NASA Astrophysics Data System (ADS)
Kalinin, A. V.; Sumin, M. I.; Tyukhtina, A. A.
2017-02-01
An initial-boundary value problem for Maxwell's equations in the quasi-stationary magnetic approximation is investigated. Special gauge conditions are presented that make it possible to state the problem of independently determining the vector magnetic potential. The well-posedness of the problem is proved under general conditions on the coefficients. For quasi-stationary Maxwell equations, final observation problems formulated in terms of the vector magnetic potential are considered. They are treated as convex programming problems in a Hilbert space with an operator equality constraint. Stable sequential Lagrange principles are stated in the form of theorems on the existence of a minimizing approximate solution of the optimization problems under consideration. The possibility of applying algorithms of dual regularization and iterative dual regularization with a stopping rule is justified in the case of a finite observation error.
Quasi-stationary distributions for models of heterogeneous catalysis
NASA Astrophysics Data System (ADS)
de Oliveira, Marcelo M.; Dickman, Ronald
2004-11-01
We construct the quasi-stationary (QS) distribution for two models of heterogeneous catalysis having two absorbing states: the ZGB model for the oxidation of CO, and a version with noninstantaneous reactions. Using a mean-field-like approximation, we study the quasi-stationary surface coverages, moment ratios and the lifetime of the QS state. We also derive an improved, consistent one-site mean-field theory for the ZGB model.
On the quasi-stationary distribution of the Ross malaria model.
Nåsell, I
1991-12-01
Approximations are derived for the quasi-stationary distribution of the fully stochastic version of the classical Ross malaria model. The approximations are developed in two stages. In the first stage, the Ross process is approximated with a bivariate Markov chain without an absorbing state. The second stage of the approximation uses ideas from perturbation theory to derive explicit expressions that serve as approximations of the joint stationary distribution of the approximating process. Numerical comparisons are made between the approximations and the quasi-stationary distribution.
Quasi-Stationary Planetary Wave in the MLT During Summer
NASA Astrophysics Data System (ADS)
Stray, N. H.; Espy, P. J.; Hibbins, R. E.
2014-12-01
A network of 8 northern hemispheric SuperDARN radars (51-66N) has been used to study planetary wave activity in the mesosphere lower thermosphere (MLT). The meridional meteor winds from the longitudinally spaced SuperDARN network are used to derive the planetary wave activity with zonal wave numbers 1 and 2 in the polar summer MLT (~95 km). In addition planetary wave amplitudes throughout the middle atmosphere have been retrieved from the meridional wind data of the Modern-Era Retrospective Analysis for Research and Application (MERRA) of the NASA Global Modelling and Assimilation Office. The fitting technique used to derive the planetary wave amplitudes will be presented, and it will be shown that there are strong quasi-stationary longitudinal differences in the strength of the meridional wind in the MLT during summer which can be described as a quasi-stationary planetary wave number 1. The ground-based network allows this planetary wave to be separated from tidal perturbations that are aliased in satellite observations, and the combination of these two data sets provides evidence that the mesopause planetary wave activity is produced in situ in the MLT rather than propagating upwards from lower altitudes. Finally, the impact of this planetary wave feature on Polar Mesospheric Clouds (PMC) and Polar Mesospheric Summer Echoes (PMSE) will be discussed.
NASA Astrophysics Data System (ADS)
Ivanov, M. I.; Kremer, I. A.; Urev, M. V.
2012-03-01
Nedelec vector finite elements are used for the numerical solution of a regularized version of the quasi-stationary Maxwell equations written in terms of a scalar and a vector magnetic potential with special calibration taking into account the conductivity of the medium. An optimal energy estimate for the error of the approximate solution in Lipschitz polyhedral domains is established. Numerical results are presented that demonstrate the stability of the method.
Quasi-stationary phase change heat transfer on a fin
NASA Astrophysics Data System (ADS)
Orzechowski, Tadeusz; Stokowiec, Katarzyna
2016-03-01
The paper presents heat transfer research basing on a long fin with a circular cross-section. Its basis is welded to the pipe where the hot liquid paraffin, having a temperature of 70°C at the inflow, is pumped. The analyzed element is a recurrent part of a refrigeration's condenser, which is immersed in a paraffin. The temperature of the inflowing liquid is higher than the temperature of the melting process for paraffin, which allows the paraffin to liquify. The temperature at the basis of the rib changes and it is assumed that the heat transfer is quasi-stationary. On this basis the estimation of the mean value of heat transfer coefficient was conducted. The unsteady thermal field of the investigated system was registered with an infrared camera V50 produced by a Polish company Vigo System. This device is equipped with a microbolometric detector with 384 × 288 elements and the single pixel size 25 × 25 μm. Their thermal resolution is lower than 70 mK at a temperature of 30 °C. The camera operates at 7,5 ÷ 14 μm long-wave infrared radiation range. For a typical lens 35 mm the special resolution is 0.7 mrad. The result of the calculations is mean heat transfer coefficient for the considered time series. It is equal to 50 W m -2 K-1 and 47 W m -2 K-1 on the left and right side of the fin, respectively. The distance between the experimental data and the curve approximating the temperature distribution was assessed with the standard deviation, Sd = 0.04 K.
Quasi-stationary states in the Southern Hemisphere
NASA Technical Reports Server (NTRS)
Mo, K. C.
1986-01-01
Pattern correlations between daily anomalies have been used to study the persistence of the Southern Hemisphere circulations. The dataset consists of daily Australian analyses of 500 mb heights and sea level pressure for the period from 1972 to 1983. Compared to the Northern Hemisphere, the pattern correlations are much lower and more variable in the Southern Hemisphere. The mean one-day lag autocorrelation is only 0.57, compared to 0.81 in the Northern Hemisphere. The correlations increase significantly for the filtered anomalies, which consist of the planetary wavenumbers from 0 to 4. Subjective criteria based on the pattern correlations are used to select quasi-stationary events. A series of 5 or more daily maps is defined to be quasi-stationary if the pattern correlations between all pairs of five consecutive maps in this time series are larger than or equal to 0.5. In winter, quasi-stationary events can be classified in terms of wavenumbers. Waves 3 and 4 are by far the dominant waves. More than half of the events have large wave 3 amplitude with geographically fixed orientations.
Rare meshes FEM scheme for quasi-stationary electromagnetic fields determination 3D problems
NASA Astrophysics Data System (ADS)
Chekmarev, D. T.; Kalinin, A. V.; Sadovsky, V. V.; Tiukhtina, A. A.
2016-11-01
The initial-boundary value problem for the quasi-stationary magnetic approximation of the Maxwell equations in inhomogeneous media is studied. The considered problem is reduced to the variational problem of determining the vector magnetic potential. The special gauge for vector magnetic and scalar electrical potentials is used. The well-posedness of the problems is established under general conditions on the coefficients and the applicability of the projection methods for these problems is validated. For the numerical solution of this problem provides to use the effective rare mesh FEM scheme for 3D problems. This scheme is well- proven in 3D elasticity and plasticity problems solving.
Free energy for non-equilibrium quasi-stationary states
NASA Astrophysics Data System (ADS)
Allahverdyan, A. E.; Martirosyan, N. H.
2017-03-01
We study a class of non-equilibrium quasi-stationary states for a Markov system interacting with two different thermal baths. We show that the work done under a slow, external change of parameters admits a potential, i.e., the free energy. Three conditions are needed for the existence of free energy in this non-equilibrium system: time-scale separation between variables of the system, partial controllability (external fields couple only with the slow variable), and an effective detailed balance. These conditions are facilitated in the continuous limit for the slow variable. In contrast to its equilibrium counterpart, the non-equilibrium free energy can increase with temperature. One example of this is that entropy reduction by means of external fields (cooling) can be easier (in the sense of the work cost) if it starts from a higher temperature.
