Diversity among African pygmies.
Directory of Open Access Journals (Sweden)
Fernando V Ramírez Rozzi
Full Text Available Although dissimilarities in cranial and post-cranial morphology among African pygmies groups have been recognized, comparative studies on skull morphology usually pull all pygmies together assuming that morphological characters are similar among them and different with respect to other populations. The main aim of this study is to compare cranial morphology between African pygmies and non-pygmies populations from Equatorial Africa derived from both the Eastern and the Western regions in order to test if the greatest morphological difference is obtained in the comparison between pygmies and non-pygmies. Thirty three-dimensional (3D landmarks registered with Microscribe in four cranial samples (Western and Eastern pygmies and non-pygmies were obtained. Multivariate analysis (generalized Procrustes analysis, Mahalanobis distances, multivariate regression and complementary dimensions of size were evaluated with ANOVA and post hoc LSD. Results suggest that important cranial shape differentiation does occur between pygmies and non-pygmies but also between Eastern and Western populations and that size changes and allometries do not affect similarly Eastern and Western pygmies. Therefore, our findings raise serious doubt about the fact to consider African pygmies as a homogenous group in studies on skull morphology. Differences in cranial morphology among pygmies would suggest differentiation after divergence. Although not directly related to skull differentiation, the diversity among pygmies would probably suggest that the process responsible for reduced stature occurred after the split of the ancestors of modern Eastern and Western pygmies.
Pygmy resonances and nucleosynthesis
Tsoneva, Nadia
2014-01-01
A microscopic theoretical approach based on a self-consistent density functional theory for the nuclear ground state and QRPA formalism extended with multi-phonon degrees of freedom for the nuclear excited states is implemented in investigations of new low-energy modes called pygmy resonances. Advantage of the method is the unified description of low-energy multiphonon excitations, pygmy resonances and core polarization effects. This is found of crucial importance for the understanding of the fine structure of nuclear response functions at low energies. Aspects of the precise knowledge of nuclear response functions around the neutron threshold are discussed in a connection to nucleosynthesis.
Nonlinear approximation with dictionaries. II. Inverse Estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2006-01-01
In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal...
Nonlinear approximation with dictionaries,.. II: Inverse estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
In this paper we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for separated decomposable dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually...
Intelligent comparisons II inequalities and approximations
Anastassiou, George A
2017-01-01
This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.
Piekarewicz, J
2012-01-01
Understanding the equation of state (EOS) of neutron-rich matter is a central goal of nuclear physics that cuts across a variety of disciplines. Indeed, the limits of nuclear existence, the collision of energetic heavy ions, the structure of neutron stars, and the dynamics of core-collapse supernova all depend critically on the nuclear-matter EOS. In this contribution I focus on the EOS of cold baryonic matter with special emphasis on its impact on the structure, dynamics, and composition of neutron stars. In particular, I discuss how laboratory experiments on neutron skins as well as on Pygmy and Giant resonances can help us elucidate the structure of these fascinating objects.
Intelligent systems II complete approximation by neural network operators
Anastassiou, George A
2016-01-01
This monograph is the continuation and completion of the monograph, “Intelligent Systems: Approximation by Artificial Neural Networks” written by the same author and published 2011 by Springer. The book you hold in hand presents the complete recent and original work of the author in approximation by neural networks. Chapters are written in a self-contained style and can be read independently. Advanced courses and seminars can be taught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The book’s results are expected to find applications in many areas of applied mathematics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also for all science and engineering libraries. .
Total variation approximation for quasi-equilibrium distributions, II
Barbour, A D
2011-01-01
Quasi-stationary distributions, as discussed by Darroch & Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. These distributions have some drawbacks: they need not exist, nor be unique, and their calculation can present problems. In an earlier paper, we gave biologically plausible conditions under which the quasi-stationary distribution is unique, and can be closely approximated by distributions that are simple to compute. In this paper, we consider conditions under which the quasi-stationary distribution, if it exists, need not be unique, but an apparent stochastic equilibrium can nonetheless be identified and computed; we call such a distribution a quasi-equilibrium distribution.
On the collectivity of Pygmy Dipole Resonance within schematic TDA and RPA models
Baran, V; Colonna, M; Di Toro, M; Croitoru, A; Nicolin, A I
2014-01-01
Within schematic models based on the Tamm-Dancoff Approximation and the Random-Phase Approximation with separable interactions, we investigate the physical conditions which determine the emergence of the Pygmy Dipole Resonance in the E1 response of atomic nuclei. We find that if some particle-hole excitation manifests a different, weaker residual interaction, an additional mode will appear, with an energy centroid closer to the distance between two major shells and therefore well below the Giant Dipole Resonance. This state, together with Giant Dipole Resonance, exhausts all the transition strength in the Tamm-Dancoff Approximation and all the Energy Weighted Sum Rule in the Random-Phase Approximation. These features suggest a collective nature for this mode which we identify with the Pygmy Dipole Resonance.
Experimental results on the Pygmy Dipole Resonance
Directory of Open Access Journals (Sweden)
Savran Deniz
2014-03-01
Full Text Available The so-called Pygmy Dipole Resonance, an additional structure of low-lying electric dipole strength, has attracted strong interest in the last years. Different experimental approaches have been used in the last decade in order to investigate this new interesting nuclear excitation mode. In this contribution an overview on the available experimental data is given.
Pygmy dipole resonance and dipole polarizability in {sup 90}Zr
Energy Technology Data Exchange (ETDEWEB)
Iwamoto, C.; Tamii, A.; Shima, T.; Hashimoto, T.; Suzuki, T.; Fujita, H.; Hatanaka, K. [Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047 (Japan); Utsunomiya, H.; Akimune, H.; Yamagata, T.; Okamoto, A.; Kondo, T. [Department of Physics, Konan University, Okamoto 8-9-1, Higashinada, Kobe 658-8501 (Japan); Nakada, H. [Department of Physics, Graduate School of Science, Chiba University, Yayoi-cho 1-33, Inage, Chiba 263-8522 (Japan); Kawabata, T. [Department of Physics, Kyoto University, Kyoto 606-8502 (Japan); Fujita, Y. [Department of Physics, Osaka University, Toyonaka, Osaka, 560-0043 (Japan); Matsubara, H. [RIKEN Nishina Center, Wako, Saitama 351-0198 (Japan); Shimbara, Y.; Nagashima, M. [Department of Physics, Niigata University, Niigata 950-21-2 (Japan); Sakuda, M.; Mori, T. [Department of Physics, Okayama University, Okayama 900-0082 (Japan); and others
2014-05-02
Electric dipole (E1) reduced transition probability B(E1) of {sup 90}Zr was obtained by the inelastic proton scattering near 0 degrees using a 295 MeV proton beam and multipole decomposition analysis of the angular distribution by the distorted-wave Born approximation with the Hartree-Fock plus random-phase approximation model and inclusion of El Coulomb excitation, and the E1 strength of the pygmy dipole resonance was found in the vicinity of the neutron threshold in the low-energy tail of the giant dipole resonance. Using the data, we plan to determine the precise dipole polarizability α{sub D} which is defined as an inversely energy-weighted sum value of the elecrric dipole strength. The dipole polarizability is expected to constrain the symmetry energy term of the neutron matter equation of state. Thus systematical measurement of the dipole polarizability is important.
Pygmy dipole resonance and dipole polarizability in 90Zr
Iwamoto, C.; Tamii, A.; Utsunomiya, H.; Akimune, H.; Nakada, H.; Shima, T.; Hashimoto, T.; Yamagata, T.; Kawabata, T.; Fujita, Y.; Matsubara, H.; Suzuki, T.; Fujita, H.; Shimbara, Y.; Nagashima, M.; Sakuda, M.; Mori, T.; Izumi, T.; Okamoto, A.; Kondo, T.; Lui, T.-W.; Bilgier, B.; Kozer, H. C.; Hatanaka, K.
2014-05-01
Electric dipole (E1) reduced transition probability B(E1) of 90Zr was obtained by the inelastic proton scattering near 0 degrees using a 295 MeV proton beam and multipole decomposition analysis of the angular distribution by the distorted-wave Born approximation with the Hartree-Fock plus random-phase approximation model and inclusion of El Coulomb excitation, and the E1 strength of the pygmy dipole resonance was found in the vicinity of the neutron threshold in the low-energy tail of the giant dipole resonance. Using the data, we plan to determine the precise dipole polarizability αD which is defined as an inversely energy-weighted sum value of the elecrric dipole strength. The dipole polarizability is expected to constrain the symmetry energy term of the neutron matter equation of state. Thus systematical measurement of the dipole polarizability is important.
A possible proton pygmy resonance in 17Ne
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
The low-lying electric dipole strengths in proton-rich nuclei 17F and 17Ne, which can be produced at HIRFL-CSR in Lanzhou, are investigated. In the framework of the covariant density functional theory the self-consistent relativistic Hartree Bogoliubov model and the relativistic quasiparticle random phase approximation with the NL3 parameter set and Gogny pairing interaction are adopted in the calculations. A pronounced dipole peak appears below 10 MeV in17Ne, but does not occur in 17F. The prop erties of this low-lying E1 excitation in 17Ne are studied, which may correspond to a proton pygmy resonance with different characteristics from those of giant dipole resonance.
Directory of Open Access Journals (Sweden)
Mohamed Mahmoud Mohamed
2016-09-01
Full Text Available In this paper we develop approximate Bayes estimators of the parameters,reliability, and hazard rate functions of the Logistic distribution by using Lindley’sapproximation, based on progressively type-II censoring samples. Noninformativeprior distributions are used for the parameters. Quadratic, linexand general Entropy loss functions are used. The statistical performances of theBayes estimates relative to quadratic, linex and general entropy loss functionsare compared to those of the maximum likelihood based on simulation study.
Distribution and Numbers of Pygmies in Central African Forests.
Olivero, Jesús; Fa, John E; Farfán, Miguel A; Lewis, Jerome; Hewlett, Barry; Breuer, Thomas; Carpaneto, Giuseppe M; Fernández, María; Germi, Francesco; Hattori, Shiho; Head, Josephine; Ichikawa, Mitsuo; Kitanaishi, Koichi; Knights, Jessica; Matsuura, Naoki; Migliano, Andrea; Nese, Barbara; Noss, Andrew; Ekoumou, Dieudonné Ongbwa; Paulin, Pascale; Real, Raimundo; Riddell, Mike; Stevenson, Edward G J; Toda, Mikako; Vargas, J Mario; Yasuoka, Hirokazu; Nasi, Robert
2016-01-01
Pygmy populations occupy a vast territory extending west-to-east along the central African belt from the Congo Basin to Lake Victoria. However, their numbers and actual distribution is not known precisely. Here, we undertake this task by using locational data and population sizes for an unprecedented number of known Pygmy camps and settlements (n = 654) in five of the nine countries where currently distributed. With these data we develop spatial distribution models based on the favourability function, which distinguish areas with favourable environmental conditions from those less suitable for Pygmy presence. Highly favourable areas were significantly explained by presence of tropical forests, and by lower human pressure variables. For documented Pygmy settlements, we use the relationship between observed population sizes and predicted favourability values to estimate the total Pygmy population throughout Central Africa. We estimate that around 920,000 Pygmies (over 60% in DRC) is possible within favourable forest areas in Central Africa. We argue that fragmentation of the existing Pygmy populations, alongside pressure from extractive industries and sometimes conflict with conservation areas, endanger their future. There is an urgent need to inform policies that can mitigate against future external threats to these indigenous peoples' culture and lifestyles.
Distribution and Numbers of Pygmies in Central African Forests.
Directory of Open Access Journals (Sweden)
Jesús Olivero
Full Text Available Pygmy populations occupy a vast territory extending west-to-east along the central African belt from the Congo Basin to Lake Victoria. However, their numbers and actual distribution is not known precisely. Here, we undertake this task by using locational data and population sizes for an unprecedented number of known Pygmy camps and settlements (n = 654 in five of the nine countries where currently distributed. With these data we develop spatial distribution models based on the favourability function, which distinguish areas with favourable environmental conditions from those less suitable for Pygmy presence. Highly favourable areas were significantly explained by presence of tropical forests, and by lower human pressure variables. For documented Pygmy settlements, we use the relationship between observed population sizes and predicted favourability values to estimate the total Pygmy population throughout Central Africa. We estimate that around 920,000 Pygmies (over 60% in DRC is possible within favourable forest areas in Central Africa. We argue that fragmentation of the existing Pygmy populations, alongside pressure from extractive industries and sometimes conflict with conservation areas, endanger their future. There is an urgent need to inform policies that can mitigate against future external threats to these indigenous peoples' culture and lifestyles.
Proton pygmy resonances: predictions for N=20 isotones
Kim, Y
2015-01-01
We study theoretically the low-energy electric-dipole response of N=20 isotones to assess the possibility of detecting a proton-pygmy mode in the near future and to examine the factors that would determine such an outcome. We present results from a quasiparticle random-phase approximation (QRPA) and a continuum random-phase approximation (CRPA), and we compare our results with other calculations of proton-rich nuclei. According to our analysis, enhanced E1 strength is expected energetically well below the giant dipole resonance in the proton-rich isotones. A proton-skin oscillation could develop especially in 46Fe. We identify factors which affect theoretical predictions, besides the equation of state (EoS) of infinite matter: the nucleon separation energy, accordingly the proper description of non localized threshold transitions, and the nucleon effective mass in mean-field treatments. Future measurements of E1 transitions in proton-rich nuclei and comparisons with mirror stable nuclei could help disentangle...
Pygmy dipole resonance in stable nuclei
Indian Academy of Sciences (India)
P Von Neumann-Cosel
2010-07-01
Two examples of recent work on the structure of low-energy electric dipole modes are presented. The first part discusses the systematics of the pygmy dipole resonance (PDR) in stable tin isotopes deduced from high-resolution (, ′) experiments. These help to distinguish between microscopic QRPA calculations based on either a relativistic or a non-relativistic mean-field description, predicting significantly different properties of the PDR. The second part presents a novel approach to measure the complete electric dipole strength distribution from excitation energies starting at about 5 MeV across the giant dipole resonance (GDR) with high-resolution inelastic proton scattering under 0° at energies of a few 100 MeV/nucleon. The case of 208Pb is discussed in detail and first result from a recent experiment on 120Sn is presented.
Pygmy dipole resonance in 208Pb
Poltoratska, I; Tamii, A; Adachi, T; Bertulani, C A; Carter, J; Dozono, M; Fujita, H; Fujita, K; Fujita, Y; Hatanaka, K; Itoh, M; Kawabata, T; Kalmykov, Y; Krumbholz, A M; Litvinova, E; Matsubara, H; Nakanishi, K; Neveling, R; Okamura, H; Ong, H J; Özel-Tashenov, B; Ponomarev, V Yu; Richter, A; Rubio, B; Sakaguchi, H; Sakemi, Y; Sasamoto, Y; Shimbara, Y; Shimizu, Y; Smit, F D; Suzuki, T; Tameshige, Y; Wambach, J; Yosoi, M; Zenihiro, J
2012-01-01
Scattering of protons of several hundred MeV is a promising new spectroscopic tool for the study of electric dipole strength in nuclei. A case study of 208Pb shows that at very forward angles J^pi = 1- states are strongly populated via Coulomb excitation. A separation from nuclear excitation of other modes is achieved by a multipole decomposition analysis of the experimental cross sections based on theoretical angular distributions calculated within the quasiparticle-phonon model. The B(E1) transition strength distribution is extracted for excitation energies up to 9 MeV, i.e., in the region of the so-called pygmy dipole resonance (PDR). The Coulomb-nuclear interference shows sensitivity to the underlying structure of the E1 transitions, which allows for the first time an experimental extraction of the strength and energy centroid of the PDR.
Pygmy Rabbit Surveys on State Lands in Oregon
Hagar, Joan; Lienkaemper, George
2007-01-01
Introduction The pygmy rabbit (Brachylagus idahoensis) is classified by the federal government as a species of concern (i.e., under review by the U.S. Fish and Wildlife Service for consideration as a candidate for listing as threatened or endangered under the Endangered Species Act) because of its specialized habitat requirements and evidence of declining populations. The Oregon Department of Fish and Wildlife (ODFW) lists pygmy rabbits as 'sensitive-vulnerable,' meaning that protective measures are needed if sustainable populations are to be maintained over time (Oregon Natural Heritage Program, 2001). The Oregon Natural Heritage Program considers this species to be threatened with extirpation from Oregon. Pygmy rabbits also are a species of concern in all the other states where they occur (NatureServe, 2004). The Washington population, known as the Columbia Basin pygmy rabbit, was listed as endangered by the federal government in 2003. Historically, pygmy rabbits have been collected from Deschutes, Klamath, Crook, Lake, Grant, Harney, Baker, and Malheur Counties in Oregon. However, the geographic range of pygmy rabbit in Oregon may have decreased in historic times (Verts and Carraway, 1998), and boundaries of the current distribution are not known. Not all potentially suitable sites appear to be occupied, and populations are susceptible to rapid declines and local extirpation (Weiss and Verts, 1984). In order to protect and manage remaining populations on State of Oregon lands, Oregon Department of Fish and Wildlife needs to identify areas currently occupied by pygmy rabbits, as well as suitable habitats. The main objective of this survey was document to presence or absence of pygmy rabbits on state lands in Malheur, Harney, Lake, and Deschutes counties. Knowledge of the location and extent of pygmy rabbit populations can provide a foundation for the conservation and management of this species in Oregon. The pygmy rabbit is just one of a suite of species of
Excitation energy and strength of the pygmy dipole resonance in stable tin isotopes
Özel, B; Lenske, H; Von Neumann-Cosel, P; Poltoratska, I; Ponomarev, V Yu; Richter, A; Savran, D; Tsoneva, N
2009-01-01
The $^{112,120}$Sn$(\\gamma,\\gamma')$ reactions have been studied at the S-DALINAC. Electric dipole (E1) strength distributions have been determined including contributions from unresolved strength extracted by a fluctuation analysis. Together with available data on $^{116,124}$Sn, an experimental systematics of the pygmy dipole resonance (PDR) in stable even-mass tin isotopes is established. The PDR centroid excitation energies and summed strengths are in reasonable agreement with quasiparticle-phonon model calculations based on a nonrelativistic description of the mean field but disagree with relativistic quasiparticle random-phase approximation predictions.
Physical comparison between Rampasasa Pygmy and Yogyakarta children of Indonesia
Directory of Open Access Journals (Sweden)
Neni Trilusiana Rahmawati
2016-06-01
Full Text Available ABSTRACT In growth studies, somatotyping allows one to characterize changes in physique during growth in order to monitor growth patterns and to better understand variations in adult physique. Information on the physique of children with short stature is limited In Indonesia the study of somatotype for Pygmy children had never been done. The aims of this study were to compare the physiques of Rampasasa Pygmy and Yogyakarta children and to evaluate factors that might lead to variability in physiques. The sample consisted of 61 Rampasasa Pygmy (32 boys and 29 girls and 319 Javanese children in Yogyakarta (173 boys and 146 girls aged 8–13 years. Height, weight, biepicondylar breadths of the humerus and femur, calf and upper arm circumferences, and skinfolds (at triceps, subscapula, calf, and supraspine were measured on each subject. We used somatotyped by the Heath-Carter method. The results showed that the Pygmy children were shorter, lighter, and less endomorphic than the Yogyakarta children. Our findings suggest that the observed differences between Rampasasa Pygmy and Yogyakarta children could be related mainly to environment background in the two areas.
Structure of the pygmy dipole resonance in Sn-124
Endres, J.; Savran, D.; Butler, P. A.; Harakeh, M. N.; Harissopulos, S.; Herzberg, R. -D.; Kruecken, R.; Lagoyannis, A.; Litvinova, E.; Pietralla, N.; Ponomarev, V. Yu.; Popescu, L.; Ring, P.; Scheck, M.; Schlueter, F.; Sonnabend, K.; Stoica, V. I.; Zilges, A.; Wortche, Heinrich
2012-01-01
Background: In atomic nuclei, a concentration of electric dipole strength around the particle threshold, commonly denoted as pygmy dipole resonance, may have a significant impact on nuclear structure properties and astrophysical scenarios. A clear identification of these states and the structure of
Two novel arenaviruses detected in pygmy mice, Ghana.
Kronmann, Karl C; Nimo-Paintsil, Shirley; Guirguis, Fady; Kronmann, Lisha C; Bonney, Kofi; Obiri-Danso, Kwasi; Ampofo, William; Fichet-Calvet, Elisabeth
2013-11-01
Two arenaviruses were detected in pygmy mice (Mus spp.) by screening 764 small mammals in Ghana. The Natal multimammate mouse (Mastomys natalensis), the known Lassa virus reservoir, was the dominant indoor rodent species in 4 of 10 sites, and accounted for 27% of all captured rodents. No rodent captured indoors tested positive for an arenavirus.
Polycystic kidney disease in the pygmy hippopotamus (Hexaprotodon liberiensis).
Nees, Stephanie; Schade, Benjamin; Clauss, Marcus; Steinmetz, Hanspeter W; Ehrensperger, Felix; Steck, Beatrice; Hatt, Jean-Michel
2009-09-01
Polycystic kidney disease (PKD) was diagnosed at necropsy in a captive aged female pygmy hippopotamus (Hexaprotodon liberiensis), which presented with numerous cysts in both kidneys, the liver, and the duodenum and with one single cyst in the pancreas. There were no premonitory clinical signs of a nephropathy observed prior to its death. Similar findings were made in a male cage mate 6 mo later. Both animals had been wild caught. A literature review revealed that another seven cases of PKD have been reported in pygmy hippopotamuses, and an additional screening of records available from the international studbook for the species revealed yet another six cases. In all cases, aged females were affected, and in several instances, affected animals were related to each other. These patterns indicated familiar transmission similar that associated with PKD in humans and other animals. The disease, and especially the presumptive bias in diagnosis toward females, indicated that the male animal of this report was the first case of PKD reported in a male pygmy hippopotamus; thus, further investigation is warranted. The status of the kidneys with respect to PKD should be assessed (including histology) in every deceased pygmy hippopotamus, and whenever possible by ultrasonography in live animals.
Nuclear deformation and neutron excess as competing effects for pygmy dipole strength
Massarczyk, R; Dönau, F; Frauendorf, S; Anders, M; Bemmerer, D; Beyer, R; Bhatia, C; Birgersson, E; Butterling, M; Elekes, Z; Ferrari, A; Gooden, M E; Hannaske, R; Junghans, A R; Kempe, M; Kelley, J H; Kögler, T; Matic, A; Menzel, M L; Müller, S; Reinhardt, T P; Röder, M; Rusev, G; Schilling, K D; Schmidt, K; Schramm, G; Tonchev, A P; Tornow, W; Wagner, A
2013-01-01
The electromagnetic dipole strength below the neutron-separation energy has been studied for the xenon isotopes with mass numbers A = 124, 128, 132, and 134 in nuclear resonance fluorescence experiments using the ELBE bremsstrahlung facility at Helmholtz-Zentrum Dresden-Rossendorf and the HIgS facility at Triangle Universities Nuclear Laboratory Durham. The systematic study gained new information about the influence of the neutron excess as well as of nuclear deformation on the strength in the region of the pygmy dipole resonance. The results are compared with those obtained for the chain of molybdenum isotopes and with predictions of a random-phase approximation in a deformed basis. It turned out that the effect of nuclear deformation plays a minor role compared with the one caused by neutron excess. A global parametrization of the strength in terms of neutron and proton numbers allowed us to derive a formula capable of predicting the summed E1 strengths in the pygmy region for a wide mass range of nuclides.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zhenyue [Zhejiang Univ., Hangzhou (People' s Republic of China); Zha, Hongyuan [Pennsylvania State Univ., University Park, PA (United States); Simon, Horst [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2006-07-31
In this paper, we developed numerical algorithms for computing sparse low-rank approximations of matrices, and we also provided a detailed error analysis of the proposed algorithms together with some numerical experiments. The low-rank approximations are constructed in a certain factored form with the degree of sparsity of the factors controlled by some user-specified parameters. In this paper, we cast the sparse low-rank approximation problem in the framework of penalized optimization problems. We discuss various approximation schemes for the penalized optimization problem which are more amenable to numerical computations. We also include some analysis to show the relations between the original optimization problem and the reduced one. We then develop a globally convergent discrete Newton-like iterative method for solving the approximate penalized optimization problems. We also compare the reconstruction errors of the sparse low-rank approximations computed by our new methods with those obtained using the methods in the earlier paper and several other existing methods for computing sparse low-rank approximations. Numerical examples show that the penalized methods are more robust and produce approximations with factors which have fewer columns and are sparser.
The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego; Lesgourgues, Julien [Institut de Théorie des Phénomènes Physiques, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne (Switzerland); Tram, Thomas, E-mail: diego.blas@epfl.ch, E-mail: julien.lesgourgues@cern.ch, E-mail: tram@phys.au.dk [CERN, Theory Division, CH-1211 Geneva 23 (Switzerland)
2011-07-01
Boltzmann codes are used extensively by several groups for constraining cosmological parameters with Cosmic Microwave Background and Large Scale Structure data. This activity is computationally expensive, since a typical project requires from 10{sup 4} to 10{sup 5} Boltzmann code executions. The newly released code CLASS (Cosmic Linear Anisotropy Solving System) incorporates improved approximation schemes leading to a simultaneous gain in speed and precision. We describe here the three approximations used by CLASS for basic ΛCDM models, namely: a baryon-photon tight-coupling approximation which can be set to first order, second order or to a compromise between the two; an ultra-relativistic fluid approximation which had not been implemented in public distributions before; and finally a radiation streaming approximation taking reionisation into account.
Approximation of N(k)(infinity)-functions II : Convergence of Models
Dijksma, Aad; Luger, Annemarie; Shondin, Yuri; Behrndt, J; Forster, KH; Trunk, C
2010-01-01
This paper is a continuation of Part I, [9] in the list of references, where models for N(k)(infinity)-functions have been studied in detail. In the present paper we investigate the convergence of the corresponding models as a singular N(k)(infinity)-functionis approximated by regular N(k)(infinity)
Casadei, D.
2014-10-01
The objective Bayesian treatment of a model representing two independent Poisson processes, labelled as ``signal'' and ``background'' and both contributing additively to the total number of counted events, is considered. It is shown that the reference prior for the parameter of interest (the signal intensity) can be well approximated by the widely (ab)used flat prior only when the expected background is very high. On the other hand, a very simple approximation (the limiting form of the reference prior for perfect prior background knowledge) can be safely used over a large portion of the background parameters space. The resulting approximate reference posterior is a Gamma density whose parameters are related to the observed counts. This limiting form is simpler than the result obtained with a flat prior, with the additional advantage of representing a much closer approximation to the reference posterior in all cases. Hence such limiting prior should be considered a better default or conventional prior than the uniform prior. On the computing side, it is shown that a 2-parameter fitting function is able to reproduce extremely well the reference prior for any background prior. Thus, it can be useful in applications requiring the evaluation of the reference prior for a very large number of times.
Leading corrections to local approximations. II. The case with turning points
Ribeiro, Raphael F.; Burke, Kieron
2017-03-01
Quantum corrections to Thomas-Fermi (TF) theory are investigated for noninteracting one-dimensional fermions with known uniform semiclassical approximations to the density and kinetic energy. Their structure is analyzed, and contributions from distinct phase space regions (classically-allowed versus forbidden at the Fermi energy) are derived analytically. Universal formulas are derived for both particle numbers and energy components in each region. For example, in the semiclassical limit, exactly (6π √{3 }) -1 of a particle leaks into the evanescent region beyond a turning point. The correct normalization of semiclassical densities is proven analytically in the semiclassical limit. Energies and densities are tested numerically in a variety of one-dimensional potentials, especially in the limit where TF theory becomes exact. The subtle relation between the pointwise accuracy of the semiclassical approximation and integrated expectation values is explored. The limitations of the semiclassical formulas are also investigated when the potential varies too rapidly. The approximations are shown to work for multiple wells, except right at the mid-phase point of the evanescent regions. The implications for density functional approximations are discussed.
Casadei, Diego
2014-01-01
The objective Bayesian treatment of a model representing two independent Poisson processes, labelled as "signal" and "background" and both contributing additively to the total number of counted events, is considered. It is shown that the reference prior for the parameter of interest (the signal intensity) is well approximated by the widely (ab)used flat prior only when the expected background is very high. For a large portion of the background parameters space, a very simple approximation (the asymptotic form of the reference prior for the limit of perfect prior background knowledge) can be safely used. In all cases, this approximation outperforms the uniform prior. When the asymptotic prior is not good enough, a simple 1-parameter fitting function is often sufficient to obtain an objective Bayesian solution. Otherwise, it is shown that a 2-parameters fitting function is able to reproduce the reference prior in all other cases. The latter is also useful to speed-up the computing time, which can be useful in a...
Population structure of Staphylococcus aureus from remote African Babongo Pygmies.
Directory of Open Access Journals (Sweden)
Frieder Schaumburg
Full Text Available BACKGROUND: Pandemic community-acquired methicillin-resistant Staphylococcus aureus isolates (CA-MRSA predominantly encode the Panton-Valentine leukocidin (PVL, which can be associated with severe infections. Reports from non-indigenous Sub-Saharan African populations revealed a high prevalence of PVL-positive isolates. The objective of our study was to investigate the S. aureus carriage among a remote indigenous African population and to determine the molecular characteristics of the isolates, particularly those that were PVL-positive. METHODOLOGY/PRINCIPAL FINDINGS: Nasal S. aureus carriage and risk factors of colonization were systematically assessed in remote Gabonese Babongo Pygmies. Susceptibility to antibiotics, possession of toxin-encoding genes (i.e., PVL, enterotoxins, and exfoliative toxins, S. aureus protein A (spa types and multi-locus sequence types (MLST were determined for each isolate. The carriage rate was 33%. No MRSA was detected, 61.8% of the isolates were susceptible to penicillin. Genes encoding PVL (55.9%, enterotoxin B (20.6%, exfoliative toxin D (11.7% and the epidermal cell differentiation inhibitor B (11.7% were highly prevalent. Thirteen spa types were detected and were associated with 10 STs predominated by ST15, ST30, ST72, ST80, and ST88. CONCLUSIONS: The high prevalence of PVL-positive isolates among Babongo Pygmies demands our attention as PVL can be associated with necrotinzing infection and may increase the risk of severe infections in remote Pygmy populations. Many S. aureus isolates from Babongo Pygmies and pandemic CA-MRSA-clones have a common genetic background. Surveillance is needed to control the development of resistance to antibiotic drugs and to assess the impact of the high prevalence of PVL in indigenous populations.
Yurkin, Maxim A; Hoekstra, Alfons G
2006-01-01
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many different discretizations. The quality of the extrapolation improves with refining discretization reaching extraordinary performance especially for cubically shaped particles. A two order of magnitude decrease of error was demonstrated. We also propose estimates of the extrapolation error, which were proven to be reliable. Finally we propose a simple method to directly separate shape and discretization errors and illustrated this for one test case.
A viscous-convective instability in laminar Keplerian thin discs. II. Anelastic approximation
Shakura, N
2015-01-01
Using the anelastic approximation of linearised hydrodynamic equations, we investigate the development of axially symmetric small perturbations in thin Keplerian discs. The sixth-order dispersion equation is derived and numerically solved for different values of relevant physical parameters (viscosity, heat conductivity, disc semi-thickness and vertical structure). The analysis reveals the appearance of two overstable modes which split out from the classical Rayleigh inertial modes in a wide range of the parameters in both ionized and neutral gases. These modes have a viscous-convective nature and can serve as a seed for turbulence in astrophysical discs even in the absence of magnetic fields.
Evolution of the pygmy dipole resonance in Sn isotopes
Toft, H. K.; Larsen, A. C.; Bürger, A.; Guttormsen, M.; Görgen, A.; Nyhus, H. T.; Renstrøm, T.; Siem, S.; Tveten, G. M.; Voinov, A.
2011-04-01
Nuclear level density and γ-ray strength functions of Sn121,122 below the neutron separation energy are extracted with the Oslo method using the (He3,He3'γ) and (He3,αγ) reactions. The level densities of Sn121,122 display steplike structures, interpreted as signatures of neutron pair breaking. An enhancement in both strength functions, compared to standard models for radiative strength, is observed in our measurements for Eγ≳5.2 MeV. This enhancement is compatible with pygmy resonances centered at ≈8.4(1) and ≈8.6(2) MeV, respectively, and with integrated strengths corresponding to ≈1.8-5+1% of the classical Thomas-Reiche-Kuhn sum rule. Similar resonances were also seen in Sn116-119. Experimental neutron-capture cross reactions are well reproduced by our pygmy resonance predictions, while standard strength models are less successful. The evolution as a function of neutron number of the pygmy resonance in Sn116-122 is described as a clear increase of centroid energy from 8.0(1) to 8.6(2) MeV, but with no observable difference in integrated strengths.
Montoya-Castillo, Andrés
2016-01-01
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. $\\bf{144}$, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function $\\mathcal{C}_{zz}...
Heng, Kevin; Lee, Jaemin
2014-01-01
We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We further demonstrate that traditional non-isothermal treatments of each atmospheric layer lead to unphysical contributions to the ...
Energy Technology Data Exchange (ETDEWEB)
Novaes, Marcel [Instituto de Física, Universidade Federal de Uberlândia, Av. João Naves de Ávila, 2121, Uberlândia, MG 38408-100 (Brazil)
2015-06-15
We consider S-matrix correlation functions for a chaotic cavity having M open channels, in the absence of time-reversal invariance. Relying on a semiclassical approximation, we compute the average over E of the quantities Tr[S{sup †}(E − ϵ) S(E + ϵ)]{sup n}, for general positive integer n. Our result is an infinite series in ϵ, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = − iħS{sup †}dS/dE and check that the first 8 of them agree with the random matrix theory prediction from our previous paper [M. Novaes, J. Math. Phys. 56, 062110 (2015)].
Montoya-Castillo, Andrés; Reichman, David R
2017-02-28
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩, we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.
Energy Technology Data Exchange (ETDEWEB)
Ashley, Paul
1992-06-01
The Northwest Power Planning Council and the Bonneville Power Administration approved the pygmy rabbit project as partial mitigation for impacts caused by the construction of Grand Coulee Dam. The focus of this project is the protection and enhancement of shrub-steppe/pygmy rabbit habitat in northeastern Washington.
Fine structure of the pygmy dipole resonance in (136)Xe.
Savran, D; Fritzsche, M; Hasper, J; Lindenberg, K; Müller, S; Ponomarev, V Yu; Sonnabend, K; Zilges, A
2008-06-13
The photoresponse of the semimagic N=82 nucleus (136)Xe was measured up to the neutron separation energy S(n) using the (gamma, gamma') reaction. A concentration of strong dipole excitations is observed well below S(n) showing a fragmented resonancelike structure. Microscopic calculations in the quasiparticle phonon model including complex configurations of up to three phonons agree well with the experimental data in the total integrated strength, in the shape and the fragmentation of the resonance, which allows us to draw conclusions on the damping mechanism of the pygmy dipole resonance.
Energy Technology Data Exchange (ETDEWEB)
Blain, M.A.; Bonnaud, G.; Chiron, A.; Riazuelo, G.
1996-02-01
This report addresses the propagation of an intense laser beam in a unmagnetized plasma, which is relevant for both the inertial confinement fusion (ICF) and the ultra-high intensity (UHI) pulses. The width and the irradiance of the laser pulses are respectively: (0.1-10) nanosecond and (10{sup 13}-10{sup 16}) W/cm{sup 2} for the ICF context and (0.1-1) picosecond and in excess of 10{sup 1}8 W/cm{sup 2} for the UHI context. The nonlinear mechanisms for beam self-focusing and filamentation, induced by both the ponderomotive expelling of charged particles and the relativistic increase of the electron mass, are specified studied. Part I deals with the theoretical aspects and part II is concerned with the results of two-dimensional simulations. The results have been obtained within the framework of the paraxial approximation and the stationary response of the plasma. The large set of scenarios that characterize the behavior of Gaussian beam and a modulated beam is presented; a synthetic overview of the previous theoretical works is also provided. The interplay of two crossing beams is discussed. This report will be a help to improve the uniformity of the laser irradiation in the ICF context and to channel a very intense laser beam over large distance in the UHI context. (authors). 17 refs., 53 figs., 14 tabs.
Recent acquisition of Helicobacter pylori by Baka pygmies.
Directory of Open Access Journals (Sweden)
Sandra Nell
Full Text Available Both anatomically modern humans and the gastric pathogen Helicobacter pylori originated in Africa, and both species have been associated for at least 100,000 years. Seven geographically distinct H. pylori populations exist, three of which are indigenous to Africa: hpAfrica1, hpAfrica2, and hpNEAfrica. The oldest and most divergent population, hpAfrica2, evolved within San hunter-gatherers, who represent one of the deepest branches of the human population tree. Anticipating the presence of ancient H. pylori lineages within all hunter-gatherer populations, we investigated the prevalence and population structure of H. pylori within Baka Pygmies in Cameroon. Gastric biopsies were obtained by esophagogastroduodenoscopy from 77 Baka from two geographically separated populations, and from 101 non-Baka individuals from neighboring agriculturalist populations, and subsequently cultured for H. pylori. Unexpectedly, Baka Pygmies showed a significantly lower H. pylori infection rate (20.8% than non-Baka (80.2%. We generated multilocus haplotypes for each H. pylori isolate by DNA sequencing, but were not able to identify Baka-specific lineages, and most isolates in our sample were assigned to hpNEAfrica or hpAfrica1. The population hpNEAfrica, a marker for the expansion of the Nilo-Saharan language family, was divided into East African and Central West African subpopulations. Similarly, a new hpAfrica1 subpopulation, identified mainly among Cameroonians, supports eastern and western expansions of Bantu languages. An age-structured transmission model shows that the low H. pylori prevalence among Baka Pygmies is achievable within the timeframe of a few hundred years and suggests that demographic factors such as small population size and unusually low life expectancy can lead to the eradication of H. pylori from individual human populations. The Baka were thus either H. pylori-free or lost their ancient lineages during past demographic fluctuations. Using
Tsai, Cheng-Hsiu; Fordyce, R. Ewan
2015-01-01
Ancestor–descendant relationships (ADRs), involving descent with modification, are the fundamental concept in evolution, but are usually difficult to recognize. We examined the cladistic relationship between the only reported fossil pygmy right whale, †Miocaperea pulchra, and its sole living relative, the enigmatic pygmy right whale Caperea marginata, the latter represented by both adult and juvenile specimens. †Miocaperea is phylogenetically bracketed between juvenile and adult Caperea margi...
