon within eikonal-like reaction models.
Mapping moveout approximations in TI media
Stovas, Alexey; Alkhalifah, Tariq Ali
2013-01-01
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.
Analytical approximation of neutron physics data
International Nuclear Information System (INIS)
Badikov, S.A.; Vinogradov, V.A.; Gaj, E.V.; Rabotnov, N.S.
1984-01-01
The method for experimental neutron-physical data analytical approximation by rational functions based on the Pade approximation is suggested. It is shown that the existence of the Pade approximation specific properties in polar zones is an extremely favourable analytical property essentially extending the convergence range and increasing its rate as compared with polynomial approximation. The Pade approximation is the particularly natural instrument for resonance curve processing as the resonances conform to the complex poles of the approximant. But even in a general case analytical representation of the data in this form is convenient and compact. Thus representation of the data on the neutron threshold reaction cross sections (BOSPOR constant library) in the form of rational functions lead to approximately twenty fold reduction of the storaged numerical information as compared with the by-point calculation at the same accWracy
A unified approach to the Darwin approximation
International Nuclear Information System (INIS)
Krause, Todd B.; Apte, A.; Morrison, P. J.
2007-01-01
There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting
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.
An Approximate Approach to Automatic Kernel Selection.
Ding, Lizhong; Liao, Shizhong
2016-02-02
Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.
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.
Improved stochastic approximation methods for discretized parabolic partial differential equations
Guiaş, Flavius
2016-12-01
We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).
Cosmological applications of Padé approximant
International Nuclear Information System (INIS)
Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan
2014-01-01
As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation
Cosmological applications of Padé approximant
Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan
2014-01-01
As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.
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.
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.
Exact and approximate multiple diffraction calculations
International Nuclear Information System (INIS)
Alexander, Y.; Wallace, S.J.; Sparrow, D.A.
1976-08-01
A three-body potential scattering problem is solved in the fixed scatterer model exactly and approximately to test the validity of commonly used assumptions of multiple scattering calculations. The model problem involves two-body amplitudes that show diffraction-like differential scattering similar to high energy hadron-nucleon amplitudes. The exact fixed scatterer calculations are compared to Glauber approximation, eikonal-expansion results and a noneikonal approximation
Bent approximations to synchrotron radiation optics
International Nuclear Information System (INIS)
Heald, S.
1981-01-01
Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors
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.
APPROXIMATIONS TO PERFORMANCE MEASURES IN QUEUING SYSTEMS
Directory of Open Access Journals (Sweden)
Kambo, N. S.
2012-11-01
Full Text Available Approximations to various performance measures in queuing systems have received considerable attention because these measures have wide applicability. In this paper we propose two methods to approximate the queuing characteristics of a GI/M/1 system. The first method is non-parametric in nature, using only the first three moments of the arrival distribution. The second method treads the known path of approximating the arrival distribution by a mixture of two exponential distributions by matching the first three moments. Numerical examples and optimal analysis of performance measures of GI/M/1 queues are provided to illustrate the efficacy of the methods, and are compared with benchmark approximations.
Online feature selection with streaming features.
Wu, Xindong; Yu, Kui; Ding, Wei; Wang, Hao; Zhu, Xingquan
2013-05-01
We propose a new online feature selection framework for applications with streaming features where the knowledge of the full feature space is unknown in advance. We define streaming features as features that flow in one by one over time whereas the number of training examples remains fixed. This is in contrast with traditional online learning methods that only deal with sequentially added observations, with little attention being paid to streaming features. The critical challenges for Online Streaming Feature Selection (OSFS) include 1) the continuous growth of feature volumes over time, 2) a large feature space, possibly of unknown or infinite size, and 3) the unavailability of the entire feature set before learning starts. In the paper, we present a novel Online Streaming Feature Selection method to select strongly relevant and nonredundant features on the fly. An efficient Fast-OSFS algorithm is proposed to improve feature selection performance. The proposed algorithms are evaluated extensively on high-dimensional datasets and also with a real-world case study on impact crater detection. Experimental results demonstrate that the algorithms achieve better compactness and higher prediction accuracy than existing streaming feature selection algorithms.
Approximate Boundaries for West Lake Landfill, Missouri, 2014, EPA REG 07
U.S. Environmental Protection Agency — This ESRI File Geodatabase Feature Class contains polygons for GIS depicting the approximate boundaries for West Lake Landfill (MOD079900932), Missouri, 2014, EPA...
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
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 ...
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
2010 Mathematics Subject Classification. 46L07. 1. Introduction. Given a countable discrete group G, some nice approximation properties for the reduced. C∗-algebras C∗ r (G) can give us the approximation properties of G. For example, Lance. [7] proved that the nuclearity of C∗ r (G) is equivalent to the amenability of G; ...
Non-Linear Approximation of Bayesian Update
Litvinenko, Alexander
2016-01-01
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.
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 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 ...
Efficient automata constructions and approximate automata
Watson, B.W.; Kourie, D.G.; Ngassam, E.K.; Strauss, T.; Cleophas, L.G.W.A.
2008-01-01
In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at least L. Such automata can be used in a variety of practical applications, including network security pattern
Efficient automata constructions and approximate automata
Watson, B.W.; Kourie, D.G.; Ngassam, E.K.; Strauss, T.; Cleophas, L.G.W.A.; Holub, J.; Zdárek, J.
2006-01-01
In this paper, we present data structures and algorithms for efficiently constructing approximate automata. An approximate automaton for a regular language L is one which accepts at least L. Such automata can be used in a variety of practical applications, including network security pattern
Spline approximation, Part 1: Basic methodology
Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar
2018-04-01
In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.
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…
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.
Approximations for stop-loss reinsurance premiums
Reijnen, Rajko; Albers, Willem/Wim; Kallenberg, W.C.M.
2005-01-01
Various approximations of stop-loss reinsurance premiums are described in literature. For a wide variety of claim size distributions and retention levels, such approximations are compared in this paper to each other, as well as to a quantitative criterion. For the aggregate claims two models are
International Nuclear Information System (INIS)
Rege, Aarti C.; Venkataramani, B.; Gupta, A.R.
1999-06-01
Preferential solvation of single ion solutions has been studied with Li + , Na + , K + and Ag +- forms of Dowex 50W resins of different cross-linkings in methanol-water and acetonitrile (AN)- water mixtures. The solvent uptake by this alkali metal ionic forms of Dowex 50W resins was studied in an isopiestic set-up using 2,4,6 and 8 m LiCl solutions in 11.0, 20.8, 44.3 and 70.2 % (w/w) methanol-water mixtures and that of Na +- and Ag +- forms using 14.6 to 94.3 % (w/w) AN - water mixtures. The solvent sorbed in the resin phase was extracted by Rayleigh-type distillation and analysed gas chromatographically. The data were analysed by the N s (mole fraction of the organic solvent in the resin phase) vs n t au (total solvent content in the resin phase) plots and separation factor, alpha(ratio of mole fraction of the solvents in the resin and solution phases) or N s vs m (molality in the resin phase) plots. The limiting values of these plots gave the composition of the solvent in the primary solvation shell around the single ion. The compositions of the primary solvation shell around Li + , Na + , and K + in methanol-water mixtures and Na + and Ag + in acetonitrile (AN) - water mixtures have been computed using Franks equation and the approach of Marcus and compared with the experimental results obtained with the above mentioned ionic forms of Dowex 50W resins in different mixed solvents. The experimental results for Li + showed good agreement with the values computed using Franks equation for all methanol-water composition. However, in the case of Na + and K + in methanol-water mixtures and Na + in AN-water mixtures, there was agreement only at lower organic solvent content and the Franks equation predicted higher values for the organic solvent in the primary solvation shell around the cation at higher organic solvent content as compared to experimental results
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.
Identifying significant environmental features using feature recognition.
2015-10-01
The Department of Environmental Analysis at the Kentucky Transportation Cabinet has expressed an interest in feature-recognition capability because it may help analysts identify environmentally sensitive features in the landscape, : including those r...
Sparse linear models: Variational approximate inference and Bayesian experimental design
International Nuclear Information System (INIS)
Seeger, Matthias W
2009-01-01
A wide range of problems such as signal reconstruction, denoising, source separation, feature selection, and graphical model search are addressed today by posterior maximization for linear models with sparsity-favouring prior distributions. The Bayesian posterior contains useful information far beyond its mode, which can be used to drive methods for sampling optimization (active learning), feature relevance ranking, or hyperparameter estimation, if only this representation of uncertainty can be approximated in a tractable manner. In this paper, we review recent results for variational sparse inference, and show that they share underlying computational primitives. We discuss how sampling optimization can be implemented as sequential Bayesian experimental design. While there has been tremendous recent activity to develop sparse estimation, little attendance has been given to sparse approximate inference. In this paper, we argue that many problems in practice, such as compressive sensing for real-world image reconstruction, are served much better by proper uncertainty approximations than by ever more aggressive sparse estimation algorithms. Moreover, since some variational inference methods have been given strong convex optimization characterizations recently, theoretical analysis may become possible, promising new insights into nonlinear experimental design.
Sparse linear models: Variational approximate inference and Bayesian experimental design
Energy Technology Data Exchange (ETDEWEB)
Seeger, Matthias W [Saarland University and Max Planck Institute for Informatics, Campus E1.4, 66123 Saarbruecken (Germany)
2009-12-01
A wide range of problems such as signal reconstruction, denoising, source separation, feature selection, and graphical model search are addressed today by posterior maximization for linear models with sparsity-favouring prior distributions. The Bayesian posterior contains useful information far beyond its mode, which can be used to drive methods for sampling optimization (active learning), feature relevance ranking, or hyperparameter estimation, if only this representation of uncertainty can be approximated in a tractable manner. In this paper, we review recent results for variational sparse inference, and show that they share underlying computational primitives. We discuss how sampling optimization can be implemented as sequential Bayesian experimental design. While there has been tremendous recent activity to develop sparse estimation, little attendance has been given to sparse approximate inference. In this paper, we argue that many problems in practice, such as compressive sensing for real-world image reconstruction, are served much better by proper uncertainty approximations than by ever more aggressive sparse estimation algorithms. Moreover, since some variational inference methods have been given strong convex optimization characterizations recently, theoretical analysis may become possible, promising new insights into nonlinear experimental design.
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...
Conditional Density Approximations with Mixtures of Polynomials
DEFF Research Database (Denmark)
Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre
2015-01-01
Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce...... two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities...
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)}...
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.
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.
Directory of Open Access Journals (Sweden)
Dong Shao
2017-12-01
Full Text Available We herein reported the syntheses, crystal structures, and magnetic properties of a two-dimensional coordination polymer {[CoII(TPT2/3(H2O4][CH3COO]2·(H2O4}n (1 and a chain compound {[CoII(TPT2(CHOO2(H2O2]}n (2 based on the 2,4,6-Tris(4-pyridyl-1,3,5-triazine (TPT ligand. Structure analyses showed that complex 1 had a cationic hexagonal framework structure, while 2 was a neutral zig-zag chain structure with different distorted octahedral coordination environments. Magnetic measurements revealed that both complexes exhibit large easy-plane magnetic anisotropy with the zero-field splitting parameter D = 47.7 and 62.1 cm−1 for 1 and 2, respectively. This magnetic anisotropy leads to the field-induced slow magnetic relaxation behaviour. However, their magnetic dynamics are quite different; while complex 1 experienced a dominating thermally activated Orbach relaxation at the whole measured temperature region, 2 exhibited multiple relaxation pathways involving direct, Raman, and quantum tunneling (QTM processes at low temperatures and Orbach relaxation at high temperatures. The present complexes enlarge the family of framework-based single-ion magnets (SIMs and highlight the significance of the structural dimensionality to the final magnetic properties.
Multilevel weighted least squares polynomial approximation
Haji-Ali, Abdul-Lateef; Nobile, Fabio; Tempone, Raul; Wolfers, Sö ren
2017-01-01
, 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
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; ...
Nonlinear Ritz approximation for Fredholm functionals
Directory of Open Access Journals (Sweden)
Mudhir A. Abdul Hussain
2015-11-01
Full Text Available In this article we use the modify Lyapunov-Schmidt reduction to find nonlinear Ritz approximation for a Fredholm functional. This functional corresponds to a nonlinear Fredholm operator defined by a nonlinear fourth-order differential equation.
Euclidean shortest paths exact or approximate algorithms
Li, Fajie
2014-01-01
This book reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. The coverage includes mathematical proofs for many of the given statements.
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)
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)
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...
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.
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
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
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
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.
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.
Approximate Computing Techniques for Iterative Graph Algorithms
Energy Technology Data Exchange (ETDEWEB)
Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh; Kalyanaraman, Anantharaman; Chavarria Miranda, Daniel G.; Krishnamoorthy, Sriram
2017-12-18
Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with low impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.