On the structure of quasi-stationary laser ablation fronts in strongly radiating plasmas
NASA Astrophysics Data System (ADS)
Basko, M. M.; Novikov, V. G.; Grushin, A. S.
2015-05-01
The effect of strong thermal radiation on the structure of quasi-stationary laser ablation fronts is investigated under the assumption that all the laser flux is absorbed at the critical surface. Special attention is paid to adequate formulation of the boundary-value problem for a steady-state planar ablation flow. The dependence of the laser-to-x-ray conversion efficiency ϕ r on the laser intensity IL and wavelength λL is analyzed within the non-equilibrium diffusion approximation for radiation transfer. The scaling of the main ablation parameters with IL and λL in the strongly radiative regime 1 - ϕ r ≪ 1 is derived. It is demonstrated that strongly radiating ablation fronts develop a characteristic extended cushion of "radiation-soaked" plasma between the condensed ablated material and the critical surface, which can efficiently suppress perturbations from the instabilities at the critical surface.
The Southern Hemisphere quasi-stationary eddies and their relationship with Antarctic sea ice
NASA Astrophysics Data System (ADS)
Hobbs, William Richard
The west Antarctic region shows one of the strongest warming trends globally over the late 20th century, whilst much of the Antarctic continent shows little trend or even cooling. Additionally, sea ice reductions in the Antarctic Peninsula region have been balanced by sea ice increases in the Ross Sea region. Despite this heterogeneity, much recent research in the Southern Hemisphere has focused on the approximately zonally-symmetric Southern Annular Mode. In this research, reanalysis and satellite data are analyzed to show that at monthly and annual timescales the zonally asymmetric circulation over the Southern Ocean is dominated by two quasi-stationary anticyclones; a stable western anticyclone approximately located south of New Zealand, and a more variable eastern anticyclone located over the Drake Passage region. Time series describing each anticyclone's strength and longitude, and these time series are used to investigate the physical nature and influence of the anticyclones. The anticyclones are found to have some covariance, and in particular they tend to shift in phase, but their strengths are negatively correlated. Quasi-geostrophic diagnosis indicates that the west anticyclone is maintained by meridional vorticity advection by poleward airflow south of Australia, whereas the east anticyclone is forced by zonal convergence over the Pacific Ocean. The differences in variability and dynamic nature between the anticyclones bring into question the utility of the zonal wave decomposition, which is commonly used in analysis of the Southern Hemisphere zonally asymmetric circulation. It is shown that the quasi-stationary anticyclones influence west Antarctic sea ice in a pattern that resembles the 1st and 3rd principal components of ice variability. The anticyclones have some effect on wind-driven sea ice motion, but the primary mechanism explaining their link to sea ice appears to be meridional thermal advection.
Damping of Quasi-stationary Waves Between Two Miscible Liquids
NASA Technical Reports Server (NTRS)
Duval, Walter M. B.
2002-01-01
Two viscous miscible liquids with an initially sharp interface oriented vertically inside a cavity become unstable against oscillatory external forcing due to Kelvin-Helmholtz instability. The instability causes growth of quasi-stationary (q-s) waves at the interface between the two liquids. We examine computationally the dynamics of a four-mode q-s wave, for a fixed energy input, when one of the components of the external forcing is suddenly ceased. The external forcing consists of a steady and oscillatory component as realizable in a microgravity environment. Results show that when there is a jump discontinuity in the oscillatory excitation that produced the four-mode q-s wave, the interface does not return to its equilibrium position, the structure of the q-s wave remains imbedded between the two fluids over a long time scale. The damping characteristics of the q-s wave from the time history of the velocity field show overdamped and critically damped response; there is no underdamped oscillation as the flow field approaches steady state. Viscous effects serve as a dissipative mechanism to effectively damp the system. The stability of the four-mode q-s wave is dependent on both a geometric length scale as well as the level of background steady acceleration.
Autoregression of Quasi-Stationary Time Series (Invited)
NASA Astrophysics Data System (ADS)
Meier, T. M.; Küperkoch, L.
2009-12-01
Autoregression is a model based tool for spectral analysis and prediction of time series. It has the potential to increase the resolution of spectral estimates. However, the validity of the assumed model has to be tested. Here we review shortly methods for the determination of the parameters of autoregression and summarize properties of autoregressive prediction and autoregressive spectral analysis. Time series with a limited number of dominant frequencies varying slowly in time (quasi-stationary time series) may well be described by a time-dependent autoregressive model of low order. An algorithm for the estimation of the autoregression parameters in a moving window is presented. Time-varying dominant frequencies are estimated. The comparison to results obtained by Fourier transform based methods and the visualization of the time dependent normalized prediction error are essential for quality assessment of the results. The algorithm is applied to synthetic examples as well as to mircoseism and tremor. The sensitivity of the results to the choice of model and filter parameters is discussed. Autoregressive forward prediction offers the opportunity to detect body wave phases in seismograms and to determine arrival times automatically. Examples are shown for P- and S-phases at local and regional distances. In order to determine S-wave arrival times the autoregressive model is extended to multi-component recordings. For the detection of significant temporal changes in waveforms, the choice of the model appears to be less crucial compared to spectral analysis. Temporal changes in frequency, amplitude, phase, and polarisation are detectable by autoregressive prediction. Quality estimates of automatically determined onset times may be obtained from the slope of the absolute prediction error as a function of time and the signal-to-noise ratio. Results are compared to manual readings.
Quasi-stationary fluid theory of the hole-boring process
Pei, Zhikun; Shen, Baifei Shi, Yin; Ji, Liangliang; Wang, Wenpeng; Zhang, Xiaomei; Zhang, Lingang; Xu, Tongjun; Liu, Chen
2016-04-15
We present a quasi-stationary fluid theory to precisely describe the hole-boring process. The corresponding distributions of the electrostatic field and the particle density are theoretically obtained, which give more details than the previous stationary theory. The theoretical result is confirmed by one-dimensional particle-in-cell simulations. Such quasi-stationary fluid theory may help in understanding the basic mechanisms of ion acceleration in the radiation pressure acceleration.
Quasi-stationary waves and their connection to oceanic and atmospheric anomalies
NASA Astrophysics Data System (ADS)
Wolf, Gabriel; Brayshaw, David; Klingaman, Nicholas; Czaja, Arnaud
2017-04-01
Strong quasi-stationary atmospheric waves are known to be associated with persistent extreme weather events. We are especially interested in possible oceanic drivers for such quasi-stationary waves over the European-Atlantic region. The existence of such oceanic drivers would suggest potential predictability, or at least a better risk assessment of such events, on a timescale of several weeks or more. We define quasi-stationary waves by the longitudinal envelope of the lowpass filtered meridional wind. For a deeper understanding of these waves and the associated large-scale weather, we created and analysed a climatology of these waves. Besides a clear connection between quasi-stationary waves and persistent extreme temperature and precipitation events, these waves are strongly associated with well-known global pattern indices, especially the Arctic Oscillation/North Atlantic Oscillation and the El Nino-Southern Oscillation. An extensive analysis of the connection between these waves and oceanic anomalies further revealed a connection between Pacific surface heat fluxes and large scale quasi-stationary waves over the Atlantic and Europe. We investigate these connections to better understand the evolution of such quasi-stationary waves and the importance of oceanic anomalies as possible drivers.
NASA Astrophysics Data System (ADS)
Lamy, H.; Simon, C.; Echim, M.; de Keyser, J. M.; Gustavsson, B.; Sergienko, T.; Sandahl, I.; Brandstrom, U.