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Hauke eEgermann
2015-01-01
Full Text Available Subjective and psychophysiological emotional responses to music from two different cultures were compared within these two cultures. Two identical experiments were conducted: the first in the Congolese rainforest with an isolated population of Mbenzélé Pygmies without any exposure to Western music and culture, the second with a group of Western music listeners, with no experience with Congolese music. Forty Pygmies and 40 Canadians listened in pairs to 19 music excerpts of 29 to 99 seconds in duration in random order (8 from the Pygmy population and 11 Western instrumental excerpts. For both groups, emotion components were continuously measured: subjective feeling (using a two- dimensional valence and arousal rating interface, peripheral physiological activation, and facial expression. While Pygmy music was rated as positive and arousing by Pygmies, ratings of Western music by Westerners covered the range from arousing to calming and from positive to negative. Comparing psychophysiological responses to emotional qualities of Pygmy music across participant groups showed no similarities. However, Western stimuli, rated as high and low arousing by Canadians, created similar responses in both participant groups (with high arousal associated with increases in subjective and physiological activation. Several low-level acoustical features of the music presented (tempo, pitch, and timbre were shown to affect subjective and physiological arousal similarly in both cultures. Results suggest that while the subjective dimension of emotional valence might be mediated by cultural learning, changes in arousal might involve a more basic, universal response to low-level acoustical characteristics of music.
XY females do better than the XX in the African pygmy mouse, Mus minutoides.
Saunders, Paul A; Perez, Julie; Rahmoun, Massilva; Ronce, Ophélie; Crochet, Pierre-André; Veyrunes, Frédéric
2014-07-01
All therian mammals have a similar XY/XX sex-determination system except for a dozen species. The African pygmy mouse, Mus minutoides, harbors an unconventional system in which all males are XY, and there are three types of females: the usual XX but also XX* and X*Y ones (the asterisk designates a sex-reversal mutation on the X chromosome). The long-term evolution of such a system is a paradox, because X*Y females are expected to face high reproductive costs (e.g., meiotic disruption and loss of unviable YY embryos), which should prevent invasion and maintenance of a sex-reversal mutation. Hence, mechanisms for compensating for the costs could have evolved in M. minutoides. Data gathered from our laboratory colony revealed that X*Y females do compensate and even show enhanced reproductive performance in comparison to the XX and XX*; they produce significantly more offspring due to (i) a higher probability of breeding, (ii) an earlier first litter, and (iii) a larger litter size, linked to (iv) a greater ovulation rate. These findings confirm that rare conditions are needed for an atypical sex-determination mechanism to evolve in mammals, and provide valuable insight into understanding modifications of systems with highly heteromorphic sex chromosomes.
Isospin Character of Low-Lying Pygmy Dipole States in Pb208 via Inelastic Scattering of O17 Ions
Crespi, F. C. L.; Bracco, A.; Nicolini, R.; Mengoni, D.; Pellegri, L.; Lanza, E. G.; Leoni, S.; Maj, A.; Kmiecik, M.; Avigo, R.; Benzoni, G.; Blasi, N.; Boiano, C.; Bottoni, S.; Brambilla, S.; Camera, F.; Ceruti, S.; Giaz, A.; Million, B.; Morales, A. I.; Vandone, V.; Wieland, O.; Bednarczyk, P.; Ciemała, M.; Grebosz, J.; Krzysiek, M.; Mazurek, K.; Zieblinski, M.; Bazzacco, D.; Bellato, M.; Birkenbach, B.; Bortolato, D.; Calore, E.; Cederwall, B.; Charles, L.; de Angelis, G.; Désesquelles, P.; Eberth, J.; Farnea, E.; Gadea, A.; Görgen, A.; Gottardo, A.; Isocrate, R.; Jolie, J.; Jungclaus, A.; Karkour, N.; Korten, W.; Menegazzo, R.; Michelagnoli, C.; Molini, P.; Napoli, D. R.; Pullia, A.; Recchia, F.; Reiter, P.; Rosso, D.; Sahin, E.; Salsac, M. D.; Siebeck, B.; Siem, S.; Simpson, J.; Söderström, P.-A.; Stezowski, O.; Theisen, Ch.; Ur, C.; Valiente-Dobón, J. J.
2014-07-01
The properties of pygmy dipole states in Pb208 were investigated using the Pb208(O17, O17'γ) reaction at 340 MeV and measuring the γ decay with high resolution with the AGATA demonstrator array. Cross sections and angular distributions of the emitted γ rays and of the scattered particles were measured. The results are compared with (γ, γ') and (p, p') data. The data analysis with the distorted wave Born approximation approach gives a good description of the elastic scattering and of the inelastic excitation of the 2+ and 3- states. For the dipole transitions a form factor obtained by folding a microscopically calculated transition density was used for the first time. This has allowed us to extract the isoscalar component of the 1- excited states from 4 to 8 MeV.
Isospin character of low-lying pygmy dipole states in 208Pb via inelastic scattering of 17O ions.
Crespi, F C L; Bracco, A; Nicolini, R; Mengoni, D; Pellegri, L; Lanza, E G; Leoni, S; Maj, A; Kmiecik, M; Avigo, R; Benzoni, G; Blasi, N; Boiano, C; Bottoni, S; Brambilla, S; Camera, F; Ceruti, S; Giaz, A; Million, B; Morales, A I; Vandone, V; Wieland, O; Bednarczyk, P; Ciemała, M; Grebosz, J; Krzysiek, M; Mazurek, K; Zieblinski, M; Bazzacco, D; Bellato, M; Birkenbach, B; Bortolato, D; Calore, E; Cederwall, B; Charles, L; de Angelis, G; Désesquelles, P; Eberth, J; Farnea, E; Gadea, A; Görgen, A; Gottardo, A; Isocrate, R; Jolie, J; Jungclaus, A; Karkour, N; Korten, W; Menegazzo, R; Michelagnoli, C; Molini, P; Napoli, D R; Pullia, A; Recchia, F; Reiter, P; Rosso, D; Sahin, E; Salsac, M D; Siebeck, B; Siem, S; Simpson, J; Söderström, P-A; Stezowski, O; Theisen, Ch; Ur, C; Valiente-Dobón, J J
2014-07-04
The properties of pygmy dipole states in 208Pb were investigated using the 208Pb(17O, 17O'γ) reaction at 340 MeV and measuring the γ decay with high resolution with the AGATA demonstrator array. Cross sections and angular distributions of the emitted γ rays and of the scattered particles were measured. The results are compared with (γ, γ') and (p, p') data. The data analysis with the distorted wave Born approximation approach gives a good description of the elastic scattering and of the inelastic excitation of the 2+ and 3- states. For the dipole transitions a form factor obtained by folding a microscopically calculated transition density was used for the first time. This has allowed us to extract the isoscalar component of the 1- excited states from 4 to 8 MeV.
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Alejandro Romero
Full Text Available Pygmy hunter-gatherers from Central Africa have shared a network of socioeconomic interactions with non-Pygmy Bantu speakers since agropastoral lifestyle spread across sub-Saharan Africa. Ethnographic studies have reported that their diets differ in consumption of both animal proteins and starch grains. Hunted meat and gathered plant foods, especially underground storage organs (USOs, are dietary staples for pygmies. However, scarce information exists about forager-farmer interaction and the agricultural products used by pygmies. Since the effects of dietary preferences on teeth in modern and past pygmies remain unknown, we explored dietary history through quantitative analysis of buccal microwear on cheek teeth in well-documented Baka pygmies. We then determined if microwear patterns differ among other Pygmy groups (Aka, Mbuti, and Babongo and between Bantu-speaking farmer and pastoralist populations from past centuries. The buccal dental microwear patterns of Pygmy hunter-gatherers and non-Pygmy Bantu pastoralists show lower scratch densities, indicative of diets more intensively based on nonabrasive foodstuffs, compared with Bantu farmers, who consume larger amounts of grit from stoneground foods. The Baka pygmies showed microwear patterns similar to those of ancient Aka and Mbuti, suggesting that the mechanical properties of their preferred diets have not significantly changed through time. In contrast, Babongo pygmies showed scratch densities and lengths similar to those of the farmers, consistent with sociocultural contacts and genetic factors. Our findings support that buccal microwear patterns predict dietary habits independent of ecological conditions and reflect the abrasive properties of preferred or fallback foods such as USOs, which may have contributed to the dietary specializations of ancient human populations.
Dratman, Ezequiel
2011-01-01
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if the absorption is large enough, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the "continuous" equation. Furthermore, we exhibit an algorithm computing an $\\epsilon$-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is {\\em linear} in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.
Addisonian Crisis due to Metastatic Adenocarcinoma in a Pygmy Goat
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Nora Nogradi
2013-01-01
Full Text Available A 15-year-old Pygmy doe was evaluated for acute onset of lethargy, anorexia, and weakness. Adrenal insufficiency was diagnosed based on physical exam findings, blood work abnormalities (hyponatremia, hyperkalemia, azotemia, and hypoglycemia, and lack of cortisol response to the ACTH stimulation test. Abdominal ultrasound exam revealed an intact urinary tract and multiple bilateral peri-renal masses. The doe was treated with intravenous fluid therapy aimed at correcting the electrolyte abnormalities and intravenous corticosteroids. She responded favorably to medical therapy in 24 hours, with dramatic improvement in attitude and appetite. Fluid therapy was discontinued, and the doe was discharged from the hospital on steroid supplementation. She deteriorated rapidly and died at home 36 hours after discharge. Necropsy results revealed metastatic adenocarcinoma originating from the uterus that infiltrated the urinary bladder, the region of the adrenal glands, the left and right renal lymph nodes, the left kidney, the caudal vena cava, the submandibular lymph nodes, the diaphragm, the lungs, and the omentum. Addison’s syndrome in ruminants should be considered as an uncommon sequel of intra-abdominal neoplastic processes.
Iwamoto, C.; Utsunomiya, H.; Tamii, A.; Akimune, H.; Nakada, H.; Shima, T.; Yamagata, T.; Kawabata, T.; Fujita, Y.; Matsubara, H.; Shimbara, Y.; Nagashima, M.; Suzuki, T.; Fujita, H.; Sakuda, M.; Mori, T.; Izumi, T.; Okamoto, A.; Kondo, T.; Bilgier, B.; Kozer, H. C.; Lui, Y.-W.; Hatanaka, K.
2012-06-01
A high-resolution measurement of inelastic proton scattering off Zr90 near 0° was performed at 295 MeV with a focus on a pronounced strength previously reported in the low-energy tail of giant dipole resonance. A forest of fine structure was observed in the excitation energy region 7-12 MeV. A multipole decomposition analysis of the angular distribution for the forest was carried out using the ECIS95 distorted-wave Born approximation code with the Hartree-Fock plus random-phase approximation model of E1 and M1 transition densities and inclusion of E1 Coulomb excitation. The analysis separated pygmy dipole and M1 resonances in the forest at EPDR=9.15±0.18MeV with ΓPDR=2.91±0.64MeV and at EM1=9.53±0.06MeV with ΓM1=2.70±0.17MeV in the Lorentzian function, respectively. The B(E1)↑ value for pygmy dipole resonance over 7-11 MeV is 0.75±0.08e2fm2, which corresponds to 2.1±0.2% of the Thomas-Reiche-Kuhn sum rule.
Kovács, M; Lindgren, F
2012-01-01
We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation.
Observation of double pygmy resonances in $^{195,196}$Pt and enhanced astrophysical reaction rates
Giacoppo, F; Eriksen, T K; Görgen, A; Guttormsen, M; Hagen, T W; Larsen, A C; Kheswa, B V; Klintefjord, M; Koehler, P E; Nyhus, H T; Renstr\\om, T; Sahin, E; Siem, S; Tornyi, T G
2014-01-01
Our measurements of $^{195,196}$Pt $\\gamma$-strength functions show a double-humped enhancement in the $E_{\\gamma}= 4-8$ MeV region. For the first time, the detailed shape of these resonances is revealed for excitation energies in the quasicontinuum. We demonstrate that the corresponding neutron-capture cross sections and astrophysical reaction rates are increased by up to a factor of 2 when these newly observed pygmy resonances are included. These results lend credence to theoretical predictions of enhanced reaction rates due to such pygmy resonances and hence are important for a better understanding of r-process nucleosynthesis.
Tsai, Cheng-Hsiu; Fordyce, R Ewan
2015-01-01
Ancestor-descendant relationships (ADRs), involving descent with modification, are the fundamental concept in evolution, but are usually difficult to recognize. We examined the cladistic relationship between the only reported fossil pygmy right whale, †Miocaperea pulchra, and its sole living relative, the enigmatic pygmy right whale Caperea marginata, the latter represented by both adult and juvenile specimens. †Miocaperea is phylogenetically bracketed between juvenile and adult Caperea marginata in morphologically based analyses, thus suggesting a possible ADR-the first so far identified within baleen whales (Cetacea: Mysticeti). The †Miocaperea-Caperea lineage may show long-term morphological stasis and, in turn, punctuated equilibrium.
Control of luminescence from pygmy shark (Squaliolus aliae) photophores.
Claes, Julien M; Ho, Hsuan-Ching; Mallefet, Jérôme
2012-05-15
The smalleye pygmy shark (Squaliolus aliae) is a dwarf pelagic shark from the Dalatiidae family that harbours thousands of tiny photophores. In this work, we studied the organisation and physiological control of these photogenic organs. Results show that they are mainly situated on the ventral side of the shark, forming a homogeneous ventral photogenic area that appears well suited for counterillumination, a well-known camouflage technique of pelagic organisms. Isolated ventral skin patches containing photophores did not respond to classical neurotransmitters and nitric oxide but produced light after melatonin (MT) application. Prolactin and α-melanocyte-stimulating hormone inhibited this hormonally induced luminescence as well as the spontaneous luminescence from the photogenic tissue. The action of MT seems to be mediated by binding to the MT(2) receptor subtype, as the MT(2) receptor agonist 4P-PDOT inhibited the luminescence induced by this hormone. Binding to this receptor probably decreases the intracellular cAMP concentration because forskolin inhibited spontaneous and MT-induced luminescence. In addition, a GABA inhibitory tonus seems to be present in the photogenic tissue as well, as GABA inhibited MT-induced luminescence and the application of bicuculline provoked luminescence from S. aliae photophores. Similarly to what has been found in Etmopteridae, the other luminous shark family, the main target of the luminescence control appears to be the melanophores covering the photocytes. Results suggest that bioluminescence first appeared in Dalatiidae when they adopted a pelagic style at the Cretaceous/Tertiary boundary, and was modified by Etmopteridae when they started to colonize deep-water niches and rely on this light for intraspecific behaviours.
DEFF Research Database (Denmark)
Ruban, Andrei; Simak, S.I.; Korzhavyi, P.A.
2002-01-01
-electron potential and energy. In the case of a random alloy such interactions can be accounted for only by lifting the atomic-sphere and single-site approximations, in order to include the polarization due to local environment effects. Nevertheless, a simple parametrization of the screened Coulomb interactions...... for the ordinary single-site methods, including the generalized perturbation method, is still possible. We obtained such a parametrization for bulk and surface NiPt alloys, which allows one to obtain quantitatively accurate effective interactions in this system....
Nature of the pygmy dipole resonance in Ce-140 studied in (alpha, alpha 'gamma) experiments
Savran, D.; Babilon, M.; van den Berg, A. M.; Harakeh, M. N.; Hasper, J.; Matic, A.; Wortche, H. J.; Zilges, A.
2006-01-01
A concentration of electric-dipole excitations below the particle threshold, which is frequently denoted as the pygmy dipole resonance, has been studied in the semimagic nucleus Ce-140 in (alpha, alpha(')gamma) experiments at E-alpha=136 MeV. The technique of alpha-gamma coincidence experiments allo
Investigation of the Pygmy Dipole Resonance in (alpha, alpha 'gamma) coincidence experiments
Savran, D.; Babilon, M.; van den Berg, A. M.; Harakeh, M. N.; Hasper, J.; Wortche, H. J.; Zilges, A.
2007-01-01
We report on first results from experiments using the (alpha, alpha'gamma) reaction at E alpha = 136 MeV to investigate bound electric dipole (El) excitations building the so-called Pygmy Dipole Resonance (PDR) in the semi-magic nucleus Ce-140. The method of (alpha, alpha'gamma) allows the separatio
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E Biezakala Mudiandambu
2012-01-01
Full Text Available In a survey among the pygmies of central Democratic Republic of Congo, the incidence of scorpion stings seemed very high with a severity greater than expected. Species responsible were not identified. Specific studies are needed to clarify the risk emerging in the equatorial African forest.
2013-10-02
... from juried (peer-reviewed) professional journals whenever available. All decisions are made on the... commenter postulated that mechanical disturbance and siltation actually benefit the spring pygmy sunfish. He... the species weighed against the benefits provided through the current and proposed CCAAs. The...
Klabucar, D; Mekterovic, D; Podobnik, B
2003-01-01
If instantons are introduced into the MIT bag model in such a way that bag radii are allowed to vary, the MIT bag interior can accommodate instanton density which is by an order of magnitude larger than in the case when the radii are fixed (although it is still significantly smaller than in the nonperturbative QCD vacuum). The instanton contribution to baryon mass shifts is also correspondingly larger. The instanton-induced part of the scalar strangeness of the nucleon MIT bag is an order of magnitude larger than found previously, within the linearized approximation. The decrease of the model radii (which is associated with the increase of the instanton density) is very favorable from the standpoint of nuclear physics.
DiBattista, Joseph D.; Waldrop, Ellen; Bowen, Brian W.; Schultz, Jennifer K.; Gaither, Michelle R.; Pyle, Richard L.; Rocha, Luiz A.
2012-09-01
The delineation of reef fish species by coloration is problematic, particularly for the pygmy angelfishes (genus Centropyge), whose vivid colors are sometimes the only characters available for taxonomic classification. The Lemonpeel Angelfish ( Centropyge flavissima) has Pacific and Indian Ocean forms separated by approximately 3,000 km and slight differences in coloration. These disjunct populations hybridize with Eibl's Angelfish ( Centropyge eibli) in the eastern Indian Ocean and the Pearl-Scaled Angelfish ( Centropyge vrolikii) in the western Pacific. To resolve the evolutionary history of these species and color morphs, we employed mitochondrial DNA (mtDNA) cytochrome b and three nuclear introns (TMO, RAG2, and S7). Phylogenetic analyses reveal three deep mtDNA lineages ( d = 7.0-8.3 %) that conform not to species designation or color morph but to geographic region: (1) most Pacific C. flavissima plus C. vrolikii, (2) C. flavissima from the Society Islands in French Polynesia, and (3) Indian Ocean C. flavissima plus C. eibli. In contrast, the nuclear introns each show a cluster of closely related alleles, with frequency differences between the three geographic groups. Hence, the mtDNA phylogeny reveals a period of isolation (ca . 3.5-4.2 million years) typical of congeneric species, whereas the within-lineage mtDNA ΦST values and the nuclear DNA data reveal recent or ongoing gene flow between species. We conclude that an ancient divergence of C. flavissima, recorded in the non-recombining mtDNA, was subsequently swamped by introgression and hybridization in two of the three regions, with only the Society Islands retaining the original C. flavissima haplotypes among our sample locations. Alternatively, the yellow color pattern of C. flavissima may have appeared independently in the central Pacific Ocean and eastern Indian Ocean. Regardless of how the pattern arose, C. flavissima seems to be retaining species identity where it interbreeds with C. vrolikii and C
Epidemiology and genetic variability of HHV-8/KSHV in Pygmy and Bantu populations in Cameroon.
Directory of Open Access Journals (Sweden)
Edouard Betsem
2014-05-01
Full Text Available BACKGROUND: Kaposi's sarcoma associated herpesvirus (KSHV/HHV-8 is the causal agent of all forms of Kaposi sarcoma. Molecular epidemiology of the variable K1 region identified five major subtypes exhibiting a clear geographical clustering. The present study is designed to gain new insights into the KSHV epidemiology and genetic diversity in Cameroon. METHODOLOGY/PRINCIPAL FINDINGS: Bantu and Pygmy populations from remote rural villages were studied. Antibodies directed against latent nuclear antigens (LANA were detected by indirect immunofluorescence using BC3 cells. Peripheral blood cell DNAs were subjected to a nested PCR amplifying a 737 bp K1 gene fragment. Consensus sequences were phylogenetically analyzed. We studied 2,063 persons (967 females, 1,096 males, mean age 39 years, either Bantus (1,276 or Pygmies (787. The Bantu group was older (42 versus 35 years: P<10(-4. KSHV anti-LANA seroprevalence was of 37.2% (768/2063, with a significant increase with age (P<10(-4 but no difference according to sex. Seroprevalence, as well as the anti-LANA antibodies titres, were higher in Bantus (43.2% than in Pygmies (27.6% (P<10(-4, independently of age. We generated 29 K1 sequences, comprising 24 Bantus and five Pygmies. These sequences belonged to A5 (24 cases or B (five cases subtypes. They exhibited neither geographical nor ethnic aggregation. A5 strains showed a wide genetic diversity while the B strains were more homogenous and belonged to the B1 subgroup. CONCLUSION: These data demonstrate high KSHV seroprevalence in the two major populations living in Southern and Eastern Cameroon with presence of mostly genetically diverse A5 but also B K1 subtypes.
Excitation of pygmy dipole resonance in neutron-rich nuclei via Coulomb and nuclear fields
Indian Academy of Sciences (India)
A Vitturi; E G Lanza; M V Andrés; F Catara; D Gambacurta
2010-07-01
We study the nature of the low-lying dipole strength in neutron-rich nuclei, often associated with the pygmy dipole resonance. The states are described within the Hartree–Fock plus RPA formalism, using different parametrizations of the Skyrme inter-action. We show how the information from combined reaction processes involving the Coulomb and different mixtures of isoscalar and isovector nuclear interactions can provide a clue to reveal the characteristic features of these states.
Detection of shrew-borne hantavirus in Eurasian pygmy shrew (Sorex minutus) in Central Europe.
Radosa, Lukáš; Schlegel, Mathias; Gebauer, Petra; Ansorge, Hermann; Heroldová, Marta; Jánová, Eva; Stanko, Michal; Mošanský, Ladislav; Fričová, Jana; Pejčoch, Milan; Suchomel, Josef; Purchart, Luboš; Groschup, Martin H; Krüger, Detlev H; Ulrich, Rainer G; Klempa, Boris
2013-10-01
Recently, it was found that not only rodents but also shrews are reservoir hosts of hantaviruses. In Central Europe, only Seewis virus, associated with the Eurasian common shrew (Sorex araneus), has been recognized until now. In the present report, tissue samples from shrews belonging to Crocidurinae and Soricinae subfamilies, trapped in Czech Republic, Germany, and Slovakia, were screened for the presence of novel hantaviruses. Three new hantavirus partial L-segment sequences were obtained from pygmy shrews (Sorex minutus) trapped in Czech Republic and Germany. Complete nucleocapsid protein- and glycoprotein precursor-coding S- and M-segment sequences were then determined for the newly recognized hantavirus strains, CZ/Beskydy/412/2010/Sm, CZ/Drahany/420/2010/Sm, and DE/Dürrbach/1912/2009/Sm. Phylogenetic analyses showed that they represent strains of Asikkala virus (ASIV), a novel hantavirus also found in pygmy shrews from Finland. Our study reveals a broad geographic distribution of ASIV across Europe and indicates pygmy shrew as the primary reservoir host. Future studies will have to determine the pathogenic relevance of ASIV.
Relativistic quasiparticle random phase approximation in deformed nuclei
Energy Technology Data Exchange (ETDEWEB)
Pena Arteaga, D.
2007-06-25
Covariant density functional theory is used to study the influence of electromagnetic radiation on deformed superfluid nuclei. The relativistic Hartree-Bogolyubov equations and the resulting diagonalization problem of the quasiparticle random phase approximation are solved for axially symmetric systems in a fully self-consistent way by a newly developed parallel code. Three different kinds of high precision energy functionals are investigated and special care is taken for the decoupling of the Goldstone modes. This allows the microscopic investigation of Pygmy and scissor resonances in electric and magnetic dipole fields. Excellent agreement with recent experiments is found and new types of modes are predicted for deformed systems with large neutron excess. (orig.)
Hierarchical spatial models for predicting pygmy rabbit distribution and relative abundance
Wilson, T.L.; Odei, J.B.; Hooten, M.B.; Edwards, T.C.
2010-01-01
Conservationists routinely use species distribution models to plan conservation, restoration and development actions, while ecologists use them to infer process from pattern. These models tend to work well for common or easily observable species, but are of limited utility for rare and cryptic species. This may be because honest accounting of known observation bias and spatial autocorrelation are rarely included, thereby limiting statistical inference of resulting distribution maps. We specified and implemented a spatially explicit Bayesian hierarchical model for a cryptic mammal species (pygmy rabbit Brachylagus idahoensis). Our approach used two levels of indirect sign that are naturally hierarchical (burrows and faecal pellets) to build a model that allows for inference on regression coefficients as well as spatially explicit model parameters. We also produced maps of rabbit distribution (occupied burrows) and relative abundance (number of burrows expected to be occupied by pygmy rabbits). The model demonstrated statistically rigorous spatial prediction by including spatial autocorrelation and measurement uncertainty. We demonstrated flexibility of our modelling framework by depicting probabilistic distribution predictions using different assumptions of pygmy rabbit habitat requirements. Spatial representations of the variance of posterior predictive distributions were obtained to evaluate heterogeneity in model fit across the spatial domain. Leave-one-out cross-validation was conducted to evaluate the overall model fit. Synthesis and applications. Our method draws on the strengths of previous work, thereby bridging and extending two active areas of ecological research: species distribution models and multi-state occupancy modelling. Our framework can be extended to encompass both larger extents and other species for which direct estimation of abundance is difficult. ?? 2010 The Authors. Journal compilation ?? 2010 British Ecological Society.
Test of the Brink-Axel hypothesis for the pygmy dipole resonance
Martin, D; Tamii, A; Aoi, N; Bassauer, S; Bertulani, C A; Carter, J; Donaldson, L; Fujita, H; Fujita, Y; Hashimoto, T; Hatanaka, K; Ito, T; Krugmann, A; Liu, B; Maeda, Y; Miki, K; Neveling, R; Pietralla, N; Poltoratska, I; Ponomarev, V Yu; Richter, A; Shima, T; Yamamoto, T; Zweidinger, M
2016-01-01
The gamma strength function (GSF) and level density (LD) of 1- states in 96Mo have been extracted from a high-resolution study of the (p,p') reaction at 295 MeV and extreme forward angles. The GSF agrees with results of compound nucleus gamma decay experiments in the energy region of the Pygmy Dipole Resonance (PDR), validating the generalized Brink-Axel hypothesis commonly assumed in astrophysical reaction network calculations. The consistency of the LD deduced from the present data with those of the gamma decay experiments provides independent confirmation of the methods used to separate GSF and LD in Oslo-type experiments.
Annalaura Mancia; Spyropoulos, Demetri D; McFee, Wayne E; Newton, Danforth A; Baatz, John E
2012-01-01
Current models for in vitro studies of tissue function and physiology, including responses to hypoxia or environmental toxins, are limited and rely heavily on standard 2-dimensional (2-D) cultures with immortalized murine or human cell lines. To develop a new more powerful model system, we have pursued methods to establish and expand cultures of primary lung cell types and reconstituted tissues from marine mammals. What little is known about the physiology of the deep-sea diving pygmy sperm whale (PSW), Kogia breviceps, comes primarily from stranding events that occur along the coast of the southeastern United States. Thus, development of a method for preserving live tissues and retrieving live cells from deceased stranded individuals was initiated. This report documents successful cryopreservation of PSW lung tissue. We established in vitro cultures of primary lung cell types from tissue fragments that had been cryopreserved several months earlier at the stranding event. Dissociation of cryopreserved lung tissues readily provides a variety of primary cell types that, to varying degrees, can be expanded and further studied/manipulated in cell culture. In addition, PSW-specific molecular markers have been developed that permitted the monitoring of fibroblast, alveolar type II, and vascular endothelial cell types. Reconstitution of 3-D cultures of lung tissues with these cell types is now underway. This novel system may facilitate the development of rare or disease-specific lung tissue models (e.g., to test causes of PSW stranding events and lead to improved treatments for pulmonary hypertension or reperfusion injury in humans). Also, the establishment of a "living" tissue bank biorepository for rare/endangered species could serve multiple purposes as surrogates for freshly isolated samples.
The pygmy quadrupole resonance and neutron-skin modes in 124Sn
Spieker, M.; Tsoneva, N.; Derya, V.; Endres, J.; Savran, D.; Harakeh, M. N.; Harissopulos, S.; Herzberg, R.-D.; Lagoyannis, A.; Lenske, H.; Pietralla, N.; Popescu, L.; Scheck, M.; Schlüter, F.; Sonnabend, K.; Stoica, V. I.; Wörtche, H. J.; Zilges, A.
2016-01-01
We present an extensive experimental study of the recently predicted pygmy quadrupole resonance (PQR) in Sn isotopes, where complementary probes were used. In this study, (α ,α‧ γ) and (γ ,γ‧) experiments were performed on 124Sn. In both reactions, Jπ =2+ states below an excitation energy of 5 MeV were populated. The E2 strength integrated over the full transition densities could be extracted from the (γ ,γ‧) experiment, while the (α ,α‧ γ) experiment at the chosen kinematics strongly favors the excitation of surface modes because of the strong α-particle absorption in the nuclear interior. The excitation of such modes is in accordance with the quadrupole-type oscillation of the neutron skin predicted by a microscopic approach based on self-consistent density functional theory and the quasiparticle-phonon model (QPM). The newly determined γ-decay branching ratios hint at a non-statistical character of the E2 strength, as it has also been recently pointed out for the case of the pygmy dipole resonance (PDR). This allows us to distinguish between PQR-type and multiphonon excitations and, consequently, supports the recent first experimental indications of a PQR in 124Sn.
Organochlorine Pesticides in the Ferruginous Pygmy Owl (Glaucidium brasilianum) in Chiapas, Mexico.
Arrona-Rivera, Alicia E; Enríquez, Paula L; García-Feria, Luis M; Orellana, Sergio Alvarado; von Osten, Jaime Rendón
2016-09-01
Concentrations of organochlorine pesticides were quantified in samples of feathers (n = 17) and blood (n = 15) of the ferruginous pygmy owl (Glaucidium brasilianum). The individuals were captured near the Protected Natural Area Cerro Sonsonate, Chiapas, Mexico, between February and June 2014. In both tissues, pesticides belonging to seven organochlorine chemical families were detected. However, the organochlorine pesticide concentrations differed between feathers and blood. The highest concentrations of hexachlorocyclohexanes were found in feathers (0.63 ± 0.89 μg/g), whereas the highest concentrations of ΣDrines were found in blood (0.31 ± 0.47 μg/mL). By using the summed concentrations for each of the seven families of pesticides found in feathers, we did not find any significant correlation between the pesticides and pectoral muscle or body weight (p > 0.15). The ΣDDT group was the only pesticide family that showed a positive correlation with owl body weight (r = 0.60, p = 0.05); the concentrations of these pesticides were also high in feather and blood tissues (r = 0.87, p = 0.02). Our results confirm that ferruginous pygmy owls in the study area are exposed to these pesticides.
The pygmy right whale Caperea marginata: the last of the cetotheres.
Fordyce, R Ewan; Marx, Felix G
2013-02-22
The pygmy right whale, Caperea marginata, is the most enigmatic of the living baleen whales (Mysticeti). Its highly disparate morphology and the virtual absence of a described fossil record have made it extremely difficult to place Caperea into a broader evolutionary context, and molecular and morphological studies have frequently contradicted each other as to the origins and phylogenetic relationships of the species. Our study of a wealth of material from New Zealand collections, representing a wide range of ontogenetic stages, has identified several new features previously unreported in Caperea, which suggest that the pygmy right whale may be the last survivor of the supposedly extinct family Cetotheriidae. This hypothesis is corroborated by both morphology-based and total evidence cladistic analyses, including 166 morphological characters and 23 taxa, representing all the living and extinct families of toothless baleen whales. Our results allow us to formally refer Caperea to Cetotheriidae, thus resurrecting the latter from extinction and helping to clarify the origins of a long-problematic living species.
Gál, János; Hornyák, Ákos; Mándoki, Míra; Bakonyi, Tamás; Balka, Gyula; Szeredi, Levente; Marosán, Miklós; Ludányi, Tibor; Forgách, Petra; Sós, Endre; Demeter, Zoltán; Farkas, Szilvia L
2013-12-27
We describe the detection and successful isolation of a novel mastadenovirus from a pygmy marmoset (Callithrix [Cebuella] pygmaea) that died following an episode of severe respiratory signs. Pathologic/histopathologic examination revealed hydrothorax and catarrhal bronchopneumonia with pronounced desquamation of the bronchiolar epithelial cells, while in other airways a marked hyperplasia of the epithelial lining and numerous giant cells could be observed. We obtained partial sequence data from the adenoviral DNA-dependent DNA-polymerase gene of the isolated strain and analyses of this region showed the highest level of identity to the recently described bat adenoviruses (strains PPV1 and TJM) and the type 2 canine adenovirus. Similar results were gained by phylogenetic calculations indicating that this novel marmoset adenovirus is only distantly related to reference Old and New World primate adenoviruses and formed a monophyletic group with bat and canine adenoviruses and the equine adenovirus 1. Even though the source of the infection remained unknown, our results could imply the possibility of a cross-species transmission of the virus from an anonymous host to the pygmy marmoset.
Graczyk, Magdalena; Cwiertnia, Piotr; Borowska, Alicja; Barczak, Elżbieta; Szwaczkowski, Tomasz
2015-01-01
The aim of this study was to estimate the inbreeding level and its impact on offspring sex ratio in the pygmy hippopotamus population kept in zoological gardens. Records of pygmy hippopotamus born between 1873-2013 were extracted from the international studbook. Totally, 1357 individuals originating from 148 breeding units were included (individuals with unknown sex were omitted). The offspring sex ratio is defined as the number of sons to the total number of progeny of each dam and sire. Spearman's rank correlation was employed to examine the relationships between the inbreeding level and offspring sex ratio. Inbreeding coefficients and individual increase in inbreeding coefficients (included as a linear co-variable) were examined as well as the geographic region and birth period using general linear models. The average inbreeding coefficient was 5.39%. The following sex proportion was observed for the inbred population: 57% and 43% for females and males, respectively. A significant relationship between inbreeding level of parents and their offspring sex ratio were estimated for European zoological gardens, whereas in others geographic regions the dependencies were insignificant.
Quiazon, Karl Marx A
2016-09-01
Cetaceans are definitive hosts of anisakid nematodes known to cause human anisakidosis. Despite the reported strandings of different cetaceans in the Philippines, studies on anisakids from these definitive hosts are limited. Here, the morphologically and molecularly identified anisakid species, specifically those of the genus Anisakis Dujardin, 1845 in stranded Pygmy Sperm Whale Kogia breviceps Blainville, 1838 in the west Pacific region off Philippine waters are presented. Morphological data using SEM and LM revealed multi-infections with different Anisakis species belonging to Anisakis type I and type II groups. Molecularly, PCR-RFLP on the ITS rDNA and sequence data analyses of both ITS rDNA and mtDNA cox2 regions identified those from Anisakis type I group as A. typica (Diesing, 1860), whereas those from type II group as A. brevispiculata Dollfus, 1968, and A. paggiae Mattiucci et al. (Syst Parasitol 61:157-171, 2005). This is the first record of Anisakis infection from this host stranded in the west Pacific region off the coast of Philippine waters and new geographical record for A. paggiae.
Approximate Representations and Approximate Homomorphisms
Moore, Cristopher
2010-01-01
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups: functions f:G -> U_d such that Pr[f(xy) = f(x) f(y)] is large, or more generally Exp_{x,y} ||f(xy) - f(x)f(y)||^2$ is small, where x and y are uniformly random elements of the group G and U_d denotes the unitary group of degree d. We bound these quantities in terms of the ratio d / d_min where d_min is the dimension of the smallest nontrivial representation of G. As an application, we bound the extent to which a function f : G -> H can be an approximate homomorphism where H is another finite group. We show that if H's representations are significantly smaller than G's, no such f can be much more homomorphic than a random function. We interpret these results as showing that if G is quasirandom, that is, if d_min is large, then G cannot be embedded in a small number of dimensi...
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...
Pygmy and Giant Dipole Resonances by Coulomb Excitation using a Quantum Molecular Dynamics model
Tao, C; Zhang, G Q; Cao, X G; Wang, D Q Fang H W
2012-01-01
Pygmy and Giant Dipole Resonance (PDR and GDR) in Ni isotopes have been investigated by Coulomb excitation in the framework of the Isospin-dependent Quantum Molecular Dynamics model (IQMD). The spectra of $\\gamma$ rays are calculated and the peak energy, the strength and Full Width at Half Maximum (FWHM) of GDR and PDR have been extracted. Their sensitivities to nuclear equation of state, especially to its symmetry energy term are also explored. By a comparison with the other mean-field calculations, we obtain the reasonable values for symmetry energy and its slope parameter at saturation, which gives an important constrain for IQMD model. In addition, we also studied the neutron excess dependence of GDR and PDR parameters for Ni isotopes and found that the energy-weighted sum rule (EWSR) $PDR_{m_1}/GDR_{m_1}%$ increases linearly with the neutron excess.
Energy Technology Data Exchange (ETDEWEB)
Savran, D. [Institut fuer Kernphysik, TU Darmstadt, Schlossgartenstrasse 9, D-64289 Darmstadt (Germany); Babilon, M. [Institut fuer Kernphysik, TU Darmstadt, Schlossgartenstrasse 9, D-64289 Darmstadt (Germany); Berg, A.M. van den [Kernfysisch Versneller Instituut, Rijksuniversiteit Groningen, Zernikelaan 25, NL-9747 AA Groningen (Netherlands); Harakeh, M.N. [Kernfysisch Versneller Instituut, Rijksuniversiteit Groningen, Zernikelaan 25, NL-9747 AA Groningen (Netherlands); Hasper, J. [Institut fuer Kernphysik, TU Darmstadt, Schlossgartenstrasse 9, D-64289 Darmstadt (Germany); Woertche, H.J. [Kernfysisch Versneller Instituut, Rijksuniversiteit Groningen, Zernikelaan 25, NL-9747 AA Groningen (Netherlands); Zilges, A. [Institut fuer Kernphysik, TU Darmstadt, Schlossgartenstrasse 9, D-64289 Darmstadt (Germany)
2007-05-15
We report on first results from experiments using the ({alpha},{alpha}{sup '}{gamma}) reaction at E{sub {alpha}}=136 MeV to investigate bound electric dipole (E1) excitations building the so-called Pygmy Dipole Resonance (PDR) in the semi-magic nucleus {sup 140}Ce. The method of ({alpha},{alpha}{sup '}{gamma}) allows the separation of E1 excitations from states of higher multipolarity, provides an excellent energy resolution and therefore allows a detailed analysis for each single state. Studying bound E1 excitations in {alpha}-scattering experiments at intermediate energies becomes feasible for the first time even in nuclei with a high level density. The surprising results of the first experiment on {sup 140}Ce point to a splitting of the PDR in this nucleus.