Nucleon-pair approximation to the nuclear shell model
Energy Technology Data Exchange (ETDEWEB)
Zhao, Y.M., E-mail: ymzhao@sjtu.edu.cn [Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Arima, A. [Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Musashi Gakuen, 1-26-1 Toyotamakami Nerima-ku, Tokyo 176-8533 (Japan)
2014-12-01
Atomic nuclei are complex systems of nucleons–protons and neutrons. Nucleons interact with each other via an attractive and short-range force. This feature of the interaction leads to a pattern of dominantly monopole and quadrupole correlations between like particles (i.e., proton–proton and neutron–neutron correlations) in low-lying states of atomic nuclei. As a consequence, among dozens or even hundreds of possible types of nucleon pairs, very few nucleon pairs such as proton and neutron pairs with spin zero, two (in some cases spin four), and occasionally isoscalar spin-aligned proton–neutron pairs, play important roles in low-energy nuclear structure. The nucleon-pair approximation therefore provides us with an efficient truncation scheme of the full shell model configurations which are otherwise too large to handle for medium and heavy nuclei in foreseeable future. Furthermore, the nucleon-pair approximation leads to simple pictures in physics, as the dimension of nucleon-pair subspace is always small. The present paper aims at a sound review of its history, formulation, validity, applications, as well as its link to previous approaches, with the focus on the new developments in the last two decades. The applicability of the nucleon-pair approximation and numerical calculations of low-lying states for realistic atomic nuclei are demonstrated with examples. Applications of pair approximations to other problems are also discussed.
Gaussian and 1/N approximations in semiclassical cosmology
International Nuclear Information System (INIS)
Mazzitelli, F.D.; Paz, J.P.
1989-01-01
We study the λphi 4 theory and the interacting O(N) model in a curved background using the Gaussian approximation for the former and the large-N approximation for the latter. We obtain the renormalized version of the semiclassical Einstein equations having in mind a future application of these models to investigate the physics of the very early Universe. We show that, while the Gaussian approximation has two different phases, in the large-N limit only one is present. The different features of the two phases are analyzed at the level of the effective field equations. We discuss the initial-value problem and find the initial conditions that make the theory renormalizable. As an example, we study the de Sitter self-consistent solutions of the semiclassical Einstein equations. Finally, for an identically zero mean value of the field we find the evolution equations for the classical field Ω(x) = (λ 2 >)/sup 1/2/ and the spacetime metric. They are very similar to the ones obtained by replacing the classical potential by the one-loop effective potential in the classical equations but do not have the drawbacks of the one-loop approximation
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
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.)
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...... for approximate Bayesian inference. We demonstrate our approach on regression with Gaussian processes. A comparison with averages obtained by Monte-Carlo sampling shows that our method achieves good accuracy....
Stochastic quantization and mean field approximation
International Nuclear Information System (INIS)
Jengo, R.; Parga, N.
1983-09-01
In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)
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
Magnus approximation in the adiabatic picture
International Nuclear Information System (INIS)
Klarsfeld, S.; Oteo, J.A.
1991-01-01
A simple approximate nonperturbative method is described for treating time-dependent problems that works well in the intermediate regime far from both the sudden and the adiabatic limits. The method consists of applying the Magnus expansion after transforming to the adiabatic basis defined by the eigenstates of the instantaneous Hamiltonian. A few exactly soluble examples are considered in order to assess the domain of validity of the approximation. (author) 32 refs., 4 figs
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.)
Unitary pole approximations and expansions in few-body systems
International Nuclear Information System (INIS)
Casel, A.; Haberzettl, H.; Sandhas, W.
1982-01-01
The unitary pole approximations or expansions of the two-body subsystem operators are well known, and particularly efficient and practical, methods to reduce the three-body problem to an effective two-body theory. In the present investigation we develop generalizations of these approximation techniques to the subsystem amplitudes of problems with higher particle numbers. They are based on the expansion of effective potentials which, in contrast to the genuine two-body interactions, are now energy dependent. Despite this feature our generalizations require only energy independent form factors, thus preserving one of the essential advantages of the genuine two-body approach. The application of these techniques to the four-body case is discussed in detail
5th International Conference on Algorithms for Approximation
Levesley, Jeremy
2007-01-01
Approximation methods are vital in many challenging applications of computational science and engineering. This is a collection of papers from world experts in a broad variety of relevant applications, including pattern recognition, machine learning, multiscale modelling of fluid flow, metrology, geometric modelling, tomography, signal and image processing. It documents recent theoretical developments which have lead to new trends in approximation, it gives important computational aspects and multidisciplinary applications, thus making it a perfect fit for graduate students and researchers in science and engineering who wish to understand and develop numerical algorithms for the solution of their specific problems. An important feature of the book is that it brings together modern methods from statistics, mathematical modelling and numerical simulation for the solution of relevant problems, with a wide range of inherent scales. Contributions of industrial mathematicians, including representatives from Microso...
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.
Single-ion nonlinear mechanical oscillator
International Nuclear Information System (INIS)
Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.
2010-01-01
We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.
Space-Efficient Approximation Scheme for Circular Earth Mover Distance
DEFF Research Database (Denmark)
Brody, Joshua Eric; Liang, Hongyu; Sun, Xiaoming
2012-01-01
The Earth Mover Distance (EMD) between point sets A and B is the minimum cost of a bipartite matching between A and B. EMD is an important measure for estimating similarities between objects with quantifiable features and has important applications in several areas including computer vision...... to computer vision [13] and can be seen as a special case of computing EMD on a discretized grid. We achieve a (1 ±ε) approximation for EMD in $\\tilde O(\\varepsilon^{-3})$ space, for every 0 ... that matches the space bound asked in [9]....
Magnetic analysis of tokamak plasma with approximate MHD equilibrium solution
International Nuclear Information System (INIS)
Moriyama, Shin-ichi; Hiraki, Naoji
1993-01-01
A magnetic analysis method for determining equilibrium configuration parameters (plasma shape, poloidal beta and internal inductance) on a non-circular tokamak is described. The feature is to utilize an approximate MHD equilibrium solution which explicitly relates the configuration parameters with the magnetic fields picked up by magnetic sensors. So this method is suitable for the real-time analysis performed during a tokamak discharge. A least-squares fitting procedure is added to the analytical algorithm in order to reduce the errors in the magnetic analysis. The validity is investigated through the numerical calculation for a tokamak equilibrium model. (author)
Diffusive Wave Approximation to the Shallow Water Equations: Computational Approach
Collier, Nathan
2011-05-14
We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity. This robust adaptive time discretization corrects the initial time step size to achieve a user specified bound on the discretization error and allows time step size variations of several orders of magnitude. In particular, in the one dimensional results presented in this work feature a change of four orders of magnitudes for the time step over the entire simulation.
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.
'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.
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.
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.
Spectral features in the cosmic ray fluxes
Lipari, Paolo
2018-01-01
The cosmic ray energy distributions contain spectral features, that is narrow energy regions where the slope of the spectrum changes rapidly. The identification and study of these features is of great importance to understand the astrophysical mechanisms of acceleration and propagation that form the spectra. In first approximation a spectral feature is often described as a discontinuous change in slope, however very valuable information is also contained in its width, that is the length of the energy interval where the change in spectral index develops. In this work we discuss the best way to define and parameterize the width a spectral feature, and for illustration discuss some of the most prominent known structures.
Feature curve extraction from point clouds via developable strip intersection
Directory of Open Access Journals (Sweden)
Kai Wah Lee
2016-04-01
Full Text Available In this paper, we study the problem of computing smooth feature curves from CAD type point clouds models. The proposed method reconstructs feature curves from the intersections of developable strip pairs which approximate the regions along both sides of the features. The generation of developable surfaces is based on a linear approximation of the given point cloud through a variational shape approximation approach. A line segment sequencing algorithm is proposed for collecting feature line segments into different feature sequences as well as sequential groups of data points. A developable surface approximation procedure is employed to refine incident approximation planes of data points into developable strips. Some experimental results are included to demonstrate the performance of the proposed method.
Smooth function approximation using neural networks.
Ferrari, Silvia; Stengel, Robert F
2005-01-01
An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.
Modified semiclassical approximation for trapped Bose gases
International Nuclear Information System (INIS)
Yukalov, V.I.
2005-01-01
A generalization of the semiclassical approximation is suggested allowing for an essential extension of its region of applicability. In particular, it becomes possible to describe Bose-Einstein condensation of a trapped gas in low-dimensional traps and in traps of low confining dimensions, for which the standard semiclassical approximation is not applicable. The result of the modified approach is shown to coincide with purely quantum-mechanical calculations for harmonic traps, including the one-dimensional harmonic trap. The advantage of the semiclassical approximation is in its simplicity and generality. Power-law potentials of arbitrary powers are considered. The effective thermodynamic limit is defined for any confining dimension. The behavior of the specific heat, isothermal compressibility, and density fluctuations is analyzed, with an emphasis on low confining dimensions, where the usual semiclassical method fails. The peculiarities of the thermodynamic characteristics in the effective thermodynamic limit are discussed
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
Self-similar continued root approximants
International Nuclear Information System (INIS)
Gluzman, S.; Yukalov, V.I.
2012-01-01
A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Padé approximants. A theorem on the convergence of the self-similar continued roots is proved. The method is illustrated by several examples from condensed-matter physics.
Ancilla-approximable quantum state transformations
Energy Technology Data Exchange (ETDEWEB)
Blass, Andreas [Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 (United States); Gurevich, Yuri [Microsoft Research, Redmond, Washington 98052 (United States)
2015-04-15
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation.
On Born approximation in black hole scattering
Batic, D.; Kelkar, N. G.; Nowakowski, M.
2011-12-01
A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordström and Reissner-Nordström-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.
Ancilla-approximable quantum state transformations
International Nuclear Information System (INIS)
Blass, Andreas; Gurevich, Yuri
2015-01-01
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation
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.)
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)
Resummation of perturbative QCD by pade approximants
International Nuclear Information System (INIS)
Gardi, E.
1997-01-01
In this lecture I present some of the new developments concerning the use of Pade Approximants (PA's) for resuming perturbative series in QCD. It is shown that PA's tend to reduce the renormalization scale and scheme dependence as compared to truncated series. In particular it is proven that in the limit where the β function is dominated by the 1-loop contribution, there is an exact symmetry that guarantees invariance of diagonal PA's under changing the renormalization scale. In addition it is shown that in the large β 0 approximation diagonal PA's can be interpreted as a systematic method for approximating the flow of momentum in Feynman diagrams. This corresponds to a new multiple scale generalization of the Brodsky-Lepage-Mackenzie (BLM) method to higher orders. I illustrate the method with the Bjorken sum rule and the vacuum polarization function. (author)
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.
Perturbation expansions generated by an approximate propagator
International Nuclear Information System (INIS)
Znojil, M.
1987-01-01
Starting from a knowledge of an approximate propagator R at some trial energy guess E 0 , a new perturbative prescription for p-plet of bound states and of their energies is proposed. It generalizes the Rayleigh-Schroedinger (RS) degenerate perturbation theory to the nondiagonal operators R (eliminates a RS need of their diagnolisation) and defines an approximate Hamiltonian T by mere inversion. The deviation V of T from the exact Hamiltonian H is assumed small only after a substraction of a further auxiliary Hartree-Fock-like separable ''selfconsistent'' potential U of rank p. The convergence is illustrated numerically on the anharmonic oscillator example
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.
Unambiguous results from variational matrix Pade approximants
International Nuclear Information System (INIS)
Pindor, Maciej.
1979-10-01
Variational Matrix Pade Approximants are studied as a nonlinear variational problem. It is shown that although a stationary value of the Schwinger functional is a stationary value of VMPA, the latter has also another stationary value. It is therefore proposed that instead of looking for a stationary point of VMPA, one minimizes some non-negative functional and then one calculates VMPA at the point where the former has the absolute minimum. This approach, which we call the Method of the Variational Gradient (MVG) gives unambiguous results and is also shown to minimize a distance between the approximate and the exact stationary values of the Schwinger functional
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.
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.
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.
Congruence Approximations for Entrophy Endowed Hyperbolic Systems
Barth, Timothy J.; Saini, Subhash (Technical Monitor)
1998-01-01
Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.
Hardness of approximation for strip packing
DEFF Research Database (Denmark)
Adamaszek, Anna Maria; Kociumaka, Tomasz; Pilipczuk, Marcin
2017-01-01
Strip packing is a classical packing problem, where the goal is to pack a set of rectangular objects into a strip of a given width, while minimizing the total height of the packing. The problem has multiple applications, for example, in scheduling and stock-cutting, and has been studied extensively......)-approximation by two independent research groups [FSTTCS 2016,WALCOM 2017]. This raises a questionwhether strip packing with polynomially bounded input data admits a quasi-polynomial time approximation scheme, as is the case for related twodimensional packing problems like maximum independent set of rectangles or two...
Weighted Polynomial Approximation for Automated Detection of Inspiratory Flow Limitation
Directory of Open Access Journals (Sweden)
Sheng-Cheng Huang
2017-01-01
Full Text Available Inspiratory flow limitation (IFL is a critical symptom of sleep breathing disorders. A characteristic flattened flow-time curve indicates the presence of highest resistance flow limitation. This study involved investigating a real-time algorithm for detecting IFL during sleep. Three categories of inspiratory flow shape were collected from previous studies for use as a development set. Of these, 16 cases were labeled as non-IFL and 78 as IFL which were further categorized into minor level (20 cases and severe level (58 cases of obstruction. In this study, algorithms using polynomial functions were proposed for extracting the features of IFL. Methods using first- to third-order polynomial approximations were applied to calculate the fitting curve to obtain the mean absolute error. The proposed algorithm is described by the weighted third-order (w.3rd-order polynomial function. For validation, a total of 1,093 inspiratory breaths were acquired as a test set. The accuracy levels of the classifications produced by the presented feature detection methods were analyzed, and the performance levels were compared using a misclassification cobweb. According to the results, the algorithm using the w.3rd-order polynomial approximation achieved an accuracy of 94.14% for IFL classification. We concluded that this algorithm achieved effective automatic IFL detection during sleep.