2010-12-01
From a series of images obtained simultaneously with the CCD cameras of the ALIS (Auroral Large Imaging System) network located in Scandinavia, three-dimensional (3D) large-scale structures of discrete auroral arcs can be retrieved in several filters with tomography-like techniques. In particular, the 3D reconstructed volume emission rates at 4278 Å can be used to derive the energy spectra of precipitating magnetospheric electrons in 2D, along and across the arc, with a spatial resolution of approximately 3 km. These spectra directly provide E0, the characteristic energy and ɛm, the total flux energy of precipitating electrons. The latter can be used together with a kinetic modelling of adiabatic motion of particles (Lundin & Sandahl, 1978) and assuming a Maxwellian distribution for magnetospheric electrons, to derive ΔΦ, the field-aligned potential difference between the ionosphere and magnetosphere. The next step is to use a quasi-static magnetosphere-ionosphere coupling model based on the current continuity in the ionosphere (Echim et al, 2007) and the model of tangential discontinuity generators (Roth et al 1993) to determine densities (ne) and temperatures (Te) of the magnetospheric electrons. The model is run iteratively for typical values of magnetospheric ne and Te that are adjusted until ΔΦ provided by the model is in agreement with the one determined from ALIS observations. This technique allows to obtain information about the properties of the generator of the auroral arc, from ground-based observations and quasi-stationary modeling. Future conjugated observations between ALIS and a spacecraft crossing the same magnetic field lines above the acceleration region could be used to validate this novel technique.
On the structure of quasi-stationary laser ablation fronts in strongly radiating plasmas
Basko, M. M. Novikov, V. G.; Grushin, A. S.
2015-05-15
The effect of strong thermal radiation on the structure of quasi-stationary laser ablation fronts is investigated under the assumption that all the laser flux is absorbed at the critical surface. Special attention is paid to adequate formulation of the boundary-value problem for a steady-state planar ablation flow. The dependence of the laser-to-x-ray conversion efficiency ϕ{sub r} on the laser intensity I{sub L} and wavelength λ{sub L} is analyzed within the non-equilibrium diffusion approximation for radiation transfer. The scaling of the main ablation parameters with I{sub L} and λ{sub L} in the strongly radiative regime 1−ϕ{sub r}≪1 is derived. It is demonstrated that strongly radiating ablation fronts develop a characteristic extended cushion of “radiation-soaked” plasma between the condensed ablated material and the critical surface, which can efficiently suppress perturbations from the instabilities at the critical surface.
Maintenance of quasi-stationary waves in a 2-level quasi-geostrophic spectral model with topography
NASA Technical Reports Server (NTRS)
Yao, M. S.
1979-01-01
The maintenance of the quasi-stationary waves obtained through numerically integrating a 2-level quasi-geostrophic spectral model on a beta-plane is investigated. An idealized topography which has only wavenumber n in the zonal direction and the first mode in the meridional direction is used to force the quasi-stationary waves. It is shown that the topographical forcing is not necessarily the mechanism for maintaining the quasi-stationary waves.
Evolutionary stability and quasi-stationary strategy in stochastic evolutionary game dynamics.
Zhou, Da; Wu, Bin; Ge, Hao
2010-06-07
Stochastic evolutionary game dynamics for finite populations has recently been widely explored in the study of evolutionary game theory. It is known from the work of Traulsen et al. [2005. Phys. Rev. Lett. 95, 238701] that the stochastic evolutionary dynamics approaches the deterministic replicator dynamics in the limit of large population size. However, sometimes the limiting behavior predicted by the stochastic evolutionary dynamics is not quite in agreement with the steady-state behavior of the replicator dynamics. This paradox inspired us to give reasonable explanations of the traditional concept of evolutionarily stable strategy (ESS) in the context of finite populations. A quasi-stationary analysis of the stochastic evolutionary game dynamics is put forward in this study and we present a new concept of quasi-stationary strategy (QSS) for large but finite populations. It is shown that the consistency between the QSS and the ESS implies that the long-term behavior of the replicator dynamics can be predicted by the quasi-stationary behavior of the stochastic dynamics. We relate the paradox to the time scales and find that the contradiction occurs only when the fixation time scale is much longer than the quasi-stationary time scale. Our work may shed light on understanding the relationship between the deterministic and stochastic methods of modeling evolutionary game dynamics. Copyright (c) 2010 Elsevier Ltd. All rights reserved.
Quasi-Stationary Regime of a Branching Random Walk in Presence of an Absorbing Wall
NASA Astrophysics Data System (ADS)
Simon, Damien; Derrida, Bernard
2008-04-01
A branching random walk in presence of an absorbing wall moving at a constant velocity v undergoes a phase transition as the velocity v of the wall varies. Below the critical velocity v c , the population has a non-zero survival probability and when the population survives its size grows exponentially. We investigate the histories of the population conditioned on having a single survivor at some final time T. We study the quasi-stationary regime for v< v c when T is large. To do so, one can construct a modified stochastic process which is equivalent to the original process conditioned on having a single survivor at final time T. We then use this construction to show that the properties of the quasi-stationary regime are universal when v→ v c . We also solve exactly a simple version of the problem, the exponential model, for which the study of the quasi-stationary regime can be reduced to the analysis of a single one-dimensional map.
Signal Approximation with a Wavelet Neural Network
1992-12-01
specialized electronic devices like the Intel Electronically Trainable Analog Neural Network (ETANN) chip. The WNN representation allows the...accurately approximated with a WNN trained with irregularly sampled data. Signal approximation, Wavelet neural network .
Poly-coil design for a 60 tesla quasi-stationary magnet
NASA Astrophysics Data System (ADS)
Boenig, H. J.; Campbell, L. J.; Hodgdon, M. L.; Lopez, E. A.; Rickel, D. G.; Rogers, J. D.; Schillig, J. B.; Sims, J. R.; Pernambuco-Wise, P.; Schneider-Muntau, H. J.
1993-02-01
Among the new facilities to be offered by the National Science Foundation through the National High Magnetic Field Laboratory (NHMFL) are pulsed fields that can only be achieved at a national user facility by virtue of their strength, duration, and volume. In particular, a 44 mm bore pulsed magnet giving a 60 tesla field for 100 ms is in the final design stage. This magnet will be powered by a 1.4 GW motor-generator at Los Alamos and is an important step toward proving design principles that will be needed for the higher field quasi-stationary pulsed magnets that this power source is capable of driving.
High-current lanthanum-hexaboride electron emitter for a quasi-stationary arc plasma generator
Davydenko, V. I. Ivanov, A. A. Shul’zhenko, G. I.
2015-11-15
A high-current electron emitter on the basis of lanthanum hexaboride is developed for quasi-stationary arc plasma generators of ion sources. The emitter consists of a set of LaB{sub 6} washers interleaved with washers made of thermally extended graphite. The emitter is heated by the current flowing through the graphite washers. The thermal regime of emitter operation during plasma generation is considered. The emitter has been successfully used in the ion sources of the diagnostic injectors of fast hydrogen atomic beams.
Stability and hierarchy of quasi-stationary states: financial markets as an example
NASA Astrophysics Data System (ADS)
Stepanov, Yuriy; Rinn, Philip; Guhr, Thomas; Peinke, Joachim; Schäfer, Rudi
2015-08-01
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure. We identify the dominating variable and extract its explicit stochastic model. This allows us to establish a connection between its time evolution and known historical events on the market. We discuss the dynamics, the stability and the hierarchy of the recently proposed quasi-stationary market states.