Structure and decay of the pygmy dipole resonance in 26Ne
Kimura, M
2016-01-01
The low-lying spectra of $^{24,25,26}{\\rm Ne}$ and the structure of the pygmy dipole resonance (PDR) in $^{26}{\\rm Ne}$ have been theoretically studied by the antisymmetrized molecular dynamics (AMD) and its extended version called shifted-basis AMD. The calculated energy and strength of the PDR reasonably agree with the observation, and the analysis of the wave function shows that the PDR is dominated by neutron excitation coupled to the quadrupole excited core nucleus $^{25}{\\rm Ne}$, which explains the observed unexpected decay of PDR to the excited states of $^{25}{\\rm Ne}$. The large isoscalar component of PDR is also shown and the enhancement of the core excitation in neutron-rich Ne isotopes is conjectured.
Pygmy dipole strength close to particle-separation energies - the case of the Mo isotopes
Rusev, G; Erhard, M; Junghans, A; Kosev, K; Schilling, K D; Schwengner, R; Wagner, A; Rusev, Gencho; Grosse, Eckart; Erhard, Martin; Junghans, Arnd; Kosev, Krasimir; Schilling, Klaus-Dieter; Schwengner, Ronald; Wagner, Andreas
2005-01-01
The distribution of electromagnetic dipole strength in 92, 98, 100 Mo has been investigated by photon scattering using bremsstrahlung from the new ELBE facility. The experimental data for well separated nuclear resonances indicate a transition from a regular to a chaotic behaviour above 4 MeV of excitation energy. As the strength distributions follow a Porter-Thomas distribution much of the dipole strength is found in weak and in unresolved resonances appearing as fluctuating cross section. An analysis of this quasi-continuum - here applied to nuclear resonance fluorescence in a novel way - delivers dipole strength functions, which are combining smoothly to those obtained from (g,n)-data. Enhancements at 6.5 MeV and at ~9 MeV are linked to the pygmy dipole resonances postulated to occur in heavy nuclei.
Characterization and analysis of a de novo transcriptome from the pygmy grasshopper Tetrix japonica.
Qiu, Zhongying; Liu, Fei; Lu, Huimeng; Huang, Yuan
2016-06-11
The pygmy grasshopper Tetrix japonica is a common insect distributed throughout the world, and it has the potential for use in studies of body colour polymorphism, genomics and the biology of Tetrigoidea (Insecta: Orthoptera). However, limited biological information is available for this insect. Here, we conducted a de novo transcriptome study of adult and larval T. japonica to provide a better understanding of its gene expression and develop genomic resources for future work. We sequenced and explored the characteristics of the de novo transcriptome of T. japonica using Illumina HiSeq 2000 platform. A total of 107 608 206 paired-end clean reads were assembled into 61 141 unigenes using the trinity software; the mean unigene size was 771 bp, and the N50 length was 1238 bp. A total of 29 225 unigenes were functionally annotated to the NCBI nonredundant protein sequences (Nr), NCBI nonredundant nucleotide sequences (Nt), a manually annotated and reviewed protein sequence database (Swiss-Prot), Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) databases. A large number of putative genes that are potentially involved in pigment pathways, juvenile hormone (JH) metabolism and signalling pathways were identified in the T. japonica transcriptome. Additionally, 165 769 and 156 796 putative single nucleotide polymorphisms occurred in the adult and larvae transcriptomes, respectively, and a total of 3162 simple sequence repeats were detected in this assembly. This comprehensive transcriptomic data for T. japonica will provide a usable resource for gene predictions, signalling pathway investigations and molecular marker development for this species and other pygmy grasshoppers.
Polyphenols, fungal enzymes, and the fate of organic nitrogen in a Californian pygmy forest
Slessarev, E.
2011-12-01
Polyphenols are a diverse family of plant secondary compounds which may influence litter decay and soil nutrient turnover. The "short circuit" hypothesis for polyphenol function proposes that polyphenolic compounds provision plants with nitrogen in nutrient-poor soils by facilitating the accumulation of organic nitrogen in soil humus. By binding peptides, polyphenols may sequester nitrogen in a bank of recalcitrant organic matter, granting competitive advantage to plants with the mycorrhizal fungi most capable of recapturing the tightly bound organic nitrogen. Specifically, fungi may retrieve nitrogen from polyphenol-peptide complexes with an extracellular enzyme, polyphenol oxidase (PPO). In order to evaluate the "short circuit" hypothesis, I measured soil PPO activity during four seasons in the Mendocino "ecological staircase," a soil age-gradient consisting of a series of wave-cut terraces along stretches of the northern California coast. Stunted, pygmy-forest plants growing in the nutrient-poor soils of the older marine terraces produce more polyphenols than their con-specifics on nutrient-rich younger terraces, potentially influencing PPO facilitated nitrogen cycling. I found that PPO activity reached its maximum in the younger terrace forest during the spring, achieving levels nearly twice as high as those observed on the younger terrace in other seasons and in the older terrace forest year-round. In both terraces, PPO activity was greatest in the organic humus at the soil surface, decreasing dramatically in the lower mineral horizon. When PPO activity reached its maximum in the younger terrace, I found that soil polyphenol content positively correlated (Rsq=0.63) with enzyme activity, suggesting that polyphenols might induce enzyme production. However, in the tannin-rich soil of the pygmy forest on the older terrace, enzyme activity remained low, and was most strongly correlated with soil moisture. The results do not support the hypothesis that nutrient
Sousounis, Konstantinos; Ogura, Atsushi; Tsonis, Panagiotis A
2013-01-01
Coleoid cephalopods like squids have a camera-type eye similar to vertebrates. On the other hand, Nautilus (Nautiloids) has a pinhole eye that lacks lens and cornea. Since pygmy squid and Nautilus are closely related species they are excellent model organisms to study eye evolution. Having being able to collect Nautilus embryos, we employed next-generation RNA sequencing using Nautilus and pygmy squid developing eyes. Their transcriptomes were compared and analyzed. Enrichment analysis of Gene Ontology revealed that contigs related to nucleic acid binding were largely up-regulated in squid, while the ones related to metabolic processes and extracellular matrix-related genes were up-regulated in Nautilus. These differences are most likely correlated with the complexity of tissue organization in these species. Moreover, when the analysis focused on the eye-related contigs several interesting patterns emerged. First, contigs from both species related to eye tissue differentiation and morphogenesis as well as to cilia showed best hits with their Human counterparts, while contigs related to rabdomeric photoreceptors showed the best hit with their Drosophila counterparts. This bolsters the idea that eye morphogenesis genes have been generally conserved in evolution, and compliments other studies showing that genes involved in photoreceptor differentiation clearly follow the diversification of invertebrate (rabdomeric) and vertebrate (ciliated) photoreceptors. Interestingly some contigs showed as good a hit with Drosophila and Human homologues in Nautilus and squid samples. One of them, capt/CAP1, is known to be preferentially expressed in Drosophila developing eye and in vertebrate lens. Importantly our analysis also provided evidence of gene duplication and diversification of their function in both species. One of these genes is the Neurofibromatosis 1 (NF1/Nf1), which in mice has been implicated in lens formation, suggesting a hitherto unsuspected role in the evolution
Veenhoff, L.M.; Geertsma, E.R.; Poolman, B.; Knol, J.
2000-01-01
The lactose transport protein (LacS) of Streptococcus thermophilus belongs to a family of transporters in which putative α-helices II and IV have been implicated in cation binding and the coupled transport of the substrate and the cation. Here, the analysis of site-directed mutants shows that a posi
Double, Michael C.; Virginia Andrews-Goff; Jenner, K. Curt S.; Micheline-Nicole Jenner; Laverick, Sarah M.; Branch, Trevor A; Nicholas J. Gales
2014-01-01
In Australian waters during the austral summer, pygmy blue whales (Balaenoptera musculus brevicauda) occur predictably in two distinct feeding areas off western and southern Australia. As with other blue whale subspecies, outside the austral summer their distribution and movements are poorly understood. In order to describe the migratory movements of these whales, we present the satellite telemetry derived movements of eleven individuals tagged off western Australia over two years. Whales wer...
Gaither, Michelle R.
2014-05-01
The pygmy angelfishes (genus Centropyge, family Pomacanthidae) are brightly colored species that occupy reef habitats in every tropical ocean. Some species are rarely observed because they occur below conventional scuba depths. Their striking coloration can command thousands of U.S. dollars in the aquarium trade, and closely related species are often distinguished only by coloration. These factors have impeded phylogenetic resolution, and every phylogeographic survey to date has reported discordance between coloration, taxonomy, and genetic partitions. Here we report a phylogenetic survey of 29 of the 34 recognized species (N= 94 plus 23 outgroups), based on two mtDNA and three nuclear loci, totaling 2272. bp. The resulting ML and Baysian trees are highly concordant and indicate that the genus Centropyge is paraphyletic, consistent with a previous analysis of the family Pomacanthidae. Two recognized genera (Apolemichthys and Genicanthus) nest within Centropyge, and two subgenera (Xiphypops and Paracentropyge) comprise monophyletic lineages that should be elevated to genus level. Based on an age estimate of 38. Ma for the family Pomacanthidae, Centropyge diverged from the closest extant genus Pygoplites about 33. Ma, three deep lineages within Centropyge diverged about 18-28. Ma, and four species complexes diverged 3-12. Ma. However, in 11 of 13 cases, putative species in these complexes are indistinguishable based on morphology and genetics, being defined solely by coloration. These cases indicate either emerging species or excessive taxonomic splitting based on brightly colored variants. © 2014 Elsevier Inc.
Song, Zhongchang; Xu, Xiao; Dong, Jianchen; Xing, Luru; Zhang, Meng; Liu, Xuecheng; Zhang, Yu; Li, Songhai; Berggren, Per
2015-11-01
Computed tomography (CT) imaging and sound experimental measurements were used to reconstruct the acoustic properties (density, velocity, and impedance) of the forehead tissues of a deceased pygmy sperm whale (Kogia breviceps). The forehead was segmented along the body axis and sectioned into cross section slices, which were further cut into sample pieces for measurements. Hounsfield units (HUs) of the corresponding measured pieces were obtained from CT scans, and regression analyses were conducted to investigate the linear relationships between the tissues' HUs and velocity, and HUs and density. The distributions of the acoustic properties of the head at axial, coronal, and sagittal cross sections were reconstructed, revealing that the nasal passage system was asymmetric and the cornucopia-shaped spermaceti organ was in the right nasal passage, surrounded by tissues and airsacs. A distinct dense theca was discovered in the posterior-dorsal area of the melon, which was characterized by low velocity in the inner core and high velocity in the outer region. Statistical analyses revealed significant differences in density, velocity, and acoustic impedance between all four structures, melon, spermaceti organ, muscle, and connective tissue (p acoustic properties of the forehead tissues provide important information for understanding the species' bioacoustic characteristics.
Decay Pattern of Pygmy States Observed in Neutron-Rich Ne26
Gibelin, J.; Beaumel, D.; Motobayashi, T.; Blumenfeld, Y.; Aoi, N.; Baba, H.; Elekes, Z.; Fortier, S.; Frascaria, N.; Fukuda, N.; Gomi, T.; Ishikawa, K.; Kondo, Y.; Kubo, T.; Lima, V.; Nakamura, T.; Saito, A.; Satou, Y.; Scarpaci, J.-A.; Takeshita, E.; Takeuchi, S.; Teranishi, T.; Togano, Y.; Vinodkumar, A. M.; Yanagisawa, Y.; Yoshida, K.
2008-11-01
Coulomb excitation of the exotic neutron-rich nucleus Ne26 on a Pb208 target was measured at 58MeV/u in order to search for low-lying E1 strength above the neutron emission threshold. This radioactive beam experiment was carried out at the RIKEN Accelerator Research Facility. Using the invariant mass method in the Ne25+n channel, we observe a sizable amount of E1 strength between 6 and 10 MeV excitation energy. By performing a multipole decomposition of the differential cross section, a reduced dipole transition probability of B(E1)=0.49±0.16e2fm2 is deduced, corresponding to 4.9±1.6% of the Thomas-Reiche-Kuhn sum rule. For the first time, the decay pattern of low-lying strength in a neutron-rich nucleus is measured. The extracted decay pattern is not consistent with several mean-field theory descriptions of the pygmy states.
Pygmy dipole strength in {sup 86}Kr and systematics of N=50 isotones
Energy Technology Data Exchange (ETDEWEB)
Schwengner, R.; Bemmerer, D.; Beyer, R.; Junghans, A.R.; Marta, M.; Schilling, K.D.; Wagner, A. [Helmholtz-Zentrum Dresden-Rossendorf (HZDR) (Germany); Massarczyk, R.; Hannaske, R. [Helmholtz-Zentrum Dresden-Rossendorf (HZDR) (Germany); TU Dresden (Germany); Rusev, G.; Kelley, J.H.; Kwan, E.; Raut, R.; Tonchev, A.; Tornow, W. [Triangle Universities Nuclear Laboratory (TUNL), Durham NC (United States); Tsoneva, N.; Lenske, H. [Universitaet Giessen (Germany)
2013-07-01
We present results of the first photon-scattering study of {sup 86}Kr. Experiments were carried out with bremsstrahlung at the ELBE accelerator of HZDR and with monoenergetic, polarized γ rays at the HIγS facility of TUNL. A high-pressure gas target was used. We identified about 40 states with J{sup π} = 1{sup -} up to the neutron-separation energy for the first time. For the determination of the absorption cross section, strength in the quasicontinuum was taken into account and a correction of the cross section for inelastic transitions was performed on the basis of simulations of statistical γ-ray cascades. The resulting absorption cross section shows enhanced strength considered as a pygmy dipole resonance (PDR) and is compared with predictions of the quasiparticle-phonon model. The behavior of PDR strength within the series of N=50 isotones is discussed. Enhanced photon strength may influence neutron-capture reaction rates relevant for transmutation studies.
Drechsler, Wolfgang; Havas, Peter; Rosenblum, Arnold
1984-02-01
In the preceding paper, the laws of motion were established for classical particles with spin which are monopole-dipole singularities of Yang-Mills-Higgs fields. In this paper, a systematic approximation scheme is developed for solving the coupled nonlinear field equations in any order and for determining the corresponding equations of motion. In zeroth order the potentials are taken as the usual Liénard-Wiechert and Bhabha-Harish-Chandra potentials (generalized to isospace); in this order the solutions are necessarily Abelian, since the isovector describing the charge is constant. The regularization necessary to obtain expressions finite on the world lines of the particles is achieved by the method of Riesz potentials. All fields are taken as retarded and are expressed in integral form. Omitting dipole interactions, the integrals for the various terms are carried out as far as possible for general motions, including radiation-reaction terms. In first order, the charge isovectors are no longer necessarily constant; thus the solutions are not necessarily Abelian, and it is possible for charge to be radiated away. The cases of time-symmetric field theory and of an action-at-a-distance formulation of the theory are discussed in an appendix.
Directory of Open Access Journals (Sweden)
Salvatore Siciliano
2015-12-01
Full Text Available Abstract Melon-headed whale (Peponocephala electra and Pygmy killer whale (Feresa attenuata are very poorly known species and are often confused with each other. We examined in detail Figure 3 in MARIGO and GIFFONI (2010 who reported that two melon-headed whales were taken in a surface driftnet about 90 nm off Santos, Brazil. We concluded they were in fact pygmy killer whales and explain our reasoning. To aid in future identifications, we illustrate and describe some of the main differences between these two species of small cetaceans. The incident reported by MARIGO and GIFFONI (2010 might represent the 'tip of the iceberg' regarding the incidental catches of cetaceans by pelagic drift nets off Brazil. Offshore driftnetting operating along the south-southeastern coast of Brazil may threaten pygmy killer whales.
Directory of Open Access Journals (Sweden)
Manirakiza Alexandre
2011-12-01
Full Text Available Abstract Background Yaws is a bacterial skin and bone infectious disease caused by Treponema pallidum pertenue. It is endemic, particularly among pygmies in Central African Republic. To assess the clinical cure rate after treatment with benzathinepenicillin in this population, we conducted a cohort survey of 243 patients in the Lobaye region. Findings and conclusion The rate of healing of lesions after 5 months was 95.9%. This relatively satisfactory level of therapeutic response implies that yaws could be controlled in the Central African Republic. Thus, reinforcement of the management of new cases and of contacts is suggested.
Bryan, Colleen E; Davis, W Clay; McFee, Wayne E; Neumann, Carola A; Schulte, Jennifer; Bossart, Gregory D; Christopher, Steven J
2012-10-01
More than half of pygmy sperm whales (Kogia breviceps) that strand exhibit signs of cardiomyopathy (CMP). Many factors may contribute to the development of idiopathic CMP in K. breviceps, including genetics, infectious agents, contaminants, biotoxins, and dietary intake (e.g. selenium, mercury, and pro-oxidants). This study assessed trace elements in K. breviceps at various stages of CMP progression using fresh frozen liver and heart samples collected from individuals that stranded along US Atlantic and Gulf coasts between 1993 and 2007. Standard addition calibration and collision cell inductively coupled plasma mass spectrometry (ICP-MS) were employed for total Se analysis and pyrolysis atomic absorption (AA) was utilized for total Hg analysis to examine if the Se/Hg detoxification pathway inhibits the bioavailability of Se. Double spike speciated isotope dilution gas chromatography ICP-MS was utilized to measure methyl Hg and inorganic Hg. Immunoblot detection and colorimetric assays were used to assess protein oxidation status. Data collected on trace elements, selenoproteins, and oxidative status were evaluated in the context of animal life history and other complementary histological information to gain insight into the biochemical pathways contributing to the development of CMP in K. breviceps. Cardiomyopathy was only observed in adult pygmy sperm whales, predominantly in male animals. Both Hg:Se molar ratios and overall protein oxidation were greater in males than females and increased with progression of CMP.
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......Let (X,d) be a metric space and (Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Omega. Loosely speaking, these consist of points in Omega which `stay clear' of some given set of points in X....... Applications of our general framework include those from number theory (classical, complex, p-adic and formal power series) and dynamical systems (iterated function schemes, rational maps and Kleinian groups)....
Egorova, Irina A
2016-01-01
New results for electric dipole strength in the chain of even-even Calcium isotopes with the mass numbers A = 40 - 54 are presented. Starting from the covariant Lagrangian of Quantum Hadrodynamics, spectra of collective vibrations (phonons) and phonon-nucleon coupling vertices for $J \\leq 6$ and normal parity were computed in a self-consistent relativistic quasiparticle random phase approximation (RQRPA). These vibrations coupled to Bogoliubov two-quasiparticle configurations (2q$\\otimes$phonon) form the model space for the calculations of the dipole response function in the relativistic quasiparticle time blocking approximation (RQTBA). The results for giant dipole resonance in the latter approach are compared to those obtained in RQRPA and to available data. Evolution of the dipole strength with neutron number is investigated for both high-frequency giant dipole resonance (GDR) and low-lying strength. Development of a pygmy resonant structure on the low-energy shoulder of GDR is traced and analyzed in terms...
Directory of Open Access Journals (Sweden)
CAR. Dias
Full Text Available Two groups of pygmy marmoset (Cebuella pygmaea were rescued along the left bank of the Madeira River during the formation of Santo Antônio Hydroelectric Dam reservoir in the state of Rondônia, Northern Brazil. Reintroduction of both groups occurred in areas of open Tropical rainforest located within the project´s Permanent Preservation Area. A post-release monitoring was conducted for three months using radio-telemetry. Individuals of each group remained together and settled in stable home ranges near their respective release sites. The mortality rate of translocated animals was about 7%. This seems to be the first report documenting the complete group translocation of C. pygmaea and the first to successfully employ radio-telemetry techniques in monitoring this species. This study demonstrated the feasibility of translocation and the use of radio-telemetry in monitoring C. pygmaea.
Directory of Open Access Journals (Sweden)
Michael C Double
Full Text Available In Australian waters during the austral summer, pygmy blue whales (Balaenoptera musculus brevicauda occur predictably in two distinct feeding areas off western and southern Australia. As with other blue whale subspecies, outside the austral summer their distribution and movements are poorly understood. In order to describe the migratory movements of these whales, we present the satellite telemetry derived movements of eleven individuals tagged off western Australia over two years. Whales were tracked from between 8 and 308 days covering an average distance of 3,009±892 km (mean ± se; range: 832 km-14,101 km at a rate of 21.94±0.74 km per day (0.09 km-455.80 km/day. Whales were tagged during March and April and ultimately migrated northwards post tag deployment with the exception of a single animal which remained in the vicinity of the Perth Canyon/Naturaliste Plateau for its eight day tracking period. The tagged whales travelled relatively near to the Australian coastline (100.0±1.7 km until reaching a prominent peninsula in the north-west of the state of Western Australia (North West Cape after which they travelled offshore (238.0±13.9 km. Whales reached the northern terminus of their migration and potential breeding grounds in Indonesian waters by June. One satellite tag relayed intermittent information to describe aspects of the southern migration from Indonesia with the animal departing around September to arrive in the subtropical frontal zone, south of western Australia in December. Throughout their migratory range, these whales are exposed to impacts associated with industry, fishing and vessel traffic. These movements therefore provide a valuable tool to industry when assessing potential interactions with pygmy blue whales and should be considered by conservation managers and regulators when mitigating impacts of development. This is particularly relevant for this species as it continues to recover from past exploitation.
Double, Michael C; Andrews-Goff, Virginia; Jenner, K Curt S; Jenner, Micheline-Nicole; Laverick, Sarah M; Branch, Trevor A; Gales, Nicholas J
2014-01-01
In Australian waters during the austral summer, pygmy blue whales (Balaenoptera musculus brevicauda) occur predictably in two distinct feeding areas off western and southern Australia. As with other blue whale subspecies, outside the austral summer their distribution and movements are poorly understood. In order to describe the migratory movements of these whales, we present the satellite telemetry derived movements of eleven individuals tagged off western Australia over two years. Whales were tracked from between 8 and 308 days covering an average distance of 3,009±892 km (mean ± se; range: 832 km-14,101 km) at a rate of 21.94±0.74 km per day (0.09 km-455.80 km/day). Whales were tagged during March and April and ultimately migrated northwards post tag deployment with the exception of a single animal which remained in the vicinity of the Perth Canyon/Naturaliste Plateau for its eight day tracking period. The tagged whales travelled relatively near to the Australian coastline (100.0±1.7 km) until reaching a prominent peninsula in the north-west of the state of Western Australia (North West Cape) after which they travelled offshore (238.0±13.9 km). Whales reached the northern terminus of their migration and potential breeding grounds in Indonesian waters by June. One satellite tag relayed intermittent information to describe aspects of the southern migration from Indonesia with the animal departing around September to arrive in the subtropical frontal zone, south of western Australia in December. Throughout their migratory range, these whales are exposed to impacts associated with industry, fishing and vessel traffic. These movements therefore provide a valuable tool to industry when assessing potential interactions with pygmy blue whales and should be considered by conservation managers and regulators when mitigating impacts of development. This is particularly relevant for this species as it continues to recover from past exploitation.
蜂猴、倭蜂猴肢端特征%Characteristics of the limb in slow loris and pygmy loris
Institute of Scientific and Technical Information of China (English)
谢朝晖; 胡建业; 周孟业; 邓大军
2013-01-01
Objective:To explore the morphological characteristics of the limbs in slow loris (Nycticebus coucang)and pygmy loris (Nycticebus pygmaeus).Methods:7 adult slow loris (2 male,5 female) and 4 adult pygmy loris (3 male,1 female) were observed and their length of the digit was measured.Results:The limbs in the slow loris were bigger than those in the pygmy loris.Both the second digit in the slow loris and the pygmy loris had 1-1.2 cm nail in the length curling to middle part,others digits were flat.The order of the length of the digit in the forelimb was 4＞3＞5＞1＞2 and 4＞3＞5＞2＞1 in the hindlimb in the slow loris.There existed differences between the lengths of the digit of the forelimb and hindlimb in the slow loris.However,the order of the digit of the forelimb and hindlimb in length was 4＞3＞5＞1＞2 in pygmy loris.Conclusion:Those distinctive morphological differences in forelimb and hindlimb between the slow loris and pygmy loris are related with the species feature.%目的:研究蜂猴、倭蜂猴肢端形态的种属特征.方法:本研究通过观察成年7只蜂猴(2雄,5雌)和4只倭蜂猴(3雄,1雌),测量了它们的指(趾)骨长度,并将所得数据进行了分析.结果:蜂猴肢端大于倭蜂猴；蜂猴和倭蜂猴的第2趾端均有长1～1.2cm卷向内侧的细长趾甲,而其他指(趾)甲均呈扁平状.蜂猴的指骨长度顺序依次为4＞3＞5＞1＞2,趾骨顺序为4＞3＞5＞2＞1,指骨与趾骨长度排序有差异；倭蜂猴的指骨与趾骨排序无差异,都是4＞3＞5＞1＞2.结论:蜂猴和倭蜂猴其肢端形态差异与种属特征相关.
Leike, Reimar H
2016-01-01
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a ranking function that quantifies how "embarrassing" it is to communicate a given approximation. We show that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. We find that this ranking is equivalent to the Kullback-Leibler divergence that is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments, the approximated and non-approximated beliefs, should be used. We hope that our elementary derivation settles the apparent confusion. We show for example that when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many su...
On Element SDD Approximability
Avron, Haim; Toledo, Sivan
2009-01-01
This short communication shows that in some cases scalar elliptic finite element matrices cannot be approximated well by an SDD matrix. We also give a theoretical analysis of a simple heuristic method for approximating an element by an SDD matrix.
Approximate iterative algorithms
Almudevar, Anthony Louis
2014-01-01
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such algorithms. Techniques of functional analysis are used to derive analytical relationships between approximation methods and convergence properties for general classes of algorithms. This work provides the necessary background in functional analysis a
Isobe, H; Shoji, M; Yamanaka, S; Mino, H; Umena, Y; Kawakami, K; Kamiya, N; Shen, J-R; Yamaguchi, K
2014-06-28
Full geometry optimizations followed by the vibrational analysis were performed for eight spin configurations of the CaMn4O4X(H2O)3Y (X = O, OH; Y = H2O, OH) cluster in the S1 and S3 states of the oxygen evolution complex (OEC) of photosystem II (PSII). The energy gaps among these configurations obtained by vertical, adiabatic and adiabatic plus zero-point-energy (ZPE) correction procedures have been used for computation of the effective exchange integrals (J) in the spin Hamiltonian model. The J values are calculated by the (1) analytical method and the (2) generalized approximate spin projection (AP) method that eliminates the spin contamination errors of UB3LYP solutions. Using J values derived from these methods, exact diagonalization of the spin Hamiltonian matrix was carried out, yielding excitation energies and spin densities of the ground and lower-excited states of the cluster. The obtained results for the right (R)- and left (L)-opened structures in the S1 and S3 states are found to be consistent with available optical and magnetic experimental results. Implications of the computational results are discussed in relation to (a) the necessity of the exact diagonalization for computations of reliable energy levels, (b) magneto-structural correlations in the CaMn4O5 cluster of the OEC of PSII, (c) structural symmetry breaking in the S1 and S3 states, and (d) the right- and left-handed scenarios for the O-O bond formation for water oxidation.
Approximation of distributed delays
Lu, Hao; Eberard, Damien; Simon, Jean-Pierre
2010-01-01
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and work with the norm defined over the convolution Banach algebra. The class of rational approximates is described, and a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control problem, for which simulations results show the effectiveness of the proposed methodology.
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...
Relativistic continuum random phase approximation in spherical nuclei
Energy Technology Data Exchange (ETDEWEB)
Daoutidis, Ioannis
2009-10-01
Covariant density functional theory is used to analyze the nuclear response in the external multipole fields. The investigations are based on modern functionals with zero range and density dependent coupling constants. After a self-consistent solution of the Relativistic Mean Field (RMF) equations for the nuclear ground states multipole giant resonances are studied within the Relativistic Random Phase Approximation (RRPA), the small amplitude limit of the time-dependent RMF. The coupling to the continuum is treated precisely by calculating the single particle Greens-function of the corresponding Dirac equation. In conventional methods based on a discretization of the continuum this was not possible. The residual interaction is derived from the same RMF Lagrangian. This guarantees current conservation and a precise decoupling of the Goldstone modes. For nuclei with open shells pairing correlations are taken into account in the framework of BCS theory and relativistic quasiparticle RPA. Continuum RPA (CRPA) presents a robust method connected with an astonishing reduction of the numerical effort as compared to conventional methods. Modes of various multipolarities and isospin are investigated, in particular also the newly discovered Pygmy modes in the vicinity of the neutron evaporation threshold. The results are compared with conventional discrete RPA calculations as well as with experimental data. We find that the full treatment of the continuum is essential for light nuclei and the study of resonances in the neighborhood of the threshold. (orig.)
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.
Achieser, N I
2004-01-01
A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of pr
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...
Approximate Modified Policy Iteration
Scherrer, Bruno; Ghavamzadeh, Mohammad; Geist, Matthieu
2012-01-01
Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three approximate MPI (AMPI) algorithms that are extensions of the well-known approximate DP algorithms: fitted-value iteration, fitted-Q iteration, and classification-based policy iteration. We provide an error propagation analysis for AMPI that unifies those for approximate policy and value iteration. We also provide a finite-sample analysis for the classification-based implementation of AMPI (CBMPI), which is more general (and somehow contains) than the analysis of the other presented AMPI algorithms. An interesting observation is that the MPI's parameter allows us to control the balance of errors (in value function approximation and in estimating the greedy policy) in the fina...
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.
Directory of Open Access Journals (Sweden)
Sam Kaviar
Full Text Available Our objective was to ascertain the population status of the Pygmy Three-toed Sloth, Bradypus pygmaeus, an IUCN Critically Endangered species, on Isla Escudo de Veraguas, Panama. Bradypus pygmaeus are thought to be folivorous mangrove specialists; therefore we conducted a visual systematic survey of all 10 mangrove thickets on the island. The total mangrove habitat area was measured to be 1.67 ha, comprising 0.024% of the total island area. The population survey found low numbers of B. pygmaeus in the mangrove thickets and far lower numbers outside of them. The connectivity of subpopulations between these thickets on the island is not established, as B. pygmaeus movement data is still lacking. We found 79 individuals of B. pygmaeus; 70 were found in mangroves and 9 were observed just beyond the periphery of the mangroves in non-mangrove tree species. Low population number, habitat fragmentation and habitat loss could lead to inbreeding, a loss of genetic diversity, and extinction of B. pygmaeus.
Directory of Open Access Journals (Sweden)
Chris J Brauer
Full Text Available Habitat fragmentation caused by human activities alters metapopulation dynamics and decreases biological connectivity through reduced migration and gene flow, leading to lowered levels of population genetic diversity and to local extinctions. The threatened Yarra pygmy perch, Nannoperca obscura, is a poor disperser found in small, isolated populations in wetlands and streams of southeastern Australia. Modifications to natural flow regimes in anthropogenically-impacted river systems have recently reduced the amount of habitat for this species and likely further limited its opportunity to disperse. We employed highly resolving microsatellite DNA markers to assess genetic variation, population structure and the spatial scale that dispersal takes place across the distribution of this freshwater fish and used this information to identify conservation units for management. The levels of genetic variation found for N. obscura are amongst the lowest reported for a fish species (mean heterozygosity of 0.318 and mean allelic richness of 1.92. We identified very strong population genetic structure, nil to little evidence of recent migration among demes and a minimum of 11 units for conservation management, hierarchically nested within four major genetic lineages. A combination of spatial analytical methods revealed hierarchical genetic structure corresponding with catchment boundaries and also demonstrated significant isolation by riverine distance. Our findings have implications for the national recovery plan of this species by demonstrating that N. obscura populations should be managed at a catchment level and highlighting the need to restore habitat and avoid further alteration of the natural hydrology.
Attard, Catherine R M; Beheregaray, Luciano B; Jenner, K Curt S; Gill, Peter C; Jenner, Micheline-Nicole M; Morrice, Margaret G; Teske, Peter R; Möller, Luciana M
2015-05-01
Unusually low genetic diversity can be a warning of an urgent need to mitigate causative anthropogenic activities. However, current low levels of genetic diversity in a population could also be due to natural historical events, including recent evolutionary divergence, or long-term persistence at a small population size. Here, we determine whether the relatively low genetic diversity of pygmy blue whales (Balaenoptera musculus brevicauda) in Australia is due to natural causes or overexploitation. We apply recently developed analytical approaches in the largest genetic dataset ever compiled to study blue whales (297 samples collected after whaling and representing lineages from Australia, Antarctica and Chile). We find that low levels of genetic diversity in Australia are due to a natural founder event from Antarctic blue whales (Balaenoptera musculus intermedia) that occurred around the Last Glacial Maximum, followed by evolutionary divergence. Historical climate change has therefore driven the evolution of blue whales into genetically, phenotypically and behaviourally distinct lineages that will likely be influenced by future climate change.
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.)
Approximating Stationary Statistical Properties
Institute of Scientific and Technical Information of China (English)
Xiaoming WANG
2009-01-01
It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. The main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. The result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.
Directory of Open Access Journals (Sweden)
Malvina Baica
1985-01-01
Full Text Available The author uses a new modification of Jacobi-Perron Algorithm which holds for complex fields of any degree (abbr. ACF, and defines it as Generalized Euclidean Algorithm (abbr. GEA to approximate irrationals.
Approximations in Inspection Planning
DEFF Research Database (Denmark)
Engelund, S.; Sørensen, John Dalsgaard; Faber, M. H.
2000-01-01
Planning of inspections of civil engineering structures may be performed within the framework of Bayesian decision analysis. The effort involved in a full Bayesian decision analysis is relatively large. Therefore, the actual inspection planning is usually performed using a number of approximations....... One of the more important of these approximations is the assumption that all inspections will reveal no defects. Using this approximation the optimal inspection plan may be determined on the basis of conditional probabilities, i.e. the probability of failure given no defects have been found...... by the inspection. In this paper the quality of this approximation is investigated. The inspection planning is formulated both as a full Bayesian decision problem and on the basis of the assumption that the inspection will reveal no defects....
The Karlqvist approximation revisited
Tannous, C
2015-01-01
The Karlqvist approximation signaling the historical beginning of magnetic recording head theory is reviewed and compared to various approaches progressing from Green, Fourier, Conformal mapping that obeys the Sommerfeld edge condition at angular points and leads to exact results.
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
Directory of Open Access Journals (Sweden)
Maksim Duškin
2015-11-01
Full Text Available Approximation and supposition This article compares exponents of approximation (expressions like Russian около, примерно, приблизительно, более, свыше and the words expressing supposition (for example Russian скорее всего, наверное, возможно. These words are often confused in research, in particular researchers often mention exponents of supposition in case of exponents of approximation. Such approach arouses some objections. The author intends to demonstrate in this article a notional difference between approximation and supposition, therefore the difference between exponents of these two notions. This difference could be described by specifying different attitude of approximation and supposition to the notion of knowledge. Supposition implies speaker’s ignorance of the exact number, while approximation does not mean such ignorance. The article offers examples proving this point of view.
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.
Effects of phonon-phonon coupling on properties of pygmy resonance in 124-132Sn
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Voronov V. V.
2012-12-01
Full Text Available Starting from an effective Skyrme interaction we study effects of phonon-phonon coupling on the low-energy electric dipole response in 124-132Sn. The QRPA calculations are performed within a finite rank separable approximation. The inclusion of two-phonon configurations gives a considerable contribution to low-lying strength. Comparison with available experimental data shows a reasonable agreement for the low-energy E1 strength distribution.
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Kang Hae Ji
2011-07-01
Full Text Available Abstract Background Tanganya virus (TGNV, the only shrew-associated hantavirus reported to date from sub-Saharan Africa, is harbored by the Therese's shrew (Crocidura theresae, and is phylogenetically distinct from Thottapalayam virus (TPMV in the Asian house shrew (Suncus murinus and Imjin virus (MJNV in the Ussuri white-toothed shrew (Crocidura lasiura. The existence of myriad soricid-borne hantaviruses in Eurasia and North America would predict the presence of additional hantaviruses in sub-Saharan Africa, where multiple shrew lineages have evolved and diversified. Methods Lung tissues, collected in RNAlater®, from 39 Buettikofer's shrews (Crocidura buettikoferi, 5 Jouvenet's shrews (Crocidura jouvenetae, 9 West African pygmy shrews (Crocidura obscurior and 21 African giant shrews (Crocidura olivieri captured in Côte d'Ivoire during 2009, were systematically examined for hantavirus RNA by RT-PCR. Results A genetically distinct hantavirus, designated Azagny virus (AZGV, was detected in the West African pygmy shrew. Phylogenetic analysis of the S, M and L segments, using maximum-likelihood and Bayesian methods, under the GTR+I+Γ model of evolution, showed that AZGV shared a common ancestry with TGNV and was more closely related to hantaviruses harbored by soricine shrews than to TPMV and MJNV. That is, AZGV in the West African pygmy shrew, like TGNV in the Therese's shrew, did not form a monophyletic group with TPMV and MJNV, which were deeply divergent and basal to other rodent- and soricomorph-borne hantaviruses. Ancestral distributions of each hantavirus lineage, reconstructed using Mesquite 2.74, suggested that the common ancestor of all hantaviruses was most likely of Eurasian, not African, origin. Conclusions Genome-wide analysis of many more hantaviruses from sub-Saharan Africa are required to better understand how the biogeographic origin and radiation of African shrews might have contributed to, or have resulted from, the evolution
Monotone Boolean approximation
Energy Technology Data Exchange (ETDEWEB)
Hulme, B.L.
1982-12-01
This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application for the analysis of noncoherent fault trees and event tree sequences.
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
2013-09-01
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.
Norton, Andrew H.
1991-01-01
Local spline approximants offer a means for constructing finite difference formulae for numerical solution of PDEs. These formulae seem particularly well suited to situations in which the use of conventional formulae leads to non-linear computational instability of the time integration. This is explained in terms of frequency responses of the FDF.
Directory of Open Access Journals (Sweden)
Kim Kyu-Rim
2012-08-01
Full Text Available Abstract Background The efficacy and safety of a combination formulation of 10% imidacloprid + 1.0% moxidectin spot-on (Advocate® for Cats, Bayer Animal Health GmbH, Leverkusen, Germany was tested in 40 African pygmy hedgehogs (Atelerix albiventris naturally infested with Caparinia tripilis. Methods The optimal dosage level of the combination for hedgehogs was determined by assigning 20 hedgehogs into three treatment groups (0.1, 0.4 and 1.6 ml/Kg b.w., and one untreated control group of 5 hedgehogs each. Twenty naturally infested hedgehogs were then randomly assigned to either treatment or control group with 10 animals each, and the number of live mites was counted from 13 body regions on day 0, 3, 9, 16, and 30 after single treatment at the dosage level of 0.1 ml/Kg. Results Before the chemotherapy, the highest density of mite was observed in external ear canals followed by the dorsal and the lowest in the ventral regions of the body surface. The dosage level of 0.1 ml/Kg, which corresponded to the recommended dosage level for cats, containing 10 mg imidacloprid and 1 mg moxidectin was also the optimal dosage level for hedgehogs. No hedgehogs in the treatment group showed live mites from day 3 post treatment. Side effects such as ataxia, depression, nausea, and weight fluctuation were not observed during the whole period of study. Conclusions This report suggests that a combination formulation of 0.1 ml/Kg of 10% imidacloprid + 1% moxidectin spot-on for cats is also useful for the control of Caparinia tripilis infestation in hedgehogs.