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander; Genton, Marc G.; Sun, Ying
2015-01-01
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.
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.)
Approximate Networking for Universal Internet Access
Directory of Open Access Journals (Sweden)
Junaid Qadir
2017-12-01
Full Text Available Despite the best efforts of networking researchers and practitioners, an ideal Internet experience is inaccessible to an overwhelming majority of people the world over, mainly due to the lack of cost-efficient ways of provisioning high-performance, global Internet. In this paper, we argue that instead of an exclusive focus on a utopian goal of universally accessible “ideal networking” (in which we have a high throughput and quality of service as well as low latency and congestion, we should consider providing “approximate networking” through the adoption of context-appropriate trade-offs. In this regard, we propose to leverage the advances in the emerging trend of “approximate computing” that rely on relaxing the bounds of precise/exact computing to provide new opportunities for improving the area, power, and performance efficiency of systems by orders of magnitude by embracing output errors in resilient applications. Furthermore, we propose to extend the dimensions of approximate computing towards various knobs available at network layers. Approximate networking can be used to provision “Global Access to the Internet for All” (GAIA in a pragmatically tiered fashion, in which different users around the world are provided a different context-appropriate (but still contextually functional Internet experience.
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.
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.
Intrinsic Diophantine approximation on general polynomial surfaces
DEFF Research Database (Denmark)
Tiljeset, Morten Hein
2017-01-01
We study the Hausdorff measure and dimension of the set of intrinsically simultaneously -approximable points on a curve, surface, etc, given as a graph of integer polynomials. We obtain complete answers to these questions for algebraically “nice” manifolds. This generalizes earlier work done...
Perturbation of operators and approximation of spectrum
Indian Academy of Sciences (India)
outside the bounds of essential spectrum of A(x) can be approximated ... some perturbed discrete Schrödinger operators treating them as block ...... particular, one may think of estimating the spectrum and spectral gaps of Schrödinger.
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
Rational approximations and quantum algorithms with postselection
Mahadev, U.; de Wolf, R.
2015-01-01
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using post-selection. We show that the minimal degree of the former equals (up to a factor of 2) the minimal query complexity of the latter. We
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.
Approximate systems with confluent bonding mappings
Lončar, Ivan
2001-01-01
If X = {Xn, pnm, N} is a usual inverse system with confluent (monotone) bonding mappings, then the projections are confluent (monotone). This is not true for approximate inverse system. The main purpose of this paper is to show that the property of Kelley (smoothness) of the space Xn is a sufficient condition for the confluence (monotonicity) of the projections.
Function approximation with polynomial regression slines
International Nuclear Information System (INIS)
Urbanski, P.
1996-01-01
Principles of the polynomial regression splines as well as algorithms and programs for their computation are presented. The programs prepared using software package MATLAB are generally intended for approximation of the X-ray spectra and can be applied in the multivariate calibration of radiometric gauges. (author)
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
On the parametric approximation in quantum optics
Energy Technology Data Exchange (ETDEWEB)
D' Ariano, G.M.; Paris, M.G.A.; Sacchi, M.F. [Istituto Nazionale di Fisica Nucleare, Pavia (Italy); Pavia Univ. (Italy). Dipt. di Fisica ' Alessandro Volta'
1999-03-01
The authors perform the exact numerical diagonalization of Hamiltonians that describe both degenerate and nondegenerate parametric amplifiers, by exploiting the conservation laws pertaining each device. It is clarify the conditions under which the parametric approximation holds, showing that the most relevant requirements is the coherence of the pump after the interaction, rather than its un depletion.
On the parametric approximation in quantum optics
International Nuclear Information System (INIS)
D'Ariano, G.M.; Paris, M.G.A.; Sacchi, M.F.; Pavia Univ.
1999-01-01
The authors perform the exact numerical diagonalization of Hamiltonians that describe both degenerate and nondegenerate parametric amplifiers, by exploiting the conservation laws pertaining each device. It is clarify the conditions under which the parametric approximation holds, showing that the most relevant requirements is the coherence of the pump after the interaction, rather than its un depletion
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
Variational Gaussian approximation for Poisson data
Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen
2018-02-01
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.
Quasiclassical approximation for ultralocal scalar fields
International Nuclear Information System (INIS)
Francisco, G.
1984-01-01
It is shown how to obtain the quasiclassical evolution of a class of field theories called ultralocal fields. Coherent states that follow the 'classical' orbit as defined by Klauder's weak corespondence principle and restricted action principle is explicitly shown to approximate the quantum evolutions as (h/2π) → o. (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.
Multilevel Monte Carlo in Approximate Bayesian Computation
Jasra, Ajay; Jo, Seongil; Nott, David; Shoemaker, Christine; Tempone, Raul
2017-01-01
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.
Multidimensional stochastic approximation using locally contractive functions
Lawton, W. M.
1975-01-01
A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
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)
Optical bistability without the rotating wave approximation
Energy Technology Data Exchange (ETDEWEB)
Sharaby, Yasser A., E-mail: Yasser_Sharaby@hotmail.co [Physics Department, Faculty of Applied Sciences, Suez Canal University, Suez (Egypt); Joshi, Amitabh, E-mail: ajoshi@eiu.ed [Department of Physics, Eastern Illinois University, Charleston, IL 61920 (United States); Hassan, Shoukry S., E-mail: Shoukryhassan@hotmail.co [Mathematics Department, College of Science, University of Bahrain, P.O. Box 32038 (Bahrain)
2010-04-26
Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.
Optical bistability without the rotating wave approximation
International Nuclear Information System (INIS)
Sharaby, Yasser A.; Joshi, Amitabh; Hassan, Shoukry S.
2010-01-01
Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.
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.
RATIONAL APPROXIMATIONS TO GENERALIZED HYPERGEOMETRIC FUNCTIONS.
Under weak restrictions on the various free parameters, general theorems for rational representations of the generalized hypergeometric functions...and certain Meijer G-functions are developed. Upon specialization, these theorems yield a sequency of rational approximations which converge to the
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...
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
Approximate solution methods in engineering mechanics
International Nuclear Information System (INIS)
Boresi, A.P.; Cong, K.P.
1991-01-01
This is a short book of 147 pages including references and sometimes bibliographies at the end of each chapter, and subject and author indices at the end of the book. The test includes an introduction of 3 pages, 29 pages explaining approximate analysis, 41 pages on finite differences, 36 pages on finite elements, and 17 pages on specialized methods
Traveling-cluster approximation for uncorrelated amorphous systems
International Nuclear Information System (INIS)
Sen, A.K.; Mills, R.; Kaplan, T.; Gray, L.J.
1984-01-01
We have developed a formalism for including cluster effects in the one-electron Green's function for a positionally disordered (liquid or amorphous) system without any correlation among the scattering sites. This method is an extension of the technique known as the traveling-cluster approximation (TCA) originally obtained and applied to a substitutional alloy by Mills and Ratanavararaksa. We have also proved the appropriate fixed-point theorem, which guarantees, for a bounded local potential, that the self-consistent equations always converge upon iteration to a unique, Herglotz solution. To our knowledge, this is the only analytic theory for considering cluster effects. Furthermore, we have performed some computer calculations in the pair TCA, for the model case of delta-function potentials on a one-dimensional random chain. These results have been compared with ''exact calculations'' (which, in principle, take into account all cluster effects) and with the coherent-potential approximation (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
Unsupervised Feature Subset Selection
DEFF Research Database (Denmark)
Søndberg-Madsen, Nicolaj; Thomsen, C.; Pena, Jose
2003-01-01
This paper studies filter and hybrid filter-wrapper feature subset selection for unsupervised learning (data clustering). We constrain the search for the best feature subset by scoring the dependence of every feature on the rest of the features, conjecturing that these scores discriminate some ir...... irrelevant features. We report experimental results on artificial and real data for unsupervised learning of naive Bayes models. Both the filter and hybrid approaches perform satisfactorily....
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.
The Hartree-Fock seniority approximation
International Nuclear Information System (INIS)
Gomez, J.M.G.; Prieto, C.
1986-01-01
A new self-consistent method is used to take into account the mean-field and the pairing correlations in nuclei at the same time. We call it the Hartree-Fock seniority approximation, because the long-range and short-range correlations are treated in the frameworks of Hartree-Fock theory and the seniority scheme. The method is developed in detail for a minimum-seniority variational wave function in the coordinate representation for an effective interaction of the Skyrme type. An advantage of the present approach over the Hartree-Fock-Bogoliubov theory is the exact conservation of angular momentum and particle number. Furthermore, the computational effort required in the Hartree-Fock seniority approximation is similar to that ofthe pure Hartree-Fock picture. Some numerical calculations for Ca isotopes are presented. (orig.)
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.
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...
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
International Nuclear Information System (INIS)
Ferraro, Rafael; Nigro, Mauro
2016-01-01
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.
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.
Approximate radiative solutions of the Einstein equations
International Nuclear Information System (INIS)
Kuusk, P.; Unt, V.
1976-01-01
In this paper the external field of a bounded source emitting gravitational radiation is considered. A successive approximation method is used to integrate the Einstein equations in Bondi's coordinates (Bondi et al, Proc. R. Soc.; A269:21 (1962)). A method of separation of angular variables is worked out and the approximate Einstein equations are reduced to key equations. The losses of mass, momentum, and angular momentum due to gravitational multipole radiation are found. It is demonstrated that in the case of proper treatment a real mass occurs instead of a mass aspect in a solution of the Einstein equations. In an appendix Bondi's new function is given in terms of sources. (author)
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.
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
Finite-rank potential that reproduces the Pade approximant
International Nuclear Information System (INIS)
Tani, S.
1979-01-01
If a scattering potential is of a finite rank, say N, the exact solution of the problem can be obtained from the Born series, if the potential strength is within the radius of convergence; the exact solution can be obtained from the analytical continuation of the formal Born series outside the radius of convergence. Beyond the first 2N terms of the Born series, an individual term of the Born series depends on the first 2N terms, and the [N/N] Pade approximant and the exact solution agree with each other. The above-mentioned features of a finite-rank problem are relevant to scattering theory in general, because most scattering problems may be handled as an extension of the rank-N problem, in which the rank N tends to infinity. The foregoing aspects of scattering theory will be studied in depth in the present paper, and in so doing we proceed in the opposite direction. Namely, given a potential, we calculate the first 2N terms of the Born series for the K matrix and the first N terms of the Born series for the wave function. Using these data, a special rank-N potential is constructed in such a way that it reproduces the [N/N] Pade approximant of the K matrix of the original scattering problem. One great advantage of obtaining such a rank-N potential is that the wave function of the system may be approximated in the same spirit as done for the K matrix; hence, we can introduce a new approximation method for dealing with an off-shell T matrix. A part of the mathematical work is incomplete, but the physical aspects are thoroughly discussed
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
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
On approximation of functions by product operators
Directory of Open Access Journals (Sweden)
Hare Krishna Nigam
2013-12-01
Full Text Available In the present paper, two quite new reults on the degree of approximation of a function f belonging to the class Lip(α,r, 1≤ r <∞ and the weighted class W(Lr,ξ(t, 1≤ r <∞ by (C,2(E,1 product operators have been obtained. The results obtained in the present paper generalize various known results on single operators.
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.
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.
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
Semiclassical approximation in Batalin-Vilkovisky formalism
International Nuclear Information System (INIS)
Schwarz, A.
1993-01-01
The geometry of supermanifolds provided with a Q-structure (i.e. with an odd vector field Q satisfying {Q, Q}=0), a P-structure (odd symplectic structure) and an S-structure (volume element) or with various combinations of these structures is studied. The results are applied to the analysis of the Batalin-Vilkovisky approach to the quantization of gauge theories. In particular the semiclassical approximation in this approach is expressed in terms of Reidemeister torsion. (orig.)
Approximation for limit cycles and their isochrons.
Demongeot, Jacques; Françoise, Jean-Pierre
2006-12-01
Local analysis of trajectories of dynamical systems near an attractive periodic orbit displays the notion of asymptotic phase and isochrons. These notions are quite useful in applications to biosciences. In this note, we give an expression for the first approximation of equations of isochrons in the setting of perturbations of polynomial Hamiltonian systems. This method can be generalized to perturbations of systems that have a polynomial integral factor (like the Lotka-Volterra equation).
Hierarchical matrix approximation of large covariance matrices
Litvinenko, Alexander; Genton, Marc G.; Sun, Ying; Tempone, Raul
2015-01-01
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; Genton, Marc G.; Sun, Ying; Tempone, Raul
2015-01-01
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.
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
Approximations and Implementations of Nonlinear Filtering Schemes.
1988-02-01
sias k an Ykar repctively the input and the output vectors. Asfold. First, there are intrinsic errors, due to explained in the previous section, the...e.g.[BV,P]). In the above example of a a-algebra, the distributive property SIA (S 2vS3) - (SIAS2)v(SIAS3) holds. A complete orthocomplemented...process can be approximated by a switched Control Systems: Stochastic Stability and parameter process depending on the aggregated slow Dynamic Relaibility
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
Conference on Abstract Spaces and Approximation
Szökefalvi-Nagy, B; Abstrakte Räume und Approximation; Abstract spaces and approximation
1969-01-01
The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, Wiener-Hopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs littl...
Development of the relativistic impulse approximation
International Nuclear Information System (INIS)
Wallace, S.J.