The quasilinear theory in the approach of long-range systems to quasi-stationary states
NASA Astrophysics Data System (ADS)
Campa, Alessandro; Chavanis, Pierre-Henri
2017-05-01
We develop a quasilinear theory of the Vlasov equation in order to describe the approach of systems with long-range interactions to quasi-stationary states. The quasilinear theory is based on the assumption that, although the initial distribution is not Vlasov stable, nevertheless its evolution towards a Vlasov stable stationary state is such that it is always only slightly inhomogeneous. We derive a diffusion equation governing the evolution of the velocity distribution of the system towards a steady state. This steady state is expected to correspond to the space-averaged quasi-stationary distribution function reached by the Vlasov equation as a result of a collisionless relaxation. We compare the prediction of the quasilinear theory to direct numerical simulations of the Hamiltonian mean field model, starting from an unstable spatially homogeneous distribution, either Gaussian or semi-elliptical. In the Gaussian case, we find that the quasilinear theory works reasonably well for weakly unstable initial conditions (i.e. close to the critical energy ε_c=3/4=0.75 ) and that it is able to predict the energy ε_t≃ 0.735 marking the effective out-of-equilibrium phase transition between unmagnetized and magnetized quasi-stationary states found in the numerical simulations. Similarly, the quasilinear theory works well for energies close to the instability threshold of the semi-elliptical case ε^*c =5/8=0.625 , and it predicts an effective out-of-equilibrium transition at εt≃ 0.619 . In both situations, the quasilinear theory works less well at energies lower than the out-of-equilibrium transition, the disagreement with the numerical simulations increasing with decreasing energy. In that case, we observe, in agreement with our previous numerical study (Campa and Chavanis 2013 Eur. Phys. J. B 86 170), that the quasi-stationary states are remarkably well fitted by polytropic distributions (Tsallis distributions) with index n = 2 (Gaussian case) or n
NASA Astrophysics Data System (ADS)
Troppová, Eva; Tippner, Jan; Hrčka, Richard
2017-01-01
This paper presents an experimental measurement of thermal properties of medium density fiberboards with different thicknesses (12, 18 and 25 mm) and sample sizes (50 × 50 mm and 100 × 100 mm) by quasi-stationary method. The quasi-stationary method is a transient method which allows measurement of three thermal parameters (thermal conductivity, thermal diffusivity and heat capacity). The experimentally gained values were used to verify a numerical model and furthermore served as input parameters for the numerical probabilistic analysis. The sensitivity of measured outputs (time course of temperature) to influential factors (density, heat transfer coefficient and thermal conductivities) was established and described by the Spearman's rank correlation coefficients. The dependence of thermal properties on density was confirmed by the data measured. Density was also proved to be an important factor for sensitivity analyses as it highly correlated with all output parameters. The accuracy of the measurement method can be improved based on the results of the probabilistic analysis. The relevancy of the experiment is mainly influenced by the choice of a proper ratio between thickness and width of samples.
Multiwavelet neural network and its approximation properties.
Jiao, L; Pan, J; Fang, Y
2001-01-01
A model of multiwavelet-based neural networks is proposed. Its universal and L(2) approximation properties, together with its consistency are proved, and the convergence rates associated with these properties are estimated. The structure of this network is similar to that of the wavelet network, except that the orthonormal scaling functions are replaced by orthonormal multiscaling functions. The theoretical analyses show that the multiwavelet network converges more rapidly than the wavelet network, especially for smooth functions. To make a comparison between both networks, experiments are carried out with the Lemarie-Meyer wavelet network, the Daubechies2 wavelet network and the GHM multiwavelet network, and the results support the theoretical analysis well. In addition, the results also illustrate that at the jump discontinuities, the approximation performance of the two networks are about the same.
Rogue wave formation under the action of quasi-stationary pressure
NASA Astrophysics Data System (ADS)
Abrashkin, A. A.; Oshmarina, O. E.
2016-05-01
The process of rogue wave formation on deep water is considered. A wave of extreme amplitude is born against the background of uniform waves (Gerstner waves) under the action of external pressure on free surface. The pressure distribution has a form of a quasi-stationary "pit". The fluid motion is supposed to be a vortex one and is described by an exact solution of equations of 2D hydrodynamics for an ideal fluid in Lagrangian coordinates. Liquid particles are moving around circumferences of different radii in the absence of drift flow. Values of amplitude and wave steepness optimal for rogue wave formation are found numerically. The influence of vorticity distribution and pressure drop on parameters of the fluid is investigated.
Jump Markov models and transition state theory: the quasi-stationary distribution approach.
Di Gesù, Giacomo; Lelièvre, Tony; Le Peutrec, Dorian; Nectoux, Boris
2016-12-22
We are interested in the connection between a metastable continuous state space Markov process (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space. More precisely, we use the notion of quasi-stationary distribution within a metastable state for the continuous state space Markov process to parametrize the exit event from the state. This approach is useful to analyze and justify methods which use the jump Markov process underlying a metastable dynamics as a support to efficiently sample the state-to-state dynamics (accelerated dynamics techniques). Moreover, it is possible by this approach to quantify the error on the exit event when the parametrization of the jump Markov model is based on the Eyring-Kramers formula. This therefore provides a mathematical framework to justify the use of transition state theory and the Eyring-Kramers formula to build kinetic Monte Carlo or Markov state models.
Quasi-stationary mechanics of elastic continua with bending stiffness wrapping on a pulley system
NASA Astrophysics Data System (ADS)
Kaczmarczyk, S.; Mirhadizadeh, S.
2016-05-01
In many engineering applications elastic continua such as ropes and belts often are subject to bending when they pass over pulleys / sheaves. In this paper the quasi-stationary mechanics of a cable-pulley system is studied. The cable is modelled as a moving Euler- Bernoulli beam. The distribution of tension is non-uniform along its span and due to the bending stiffness the contact points at the pulley-beam boundaries are not unknown. The system is described by a set of nonlinear ordinary differential equations with undetermined boundary conditions. The resulting nonlinear Boundary Value Problem (BVP) with unknown boundaries is solved by converting the problem into the ‘standard’ form defined over a fixed interval. Numerical results obtained for a range of typical configurations with relevant boundary conditions applied demonstrate that due to the effects of bending stiffness the angels of wrap are reduced and the span tensions are increased.
Quasi-Stationary Shear-parallel MCS in a Near-saturated Environment
NASA Astrophysics Data System (ADS)
Liu, Changhai; Moncrieff, Mitchell
2016-04-01
Idealized simulations are performed to investigate a poorly-understood category of Mesoscale Convective Systems (MCSs) - quasi-stationary convective lines with upstream-building and downstream stratiform observed in very moist environments. A specific feature in the experimental design is the inclusion of a highly idealized moisture front, mimicking the water vapor variations across the large-scale quasi-stationary (Mei-Yu) front during the Asian summer monsoon, where this regime of convective organization has been frequently observed. The numerical experiment with a wind profile of significant low-level vertical shear, plus a moist thermodynamic sounding with low convective inhibition, generates a long-lasting convective system which is down-shear tilted with a morphology resembling the documented MCSs with back-building or parallel stratiform in East Asia and North America. This is the first successful simulations of the carrot-like MCS morphology, where cells initiate near the upstream edge in either back-building or forward-building form depending on the system propagation direction. A major disparity from most types of MCSs, especially the well-studied squall line, is the weak and shallow cold pool and its negligible effect on system sustenance and propagation. Instead of the cold-pool-shear interaction, it is found that convectively-excited gravity waves are responsible for the intermittent upstream initiation of convective elements. Sensitivity tests show that both the moisture front and shear are critical for this MCS category. Our study suggests that the background spatial moisture variability affects the selection of the modes of organization, and that a systematic investigation of its role in convective organization in various wind shear conditions should be explored.