Bakaleinikov, L. A.; Silbergleit, A. S.
The uniform closeness of coordinates partial derivatives of the approximate and exact Poincaré maps for ODE systems with hyperbolic fixed point possessing the homoclinic orbit connecting this point to itself is studied. The conditions of the uniform bound existence for the difference between these derivatives in the domain of uniform closeness of the approximate and exact Poincaré maps are found. It is shown that partial derivatives for the systems with more than one unstable direction are generally not uniformly close.
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.
Topics in Metric Approximation
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
Study of the pygmy dipole resonance in {sup 94}Mo using the (α,α{sup ′}γ) coincidence technique
Energy Technology Data Exchange (ETDEWEB)
Derya, V., E-mail: derya@ikp.uni-koeln.de [Institut für Kernphysik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln (Germany); Endres, J.; Elvers, M. [Institut für Kernphysik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln (Germany); Harakeh, M.N. [Kernfysisch Versneller Instituut, Rijksuniversiteit Groningen, Zernikelaan 25, 9747 AA Groningen (Netherlands); Pietralla, N.; Romig, C. [Institut für Kernphysik, TU Darmstadt, Schlossgartenstraße 9, 64289 Darmstadt (Germany); Savran, D. [ExtreMe Matter Institute EMMI and Research Division, GSI, Planckstraße 1, 64291 Darmstadt (Germany); Frankfurt Institute for Advanced Studies FIAS, Ruth-Moufang-Straße 1, 60438 Frankfurt am Main (Germany); Scheck, M.; Siebenhühner, F. [Institut für Kernphysik, TU Darmstadt, Schlossgartenstraße 9, 64289 Darmstadt (Germany); Stoica, V.I. [Kernfysisch Versneller Instituut, Rijksuniversiteit Groningen, Zernikelaan 25, 9747 AA Groningen (Netherlands); Department of Sociology/ICS, Rijksuniversiteit Groningen, Grote Rozenstraat 31, 9712 TG Groningen (Netherlands); Wörtche, H.J. [Kernfysisch Versneller Instituut, Rijksuniversiteit Groningen, Zernikelaan 25, 9747 AA Groningen (Netherlands); and others
2013-05-15
The (α,α{sup ′}γ) reaction at E{sub α}=136 MeV was used to study the electric dipole response in the open-shell vibrational nucleus {sup 94}Mo below the neutron-separation threshold. The coincidence experiment has been performed at the Kernfysisch Versneller Instituut in Groningen, The Netherlands, exploiting the Big-Bite Spectrometer and an array of large volume High-Purity Germanium (HPGe) detectors. Due to the excellent energy resolution and high selectivity to transitions stemming from the pygmy dipole resonance, singles α-scattering cross sections could be determined for individual electric dipole excitations between 4 and 8 MeV. For three of the excited low-lying J{sup π}=1{sup −} states in {sup 94}Mo a γ-decay branch into the J{sup π}=2{sub 1}{sup +} state could be observed. The experiment extends the systematic studies of the pygmy dipole resonance by real-photon scattering (γ,γ{sup ′}) experiments and (α,α{sup ′}γ) experiments. Recently, a (γ,γ{sup ′}) experiment on {sup 94}Mo was performed at the Darmstadt High-Intensity Photon Setup at the S-DALINAC in Darmstadt, Germany, permitting the comparison of B(E1)↑ strength distribution and α-scattering cross sections.
Directory of Open Access Journals (Sweden)
Giuseppe Carpaneto
1989-07-01
Full Text Available Abstract This work deals with the mammals and their role in the zoological culture of the Mbuti Pygmies, hunter-gatherers of the Ituri Forest of Zaire. The ethnozoological information was gathered in parallel to faunistic investigation. A checklist of the mammals inhabiting the Ituri Forest was compiled on the basis of both carefully selected literature and direct field research. Field work was conducted in many study sites (pygmy camps and agriculturalists' settlements throughout the region. Several Mbuti hunters of each band were interviewed in order to ensure reliability to the information they were giving. Direct observation of their hunting activities, feeding habits and relations with animals were also carried out. For each mammalian species the exact words of the Pygmies were translated into English. From their own culture, the Pygmies gave a great deal of information about habits, food, interspecific relations, reproduction and behaviour of 59 species of mammals. Details were also given by the Mbuti hunters on their own taboos, food restrictions, medicine and villagers' witchcraft, concerning mammals, as well as the utilization of animal parts for making objects and tools. Vernacular names of the mammals are reported in six local languages, as well as the names of plants which, according to the Mbuti, are used by the animals as food. The hunting techniques of the Ituri Pygmies are summarized together with quantitative data from 60 net casts and 4 bow-hunting days. Riassunto Nel presente lavoro vengono studiati i mammiferi nella cultura zoologica dei Pigmei Mbuti, cacciatori-raccoglitori della Foresta dell'Ituri in Zaire. Gli autori hanno condotto parallelamente sia l'indagine etnozoologica che ricerche faunistiche di base sui mammiferi. Un elenco sistematico delle specie viventi nella regione studiata è stato compilato sia sulla base di osservazioni dirette che attraverso una revisione critica dei
Pygmy dipole mode in deformed neutron-rich Mg isotopes close to the drip line
Yoshida, Kenichi
2009-10-01
We investigate the microscopic structure of the low-lying isovector-dipole excitation mode in neutron-rich Mg36,38,40 close to the drip line by means of the deformed quasiparticle random-phase approximation employing the Skyrme and the local pairing energy-density functionals. It is found that the low-lying bump structure above the neutron emission-threshold energy develops when the drip line is approached, and that the isovector dipole strength at ExThomas-Reiche-Kuhn dipole sum rule in Mg40. We obtained the collective dipole modes at around 8-10 MeV in Mg isotopes, that consist of many two-quasiparticle excitations of the neutron. The transition density clearly shows an oscillation of the neutron skin against the isoscalar core. We found significant coupling effects between the dipole and octupole excitation modes due to the nuclear deformation. It is also found that the responses for the compressional dipole and isoscalar octupole excitations are much enhanced in the lower energy region.
Energy Technology Data Exchange (ETDEWEB)
Chalasani, P.; Saias, I. [Los Alamos National Lab., NM (United States); Jha, S. [Carnegie Mellon Univ., Pittsburgh, PA (United States)
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
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.
Livermore, R. C.; Jones, T.; Richard, J.; Bower, R. G.; Ellis, R. S.; Swinbank, A. M.; Rigby, J. R.; Smail, Ian; Arribas, S.; Rodriguez-Zaurin, J.; Colina, L.; Ebeling, H.; Crain, R. A.
2013-01-01
We present Hubble Space Telescope/Wide Field Camera 3 narrow-band imaging of the Ha emission in a sample of eight gravitationally lensed galaxies at z = 1-1.5. The magnification caused by the foreground clusters enables us to obtain a median source plane spatial resolution of 360 pc, as well as providing magnifications in flux ranging from approximately 10× to approximately 50×. This enables us to identify resolved star-forming HII regions at this epoch and therefore study their Ha luminosity distributions for comparisons with equivalent samples at z approximately 2 and in the local Universe. We find evolution in the both luminosity and surface brightness of HII regions with redshift. The distribution of clump properties can be quantified with an HII region luminosity function, which can be fit by a power law with an exponential break at some cut-off, and we find that the cut-off evolves with redshift. We therefore conclude that 'clumpy' galaxies are seen at high redshift because of the evolution of the cut-off mass; the galaxies themselves follow similar scaling relations to those at z = 0, but their HII regions are larger and brighter and thus appear as clumps which dominate the morphology of the galaxy. A simple theoretical argument based on gas collapsing on scales of the Jeans mass in a marginally unstable disc shows that the clumpy morphologies of high-z galaxies are driven by the competing effects of higher gas fractions causing perturbations on larger scales, partially compensated by higher epicyclic frequencies which stabilize the disc.
S-Approximation: A New Approach to Algebraic Approximation
Directory of Open Access Journals (Sweden)
M. R. Hooshmandasl
2014-01-01
Full Text Available We intend to study a new class of algebraic approximations, called S-approximations, and their properties. We have shown that S-approximations can be used for applied problems which cannot be modeled by inclusion based approximations. Also, in this work, we studied a subclass of S-approximations, called Sℳ-approximations, and showed that this subclass preserves most of the properties of inclusion based approximations but is not necessarily inclusionbased. The paper concludes by studying some basic operations on S-approximations and counting the number of S-min functions.
Pratiwi, B. N.; Suparmi, A.; Cari, C.; Husein, A. S.; Yunianto, M.
2016-08-01
We apllied asymptotic iteration method (AIM) to obtain the analytical solution of the Dirac equation in case exact pseudospin symmetry in the presence of modified Pcischl- Teller potential and trigonometric Scarf II non-central potential. The Dirac equation was solved by variables separation into one dimensional Dirac equation, the radial part and angular part equation. The radial and angular part equation can be reduced into hypergeometric type equation by variable substitution and wavefunction substitution and then transform it into AIM type equation to obtain relativistic energy eigenvalue and wavefunctions. Relativistic energy was calculated numerically by Matlab software. And then relativistic energy spectrum and wavefunctions were visualized by Matlab software. The results show that the increase in the radial quantum number nr causes decrease in the relativistic energy spectrum. The negative value of energy is taken due to the pseudospin symmetry limit. Several quantum wavefunctions were presented in terms of the hypergeometric functions.
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.
Mas-Coma, S; Fons, R; Galan-Puchades, M T; Valero, M A
1986-01-01
Description and differentiation of the adult stage of Hymenolepis cerberensis n. sp. (Cestoda: Hymenolepididae), an intestinal parasite of the Pygmy white-toothed shrew, Suncus etruscus (Savi, 1822) (Insectivora: Soricidae: Crocidurinae) in the region of Banyuls-sur-Mer and Cerbère (Oriental Pyrenees, France). The new species is characterized by the size of the gravid specimens and by the presence of 18-21 rostellar hooks of 18.5-20 micron and of filaments around the embryophore. The general composition of the fauna of Cyclophyllidea parasitizing S. etruscus is analysed. There are three less specialised Hymenolepis species with a scolex of the same type and one Pseudhymenolepis species, with the absence of unarmed species lacking a rostrum. The oioxenous character of the Cestodes parasitizing Suncus species sustains the validity of the genus Suncus. The resemblance of the Cestodefaunas suggests a narrow phyletic relationship between the genera Suncus and Crocidura.
Operators of Approximations and Approximate Power Set Spaces
Institute of Scientific and Technical Information of China (English)
ZHANG Xian-yong; MO Zhi-wen; SHU Lan
2004-01-01
Boundary inner and outer operators are introduced; and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space.
Nonlinear Approximation Using Gaussian Kernels
Hangelbroek, Thomas
2009-01-01
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface spline) approximations. However, no such results are known for the Gaussian function. The crux of the difficulty lies in the necessity to vary the tension parameter in the Gaussian function spatially according to local information about the approximand: error analysis of Gaussian approximation schemes with varying tension are, by and large, an elusive target for approximators. We introduce and analyze in this paper a new algorithm for approximating functions using translates of Gaussian functions with varying tension parameters. Our scheme is sophisticated to a degree that it employs even locally Gaussians with varying tensions, and that it resolves local ...
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.
Least Square Approximation by Linear Combinations of Multi(Poles).
1983-04-01
ID-R134 069 LEAST SQUARE APPROXIMATION BY LINEAR COMBINATIONS OF i/i MULTI(POLES). 1U OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE AND SURVEY...TR-83-0 117 LEAST SQUARE APPROXIMATION BY LINEAR COMBINATIONS OF (MULTI)POLES WILLI FREEDEN DEPARTMENT OF GEODETIC SCIENCE AND SURVEYING THE OHIO...Subtitle) S. TYPE OF REPORT & PERIOD COVERED LEAST SQUARE APPROXIMATION BY LINEAR Scientific Report No. 3 COMBINATIONS OF (MULTI)POLES 6. PERFORMING ORG
International Conference Approximation Theory XIV
Schumaker, Larry
2014-01-01
This volume developed from papers presented at the international conference Approximation Theory XIV, held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Quasi-chemical approximation for polyatomic mixtures
Dávila, M V; Matoz-Fernandez, D A; Ramirez-Pastor, A J
2016-01-01
The statistical thermodynamics of binary mixtures of polyatomic species was developed on a generalization in the spirit of the lattice-gas model and the quasi-chemical approximation (QCA). The new theoretical framework is obtained by combining: (i) the exact analytical expression for the partition function of non-interacting mixtures of linear $k$-mers and $l$-mers (species occupying $k$ sites and $l$ sites, respectively) adsorbed in one dimension, and its extension to higher dimensions; and (ii) a generalization of the classical QCA for multicomponent adsorbates and multisite-occupancy adsorption. The process is analyzed through the partial adsorption isotherms corresponding to both species of the mixture. Comparisons with analytical data from Bragg-Williams approximation (BWA) and Monte Carlo simulations are performed in order to test the validity of the theoretical model. Even though a good fitting is obtained from BWA, it is found that QCA provides a more accurate description of the phenomenon of adsorpti...
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
XU Yuesheng; ZOU Qingsong
2005-01-01
We construct a tree wavelet approximation by using a constructive greedy scheme(CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.
Intelligent mathematics II applied mathematics and approximation theory
Duman, Oktay
2016-01-01
This special volume is a collection of outstanding more applied articles presented in AMAT 2015 held in Ankara, May 28-31, 2015, at TOBB Economics and Technology University. The collection is suitable for Applied and Computational Mathematics and Engineering practitioners, also for related graduate students and researchers. Furthermore it will be a useful resource for all science and engineering libraries. This book includes 29 self-contained and well-edited chapters that can be among others useful for seminars in applied and computational mathematics, as well as in engineering.
Uniform approximation by (quantum) polynomials
Drucker, A.; de Wolf, R.
2011-01-01
We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous functions by polynomials. We provide two proofs, based respectivel
Diophantine approximation and automorphic spectrum
Ghosh, Anish; Nevo, Amos
2010-01-01
The present paper establishes qunatitative estimates on the rate of diophantine approximation in homogeneous varieties of semisimple algebraic groups. The estimates established generalize and improve previous ones, and are sharp in a number of cases. We show that the rate of diophantine approximation is controlled by the spectrum of the automorphic representation, and is thus subject to the generalised Ramanujan conjectures.
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...
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...
Nonlinear approximation with redundant dictionaries
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, M.; Gribonval, R.
2005-01-01
In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general...
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
Hamlet, Jason R.; Mayo, Jackson R.
2015-12-22
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.
Approximate circuits for increased reliability
Energy Technology Data Exchange (ETDEWEB)
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.
Global approximation of convex functions
Azagra, D
2011-01-01
We show that for every (not necessarily bounded) open convex subset $U$ of $\\R^n$, every (not necessarily Lipschitz or strongly) convex function $f:U\\to\\R$ can be approximated by real analytic convex functions, uniformly on all of $U$. In doing so we provide a technique which transfers results on uniform approximation on bounded sets to results on uniform approximation on unbounded sets, in such a way that not only convexity and $C^k$ smoothness, but also local Lipschitz constants, minimizers, order, and strict or strong convexity, are preserved. This transfer method is quite general and it can also be used to obtain new results on approximation of convex functions defined on Riemannian manifolds or Banach spaces. We also provide a characterization of the class of convex functions which can be uniformly approximated on $\\R^n$ by strongly convex functions.
Study of the Pygmy Dipole Resonance in (p,p'γ) and (d,pγ) experiments with SONIC@HORUS
Pickstone, S. G.; Derya, V.; Hennig, A.; Mayer, J.; Spieker, M.; Weinert, M.; Wilhelmy, J.; Zilges, A.
2015-05-01
Last year, the new silicon-detector array SONIC with up to 8 silicon-detector positions was installed inside the existing γ-ray spectrometer HORUS consisting of 14 HPGe detectors. The combined setup SONIC@HORUS allows for a coincident detection of γ-rays and light charged particles in the exit channel of inelastic scattering and transfer reactions. As a first physics case, the Pygmy Dipole Resonance (PDR) in 92Mo has been investigated in a (p,p'γ) experiment at Ep = 10.5 MeV. Since specific excitation energy can be chosen oﬄine in the coincidence data, the sensitivity to weak decay branchings of PDR states is increased. Additionally, a second reaction mechanism for the excitation of PDR states has been tested with the new setup. In a 119Sn(d,pγ) transfer reaction at Ed = 8.5 MeV, PDR states in 120Sn could be excited. Since this one-neutron transfer reaction is sensitive to the neutron single-particle structure, it could reveal new information on the microscopic structure of the PDR.
Study of the Pygmy Dipole Resonance in (p,p’γ and (d,pγ experiments with SONIC@HORUS
Directory of Open Access Journals (Sweden)
Pickstone S. G.
2015-01-01
Full Text Available Last year, the new silicon-detector array SONIC with up to 8 silicon-detector positions was installed inside the existing γ-ray spectrometer HORUS consisting of 14 HPGe detectors. The combined setup SONIC@HORUS allows for a coincident detection of γ-rays and light charged particles in the exit channel of inelastic scattering and transfer reactions. As a first physics case, the Pygmy Dipole Resonance (PDR in 92Mo has been investigated in a (p,p’γ experiment at Ep = 10.5 MeV. Since specific excitation energy can be chosen oﬄine in the coincidence data, the sensitivity to weak decay branchings of PDR states is increased. Additionally, a second reaction mechanism for the excitation of PDR states has been tested with the new setup. In a 119Sn(d,pγ transfer reaction at Ed = 8.5 MeV, PDR states in 120Sn could be excited. Since this one-neutron transfer reaction is sensitive to the neutron single-particle structure, it could reveal new information on the microscopic structure of the PDR.
Vendl, Catharina; Frei, Samuel; Dittmann, Marie Theres; Furrer, Samuel; Ortmann, Sylvia; Lawrenz, Arne; Lange, Bastian; Munn, Adam; Kreuzer, Michael; Clauss, Marcus
2016-01-01
Methane (CH4) production varies between herbivore species, but reasons for this variation remain to be elucidated. Here, we report open-circuit chamber respiration measurements of CH4 production in four specimens each of two non-ruminant mammalian herbivores with a complex forestomach but largely differing in body size, the collared peccary (Pecari tajacu, mean body mass 17kg) and the pygmy hippopotamus (Hexaprotodon liberiensis, 229kg) fed lucerne-based diets. In addition, food intake, digestibility and mean retention times were measured in the same experiments. CH4 production averaged 8 and 72L/d, 18 and 19L/kg dry matter intake, and 4.0 and 4.2% of gross energy intake for the two species, respectively. When compared with previously reported data on CH4 production in other non-ruminant and ruminant foregut-fermenting as well as hindgut-fermenting species, it is evident that neither the question whether a species is a foregut fermenter or not, or whether it ruminates or not, is of the relevance previously suggested to explain variation in CH4 production between species. Rather, differences in CH4 production between species on similar diets appear related to species-specific differences in food intake and digesta retention kinetics.
Fisher, Heidi S; Swaisgood, R R; Fitch-Snyder, H
2003-11-01
Here we use sexual selection theory to develop a logistically simple, yet effective, method for the manipulation of female reproductive behavior for conservation goals. Mate choice leading to nonrandom mating patterns can exacerbate the loss of genetic diversity in small populations. On theoretical grounds, females should choose high-quality mates. A prediction stemming from chemical communication theory is that competitive males will be better able to saturate an area with scent marks. If this is true, females should mate preferentially with males whose odors they encounter most frequently. We tested this hypothesis with the pygmy loris, Nycticebus pygmaeus, a threatened and poorly studied nocturnal prosimian. For several weeks females were exposed repeatedly to the urine from a particular male, and were then allowed to choose between a male whose odors were familiar and one whose odors were novel. Females showed an unusually strong preference for the familiar-odor male, as indicated by several behavioral measures of mate preference. Conservation managers can use this method as a tool to obtain reproductive pairings that will maximize genetic compatibility and diversity. For example, unsuccessful males may be given the opportunity to reproduce. In captive populations, studbook managers often select pairs in order to optimize outbreeding, but these selected pairings may not coincide with the preferences of the individual animals involved. Although several authors have made theoretical arguments for manipulating mate choice for conservation, this is a novel test of a proximate mechanism that can be manipulated, cultivating applications rather than mere implications.
Binary nucleation beyond capillarity approximation
Kalikmanov, V.I.
2010-01-01
Large discrepancies between binary classical nucleation theory (BCNT) and experiments result from adsorption effects and inability of BCNT, based on the phenomenological capillarity approximation, to treat small clusters. We propose a model aimed at eliminating both of these deficiencies. Adsorption
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.
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.
Approximate common divisors via lattices
Cohn, Henry
2011-01-01
We analyze the multivariate generalization of Howgrave-Graham's algorithm for the approximate common divisor problem. In the m-variable case with modulus N and approximate common divisor of size N^beta, this improves the size of the error tolerated from N^(beta^2) to N^(beta^((m+1)/m)), under a commonly used heuristic assumption. This gives a more detailed analysis of the hardness assumption underlying the recent fully homomorphic cryptosystem of van Dijk, Gentry, Halevi, and Vaikuntanathan. While these results do not challenge the suggested parameters, a 2^sqrt(n) approximation algorithm for lattice basis reduction in n dimensions could be used to break these parameters. We have implemented our algorithm, and it performs better in practice than the theoretical analysis suggests. Our results fit into a broader context of analogies between cryptanalysis and coding theory. The multivariate approximate common divisor problem is the number-theoretic analogue of noisy multivariate polynomial interpolation, and we ...
Reliable Function Approximation and Estimation
2016-08-16
AFRL-AFOSR-VA-TR-2016-0293 Reliable Function Approximation and Estimation Rachel Ward UNIVERSITY OF TEXAS AT AUSTIN 101 EAST 27TH STREET STE 4308...orthogonal polynomial bases from a minimal number of pointwise function evaluations. Based on a model of weighted sparsity which we in- troduced, we...Institution name University of Texas at Austin Grant/Contract Title The full title of the funded effort. (YIP): Reliable function approximation and estimation
Mathematical algorithms for approximate reasoning
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
Twisted inhomogeneous Diophantine approximation and badly approximable sets
Harrap, Stephen
2010-01-01
For any real pair i, j geq 0 with i+j=1 let Bad(i, j) denote the set of (i, j)-badly approximable pairs. That is, Bad(i, j) consists of irrational vectors x:=(x_1, x_2) in R^2 for which there exists a positive constant c(x) such that max {||qx_1||^(-i), ||qx_2||^(-j)} > c(x)/q for all q in N. Building on a result of Kurzweil, a new characterization of the set Bad(i, j) in terms of `well-approximable' vectors in the area of `twisted' inhomogeneous Diophantine approximation is established. In addition, it is shown that Bad^x(i, j), the `twisted' inhomogeneous analogue of Bad(i, j), has full Hausdorff dimension 2 when x is chosen from the set Bad(i, j).
Approximating Graphic TSP by Matchings
Mömke, Tobias
2011-01-01
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leading to a decreased cost. For the TSP on graphic metrics (graph-TSP), the approach yields a 1.461-approximation algorithm with respect to the Held-Karp lower bound. For graph-TSP restricted to a class of graphs that contains degree three bounded and claw-free graphs, we show that the integrality gap of the Held-Karp relaxation matches the conjectured ratio 4/3. The framework allows for generalizations in a natural way and also leads to a 1.586-approximation algorithm for the traveling salesman path problem on graphic metrics where the start and end vertices are prespecified.
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.
Reinforcement Learning via AIXI Approximation
Veness, Joel; Hutter, Marcus; Silver, David
2010-01-01
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.
Concept Approximation between Fuzzy Ontologies
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Fuzzy ontologies are efficient tools to handle fuzzy and uncertain knowledge on the semantic web; but there are heterogeneity problems when gaining interoperability among different fuzzy ontologies. This paper uses concept approximation between fuzzy ontologies based on instances to solve the heterogeneity problems. It firstly proposes an instance selection technology based on instance clustering and weighting to unify the fuzzy interpretation of different ontologies and reduce the number of instances to increase the efficiency. Then the paper resolves the problem of computing the approximations of concepts into the problem of computing the least upper approximations of atom concepts. It optimizes the search strategies by extending atom concept sets and defining the least upper bounds of concepts to reduce the searching space of the problem. An efficient algorithm for searching the least upper bounds of concept is given.
Approximate Sparse Regularized Hyperspectral Unmixing
Directory of Open Access Journals (Sweden)
Chengzhi Deng
2014-01-01
Full Text Available Sparse regression based unmixing has been recently proposed to estimate the abundance of materials present in hyperspectral image pixel. In this paper, a novel sparse unmixing optimization model based on approximate sparsity, namely, approximate sparse unmixing (ASU, is firstly proposed to perform the unmixing task for hyperspectral remote sensing imagery. And then, a variable splitting and augmented Lagrangian algorithm is introduced to tackle the optimization problem. In ASU, approximate sparsity is used as a regularizer for sparse unmixing, which is sparser than l1 regularizer and much easier to be solved than l0 regularizer. Three simulated and one real hyperspectral images were used to evaluate the performance of the proposed algorithm in comparison to l1 regularizer. Experimental results demonstrate that the proposed algorithm is more effective and accurate for hyperspectral unmixing than state-of-the-art l1 regularizer.
Transfinite Approximation of Hindman's Theorem
Beiglböck, Mathias
2010-01-01
Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the corresponding finite form, stating that in any finite coloring of the integers there are arbitrarily long finite sets with the same property. We extend the finite form of Hindman's Theorem to a "transfinite" version for each countable ordinal, and show that Hindman's Theorem is equivalent to the appropriate transfinite approximation holding for every countable ordinal. We then give a proof of Hindman's Theorem by directly proving these transfinite approximations.
Tree wavelet approximations with applications
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Baraniuk, R. G., DeVore, R. A., Kyriazis, G., Yu, X. M., Near best tree approximation, Adv. Comput. Math.,2002, 16: 357-373.[2]Cohen, A., Dahmen, W., Daubechies, I., DeVore, R., Tree approximation and optimal encoding, Appl. Comput.Harmonic Anal., 2001, 11: 192-226.[3]Dahmen, W., Schneider, R., Xu, Y., Nonlinear functionals of wavelet expansions-adaptive reconstruction and fast evaluation, Numer. Math., 2000, 86: 49-101.[4]DeVore, R. A., Nonlinear approximation, Acta Numer., 1998, 7: 51-150.[5]Davis, G., Mallat, S., Avellaneda, M., Adaptive greedy approximations, Const. Approx., 1997, 13: 57-98.[6]DeVore, R. A., Temlyakov, V. N., Some remarks on greedy algorithms, Adv. Comput. Math., 1996, 5: 173-187.[7]Kashin, B. S., Temlyakov, V. N., Best m-term approximations and the entropy of sets in the space L1, Mat.Zametki (in Russian), 1994, 56: 57-86.[8]Temlyakov, V. N., The best m-term approximation and greedy algorithms, Adv. Comput. Math., 1998, 8:249-265.[9]Temlyakov, V. N., Greedy algorithm and m-term trigonometric approximation, Constr. Approx., 1998, 14:569-587.[10]Hutchinson, J. E., Fractals and self similarity, Indiana. Univ. Math. J., 1981, 30: 713-747.[11]Binev, P., Dahmen, W., DeVore, R. A., Petruchev, P., Approximation classes for adaptive methods, Serdica Math.J., 2002, 28: 1001-1026.[12]Gilbarg, D., Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Berlin: Springer-Verlag,1983.[13]Ciarlet, P. G., The Finite Element Method for Elliptic Problems, New York: North Holland, 1978.[14]Birman, M. S., Solomiak, M. Z., Piecewise polynomial approximation of functions of the class Wαp, Math. Sb.,1967, 73: 295-317.[15]DeVore, R. A., Lorentz, G. G., Constructive Approximation, New York: Springer-Verlag, 1993.[16]DeVore, R. A., Popov, V., Interpolation of Besov spaces, Trans. Amer. Math. Soc., 1988, 305: 397-414.[17]Devore, R., Jawerth, B., Popov, V., Compression of wavelet decompositions, Amer. J. Math., 1992, 114: 737-785.[18]Storozhenko, E
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.
Approximate Reasoning with Fuzzy Booleans
Broek, van den P.M.; Noppen, J.A.R.
2004-01-01
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante
Some results in Diophantine approximation
DEFF Research Database (Denmark)
in the formal Laurent series over F3. The first paper is on intrinsic Diophantine approximation in the Cantor set in the formal Laurent series over F3. The summary contains a short motivation, the results of the paper and sketches of the proofs, mainly focusing on the ideas involved. The details of the proofs...
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...
Approximation on the complex sphere
Alsaud, Huda; Kushpel, Alexander; Levesley, Jeremy
2012-01-01
We develop new elements of harmonic analysis on the complex sphere on the basis of which Bernstein's, Jackson's and Kolmogorov's inequalities are established. We apply these results to get order sharp estimates of $m$-term approximations. The results obtained is a synthesis of new results on classical orthogonal polynomials, harmonic analysis on manifolds and geometric properties of Euclidean spaces.
WKB Approximation in Noncommutative Gravity
Directory of Open Access Journals (Sweden)
Maja Buric
2007-12-01
Full Text Available We consider the quasi-commutative approximation to a noncommutative geometry defined as a generalization of the moving frame formalism. The relation which exists between noncommutativity and geometry is used to study the properties of the high-frequency waves on the flat background.
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...
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.
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…
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...
Low Rank Approximation in $G_0W_0$ Approximation
Shao, Meiyue; Yang, Chao; Liu, Fang; da Jornada, Felipe H; Deslippe, Jack; Louie, Steven G
2016-01-01
The single particle energies obtained in a Kohn--Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green's function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The $G_0W_0$ approximation is a widely used technique in which the self energy is expressed as the convolution of a non-interacting Green's function ($G_0$) and a screened Coulomb interaction ($W_0$) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating $W_0$ at multiple frequencies. In this paper, we discuss how the cos...
Orekhova, Natal'ya A; Modorov, Makar V
2016-09-01
This work is based on the comparative analysis of data obtained in the course of monitoring pygmy wood mouse populations (Apodemus uralensis Pallas, 1811) in the East-Urals Radioactive Trace (EURT) area and background territories. The effect of population size and its interaction with the radioactivity on biochemical parameters in the spleen and adrenal glands was studied. The concentrations of total lipids, proteins, DNA and RNA, activity of glucose-6-phosphate isomerase and catalase as well as the level of lipid peroxidation (LPO) were evaluated. The functional-metabolic shifts seen with large population sizes were characterized by delipidisation of adrenocortical cells, increased LPO as the main mechanism for steroidogenesis, growth of the protein components of the adrenal glands to maintain their hyperfunction, as well as immunosuppression associated with the restriction of carbohydrates providing splenocytes, reduction of DNA synthesis, and the development of a pro-/antioxidant imbalance. Reactivity of the neuroendocrine and hematopoietic systems of animals experiencing a high population density was higher in the EURT zone compared with the reference group. This difference can be explained by the additional stress from the chronic radiation exposure. The level of LPO, catalase activity, and DNA/protein ratio in the spleen and the total protein content in the adrenal glands were the most sensitive to the interaction of population size and radiation exposure. The harmful effect (distress) of the interaction of non-radiation and radiation factors can manifest when there is a population abundance above 30 ind./100 trap-day and a radiation burden which exceeds the lower boundary of the Derived Consideration Reference Levels, which is above 0.1 mGy/day.
Effect of Cu(II), Cd(II) and Zn(II) on Pb(II) biosorption by algae Gelidium-derived materials.
Vilar, Vítor J P; Botelho, Cidália M S; Boaventura, Rui A R
2008-06-15
Biosorption of Pb(II), Cu(II), Cd(II) and Zn(II) from binary metal solutions onto the algae Gelidium sesquipedale, an algal industrial waste and a waste-based composite material was investigated at pH 5.3, in a batch system. Binary Pb(II)/Cu(II), Pb(II)/Cd(II) and Pb(II)/Zn(II) solutions have been tested. For the same equilibrium concentrations of both metal ions (1 mmol l(-1)), approximately 66, 85 and 86% of the total uptake capacity of the biosorbents is taken by lead ions in the systems Pb(II)/Cu(II), Pb(II)/Cd(II) and Pb(II)/Zn(II), respectively. Two-metal results were fitted to a discrete and a continuous model, showing the inhibition of the primary metal biosorption by the co-cation. The model parameters suggest that Cd(II) and Zn(II) have the same decreasing effect on the Pb(II) uptake capacity. The uptake of Pb(II) was highly sensitive to the presence of Cu(II). From the discrete model it was possible to obtain the Langmuir affinity constant for Pb(II) biosorption. The presence of the co-cations decreases the apparent affinity of Pb(II). The experimental results were successfully fitted by the continuous model, at different pH values, for each biosorbent. The following sequence for the equilibrium affinity constants was found: Pb>Cu>Cd approximately Zn.
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...... complexity can potentially lead to limited power consumption, which translates into longer battery life-time in the handsets. The scope of the thesis is more specifically to investigate approximate (nearoptimal) detection methods that can reduce the computationally complexity significantly compared...... 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...
Approximate Privacy: Foundations and Quantification
Feigenbaum, Joan; Schapira, Michael
2009-01-01
Increasing use of computers and networks in business, government, recreation, and almost all aspects of daily life has led to a proliferation of online sensitive data about individuals and organizations. Consequently, concern about the privacy of these data has become a top priority, particularly those data that are created and used in electronic commerce. There have been many formulations of privacy and, unfortunately, many negative results about the feasibility of maintaining privacy of sensitive data in realistic networked environments. We formulate communication-complexity-based definitions, both worst-case and average-case, of a problem's privacy-approximation ratio. We use our definitions to investigate the extent to which approximate privacy is achievable in two standard problems: the second-price Vickrey auction and the millionaires problem of Yao. For both the second-price Vickrey auction and the millionaires problem, we show that not only is perfect privacy impossible or infeasibly costly to achieve...
Hydrogen Beyond the Classic Approximation
Scivetti, I
2003-01-01
The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position
Validity of the Eikonal Approximation
Kabat, Daniel
1992-01-01
We summarize results on the reliability of the eikonal approximation in obtaining the high energy behavior of a two particle forward scattering amplitude. Reliability depends on the spin of the exchanged field. For scalar fields the eikonal fails at eighth order in perturbation theory, when it misses the leading behavior of the exchange-type diagrams. In a vector theory the eikonal gets the exchange diagrams correctly, but fails by ignoring certain non-exchange graphs which dominate the asymp...
Many Faces of Boussinesq Approximations
Vladimirov, Vladimir A
2016-01-01
The \\emph{equations of Boussinesq approximation} (EBA) for an incompressible and inhomogeneous in density fluid are analyzed from a viewpoint of the asymptotic theory. A systematic scaling shows that there is an infinite number of related asymptotic models. We have divided them into three classes: `poor', `reasonable' and `good' Boussinesq approximations. Each model can be characterized by two parameters $q$ and $k$, where $q =1, 2, 3, \\dots$ and $k=0, \\pm 1, \\pm 2,\\dots$. Parameter $q$ is related to the `quality' of approximation, while $k$ gives us an infinite set of possible scales of velocity, time, viscosity, \\emph{etc.} Increasing $q$ improves the quality of a model, but narrows the limits of its applicability. Parameter $k$ allows us to vary the scales of time, velocity and viscosity and gives us the possibility to consider any initial and boundary conditions. In general, we discover and classify a rich variety of possibilities and restrictions, which are hidden behind the routine use of the Boussinesq...
Approximate Counting of Graphical Realizations.
Erdős, Péter L; Kiss, Sándor Z; Miklós, István; Soukup, Lajos
2015-01-01
In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007), for regular directed graphs (by Greenhill, 2011) and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013). Several heuristics on counting the number of possible realizations exist (via sampling processes), and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases) the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS) for counting of all realizations.
Approximate Counting of Graphical Realizations.
Directory of Open Access Journals (Sweden)
Péter L Erdős
Full Text Available In 1999 Kannan, Tetali and Vempala proposed a MCMC method to uniformly sample all possible realizations of a given graphical degree sequence and conjectured its rapidly mixing nature. Recently their conjecture was proved affirmative for regular graphs (by Cooper, Dyer and Greenhill, 2007, for regular directed graphs (by Greenhill, 2011 and for half-regular bipartite graphs (by Miklós, Erdős and Soukup, 2013. Several heuristics on counting the number of possible realizations exist (via sampling processes, and while they work well in practice, so far no approximation guarantees exist for such an approach. This paper is the first to develop a method for counting realizations with provable approximation guarantee. In fact, we solve a slightly more general problem; besides the graphical degree sequence a small set of forbidden edges is also given. We show that for the general problem (which contains the Greenhill problem and the Miklós, Erdős and Soukup problem as special cases the derived MCMC process is rapidly mixing. Further, we show that this new problem is self-reducible therefore it provides a fully polynomial randomized approximation scheme (a.k.a. FPRAS for counting of all realizations.
Energy Technology Data Exchange (ETDEWEB)
Semmler, Diego; Aumann, T.; Bauer, C.; Baumann, M.; Beckstein, M.; Beller, J.; Blecher, A.; Cvejin, N.; Duchene, M.; Hug, F.; Kahlbow, J.; Knoerzer, M.; Kreis, K.; Kremer, C.; Ries, P.; Romig, C.; Scheit, H.; Schnorrenberger, L.; Symochko, D.; Walz, C. [Institut fuer Kernphysik, Darmstadt (Germany); Lefol, R. [University of Saskatchewan, Saskatoon (Canada); Loeher, B. [ExtreMe Matter Institute EMMI and Research Division, Frankfurt (Germany); Institute for Advanced Studies FIAS, Frankfurt (Germany)
2014-07-01
The low energy photon tagger NEPTUN at the S-DALINAC delivers a quasi-monoenergetic photon beam between about 4 MeV and 20 MeV with a resolution of approximately 25 keV. Tagged photons provide the possibility to measure the dipole strength of nuclei in the energy range below and above the neutron threshold. The highly efficient LaBr{sub 3} based spectrometer GALATEA will be used to detect not only the direct decays to the ground state, but also cascading decays can be measured with suitable efficiency. We will measure (γ,n)- and (γ,nγ)-reactions with neutron detectors based on plastic scintillators. This talk provides an overview about setup and goals of the NEPTUN experiment as well as the current state of the commissioning phase. Planned optimizations of the setup, based on the results of a test beam time in June 2013, are also presented.