1985-01-01
This talk contains three parts. Part I reviews the developments which led to the relativistic impulse approximation for proton-nucleus scattering. In Part II, problems with the impulse approximation in its original form - principally the low energy problem - are discussed and traced to pionic contributions. Use of pseudovector covariants in place of pseudoscalar ones in the NN amplitude provides more satisfactory low energy results, however, the difference between pseudovector and pseudoscalar results is ambiguous in the sense that it is not controlled by NN data. Only with further theoretical input can the ambiguity be removed. Part III of the talk presents a new development of the relativistic impulse approximation which is the result of work done in the past year and a half in collaboration with J.A. Tjon. A complete NN amplitude representation is developed and a complete set of Lorentz invariant amplitudes are calculated based on a one-meson exchange model and appropriate integral equations. A meson theoretical basis for the important pair contributions to proton-nucleus scattering is established by the new developments. 28 references
A Gaussian Approximation Potential for Silicon
Bernstein, Noam; Bartók, Albert; Kermode, James; Csányi, Gábor
We present an interatomic potential for silicon using the Gaussian Approximation Potential (GAP) approach, which uses the Gaussian process regression method to approximate the reference potential energy surface as a sum of atomic energies. Each atomic energy is approximated as a function of the local environment around the atom, which is described with the smooth overlap of atomic environments (SOAP) descriptor. The potential is fit to a database of energies, forces, and stresses calculated using density functional theory (DFT) on a wide range of configurations from zero and finite temperature simulations. These include crystalline phases, liquid, amorphous, and low coordination structures, and diamond-structure point defects, dislocations, surfaces, and cracks. We compare the results of the potential to DFT calculations, as well as to previously published models including Stillinger-Weber, Tersoff, modified embedded atom method (MEAM), and ReaxFF. We show that it is very accurate as compared to the DFT reference results for a wide range of properties, including low energy bulk phases, liquid structure, as well as point, line, and plane defects in the diamond structure.
Approximate modal analysis using Fourier decomposition
International Nuclear Information System (INIS)
Kozar, Ivica; Jericevic, Zeljko; Pecak, Tatjana
2010-01-01
The paper presents a novel numerical approach for approximate solution of eigenvalue problem and investigates its suitability for modal analysis of structures with special attention on plate structures. The approach is based on Fourier transformation of the matrix equation into frequency domain and subsequent removal of potentially less significant frequencies. The procedure results in a much reduced problem that is used in eigenvalue calculation. After calculation eigenvectors are expanded and transformed back into time domain. The principles are presented in Jericevic [1]. Fourier transform can be formulated in a way that some parts of the matrix that should not be approximated are not transformed but are fully preserved. In this paper we present formulation that preserves central or edge parts of the matrix and compare it with the formulation that performs transform on the whole matrix. Numerical experiments on transformed structural dynamic matrices describe quality of the approximations obtained in modal analysis of structures. On the basis of the numerical experiments, from the three approaches to matrix reduction one is recommended.
Green-Ampt approximations: A comprehensive analysis
Ali, Shakir; Islam, Adlul; Mishra, P. K.; Sikka, Alok K.
2016-04-01
Green-Ampt (GA) model and its modifications are widely used for simulating infiltration process. Several explicit approximate solutions to the implicit GA model have been developed with varying degree of accuracy. In this study, performance of nine explicit approximations to the GA model is compared with the implicit GA model using the published data for broad range of soil classes and infiltration time. The explicit GA models considered are Li et al. (1976) (LI), Stone et al. (1994) (ST), Salvucci and Entekhabi (1994) (SE), Parlange et al. (2002) (PA), Barry et al. (2005) (BA), Swamee et al. (2012) (SW), Ali et al. (2013) (AL), Almedeij and Esen (2014) (AE), and Vatankhah (2015) (VA). Six statistical indicators (e.g., percent relative error, maximum absolute percent relative error, average absolute percent relative errors, percent bias, index of agreement, and Nash-Sutcliffe efficiency) and relative computer computation time are used for assessing the model performance. Models are ranked based on the overall performance index (OPI). The BA model is found to be the most accurate followed by the PA and VA models for variety of soil classes and infiltration periods. The AE, SW, SE, and LI model also performed comparatively better. Based on the overall performance index, the explicit models are ranked as BA > PA > VA > LI > AE > SE > SW > ST > AL. Results of this study will be helpful in selection of accurate and simple explicit approximate GA models for solving variety of hydrological problems.
An Origami Approximation to the Cosmic Web
Neyrinck, Mark C.
2016-10-01
The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in `polygonal' or `polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls to be more easily understood, and may aid in understanding spin correlations between nearby galaxies. This contribution explores kinematic origami-approximation models giving velocity fields for the first time.
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.
Blind sensor calibration using approximate message passing
International Nuclear Information System (INIS)
Schülke, Christophe; Caltagirone, Francesco; Zdeborová, Lenka
2015-01-01
The ubiquity of approximately sparse data has led a variety of communities to take great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying them to real data can be problematic if imperfect sensing devices introduce deviations from this ideal signal acquisition process, caused by sensor decalibration or failure. We propose a message passing algorithm called calibration approximate message passing (Cal-AMP) that can treat a variety of such sensor-induced imperfections. In addition to deriving the general form of the algorithm, we numerically investigate two particular settings. In the first, a fraction of the sensors is faulty, giving readings unrelated to the signal. In the second, sensors are decalibrated and each one introduces a different multiplicative gain to the measurements. Cal-AMP shares the scalability of approximate message passing, allowing us to treat large sized instances of these problems, and experimentally exhibits a phase transition between domains of success and failure. (paper)
Simultaneous perturbation stochastic approximation for tidal models
Altaf, M.U.; Heemink, A.W.; Verlaan, M.; Hoteit, Ibrahim
2011-01-01
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.
Local approximation of a metapopulation's equilibrium.
Barbour, A D; McVinish, R; Pollett, P K
2018-04-18
We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously.
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
Nonresonant approximations to the optical potential
International Nuclear Information System (INIS)
Kowalski, K.L.
1982-01-01
A new class of approximations to the optical potential, which includes those of the multiple-scattering variety, is investigated. These approximations are constructed so that the optical potential maintains the correct unitarity properties along with a proper treatment of nucleon identity. The special case of nucleon-nucleus scattering with complete inclusion of Pauli effects is studied in detail. The treatment is such that the optical potential receives contributions only from subsystems embedded in their own physically correct antisymmetrized subspaces. It is found that a systematic development of even the lowest-order approximations requires the use of the off-shell extension due to Alt, Grassberger, and Sandhas along with a consistent set of dynamical equations for the optical potential. In nucleon-nucleus scattering a lowest-order optical potential is obtained as part of a systematic, exact, inclusive connectivity expansion which is expected to be useful at moderately high energies. This lowest-order potential consists of an energy-shifted (trho)-type term with three-body kinematics plus a heavy-particle exchange or pickup term. The natural appearance of the exchange term additivity in the optical potential clarifies the role of the elastic distortion in connection with the treatment of these processes. The relationship of the relevant aspects of the present analysis of the optical potential to conventional multiple scattering methods is discussed
Understanding operational risk capital approximations: First and second orders
Directory of Open Access Journals (Sweden)
Gareth W. Peters
2013-07-01
Full Text Available We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. In this regard, we provide a summary of the role of capital adequacy in the new accord, highlighting along the way the significant loss events that have been attributed to the Operational Risk class that was introduced in the Basel II and III accords. Then we provide a semi-tutorial discussion on the modelling aspects of capital estimation under a Loss Distributional Approach (LDA. Our emphasis is to focuss on the important loss processes with regard to those that contribute most to capital, the so called “high consequence, low frequency" loss processes. This leads us to provide a tutorial overview of heavy tailed loss process modelling in OpRisk under Basel III, with discussion on the implications of such tail assumptions for the severity model in an LDA structure. This provides practitioners with a clear understanding of the features that they may wish to consider when developing OpRisk severity models in practice. From this discussion on heavy tailed severity models, we then develop an understanding of the impact such models have on the right tail asymptotics of the compound loss process and we provide detailed presentation of what are known as first and second order tail approximations for the resulting heavy tailed loss process. From this we develop a tutorial on three key families of risk measures and their equivalent second order asymptotic approximations: Value-at-Risk (Basel III industry standard; Expected Shortfall (ES and the Spectral Risk Measure. These then form the capital approximations. We then provide a few example case studies to illustrate the accuracy of these asymptotic captial approximations, the rate of the convergence of the assymptotic result as a function of the LDA frequency and severity model parameters, the sensitivity
DEFF Research Database (Denmark)
Sadegh, Payman; Spall, J. C.
1998-01-01
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...
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
Feature Selection by Reordering
Czech Academy of Sciences Publication Activity Database
Jiřina, Marcel; Jiřina jr., M.
2005-01-01
Roč. 2, č. 1 (2005), s. 155-161 ISSN 1738-6438 Institutional research plan: CEZ:AV0Z10300504 Keywords : feature selection * data reduction * ordering of features Subject RIV: BA - General Mathematics
The virtual environment student. An initial approximation
Federico Borges Sáiz
2007-01-01
The quote at the start of the "Introduction" ("Education follows an agricultural timetable, has an industrial structure and operation and is set in an increasingly digitalised society") illustrates the need for an in-depth understanding of training in virtual environments. This understanding rests on knowing its central element: the student.This article invites the reader to take a look at the figure and the performance of the virtual environment student. One of the features of the twenty-fir...
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.
Heijden, van der G.W.A.M.; Polder, G.
2015-01-01
In this chapter, an overview of different plant features is given, from (sub)cellular to canopy level. A myriad of methods is available to measure these features using image analysis, and often, multiple methods can be used to measure the same feature. Several criteria are listed for choosing a
Pentaquarks in the Jaffe-Wilczek approximation
International Nuclear Information System (INIS)
Narodetskii, I.M.; Simonov, Yu.A.; Trusov, M.A.; Semay, C.; Silvestre-Brac, B.
2005-01-01
The masses of uudds-bar, uuddd-bar, and uussd-bar pentaquarks are evaluated in a framework of both the effective Hamiltonian approach to QCD and spinless Salpeter equation using the Jaffe-Wilczek diquark approximation and the string interaction for the diquark-diquark-antiquark system. The pentaquark masses are found to be in the region above 2 GeV. That indicates that the Goldstone-boson-exchange effects may play an important role in the light pentaquarks. The same calculations yield the mass of [ud] 2 c-bar pentaquark ∼3250 MeV and [ud] 2 b-bar pentaquark ∼6509 MeV [ru
Localization and stationary phase approximation on supermanifolds
Zakharevich, Valentin
2017-08-01
Given an odd vector field Q on a supermanifold M and a Q-invariant density μ on M, under certain compactness conditions on Q, the value of the integral ∫Mμ is determined by the value of μ on any neighborhood of the vanishing locus N of Q. We present a formula for the integral in the case where N is a subsupermanifold which is appropriately non-degenerate with respect to Q. In the process, we discuss the linear algebra necessary to express our result in a coordinate independent way. We also extend the stationary phase approximation and the Morse-Bott lemma to supermanifolds.
SAM revisited: uniform semiclassical approximation with absorption
International Nuclear Information System (INIS)
Hussein, M.S.; Pato, M.P.
1986-01-01
The uniform semiclassical approximation is modified to take into account strong absorption. The resulting theory, very similar to the one developed by Frahn and Gross is used to discuss heavy-ion elastic scattering at intermediate energies. The theory permits a reasonably unambiguos separation of refractive and diffractive effects. The systems 12 C+ 12 C and 12 C+ 16 O, which seem to exhibit a remnant of a nuclear rainbow at E=20 Mev/N, are analysed with theory which is built directly on a model for the S-matrix. Simple relations between the fit S-matrix and the underlying complex potential are derived. (Author) [pt
TMB: Automatic differentiation and laplace approximation
DEFF Research Database (Denmark)
Kristensen, Kasper; Nielsen, Anders; Berg, Casper Willestofte
2016-01-01
TMB is an open source R package that enables quick implementation of complex nonlinear random effects (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, http://admb-project.org/; Fournier et al. 2011). In addition, it offers easy access to parallel...... 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...
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
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
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...... and confirms that BSE greatly improves the RPA and TDHF results despite the fact that the BSE excitation spectrum breaks down in the dissociation limit. In contrast, second order screened exchange gives a poor description of the dissociation limit, which can be attributed to the fact that it cannot be derived...
Multi-compartment linear noise approximation
International Nuclear Information System (INIS)
Challenger, Joseph D; McKane, Alan J; Pahle, Jürgen
2012-01-01
The ability to quantify the stochastic fluctuations present in biochemical and other systems is becoming increasing important. Analytical descriptions of these fluctuations are attractive, as stochastic simulations are computationally expensive. Building on previous work, a linear noise approximation is developed for biochemical models with many compartments, for example cells. The procedure is then implemented in the software package COPASI. This technique is illustrated with two simple examples and is then applied to a more realistic biochemical model. Expressions for the noise, given in the form of covariance matrices, are presented. (paper)
Approximation of Moessbauer spectra of metallic glasses
International Nuclear Information System (INIS)
Miglierini, M.; Sitek, J.
1988-01-01
Moessbauer spectra of iron-rich metallic glasses are approximated by means of six broadened lines which have line position relations similar to those of α-Fe. It is shown via the results of the DISPA (dispersion mode vs. absorption mode) line shape analysis that each spectral peak is broadened owing to a sum of Lorentzian lines weighted by a Gaussian distribution in the peak position. Moessbauer parameters of amorphous metallic Fe 83 B 17 and Fe 40 Ni 40 B 20 alloys are presented, derived from the fitted spectra. (author). 2 figs., 2 tabs., 21 refs
High energy approximations in quantum field theory
International Nuclear Information System (INIS)
Orzalesi, C.A.