Cremaschini, Claudio; Stuchlík, Zdeněk; Tessarotto, Massimo
2013-05-15
The problem of formulating a kinetic treatment for quasi-stationary collisionless plasmas in axisymmetric systems subject to the possibly independent presence of local strong velocity-shear and supersonic rotation velocities is posed. The theory is developed in the framework of the Vlasov-Maxwell description for multi-species non-relativistic plasmas. Applications to astrophysical accretion discs arising around compact objects and to plasmas in laboratory devices are considered. Explicit solutions for the equilibrium kinetic distribution function (KDF) are constructed based on the identification of the relevant particle adiabatic invariants. These are shown to be expressed in terms of generalized non-isotropic Gaussian distributions. A suitable perturbative theory is then developed which allows for the treatment of non-uniform strong velocity-shear/supersonic plasmas. This yields a series representation for the equilibrium KDF in which the leading-order term depends on both a finite set of fluid fields as well as on the gradients of an appropriate rotational frequency. Constitutive equations for the fluid number density, flow velocity, and pressure tensor are explicitly calculated. As a notable outcome, the discovery of a new mechanism for generating temperature and pressure anisotropies is pointed out, which represents a characteristic feature of plasmas considered here. This is shown to arise as a consequence of the canonical momentum conservation and to contribute to the occurrence of temperature anisotropy in combination with the adiabatic conservation of the particle magnetic moment. The physical relevance of the result and the implications of the kinetic solution for the self-generation of quasi-stationary electrostatic and magnetic fields through a kinetic dynamo are discussed.
Approximation by Ridge Functions and Neural Networks
1997-01-01
univariate spaces Xn Other authors most notably Micchelli and Mhaskar MM MM and Mhaskar M have also considered approximation problems of the...type treated here The work of Micchelli and Mhaskar does not give the best order of approximation Mhaskar M has given best possible results but...function from its projections Duke Math J pp M H Mhaskar Neural networks for optimal approximation of smooth and ana lytic
Quasi-stationary states in nonlocal stochastic growth models with infinitely many absorbing states
NASA Astrophysics Data System (ADS)
Jara, D. A. C.; Alcaraz, F. C.
2017-04-01
We study a two parameter (u, p) extension of the conformally invariant raise and peel model. The model also represents a nonlocal and biased-asymmetric exclusion process with local and nonlocal jumps of excluded volume particles in the lattice. The model exhibits an unusual and interesting critical phase where, in the bulk limit, there are an infinite number of absorbing states. In spite of these absorbing states the system stays, during a time that increases exponentially with the lattice size, in a critical quasi-stationary state. In this critical phase the critical exponents depend only on one of the parameters defining the model (u). The endpoint of this critical phase, where the system changes from an active to an inactive frozen phase, belongs to a distinct universality class. This new behavior, we believe, is due to the appearance of Jordan cells in the Hamiltonian describing the time evolution. The dimensions of these cells increase with the lattice size. In a special case (u = 0) where the model has no adsorptions we are able to calculate analytically the time evolution of some observables. A polynomial time dependence is obtained thanks to the appearance of Jordan cells structures in the Hamiltonian.
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.
Kuznetsova, Irina M; Povarova, Olga I; Uversky, Vladimir N; Turoverov, Konstantin K
2016-02-01
The native form of globular actin, G-actin, is formed in vivo as a result of complex post-translational folding processes that require ATP energy expenditure and are assisted by the 70 kDa heat shock protein, prefoldin and chaperonin containing TCP-1. G-actin is stabilized by the binding of one ATP molecule and one Ca(2+) ion (or Mg(2+) in vivo). Chemical denaturants, heating or Ca(2+) removal transform native actin (N) into 'inactivated actin' (I), a compact oligomer comprising 14-16 subunits. Viscogenic and crowding agents slow this process but do not stop it. The lack of calcium in the solution accelerates the spontaneous N → I transition. Thus, native G-actin has a kinetically stable (as a result of the high free energy barrier between the N and I states) but thermodynamically unstable structure, which, in the absence of Ca(2+) or other bivalent metal ions, spontaneously converts to the thermodynamically stable I state. It was noted that native actin has much in common with intrinsically disordered proteins: it has functionally important disordered regions; it is constantly in complex with one of its numerous partners; and it plays key roles in many cellular processes, in a manner similar to disordered hub proteins. By analyzing actin folding in vivo and unfolding in vitro, we advanced the hypothesis that proteins in a native state may have a thermodynamically unstable quasi-stationary structure. The kinetically stable native state of these proteins appears forcibly under the influence of intracellular folding machinery. The denaturation of such proteins is always irreversible because the inactivated state, for which the structure is determined by the amino acid sequence of a protein, comprises the thermodynamically stable state under physiological conditions.
Approximation abilities of neuro-fuzzy networks
NASA Astrophysics Data System (ADS)
Mrówczyńska, Maria
2010-01-01
The paper presents the operation of two neuro-fuzzy systems of an adaptive type, intended for solving problems of the approximation of multi-variable functions in the domain of real numbers. Neuro-fuzzy systems being a combination of the methodology of artificial neural networks and fuzzy sets operate on the basis of a set of fuzzy rules "if-then", generated by means of the self-organization of data grouping and the estimation of relations between fuzzy experiment results. The article includes a description of neuro-fuzzy systems by Takaga-Sugeno-Kang (TSK) and Wang-Mendel (WM), and in order to complement the problem in question, a hierarchical structural self-organizing method of teaching a fuzzy network. A multi-layer structure of the systems is a structure analogous to the structure of "classic" neural networks. In its final part the article presents selected areas of application of neuro-fuzzy systems in the field of geodesy and surveying engineering. Numerical examples showing how the systems work concerned: the approximation of functions of several variables to be used as algorithms in the Geographic Information Systems (the approximation of a terrain model), the transformation of coordinates, and the prediction of a time series. The accuracy characteristics of the results obtained have been taken into consideration.
Evolution of the eastward shift in the quasi-stationary minimum of the Antarctic total ozone column
NASA Astrophysics Data System (ADS)
Grytsai, Asen; Klekociuk, Andrew; Milinevsky, Gennadi; Evtushevsky, Oleksandr; Stone, Kane
2017-02-01
The quasi-stationary pattern of the Antarctic total ozone has changed during the last 4 decades, showing an eastward shift in the zonal ozone minimum. In this work, the association between the longitudinal shift of the zonal ozone minimum and changes in meteorological fields in austral spring (September-November) for 1979-2014 is analyzed using ERA-Interim and NCEP-NCAR reanalyses. Regressive, correlative and anomaly composite analyses are applied to reanalysis data. Patterns of the Southern Annular Mode and quasi-stationary zonal waves 1 and 3 in the meteorological fields show relationships with interannual variability in the longitude of the zonal ozone minimum. On decadal timescales, consistent longitudinal shifts of the zonal ozone minimum and zonal wave 3 pattern in the middle-troposphere temperature at the southern midlatitudes are shown. Attribution runs of the chemistry-climate version of the Australian Community Climate and Earth System Simulator (ACCESS-CCM) model suggest that long-term shifts of the zonal ozone minimum are separately contributed by changes in ozone-depleting substances and greenhouse gases. As is known, Antarctic ozone depletion in spring is strongly projected on the Southern Annular Mode in summer and impacts summertime surface climate across the Southern Hemisphere. The results of this study suggest that changes in zonal ozone asymmetry accompanying ozone depletion could be associated with regional climate changes in the Southern Hemisphere in spring.
NASA Astrophysics Data System (ADS)
Chen, Sheng; Täuber, Uwe C.
2015-03-01
Spatially extended stochastic models for predator-prey competition and coexistence display complex, correlated spatio-temporal structures and are governed by remarkably large fluctuations. Both populations are characterized by damped erratic oscillations whose properties are governed by the reaction rates. Here, we specifically study a stochastic lattice Lotka-Volterra model by means of Monte Carlo simulations that impose spatial restrictions on the number of occupants per site. The system tends to relax into a quasi-stationary state, independent of the imposed initial conditions. We investigate the non-equilibrium relaxation between two such quasi-stationary states, following an instantaneous change of the predation rate. The ensuing relaxation times are measured via the peak width of the population density Fourier transforms. As expected, we find that the initial state only influences the oscillations for the duration of this relaxation time, implying that the system quickly loses any memory of the initial configuration. Research supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-FG02-09ER46613.
NASA Astrophysics Data System (ADS)
Hutt, A.; Riedel, H.