Effective restoration of dipole sum rules within the renormalized random-phase approximation
Hung, N. Quang; Dang, N. Dinh; Hao, T. V. Nhan; Phuc, L. Tan
2016-12-01
The dipole excitations for calcium and zirconium isotopes are studied within the fully self-consistent Hartree-Fock mean field incorporated with the renormalized random-phase approximation (RRPA) using the Skyrme interaction SLy5. The RRPA takes into account the effect of ground-state correlations beyond RPA owing to the Pauli principle between the particle-hole pairs that form the RPA excitations as well as the correlations due to the particle-particle and hole-hole transitions, whose effects are treated here in an effective way. By comparing the RPA results with the RRPA ones, which are obtained for isoscalar (IS) and isovector (IV) dipole excitations in 48,52,58Ca and 90,96,110Zr, it is shown that ground-state correlations beyond the RPA reduce the IS transition strengths. They also shift up the energy of the lowest IV dipole state and slightly push down the peak energy of the IV giant dipole resonance. As the result, the energy-weighted sums of strengths of both IS and IV modes decrease, causing the violation of the corresponding energy-weighted sum rules (EWSR). It is shown that this sum rule violation can be eliminated by taking into account the contribution of the particle-particle and hole-hole excitations together with the particle-hole ones in a simple and perturbative way. Consequently, the ratio of the energy-weighted sum of strengths of the pygmy dipole resonance to that of the giant dipole resonance increases.
Ji, Fei-Yu; Zhang, Shun-Li
2013-11-01
In this paper, the generalized diffusion equation with perturbation ut = A(u;ux)uII+eB(u;ux) is studied in terms of the approximate functional variable separation approach. A complete classification of these perturbed equations which admit approximate functional separable solutions is presented. Some approximate solutions to the resulting perturbed equations are obtained by examples.
Rollout Sampling Approximate Policy Iteration
Dimitrakakis, Christos
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 supervised learning problem. This paper proposes variants of an improved policy iteration scheme which addresses the core sampling problem in evaluating a policy through simulation as a multi-armed bandit machine. The resulting algorithm offers comparable performance to the previous algorithm achieved, however, with significantly less computational effort. An order of magnitude improvement is demonstrated experimentally in two standard reinforcement learning domains: inverted pendulum and mountain-car.
Approximate Deconvolution Reduced Order Modeling
Xie, Xuping; Wang, Zhu; Iliescu, Traian
2015-01-01
This paper proposes a large eddy simulation reduced order model(LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition(POD) is used to define the ROM basis and a POD differential filter is used to define the large ROM structures. An approximate deconvolution(AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient(10^{-3})
Plasma Physics Approximations in Ares
Energy Technology Data Exchange (ETDEWEB)
Managan, R. A.
2015-01-08
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, F_{n}( 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.
Analytical approximations for spiral waves
Energy Technology Data Exchange (ETDEWEB)
Löber, Jakob, E-mail: jakob@physik.tu-berlin.de; Engel, Harald [Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, EW 7-1, 10623 Berlin (Germany)
2013-12-15
We propose a non-perturbative attempt to solve the kinematic equations for spiral waves in excitable media. From the eikonal equation for the wave front we derive an implicit analytical relation between rotation frequency Ω and core radius R{sub 0}. For free, rigidly rotating spiral waves our analytical prediction is in good agreement with numerical solutions of the linear eikonal equation not only for very large but also for intermediate and small values of the core radius. An equivalent Ω(R{sub +}) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R{sub +} with Neumann boundaries at the periphery. Simultaneously, analytical approximations for the shape of free and pinned spirals are given. We discuss the reasons why the ansatz fails to correctly describe the dependence of the rotation frequency on the excitability of the medium.
Dodgson's Rule Approximations and Absurdity
McCabe-Dansted, John C
2010-01-01
With the Dodgson rule, cloning the electorate can change the winner, which Young (1977) considers an "absurdity". Removing this absurdity results in a new rule (Fishburn, 1977) for which we can compute the winner in polynomial time (Rothe et al., 2003), unlike the traditional Dodgson rule. We call this rule DC and introduce two new related rules (DR and D&). Dodgson did not explicitly propose the "Dodgson rule" (Tideman, 1987); we argue that DC and DR are better realizations of the principle behind the Dodgson rule than the traditional Dodgson rule. These rules, especially D&, are also effective approximations to the traditional Dodgson's rule. We show that, unlike the rules we have considered previously, the DC, DR and D& scores differ from the Dodgson score by no more than a fixed amount given a fixed number of alternatives, and thus these new rules converge to Dodgson under any reasonable assumption on voter behaviour, including the Impartial Anonymous Culture assumption.
Approximate reduction of dynamical systems
Tabuada, Paulo; Julius, Agung; Pappas, George J
2007-01-01
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with mechanical systems with symmetry--which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamical system can be projected to a lower dimensional space while providing hard bounds on the induced errors, i.e., when it is behaviorally similar to a dynamical system on a lower dimensional space. These concepts are illustrated on a series of examples.
Approximation by double Walsh polynomials
Directory of Open Access Journals (Sweden)
Ferenc Móricz
1992-01-01
Full Text Available We study the rate of approximation by rectangular partial sums, Cesàro means, and de la Vallée Poussin means of double Walsh-Fourier series of a function in a homogeneous Banach space X. In particular, X may be Lp(I2, where 1≦p<∞ and I2=[0,1×[0,1, or CW(I2, the latter being the collection of uniformly W-continuous functions on I2. We extend the results by Watari, Fine, Yano, Jastrebova, Bljumin, Esfahanizadeh and Siddiqi from univariate to multivariate cases. As by-products, we deduce sufficient conditions for convergence in Lp(I2-norm and uniform convergence on I2 as well as characterizations of Lipschitz classes of functions. At the end, we raise three problems.
Diophantine approximations and Diophantine equations
Schmidt, Wolfgang M
1991-01-01
"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum
On quantum and approximate privacy
Klauck, H
2001-01-01
This paper studies privacy in communication complexity. The focus is on quantum versions of the model and on protocols with only approximate privacy against honest players. We show that the privacy loss (the minimum divulged information) in computing a function can be decreased exponentially by using quantum protocols, while the class of privately computable functions (i.e., those with privacy loss 0) is not increased by quantum protocols. Quantum communication combined with small information leakage on the other hand makes certain functions computable (almost) privately which are not computable using quantum communication without leakage or using classical communication with leakage. We also give an example of an exponential reduction of the communication complexity of a function by allowing a privacy loss of o(1) instead of privacy loss 0.
Approximate analytic solutions to the NPDD: Short exposure approximations
Close, Ciara E.; Sheridan, John T.
2014-04-01
There have been many attempts to accurately describe the photochemical processes that take places in photopolymer materials. As the models have become more accurate, solving them has become more numerically intensive and more 'opaque'. Recent models incorporate the major photochemical reactions taking place as well as the diffusion effects resulting from the photo-polymerisation process, and have accurately described these processes in a number of different materials. It is our aim to develop accessible mathematical expressions which provide physical insights and simple quantitative predictions of practical value to material designers and users. In this paper, starting with the Non-Local Photo-Polymerisation Driven Diffusion (NPDD) model coupled integro-differential equations, we first simplify these equations and validate the accuracy of the resulting approximate model. This new set of governing equations are then used to produce accurate analytic solutions (polynomials) describing the evolution of the monomer and polymer concentrations, and the grating refractive index modulation, in the case of short low intensity sinusoidal exposures. The physical significance of the results and their consequences for holographic data storage (HDS) are then discussed.
Randomized approximate nearest neighbors algorithm.
Jones, Peter Wilcox; Osipov, Andrei; Rokhlin, Vladimir
2011-09-20
We present a randomized algorithm for the approximate nearest neighbor problem in d-dimensional Euclidean space. Given N points {x(j)} in R(d), the algorithm attempts to find k nearest neighbors for each of x(j), where k is a user-specified integer parameter. The algorithm is iterative, and its running time requirements are proportional to T·N·(d·(log d) + k·(d + log k)·(log N)) + N·k(2)·(d + log k), with T the number of iterations performed. The memory requirements of the procedure are of the order N·(d + k). A by-product of the scheme is a data structure, permitting a rapid search for the k nearest neighbors among {x(j)} for an arbitrary point x ∈ R(d). The cost of each such query is proportional to T·(d·(log d) + log(N/k)·k·(d + log k)), and the memory requirements for the requisite data structure are of the order N·(d + k) + T·(d + N). The algorithm utilizes random rotations and a basic divide-and-conquer scheme, followed by a local graph search. We analyze the scheme's behavior for certain types of distributions of {x(j)} and illustrate its performance via several numerical examples.
Obtaining exact value by approximate computations
Institute of Scientific and Technical Information of China (English)
Jing-zhong ZHANG; Yong FENG
2007-01-01
Numerical approximate computations can solve large and complex problems fast. They have the advantage of high efficiency. However they only give approximate results, whereas we need exact results in some fields. There is a gap between approximate computations and exact results.In this paper, we build a bridge by which exact results can be obtained by numerical approximate computations.
Fuzzy Set Approximations in Fuzzy Formal Contexts
Institute of Scientific and Technical Information of China (English)
Mingwen Shao; Shiqing Fan
2006-01-01
In this paper, a kind of multi-level formal concept is introduced. Based on the proposed multi-level formal concept, we present a pair of rough fuzzy set approximations within fuzzy formal contexts. By the proposed rough fuzzy set approximations, we can approximate a fuzzy set according to different precision level. We discuss the properties of the proposed approximation operators in detail.
Obtaining exact value by approximate computations
Institute of Scientific and Technical Information of China (English)
2007-01-01
Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.
The periodic standing-wave approximation: post-Minkowski computation
Beetle, Christopher; Hernández, Napoleón; Price, Richard H
2007-01-01
The periodic standing wave method studies circular orbits of compact objects coupled to helically symmetric standing wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling motion of black holes and binary stars. Previous work on this model has dealt with nonlinear scalar models, and with linearized general relativity. Here we present the results of the method for the post-Minkowski (PM) approximation to general relativity, the first step beyond linearized gravity. We compute the PM approximation in two ways: first, via the standard approach of computing linearized gravitational fields and constructing from them quadratic driving sources for second-order fields, and second, by solving the second-order equations as an ``exact'' nonlinear system. The results of these computations have two distinct applications: (i) The computational infrastructure for the ``exact'' PM solution will be directly applicable to full general relativity. (ii) The results w...
APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION
Institute of Scientific and Technical Information of China (English)
杨守志; 程正兴; 唐远炎
2003-01-01
An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution. The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation, a piece-wise linear function, and posseses an explicit computation formula. Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function.
Bernstein-type approximations of smooth functions
Directory of Open Access Journals (Sweden)
Andrea Pallini
2007-10-01
Full Text Available The Bernstein-type approximation for smooth functions is proposed and studied. We propose the Bernstein-type approximation with definitions that directly apply the binomial distribution and the multivariate binomial distribution. The Bernstein-type approximations generalize the corresponding Bernstein polynomials, by considering definitions that depend on a convenient approximation coefficient in linear kernels. In the Bernstein-type approximations, we study the uniform convergence and the degree of approximation. The Bernstein-type estimators of smooth functions of population means are also proposed and studied.
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.
Approximation properties of fine hyperbolic graphs
Indian Academy of Sciences (India)
Benyin Fu
2016-05-01
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 the techniques of Ozawa’s to prove that a fine hyperbolic graph has the metric invariant translation approximation property.
NONLINEAR APPROXIMATION WITH GENERAL WAVE PACKETS
Institute of Scientific and Technical Information of China (English)
L. Borup; M. Nielsen
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 characterization of the approximation spaces is derived.
Applications of Discrepancy Theory in Multiobjective Approximation
Glaßer, Christian; Witek, Maximilian
2011-01-01
We apply a multi-color extension of the Beck-Fiala theorem to show that the multiobjective maximum traveling salesman problem is randomized 1/2-approximable on directed graphs and randomized 2/3-approximable on undirected graphs. Using the same technique we show that the multiobjective maximum satisfiablilty problem is 1/2-approximable.
Advanced Concepts and Methods of Approximate Reasoning
1989-12-01
and L. Valverde. On mode and implication in approximate reasoning. In M.M. Gupta, A. Kandel, W. Bandler , J.B. Kiszka, editors, Approximate Reasoning and...190, 1981. [43] E. Trillas and L. Valverde. On mode and implication in approximate reasoning. In M.M. Gupta, A. Kandel, W. Bandler , J.B. Kiszka
Nonlinear approximation with dictionaries, I: Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
$-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space...
Nonlinear approximation with bi-framelets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten; Gribonval, Rémi
2005-01-01
We study the approximation in Lebesgue spaces of wavelet bi-frame systems given by translations and dilations of a finite set of generators. A complete characterization of the approximation spaces associated with best m-term approximation of wavelet bi-framelet systems is given. The characterizat...
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.
Fractal Trigonometric Polynomials for Restricted Range Approximation
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016-05-01
One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided uniform approximants for some classes of continuous functions.
Approximate Nearest Neighbor Queries among Parallel Segments
DEFF Research Database (Denmark)
Emiris, Ioannis Z.; Malamatos, Theocharis; Tsigaridas, Elias
2010-01-01
We develop a data structure for answering efficiently approximate nearest neighbor queries over a set of parallel segments in three dimensions. We connect this problem to approximate nearest neighbor searching under weight constraints and approximate nearest neighbor searching on historical data...
Resonant-state expansion Born Approximation
Doost, M B
2015-01-01
The Born Approximation is a fundamental formula in Physics, it allows the calculation of weak scattering via the Fourier transform of the scattering potential. I extend the Born Approximation by including in the formula the Fourier transform of a truncated basis of the infinite number of appropriately normalised resonant states. This extension of the Born Approximation is named the Resonant-State Expansion Born Approximation or RSE Born Approximation. The resonant-states of the system can be calculated using the recently discovered RSE perturbation theory for electrodynamics and normalised correctly to appear in spectral Green's functions via the flux volume normalisation.
Canonical Sets of Best L1-Approximation
Directory of Open Access Journals (Sweden)
Dimiter Dryanov
2012-01-01
Full Text Available In mathematics, the term approximation usually means either interpolation on a point set or approximation with respect to a given distance. There is a concept, which joins the two approaches together, and this is the concept of characterization of the best approximants via interpolation. It turns out that for some large classes of functions the best approximants with respect to a certain distance can be constructed by interpolation on a point set that does not depend on the choice of the function to be approximated. Such point sets are called canonical sets of best approximation. The present paper summarizes results on canonical sets of best L1-approximation with emphasis on multivariate interpolation and best L1-approximation by blending functions. The best L1-approximants are characterized as transfinite interpolants on canonical sets. The notion of a Haar-Chebyshev system in the multivariate case is discussed also. In this context, it is shown that some multivariate interpolation spaces share properties of univariate Haar-Chebyshev systems. We study also the problem of best one-sided multivariate L1-approximation by sums of univariate functions. Explicit constructions of best one-sided L1-approximants give rise to well-known and new inequalities.
Zegarelli, Mark
2012-01-01
An easy-to-understand primer on advanced calculus topics Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals. This hands-on guide also covers sequences and series, wit
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.
On Gakerkin approximations for the quasigeostrophic equations
Rocha, Cesar B; Grooms, Ian
2015-01-01
We study the representation of approximate solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes. In particular, we show that standard modes are compatible with nonzero buoyancy at the surfaces and can be used to solve the Eady problem. We extend two existing Galerkin approaches (A and B) and develop a new Galerkin approximation (C). Approximation A, due to Flierl (1978), represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith (2009b), represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series, but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the b...
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.
Approximate nearest neighbors via dictionary learning
Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos
2011-06-01
Approximate Nearest Neighbors (ANN) in high dimensional vector spaces is a fundamental, yet challenging problem in many areas of computer science, including computer vision, data mining and robotics. In this work, we investigate this problem from the perspective of compressive sensing, especially the dictionary learning aspect. High dimensional feature vectors are seldom seen to be sparse in the feature domain; examples include, but not limited to Scale Invariant Feature Transform (SIFT) descriptors, Histogram Of Gradients, Shape Contexts, etc. Compressive sensing advocates that if a given vector has a dense support in a feature space, then there should exist an alternative high dimensional subspace where the features are sparse. This idea is leveraged by dictionary learning techniques through learning an overcomplete projection from the feature space so that the vectors are sparse in the new space. The learned dictionary aids in refining the search for the nearest neighbors to a query feature vector into the most likely subspace combination indexed by its non-zero active basis elements. Since the size of the dictionary is generally very large, distinct feature vectors are most likely to have distinct non-zero basis. Utilizing this observation, we propose a novel representation of the feature vectors as tuples of non-zero dictionary indices, which then reduces the ANN search problem into hashing the tuples to an index table; thereby dramatically improving the speed of the search. A drawback of this naive approach is that it is very sensitive to feature perturbations. This can be due to two possibilities: (i) the feature vectors are corrupted by noise, (ii) the true data vectors undergo perturbations themselves. Existing dictionary learning methods address the first possibility. In this work we investigate the second possibility and approach it from a robust optimization perspective. This boils down to the problem of learning a dictionary robust to feature
Frankenstein's Glue: Transition functions for approximate solutions
Yunes, N
2006-01-01
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate solutions together. In particular, we propose certain sufficient conditions on these functions and proof that these conditions guarantee that the joined solution still satisfies the Einstein equations to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the...
Improving biconnectivity approximation via local optimization
Energy Technology Data Exchange (ETDEWEB)
Ka Wong Chong; Tak Wah Lam [Univ. of Hong Kong (Hong Kong)
1996-12-31
The problem of finding the minimum biconnected spanning subgraph of an undirected graph is NP-hard. A lot of effort has been made to find biconnected spanning subgraphs that approximate to the minimum one as close as possible. Recently, new polynomial-time (sequential) approximation algorithms have been devised to improve the approximation factor from 2 to 5/3 , then 3/2, while NC algorithms have also been known to achieve 7/4 + {epsilon}. This paper presents a new technique which can be used to further improve parallel approximation factors to 5/3 + {epsilon}. In the sequential context, the technique reveals an algorithm with a factor of {alpha} + 1/5, where a is the approximation factor of any 2-edge connectivity approximation algorithm.
Approximately liner phase IIR digital filter banks
J. D. Ćertić; M. D. Lutovac; L. D. Milić
2013-01-01
In this paper, uniform and nonuniform digital filter banks based on approximately linear phase IIR filters and frequency response masking technique (FRM) are presented. Both filter banks are realized as a connection of an interpolated half-band approximately linear phase IIR filter as a first stage of the FRM design and an appropriate number of masking filters. The masking filters are half-band IIR filters with an approximately linear phase. The resulting IIR filter banks are compared with li...
Metric Diophantine approximation on homogeneous varieties
Ghosh, Anish; Nevo, Amos
2012-01-01
We develop the metric theory of Diophantine approximation on homogeneous varieties of semisimple algebraic groups and prove results analogous to the classical Khinchin and Jarnik theorems. In full generality our results establish simultaneous Diophantine approximation with respect to several completions, and Diophantine approximation over general number fields using S-algebraic integers. In several important examples, the metric results we obtain are optimal. The proof uses quantitative equidistribution properties of suitable averaging operators, which are derived from spectral bounds in automorphic representations.
Floating-Point $L^2$-Approximations
Brisebarre, Nicolas; Hanrot, Guillaume
2007-01-01
International audience; Computing good polynomial approximations to usual functions is an important topic for the computer evaluation of those functions. These approximations can be good under several criteria, the most desirable being probably that the relative error is as small as possible in the $L^{\\infty}$ sense, i.e. everywhere on the interval under study. In the present paper, we investigate a simpler criterion, the $L^2$ case. Though finding a best polynomial $L^2$-approximation with ...
Approximation Problems in System Identification With Neural Networks
Institute of Scientific and Technical Information of China (English)
陈天平
1994-01-01
In this paper, the capability of neural networks and some approximation problens in system identification with neural networks are investigated. Some results are given: (i) For any function g ∈Llocp (R1) ∩S’ (R1) to be an Lp-Tauber-Wiener function, it is necessary and sufficient that g is not apolynomial; (ii) If g∈(Lp TW), then the set of is dense in Lp(K)’ (iii) It is proved that bycompositions of some functions of one variable, one can approximate continuous functional defined on compact Lp(K) and continuous operators from compact Lp1(K1) to LP2(K2). These results confirm the capability of neural networks in identifying dynamic systems.
A Note on Generalized Approximation Property
Directory of Open Access Journals (Sweden)
Antara Bhar
2013-01-01
Full Text Available We introduce a notion of generalized approximation property, which we refer to as --AP possessed by a Banach space , corresponding to an arbitrary Banach sequence space and a convex subset of , the class of bounded linear operators on . This property includes approximation property studied by Grothendieck, -approximation property considered by Sinha and Karn and Delgado et al., and also approximation property studied by Lissitsin et al. We characterize a Banach space having --AP with the help of -compact operators, -nuclear operators, and quasi--nuclear operators. A particular case for ( has also been characterized.
Function Approximation Using Probabilistic Fuzzy Systems
J.H. van den Berg (Jan); U. Kaymak (Uzay); R.J. Almeida e Santos Nogueira (Rui Jorge)
2011-01-01
textabstractWe consider function approximation by fuzzy systems. Fuzzy systems are typically used for approximating deterministic functions, in which the stochastic uncertainty is ignored. We propose probabilistic fuzzy systems in which the probabilistic nature of uncertainty is taken into account.
Approximation of the Inverse -Frame Operator
Indian Academy of Sciences (India)
M R Abdollahpour; A Najati
2011-05-01
In this paper, we introduce the concept of (strong) projection method for -frames which works for all conditional -Riesz frames. We also derive a method for approximation of the inverse -frame operator which is efficient for all -frames. We show how the inverse of -frame operator can be approximated as close as we like using finite-dimensional linear algebra.
INVARIANT RANDOM APPROXIMATION IN NONCONVEX DOMAIN
Directory of Open Access Journals (Sweden)
R. Shrivastava
2012-05-01
Full Text Available Random fixed point results in the setup of compact and weakly compact domain of Banach spaces which is not necessary starshaped have been obtained in the present work. Invariant random approximation results have also been determined asits application. In this way, random version of invariant approximation results due toMukherjee and Som [13] and Singh [17] have been given.
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…
Random Attractors of Stochastic Modified Boussinesq Approximation
Institute of Scientific and Technical Information of China (English)
郭春晓
2011-01-01
The Boussinesq approximation is a reasonable model to describe processes in body interior in planetary physics. We refer to [1] and [2] for a derivation of the Boussinesq approximation, and [3] for some related results of existence and uniqueness of solution.
Approximating a harmonizable isotropic random field
Directory of Open Access Journals (Sweden)
Randall J. Swift
2001-01-01
Full Text Available The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers a stochastic series approximation of a harmonizable isotropic random field. This approximation is useful for numerical simulation of such a field.
Lifetime of the Nonlinear Geometric Optics Approximation
DEFF Research Database (Denmark)
Binzer, Knud Andreas
The subject of the thesis is to study acertain approximation method for highly oscillatory solutions to nonlinear partial differential equations.......The subject of the thesis is to study acertain approximation method for highly oscillatory solutions to nonlinear partial differential equations....
On approximating multi-criteria TSP
Manthey, Bodo; Albers, S.; Marion, J.-Y.
2009-01-01
We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP), whose performances are independent of the number $k$ of criteria and come close to the approximation ratios obtained for TSP with a single objective function. We present randomized app
Nonlinear approximation with dictionaries I. Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2004-01-01
with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove...
A case where BO Approximation breaks down
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
@@ The Bom-Oppenheimer (BO)Approximation is ubiquitous in molecular physics,quantum physics and quantum chemistry. However, CAS researchers recently observed a breakdown of the Approximation in the reaction of fluorine with deuterium atoms.The result has been published in the August 24 issue of Science.
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...
Two Point Pade Approximants and Duality
Banks, Tom
2013-01-01
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a strong/weak duality, when the symmetries do not determine exact expressions for some quantity.
Computing Functions by Approximating the Input
Goldberg, Mayer
2012-01-01
In computing real-valued functions, it is ordinarily assumed that the input to the function is known, and it is the output that we need to approximate. In this work, we take the opposite approach: we show how to compute the values of some transcendental functions by approximating the input to these functions, and obtaining exact answers for their…
Inversion and approximation of Laplace transforms
Lear, W. M.
1980-01-01
A method of inverting Laplace transforms by using a set of orthonormal functions is reported. As a byproduct of the inversion, approximation of complicated Laplace transforms by a transform with a series of simple poles along the left half plane real axis is shown. The inversion and approximation process is simple enough to be put on a programmable hand calculator.
Approximability and Parameterized Complexity of Minmax Values
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Hansen, Thomas Dueholm; Miltersen, Peter Bro;
2008-01-01
We consider approximating the minmax value of a multi player game in strategic form. Tightening recent bounds by Borgs et al., we observe that approximating the value with a precision of ε log n digits (for any constant ε > 0) is NP-hard, where n is the size of the game. On the other hand...
Approximations for stop-loss reinsurance premiums
Reijnen, Rajko; Albers, Willem; Kallenberg, Wilbert 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 use
Approximations for stop-loss reinsurance premiums
Reijnen, R.; Albers, W.; Kallenberg, W.C.M.
2003-01-01
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 use
Trajectory averaging for stochastic approximation MCMC algorithms
Liang, Faming
2010-01-01
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 approximation MCMC algorithms, for example, a stochastic approximation MLE al...
Approximating maximum clique with a Hopfield network.
Jagota, A
1995-01-01
In a graph, a clique is a set of vertices such that every pair is connected by an edge. MAX-CLIQUE is the optimization problem of finding the largest clique in a given graph and is NP-hard, even to approximate well. Several real-world and theory problems can be modeled as MAX-CLIQUE. In this paper, we efficiently approximate MAX-CLIQUE in a special case of the Hopfield network whose stable states are maximal cliques. We present several energy-descent optimizing dynamics; both discrete (deterministic and stochastic) and continuous. One of these emulates, as special cases, two well-known greedy algorithms for approximating MAX-CLIQUE. We report on detailed empirical comparisons on random graphs and on harder ones. Mean-field annealing, an efficient approximation to simulated annealing, and a stochastic dynamics are the narrow but clear winners. All dynamics approximate much better than one which emulates a "naive" greedy heuristic.
Approximate Furthest Neighbor in High Dimensions
DEFF Research Database (Denmark)
Pagh, Rasmus; Silvestri, Francesco; Sivertsen, Johan von Tangen;
2015-01-01
Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries. We present a simple, fast, and highly practical data structure for answering AFN queries in high-dimensional Euclid......Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries. We present a simple, fast, and highly practical data structure for answering AFN queries in high......-dimensional Euclidean space. We build on the technique of Indyk (SODA 2003), storing random projections to provide sublinear query time for AFN. However, we introduce a different query algorithm, improving on Indyk’s approximation factor and reducing the running time by a logarithmic factor. We also present a variation...
A systematic sequence of relativistic approximations.
Dyall, Kenneth G
2002-06-01
An approach to the development of a systematic sequence of relativistic approximations is reviewed. The approach depends on the atomically localized nature of relativistic effects, and is based on the normalized elimination of the small component in the matrix modified Dirac equation. Errors in the approximations are assessed relative to four-component Dirac-Hartree-Fock calculations or other reference points. Projection onto the positive energy states of the isolated atoms provides an approximation in which the energy-dependent parts of the matrices can be evaluated in separate atomic calculations and implemented in terms of two sets of contraction coefficients. The errors in this approximation are extremely small, of the order of 0.001 pm in bond lengths and tens of microhartrees in absolute energies. From this approximation it is possible to partition the atoms into relativistic and nonrelativistic groups and to treat the latter with the standard operators of nonrelativistic quantum mechanics. This partitioning is shared with the relativistic effective core potential approximation. For atoms in the second period, errors in the approximation are of the order of a few hundredths of a picometer in bond lengths and less than 1 kJ mol(-1) in dissociation energies; for atoms in the third period, errors are a few tenths of a picometer and a few kilojoule/mole, respectively. A third approximation for scalar relativistic effects replaces the relativistic two-electron integrals with the nonrelativistic integrals evaluated with the atomic Foldy-Wouthuysen coefficients as contraction coefficients. It is similar to the Douglas-Kroll-Hess approximation, and is accurate to about 0.1 pm and a few tenths of a kilojoule/mole. The integrals in all the approximations are no more complicated than the integrals in the full relativistic methods, and their derivatives are correspondingly easy to formulate and evaluate.
Frankenstein's glue: transition functions for approximate solutions
Yunes, Nicolás
2007-09-01
Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we provide an attempt to formalize this gluing scheme by studying transition functions that join approximate analytic solutions together. In particular, we propose certain sufficient conditions on these functions and prove that these conditions guarantee that the joined solution still satisfies the Einstein equations analytically to the same order as the approximate ones. An example is also provided for a binary system of non-spinning black holes, where the approximate solutions are taken to be given by a post-Newtonian expansion and a perturbed Schwarzschild solution. For this specific case, we show that if the transition functions satisfy the proposed conditions, then the joined solution does not contain any violations to the Einstein equations larger than those already inherent in the approximations. We further show that if these functions violate the proposed conditions, then the matter content of the spacetime is modified by the introduction of a matter shell, whose stress energy tensor depends on derivatives of these functions.
Entanglement in the Born-Oppenheimer Approximation
Izmaylov, Artur F
2016-01-01
The role of electron-nuclear entanglement on the validity of the Born-Oppenheimer (BO) approximation is investigated. While nonadiabatic couplings generally lead to entanglement and to a failure of the BO approximation, surprisingly the degree of electron-nuclear entanglement is found to be uncorrelated with the degree of validity of the BO approximation. This is because while the degree of entanglement of BO states is determined by their deviation from the corresponding states in the crude BO approximation, the accuracy of the BO approximation is dictated, instead, by the deviation of the BO states from the exact electron-nuclear states. In fact, in the context of a minimal avoided crossing model, extreme cases are identified where an adequate BO state is seen to be maximally entangled, and where the BO approximation fails but the associated BO state remains approximately unentangled. Further, the BO states are found to not preserve the entanglement properties of the exact electron-nuclear eigenstates, and t...
Approximate equivalence in von Neumann algebras
Institute of Scientific and Technical Information of China (English)
DING; Huiru; Don; Hadwin
2005-01-01
One formulation of D. Voiculescu's theorem on approximate unitary equivalence is that two unital representations π and ρ of a separable C*-algebra are approximately unitarily equivalent if and only if rank o π = rank o ρ. We study the analog when the ranges of π and ρ are contained in a von Neumann algebra R, the unitaries inducing the approximate equivalence must come from R, and "rank" is replaced with "R-rank" (defined as the Murray-von Neumann equivalence of the range projection).
Orthorhombic rational approximants for decagonal quasicrystals
Indian Academy of Sciences (India)
S Ranganathan; Anandh Subramaniam
2003-10-01
An important exercise in the study of rational approximants is to derive their metric, especially in relation to the corresponding quasicrystal or the underlying clusters. Kuo’s model has been the widely accepted model to calculate the metric of the decagonal approximants. Using an alternate model, the metric of the approximants and other complex structures with the icosahedral cluster are explained elsewhere. In this work a comparison is made between the two models bringing out their equivalence. Further, using the concept of average lattices, a modified model is proposed.
Approximation of free-discontinuity problems
Braides, Andrea
1998-01-01
Functionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.
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.
DIFFERENCE SCHEMES BASING ON COEFFICIENT APPROXIMATION
Institute of Scientific and Technical Information of China (English)
MOU Zong-ze; LONG Yong-xing; QU Wen-xiao
2005-01-01
In respect of variable coefficient differential equations, the equations of coefficient function approximation were more accurate than the coefficient to be frozen as a constant in every discrete subinterval. Usually, the difference schemes constructed based on Taylor expansion approximation of the solution do not suit the solution with sharp function.Introducing into local bases to be combined with coefficient function approximation, the difference can well depict more complex physical phenomena, for example, boundary layer as well as high oscillatory, with sharp behavior. The numerical test shows the method is more effective than the traditional one.
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.
Choi, B. H.; Poe, R. T.
1977-01-01
A detailed vibrational-rotational (V-R) close-coupling formulation of electron-diatomic-molecule scattering is developed in which the target molecular axis is chosen to be the z-axis and the resulting coupled differential equation is solved in the moving body-fixed frame throughout the entire interaction region. The coupled differential equation and asymptotic boundary conditions in the body-fixed frame are given for each parity, and procedures are outlined for evaluating V-R transition cross sections on the basis of the body-fixed transition and reactance matrix elements. Conditions are discussed for obtaining identical results from the space-fixed and body-fixed formulations in the case where a finite truncated basis set is used. The hybrid theory of Chandra and Temkin (1976) is then reformulated, relevant expressions and formulas for the simultaneous V-R transitions of the hybrid theory are obtained in the same forms as those of the V-R close-coupling theory, and distorted-wave Born-approximation expressions for the cross sections of the hybrid theory are presented. A close-coupling approximation that conserves the internuclear axis component of the incident electronic angular momentum (l subscript z-prime) is derived from the V-R close-coupling formulation in the moving body-fixed frame.
Approximations of solutions to retarded integrodifferential equations
Directory of Open Access Journals (Sweden)
Dhirendra Bahuguna
2004-11-01
Full Text Available In this paper we consider a retarded integrodifferential equation and prove existence, uniqueness and convergence of approximate solutions. We also give some examples to illustrate the applications of the abstract results.
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.
Approximation methods in gravitational-radiation theory
Will, C. M.
1986-02-01
The observation of gravitational-radiation damping in the binary pulsar PSR 1913+16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. The author summarizes recent developments in two areas in which approximations are important: (1) the quadrupole approximation, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (2) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
APPROXIMATE DEVELOPMENTS FOR SURFACES OF REVOLUTION
Directory of Open Access Journals (Sweden)
Mădălina Roxana Buneci
2016-12-01
Full Text Available The purpose of this paper is provide a set of Maple procedures to construct approximate developments of a general surface of revolution generalizing the well-known gore method for sphere
An approximate Expression for Viscosity of Nanosuspensions
Domostroeva, N G
2009-01-01
We consider liquid suspensions with dispersed nanoparticles. Using two-points Pade approximants and combining results of both hydrodynamic and molecular dynamics methods, we obtain the effective viscosity for any diameters of nanoparticles
Asynchronous stochastic approximation with differential inclusions
Directory of Open Access Journals (Sweden)
David S. Leslie
2012-01-01
Full Text Available The asymptotic pseudo-trajectory approach to stochastic approximation of Benaïm, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into the mean field to produce convergence results which remain similar to those of an equivalent synchronous process. In addition, this allows many of the restrictive assumptions previously associated with asynchronous stochastic approximation to be removed. The framework is extended for a coupled asynchronous stochastic approximation process with set-valued mean fields. Two-timescales arguments are used here in a similar manner to the original work in this area by Borkar. The applicability of this approach is demonstrated through learning in a Markov decision process.
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; ...
On Approximating Four Covering and Packing Problems
Ashley, Mary; Berman, Piotr; Chaovalitwongse, Wanpracha; DasGupta, Bhaskar; Kao, Ming-Yang; 10.1016/j.jcss.2009.01.002
2011-01-01
In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and have applications in biology ranging from full-sibling reconstructions in wild populations to biomolecular clusterings; however, as this paper shows, their approximability properties differ considerably. Our inapproximability constant for the triangle packing problem improves upon the previous results; this is done by directly transforming the inapproximability gap of Haastad for the problem of maximizing the number of satisfied equations for a set of equations over GF(2) and is interesting in its own right. Our approximability results on the full siblings reconstruction problems answers questions originally posed by Berger-Wolf et al. and our results on the maximum profit coverage problem provides almost matching upper and lower bounds on the approximation ratio, answering a...
Trigonometric Approximations for Some Bessel Functions
Muhammad Taher Abuelma'atti
1999-01-01
Formulas are obtained for approximating the tabulated Bessel functions Jn(x), n = 0–9 in terms of trigonometric functions. These formulas can be easily integrated and differentiated and are convenient for personal computers and pocket calculators.
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.
Approximations for the Erlang Loss Function
DEFF Research Database (Denmark)
Mejlbro, Leif
1998-01-01
Theoretically, at least three formulae are needed for arbitrarily good approximates of the Erlang Loss Function. In the paper, for convenience five formulae are presented guaranteeing a relative error <1E-2, and methods are indicated for improving this bound.......Theoretically, at least three formulae are needed for arbitrarily good approximates of the Erlang Loss Function. In the paper, for convenience five formulae are presented guaranteeing a relative error
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.)
Parallel local approximation MCMC for expensive models
Conrad, Patrick; Davis, Andrew; Marzouk, Youssef; Pillai, Natesh; Smith, Aaron
2016-01-01
Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be exceedingly expensive when posterior evaluations invoke the evaluation of a computationally expensive model, such as a system of partial differential equations. In recent work [Conrad et al. JASA 2015, arXiv:1402.1694] we described a framework for constructing and refining local approximations of such models during an MCMC simulation. These posterior--adapted approximations harness regularity of the model to reduce the c...
Pointwise approximation by elementary complete contractions
Magajna, Bojan
2009-01-01
A complete contraction on a C*-algebra A, which preserves all closed two sided ideals J, can be approximated pointwise by elementary complete contractions if and only if the induced map on the tensor product of B with A/J is contractive for every C*-algebra B, ideal J in A and C*-tensor norm on the tensor product. A lifting obstruction for such an approximation is also obtained.
Intuitionistic Fuzzy Automaton for Approximate String Matching
Directory of Open Access Journals (Sweden)
K.M. Ravi
2014-03-01
Full Text Available This paper introduces an intuitionistic fuzzy automaton model for computing the similarity between pairs of strings. The model details the possible edit operations needed to transform any input (observed string into a target (pattern string by providing a membership and non-membership value between them. In the end, an algorithm is given for approximate string matching and the proposed model computes the similarity and dissimilarity between the pair of strings leading to better approximation.
The Actinide Transition Revisited by Gutzwiller Approximation
Xu, Wenhu; Lanata, Nicola; Yao, Yongxin; Kotliar, Gabriel
2015-03-01
We revisit the problem of the actinide transition using the Gutzwiller approximation (GA) in combination with the local density approximation (LDA). In particular, we compute the equilibrium volumes of the actinide series and reproduce the abrupt change of density found experimentally near plutonium as a function of the atomic number. We discuss how this behavior relates with the electron correlations in the 5 f states, the lattice structure, and the spin-orbit interaction. Our results are in good agreement with the experiments.
Polynomial approximation of functions in Sobolev spaces
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 polynomial 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.
Staying Thermal with Hartree Ensemble Approximations
Salle, M; Vink, Jeroen C
2000-01-01
Using Hartree ensemble approximations to compute the real time dynamics of scalar fields in 1+1 dimension, we find that with suitable initial conditions, approximate thermalization is achieved much faster than found in our previous work. At large times, depending on the interaction strength and temperature, the particle distribution slowly changes: the Bose-Einstein distribution of the particle densities develops classical features. We also discuss variations of our method which are numerically more efficient.
Differential geometry of proteins. Helical approximations.
Louie, A H; Somorjai, R L
1983-07-25
We regard a protein molecule as a geometric object, and in a first approximation represent it as a regular parametrized space curve passing through its alpha-carbon atoms (the backbone). In an earlier paper we argued that the regular patterns of secondary structures of proteins (morphons) correspond to geodesics on minimal surfaces. In this paper we discuss methods of recognizing these morphons on space curves that represent the protein backbone conformation. The mathematical tool we employ is the differential geometry of curves and surfaces. We introduce a natural approximation of backbone space curves in terms of helical approximating elements and present a computer algorithm to implement the approximation. Simple recognition criteria are given for the various morphons of proteins. These are incorporated into our helical approximation algorithm, together with more non-local criteria for the recognition of beta-sheet topologies. The method and the algorithm are illustrated with several examples of representative proteins. Generalizations of the helical approximation method are considered and their possible implications for protein energetics are sketched.