1975-01-01
New theoretical methods in hadron physics based on a high-energy perturbation theory are discussed. The approximated solutions to quantum field theory obtained by this method appear to be sufficiently simple and rich in structure to encourage hadron dynamics studies. Operator eikonal form for field - theoretic Green's functions is derived and discussion is held on how the eikonal perturbation theory is to be renormalized. This method is extended to massive quantum electrodynamics of scalar charged bosons. Possible developments and applications of this theory are given [pt
Weak field approximation of new general relativity
International Nuclear Information System (INIS)
Fukui, Masayasu; Masukawa, Junnichi
1985-01-01
In the weak field approximation, gravitational field equations of new general relativity with arbitrary parameters are examined. Assuming a conservation law delta sup(μ)T sub(μν) = 0 of the energy-momentum tensor T sub(μν) for matter fields in addition to the usual one delta sup(ν)T sub(μν) = 0, we show that the linearized gravitational field equations are decomposed into equations for a Lorentz scalar field and symmetric and antisymmetric Lorentz tensor fields. (author)
Pentaquarks in the Jaffe-Wilczek Approximation
International Nuclear Information System (INIS)
Narodetskii, I.M.; Simonov, Yu.A.; Trusov, M.A.; Semay, C.; Silvestre-Brac, B.
2005-01-01
The masses of uudds-bar, uuddd-bar, and uussd-bar pentaquarks are evaluated in a framework of both the effective Hamiltonian approach to QCD and the spinless Salpeter equation using the Jaffe-Wilczek diquark approximation and the string interaction for the diquark-diquark-antiquark system. The pentaquark masses are found to be in the region above 2 GeV. That indicates that the Goldstone boson exchange effects may play an important role in the light pentaquarks. The same calculations yield the mass of [ud] 2 c-bar pentaquark ∼3250 MeV and [ud] 2 b-bar pentaquark ∼6509 MeV
Turbo Equalization Using Partial Gaussian Approximation
DEFF Research Database (Denmark)
Zhang, Chuanzong; Wang, Zhongyong; Manchón, Carles Navarro
2016-01-01
This letter deals with turbo equalization for coded data transmission over intersymbol interference (ISI) channels. We propose a message-passing algorithm that uses the expectation propagation rule to convert messages passed from the demodulator and decoder to the equalizer and computes messages...... returned by the equalizer by using a partial Gaussian approximation (PGA). We exploit the specific structure of the ISI channel model to compute the latter messages from the beliefs obtained using a Kalman smoother/equalizer. Doing so leads to a significant complexity reduction compared to the initial PGA...
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
Mathematics of epidemics on networks from exact to approximate models
Kiss, István Z; Simon, Péter L
2017-01-01
This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...
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.
TMB: Automatic Differentiation and Laplace Approximation
Directory of Open Access Journals (Sweden)
Kasper Kristensen
2016-04-01
Full Text Available TMB is an open source R package that enables quick implementation of complex nonlinear random effects (latent variable models in a manner similar to the established AD Model Builder package (ADMB, http://admb-project.org/; Fournier et al. 2011. In addition, it offers easy access to parallel 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 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 (≈ 106 and parameters (≈ 103 . 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. The package and examples are available at http://tmb-project.org/.
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].
Detecting Change-Point via Saddlepoint Approximations
Institute of Scientific and Technical Information of China (English)
Zhaoyuan LI; Maozai TIAN
2017-01-01
It's well-known that change-point problem is an important part of model statistical analysis.Most of the existing methods are not robust to criteria of the evaluation of change-point problem.In this article,we consider "mean-shift" problem in change-point studies.A quantile test of single quantile is proposed based on saddlepoint approximation method.In order to utilize the information at different quantile of the sequence,we further construct a "composite quantile test" to calculate the probability of every location of the sequence to be a change-point.The location of change-point can be pinpointed rather than estimated within a interval.The proposed tests make no assumptions about the functional forms of the sequence distribution and work sensitively on both large and small size samples,the case of change-point in the tails,and multiple change-points situation.The good performances of the tests are confirmed by simulations and real data analysis.The saddlepoint approximation based distribution of the test statistic that is developed in the paper is of independent interest and appealing.This finding may be of independent interest to the readers in this research area.
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
Approximation to estimation of critical state
International Nuclear Information System (INIS)
Orso, Jose A.; Rosario, Universidad Nacional
2011-01-01
The position of the control rod for the critical state of the nuclear reactor depends on several factors; including, but not limited to the temperature and configuration of the fuel elements inside the core. Therefore, the position can not be known in advance. In this paper theoretical estimations are developed to obtain an equation that allows calculating the position of the control rod for the critical state (approximation to critical) of the nuclear reactor RA-4; and will be used to create a software performing the estimation by entering the count rate of the reactor pulse channel and the length obtained from the control rod (in cm). For the final estimation of the approximation to critical state, a function obtained experimentally indicating control rods reactivity according to the function of their position is used, work is done mathematically to obtain a linear function, which gets the length of the control rod, which has to be removed to get the reactor in critical position. (author) [es
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.
Approximate analytic theory of the multijunction grill
International Nuclear Information System (INIS)
Hurtak, O.; Preinhaelter, J.
1991-03-01
An approximate analytic theory of the general multijunction grill is developed. Omitting the evanescent modes in the subsidiary waveguides both at the junction and at the grill mouth and neglecting multiple wave reflection, simple formulae are derived for the reflection coefficient, the amplitudes of the incident and reflected waves and the spectral power density. These quantities are expressed through the basic grill parameters (the electric length of the structure and phase shift between adjacent waveguides) and two sets of reflection coefficients describing wave reflections in the subsidiary waveguides at the junction and at the plasma. Approximate expressions for these coefficients are also given. The results are compared with a numerical solution of two specific examples; they were shown to be useful for the optimization and design of multijunction grills.For the JET structure it is shown that, in the case of a dense plasma,many results can be obtained from the simple formulae for a two-waveguide multijunction grill. (author) 12 figs., 12 refs
Robust surface registration using N-points approximate congruent sets
Directory of Open Access Journals (Sweden)
Yao Jian
2011-01-01
Full Text Available Abstract Scans acquired by 3D sensors are typically represented in a local coordinate system. When multiple scans, taken from different locations, represent the same scene these must be registered to a common reference frame. We propose a fast and robust registration approach to automatically align two scans by finding two sets of N-points, that are approximately congruent under rigid transformation and leading to a good estimate of the transformation between their corresponding point clouds. Given two scans, our algorithm randomly searches for the best sets of congruent groups of points using a RANSAC-based approach. To successfully and reliably align two scans when there is only a small overlap, we improve the basic RANSAC random selection step by employing a weight function that approximates the probability of each pair of points in one scan to match one pair in the other. The search time to find pairs of congruent sets of N-points is greatly reduced by employing a fast search codebook based on both binary and multi-dimensional lookup tables. Moreover, we introduce a novel indicator of the overlapping region quality which is used to verify the estimated rigid transformation and to improve the alignment robustness. Our framework is general enough to incorporate and efficiently combine different point descriptors derived from geometric and texture-based feature points or scene geometrical characteristics. We also present a method to improve the matching effectiveness of texture feature descriptors by extracting them from an atlas of rectified images recovered from the scan reflectance image. Our algorithm is robust with respect to different sampling densities and also resilient to noise and outliers. We demonstrate its robustness and efficiency on several challenging scan datasets with varying degree of noise, outliers, extent of overlap, acquired from indoor and outdoor scenarios.
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....
Elements of the interacting boson approximation
International Nuclear Information System (INIS)
Cseh, Jozsef
1985-01-01
The main features of the interacting boson model family are briefly summarized. The main tool of the model is the group theory; its basic useful results (symmetry groups, spectrum generating algebra, dynamic groups and symmetries, tensor representations, broken symmetries, subgroup chains) are summarized. The emission and annihilation operators of the individual boson degrees of freedom form a U(n) algebra. Its reprezentation theory can be used to classify the basic states and energy levels of the system. A simple variant of the interacting boson model is analyzed in detail. The genealogy of different interacting boson models from vibron model to supersymmetric ones is surveyed. (D.Gy.)
Calculating properties with the coherent-potential approximation
International Nuclear Information System (INIS)
Faulkner, J.S.; Stocks, G.M.
1980-01-01
It is demonstrated that the expression that has hitherto been used for calculating the Bloch spectral-density function A/sup B/(E,k) in the Korringa-Kohn-Rostoker coherent-potential-approximation theory of alloys leads to manifestly unphysical results. No manipulation of the expression can eliminate this behavior. We develop an averaged Green's-function formulation and from it derive a new expression for A/sup B/(E,k) which does not contain unphysical features. The earlier expression for A/sup B/(E,k) was suggested as plausible on the basis that it is a spectral decomposition of the Lloyd formula. Expressions for many other properties of alloys have been obtained by manipulations of the Lloyd formula, and it is now clear that all such expressions must be considered suspect. It is shown by numerical and algebraic comparisons that some of the expressions obtained in this way are equivalent to the ones obtained from a Green's function, while others are not. In addition to studying these questions, the averaged Green's-function formulation developed in this paper is shown to furnish an interesting new way to approach many problems in alloy theory. The method is described in such a way that the aspects of the formulation that arise from the single-site approximation can be distinguished from those that depend on a specific choice for the effective scatterer
New Tests of the Fixed Hotspot Approximation
Gordon, R. G.; Andrews, D. L.; Horner-Johnson, B. C.; Kumar, R. R.
2005-05-01
We present new methods for estimating uncertainties in plate reconstructions relative to the hotspots and new tests of the fixed hotspot approximation. We find no significant motion between Pacific hotspots, on the one hand, and Indo-Atlantic hotspots, on the other, for the past ~ 50 Myr, but large and significant apparent motion before 50 Ma. Whether this motion is truly due to motion between hotspots or alternatively due to flaws in the global plate motion circuit can be tested with paleomagnetic data. These tests give results consistent with the fixed hotspot approximation and indicate significant misfits when a relative plate motion circuit through Antarctica is employed for times before 50 Ma. If all of the misfit to the global plate motion circuit is due to motion between East and West Antarctica, then that motion is 800 ± 500 km near the Ross Sea Embayment and progressively less along the Trans-Antarctic Mountains toward the Weddell Sea. Further paleomagnetic tests of the fixed hotspot approximation can be made. Cenozoic and Cretaceous paleomagnetic data from the Pacific plate, along with reconstructions of the Pacific plate relative to the hotspots, can be used to estimate an apparent polar wander (APW) path of Pacific hotspots. An APW path of Indo-Atlantic hotspots can be similarly estimated (e.g. Besse & Courtillot 2002). If both paths diverge in similar ways from the north pole of the hotspot reference frame, it would indicate that the hotspots have moved in unison relative to the spin axis, which may be attributed to true polar wander. If the two paths diverge from one another, motion between Pacific hotspots and Indo-Atlantic hotspots would be indicated. The general agreement of the two paths shows that the former is more important than the latter. The data require little or no motion between groups of hotspots, but up to ~10 mm/yr of motion is allowed within uncertainties. The results disagree, in particular, with the recent extreme interpretation of
Matrix model approximations of fuzzy scalar field theories and their phase diagrams
Energy Technology Data Exchange (ETDEWEB)
Tekel, Juraj [Department of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina, Bratislava, 842 48 (Slovakia)
2015-12-29
We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram with correct features in a qualitative agreement with the previous numerical studies and that the latter gives a phase diagram with features not expected in the phase diagram of the field theory.
Ito, K.
1983-01-01
Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.
Random phase approximation in relativistic approach
International Nuclear Information System (INIS)
Ma Zhongyu; Yang Ding; Tian Yuan; Cao Ligang
2009-01-01
Some special issues of the random phase approximation(RPA) in the relativistic approach are reviewed. A full consistency and proper treatment of coupling to the continuum are responsible for the successful application of the RPA in the description of dynamical properties of finite nuclei. The fully consistent relativistic RPA(RRPA) requires that the relativistic mean filed (RMF) wave function of the nucleus and the RRPA correlations are calculated in a same effective Lagrangian and the consistent treatment of the Dirac sea of negative energy states. The proper treatment of the single particle continuum with scattering asymptotic conditions in the RMF and RRPA is discussed. The full continuum spectrum can be described by the single particle Green's function and the relativistic continuum RPA is established. A separable form of the paring force is introduced in the relativistic quasi-particle RPA. (authors)
Random-phase approximation and broken symmetry
International Nuclear Information System (INIS)
Davis, E.D.; Heiss, W.D.
1986-01-01
The validity of the random-phase approximation (RPA) in broken-symmetry bases is tested in an appropriate many-body system for which exact solutions are available. Initially the regions of stability of the self-consistent quasiparticle bases in this system are established and depicted in a 'phase' diagram. It is found that only stable bases can be used in an RPA calculation. This is particularly true for those RPA modes which are not associated with the onset of instability of the basis; it is seen that these modes do not describe any excited state when the basis is unstable, although from a formal point of view they remain acceptable. The RPA does well in a stable broken-symmetry basis provided one is not too close to a point where a phase transition occurs. This is true for both energies and matrix elements. (author)
Local facet approximation for image stitching
Li, Jing; Lai, Shiming; Liu, Yu; Wang, Zhengming; Zhang, Maojun
2018-01-01
Image stitching aims at eliminating multiview parallax and generating a seamless panorama given a set of input images. This paper proposes a local adaptive stitching method, which could achieve both accurate and robust image alignments across the whole panorama. A transformation estimation model is introduced by approximating the scene as a combination of neighboring facets. Then, the local adaptive stitching field is constructed using a series of linear systems of the facet parameters, which enables the parallax handling in three-dimensional space. We also provide a concise but effective global projectivity preserving technique that smoothly varies the transformations from local adaptive to global planar. The proposed model is capable of stitching both normal images and fisheye images. The efficiency of our method is quantitatively demonstrated in the comparative experiments on several challenging cases.