2003-03-01
A methodological framework for analyzing and modeling of multivariate data is introduced. In a first step, a cluster method extracts data segments of quasi-stationary states. A novel cluster criterion for segment borders is introduced, which is independent of the number of clusters. Its assessment reveals additional robustness towards initial conditions. A subsequent dynamical systems based modeling (DSBM) approach focuses on data segments and fits low-dimensional dynamical systems for each segment. Applications to middle latent auditory evoked potentials yield data segments, which are equivalent to well-known waves from electroencephalography studies. Focussing to wave Pa, two-dimensional dynamical systems with common topological properties are extracted. These findings reveal the common underlying dynamics of Pa and indicate self-organized brain activity.
NASA Astrophysics Data System (ADS)
Andritsanos, Vassilios D.; Tziavos, Ilias N.
2016-08-01
The Multiple Input / Multiple Output System (MIMOS) Theory is used in the spectral combination of marine and satellite data for Quasi-stationary Sea Surface Topography (QSST) estimation. 15 years (2000 - 2015) of altimetric data from ERS2, GEOSAT FOLLOW-ON, ENVISAT and SARAL / Altika satellites are optimally combined with in situ marine gravity observations. The repeated character of the altimetric missions provides more than one sample of Sea Surface Height (SSH) data sets, and the approximation of the input signal and output error power spectral densities is feasible using this successive information. The assimilation of low frequency global gravity information from GOCE/GRACE satellites is considered in data reductions. The geodynamically active area of the Eastern Mediterranean Sea is chosen as test area and the evolution of yearly SST is presented.
Neural networks for functional approximation and system identification.
Mhaskar, H N; Hahm, N
1997-01-01
We construct generalized translation networks to approximate uniformly a class of nonlinear, continuous functionals defined on Lp ([-1, 1]s) for integer s > or = 1, 1 < or = p < infinity, or C ([-1, 1]s). We obtain lower bounds on the possible order of approximation for such functionals in terms of any approximation process depending continuously on a given number of parameters. Our networks almost achieve this order of approximation in terms of the number of parameters (neurons) involved in the network. The training is simple and noniterative; in particular, we avoid any optimization such as that involved in the usual backpropagation.
NASA Astrophysics Data System (ADS)
Kornhuber, K.; Petoukhov, V.; Petri, S.; Rahmstorf, S.; Coumou, D.
2017-09-01
Several recent northern hemisphere summer extremes have been linked to persistent high-amplitude wave patterns (e.g. heat waves in Europe 2003, Russia 2010 and in the US 2011, Floods in Pakistan 2010 and Europe 2013). Recently quasi-resonant amplification (QRA) was proposed as a mechanism that, when certain dynamical conditions are fulfilled, can lead to such high-amplitude wave events. Based on these resonance conditions a detection scheme to scan reanalysis data for QRA events in boreal summer months was implemented. With this objective detection scheme we analyzed the occurrence and duration of QRA events and the associated atmospheric flow patterns in 1979-2015 reanalysis data. We detect a total number of 178 events for wave 6, 7 and 8 and find that during roughly one-third of all high amplitude events QRA conditions were met for respective waves. Our analysis reveals a significant shift for quasi-stationary waves 6 and 7 towards high amplitudes during QRA events, lagging first QRA-detection by typically one week. The results provide further evidence for the validity of the QRA hypothesis and its important role in generating high amplitude waves in boreal summer.
Shekhtman, V.L.
1995-12-01
A theoretical investigation of the correlation between the resonance scattering from a quasi-stationary state and the Einstein relations in the quantum theory of radiation was carried out. On the basis of the Einstein relations, the mode-averaged value of the total scattering cross section at the frequency of the resonance maximum was obtained in the general form. With allowance for radiative, vibronic, transverse, and inhomogeneous widths of a zero-phonon line, relations were obtained that permit the oscillator strength of a resonance electronic transition to be found from measurements of the absorption cross section at the resonance frequency and the half-width of the absorption spectral line. The relations depend on the shape of the absorption spectrum. The cases of the Lorentzian, Gaussian, and Voigt line shapes were considered. Using the E-2A transitions in an optically excited ruby as an example, the cross section of the phonon resonance scattering from impurity centers in crystals with a sufficiently large value of the Debye-Waller factor, e{sup {minus}2M}{ge} 0.5, was considered. The results can be applied in phonon spectroscopy. The main results are interpreted in detail in terms of the Bohr spectroscopic correspondence principle. A new derivation is given of the Ladenburg formula relating the transition probabilities and the dispersion constants. 23 refs., 1 fig.
NASA Astrophysics Data System (ADS)
Kornhuber, K.; Petoukhov, V.; Petri, S.; Rahmstorf, S.; Coumou, D.
2016-11-01
Several recent northern hemisphere summer extremes have been linked to persistent high-amplitude wave patterns (e.g. heat waves in Europe 2003, Russia 2010 and in the US 2011, Floods in Pakistan 2010 and Europe 2013). Recently quasi-resonant amplification (QRA) was proposed as a mechanism that, when certain dynamical conditions are fulfilled, can lead to such high-amplitude wave events. Based on these resonance conditions a detection scheme to scan reanalysis data for QRA events in boreal summer months was implemented. With this objective detection scheme we analyzed the occurrence and duration of QRA events and the associated atmospheric flow patterns in 1979-2015 reanalysis data. We detect a total number of 178 events for wave 6, 7 and 8 and find that during roughly one-third of all high amplitude events QRA conditions were met for respective waves. Our analysis reveals a significant shift for quasi-stationary waves 6 and 7 towards high amplitudes during QRA events, lagging first QRA-detection by typically one week. The results provide further evidence for the validity of the QRA hypothesis and its important role in generating high amplitude waves in boreal summer.
Existence and uniqueness results for neural network approximations.
Williamson, R C; Helmke, U
1995-01-01
Some approximation theoretic questions concerning a certain class of neural networks are considered. The networks considered are single input, single output, single hidden layer, feedforward neural networks with continuous sigmoidal activation functions, no input weights but with hidden layer thresholds and output layer weights. Specifically, questions of existence and uniqueness of best approximations on a closed interval of the real line under mean-square and uniform approximation error measures are studied. A by-product of this study is a reparametrization of the class of networks considered in terms of rational functions of a single variable. This rational reparametrization is used to apply the theory of Pade approximation to the class of networks considered. In addition, a question related to the number of local minima arising in gradient algorithms for learning is examined.
A spiking neural network architecture for nonlinear function approximation.
Iannella, N; Back, A D
2001-01-01
Multilayer perceptrons have received much attention in recent years due to their universal approximation capabilities. Normally, such models use real valued continuous signals, although they are loosely based on biological neuronal networks that encode signals using spike trains. Spiking neural networks are of interest both from a biological point of view and in terms of a method of robust signaling in particularly noisy or difficult environments. It is important to consider networks based on spike trains. A basic question that needs to be considered however, is what type of architecture can be used to provide universal function approximation capabilities in spiking networks? In this paper, we propose a spiking neural network architecture using both integrate-and-fire units as well as delays, that is capable of approximating a real valued function mapping to within a specified degree of accuracy.
PAC learning algorithms for functions approximated by feedforward networks
Rao, N.S.V.; Protopopescu, V.
1996-06-01
The authors present a class of efficient algorithms for PAC learning continuous functions and regressions that are approximated by feedforward networks. The algorithms are applicable to networks with unknown weights located only in the output layer and are obtained by utilizing the potential function methods of Aizerman et al. Conditions relating the sample sizes to the error bounds are derived using martingale-type inequalities. For concreteness, the discussion is presented in terms of neural networks, but the results are applicable to general feedforward networks, in particular to wavelet networks. The algorithms can be directly adapted to concept learning problems.
Systematic Approximations to Susceptible-Infectious-Susceptible Dynamics on Networks
Cooper, Alison J.