Ito, K.
1984-01-01
The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.
Ito, K.
1985-01-01
The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A characteristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.
On the Taylor Approximation of Control Systems.
1984-01-01
80-C-0041 UNCLASIFIED 12/EhE~hhhEID S11U MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS-0963.A tliLi ~ ii : MRC Technical Summary Report...control systems, Picard iterates, Taylor expansion. Work Unit Number 5 (Optimization and Large Scale Systems) Istituto di Matematica Applicata...control system on Ad: I _~~d x~)= m g(x(t))ou (t), x(o) = O ii 1 Given a control u, in general there exists no explicit formula to exactly compute the
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.
Tree-fold loop approximation of AMD
Energy Technology Data Exchange (ETDEWEB)
Ono, Akira [Tohoku Univ., Sendai (Japan). Faculty of Science
1997-05-01
AMD (antisymmetrized molecular dynamics) is a frame work for describing a wave function of nucleon multi-body system by Slater determinant of Gaussian wave flux, and a theory for integrally describing a wide range of nuclear reactions such as intermittent energy heavy ion reaction, nucleon incident reaction and so forth. The aim of this study is induction on approximation equation of expected value, {nu}, in correlation capable of calculation with time proportional A (exp 3) (or lower), and to make AMD applicable to the heavier system such as Au+Au. As it must be avoided to break characteristics of AMD, it needs not to be anxious only by approximating the {nu}-value. However, in order to give this approximation any meaning, error of this approximation will have to be sufficiently small in comparison with bond energy of atomic nucleus and smaller than 1 MeV/nucleon. As the absolute expected value in correlation may be larger than 50 MeV/nucleon, the approximation is required to have a high accuracy within 2 percent. (G.K.)
Baraklianou, Stella
2016-01-01
Container II, self-published artists book.\\ud The book was made on the occasion of the artists residency at the Banff Arts Centre, in Alberta Canada. \\ud \\ud Container II is a performative piece, it worked in conjunction with the photographic installation "Stage Set: Cool Tone" . (photographic floor installation, Reclaimed wood, frames, 130x145cm, 2016) \\ud The photographic installation was also part of the artists residency titled "New Materiality" at the Banff Arts Centre. \\ud \\ud Limited E...
On the approximate zero of Newton method
Institute of Scientific and Technical Information of China (English)
黄正达
2003-01-01
A judgment criterion to guarantee a point to be a Chen' s approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen' s approximate zero may not be a Smale' s approximate zero. The error estimate obtained indicated the convergent order when we use |f(x) | < ε to stop computation in software.The result can also be applied for solving partial derivative and integration equations.
On the approximate zero of Newton method
Institute of Scientific and Technical Information of China (English)
黄正达
2003-01-01
A judgment criterion to guarantee a point to be a Chen's approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen's approximate zero may not be a Smale's approximate zero. The error estimate obtained indicated the convergent order when we use |f(x)|<ε to stop computation in software. The result can also be applied for solving partial derivative and integration equations.
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.
Approximating light rays in the Schwarzschild field
Semerak, Oldrich
2014-01-01
A short formula is suggested which approximates photon trajectories in the Schwarzschild field better than other simple prescriptions from the literature. We compare it with various "low-order competitors", namely with those following from exact formulas for small $M$, with one of the results based on pseudo-Newtonian potentials, with a suitably adjusted hyperbola, and with the effective and often employed approximation by Beloborodov. Our main concern is the shape of the photon trajectories at finite radii, yet asymptotic behaviour is also discussed, important for lensing. An example is attached indicating that the newly suggested approximation is usable--and very accurate--for practical solving of the ray-deflection exercise.
Approximation Limits of Linear Programs (Beyond Hierarchies)
Braun, Gábor; Pokutta, Sebastian; Steurer, David
2012-01-01
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any linear program as opposed to only programs generated by hierarchies. Using our framework, we prove that O(n^{1/2-eps})-approximations for CLIQUE require linear programs of size 2^{n^\\Omega(eps)}. (This lower bound applies to linear programs using a certain encoding of CLIQUE as a linear optimization problem.) Moreover, we establish a similar result for approximations of semidefinite programs by linear programs. Our main ingredient is a quantitative improvement of Razborov's rectangle corruption lemma for the high error regime, which gives strong lower bounds on the nonnegative rank of certain perturbations of the unique disjointness matrix.
On Born approximation in black hole scattering
Energy Technology Data Exchange (ETDEWEB)
Batic, D. [University of West Indies, Department of Mathematics, Kingston (Jamaica); Kelkar, N.G.; Nowakowski, M. [Universidad de los Andes, Departamento de Fisica, Bogota (Colombia)
2011-12-15
A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordstroem and Reissner-Nordstroem-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. (orig.)
Numerical approximation of partial differential equations
Bartels, Sören
2016-01-01
Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular ...
Exponential Approximations Using Fourier Series Partial Sums
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
An Approximate Bayesian Fundamental Frequency Estimator
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt
2012-01-01
Joint fundamental frequency and model order estimation is an important problem in several applications such as speech and music processing. In this paper, we develop an approximate estimation algorithm of these quantities using Bayesian inference. The inference about the fundamental frequency...... and the model order is based on a probability model which corresponds to a minimum of prior information. From this probability model, we give the exact posterior distributions on the fundamental frequency and the model order, and we also present analytical approximations of these distributions which lower...
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A. V.
2016-08-01
We consider the eikonal approximation for moderately small scattering amplitudes. To find numerical estimates of these approximations, we derive formulas that contain no Bessel functions and consequently no rapidly oscillating integrands. To obtain these formulas, we study improper integrals of the first kind containing products of the Bessel functions J0(z). We generalize the expression with four functions J0(z) and also find expressions for the integrals with the product of five and six Bessel functions. We generalize a known formula for the improper integral with two functions Jυ (az) to the case with noninteger υ and complex a.
An approximate analytical approach to resampling averages
DEFF Research Database (Denmark)
Malzahn, Dorthe; Opper, M.
2004-01-01
Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach for appr......Using a novel reformulation, we develop a framework to compute approximate resampling data averages analytically. The method avoids multiple retraining of statistical models on the samples. Our approach uses a combination of the replica "trick" of statistical physics and the TAP approach...
Extending the Eikonal Approximation to Low Energy
Capel, Pierre; Ogata, Kazuyuki
2014-01-01
E-CDCC and DEA, two eikonal-based reaction models are compared to CDCC at low energy (e.g. 20AMeV) to study their behaviour in the regime at which the eikonal approximation is supposed to fail. We confirm that these models lack the Coulomb deflection of the projectile by the target. We show that a hybrid model, built on the CDCC framework at low angular momenta and the eikonal approximation at larger angular momenta gives a perfect agreement with CDCC. An empirical shift in impact parameter can also be used reliably to simulate this missing Coulomb deflection.
Local density approximations from finite systems
Entwistle, Mike; Wetherell, Jack; Longstaff, Bradley; Ramsden, James; Godby, Rex
2016-01-01
The local density approximation (LDA) constructed through quantum Monte Carlo calculations of the homogeneous electron gas (HEG) is the most common approximation to the exchange-correlation functional in density functional theory. We introduce an alternative set of LDAs constructed from slab-like systems of one, two and three electrons that resemble the HEG within a finite region, and illustrate the concept in one dimension. Comparing with the exact densities and Kohn-Sham potentials for various test systems, we find that the LDAs give a good account of the self-interaction correction, but are less reliable when correlation is stronger or currents flow.
Approximately-Balanced Drilling in Daqing Oilfield
Institute of Scientific and Technical Information of China (English)
Xia Bairu; Zheng Xiuhua; Li Guoqing; Tian Tuo
2004-01-01
The Daqing oilfield is a multilayered heterogeneous oil field where the pressure are different in the same vertical profile causing many troubles to the adjustment well drillings. The approximately-balanced drilling technique has been developed and proved to be efficient and successful in Daqing oilfield. This paper discusses the application of approximately-balanced drilling technique under the condition of multilayered pressure in Daqing oilfield, including the prediction of formation pressure, the pressure discharge technique for the drilling well and the control of the density of drilling fluid.
Generalized companion matrix for approximate GCD
Boito, Paola
2011-01-01
We study a variant of the univariate approximate GCD problem, where the coe?- cients of one polynomial f(x)are known exactly, whereas the coe?cients of the second polynomial g(x)may be perturbed. Our approach relies on the properties of the matrix which describes the operator of multiplication by gin the quotient ring C[x]=(f). In particular, the structure of the null space of the multiplication matrix contains all the essential information about GCD(f; g). Moreover, the multiplication matrix exhibits a displacement structure that allows us to design a fast algorithm for approximate GCD computation with quadratic complexity w.r.t. polynomial degrees.
Excluded-Volume Approximation for Supernova Matter
Yudin, A V
2014-01-01
A general scheme of the excluded-volume approximation as applied to multicomponent systems with an arbitrary degree of degeneracy has been developed. This scheme also admits an allowance for additional interactions between the components of a system. A specific form of the excluded-volume approximation for investigating supernova matter at subnuclear densities has been found from comparison with the hard-sphere model. The possibility of describing the phase transition to uniform nuclear matter in terms of the formalism under consideration is discussed.
Approximate Controllability of Fractional Integrodifferential Evolution Equations
Directory of Open Access Journals (Sweden)
R. Ganesh
2013-01-01
Full Text Available This paper addresses the issue of approximate controllability for a class of control system which is represented by nonlinear fractional integrodifferential equations with nonlocal conditions. By using semigroup theory, p-mean continuity and fractional calculations, a set of sufficient conditions, are formulated and proved for the nonlinear fractional control systems. More precisely, the results are established under the assumption that the corresponding linear system is approximately controllable and functions satisfy non-Lipschitz conditions. The results generalize and improve some known results.
BEST APPROXIMATION BY DOWNWARD SETS WITH APPLICATIONS
Institute of Scientific and Technical Information of China (English)
H.Mohebi; A. M. Rubinov
2006-01-01
We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs (W,x), where x ∈ X and W is a closed downward subset of X.
The exact renormalization group and approximation solutions
Morris, T R
1994-01-01
We investigate the structure of Polchinski's formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff greens functions are given. A promising non-perturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in `irrelevancy' of operators. We illustrate with two simple models of four dimensional $\\lambda \\varphi^4$ theory: the cactus approximation, and a model incorporating the first irrelevant correction to the renormalized coupling. The qualitative and quantitative behaviour give confidence in a fuller use of this method for obtaining accurate results.
Algebraically approximate and noisy realization of discrete-time systems and digital images
Hasegawa, Yasumichi
2009-01-01
This monograph deals with approximation and noise cancellation of dynamical systems which include linear and nonlinear input/output relationships. It also deal with approximation and noise cancellation of two dimensional arrays. It will be of special interest to researchers, engineers and graduate students who have specialized in filtering theory and system theory and digital images. This monograph is composed of two parts. Part I and Part II will deal with approximation and noise cancellation of dynamical systems or digital images respectively. From noiseless or noisy data, reduction will be
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, s.;
1999-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G(1) surface consisting of pieces of cones or cylinders of revolution or a G(r) NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...
On surface approximation using developable surfaces
DEFF Research Database (Denmark)
Chen, H. Y.; Lee, I. K.; Leopoldseder, S.;
1998-01-01
We introduce a method for approximating a given surface by a developable surface. It will be either a G_1 surface consisting of pieces of cones or cylinders of revolution or a G_r NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce...
Markov operators, positive semigroups and approximation processes
Altomare, Francesco; Leonessa, Vita; Rasa, Ioan
2015-01-01
In recent years several investigations have been devoted to the study of large classes of (mainly degenerate) initial-boundary value evolution problems in connection with the possibility to obtain a constructive approximation of the associated positive C_0-semigroups. In this research monograph we present the main lines of a theory which finds its root in the above-mentioned research field.
Approximating the DGP of China's Quarterly GDP
Ph.H.B.F. Franses (Philip Hans); H. Mees (Heleen)
2010-01-01
textabstractWe demonstrate that the data generating process (DGP) of China’s cumulated quarterly Gross Domestic Product (GDP, current prices), as it is reported by the National Bureau of Statistics of China, can be (very closely) approximated by a simple rule. This rule is that annual growth in any
Approximate Furthest Neighbor in High Dimensions
DEFF Research Database (Denmark)
Pagh, Rasmus; Silvestri, Francesco; Sivertsen, Johan von Tangen;
2015-01-01
-dimensional Euclidean space. We build on the technique of Indyk (SODA 2003), storing random projections to provide sublinear query time for AFN. However, we introduce a different query algorithm, improving on Indyk’s approximation factor and reducing the running time by a logarithmic factor. We also present a variation...
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 gi
Auction analysis by normal form game approximation
Kaisers, Michael; Tuyls, Karl; Thuijsman, Frank; Parsons, Simon
2008-01-01
Auctions are pervasive in todaypsilas society and provide a variety of real markets. This article facilitates a strategic choice between a set of available trading strategies by introducing a methodology to approximate heuristic payoff tables by normal form games. An example from the auction domain
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 a
An Approximation of Ultra-Parabolic Equations
Directory of Open Access Journals (Sweden)
Allaberen Ashyralyev
2012-01-01
Full Text Available The first and second order of accuracy difference schemes for the approximate solution of the initial boundary value problem for ultra-parabolic equations are presented. Stability of these difference schemes is established. Theoretical results are supported by the result of numerical examples.
Approximate Equilibrium Problems and Fixed Points
Directory of Open Access Journals (Sweden)
H. Mazaheri
2013-01-01
Full Text Available We find a common element of the set of fixed points of a map and the set of solutions of an approximate equilibrium problem in a Hilbert space. Then, we show that one of the sequences weakly converges. Also we obtain some theorems about equilibrium problems and fixed points.
Approximations in diagnosis: motivations and techniques
Harmelen, van F.A.H.; Teije, A. ten
1995-01-01
We argue that diagnosis should not be seen as solving a problem with a unique definition, but rather that there exists a whole space of reasonable notions of diagnosis. These notions can be seen as mutual approximations. We present a number of reasons for choosing among different notions of diagnos
Upper Bounds on Numerical Approximation Errors
DEFF Research Database (Denmark)
Raahauge, Peter
2004-01-01
This paper suggests a method for determining rigorous upper bounds on approximationerrors of numerical solutions to infinite horizon dynamic programming models.Bounds are provided for approximations of the value function and the policyfunction as well as the derivatives of the value function...
Lower Bound Approximation for Elastic Buckling Loads
Vrouwenvelder, A.; Witteveen, J.
1975-01-01
An approximate method for the elastic buckling analysis of two-dimensional frames is introduced. The method can conveniently be explained with reference to a physical interpretation: In the frame every member is replaced by two new members: - a flexural member without extensional rigidity to transmi
Eignets for function approximation on manifolds
Mhaskar, H N
2009-01-01
Let $\\XX$ be a compact, smooth, connected, Riemannian manifold without boundary, $G:\\XX\\times\\XX\\to \\RR$ be a kernel. Analogous to a radial basis function network, an eignet is an expression of the form $\\sum_{j=1}^M a_jG(\\circ,y_j)$, where $a_j\\in\\RR$, $y_j\\in\\XX$, $1\\le j\\le M$. We describe a deterministic, universal algorithm for constructing an eignet for approximating functions in $L^p(\\mu;\\XX)$ for a general class of measures $\\mu$ and kernels $G$. Our algorithm yields linear operators. Using the minimal separation amongst the centers $y_j$ as the cost of approximation, we give modulus of smoothness estimates for the degree of approximation by our eignets, and show by means of a converse theorem that these are the best possible for every \\emph{individual function}. We also give estimates on the coefficients $a_j$ in terms of the norm of the eignet. Finally, we demonstrate that if any sequence of eignets satisfies the optimal estimates for the degree of approximation of a smooth function, measured in ter...
Approximation of Aggregate Losses Using Simulation
Directory of Open Access Journals (Sweden)
Mohamed A. Mohamed
2010-01-01
Full Text Available Problem statement: The modeling of aggregate losses is one of the main objectives in actuarial theory and practice, especially in the process of making important business decisions regarding various aspects of insurance contracts. The aggregate losses over a fixed time period is often modeled by mixing the distributions of loss frequency and severity, whereby the distribution resulted from this approach is called a compound distribution. However, in many cases, realistic probability distributions for loss frequency and severity cannot be combined mathematically to derive the compound distribution of aggregate losses. Approach: This study aimed to approximate the aggregate loss distribution using simulation approach. In particular, the approximation of aggregate losses was based on a compound Poisson-Pareto distribution. The effects of deductible and policy limit on the individual loss as well as the aggregate losses were also investigated. Results: Based on the results, the approximation of compound Poisson-Pareto distribution via simulation approach agreed with the theoretical mean and variance of each of the loss frequency, loss severity and aggregate losses. Conclusion: This study approximated the compound distribution of aggregate losses using simulation approach. The investigation on retained losses and insurance claims allowed an insured or a company to select an insurance contract that fulfills its requirement. In particular, if a company wants to have an additional risk reduction, it can compare alternative policies by considering the worthiness of the additional expected total cost which can be estimated via simulation approach.
Approximations in the PE-method
DEFF Research Database (Denmark)
Arranz, Marta Galindo
1996-01-01
Two differenct sources of errors may occur in the implementation of the PE methods; a phase error introduced in the approximation of a pseudo-differential operator and an amplitude error generated from the starting field. First, the inherent phase errors introduced in the solution are analyzed...
Nonlinear approximation in alpha-modulation spaces
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2006-01-01
The α-modulation spaces are a family of spaces that contain the Besov and modulation spaces as special cases. In this paper we prove that brushlet bases can be constructed to form unconditional and even greedy bases for the α-modulation spaces. We study m -term nonlinear approximation with brushlet...
Approximate fixed point of Reich operator
Directory of Open Access Journals (Sweden)
M. Saha
2013-01-01
Full Text Available In the present paper, we study the existence of approximate fixed pointfor Reich operator together with the property that the ε-fixed points are concentrated in a set with the diameter tends to zero if ε $to$ > 0.
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.
Kravchuk functions for the finite oscillator approximation
Atakishiyev, Natig M.; Wolf, Kurt Bernardo
1995-01-01
Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion.
Image Compression Via a Fast DCT Approximation
Bayer, F. M.; Cintra, R. J.
2010-01-01
Discrete transforms play an important role in digital signal processing. In particular, due to its transform domain energy compaction properties, the discrete cosine transform (DCT) is pivotal in many image processing problems. This paper introduces a numerical approximation method for the DCT based
Improved Approximations for Multiprocessor Scheduling Under Uncertainty
Crutchfield, Christopher; Fineman, Jeremy T; Karger, David R; Scott, Jacob
2008-01-01
This paper presents improved approximation algorithms for the problem of multiprocessor scheduling under uncertainty, or SUU, in which the execution of each job may fail probabilistically. This problem is motivated by the increasing use of distributed computing to handle large, computationally intensive tasks. In the SUU problem we are given n unit-length jobs and m machines, a directed acyclic graph G of precedence constraints among jobs, and unrelated failure probabilities q_{ij} for each job j when executed on machine i for a single timestep. Our goal is to find a schedule that minimizes the expected makespan, which is the expected time at which all jobs complete. Lin and Rajaraman gave the first approximations for this NP-hard problem for the special cases of independent jobs, precedence constraints forming disjoint chains, and precedence constraints forming trees. In this paper, we present asymptotically better approximation algorithms. In particular, we give an O(loglog min(m,n))-approximation for indep...
Approximation algorithms for planning and control
Boddy, Mark; Dean, Thomas
1989-01-01
A control system operating in a complex environment will encounter a variety of different situations, with varying amounts of time available to respond to critical events. Ideally, such a control system will do the best possible with the time available. In other words, its responses should approximate those that would result from having unlimited time for computation, where the degree of the approximation depends on the amount of time it actually has. There exist approximation algorithms for a wide variety of problems. Unfortunately, the solution to any reasonably complex control problem will require solving several computationally intensive problems. Algorithms for successive approximation are a subclass of the class of anytime algorithms, algorithms that return answers for any amount of computation time, where the answers improve as more time is allotted. An architecture is described for allocating computation time to a set of anytime algorithms, based on expectations regarding the value of the answers they return. The architecture described is quite general, producing optimal schedules for a set of algorithms under widely varying conditions.
Approximations of Two-Attribute Utility Functions
1976-09-01
Introduction to Approximation Theory, McGraw-Hill, New York, 1966. Faber, G., Uber die interpolatorische Darstellung stetiger Funktionen, Deutsche...Management Review 14 (1972b) 37-50. Keeney, R. L., A decision analysis with multiple objectives: the Mexico City airport, Bell Journal of Economics
Strong washout approximation to resonant leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Garbrecht, Bjoern; Gautier, Florian; Klaric, Juraj [Physik Department T70, James-Franck-Strasse, Techniche Universitaet Muenchen, 85748 Garching (Germany)
2016-07-01
We study resonant Leptogenesis with two sterile neutrinos with masses M{sub 1} and M{sub 2}, Yukawa couplings Y{sub 1} and Y{sub 2}, and a single active flavor. Specifically, we focus on the strong washout regime, where the decay width dominates the mass splitting of the two sterile neutrinos. We show that one can approximate the effective decay asymmetry by it's late time limit ε = X sin(2 φ)/(X{sup 2}+sin{sup 2}φ), where X=8 π Δ/(vertical stroke Y{sub 1} vertical stroke {sup 2}+ vertical stroke Y{sub 2} vertical stroke {sup 2}), Δ=4(M{sub 1}-M{sub 2})/(M{sub 1}+M{sub 2}), and φ=arg(Y{sub 2}/Y{sub 1}), and establish criteria for the validity of this approximation. We compare the approximate results with numerical ones, obtained by solving the mixing and oscillations of the sterile neutrinos. We generalize the formula to the case of several active flavors, and demonstrate how it can be used to calculate the lepton asymmetry in phenomenological scenarios which are in agreement with the neutrino oscillation data. We find that that using the late time limit is an applicable approximation throughout the phenomenologically viable parameter space.
$\\Phi$-derivable approximations in gauge theories
Arrizabalaga, A
2003-01-01
We discuss the method of $\\Phi$-derivable approximations in gauge theories. There, two complications arise, namely the violation of Bose symmetry in correlation functions and the gauge dependence. For the latter we argue that the error introduced by the gauge dependent terms is controlled, therefore not invalidating the method.
Optimizing the structure of Tetracyanoplatinate(II)
DEFF Research Database (Denmark)
Dohn, Asmus Ougaard; Møller, Klaus Braagaard; Sauer, Stephan P. A.
2013-01-01
The geometry of tetracyanoplatinate(II) (TCP) has been optimized with density functional theory (DFT) calculations in order to compare different computational strategies. Two approximate scalar relativistic methods, i.e. the scalar zeroth-order regular approximation (ZORA) and non-relativistic ca...
Predictor feedback for delay systems implementations and approximations
Karafyllis, Iasson
2017-01-01
This monograph bridges the gap between the nonlinear predictor as a concept and as a practical tool, presenting a complete theory of the application of predictor feedback to time-invariant, uncertain systems with constant input delays and/or measurement delays. It supplies several methods for generating the necessary real-time solutions to the systems’ nonlinear differential equations, which the authors refer to as approximate predictors. Predictor feedback for linear time-invariant (LTI) systems is presented in Part I to provide a solid foundation on the necessary concepts, as LTI systems pose fewer technical difficulties than nonlinear systems. Part II extends all of the concepts to nonlinear time-invariant systems. Finally, Part III explores extensions of predictor feedback to systems described by integral delay equations and to discrete-time systems. The book’s core is the design of control and observer algorithms with which global stabilization, guaranteed in the previous literature with idealized (b...
Hybrid diffusion approximation in highly absorbing media and its effects of source approximation
Institute of Scientific and Technical Information of China (English)
Huijuan Tian; Ying Liu; Lijun Wang; Yuhui Zhang; Lifeng Xiao
2009-01-01
A modified diffusion approximation model called the hybrid diffusion approximation that can be used for highly absorbing media is investigated.The analytic solution of the hybrid diffusion approximation for reflectance in two-source approximation and steady-state case with extrapolated boundary is obtained.The effects of source approximation on the analytic solution are investigated,and it is validated that two-source approximation in highly absorbing media to describe the optical properties of biological tissue is necessary.Monte Carlo simulation of recovering optical parameters from reflectant data is done with the use of this model.The errors of recovering μa and μ's are smaller than 15% for the reduced albedo between 0.77 and 0.5 with the source-detector separation of 0.4-3 ram.
Approximating Smooth Step Functions Using Partial Fourier Series Sums
2012-09-01
interp1(xt(ii), smoothstepbez( t(ii), min(t(ii)), max(t(ii)), ’y’), t(ii), ’linear’, ’ extrap ’); ii = find( abs(t - tau/2) <= epi ); iii = t(ii...interp1( xt(ii), smoothstepbez( rt, min(rt), max(rt), ’y’), t(ii), ’linear’, ’ extrap ’ ); % stepm(ii) = 1 - interp1(xt(ii), smoothstepbez( t(ii...min(t(ii)), max(t(ii)), ’y’), t(ii), ’linear’, ’ extrap ’); In this case, because x is also defined as a function of the independent parameter
Counting independent sets using the Bethe approximation
Energy Technology Data Exchange (ETDEWEB)
Chertkov, Michael [Los Alamos National Laboratory; Chandrasekaran, V [MIT; Gamarmik, D [MIT; Shah, D [MIT; Sin, J [MIT
2009-01-01
The authors consider the problem of counting the number of independent sets or the partition function of a hard-core model in a graph. The problem in general is computationally hard (P hard). They study the quality of the approximation provided by the Bethe free energy. Belief propagation (BP) is a message-passing algorithm can be used to compute fixed points of the Bethe approximation; however, BP is not always guarantee to converge. As the first result, they propose a simple message-passing algorithm that converges to a BP fixed pont for any grapy. They find that their algorithm converges within a multiplicative error 1 + {var_epsilon} of a fixed point in {Omicron}(n{sup 2}E{sup -4} log{sup 3}(nE{sup -1})) iterations for any bounded degree graph of n nodes. In a nutshell, the algorithm can be thought of as a modification of BP with 'time-varying' message-passing. Next, they analyze the resulting error to the number of independent sets provided by such a fixed point of the Bethe approximation. Using the recently developed loop calculus approach by Vhertkov and Chernyak, they establish that for any bounded graph with large enough girth, the error is {Omicron}(n{sup -{gamma}}) for some {gamma} > 0. As an application, they find that for random 3-regular graph, Bethe approximation of log-partition function (log of the number of independent sets) is within o(1) of corret log-partition - this is quite surprising as previous physics-based predictions were expecting an error of o(n). In sum, their results provide a systematic way to find Bethe fixed points for any graph quickly and allow for estimating error in Bethe approximation using novel combinatorial techniques.
Polynomial approximation and cubature at approximate Fekete and Leja points of the cylinder
De Marchi, Stefano
2011-01-01
The paper deals with polynomial interpolation, least-square approximation and cubature of functions defined on the rectangular cylinder, $K=D\\times [-1,1]$, with $D$ the unit disk. The nodes used for these processes are the {\\it Approximate Fekete Points} (AFP) and the {\\it Discrete Leja Points} (DLP) extracted from suitable {\\it Weakly Admissible Meshes} (WAMs) of the cylinder. From the analysis of the growth of the Lebesgue constants, approximation and cubature errors, we show that the AFP and the DLP extracted from WAM are good points for polynomial approximation and numerical integration of functions defined on the cylinder.
DEFF Research Database (Denmark)
Rudolf, Frauke; Lemvik, Grethe; Abate, Ebba;
2013-01-01
Abstract Background: The TBscore, based on simple signs and symptoms, was introduced to predict unsuccessful outcome in tuberculosis patients on treatment. A recent inter-observer variation study showed profound variation in some variables. Further, some variables depend on a physician assessing...... them, making the score less applicable. The aim of the present study was to simplify the TBscore. Methods: Inter-observer variation assessment and exploratory factor analysis were combined to develop a simplified score, the TBscore II. To validate TBscore II we assessed the association between start...
Pade approximants of random Stieltjes series
Marklof, Jens; Wolowski, Lech
2007-01-01
We consider the random continued fraction S(t) := 1/(s_1 + t/(s_2 + t/(s_3 + >...))) where the s_n are independent random variables with the same gamma distribution. For every realisation of the sequence, S(t) defines a Stieltjes function. We study the convergence of the finite truncations of the continued fraction or, equivalently, of the diagonal Pade approximants of the function S(t). By using the Dyson--Schmidt method for an equivalent one-dimensional disordered system, and the results of Marklof et al. (2005), we obtain explicit formulae (in terms of modified Bessel functions) for the almost-sure rate of convergence of these approximants, and for the almost-sure distribution of their poles.
SOME CONVERSE RESULTS ON ONESIDED APPROXIMATION: JUSTIFICATIONS
Institute of Scientific and Technical Information of China (English)
Wang Jianli; Zhou Songping
2003-01-01
The present paper deals with best onesided approximation rate in Lp spaces ～En (f)Lp of f ∈ C2π. Although it is clear that the estimate ～En(f)Lp≤C ‖f‖ Lp cannot be correct for all f ∈ Lp2π in case p＜∞, the question whether ～En (f)Lp ≤Cω (f, n-1 )Lp or ～En(f)Lp ≤CEn(f)Lp holds for f ∈ C2π remains totally untouched.Therefore it forms a basic problem to justify onesided approximation. The present paper will provide an answer to settle down the basis.
Approximate Lesion Localization in Dermoscopy Images
Celebi, M Emre; Schaefer, Gerald; Stoecker, William V; 10.1111/j.1600-0846.2009.00357.x
2010-01-01
Background: Dermoscopy is one of the major imaging modalities used in the diagnosis of melanoma and other pigmented skin lesions. Due to the difficulty and subjectivity of human interpretation, automated analysis of dermoscopy images has become an important research area. Border detection is often the first step in this analysis. Methods: In this article, we present an approximate lesion localization method that serves as a preprocessing step for detecting borders in dermoscopy images. In this method, first the black frame around the image is removed using an iterative algorithm. The approximate location of the lesion is then determined using an ensemble of thresholding algorithms. Results: The method is tested on a set of 428 dermoscopy images. The localization error is quantified by a metric that uses dermatologist determined borders as the ground truth. Conclusion: The results demonstrate that the method presented here achieves both fast and accurate localization of lesions in dermoscopy images.
An Origami Approximation to the Cosmic Web
Neyrinck, Mark C
2014-01-01
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 ...
Improved Approximations for Some Polymer Extension Models
Petrosyan, Rafayel
2016-01-01
We propose approximations for force-extension dependencies for the freely jointed chain (FJC) and worm-like chain (WLC) models as well as for extension-force dependence for the WLC model. Proposed expressions show less than 1% relative error in the useful range of the corresponding variables. These results can be applied for fitting force-extension curves obtained in molecular force spectroscopy experiments. Particularly they can be useful for cases where one has geometries of springs in series and/or in parallel where particular combination of expressions should be used for fitting the data. All approximations have been obtained following the same procedure of determining the asymptotes and then reducing the relative error of that expression by adding an appropriate term obtained from fitting its absolute error.
Approximate gauge symemtry of composite vector bosons
Energy Technology Data Exchange (ETDEWEB)
Suzuki, Mahiko
2010-06-01
It can be shown in a solvable field theory model that the couplings of the composite vector mesons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in more an intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.
On approximative solutions of multistopping problems
Faller, Andreas; 10.1214/10-AAP747
2012-01-01
In this paper, we consider multistopping problems for finite discrete time sequences $X_1,...,X_n$. $m$-stops are allowed and the aim is to maximize the expected value of the best of these $m$ stops. The random variables are neither assumed to be independent not to be identically distributed. The basic assumption is convergence of a related imbedded point process to a continuous time Poisson process in the plane, which serves as a limiting model for the stopping problem. The optimal $m$-stopping curves for this limiting model are determined by differential equations of first order. A general approximation result is established which ensures convergence of the finite discrete time $m$-stopping problem to that in the limit model. This allows the construction of approximative solutions of the discrete time $m$-stopping problem. In detail, the case of i.i.d. sequences with discount and observation costs is discussed and explicit results are obtained.
Regularized Laplacian Estimation and Fast Eigenvector Approximation
Perry, Patrick O
2011-01-01
Recently, Mahoney and Orecchia demonstrated that popular diffusion-based procedures to compute a quick \\emph{approximation} to the first nontrivial eigenvector of a data graph Laplacian \\emph{exactly} solve certain regularized Semi-Definite Programs (SDPs). In this paper, we extend that result by providing a statistical interpretation of their approximation procedure. Our interpretation will be analogous to the manner in which $\\ell_2$-regularized or $\\ell_1$-regularized $\\ell_2$-regression (often called Ridge regression and Lasso regression, respectively) can be interpreted in terms of a Gaussian prior or a Laplace prior, respectively, on the coefficient vector of the regression problem. Our framework will imply that the solutions to the Mahoney-Orecchia regularized SDP can be interpreted as regularized estimates of the pseudoinverse of the graph Laplacian. Conversely, it will imply that the solution to this regularized estimation problem can be computed very quickly by running, e.g., the fast diffusion-base...
Flow past a porous approximate spherical shell
Srinivasacharya, D.
2007-07-01
In this paper, the creeping flow of an incompressible viscous liquid past a porous approximate spherical shell is considered. The flow in the free fluid region outside the shell and in the cavity region of the shell is governed by the Navier Stokes equation. The flow within the porous annulus region of the shell is governed by Darcy’s Law. The boundary conditions used at the interface are continuity of the normal velocity, continuity of the pressure and Beavers and Joseph slip condition. An exact solution for the problem is obtained. An expression for the drag on the porous approximate spherical shell is obtained. The drag experienced by the shell is evaluated numerically for several values of the parameters governing the flow.
Improved Approximation for Orienting Mixed Graphs
Gamzu, Iftah
2012-01-01
An instance of the maximum mixed graph orientation problem consists of a mixed graph and a collection of source-target vertex pairs. The objective is to orient the undirected edges of the graph so as to maximize the number of pairs that admit a directed source-target path. This problem has recently arisen in the study of biological networks, and it also has applications in communication networks. In this paper, we identify an interesting local-to-global orientation property. This property enables us to modify the best known algorithms for maximum mixed graph orientation and some of its special structured instances, due to Elberfeld et al. (CPM '11), and obtain improved approximation ratios. We further proceed by developing an algorithm that achieves an even better approximation guarantee for the general setting of the problem. Finally, we study several well-motivated variants of this orientation problem.
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.
Numerical and approximate solutions for plume rise
Krishnamurthy, Ramesh; Gordon Hall, J.
Numerical and approximate analytical solutions are compared for turbulent plume rise in a crosswind. The numerical solutions were calculated using the plume rise model of Hoult, Fay and Forney (1969, J. Air Pollut. Control Ass.19, 585-590), over a wide range of pertinent parameters. Some wind shear and elevated inversion effects are included. The numerical solutions are seen to agree with the approximate solutions over a fairly wide range of the parameters. For the conditions considered in the study, wind shear effects are seen to be quite small. A limited study was made of the penetration of elevated inversions by plumes. The results indicate the adequacy of a simple criterion proposed by Briggs (1969, AEC Critical Review Series, USAEC Division of Technical Information extension, Oak Ridge, Tennesse).
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.
Approximate inverse preconditioners for general sparse matrices
Energy Technology Data Exchange (ETDEWEB)
Chow, E.; Saad, Y. [Univ. of Minnesota, Minneapolis, MN (United States)
1994-12-31
Preconditioned Krylov subspace methods are often very efficient in solving sparse linear matrices that arise from the discretization of elliptic partial differential equations. However, for general sparse indifinite matrices, the usual ILU preconditioners fail, often because of the fact that the resulting factors L and U give rise to unstable forward and backward sweeps. In such cases, alternative preconditioners based on approximate inverses may be attractive. We are currently developing a number of such preconditioners based on iterating on each column to get the approximate inverse. For this approach to be efficient, the iteration must be done in sparse mode, i.e., we must use sparse-matrix by sparse-vector type operatoins. We will discuss a few options and compare their performance on standard problems from the Harwell-Boeing collection.
Rough Sets in Approximate Solution Space
Institute of Scientific and Technical Information of China (English)
Hui Sun; Wei Tian; Qing Liu
2006-01-01
As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and in complete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoretic tool to discretize the real function. As far as the real function research is concerned, the research to define rough sets in the real function is infrequent. In this paper, we exploit a new method to extend the rough set in normed linear space, in which we establish a rough set,put forward an upper and lower approximation definition, and make a preliminary research on the property of the rough set. A new tool is provided to study the approximation solutions of differential equation and functional variation in normed linear space. This research is significant in that it extends the application of rough sets to a new field.
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.
Second derivatives for approximate spin projection methods.
Thompson, Lee M; Hratchian, Hrant P
2015-02-07
The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical second derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.
A multiscale two-point flux-approximation method
Møyner, Olav; Lie, Knut-Andreas
2014-10-01
A large number of multiscale finite-volume methods have been developed over the past decade to compute conservative approximations to multiphase flow problems in heterogeneous porous media. In particular, several iterative and algebraic multiscale frameworks that seek to reduce the fine-scale residual towards machine precision have been presented. Common for all such methods is that they rely on a compatible primal-dual coarse partition, which makes it challenging to extend them to stratigraphic and unstructured grids. Herein, we propose a general idea for how one can formulate multiscale finite-volume methods using only a primal coarse partition. To this end, we use two key ingredients that are computed numerically: (i) elementary functions that correspond to flow solutions used in transmissibility upscaling, and (ii) partition-of-unity functions used to combine elementary functions into basis functions. We exemplify the idea by deriving a multiscale two-point flux-approximation (MsTPFA) method, which is robust with regards to strong heterogeneities in the permeability field and can easily handle general grids with unstructured fine- and coarse-scale connections. The method can easily be adapted to arbitrary levels of coarsening, and can be used both as a standalone solver and as a preconditioner. Several numerical experiments are presented to demonstrate that the MsTPFA method can be used to solve elliptic pressure problems on a wide variety of geological models in a robust and efficient manner.
The Complexity of Approximately Counting Stable Roommate Assignments
Chebolu, Prasad; Martin, Russell
2010-01-01
We investigate the complexity of approximately counting stable roommate assignments in two models: (i) the $k$-attribute model, in which the preference lists are determined by dot products of "preference vectors" with "attribute vectors" and (ii) the $k$-Euclidean model, in which the preference lists are determined by the closeness of the "positions" of the people to their "preferred positions". Exactly counting the number of assignments is #P-complete, since Irving and Leather demonstrated #P-completeness for the special case of the stable marriage problem. We show that counting the number of stable roommate assignments in the $k$-attribute model ($k \\geq 4$) and the $3$-Euclidean model($k \\geq 3$) is interreducible, in an approximation-preserving sense, with counting independent sets (of all sizes) (#IS) in a graph, or counting the number of satisfying assignments of a Boolean formula (#SAT). This means that there can be no FPRAS for any of these problems unless NP=RP. As a consequence, we infer that there ...