Approximated solutions to the Schroedinger equation
International Nuclear Information System (INIS)
Rico, J.F.; Fernandez-Alonso, J.I.
1977-01-01
The authors are currently working on a couple of the well-known deficiencies of the variation method and present here some of the results that have been obtained so far. The variation method does not give information a priori on the trial functions best suited for a particular problem nor does it give information a posteriori on the degree of precision attained. In order to clarify the origin of both difficulties, a geometric interpretation of the variation method is presented. This geometric interpretation is the starting point for the exact formal solution to the fundamental state and for the step-by-step approximations to the exact solution which are also given. Some comments on these results are included. (Auth.)
Approximate Stokes Drift Profiles in Deep Water
Breivik, Øyvind; Janssen, Peter A. E. M.; Bidlot, Jean-Raymond
2014-09-01
A deep-water approximation to the Stokes drift velocity profile is explored as an alternative to the monochromatic profile. The alternative profile investigated relies on the same two quantities required for the monochromatic profile, viz the Stokes transport and the surface Stokes drift velocity. Comparisons with parametric spectra and profiles under wave spectra from the ERA-Interim reanalysis and buoy observations reveal much better agreement than the monochromatic profile even for complex sea states. That the profile gives a closer match and a more correct shear has implications for ocean circulation models since the Coriolis-Stokes force depends on the magnitude and direction of the Stokes drift profile and Langmuir turbulence parameterizations depend sensitively on the shear of the profile. The alternative profile comes at no added numerical cost compared to the monochromatic profile.
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)
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
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.
Approximate spacetime symmetries and conservation laws
Energy Technology Data Exchange (ETDEWEB)
Harte, Abraham I [Enrico Fermi Institute, University of Chicago, Chicago, IL 60637 (United States)], E-mail: harte@uchicago.edu
2008-10-21
A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection near a specified observer. Any exact affine collineations that may exist are special cases. The remaining vector fields can all be interpreted as analogs of Poincare and other well-known symmetries near timelike worldlines. Approximate conservation laws generated by these objects are discussed for both geodesics and extended matter distributions. One example is a generalized Komar integral that may be taken to define the linear and angular momenta of a spacetime volume as seen by a particular observer. This is evaluated explicitly for a gravitational plane wave spacetime.
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.
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,...
Polarized constituent quarks in NLO approximation
International Nuclear Information System (INIS)
Khorramian, Ali N.; Tehrani, S. Atashbar; Mirjalili, A.
2006-01-01
The valon representation provides a basis between hadrons and quarks, in terms of which the bound-state and scattering properties of hadrons can be united and described. We studied polarized valon distributions which have an important role in describing the spin dependence of parton distribution in leading and next-to-leading order approximation. Convolution integral in frame work of valon model as a useful tool, was used in polarized case. To obtain polarized parton distributions in a proton we need to polarized valon distribution in a proton and polarized parton distributions inside the valon. We employed Bernstein polynomial averages to get unknown parameters of polarized valon distributions by fitting to available experimental data
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.
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 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)
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.)
Approximation Preserving Reductions among Item Pricing Problems
Hamane, Ryoso; Itoh, Toshiya; Tomita, Kouhei
When a store sells items to customers, the store wishes to determine the prices of the items to maximize its profit. Intuitively, if the store sells the items with low (resp. high) prices, the customers buy more (resp. less) items, which provides less profit to the store. So it would be hard for the store to decide the prices of items. Assume that the store has a set V of n items and there is a set E of m customers who wish to buy those items, and also assume that each item i ∈ V has the production cost di and each customer ej ∈ E has the valuation vj on the bundle ej ⊆ V of items. When the store sells an item i ∈ V at the price ri, the profit for the item i is pi = ri - di. The goal of the store is to decide the price of each item to maximize its total profit. We refer to this maximization problem as the item pricing problem. In most of the previous works, the item pricing problem was considered under the assumption that pi ≥ 0 for each i ∈ V, however, Balcan, et al. [In Proc. of WINE, LNCS 4858, 2007] introduced the notion of “loss-leader, ” and showed that the seller can get more total profit in the case that pi < 0 is allowed than in the case that pi < 0 is not allowed. In this paper, we derive approximation preserving reductions among several item pricing problems and show that all of them have algorithms with good approximation ratio.
Approximate direct georeferencing in national coordinates
Legat, Klaus
Direct georeferencing has gained an increasing importance in photogrammetry and remote sensing. Thereby, the parameters of exterior orientation (EO) of an image sensor are determined by GPS/INS, yielding results in a global geocentric reference frame. Photogrammetric products like digital terrain models or orthoimages, however, are often required in national geodetic datums and mapped by national map projections, i.e., in "national coordinates". As the fundamental mathematics of photogrammetry is based on Cartesian coordinates, the scene restitution is often performed in a Cartesian frame located at some central position of the image block. The subsequent transformation to national coordinates is a standard problem in geodesy and can be done in a rigorous manner-at least if the formulas of the map projection are rigorous. Drawbacks of this procedure include practical deficiencies related to the photogrammetric processing as well as the computational cost of transforming the whole scene. To avoid these problems, the paper pursues an alternative processing strategy where the EO parameters are transformed prior to the restitution. If only this transition was done, however, the scene would be systematically distorted. The reason is that the national coordinates are not Cartesian due to the earth curvature and the unavoidable length distortion of map projections. To settle these distortions, several corrections need to be applied. These are treated in detail for both passive and active imaging. Since all these corrections are approximations only, the resulting technique is termed "approximate direct georeferencing". Still, the residual distortions are usually very low as is demonstrated by simulations, rendering the technique an attractive approach to direct georeferencing.
Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias
2018-01-22
Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.
The virtual environment student. An initial approximation
Directory of Open Access Journals (Sweden)
Federico Borges Sáiz
2007-05-01
Full Text Available The quote at the start of the "Introduction" ("Education follows an agricultural timetable, has an industrial structure and operation and is set in an increasingly digitalised society" illustrates the need for an in-depth understanding of training in virtual environments. This understanding rests on knowing its central element: the student.This article invites the reader to take a look at the figure and the performance of the virtual environment student. One of the features of the twenty-first century is that of leading increasingly to a learning society, where citizens learn, formally or informally, throughout their lives. Technology sustains many of the behavioural and attitude traits of these citizens, although technology is only the first step; beyond this, the attitudes, skills and motivation required for successfully performing in a virtual environment are necessary.
On some applications of Diophantine approximations
2014-01-01
This book consists mainly of the translation, by C. Fuchs, of the 1929 landmark paper "Über einige Anwendungen diophantischer Approximationen" by C.L. Siegel. The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel’s celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel’s proof have appeared, but none seem to faithfully reproduce all features of the original one. This translation makes Siegel’s original ideas and proofs available for the first time in English. The volume also contains the original version of the paper (in German) and an article by the translator and U. Zannier, commenting on some aspects of the evolution of this field following Siegel’s paper. To end, it presents three modern proofs of Siegel’s theorem on integral points.
Undersea Feature Place Names as of June 2014
National Oceanic and Atmospheric Administration, Department of Commerce — There are approximately 5100 undersea features with names approved by the United States Board on Geographic Names (BGN) currently in the Geographic Names Data Base...
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.
Approximation algorithms for a genetic diagnostics problem.
Kosaraju, S R; Schäffer, A A; Biesecker, L G
1998-01-01
We define and study a combinatorial problem called WEIGHTED DIAGNOSTIC COVER (WDC) that models the use of a laboratory technique called genotyping in the diagnosis of an important class of chromosomal aberrations. An optimal solution to WDC would enable us to define a genetic assay that maximizes the diagnostic power for a specified cost of laboratory work. We develop approximation algorithms for WDC by making use of the well-known problem SET COVER for which the greedy heuristic has been extensively studied. We prove worst-case performance bounds on the greedy heuristic for WDC and for another heuristic we call directional greedy. We implemented both heuristics. We also implemented a local search heuristic that takes the solutions obtained by greedy and dir-greedy and applies swaps until they are locally optimal. We report their performance on a real data set that is representative of the options that a clinical geneticist faces for the real diagnostic problem. Many open problems related to WDC remain, both of theoretical interest and practical importance.
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.
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.
Quantum adiabatic approximation and the geometric phase
International Nuclear Information System (INIS)
Mostafazadeh, A.
1997-01-01
A precise definition of an adiabaticity parameter ν of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(τ)=summation scr(l) U (scr(l)) (τ) with U (scr(l)) (τ) being at least of the order ν scr(l) . In particular, U (0) (τ) corresponds to the adiabatic approximation and yields Berry close-quote s adiabatic phase. It is shown that this series expansion has nothing to do with the 1/τ expansion of U(τ). It is also shown that the nonadiabatic part of the evolution operator is generated by a transformed Hamiltonian which is off-diagonal in the eigenbasis of the initial Hamiltonian. This suggests the introduction of an adiabatic product expansion for U(τ) which turns out to yield exact expressions for U(τ) for a large number of quantum systems. In particular, a simple application of the adiabatic product expansion is used to show that for the Hamiltonian describing the dynamics of a magnetic dipole in an arbitrarily changing magnetic field, there exists another Hamiltonian with the same eigenvectors for which the Schroedinger equation is exactly solvable. Some related issues concerning geometric phases and their physical significance are also discussed. copyright 1997 The American Physical Society
Magnetic reconnection under anisotropic magnetohydrodynamic approximation
International Nuclear Information System (INIS)
Hirabayashi, K.; Hoshino, M.
2013-01-01
We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless MHD codes based on the double adiabatic approximation and the Landau closure model. We bridge the gap between the Petschek-type MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of in-situ slow shock observations. Our results showed that once magnetic reconnection takes place, a firehose-sense (p ∥ >p ⊥ ) pressure anisotropy arises in the downstream region, and the generated slow shocks are quite weak comparing with those in an isotropic MHD. In spite of the weakness of the shocks, however, the resultant reconnection rate is 10%–30% higher than that in an isotropic case. This result implies that the slow shock does not necessarily play an important role in the energy conversion in the reconnection system and is consistent with the satellite observation in the Earth's magnetosphere
When Density Functional Approximations Meet Iron Oxides.
Meng, Yu; Liu, Xing-Wu; Huo, Chun-Fang; Guo, Wen-Ping; Cao, Dong-Bo; Peng, Qing; Dearden, Albert; Gonze, Xavier; Yang, Yong; Wang, Jianguo; Jiao, Haijun; Li, Yongwang; Wen, Xiao-Dong
2016-10-11
Three density functional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe 2 O 3 , Fe 3 O 4 , and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.
DCTNet and PCANet for acoustic signal feature extraction
Xian, Yin; Thompson, Andrew; Sun, Xiaobai; Nowacek, Douglas; Nolte, Loren
2016-01-01
We introduce the use of DCTNet, an efficient approximation and alternative to PCANet, for acoustic signal classification. In PCANet, the eigenfunctions of the local sample covariance matrix (PCA) are used as filterbanks for convolution and feature extraction. When the eigenfunctions are well approximated by the Discrete Cosine Transform (DCT) functions, each layer of of PCANet and DCTNet is essentially a time-frequency representation. We relate DCTNet to spectral feature representation method...
International Nuclear Information System (INIS)
Carr, M.H.; Masursky, H.; Strom, R.G.; Terrile, R.J.
1979-01-01
The volcanic features of Io as detected during the Voyager mission are discussed. The volcanic activity is apparently higher than on any other body in the Solar System. Its volcanic landforms are compared with features on Earth to indicate the type of volcanism present on Io. (U.K.)
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
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.
Cophylogeny reconstruction via an approximate Bayesian computation.
Baudet, C; Donati, B; Sinaimeri, B; Crescenzi, P; Gautier, C; Matias, C; Sagot, M-F
2015-05-01
Despite an increasingly vast literature on cophylogenetic reconstructions for studying host-parasite associations, understanding the common evolutionary history of such systems remains a problem that is far from being solved. Most algorithms for host-parasite reconciliation use an event-based model, where the events include in general (a subset of) cospeciation, duplication, loss, and host switch. All known parsimonious event-based methods then assign a cost to each type of event in order to find a reconstruction of minimum cost. The main problem with this approach is that the cost of the events strongly influences the reconciliation obtained. Some earlier approaches attempt to avoid this problem by finding a Pareto set of solutions and hence by considering event costs under some minimization constraints. To deal with this problem, we developed an algorithm, called Coala, for estimating the frequency of the events based on an approximate Bayesian computation approach. The benefits of this method are 2-fold: (i) it provides more confidence in the set of costs to be used in a reconciliation, and (ii) it allows estimation of the frequency of the events in cases where the data set consists of trees with a large number of taxa. We evaluate our method on simulated and on biological data sets. We show that in both cases, for the same pair of host and parasite trees, different sets of frequencies for the events lead to equally probable solutions. Moreover, often these solutions differ greatly in terms of the number of inferred events. It appears crucial to take this into account before attempting any further biological interpretation of such reconciliations. More generally, we also show that the set of frequencies can vary widely depending on the input host and parasite trees. Indiscriminately applying a standard vector of costs may thus not be a good strategy. © The Author(s) 2014. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.