2016-01-01
Network-based infectious disease models have been highly effective in elucidating the role of contact structure in the spread of infection. As such, pair- and neighbourhood-based approximation models have played a key role in linking findings from network simulations to standard (random-mixing) results. Recently, for SIR-type infections (that produce one epidemic in a closed population) on locally tree-like networks, these approximations have been shown to be exact. However, network models are ideally suited for Sexually Transmitted Infections (STIs) due to the greater level of detail available for sexual contact networks, and these diseases often possess SIS-type dynamics. Here, we consider the accuracy of three systematic approximations that can be applied to arbitrary disease dynamics, including SIS behaviour. We focus in particular on low degree networks, in which the small number of neighbours causes build-up of local correlations between the state of adjacent nodes that are challenging to capture. By examining how and when these approximation models converge to simulation results, we generate insights into the role of network structure in the infection dynamics of SIS-type infections. PMID:27997542
Nearest neighbor rules PAC-approximate feedforward networks
Rao, N.S.V.
1996-05-01
The problem of function estimation using feedforward neural networks based on an indpendently and identically generated sample is addressed. The feedforward networks with a single hidden layer of 1/(1+{epsilon}{sup -{gamma}z}) units and bounded parameters are considered. It is shown that given a sufficiently large sample, a nearest neighbor rule approximates the best neural network such that the expected error is arbitrarily bounded with an arbitrary high probability. Result is extendible to other neural networks where the hidden units satisfy a suitable Lipschitz condition. A result of practical interest is that the problem of computing a neural network that approximates (in the above sense) the best possible one is computationally difficult, whereas a nearest neighbor rule is linear-time computable in terms of the sample size.
Neural networks for function approximation in nonlinear control
NASA Technical Reports Server (NTRS)
Linse, Dennis J.; Stengel, Robert F.
1990-01-01
Two neural network architectures are compared with a classical spline interpolation technique for the approximation of functions useful in a nonlinear control system. A standard back-propagation feedforward neural network and a cerebellar model articulation controller (CMAC) neural network are presented, and their results are compared with a B-spline interpolation procedure that is updated using recursive least-squares parameter identification. Each method is able to accurately represent a one-dimensional test function. Tradeoffs between size requirements, speed of operation, and speed of learning indicate that neural networks may be practical for identification and adaptation in a nonlinear control environment.
Cluster and propensity based approximation of a network
2013-01-01
Background The models in this article generalize current models for both correlation networks and multigraph networks. Correlation networks are widely applied in genomics research. In contrast to general networks, it is straightforward to test the statistical significance of an edge in a correlation network. It is also easy to decompose the underlying correlation matrix and generate informative network statistics such as the module eigenvector. However, correlation networks only capture the connections between numeric variables. An open question is whether one can find suitable decompositions of the similarity measures employed in constructing general networks. Multigraph networks are attractive because they support likelihood based inference. Unfortunately, it is unclear how to adjust current statistical methods to detect the clusters inherent in many data sets. Results Here we present an intuitive and parsimonious parametrization of a general similarity measure such as a network adjacency matrix. The cluster and propensity based approximation (CPBA) of a network not only generalizes correlation network methods but also multigraph methods. In particular, it gives rise to a novel and more realistic multigraph model that accounts for clustering and provides likelihood based tests for assessing the significance of an edge after controlling for clustering. We present a novel Majorization-Minimization (MM) algorithm for estimating the parameters of the CPBA. To illustrate the practical utility of the CPBA of a network, we apply it to gene expression data and to a bi-partite network model for diseases and disease genes from the Online Mendelian Inheritance in Man (OMIM). Conclusions The CPBA of a network is theoretically appealing since a) it generalizes correlation and multigraph network methods, b) it improves likelihood based significance tests for edge counts, c) it directly models higher-order relationships between clusters, and d) it suggests novel clustering
When is approximation by Gaussian networks necessarily a linear process?
Mhaskar, H N
2004-09-01
Let s > or = 1 be an integer. A Gaussian network is a function on Rs of the form [Formula: see text]. The minimal separation among the centers, defined by (1/2) min(1 < or = j not = k < or = N) [Formula: see text], is an important characteristic of the network that determines the stability of interpolation by Gaussian networks, the degree of approximation by such networks, etc. Let (within this abstract only) the set of all Gaussian networks with minimal separation exceeding 1/m be denoted by Gm. We prove that for functions [Formula: see text] such that [Formula: see text], if the degree of L2(nonlinear) approximation of [Formula: see text] from Gm is [Formula: see text] then necessarily the degree of approximation of [Formula: see text] by (rectangular) partial sums of degree m2 of the Hermite expansion of [Formula: see text] is also [Formula: see text]. Moreover, Gaussian networks in Gm having fixed centers in a ball of radius [Formula: see text] and coefficients being linear functionals of [Formula: see text] can be constructed to yield the same degree of approximation. Similar results are proved for the Lp norms, 1 < or = p < or =[Formula: see text] but with the condition that the number of neurons N, should satisfy logN = [Formula: see text](m2).
Fast approximation of self-similar network traffic
Paxson, V.
1995-01-01
Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94a, PF94]. One difficulty in dealing with self-similar models is how to efficiently synthesize traces (sample paths) corresponding to self-similar traffic. We present a fast Fourier transform method for synthesizing approximate self-similar sample paths and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate a closer approximation to true self-similar sample paths than the other known fast method (Random Midpoint Displacement). We then discuss issues in using such synthesized sample paths for simulating network traffic, and how an approximation used by our method can dramatically speed up evaluation of Whittle`s estimator for H, the Hurst parameter giving the strength of long-range dependence present in a self-similar time series.
Approximating spectral impact of structural perturbations in large networks.
Milanese, Attilio; Sun, Jie; Nishikawa, Takashi
2010-04-01
Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as synchronization and cascading processes on networks. Here we develop a theory for estimating the change of the largest eigenvalue of the adjacency matrix or the extreme eigenvalues of the graph Laplacian when small but arbitrary set of links are added or removed from the network. We demonstrate the effectiveness of our approximation schemes using both real and artificial networks, showing in particular that we can accurately obtain the spectral ranking of small subgraphs. We also propose a local iterative scheme which computes the relative ranking of a subgraph using only the connectivity information of its neighbors within a few links. Our results may not only contribute to our theoretical understanding of dynamical processes on networks, but also lead to practical applications in ranking subgraphs of real complex networks.
NASA Astrophysics Data System (ADS)
Echim, M. M.; Roth, M.; de Keyser, J.
2008-05-01
We discuss a model for the quasi-stationary coupling between magnetospheric sheared flows in the dusk sector and discrete auroral arcs, previously analyzed for the case of a uniform height-integrated Pedersen conductivity (ΣP). Here we introduce an ionospheric feedback as the variation of ΣP with the energy flux of precipitating magnetospheric electrons (ɛem). One key-component of the model is the kinetic description of the interface between the duskward LLBL and the plasma sheet that gives the profile of Φm, the magnetospheric electrostatic potential. The velocity shear in the dusk LLBL plays the role of a generator for the auroral circuit closing through Pedersen currents in the auroral ionosphere. The field-aligned current density, j||, and the energy flux of precipitating electrons are given by analytic functions of the field-aligned potential drop, ΔΦ, derived from standard kinetic models of the adiabatic motion of particles. The ionospheric electrostatic potential, Φi (and implicitely ΔΦ) is determined from the current continuity equation in the ionosphere. We obtain values of ΔΦ of the order of kilovolt and of j|| of the order of tens of μA/m2 in thin regions of the order of several kilometers at 200 km altitude. The spatial scale is significantly smaller and the peak values of ΔΦ, j|| and ɛem are higher than in the case of a uniform ΣP. Effects on the postnoon/evening auroral arc electrodynamics due to variations of dusk LLBL and solar wind dynamic and kinetic pressure are discussed. In thin regions (of the order of kilometer) embedding the maximum of ΔΦ we evidence a non-linear regime of the current-voltage relationship. The model predicts also that visible arcs form when the velocity shear in LLBL is above a threshold value depending on the generator and ionospheric plasma properties. Brighter arcs are obtained for increased velocity shear in the LLBL; their spatial scale remains virtually unmodified. The field-aligned potential drop
Blocking performance approximation in flexi-grid networks
NASA Astrophysics Data System (ADS)
Ge, Fei; Tan, Liansheng
2016-12-01
The blocking probability to the path requests is an important issue in flexible bandwidth optical communications. In this paper, we propose a blocking probability approximation method of path requests in flexi-grid networks. It models the bundled neighboring carrier allocation with a group of birth-death processes and provides a theoretical analysis to the blocking probability under variable bandwidth traffic. The numerical results show the effect of traffic parameters to the blocking probability of path requests. We use the first fit algorithm in network nodes to allocate neighboring carriers to path requests in simulations, and verify approximation results.