Subset Selection by Local Convex Approximation
DEFF Research Database (Denmark)
Øjelund, Henrik; Sadegh, Payman; Madsen, Henrik;
1999-01-01
least squares criterion. We propose an optimization technique for the posed probelm based on a modified version of the Newton-Raphson iterations, combined with a backward elimination type algorithm. THe Newton-Raphson modification concerns iterative approximations to the non-convex cost function....... The efficiency of the method is illustrated by a numerical example with highly correlated explanatory variables for which the commonly used techiques such as forward selection/backward elimination perform poorly....
Local characterisation of approximately finite operator algebras
Haworth, P. A.
2000-01-01
We show that the family of nest algebras with $r$ non-zero nest projections is stable, in the sense that an approximate containment of one such algebra within another is close to an exact containment. We use this result to give a local characterisation of limits formed from this family. We then consider quite general regular limit algebras and characterise these algebras using a local condition which reflects the assumed regularity of the system.
Space-Time Approximation with Sparse Grids
Energy Technology Data Exchange (ETDEWEB)
Griebel, M; Oeltz, D; Vassilevski, P S
2005-04-14
In this article we introduce approximation spaces for parabolic problems which are based on the tensor product construction of a multiscale basis in space and a multiscale basis in time. Proper truncation then leads to so-called space-time sparse grid spaces. For a uniform discretization of the spatial space of dimension d with O(N{sup d}) degrees of freedom, these spaces involve for d > 1 also only O(N{sup d}) degrees of freedom for the discretization of the whole space-time problem. But they provide the same approximation rate as classical space-time Finite Element spaces which need O(N{sup d+1}) degrees of freedoms. This makes these approximation spaces well suited for conventional parabolic and for time-dependent optimization problems. We analyze the approximation properties and the dimension of these sparse grid space-time spaces for general stable multiscale bases. We then restrict ourselves to an interpolatory multiscale basis, i.e. a hierarchical basis. Here, to be able to handle also complicated spatial domains {Omega}, we construct the hierarchical basis from a given spatial Finite Element basis as follows: First we determine coarse grid points recursively over the levels by the coarsening step of the algebraic multigrid method. Then, we derive interpolatory prolongation operators between the respective coarse and fine grid points by a least squares approach. This way we obtain an algebraic hierarchical basis for the spatial domain which we then use in our space-time sparse grid approach. We give numerical results on the convergence rate of the interpolation error of these spaces for various space-time problems with two spatial dimensions. Also implementational issues, data structures and questions of adaptivity are addressed to some extent.
APPROXIMATE OUTPUT REGULATION FOR AFFINE NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
Yali DONG; Daizhan CHENG; Huashu QIN
2003-01-01
Output regulation for affine nonlinear systems driven by an exogenous signal is investigated in this paper. In the absence of the standard exosystem hypothesis, we assume availability of the instantaneous values of the exogenous signal and its first time-derivative for use in the control law.For affine nonlinear systems, the necessary and sufficient conditions of the solvability of approximate output regulation problem are obtained. The precise form of the control law is presented under some suitable assumptions.
Onsager principle as a tool for approximation
Institute of Scientific and Technical Information of China (English)
Masao Doi
2015-01-01
Onsager principle is the variational principle proposed by Onsager in his celebrated paper on the reciprocal relation. The principle has been shown to be useful in deriving many evolution equations in soft matter physics. Here the principle is shown to be useful in solving such equations approximately. Two examples are discussed: the diffusion dynamics and gel dynamics. Both examples show that the present method is novel and gives new results which capture the essential dynamics in the system.
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 MULTIDIMENSION FUCTION WITH FUNCTIONAL NETWORK
Institute of Scientific and Technical Information of China (English)
Li Weibin; Liu Fang; Jiao Licheng; Zhang Shuling; Li Zongling
2006-01-01
The functional network was introduced by E.Catillo, which extended the neural network. Not only can it solve the problems solved, but also it can formulate the ones that cannot be solved by traditional network.This paper applies functional network to approximate the multidimension function under the ridgelet theory.The method performs more stable and faster than the traditional neural network. The numerical examples demonstrate the performance.
Neutrino Mass Matrix with Approximate Flavor Symmetry
Riazuddin, M
2003-01-01
Phenomenological implications of neutrino oscillations implied by recent experimental data on pattern of neutrino mass matrix are disscussed. It is shown that it is possible to have a neutrino mass matrix which shows approximate flavor symmetry; the neutrino mass differences arise from flavor violation in off-diagonal Yukawa couplings. Two modest extensions of the standard model, which can embed the resulting neutrino mass matix have also been discussed.
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.
Variational Bayesian Approximation methods for inverse problems
Mohammad-Djafari, Ali
2012-09-01
Variational Bayesian Approximation (VBA) methods are recent tools for effective Bayesian computations. In this paper, these tools are used for inverse problems where the prior models include hidden variables and where where the estimation of the hyper parameters has also to be addressed. In particular two specific prior models (Student-t and mixture of Gaussian models) are considered and details of the algorithms are given.
Approximate Dynamic Programming for Military Resource Allocation
2014-12-26
as a Markov decision pro- cess ( MDP ) and uses neuro-dynamic programming where the cost-to-go functional approximation is achieved through neural...followed by its formulation as an infinite horizon discrete time Markov decision process ( MDP ) in Section 5.3.2. 5.3.1 Problem Description. Consider...Formulation. This problem is modeled as an infinite horizon, discrete time Markov decision process ( MDP ) using the collection of objects {T ,S,A, p(·|S
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.
Approximation of pressure perturbations by FEM
Bichir, Cătălin - Liviu
2011-01-01
In the mathematical problem of linear hydrodynamic stability for shear flows against Tollmien-Schlichting perturbations, the continuity equation for the perturbation of the velocity is replaced by a Poisson equation for the pressure perturbation. The resulting eigenvalue problem, an alternative form for the two - point eigenvalue problem for the Orr - Sommerfeld equation, is formulated in a variational form and this one is approximated by finite element method (FEM). Possible applications to concrete cases are revealed.
Additive Approximation Algorithms for Modularity Maximization
Kawase, Yasushi; Matsui, Tomomi; Miyauchi, Atsushi
2016-01-01
The modularity is a quality function in community detection, which was introduced by Newman and Girvan (2004). Community detection in graphs is now often conducted through modularity maximization: given an undirected graph $G=(V,E)$, we are asked to find a partition $\\mathcal{C}$ of $V$ that maximizes the modularity. Although numerous algorithms have been developed to date, most of them have no theoretical approximation guarantee. Recently, to overcome this issue, the design of modularity max...
Approximate Revenue Maximization in Interdependent Value Settings
Chawla, Shuchi; Fu, Hu; Karlin, Anna
2014-01-01
We study revenue maximization in settings where agents' values are interdependent: each agent receives a signal drawn from a correlated distribution and agents' values are functions of all of the signals. We introduce a variant of the generalized VCG auction with reserve prices and random admission, and show that this auction gives a constant approximation to the optimal expected revenue in matroid environments. Our results do not require any assumptions on the signal distributions, however, ...
Approximate Equalities on Rough Intuitionistic Fuzzy Sets and an Analysis of Approximate Equalities
Directory of Open Access Journals (Sweden)
B. K. Tripathy
2012-03-01
Full Text Available In order to involve user knowledge in determining equality of sets, which may not be equal in the mathematical sense, three types of approximate (rough equalities were introduced by Novotny and Pawlak ([8, 9, 10]. These notions were generalized by Tripathy, Mitra and Ojha ([13], who introduced the concepts of approximate (rough equivalences of sets. Rough equivalences capture equality of sets at a higher level than rough equalities. More properties of these concepts were established in [14]. Combining the conditions for the two types of approximate equalities, two more approximate equalities were introduced by Tripathy [12] and a comparative analysis of their relative efficiency was provided. In [15], the four types of approximate equalities were extended by considering rough fuzzy sets instead of only rough sets. In fact the concepts of leveled approximate equalities were introduced and properties were studied. In this paper we proceed further by introducing and studying the approximate equalities based on rough intuitionistic fuzzy sets instead of rough fuzzy sets. That is we introduce the concepts of approximate (rough equalities of intuitionistic fuzzy sets and study their properties. We provide some real life examples to show the applications of rough equalities of fuzzy sets and rough equalities of intuitionistic fuzzy sets.
Symmetry and approximability of submodular maximization problems
Vondrak, Jan
2011-01-01
A number of recent results on optimization problems involving submodular functions have made use of the multilinear relaxation of the problem. These results hold typically in the value oracle model, where the objective function is accessible via a black box returning f(S) for a given S. We present a general approach to deriving inapproximability results in the value oracle model, based on the notion of symmetry gap. Our main result is that for any fixed instance that exhibits a certain symmetry gap in its multilinear relaxation, there is a naturally related class of instances for which a better approximation factor than the symmetry gap would require exponentially many oracle queries. This unifies several known hardness results for submodular maximization, and implies several new ones. In particular, we prove that there is no constant-factor approximation for the problem of maximizing a non-negative submodular function over the bases of a matroid. We also provide a closely matching approximation algorithm for...
Cylindrical Helix Spline Approximation of Spatial Curves
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, we present a new method for approximating spatial curves with a G1 cylindrical helix spline within a prescribed tolerance. We deduce the general formulation of a cylindrical helix,which has 11 freedoms. This means that it needs 11 restrictions to determine a cylindrical helix. Given a spatial parametric curve segment, including the start point and the end point of this segment, the tangent and the principal normal of the start point, we can always find a cylindrical segment to interpolate the given direction and position vectors. In order to approximate the known parametric curve within the prescribed tolerance, we adopt the trial method step by step. First, we must ensure the helix segment to interpolate the given two end points and match the principal normal and tangent of the start point, and then, we can keep the deviation between the cylindrical helix segment and the known curve segment within the prescribed tolerance everywhere. After the first segment had been formed, we can construct the next segment. Circularly, we can construct the G1 cylindrical helix spline to approximate the whole spatial parametric curve within the prescribed tolerance. Several examples are also given to show the efficiency of this method.
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.
CMB-lensing beyond the Born approximation
Marozzi, Giovanni; Fanizza, Giuseppe; Di Dio, Enea; Durrer, Ruth
2016-09-01
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles l lesssim 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.
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.
Generalized Quasilinear Approximation: Application to Zonal Jets
Marston, J. B.; Chini, G. P.; Tobias, S. M.
2016-05-01
Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. We present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through nonlocal spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta plane and show that it is accurate even for a small number of large-scale modes. As GQL is formally linear in the small zonal scales, it allows for the closure of the system and can be utilized in direct statistical simulation schemes that have proved an attractive alternative to direct numerical simulation for many geophysical and astrophysical problems.
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.
The Complexity of Approximately Counting Stable Matchings
Chebolu, Prasad; Martin, Russell
2010-01-01
We investigate the complexity of approximately counting stable matchings in the $k$-attribute model, where the preference lists are determined by dot products of "preference vectors" with "attribute vectors", or by Euclidean distances between "preference points" and "attribute points". Irving and Leather proved that counting the number of stable matchings in the general case is $#P$-complete. Counting the number of stable matchings is reducible to counting the number of downsets in a (related) partial order and is interreducible, in an approximation-preserving sense, to a class of problems that includes counting the number of independent sets in a bipartite graph ($#BIS$). It is conjectured that no FPRAS exists for this class of problems. We show this approximation-preserving interreducibilty remains even in the restricted $k$-attribute setting when $k \\geq 3$ (dot products) or $k \\geq 2$ (Euclidean distances). Finally, we show it is easy to count the number of stable matchings in the 1-attribute dot-product ...
Approximation Algorithms for Directed Width Parameters
Kintali, Shiva; Kumar, Akash
2011-01-01
Treewidth of an undirected graph measures how close the graph is to being a tree. Several problems that are NP-hard on general graphs are solvable in polynomial time on graphs with bounded treewidth. Motivated by the success of treewidth, several directed analogues of treewidth have been introduced to measure the similarity of a directed graph to a directed acyclic graph (DAG). Directed treewidth, D-width, DAG-width, Kelly-width and directed pathwidth are some such parameters. In this paper, we present the first approximation algorithms for all these five directed width parameters. For directed treewidth and D-width we achieve an approximation factor of O(sqrt{logn}). For DAG-width, Kelly-width and directed pathwidth we achieve an O({\\log}^{3/2}{n}) approximation factor. Our algorithms are constructive, i.e., they construct the decompositions associated with these parameters. The width of these decompositions are within the above mentioned factor of the corresponding optimal width.
Approximating Low-Dimensional Coverage Problems
Badanidiyuru, Ashwinkumar; Lee, Hooyeon
2011-01-01
We study the complexity of the maximum coverage problem, restricted to set systems of bounded VC-dimension. Our main result is a fixed-parameter tractable approximation scheme: an algorithm that outputs a $(1-\\eps)$-approximation to the maximum-cardinality union of $k$ sets, in running time $O(f(\\eps,k,d)\\cdot poly(n))$ where $n$ is the problem size, $d$ is the VC-dimension of the set system, and $f(\\eps,k,d)$ is exponential in $(kd/\\eps)^c$ for some constant $c$. We complement this positive result by showing that the function $f(\\eps,k,d)$ in the running-time bound cannot be replaced by a function depending only on $(\\eps,d)$ or on $(k,d)$, under standard complexity assumptions. We also present an improved upper bound on the approximation ratio of the greedy algorithm in special cases of the problem, including when the sets have bounded cardinality and when they are two-dimensional halfspaces. Complementing these positive results, we show that when the sets are four-dimensional halfspaces neither the greedy ...
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.
Approximate Graph Edit Distance in Quadratic Time.
Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst
2015-09-14
Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.
CMB-lensing beyond the Born approximation
Marozzi, Giovanni; Di Dio, Enea; Durrer, Ruth
2016-01-01
We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles $\\ell\\lesssim 2500$, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum...
On the Use of Approximations in Statistical Physics
Hoffmann, C
2003-01-01
Two approximations are frequently used in statistical physics: the first one, which we shall name the mean values approximation, is generally (and improperly) named as "maximum term approximation". The second is the "Stirling approximation". In this paper we demonstrate that the error introduced by the first approximation is exactly compensated by the second approximation in the calculation of mean values of multinomial distributions.
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.
Uniform Approximation of Vapnik-Chervonenkis Classes
Adams, Terrence M
2010-01-01
For any family of measurable sets in a probability space, we show that either (i) the family has infinite Vapnik-Chervonenkis (VC) dimension or (ii) for every epsilon > 0 there is a finite partition pi such the pi-boundary of each set has measure at most epsilon. Immediate corollaries include the fact that a family with finite VC dimension has finite bracketing numbers, and satisfies uniform laws of large numbers for every ergodic process. From these corollaries, we derive analogous results for VC major and VC graph families of functions.
Overton, J D; Sullivan, Diane J
2012-03-01
Using the information from remake request slips in a dental school's predoctoral clinic, we examined the short-term survival of Class II resin composite restorations versus Class II dental amalgam restorations. In the student clinic, resin composite is used in approximately 58 percent of Class II restorations placed, and dental amalgam is used in the remaining 42 percent. In the period examined, Class II resin composite restorations were ten times more likely to be replaced at no cost to the patient than Class II dental amalgam restorations. A total of eighty-four resin composite restorations and six amalgam restorations were replaced due to an identified failure.
Wolfensberger, Wolf
1984-01-01
The author estimates that approximately 200,000 lives of devalued disabled people (including infants and older adults) are taken or abbreviated annually through euthanasia and termination of life-supporting measures. He cites possible reasons for limited public outcry against what he compares with the holocaust. (CL)
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.
Roos, Bero
2012-01-01
Bobkov (2005) investigated an approximate de Finetti representation for probability measures on product measurable spaces, which are symmetric under permutations of coordinates. One of the main results of that paper was an explicit approximation bound for permanents of complex rectangular matrices, which was shown by a complicated induction argument. In this paper, we indicate how to avoid the induction argument using an (asymptotic) expansion. Our approach makes it possible to give new explicit higher order approximation bounds for such permanents and in turn for the probability measures mentioned above.
Institute of Scientific and Technical Information of China (English)
Zhang Zheng-Jie; Wang Ke-Lin; Qin Gan
2005-01-01
By a model of atwo-level particle coupled with boson field, we made it clear that an evolution problem can be solved beyond the rotating wave approximation. We have applied the coherent approximation method, which had been proved to be effective in dealing with stationary state problems of polaron, to the evolution problem of the system mentioned above. The results obtained showed that the coherent approximation method is effective to treat the evolution problem,and, in general cases, the non-rotating wave terms in Hamiltonian should not be ignored. Our results may provide a deep physical insight for further experiments to test the effects of non-rotating wave terms.
Approximate formulas for moderately small eikonal amplitudes
Kisselev, A V
2015-01-01
The eikonal approximation for moderately small scattering amplitudes is considered. With the purpose of using for their numerical estimations, the formulas are derived which contain no Bessel functions, and, hence, no rapidly oscillating integrands. To obtain these formulas, the improper integrals of the first kind which contain products of the Bessel functions J_0(z) are studied. The expression with four functions J_0(z) is generalized. The expressions for the integrals with the product of five and six Bessel functions J_0(z) are also found. The known formula for the improper integral with two functions J_nu(z) is generalized for non-integer nu.
Approximation algorithms for some vehicle routing problems
Bazgan, Cristina; Hassin, Refael; Monnot, Jérôme
2005-01-01
We study vehicle routing problems with constraints on the distance traveled by each vehicle or on the number of vehicles. The objective is either to minimize the total distance traveled by vehicles or to minimize the number of vehicles used. We design constant differential approximation algorithms for kVRP. Note that, using the differential bound for METRIC 3VRP, we obtain the randomized standard ratio . This is an improvement of the best-known bound of 2 given by Haimovich et al. (Vehicle Ro...
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
Error Minimization of Polynomial Approximation of Delta
Indian Academy of Sciences (India)
Islam Sana; Sadiq Muhammad; Qureshi Muhammad Shahid
2008-09-01
The difference between Universal time (UT) and Dynamical time (TD), known as Delta ( ) is tabulated for the first day of each year in the Astronomical Almanac. During the last four centuries it is found that there are large differences between its values for two consecutive years. Polynomial approximations have been developed to obtain the values of for any time of a year for the period AD 1620 to AD 2000 (Meeu 2000) as no dynamical theories describe the variations in . In this work, a new set of polynomials for is obtained for the period AD 1620 to AD 2007 that is found to produce better results compared to previous attempts.
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
Dynamic system evolution and markov chain approximation
Directory of Open Access Journals (Sweden)
Roderick V. Nicholas Melnik
1998-01-01
Full Text Available In this paper computational aspects of the mathematical modelling of dynamic system evolution have been considered as a problem in information theory. The construction of mathematical models is treated as a decision making process with limited available information.The solution of the problem is associated with a computational model based on heuristics of a Markov Chain in a discrete space–time of events. A stable approximation of the chain has been derived and the limiting cases are discussed. An intrinsic interconnection of constructive, sequential, and evolutionary approaches in related optimization problems provides new challenges for future work.
The Numerical Approximation of Functional Differential Equations
Venturi, Daniele
2016-01-01
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equations), quantum field theory (Schwinger-Dyson equations) and statistical physics (equations for generating functionals and effective action methods). However, no effective numerical method has yet been developed to compute their solution. The purpose of this manuscript is to fill this gap, and provide a new perspective on the problem of numerical approximation of nonlinear functionals and functional differential equations. The proposed methods will be described and demonstrated in various examples.
Virial expansion coefficients in the harmonic approximation
DEFF Research Database (Denmark)
R. Armstrong, J.; Zinner, Nikolaj Thomas; V. Fedorov, D.;
2012-01-01
The virial expansion method is applied within a harmonic approximation to an interacting N-body system of identical fermions. We compute the canonical partition functions for two and three particles to get the two lowest orders in the expansion. The energy spectrum is carefully interpolated...... to reproduce ground state properties at low temperature and the non-interacting large temperature limit of constant virial coefficients. This resembles the smearing of shell effects in finite systems with increasing temperature. Numerical results are discussed for the second and third virial coefficients...
Exponential Polynomial Approximation with Unrestricted Upper Density
Institute of Scientific and Technical Information of China (English)
Xiang Dong YANG
2011-01-01
We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in Lp/α, where Lp/α is the weighted Banach space of complex continuous functions f defined on the real axis (R)satisfying (∫+∞/-∞|f(t)|pe-α(t)dt)1/p, 1 < p < ∞, and α(t) is a nonnegative continuous function defined on the real axis (R). In this paper, the upper density of the sequence which forms the exponential polynomials is not required to be finite. In the study of weighted polynomial approximation, consideration of the case is new.
Approximate Distance Oracles with Improved Query Time
Wulff-Nilsen, Christian
2012-01-01
Given an undirected graph $G$ with $m$ edges, $n$ vertices, and non-negative edge weights, and given an integer $k\\geq 2$, we show that a $(2k-1)$-approximate distance oracle for $G$ of size $O(kn^{1 + 1/k})$ and with $O(\\log k)$ query time can be constructed in $O(\\min\\{kmn^{1/k},\\sqrt km + kn^{1 + c/\\sqrt k}\\})$ time for some constant $c$. This improves the $O(k)$ query time of Thorup and Zwick. For any $0 0$ and $k = O(\\log n/\\log\\log n)$.
Semiclassical approximations to quantum time correlation functions
Egorov, S. A.; Skinner, J. L.
1998-09-01
Over the last 40 years several ad hoc semiclassical approaches have been developed in order to obtain approximate quantum time correlation functions, using as input only the corresponding classical time correlation functions. The accuracy of these approaches has been tested for several exactly solvable gas-phase models. In this paper we test the accuracy of these approaches by comparing to an exactly solvable many-body condensed-phase model. We show that in the frequency domain the Egelstaff approach is the most accurate, especially at high frequencies, while in the time domain one of the other approaches is more accurate.
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.
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.
On Approximating String Selection Problems with Outliers
Boucher, Christina; Levy, Avivit; Pritchard, David; Weimann, Oren
2012-01-01
Many problems in bioinformatics are about finding strings that approximately represent a collection of given strings. We look at more general problems where some input strings can be classified as outliers. The Close to Most Strings problem is, given a set S of same-length strings, and a parameter d, find a string x that maximizes the number of "non-outliers" within Hamming distance d of x. We prove this problem has no PTAS unless ZPP=NP, correcting a decade-old mistake. The Most Strings with Few Bad Columns problem is to find a maximum-size subset of input strings so that the number of non-identical positions is at most k; we show it has no PTAS unless P=NP. We also observe Closest to k Strings has no EPTAS unless W[1]=FPT. In sum, outliers help model problems associated with using biological data, but we show the problem of finding an approximate solution is computationally difficult.
Function approximation using adaptive and overlapping intervals
Energy Technology Data Exchange (ETDEWEB)
Patil, R.B.
1995-05-01
A problem common to many disciplines is to approximate a function given only the values of the function at various points in input variable space. A method is proposed for approximating a function of several to one variable. The model takes the form of weighted averaging of overlapping basis functions defined over intervals. The number of such basis functions and their parameters (widths and centers) are automatically determined using given training data and a learning algorithm. The proposed algorithm can be seen as placing a nonuniform multidimensional grid in the input domain with overlapping cells. The non-uniformity and overlap of the cells is achieved by a learning algorithm to optimize a given objective function. This approach is motivated by the fuzzy modeling approach and a learning algorithms used for clustering and classification in pattern recognition. The basics of why and how the approach works are given. Few examples of nonlinear regression and classification are modeled. The relationship between the proposed technique, radial basis neural networks, kernel regression, probabilistic neural networks, and fuzzy modeling is explained. Finally advantages and disadvantages are discussed.
Exact and Approximate Sizes of Convex Datacubes
Nedjar, Sébastien
In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.
Perturbation of Operators and Approximation of Spectrum
Indian Academy of Sciences (India)
K Kumar; M N N Namboodiri; S Serra-Capizzano
2014-05-01
Let $A(x)$ be a norm continuous family of bounded self-adjoint operators on a separable Hilbert space $\\mathbb{H}$ and let $A(x)_n$ be the orthogonal compressions of $A(x)$ to the span of first elements of an orthonormal basis of $\\mathbb{H}$. The problem considered here is to approximate the spectrum of $A(x)$ using the sequence of eigenvalues of $A(x)_n$. We show that the bounds of the essential spectrum and the discrete spectral values outside the bounds of essential spectrum of $A(x)$ can be approximated uniformly on all compact subsets by the sequence of eigenvalue functions of $A(x)_n$. The known results, for a bounded self-adjoint operator, are translated into the case of a norm continuous family of operators. Also an attempt is made to predict the existence of spectral gaps that may occur between the bounds of essential spectrum of $A(0)=A$ and study the effect of norm continuous perturbation of operators in the prediction of spectral gaps. As an example, gap issues of some block Toeplitz–Laurent operators are discussed. The pure linear algebraic approach is the main advantage of the results here.
Chiral baryon in the coherent pair approximation
Aly, T S T
1999-01-01
We revisit the work of K. Goeke, M. Harvey, F. Grümmer, and J. N. Urbano (Phys. Rev. {\\bf D37}, 754 (1988)) who considered a chiral model for the nucleon based on the linear sigma model with scalar-isoscalar scalar-isovector mesons coupled to quarks and solved using the coherent-pair approximation. In this way the quantum pion field can be treated in a non-perturbative fashion. In this work we review this model and the coherent pair approximation correcting several errors in the earlier work. We minimize the expectation value of the chiral hamiltonian in the ansatz coherent-pair ground state configuration and solve the resulting equations for nucleon quantum numbers. We calculate the canonical set of nucleon observables and compare with the Hedgehog model and experiment. Using the corrected equations yield slightly different values for nucleon observables but do not correct the large virial deviation in the $\\pi$-nucleon coupling. Our results therefore do not significantly alter the conclusions of Goeke, et ...
Refining Approximating Betweenness Centrality Based on Samplings
Ji, Shiyu
2016-01-01
Betweenness Centrality (BC) is an important measure used widely in complex network analysis, such as social network, web page search, etc. Computing the exact BC values is highly time consuming. Currently the fastest exact BC determining algorithm is given by Brandes, taking $O(nm)$ time for unweighted graphs and $O(nm+n^2\\log n)$ time for weighted graphs, where $n$ is the number of vertices and $m$ is the number of edges in the graph. Due to the extreme difficulty of reducing the time complexity of exact BC determining problem, many researchers have considered the possibility of any satisfactory BC approximation algorithms, especially those based on samplings. Bader et al. give the currently best BC approximation algorithm, with a high probability to successfully estimate the BC of one vertex within a factor of $1/\\varepsilon$ using $\\varepsilon t$ samples, where $t$ is the ratio between $n^2$ and the BC value of the vertex. However, some of the algorithmic parameters in Bader's work are not yet tightly boun...
Approximate Sensory Data Collection: A Survey
Cheng, Siyao; Cai, Zhipeng; Li, Jianzhong
2017-01-01
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 approximate data collection algorithms. We classify them into three categories: the model-based ones, 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. PMID:28287440
Approximation of Failure Probability Using Conditional Sampling
Giesy. Daniel P.; Crespo, Luis G.; Kenney, Sean P.
2008-01-01
In analyzing systems which depend on uncertain parameters, one technique is to partition the uncertain parameter domain into a failure set and its complement, and judge the quality of the system by estimating the probability of failure. If this is done by a sampling technique such as Monte Carlo and the probability of failure is small, accurate approximation can require so many sample points that the computational expense is prohibitive. Previous work of the authors has shown how to bound the failure event by sets of such simple geometry that their probabilities can be calculated analytically. In this paper, it is shown how to make use of these failure bounding sets and conditional sampling within them to substantially reduce the computational burden of approximating failure probability. It is also shown how the use of these sampling techniques improves the confidence intervals for the failure probability estimate for a given number of sample points and how they reduce the number of sample point analyses needed to achieve a given level of confidence.
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.......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...
Approximation diophantienne et approximants de Hermite-Pad\\'e de type I de fonctions exponentielles
Khémira, Samy
2010-01-01
En utilisant des approximants de Hermite-Pad\\'e de fonctions exponentielles, ainsi que des d\\'eterminants d'interpolation de Laurent, nous minorons la distance entre un nombre alg\\'ebrique et l'exponentielle d'un nombre alg\\'ebrique non nul. ----- We use Hermite-Pad\\'e approximants of exponential functions along with Laurent's interpolation determinants to obtain lower bounds for the distance between an algebraic number and the exponential of another non-zero algebraic number.
Directory of Open Access Journals (Sweden)
Paulo Mateus
2013-07-01
Full Text Available We propose a minimum variance unbiased approximation to the conditional relative entropy of the distribution induced by the observed frequency estimates, for multi-classification tasks. Such approximation is an extension of a decomposable scoring criterion, named approximate conditional log-likelihood (aCLL, primarily used for discriminative learning of augmented Bayesian network classifiers. Our contribution is twofold: (i it addresses multi-classification tasks and not only binary-classification ones; and (ii it covers broader stochastic assumptions than uniform distribution over the parameters. Specifically, we considered a Dirichlet distribution over the parameters, which was experimentally shown to be a very good approximation to CLL. In addition, for Bayesian network classifiers, a closed-form equation is found for the parameters that maximize the scoring criterion.
Unitary Approximations in Fault Detection Filter Design
Directory of Open Access Journals (Sweden)
Dušan Krokavec
2016-01-01
Full Text Available The paper is concerned with the fault detection filter design requirements that relax the existing conditions reported in the previous literature by adapting the unitary system principle in approximation of fault detection filter transfer function matrix for continuous-time linear MIMO systems. Conditions for the existence of a unitary construction are presented under which the fault detection filter with a unitary transfer function can be designed to provide high residual signals sensitivity with respect to faults. Otherwise, reflecting the emplacement of singular values in unitary construction principle, an associated structure of linear matrix inequalities with built-in constraints is outlined to design the fault detection filter only with a Hurwitz transfer function. All proposed design conditions are verified by the numerical illustrative examples.
Formation Tracking Based on Approximate Velocities
Directory of Open Access Journals (Sweden)
Eduardo Gamaliel Hernandez-Martinez
2015-12-01
Full Text Available This paper analyses the formation tracking of groups of mobile robots moving on the plane. A leader robot is chosen to follow a prescribed trajectory whilst the rest, considered as followers, are formed in an open-chain configuration. Two formation-tracking control laws using approximate velocities are proposed, in which some velocities must be communicated between robots in order to ensure the simultaneous preservation of the formation and the following of the group path. The main result is analysis of the convergence of the two proposed control laws. The restriction of inaccurate information occurs in decentralized multi-robot platforms, in which the mobile agents are only able to measure positions and the velocities’ functions are estimated using online numerical methods. A numerical simulation of both controllers in the case of omnidirectional robots is shown. For the case of the unicycle-type robots, real-time experiments of both controllers were implemented and tested.
Approximately isometric lifting in quasidiagonal extensions
Institute of Scientific and Technical Information of China (English)
FANG XiaoChun; ZHAO YiLe
2009-01-01
Let O→I→A→A/I→O be a short exact sequence of C*-algebras with A unital.Suppose that the extension O→I→A→A/I→O is quasidiagonal,then it is shown that any positive element (projection,partial isometry,unitary element,respectively) in A/I has a lifting with the same form which commutes with some quasicentral approximate unit of I consisting of projections.Furthermore,it is shown that for any given positive number e,two positive elements (projections,As an application,it is shown that for any positive numbers e and (u) in U(A/I)0,there exists u in U(A)0which is a lifting of (u) such that cel(u) ＜ cel(u) +e.
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,...
Approximate truncation robust computed tomography—ATRACT
Dennerlein, Frank; Maier, Andreas
2013-09-01
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.
An Approximate Model of Microchannel Cooling
Institute of Scientific and Technical Information of China (English)
ShipingYu; MingdaoXin
1994-01-01
Forced convective heat transfer in micro-rectangular channels can be described by a group of two-dimensional differential equations.These equations take the conduction in microchannel wall along the direction of flow of coolants into account,which are more generalized than those which neglect the conduction.For the same reason,they are suitable particularly for gases-cooled microchannels.With only numerical solution to the equations till today,an approximate analytic solution is derived here,From this solution,a rather simple formula can be introduced further,by which the differences between considering the conduction and neglecting it are easily found.In addition,the reasonableness of the classical fin method is also discussed.An experimental example of air-cooled microchannels is illustrated.
An approximate version of Sidorenko's conjecture
Conlon, David; Sudakov, Benny
2010-01-01
A beautiful conjecture of Erd\\H{o}s-Simonovits and Sidorenko states that if H is a bipartite graph, then the random graph with edge density p has in expectation asymptotically the minimum number of copies of H over all graphs of the same order and edge density. This conjecture also has an equivalent analytic form and has connections to a broad range of topics, such as matrix theory, Markov chains, graph limits, and quasirandomness. Here we prove the conjecture if H has a vertex complete to the other part, and deduce an approximate version of the conjecture for all H. Furthermore, for a large class of bipartite graphs, we prove a stronger stability result which answers a question of Chung, Graham, and Wilson on quasirandomness for these graphs.
Approximation algorithm for multiprocessor parallel job scheduling
Institute of Scientific and Technical Information of China (English)
陈松乔; 黄金贵; 陈建二
2002-01-01
Pk|fix|Cmax problem is a new scheduling problem based on the multiprocessor parallel job, and it is proved to be NP-hard problem when k≥3. This paper focuses on the case of k=3. Some new observations and new techniques for P3|fix|Cmax problem are offered. The concept of semi-normal schedulings is introduced, and a very simple linear time algorithm Semi-normal Algorithm for constructing semi-normal schedulings is developed. With the method of the classical Graham List Scheduling, a thorough analysis of the optimal scheduling on a special instance is provided, which shows that the algorithm is an approximation algorithm of ratio of 9/8 for any instance of P3|fix|Cmax problem, and improves the previous best ratio of 7/6 by M.X.Goemans.
Approximating acyclicity parameters of sparse hypergraphs
Fomin, Fedor V; Thilikos, Dimitrios M
2008-01-01
The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx, who introduced the fractional hypertree width of a hypergraph. All these width parameters on hypergraphs are useful for extending tractability of many problems in database theory and artificial intelligence. In this paper, we study the approximability of (generalized, fractional) hyper treewidth of sparse hypergraphs where the criterion of sparsity reflects the sparsity of their incidence graphs. Our first step is to prove that the (generalized, fractional) hypertree width of a hypergraph H is constant-factor sandwiched by the treewidth of its incidence graph, when the incidence graph belongs to some apex-minor-free graph class. This determines the combinatorial borderline above which the notion of (generalized, fractional) hypertree width becomes essentially more general than treewidth...
Spectral clustering based on local linear approximations
Arias-Castro, Ery; Lerman, Gilad
2010-01-01
In the context of clustering, we assume a generative model where each cluster is the result of sampling points in the neighborhood of an embedded smooth surface, possibly contaminated with outliers. We consider a prototype for a higher-order spectral clustering method based on the residual from a local linear approximation. In an asymptotic setting where the number of points becomes large, we obtain theoretical guaranties for this algorithm and show that, both in terms of separation and robustness to outliers, it outperforms the standard spectral clustering algorithm based on pairwise distances of Ng, Jordan and Weiss (NIPS, 2001). Under some conditions on the dimension of, and the incidence angle at, an intersection, the algorithm is able to recover the intersecting clusters. The optimal choice for some of the tuning parameters depends on the dimension and thickness of the clusters. We provide estimators that come close enough for our purposes. We discuss the cases of clusters of mixed dimensions and of clus...
Approximate Methods for State-Space Models
Koyama, Shinsuke; Shalizi, Cosma Rohilla; Kass, Robert E; 10.1198/jasa.2009.tm08326
2010-01-01
State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace's method, an asymptotic series expansion, to approximate the state's conditional mean and variance, together with a Gaussian conditional distribution. This {\\em Laplace-Gaussian filter} (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulat...
Gutzwiller approximation in strongly correlated electron systems
Li, Chunhua
Gutzwiller wave function is an important theoretical technique for treating local electron-electron correlations nonperturbatively in condensed matter and materials physics. It is concerned with calculating variationally the ground state wave function by projecting out multi-occupation configurations that are energetically costly. The projection can be carried out analytically in the Gutzwiller approximation that offers an approximate way of calculating expectation values in the Gutzwiller projected wave function. This approach has proven to be very successful in strongly correlated systems such as the high temperature cuprate superconductors, the sodium cobaltates, and the heavy fermion compounds. In recent years, it has become increasingly evident that strongly correlated systems have a strong propensity towards forming inhomogeneous electronic states with spatially periodic superstrutural modulations. A good example is the commonly observed stripes and checkerboard states in high- Tc superconductors under a variety of conditions where superconductivity is weakened. There exists currently a real challenge and demand for new theoretical ideas and approaches that treats strongly correlated inhomogeneous electronic states, which is the subject matter of this thesis. This thesis contains four parts. In the first part of the thesis, the Gutzwiller approach is formulated in the grand canonical ensemble where, for the first time, a spatially (and spin) unrestricted Gutzwiller approximation (SUGA) is developed for studying inhomogeneous (both ordered and disordered) quantum electronic states in strongly correlated electron systems. The second part of the thesis applies the SUGA to the t-J model for doped Mott insulators which led to the discovery of checkerboard-like inhomogeneous electronic states competing with d-wave superconductivity, consistent with experimental observations made on several families of high-Tc superconductors. In the third part of the thesis, new
Nuclear structure aspects in A approximately 90
Energy Technology Data Exchange (ETDEWEB)
Bucurescu, D.; Constantinescu, G.; Cutoiu, D.; Ivascu, M.; Zamfir, N.V.; Avrigeanu, M.
1981-01-01
A systematic review of the experimental studies on some neutron deficient nuclei in the A approximately 90 region performed at the Bucharest FN tandem is presented. After a brief account of the measurements, several transitionality aspects are evidenced, like a change of structure in the odd Sr isotopes from N = 48 to N = 46 and the occurence of decoupled g 9/2 bands. The description of these characteristics is discussed in connection with the triaxial rotor, with the VMI model, as well as the cluster-vibration and the interacting boson-fermion model. A systematics of the B(E2) values for the 8/sub 1//sup +/ state in the N = 46 isotones is also presented. 12 references.
Exact and Approximate Probabilistic Symbolic Execution
Luckow, Kasper; Pasareanu, Corina S.; Dwyer, Matthew B.; Filieri, Antonio; Visser, Willem
2014-01-01
Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.
Squashed entanglement and approximate private states
Wilde, Mark M.