Coronal Loops: Evolving Beyond the Isothermal Approximation
Schmelz, J. T.; Cirtain, J. W.; Allen, J. D.
2002-05-01
Are coronal loops isothermal? A controversy over this question has arisen recently because different investigators using different techniques have obtained very different answers. Analysis of SOHO-EIT and TRACE data using narrowband filter ratios to obtain temperature maps has produced several key publications that suggest that coronal loops may be isothermal. We have constructed a multi-thermal distribution for several pixels along a relatively isolated coronal loop on the southwest limb of the solar disk using spectral line data from SOHO-CDS taken on 1998 Apr 20. These distributions are clearly inconsistent with isothermal plasma along either the line of sight or the length of the loop, and suggested rather that the temperature increases from the footpoints to the loop top. We speculated originally that these differences could be attributed to pixel size -- CDS pixels are larger, and more `contaminating' material would be expected along the line of sight. To test this idea, we used CDS iron line ratios from our data set to mimic the isothermal results from the narrowband filter instruments. These ratios indicated that the temperature gradient along the loop was flat, despite the fact that a more complete analysis of the same data showed this result to be false! The CDS pixel size was not the cause of the discrepancy; rather, the problem lies with the isothermal approximation used in EIT and TRACE analysis. These results should serve as a strong warning to anyone using this simplistic method to obtain temperature. This warning is echoed on the EIT web page: ``Danger! Enter at your own risk!'' In other words, values for temperature may be found, but they may have nothing to do with physical reality. Solar physics research at the University of Memphis is supported by NASA grant NAG5-9783. This research was funded in part by the NASA/TRACE MODA grant for Montana State University.
Holmes, Jon L.
1999-05-01
The Features area of JCE Online is now readily accessible through a single click from our home page. In the Features area each column is linked to its own home page. These column home pages also have links to them from the online Journal Table of Contents pages or from any article published as part of that feature column. Using these links you can easily find abstracts of additional articles that are related by topic. Of course, JCE Online+ subscribers are then just one click away from the entire article. Finding related articles is easy because each feature column "site" contains links to the online abstracts of all the articles that have appeared in the column. In addition, you can find the mission statement for the column and the email link to the column editor that I mentioned above. At the discretion of its editor, a feature column site may contain additional resources. As an example, the Chemical Information Instructor column edited by Arleen Somerville will have a periodically updated bibliography of resources for teaching and using chemical information. Due to the increase in the number of these resources available on the WWW, it only makes sense to publish this information online so that you can get to these resources with a simple click of the mouse. We expect that there will soon be additional information and resources at several other feature column sites. Following in the footsteps of the Chemical Information Instructor, up-to-date bibliographies and links to related online resources can be made available. We hope to extend the online component of our feature columns with moderated online discussion forums. If you have a suggestion for an online resource you would like to see included, let the feature editor or JCE Online (jceonline@chem.wisc.edu) know about it. JCE Internet Features JCE Internet also has several feature columns: Chemical Education Resource Shelf, Conceptual Questions and Challenge Problems, Equipment Buyers Guide, Hal's Picks, Mathcad
Parks, Connie L; Monson, Keith L
2018-01-01
This research examined how accurately 2D images (i.e., photographs) of 3D clay facial approximations were matched to corresponding photographs of the approximated individuals using an objective automated facial recognition system. Irrespective of search filter (i.e., blind, sex, or ancestry) or rank class (R 1 , R 10 , R 25 , and R 50 ) employed, few operationally informative results were observed. In only a single instance of 48 potential match opportunities was a clay approximation matched to a corresponding life photograph within the top 50 images (R 50 ) of a candidate list, even with relatively small gallery sizes created from the application of search filters (e.g., sex or ancestry search restrictions). Increasing the candidate lists to include the top 100 images (R 100 ) resulted in only two additional instances of correct match. Although other untested variables (e.g., approximation method, 2D photographic process, and practitioner skill level) may have impacted the observed results, this study suggests that 2D images of manually generated clay approximations are not readily matched to life photos by automated facial recognition systems. Further investigation is necessary in order to identify the underlying cause(s), if any, of the poor recognition results observed in this study (e.g., potential inferior facial feature detection and extraction). Additional inquiry exploring prospective remedial measures (e.g., stronger feature differentiation) is also warranted, particularly given the prominent use of clay approximations in unidentified persons casework. Copyright © 2017. Published by Elsevier B.V.
International Nuclear Information System (INIS)
Evans, K. Jr.
1999-01-01
MEDM, which is derived from Motif Editor and Display Manager, is the primary graphical interface to the EPICS control system. This paper describes new features that have been added to MEDM in the last two years. These features include new editing capabilities, a PV Info dialog box, a means of specifying limits and precision, a new implementation of the Cartesian Plot, new features for several objects, new capability for the Related Display, help, a user-configurable Execute Menu, reconfigured start-up options, and availability for Windows 95/98/NT. Over one hundred bugs have been fixed, and the program is quite stable and in extensive use
On the point-source approximation of earthquake dynamics
Directory of Open Access Journals (Sweden)
Andrea Bizzarri
2014-06-01
Full Text Available The focus on the present study is on the point-source approximation of a seismic source. First, we compare the synthetic motions on the free surface resulting from different analytical evolutions of the seismic source (the Gabor signal (G, the Bouchon ramp (B, the Cotton and Campillo ramp (CC, the Yoffe function (Y and the Liu and Archuleta function (LA. Our numerical experiments indicate that the CC and the Y functions produce synthetics with larger oscillations and correspondingly they have a higher frequency content. Moreover, the CC and the Y functions tend to produce higher peaks in the ground velocity (roughly of a factor of two. We have also found that the falloff at high frequencies is quite different: it roughly follows ω−2 in the case of G and LA functions, it decays more faster than ω−2 for the B function, while it is slow than ω−1 for both the CC and the Y solutions. Then we perform a comparison of seismic waves resulting from 3-D extended ruptures (both supershear and subshear obeying to different governing laws against those from a single point-source having the same features. It is shown that the point-source models tend to overestimate the ground motions and that they completely miss the Mach fronts emerging from the supershear transition process. When we compare the extended fault solutions against a multiple point-sources model the agreement becomes more significant, although relevant discrepancies still persist. Our results confirm that, and more importantly quantify how, the point-source approximation is unable to adequately describe the radiation emitted during a real world earthquake, even in the most idealized case of planar fault with homogeneous properties and embedded in a homogeneous, perfectly elastic medium.
No surprise in the first Born approximation for electron scattering
International Nuclear Information System (INIS)
Lentzen, M.
2014-01-01
In a recent article it is argued that the far-field expansion of electron scattering, a pillar of electron diffraction theory, is wrong (Treacy and Van Dyck, 2012 [1]). It is further argued that in the first Born approximation of electron scattering the intensity of the electron wave is not conserved to first order in the scattering potential. Thus a “mystery of the missing phase” is investigated, and the supposed flaw in scattering theory is seeked to be resolved by postulating a standing spherical electron wave (Treacy and Van Dyck, 2012 [1]). In this work we show, however, that these theses are wrong. A review of the essential parts of scattering theory with careful checks of the underlying assumptions and limitations for high-energy electron scattering yields: (1) the traditional form of the far-field expansion, comprising a propagating spherical wave, is correct; (2) there is no room for a missing phase; (3) in the first Born approximation the intensity of the scattered wave is conserved to first order in the scattering potential. The various features of high-energy electron scattering are illustrated by wave-mechanical calculations for an explicit target model, a Gaussian phase object, and for a Si atom, considering the geometric conditions in high-resolution transmission electron microscopy. - Highlights: Treacy and Van Dyck (2012) argue that the far-field expansion of electron scattering is wrong. The chief theses of that former work are wrong. There is no room for the missing phase proposed by Treacy and Van Dyck. There is no violation of the intensity conservation to first order in the scattering potential. Calculations for a phase object and an atomic target confirm traditional scattering theory
Abdominal cocoon: sonographic features.
Vijayaraghavan, S Boopathy; Palanivelu, Chinnusamy; Sendhilkumar, Karuppusamy; Parthasarathi, Ramakrishnan
2003-07-01
An abdominal cocoon is a rare condition in which the small bowel is encased in a membrane. The diagnosis is usually established at surgery. Here we describe the sonographic features of this condition.
Mesoblastic nephroma: Pathological features
African Journals Online (AJOL)
N.M. El-Badawy
determined mainly by its histologic type, we found it worthwhile to elaborate more on the gross and microscopic features of ... behavior of mesoblastic nephroma is determined mainly by its his- .... However, it exhibits a nodular growth pattern at.
Directory of Open Access Journals (Sweden)
P Neri
2012-07-01
Full Text Available Binding operations are primarily ascribed to cortex or similarly complex avian structures. My experiments show that the zebrafish, a lower vertebrate lacking cortex, supports visual feature binding of form and motion for the purpose of social behavior. These results challenge the notion that feature binding may require highly evolved neural structures and demonstrate that the nervous system of lower vertebrates can afford unexpectedly complex computations.
Toward a consistent random phase approximation based on the relativistic Hartree approximation
International Nuclear Information System (INIS)
Price, C.E.; Rost, E.; Shepard, J.R.; McNeil, J.A.
1992-01-01
We examine the random phase approximation (RPA) based on a relativistic Hartree approximation description for nuclear ground states. This model includes contributions from the negative energy sea at the one-loop level. We emphasize consistency between the treatment of the ground state and the RPA. This consistency is important in the description of low-lying collective levels but less important for the longitudinal (e,e') quasielastic response. We also study the effect of imposing a three-momentum cutoff on negative energy sea contributions. A cutoff of twice the nucleon mass improves agreement with observed spin-orbit splittings in nuclei compared to the standard infinite cutoff results, an effect traceable to the fact that imposing the cutoff reduces m * /m. Consistency is much more important than the cutoff in the description of low-lying collective levels. The cutoff model also provides excellent agreement with quasielastic (e,e') data
DEFF Research Database (Denmark)
Tregenna-Piggott, Philip L W; Sheptyakov, Denis; Keller, Lukas
2009-01-01
expectations based on the unquenched orbital angular momentum of the [Fe(CN)(6)](3-) anion, giving rise to an M(s) approximately +/-9/2 ground state, isolated by approximately 11.5 cm(-1) from the higher-lying levels. The reported INS and magnetic data should now serve as a benchmark against which theoretical...... interactions that define the low-lying states of the Mn-M(III)-Mn trimeric units. Despite the presence of an antiferromagnetic intertrimer interaction, the experimental evidence supports the classification of both the Cr(III) and Fe(III) compounds as single-molecule magnets. The value of 17(2) cm(-1...
Venus - Volcanic features in Atla Region
1991-01-01
This Magellan image from the Atla region of Venus shows several types of volcanic features and superimposed surface fractures. The area in the image is approximately 350 kilometers (217 miles) across, centered at 9 degrees south latitude, 199 degrees east longitude. Lava flows emanating from circular pits or linear fissures form flower-shaped patterns in several areas. A collapse depression approximately 20 kilometers by 10 kilometers (12 by 6 miles) near the center of the image is drained by a lava channel approximately 40 kilometers (25 miles) long. Numerous surface fractures and graben (linear valleys) criss-cross the volcanic deposits in north to northeast trends. The fractures are not buried by the lavas, indicating that the tectonic activity post-dates most of the volcanic activity.
Directory of Open Access Journals (Sweden)
A. A. Vorobeva
2017-01-01
Full Text Available The paper deals with identification and authentication of web users participating in the Internet information processes (based on features of online texts.In digital forensics web user identification based on various linguistic features can be used to discover identity of individuals, criminals or terrorists using the Internet to commit cybercrimes. Internet could be used as a tool in different types of cybercrimes (fraud and identity theft, harassment and anonymous threats, terrorist or extremist statements, distribution of illegal content and information warfare. Linguistic identification of web users is a kind of biometric identification, it can be used to narrow down the suspects, identify a criminal and prosecute him. Feature set includes various linguistic and stylistic features extracted from online texts. We propose dynamic feature selection for each web user identification task. Selection is based on calculating Manhattan distance to k-nearest neighbors (Relief-f algorithm. This approach improves the identification accuracy and minimizes the number of features. Experiments were carried out on several datasets with different level of class imbalance. Experiment results showed that features relevance varies in different set of web users (probable authors of some text; features selection for each set of web users improves identification accuracy by 4% at the average that is approximately 1% higher than with the use of static set of features. The proposed approach is most effective for a small number of training samples (messages per user.
Approximal morphology as predictor of approximal caries in primary molar teeth
DEFF Research Database (Denmark)
Cortes, A; Martignon, S; Qvist, V
2018-01-01
consent was given, participated. Upper and lower molar teeth of one randomly selected side received a 2-day temporarily separation. Bitewing radiographs and silicone impressions of interproximal area (IPA) were obtained. One-year procedures were repeated in 52 children (84%). The morphology of the distal...... surfaces of the first molar teeth and the mesial surfaces on the second molar teeth (n=208) was scored from the occlusal aspect on images from the baseline resin models resulting in four IPA variants: concave-concave; concave-convex; convex-concave, and convex-convex. Approximal caries on the surface...