2016-09-01
The squashed entanglement is a fundamental entanglement measure in quantum information theory, finding application as an upper bound on the distillable secret key or distillable entanglement of a quantum state or a quantum channel. This paper simplifies proofs that the squashed entanglement is an upper bound on distillable key for finite-dimensional quantum systems and solidifies such proofs for infinite-dimensional quantum systems. More specifically, this paper establishes that the logarithm of the dimension of the key system (call it log 2K ) in an ɛ -approximate private state is bounded from above by the squashed entanglement of that state plus a term that depends only ɛ and log 2K . Importantly, the extra term does not depend on the dimension of the shield systems of the private state. The result holds for the bipartite squashed entanglement, and an extension of this result is established for two different flavors of the multipartite squashed entanglement.
Statistical model semiquantitatively approximates arabinoxylooligosaccharides' structural diversity
DEFF Research Database (Denmark)
Dotsenko, Gleb; Nielsen, Michael Krogsgaard; Lange, Lene
2016-01-01
A statistical model describing the random distribution of substituted xylopyranosyl residues in arabinoxylooligosaccharides is suggested and compared with existing experimental data. Structural diversity of arabinoxylooligosaccharides of various length, originating from different arabinoxylans...... (wheat flour arabinoxylan (arabinose/xylose, A/X = 0.47); grass arabinoxylan (A/X = 0.24); wheat straw arabinoxylan (A/X = 0.15); and hydrothermally pretreated wheat straw arabinoxylan (A/X = 0.05)), is semiquantitatively approximated using the proposed model. The suggested approach can be applied...... not only for prediction and quantification of arabinoxylooligosaccharides' structural diversity, but also for estimate of yield and selection of the optimal source of arabinoxylan for production of arabinoxylooligosaccharides with desired structural features....
Approximate Bayesian computation with functional statistics.
Soubeyrand, Samuel; Carpentier, Florence; Guiton, François; Klein, Etienne K
2013-03-26
Functional statistics are commonly used to characterize spatial patterns in general and spatial genetic structures in population genetics in particular. Such functional statistics also enable the estimation of parameters of spatially explicit (and genetic) models. Recently, Approximate Bayesian Computation (ABC) has been proposed to estimate model parameters from functional statistics. However, applying ABC with functional statistics may be cumbersome because of the high dimension of the set of statistics and the dependences among them. To tackle this difficulty, we propose an ABC procedure which relies on an optimized weighted distance between observed and simulated functional statistics. We applied this procedure to a simple step model, a spatial point process characterized by its pair correlation function and a pollen dispersal model characterized by genetic differentiation as a function of distance. These applications showed how the optimized weighted distance improved estimation accuracy. In the discussion, we consider the application of the proposed ABC procedure to functional statistics characterizing non-spatial processes.
Wave system and its approximate similarity solutions
Institute of Scientific and Technical Information of China (English)
Liu Ping; Fu Pei-Kai
2011-01-01
Recently,a new (2+1)-dimensional shallow water wave system,the (2+1)-dimensional displacement shallow water wave system (2DDSWWS),was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS,which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis,we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS (M2DDSWWS) is studied and four similarity solutions are obtained. For the perfect fluids,the coefficient of kinematic viscosity is zero,then the M2DDSWWS will degenerate to the 2DDSWWS.
Efficient Approximate OLAP Querying Over Time Series
DEFF Research Database (Denmark)
Perera, Kasun Baruhupolage Don Kasun Sanjeewa; Hahmann, Martin; Lehner, Wolfgang;
2016-01-01
are either costly or require continuous maintenance. In this paper we propose an approach for approximate OLAP querying of time series that offers constant latency and is maintenance-free. To achieve this, we identify similarities between aggregation cuboids and propose algorithms that eliminate......The ongoing trend for data gathering not only produces larger volumes of data, but also increases the variety of recorded data types. Out of these, especially time series, e.g. various sensor readings, have attracted attention in the domains of business intelligence and decision making. As OLAP...... queries play a major role in these domains, it is desirable to also execute them on time series data. While this is not a problem on the conceptual level, it can become a bottleneck with regards to query run-time. In general, processing OLAP queries gets more computationally intensive as the volume...
Uncertainty relations and approximate quantum error correction
Renes, Joseph M.
2016-09-01
The uncertainty principle can be understood as constraining the probability of winning a game in which Alice measures one of two conjugate observables, such as position or momentum, on a system provided by Bob, and he is to guess the outcome. Two variants are possible: either Alice tells Bob which observable she measured, or he has to furnish guesses for both cases. Here I derive uncertainty relations for both, formulated directly in terms of Bob's guessing probabilities. For the former these relate to the entanglement that can be recovered by action on Bob's system alone. This gives an explicit quantum circuit for approximate quantum error correction using the guessing measurements for "amplitude" and "phase" information, implicitly used in the recent construction of efficient quantum polar codes. I also find a relation on the guessing probabilities for the latter game, which has application to wave-particle duality relations.
Goldstone modes in the random phase approximation
Neergård, Kai
2016-01-01
I show that the kernel of the random phase approximation (RPA) matrix based on a stable Hartree, Hartree-Fock, Hartree-Bogolyubov or Hartree-Fock-Bogolyubov mean field solution is decomposed into a subspace with a basis whose vectors are associated, in the equivalent formalism of a classical Hamiltonian linear in canonic coordinates, with conjugate momenta of cyclic coordinates (Goldstone modes) and a subspace with a basis whose vectors are associated with pairs of conjugate canonic coordinates that do not enter the Hamiltonian at all. In a subspace complementary to the one spanned by all these coordinates including the conjugate coordinates of the Goldstone momenta, the RPA matrix behaves as in the case of a zerodimensional kernel. This result was derived very recently by Nakada as a corollary to a general analysis of RPA matrices based on both stable and unstable mean field solutions. The present proof does not rest on Nakada's general results.
Fast approximate quadratic programming for graph matching.
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Joshua T Vogelstein
Full Text Available Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs, we find that it efficiently achieves performance.
Fast approximate quadratic programming for graph matching.
Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E
2015-01-01
Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.
Approximation diffuse Hermite et ses applications
2000-01-01
De nombreuses techniques de résolution d'équations aux dérivées partielles sans maillage ont été développées dans la dernière décennie, proposant une alternative attrayante lorsque les éléments finis atteignent leurs limites. Notre travail se concentre sur l'étude de l'approximation diffuse, de ses applications au lissage et a la résolution des équations différentielles : les éléments diffus. Cependant, les solutions proposées s'appliquent aussi à d'autres méthodes et de nombreux résultats nu...
Nanostructures: Scattering beyond the Born approximation
Grigoriev, S. V.; Syromyatnikov, A. V.; Chumakov, A. P.; Grigoryeva, N. A.; Napolskii, K. S.; Roslyakov, I. V.; Eliseev, A. A.; Petukhov, A. V.; Eckerlebe, H.
2010-03-01
The neutron scattering on a two-dimensional ordered nanostructure with the third nonperiodic dimension can go beyond the Born approximation. In our model supported by the exact theoretical solution a well-correlated hexagonal porous structure of anodic aluminum oxide films acts as a peculiar two-dimensional grating for the coherent neutron wave. The thickness of the film L (length of pores) plays important role in the transition from the weak to the strong scattering regimes. It is shown that the coherency of the standard small-angle neutron scattering setups suits to the geometry of the studied objects and often affects the intensity of scattering. The proposed theoretical solution can be applied in the small-angle neutron diffraction experiments with flux lines in superconductors, periodic arrays of magnetic or superconducting nanowires, as well as in small-angle diffraction experiments on synchrotron radiation.
Adaptive Control with Approximated Policy Search Approach
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Agus Naba
2010-05-01
Full Text Available Most of existing adaptive control schemes are designed to minimize error between plant state and goal state despite the fact that executing actions that are predicted to result in smaller errors only can mislead to non-goal states. We develop an adaptive control scheme that involves manipulating a controller of a general type to improve its performance as measured by an evaluation function. The developed method is closely related to a theory of Reinforcement Learning (RL but imposes a practical assumption made for faster learning. We assume that a value function of RL can be approximated by a function of Euclidean distance from a goal state and an action executed at the state. And, we propose to use it for the gradient search as an evaluation function. Simulation results provided through application of the proposed scheme to a pole-balancing problem using a linear state feedback controller and fuzzy controller verify the scheme’s efficacy.
The Electroweak Sudakov approximation in SHERPA
Thompson, Jennifer M
2016-01-01
As experimental particle physics becomes more and more precise, it is becoming increasingly important for Monte Carlo simulations to improve the precision of their predictions. In terms of the hard matrix element, this means calculating to a higher order in perturbation theory. To be consistent this requires both NNLO QCD corrections and NLO EW corrections to be included. There are also interference effects between these processes that are not simple to handle consistently. For a broad description of the behaviour of NLO EW corrections at high energies, the Sudakov logarithmic approach provides a good approximation, and is much less computationally expensive than the full calculation. The implementation of EW Sudakov logarithms within the SHERPA program are outlined here along with some initial results. As well as this, an overview of the status of full NLO EW computations with SHERPA is presented.
High order compact schemes for gradient approximation
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we propose three gradient recovery schemes of higher order for the linear interpolation. The first one is a weighted averaging method based on the gradients of the linear interpolation on the uniform mesh, the second is a geometric averaging method constructed from the gradients of two cubic interpolation on macro element, and the last one is a local least square method on the nodal patch with cubic polynomials. We prove that these schemes can approximate the gradient of the exact solution on the symmetry points with fourth order. In particular, for the uniform mesh, we show that these three schemes are the same on the considered points. The last scheme is more robust in general meshes. Consequently, we obtain the superconvergence results of the recovered gradient by using the aforementioned results and the supercloseness between the finite element solution and the linear interpolation of the exact solution. Finally, we provide several numerical experiments to illustrate the theoretical results.
Comparing numerical and analytic approximate gravitational waveforms
Afshari, Nousha; Lovelace, Geoffrey; SXS Collaboration
2016-03-01
A direct observation of gravitational waves will test Einstein's theory of general relativity under the most extreme conditions. The Laser Interferometer Gravitational-Wave Observatory, or LIGO, began searching for gravitational waves in September 2015 with three times the sensitivity of initial LIGO. To help Advanced LIGO detect as many gravitational waves as possible, a major research effort is underway to accurately predict the expected waves. In this poster, I will explore how the gravitational waveform produced by a long binary-black-hole inspiral, merger, and ringdown is affected by how fast the larger black hole spins. In particular, I will present results from simulations of merging black holes, completed using the Spectral Einstein Code (black-holes.org/SpEC.html), including some new, long simulations designed to mimic black hole-neutron star mergers. I will present comparisons of the numerical waveforms with analytic approximations.
Robust Generalized Low Rank Approximations of Matrices.
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Jiarong Shi
Full Text Available In recent years, the intrinsic low rank structure of some datasets has been extensively exploited to reduce dimensionality, remove noise and complete the missing entries. As a well-known technique for dimensionality reduction and data compression, Generalized Low Rank Approximations of Matrices (GLRAM claims its superiority on computation time and compression ratio over the SVD. However, GLRAM is very sensitive to sparse large noise or outliers and its robust version does not have been explored or solved yet. To address this problem, this paper proposes a robust method for GLRAM, named Robust GLRAM (RGLRAM. We first formulate RGLRAM as an l1-norm optimization problem which minimizes the l1-norm of the approximation errors. Secondly, we apply the technique of Augmented Lagrange Multipliers (ALM to solve this l1-norm minimization problem and derive a corresponding iterative scheme. Then the weak convergence of the proposed algorithm is discussed under mild conditions. Next, we investigate a special case of RGLRAM and extend RGLRAM to a general tensor case. Finally, the extensive experiments on synthetic data show that it is possible for RGLRAM to exactly recover both the low rank and the sparse components while it may be difficult for previous state-of-the-art algorithms. We also discuss three issues on RGLRAM: the sensitivity to initialization, the generalization ability and the relationship between the running time and the size/number of matrices. Moreover, the experimental results on images of faces with large corruptions illustrate that RGLRAM obtains the best denoising and compression performance than other methods.
Robust Generalized Low Rank Approximations of Matrices.
Shi, Jiarong; Yang, Wei; Zheng, Xiuyun
2015-01-01
In recent years, the intrinsic low rank structure of some datasets has been extensively exploited to reduce dimensionality, remove noise and complete the missing entries. As a well-known technique for dimensionality reduction and data compression, Generalized Low Rank Approximations of Matrices (GLRAM) claims its superiority on computation time and compression ratio over the SVD. However, GLRAM is very sensitive to sparse large noise or outliers and its robust version does not have been explored or solved yet. To address this problem, this paper proposes a robust method for GLRAM, named Robust GLRAM (RGLRAM). We first formulate RGLRAM as an l1-norm optimization problem which minimizes the l1-norm of the approximation errors. Secondly, we apply the technique of Augmented Lagrange Multipliers (ALM) to solve this l1-norm minimization problem and derive a corresponding iterative scheme. Then the weak convergence of the proposed algorithm is discussed under mild conditions. Next, we investigate a special case of RGLRAM and extend RGLRAM to a general tensor case. Finally, the extensive experiments on synthetic data show that it is possible for RGLRAM to exactly recover both the low rank and the sparse components while it may be difficult for previous state-of-the-art algorithms. We also discuss three issues on RGLRAM: the sensitivity to initialization, the generalization ability and the relationship between the running time and the size/number of matrices. Moreover, the experimental results on images of faces with large corruptions illustrate that RGLRAM obtains the best denoising and compression performance than other methods.
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.
Probabilistic flood forecast: Exact and approximate predictive distributions
Krzysztofowicz, Roman
2014-09-01
For quantification of predictive uncertainty at the forecast time t0, the future hydrograph is viewed as a discrete-time continuous-state stochastic process {Hn: n=1,…,N}, where Hn is the river stage at time instance tn>t0. The probabilistic flood forecast (PFF) should specify a sequence of exceedance functions {F‾n: n=1,…,N} such that F‾n(h)=P(Zn>h), where P stands for probability, and Zn is the maximum river stage within time interval (t0,tn], practically Zn=max{H1,…,Hn}. This article presents a method for deriving the exact PFF from a probabilistic stage transition forecast (PSTF) produced by the Bayesian forecasting system (BFS). It then recalls (i) the bounds on F‾n, which can be derived cheaply from a probabilistic river stage forecast (PRSF) produced by a simpler version of the BFS, and (ii) an approximation to F‾n, which can be constructed from the bounds via a recursive linear interpolator (RLI) without information about the stochastic dependence in the process {H1,…,Hn}, as this information is not provided by the PRSF. The RLI is substantiated by comparing the approximate PFF against the exact PFF. Being reasonably accurate and very simple, the RLI may be attractive for real-time flood forecasting in systems of lesser complexity. All methods are illustrated with a case study for a 1430 km headwater basin wherein the PFF is produced for a 72-h interval discretized into 6-h steps.
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Carlos Restrepo Canal
1962-04-01
Full Text Available Como parte de la monumental Historia de España que bajo la prestante y acertadísima dirección de don Ramón Menéndez Pidal se comenzó a dar a la prensa desde 1954 por la Editorial Espasa Calpe S. A., aparecieron en 1958 dos tomos dedicados al reinado de Felipe II; aquella época en que el imperio español alcanzó su unidad peninsular juntamente con el dilatado poderío que le constituyó en la primera potencia de Europa.
Coherent states, quantum gravity, and the Born- Oppenheimer approximation. II. Compact Lie groups
Stottmeister, Alexander; Thiemann, Thomas
2016-07-01
In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Additionally, we conjecture the existence of a new form of the Segal-Bargmann-Hall "coherent state" transform for compact Lie groups G, which we prove for G = U(1)n and support by numerical evidence for G = SU(2). The reason for conjoining this conjecture with the main topic of this article originates in the observation that the coherent state transform can be used as a basic building block of a coherent state quantisation (Berezin quantisation) for compact Lie groups G. But, as Weyl and Berezin quantisation for ℝ2d are intimately related by heat kernel evolution, it is natural to ask whether a similar connection exists for compact Lie groups as well. Moreover, since the formulation of space adiabatic perturbation theory requires a (deformation) quantisation as minimal input, we analyse the question to what extent the coherent state quantisation, defined by the Segal-Bargmann-Hall transform, can serve as basis of the former.
On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs
Bayona, Victor; Flyer, Natasha; Fornberg, Bengt; Barnett, Gregory A.
2017-03-01
RBF-generated finite differences (RBF-FD) have in the last decade emerged as a very powerful and flexible numerical approach for solving a wide range of PDEs. We find in the present study that combining polyharmonic splines (PHS) with multivariate polynomials offers an outstanding combination of simplicity, accuracy, and geometric flexibility when solving elliptic equations in irregular (or regular) regions. In particular, the drawbacks on accuracy and stability due to Runge's phenomenon are overcome once the RBF stencils exceed a certain size due to an underlying minimization property. Test problems include the classical 2-D driven cavity, and also a 3-D global electric circuit problem with the earth's irregular topography as its bottom boundary. The results we find are fully consistent with previous results for data interpolation.
On the evolution of the snow line in protoplanetary discs II: Analytic approximations
Martin, Rebecca G
2013-01-01
We examine the evolution of the snow line in a protoplanetary disc that contains a dead zone (a region of zero or low turbulence). The snow line is within a self-gravitating part of the dead zone, and we obtain a fully analytic solution for its radius. Our formula could prove useful for future observational attempts to characterise the demographics of planets outside the snow line. External sources such as comic rays or X-rays from the central star can ionise the disc surface layers and allow the magneto-rotational instability to drive turbulence there. We show that provided that the surface density in this layer is less than about 50 g/cm^2, the dead zone solution exists, after an initial outbursting phase, until the disc is dispersed by photoevaporation. We demonstrate that the snow line radius is significantly larger than that predicted by a fully turbulent disc model, and that in our own solar system it remains outside of the orbital radius of the Earth. Thus, the inclusion of a dead zone into a protoplan...
Mark, W. D.
1979-01-01
The second part of a theory for predicting the vibratory excitation of gear systems from fundamental descriptions of gear tooth elastic properties and deviations of tooth faces from perfect involute surfaces is presented. The first part of the theory provides expressions for the Fourier-series coefficients of the vibratory excitation, and this paper gives expressions for these Fourier-series coefficients in terms of easily interpreted gear tooth metrics that are readily evaluated from tooth-face measurements. Results are given for rectangular tooth-face contact regions using two-dimensional Legendre polynomial expansions of local tooth-pair stiffnesses and stiffness-weighted deviations of tooth faces from perfect involute surfaces. A rigorous transfer function approach is developed that permits separation of the effects of gear tooth errors and gear design parameters; the theory is applicable to helical and spur gears and is illustrated with measurements of tooth-spacing errors and tooth profiles obtained from a pair of spur gears.
Some Undecidable Problems on Approximability of NP Optimization Problems
Institute of Scientific and Technical Information of China (English)
黄雄
1996-01-01
In this paper some undecidable problems on approximability of NP optimization problems are investigated.In particular,the following problems are all undecidable:(1) Given an NP optimization problem,is it approximable in polynomial time?(2)For any polynomial-time computable function r(n),given a polynomial time approximable NP optimization problem,has it a polynomial-time approximation algorithm with approximation performance ratio r(n) (r(n)-approximable)?(3)For any polynomial-time computable functions r(n),r'(n),where r'(n)
Modelling CH$_3$OH masers: Sobolev approximation and accelerated lambda iteration method
Nesterenok, Aleksandr
2015-01-01
A simple one-dimensional model of CH$_3$OH maser is considered. Two techniques are used for the calculation of molecule level populations: the accelerated lambda iteration (ALI) method and the large velocity gradient (LVG), or Sobolev, approximation. The LVG approximation gives accurate results provided that the characteristic dimensions of the medium are larger than 5-10 lengths of the resonance region. We presume that this condition can be satisfied only for the largest observed maser spot distributions. Factors controlling the pumping of class I and class II methanol masers are considered.
Approximating Mathematical Semantic Web Services Using Approximation Formulas and Numerical Methods
Mogos, Andrei-Horia
2009-01-01
Mathematical semantic web services are very useful in practice, but only a small number of research results are reported in this area. In this paper we present a method of obtaining an approximation of a mathematical semantic web service, from its semantic description, using existing mathematical semantic web services, approximation formulas, and numerical methods techniques. We also give a method for automatic comparison of two complexity functions. In addition, we present a method for classifying the numerical methods mathematical semantic web services from a library.
Clustering Based Approximation in Facial Image Retrieval
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R.Pitchaiah
2016-11-01
Full Text Available The web search tool returns a great many pictures positioned by the essential words separated from the encompassing content. Existing article acknowledgment systems to prepare characterization models from human-named preparing pictures or endeavor to deduce the connection/probabilities in the middle of pictures and commented magic words. Albeit proficient in supporting in mining comparatively looking facial picture results utilizing feebly named ones, the learning phase of above bunch based close estimations is shortened with idleness elements for ongoing usage which is fundamentally highlighted in our showings. So we propose to utilize shading based division driven auto face location methodology combined with an adjusted Clustering Based Approximation (CBA plan to decrease the dormancy but then holding same proficiency amid questioning. The specialized phases of our proposed drew closer is highlighted in the accompanying stream diagram. Every phase of the above specialized procedure guarantees the question results at tremendously lessened handling time in this way making our method much achievable for ongoing usage
Approximate von Neumann entropy for directed graphs.
Ye, Cheng; Wilson, Richard C; Comin, César H; Costa, Luciano da F; Hancock, Edwin R
2014-05-01
In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks.
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.
Shock wave profiles in the burnett approximation
Uribe; Velasco; Garcia-Colin; Diaz-Herrera
2000-11-01
This paper is devoted to a discussion of the profiles of shock waves using the full nonlinear Burnett equations of hydrodynamics as they appear from the Chapman-Enskog solution to the Boltzmann equation. The system considered is a dilute gas composed of rigid spheres. The numerical analysis is carried out by transforming the hydrodynamic equations into a set of four first-order equations in four dimensions. We compare the numerical solutions of the Burnett equations, obtained using Adam's method, with the well known direct simulation Monte Carlo method for different Mach numbers. An exhaustive mathematical analysis of the results offered here has been done mainly in connection with the existence of heteroclinic trajectories between the two stationary points located upflow and downflow. The main result of this study is that such a trajectory exists for the Burnett equations for Mach numbers greater than 1. Our numerical calculations suggest that heteroclinic trajectories exist up to a critical Mach number ( approximately 2.69) where local mathematical analysis and numerical computations reveal a saddle-node-Hopf bifurcation. This upper limit for the existence of heteroclinic trajectories deserves further clarification.
Approximate Model for Turbulent Stagnation Point Flow.
Energy Technology Data Exchange (ETDEWEB)
Dechant, Lawrence [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
Here we derive an approximate turbulent self-similar model for a class of favorable pressure gradient wedge-like flows, focusing on the stagnation point limit. While the self-similar model provides a useful gross flow field estimate this approach must be combined with a near wall model is to determine skin friction and by Reynolds analogy the heat transfer coefficient. The combined approach is developed in detail for the stagnation point flow problem where turbulent skin friction and Nusselt number results are obtained. Comparison to the classical Van Driest (1958) result suggests overall reasonable agreement. Though the model is only valid near the stagnation region of cylinders and spheres it nonetheless provides a reasonable model for overall cylinder and sphere heat transfer. The enhancement effect of free stream turbulence upon the laminar flow is used to derive a similar expression which is valid for turbulent flow. Examination of free stream enhanced laminar flow suggests that the rather than enhancement of a laminar flow behavior free stream disturbance results in early transition to turbulent stagnation point behavior. Excellent agreement is shown between enhanced laminar flow and turbulent flow behavior for high levels, e.g. 5% of free stream turbulence. Finally the blunt body turbulent stagnation results are shown to provide realistic heat transfer results for turbulent jet impingement problems.
Approximately Counting Embeddings into Random Graphs
Furer, Martin
2008-01-01
Let H be a graph, and let C(H,G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C(H,G). Previous results cover only a few specific instances of this general problem, for example, the case when H has degree at most one (monomer-dimer problem). In this paper, we present the first general subcase of the subgraph isomorphism counting problem which is almost always efficiently approximable. The results rely on a new graph decomposition technique. Informally, the decomposition is a labeling of the vertices generating a sequence of bipartite graphs. The decomposition permits us to break the problem of counting embeddings of large subgraphs into that of counting embeddings of small subgraphs. Using this method, we present a simple randomized algorithm for the counting problem. For all decomposable graphs H and all graphs G, the algorithm is an unbiased estimator. Furthermore, for all graphs H having a decomposition where each of the bipa...
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.
The time-dependent Gutzwiller approximation
Fabrizio, Michele
2015-03-01
The time-dependent Gutzwiller Approximation (t-GA) is shown to be capable of tracking the off-equilibrium evolution both of coherent quasiparticles and of incoherent Hubbard bands. The method is used to demonstrate that the sharp dynamical crossover observed by time-dependent DMFT in the quench-dynamics of a half-filled Hubbard model can be identified within the t-GA as a genuine dynamical transition separating two distinct physical phases. This result, strictly variational for lattices of infinite coordination number, is intriguing as it actually questions the occurrence of thermalization. Next, we shall present how t-GA works in a multi-band model for V2O3 that displays a first-order Mott transition. We shall show that a physically accessible excitation pathway is able to collapse the Mott gap down and drive off-equilibrium the insulator into a metastable metal phase. Work supported by the European Union, Seventh Framework Programme, under the project GO FAST, Grant Agreement No. 280555.
The Graph Isomorphism Problem and approximate categories
Derksen, Harm
2010-01-01
It is unknown whether two graphs can be tested for isomorphism in polynomial time. A classical approach to the Graph Isomorphism Problem is the d-dimensional Weisfeiler-Lehman algorithm. The d-dimensional WL-algorithm can distinguish many pairs of graphs, but the pairs of non-isomorphic graphs constructed by Cai, Furer and Immerman it cannot distinguish. If d is fixed, then the WL-algorithm runs in polynomial time. We will formulate the Graph Isomorphism Problem as an Orbit Problem: Given a representation V of an algebraic group G and two elements v_1,v_2 in V, decide whether v_1 and v_2 lie in the same G-orbit. Then we attack the Orbit Problem by constructing certain approximate categories C_d(V), d=1,2,3,... whose objects include the elements of V. We show that v_1 and v_2 are not in the same orbit by showing that they are not isomorphic in the category C_d(V) for some d. For every d this gives us an algorithm for isomorphism testing. We will show that the WL-algorithms reduce to our algorithms, but that ou...
Coulomb crystals in the harmonic lattice approximation
Baiko, D A; De Witt, H E; Slattery, W L
2000-01-01
The dynamic structure factor ${\\tilde S}({\\bf k},\\omega)$ and the two-particle distribution function $g({\\bf r},t)$ of ions in a Coulomb crystal are obtained in a closed analytic form using the harmonic lattice (HL) approximation which takes into account all processes of multi-phonon excitation and absorption. The static radial two-particle distribution function $g(r)$ is calculated for classical ($T \\gtrsim \\hbar \\omega_p$, where $\\omega_p$ is the ion plasma frequency) and quantum ($T \\ll \\hbar \\omega_p$) body-centered cubic (bcc) crystals. The results for the classical crystal are in a very good agreement with extensive Monte Carlo (MC) calculations at $1.5 \\lesssim r/a calculated for classical and quantum bcc and face-centered cubic crystals, and anharmonic corrections are discussed. The inelastic part of the HL static structure factor $S''(k)$, averaged over orientations of wave-vector {\\bf k}, is shown to contain pronounced singularities at Bragg diffraction positions. The type of the singularities is di...
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.
Stochastic approximation with state-dependent noise
Institute of Scientific and Technical Information of China (English)
陈翰馥
2000-01-01
The purpose of stochastic approximation (SA) is to find the roots of f(·) or the maximiz-er (minimizer) of L(·) when the unknown function f(·) or L(·) can be observed but with noise. SA is an important tool in dealing with many problems arising from systems and control, whose solutions often rely on convergence of the SA algorithm applied. Here the pathwise convergence of SA algorithms is considered, when the observation noise may depend on state by which we mean those x at which f( x) or L( x) are observed. The conditions imposed on the observation noise are the weakest in comparison with the existing ones. When the algorithm is to find the roots of f(·), the superiority of the condition given in the paper over those used in literature consists in the fact that the present condition is directly verifiable, needless to see the behaviour of the algorithm. When the algorithm is to find the maximizer (minimizer) of L(·), the present conditioin allows the observation noise to depend on the state. The
Stochastic approximation with state-dependent noise
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The purpose of stochastic approximation (SA) is to find the roots of f(·) or the maximizer (minimizer) of L(·) when the unknown function f(·) or L(·) can be observed but with noise. SA is an important tool in dealing with many problems arising from systems and control, whose solutions often rely on convergence of the SA algorithm applied. Here the pathwise convergence of SA algorithms is considered, when the observation noise may depend on state by which we mean those x at which f(x) or L(x) are observed. The conditions imposed on the observation noise are the weakest in comparison with the existing ones. When the algorithm is to find the roots of f(·), the superiority of the condition given in the paper over those used in literature consists in the fact that the present condition is directly verifiable, needless to see the behaviour of the algorithm. When the algorithm is to find the maximizer (minimizer) of L(·), the present conditioin allows the observation noise to depend on the state. The conditions imposed on f(·) and L(·) are truly general: f(·) is required to be measurable and locally bounded if the roots of f(·) are sought, and the gradient of L(·) is required to be locally Lipschitz continuous if the maximizer (minimizer) of L(·) is searched.
Approximate Distance Oracles with Improved Preprocessing Time
Wulff-Nilsen, Christian
2011-01-01
Given an undirected graph $G$ with $m$ edges, $n$ vertices, and non-negative edge weights, and given an integer $k\\geq 1$, we show that for some universal constant $c$, a $(2k-1)$-approximate distance oracle for $G$ of size $O(kn^{1 + 1/k})$ can be constructed in $O(\\sqrt km + kn^{1 + c/\\sqrt k})$ time and can answer queries in $O(k)$ time. We also give an oracle which is faster for smaller $k$. Our results break the quadratic preprocessing time bound of Baswana and Kavitha for all $k\\geq 6$ and improve the $O(kmn^{1/k})$ time bound of Thorup and Zwick except for very sparse graphs and small $k$. When $m = \\Omega(n^{1 + c/\\sqrt k})$ and $k = O(1)$, our oracle is optimal w.r.t.\\ both stretch, size, preprocessing time, and query time, assuming a widely believed girth conjecture by Erd\\H{o}s.
Network histograms and universality of blockmodel approximation
Olhede, Sofia C.; Wolfe, Patrick J.
2014-01-01
In this paper we introduce the network histogram, a statistical summary of network interactions to be used as a tool for exploratory data analysis. A network histogram is obtained by fitting a stochastic blockmodel to a single observation of a network dataset. Blocks of edges play the role of histogram bins and community sizes that of histogram bandwidths or bin sizes. Just as standard histograms allow for varying bandwidths, different blockmodel estimates can all be considered valid representations of an underlying probability model, subject to bandwidth constraints. Here we provide methods for automatic bandwidth selection, by which the network histogram approximates the generating mechanism that gives rise to exchangeable random graphs. This makes the blockmodel a universal network representation for unlabeled graphs. With this insight, we discuss the interpretation of network communities in light of the fact that many different community assignments can all give an equally valid representation of such a network. To demonstrate the fidelity-versus-interpretability tradeoff inherent in considering different numbers and sizes of communities, we analyze two publicly available networks—political weblogs and student friendships—and discuss how to interpret the network histogram when additional information related to node and edge labeling is present. PMID:25275010
Benchmarking mean-field approximations to level densities
Alhassid, Y; Gilbreth, C N; Nakada, H
2015-01-01
We assess the accuracy of finite-temperature mean-field theory using as a standard the Hamiltonian and model space of the shell model Monte Carlo calculations. Two examples are considered: the nucleus $^{162}$Dy, representing a heavy deformed nucleus, and $^{148}$Sm, representing a nearby heavy spherical nucleus with strong pairing correlations. The errors inherent in the finite-temperature Hartree-Fock and Hartree-Fock-Bogoliubov approximations are analyzed by comparing the entropies of the grand canonical and canonical ensembles, as well as the level density at the neutron resonance threshold, with shell model Monte Carlo (SMMC) calculations, which are accurate up to well-controlled statistical errors. The main weak points in the mean-field treatments are seen to be: (i) the extraction of number-projected densities from the grand canonical ensembles, and (ii) the symmetry breaking by deformation or by the pairing condensate. In the absence of a pairing condensate, we confirm that the usual saddle-point appr...
Collisionless magnetic reconnection under anisotropic MHD approximation
Hirabayashi, Kota; Hoshino, Masahiro
We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless magneto-hydro-dynamic (MHD) simulations based on the double adiabatic approximation, which is an important step to 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 observation. According to our results, a pair of slow shocks does form in the reconnection layer. The resultant shock waves, however, are quite weak compared with those in an isotropic MHD from the point of view of the plasma compression and the amount of the magnetic energy released across the shock. Once the slow shock forms, the downstream plasma are heated in highly anisotropic manner and a firehose-sense (P_{||}>P_{⊥}) pressure anisotropy arises. The maximum anisotropy is limited by the marginal firehose criterion, 1-(P_{||}-P_{⊥})/B(2) =0. In spite of the weakness of the shocks, the resultant reconnection rate is kept at the same level compared with that in the corresponding ordinary MHD simulations. It is also revealed that the sequential order of propagation of the slow shock and the rotational discontinuity, which appears when the guide field component exists, changes depending on the magnitude of the guide field. Especially, when no guide field exists, the rotational discontinuity degenerates with the contact discontinuity remaining at the position of the initial current sheet, while with the slow shock in the isotropic MHD. Our 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.
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.
Contact with Fluoride-Releasing Restorative Materials Can Arrest Simulated Approximal Caries Lesion
Directory of Open Access Journals (Sweden)
Camila de Almeida Brandão Guglielmi
2015-01-01
Full Text Available Previous studies have suggested that the presence of white-spot lesion is very probable when adjacent surface is affected by cavitated lesions. This study evaluated the potential of different fluoride-releasing restorative materials in arresting enamel white-spot lesions in approximal surface in contact with them, in vitro (I and in situ (II. White-spot lesions were formed in 240 primary enamel specimens via pH-cycling. They were put in contact with cylindrical blocks of 6 materials (n=20: composite resin, 2 high-viscous glass ionomer cements (HVGIC, resin-modified GIC, resin-modified nanoionomer, and polyacid-modified resin. In both studies I and II, these settings were designed to simulate the contact point between the restoration and simulated approximal lesion. For study I, they were subjected to a new pH-cycling cariogenic challenge for 7 or 14 days (n=10. For study II, a randomized double-blind in situ design was conducted in two phases (7/14 days to promote cariogenic challenge. At the end of both studies, specimens were collected for mineral analysis by cross-sectional microhardness. Higher mineral loss was observed for lesions in contact with resin (p<0.001. HVGICs were the most efficient in preventing mineral loss, whereas other materials presented an intermediate behavior. It is concluded that fluoride-releasing materials can moderately reduce white-spot lesions progression, and HVGIC can arrest enamel lesion in approximal surface in contact with them.
Hydration thermodynamics beyond the linear response approximation
Raineri, Fernando O.
2016-10-01
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, {{\\Psi}\\text{A}} and {{\\Psi}\\text{B}} , with the solvent environment. Throughout the A \\to B transformation of the solute, the solvation system is described by a Hamiltonian H≤ft(ξ \\right) that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density {{\\wp}ξ}≤ft( y\\right) that the dimensionless perturbational solute-solvent interaction energy Y=β ≤ft({{\\Psi}\\text{B}}-{{\\Psi}\\text{A}}\\right) 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 {{\\wp}ξ} ≤ft( y\\right) 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 {{\\wp}ξ} ≤ft( y\\right) . 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
L0-based sparse approximation: two alternative methods and some applications
Portilla, Javier; Mancera, Luis
2007-09-01
We propose two methods for sparse approximation of images under l II error metric. First one performs an approximation error minimization given a l p-norm of the representation through alternated orthogonal projections onto two sets. We study the cases p = 0 (sub-optimal) and p = 1 (optimal), and find that the l 0-AP method is neatly superior, for typical images and overcomplete oriented pyramids. Given that l I-AP is optimal, this shows that it is not equivalent in practical image processing conditions to minimize one or the other norm, contrarily to what is often assumed. The second method is more powerful, and it performs gradient descent onto decreasingly smoothed versions of the sparse approximation cost function, yielding a method previously proposed as a heuristic. We adapt these techniques for being applied to image restoration, with very positive results.
On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy
Flyer, Natasha; Fornberg, Bengt; Bayona, Victor; Barnett, Gregory A.
2016-09-01
Radial basis function-generated finite difference (RBF-FD) approximations generalize classical grid-based finite differences (FD) from lattice-based to scattered node layouts. This greatly increases the geometric flexibility of the discretizations and makes it easier to carry out local refinement in critical areas. Many different types of radial functions have been considered in this RBF-FD context. In this study, we find that (i) polyharmonic splines (PHS) in conjunction with supplementary polynomials provide a very simple way to defeat stagnation (also known as saturation) error and (ii) give particularly good accuracy for the tasks of interpolation and derivative approximations without the hassle of determining a shape parameter. In follow-up studies, we will focus on how to best use these hybrid RBF polynomial bases for FD approximations in the contexts of solving elliptic and hyperbolic type PDEs.
Rational offset approximation of rational Bézier curves
Institute of Scientific and Technical Information of China (English)
CHENG Min; WANG Guo-jin
2006-01-01
The problem of parametric speed approximation of a rational curve is raised in this paper. Offset curves are widely used in various applications. As for the reason that in most cases the offset curves do not preserve the same polynomial or rational polynomial representations, it arouses difficulty in applications. Thus approximation methods have been introduced to solve this problem. In this paper, it has been pointed out that the crux of offset curve approximation lies in the approximation of parametric speed. Based on the Jacobi polynomial approximation theory with endpoints interpolation, an algebraic rational approximation algorithm of offset curve, which preserves the direction of normal, is presented.
APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES
Institute of Scientific and Technical Information of China (English)
Amir KHOSRAVI; Morteza MIRZAEE AZANDARYANI
2014-01-01
In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.
Approximation law for discrete-time variable structure control systems
Institute of Scientific and Technical Information of China (English)
Yan ZHENG; Yuanwei JING
2006-01-01
Two approximation laws of sliding mode for discrete-time variable structure control systems are proposed to overcome the limitations of the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the stability of origin can be guaranteed, and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation laws, the problem that the system control input is restricted is also considered, which is very important in practical systems. Finally a simulation example shows the effectiveness of the two approximation laws proposed.
Small Diameter Bomb Increment II (SDB II)
2015-12-01
Bomb Increment II (SDB II) DoD Component Air Force Joint Participants Department of the Navy Responsible Office References SAR Baseline ( Production ...Selected Acquisition Report (SAR) RCS: DD-A&T(Q&A)823-439 Small Diameter Bomb Increment II (SDB II) As of FY 2017 President’s Budget Defense...Funding 19 Low Rate Initial Production 31 Foreign Military Sales 32 Nuclear Costs 32 Unit Cost 33 Cost Variance 36 Contracts