Personality Features of Motorists
Directory of Open Access Journals (Sweden)
Andrej Justinek
1997-12-01
Full Text Available Justinek tries to answer the question whether or not motorists have specific personality features which predispose them for safe and well-mannered driving. A good driver should have sensory abilities which enable psycho-motor coordiation of a vehicle, intellectual and cognitive features that are important for solving problems in new, unknown situations, and emotional and motivational trails defining a driver's maturity. Justmek advocates the belief that in training future drivers greater attention should be paid to developing these features which are vital for safe driving and appropriate behaviour of drivers in traffic. He also suggests certain learning methods leading to development of the above mentioned personality traits. Justinek introduces the notion of the 'philosophy of driving' as an essential educational category in training future drivers.
Feature displacement interpolation
DEFF Research Database (Denmark)
Nielsen, Mads; Andresen, Per Rønsholt
1998-01-01
Given a sparse set of feature matches, we want to compute an interpolated dense displacement map. The application may be stereo disparity computation, flow computation, or non-rigid medical registration. Also estimation of missing image data, may be phrased in this framework. Since the features...... often are very sparse, the interpolation model becomes crucial. We show that a maximum likelihood estimation based on the covariance properties (Kriging) show properties more expedient than methods such as Gaussian interpolation or Tikhonov regularizations, also including scale......-selection. The computational complexities are identical. We apply the maximum likelihood interpolation to growth analysis of the mandibular bone. Here, the features used are the crest-lines of the object surface....
Introduction to Methods of Approximation in Physics and Astronomy
van Putten, Maurice H. P. M.
2017-04-01
Modern astronomy reveals an evolving Universe rife with transient sources, mostly discovered - few predicted - in multi-wavelength observations. Our window of observations now includes electromagnetic radiation, gravitational waves and neutrinos. For the practicing astronomer, these are highly interdisciplinary developments that pose a novel challenge to be well-versed in astroparticle physics and data analysis. In realizing the full discovery potential of these multimessenger approaches, the latter increasingly involves high-performance supercomputing. These lecture notes developed out of lectures on mathematical-physics in astronomy to advanced undergraduate and beginning graduate students. They are organised to be largely self-contained, starting from basic concepts and techniques in the formulation of problems and methods of approximation commonly used in computation and numerical analysis. This includes root finding, integration, signal detection algorithms involving the Fourier transform and examples of numerical integration of ordinary differential equations and some illustrative aspects of modern computational implementation. In the applications, considerable emphasis is put on fluid dynamical problems associated with accretion flows, as these are responsible for a wealth of high energy emission phenomena in astronomy. The topics chosen are largely aimed at phenomenological approaches, to capture main features of interest by effective methods of approximation at a desired level of accuracy and resolution. Formulated in terms of a system of algebraic, ordinary or partial differential equations, this may be pursued by perturbation theory through expansions in a small parameter or by direct numerical computation. Successful application of these methods requires a robust understanding of asymptotic behavior, errors and convergence. In some cases, the number of degrees of freedom may be reduced, e.g., for the purpose of (numerical) continuation or to identify
International Nuclear Information System (INIS)
Peng, Degao; Yang, Yang; Zhang, Peng; Yang, Weitao
2014-01-01
In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N 4 ). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as 〈S ^2 〉 are also developed and tested
Cheon, Sooyoung
2013-02-16
Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.
Energy Technology Data Exchange (ETDEWEB)
Peng, Degao; Yang, Yang; Zhang, Peng [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Yang, Weitao, E-mail: weitao.yang@duke.edu [Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708 (United States)
2014-12-07
In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N{sup 4}). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as 〈S{sup ^2}〉 are also developed and tested.
Cheon, Sooyoung; Liang, Faming; Chen, Yuguo; Yu, Kai
2013-01-01
Importance sampling and Markov chain Monte Carlo methods have been used in exact inference for contingency tables for a long time, however, their performances are not always very satisfactory. In this paper, we propose a stochastic approximation Monte Carlo importance sampling (SAMCIS) method for tackling this problem. SAMCIS is a combination of adaptive Markov chain Monte Carlo and importance sampling, which employs the stochastic approximation Monte Carlo algorithm (Liang et al., J. Am. Stat. Assoc., 102(477):305-320, 2007) to draw samples from an enlarged reference set with a known Markov basis. Compared to the existing importance sampling and Markov chain Monte Carlo methods, SAMCIS has a few advantages, such as fast convergence, ergodicity, and the ability to achieve a desired proportion of valid tables. The numerical results indicate that SAMCIS can outperform the existing importance sampling and Markov chain Monte Carlo methods: It can produce much more accurate estimates in much shorter CPU time than the existing methods, especially for the tables with high degrees of freedom. © 2013 Springer Science+Business Media New York.
SFU-driven transparent approximation acceleration on GPUs
Li, A.; Song, S.L.; Wijtvliet, M.; Kumar, A.; Corporaal, H.
2016-01-01
Approximate computing, the technique that sacrifices certain amount of accuracy in exchange for substantial performance boost or power reduction, is one of the most promising solutions to enable power control and performance scaling towards exascale. Although most existing approximation designs
Some approximate calculations in SU2 lattice mean field theory
International Nuclear Information System (INIS)
Hari Dass, N.D.; Lauwers, P.G.
1981-12-01
Approximate calculations are performed for small Wilson loops of SU 2 lattice gauge theory in mean field approximation. Reasonable agreement is found with Monte Carlo data. Ways of improving these calculations are discussed. (Auth.)
Coefficients Calculation in Pascal Approximation for Passive Filter Design
Directory of Open Access Journals (Sweden)
George B. Kasapoglu
2018-02-01
Full Text Available The recently modified Pascal function is further exploited in this paper in the design of passive analog filters. The Pascal approximation has non-equiripple magnitude, in contrast of the most well-known approximations, such as the Chebyshev approximation. A novelty of this work is the introduction of a precise method that calculates the coefficients of the Pascal function. Two examples are presented for the passive design to illustrate the advantages and the disadvantages of the Pascal approximation. Moreover, the values of the passive elements can be taken from tables, which are created to define the normalized values of these elements for the Pascal approximation, as Zverev had done for the Chebyshev, Elliptic, and other approximations. Although Pascal approximation can be implemented to both passive and active filter designs, a passive filter design is addressed in this paper, and the benefits and shortcomings of Pascal approximation are presented and discussed.
Approximate viability for nonlinear evolution inclusions with application to controllability
Directory of Open Access Journals (Sweden)
Omar Benniche
2016-12-01
Full Text Available We investigate approximate viability for a graph with respect to fully nonlinear quasi-autonomous evolution inclusions. As application, an approximate null controllability result is given.
International Nuclear Information System (INIS)
Lousteau, D.C.; Jernigan, T.C.; Schaffer, M.J.; Hussung, R.O.
1975-01-01
ISX, an Impurity Study Experiment, is presently being designed at Oak Ridge National Laboratory as a joint scientific effort between ORNL and General Atomic Company. ISX is a moderate size tokamak dedicated to the study of impurity production, diffusion, and control. The significant engineering features of this device are discussed
Chiu, S. H.; Kuo, T. K.
2018-03-01
The elements (squared) of the neutrino mixing matrix are found to satisfy, as functions of the induced mass, a set of differential equations. They show clearly the dominance of pole terms when the neutrino masses "cross." Using the known vacuum mixing parameters as initial conditions, it is found that these equations have very good approximate solutions, for all values of the induced mass. The results are applicable to long baseline experiments.
PWL approximation of nonlinear dynamical systems, part I: structural stability
International Nuclear Information System (INIS)
Storace, M; De Feo, O
2005-01-01
This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes the approximation method and applies it to some particularly significant dynamical systems (topological normal forms). The structural stability of the PWL approximations of such systems is investigated through a bifurcation analysis (via continuation methods)
Pawlak algebra and approximate structure on fuzzy lattice.
Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai
2014-01-01
The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.
Comparison of four support-vector based function approximators
de Kruif, B.J.; de Vries, Theodorus J.A.
2004-01-01
One of the uses of the support vector machine (SVM), as introduced in V.N. Vapnik (2000), is as a function approximator. The SVM and approximators based on it, approximate a relation in data by applying interpolation between so-called support vectors, being a limited number of samples that have been
Explicitly solvable complex Chebyshev approximation problems related to sine polynomials
Freund, Roland
1989-01-01
Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.
Aspects of three field approximations: Darwin, frozen, EMPULSE
International Nuclear Information System (INIS)
Boyd, J.K.; Lee, E.P.; Yu, S.S.
1985-01-01
The traditional approach used to study high energy beam propagation relies on the frozen field approximation. A minor modification of the frozen field approximation yields the set of equations applied to the analysis of the hose instability. These models are constrasted with the Darwin field approximation. A statement is made of the Darwin model equations relevant to the analysis of the hose instability
Approximation Properties of Certain Summation Integral Type Operators
Directory of Open Access Journals (Sweden)
Patel P.
2015-03-01
Full Text Available In the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.
On Love's approximation for fluid-filled elastic tubes
International Nuclear Information System (INIS)
Caroli, E.; Mainardi, F.
1980-01-01
A simple procedure is set up to introduce Love's approximation for wave propagation in thin-walled fluid-filled elastic tubes. The dispersion relation for linear waves and the radial profile for fluid pressure are determined in this approximation. It is shown that the Love approximation is valid in the low-frequency regime. (author)
Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients
Beck, Joakim
2011-12-22
In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new effective class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids.
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2012-01-01
The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of this approach is the improved description of dispersive forces...... while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local-density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation...... of the ALDA kernel for wave vectors q > 2kF, which is found to yield excellent results for the homogeneous electron gas. In addition, the kernel significantly improves both the absolute correlation energies and atomization energies of small molecules over RPA and ALDA. The renormalization can...
Perturbative corrections for approximate inference in gaussian latent variable models
DEFF Research Database (Denmark)
Opper, Manfred; Paquet, Ulrich; Winther, Ole
2013-01-01
Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact b...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....
Standard filter approximations for low power Continuous Wavelet Transforms.
Casson, Alexander J; Rodriguez-Villegas, Esther
2010-01-01
Analogue domain implementations of the Continuous Wavelet Transform (CWT) have proved popular in recent years as they can be implemented at very low power consumption levels. This is essential for use in wearable, long term physiological monitoring systems. Present analogue CWT implementations rely on taking mathematical a approximation of the wanted mother wavelet function to give a filter transfer function that is suitable for circuit implementation. This paper investigates the use of standard filter approximations (Butterworth, Chebyshev, Bessel) as an alternative wavelet approximation technique. This extends the number of approximation techniques available for generating analogue CWT filters. An example ECG analysis shows that signal information can be successfully extracted using these CWT approximations.
Approximate Noether symmetries and collineations for regular perturbative Lagrangians
Paliathanasis, Andronikos; Jamal, Sameerah
2018-01-01
Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying manifold. In particular we determine the generic Noether symmetry conditions for the approximate point symmetries and we find that for a class of perturbed Lagrangians, Noether symmetries are related to the elements of the Homothetic algebra of the metric which is defined by the unperturbed Lagrangian. Moreover, we discuss how exact symmetries become approximate symmetries. Finally, some applications are presented.
Methods of Approximation Theory in Complex Analysis and Mathematical Physics
Saff, Edward
1993-01-01
The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...
MRI features of chondroblastoma
International Nuclear Information System (INIS)
Cheng Xiaoguang; Liu Xia; Cheng Kebin; Liu Wei
2009-01-01
Objective: To evaluate the MR imaging features of chondroblastoma. Methods: MRI examinations of 20 patients with histological proven chondmblastoma were reviewed retrospectively. The MRI findings of chondroblastoma including the signal intensity, the shape, the growth patterns, and the surrounding bone marrow edema and the adjacent soft tissue edema, the periosteal reaction, the adjacent joint effusion were analyzed. Results: All 20 cases demonstrated heterogeneous MR signal intensity on T 1 WI and T 2 WI images and showed lobular margins. Sixteen cases demonstrated expansive growth patterns. Surrounding bone marrow edema was found in 18 cases and adjacent soft tissue edema in 14 cases. Periosteal reaction was identified in 6 cases. In 7 cases the tumor extended to adjacent soft tissue. Adjacent joint effusion was visible on MRI in 6 cases. Conclusion: Heterogeneous signal intensity, lobular margins and expansive growth pattern, adjacent bone marrow and soft tissue edema were the common features of chondroblastoma on MRI. (authors)
Imaging features of thalassemia
Energy Technology Data Exchange (ETDEWEB)
Tunaci, M.; Tunaci, A.; Engin, G.; Oezkorkmaz, B.; Acunas, G.; Acunas, B. [Dept. of Radiology, Istanbul Univ. (Turkey); Dincol, G. [Dept. of Internal Medicine, Istanbul Univ. (Turkey)
1999-07-01
Thalassemia is a kind of chronic, inherited, microcytic anemia characterized by defective hemoglobin synthesis and ineffective erythropoiesis. In all thalassemias clinical features that result from anemia, transfusional, and absorptive iron overload are similar but vary in severity. The radiographic features of {beta}-thalassemia are due in large part to marrow hyperplasia. Markedly expanded marrow space lead to various skeletal manifestations including spine, skull, facial bones, and ribs. Extramedullary hematopoiesis (ExmH), hemosiderosis, and cholelithiasis are among the non-skeletal manifestations of thalassemia. The skeletal X-ray findings show characteristics of chronic overactivity of the marrow. In this article both skeletal and non-skeletal manifestations of thalassemia are discussed with an overview of X-ray findings, including MRI and CT findings. (orig.)