Universal approximation by radial basis function networks of Delsarte translates.
Arteaga, Cristian; Marrero, Isabel
2013-10-01
We prove that, under certain mild conditions on the kernel function (or activation function), the family of radial basis function neural networks obtained by replacing the usual translation with the Delsarte one, and taking the same smoothing factor in all kernel nodes, has the universal approximation property.
An application of artificial neural networks to experimental data approximation
NASA Technical Reports Server (NTRS)
Meade, Andrew J., Jr.
1993-01-01
As an initial step in the evaluation of networks, a feedforward architecture is trained to approximate experimental data by the backpropagation algorithm. Several drawbacks were detected and an alternative learning algorithm was then developed to partially address the drawbacks. This noniterative algorithm has a number of advantages over the backpropagation method and is easily implemented on existing hardware.
Engine With Regression and Neural Network Approximators Designed
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Hopkins, Dale A.
2001-01-01
At the NASA Glenn Research Center, the NASA engine performance program (NEPP, ref. 1) and the design optimization testbed COMETBOARDS (ref. 2) with regression and neural network analysis-approximators have been coupled to obtain a preliminary engine design methodology. The solution to a high-bypass-ratio subsonic waverotor-topped turbofan engine, which is shown in the preceding figure, was obtained by the simulation depicted in the following figure. This engine is made of 16 components mounted on two shafts with 21 flow stations. The engine is designed for a flight envelope with 47 operating points. The design optimization utilized both neural network and regression approximations, along with the cascade strategy (ref. 3). The cascade used three algorithms in sequence: the method of feasible directions, the sequence of unconstrained minimizations technique, and sequential quadratic programming. The normalized optimum thrusts obtained by the three methods are shown in the following figure: the cascade algorithm with regression approximation is represented by a triangle, a circle is shown for the neural network solution, and a solid line indicates original NEPP results. The solutions obtained from both approximate methods lie within one standard deviation of the benchmark solution for each operating point. The simulation improved the maximum thrust by 5 percent. The performance of the linear regression and neural network methods as alternate engine analyzers was found to be satisfactory for the analysis and operation optimization of air-breathing propulsion engines (ref. 4).
An application of artificial neural networks to experimental data approximation
NASA Technical Reports Server (NTRS)
Meade, Andrew J., Jr.
1993-01-01
As an initial step in the evaluation of networks, a feedforward architecture is trained to approximate experimental data by the backpropagation algorithm. Several drawbacks were detected and an alternative learning algorithm was then developed to partially address the drawbacks. This noniterative algorithm has a number of advantages over the backpropagation method and is easily implemented on existing hardware.
NASA Astrophysics Data System (ADS)
Leo, Mario; Leo, Rosario Antonio; Tempesta, Piergiulio
2013-06-01
In a recent paper [M. Leo, R.A. Leo, P. Tempesta, C. Tsallis, Phys. Rev. E 85 (2012) 031149], the existence of quasi-stationary states for the Fermi-Pasta-Ulam β system has been shown numerically, by analyzing the stability properties of the N/4-mode exact nonlinear solution. Here we study the energy distribution of the modes N/4, N/3 and N/2, when they are unstable, as a function of N and of the initial excitation energy. We observe that the classical Boltzmann weight is replaced by a different weight, expressed by a q-exponential function.
Subsonic Aircraft With Regression and Neural-Network Approximators Designed
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Hopkins, Dale A.
2004-01-01
At the NASA Glenn Research Center, NASA Langley Research Center's Flight Optimization System (FLOPS) and the design optimization testbed COMETBOARDS with regression and neural-network-analysis approximators have been coupled to obtain a preliminary aircraft design methodology. For a subsonic aircraft, the optimal design, that is the airframe-engine combination, is obtained by the simulation. The aircraft is powered by two high-bypass-ratio engines with a nominal thrust of about 35,000 lbf. It is to carry 150 passengers at a cruise speed of Mach 0.8 over a range of 3000 n mi and to operate on a 6000-ft runway. The aircraft design utilized a neural network and a regression-approximations-based analysis tool, along with a multioptimizer cascade algorithm that uses sequential linear programming, sequential quadratic programming, the method of feasible directions, and then sequential quadratic programming again. Optimal aircraft weight versus the number of design iterations is shown. The central processing unit (CPU) time to solution is given. It is shown that the regression-method-based analyzer exhibited a smoother convergence pattern than the FLOPS code. The optimum weight obtained by the approximation technique and the FLOPS code differed by 1.3 percent. Prediction by the approximation technique exhibited no error for the aircraft wing area and turbine entry temperature, whereas it was within 2 percent for most other parameters. Cascade strategy was required by FLOPS as well as the approximators. The regression method had a tendency to hug the data points, whereas the neural network exhibited a propensity to follow a mean path. The performance of the neural network and regression methods was considered adequate. It was at about the same level for small, standard, and large models with redundancy ratios (defined as the number of input-output pairs to the number of unknown coefficients) of 14, 28, and 57, respectively. In an SGI octane workstation (Silicon Graphics
Analysis of Tikhonov regularization for function approximation by neural networks.
Burger, Martin; Neubauer, Andreas
2003-01-01
This paper is devoted to the convergence and stability analysis of Tikhonov regularization for function approximation by a class of feed-forward neural networks with one hidden layer and linear output layer. We investigate two frequently used approaches, namely regularization by output smoothing and regularization by weight decay, as well as a combination of both methods to combine their advantages. We show that in all cases stable approximations are obtained converging to the approximated function in a desired Sobolev space as the noise in the data tends to zero (in the weaker L(2)-norm) if the regularization parameter and the number of units in the network are chosen appropriately. Under additional smoothness assumptions we are able to show convergence rates results in terms of the noise level and the number of units in the network. In addition, we show how the theoretical results can be applied to the important classes of perceptrons with one hidden layer and to translation networks. Finally, the performance of the different approaches is compared in some numerical examples.
Approximating Attractors of Boolean Networks by Iterative CTL Model Checking
Klarner, Hannes; Siebert, Heike
2015-01-01
This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: “faithfulness” which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, “univocality” which requires that there is a unique attractor in each trap space, and “completeness” which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks. PMID:26442247
Approximating Attractors of Boolean Networks by Iterative CTL Model Checking.
Klarner, Hannes; Siebert, Heike
2015-01-01
This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: "faithfulness" which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, "univocality" which requires that there is a unique attractor in each trap space, and "completeness" which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks.
Approximating frustration scores in complex networks via perturbed Laplacian spectra
NASA Astrophysics Data System (ADS)
Savol, Andrej J.; Chennubhotla, Chakra S.
2015-12-01
Systems of many interacting components, as found in physics, biology, infrastructure, and the social sciences, are often modeled by simple networks of nodes and edges. The real-world systems frequently confront outside intervention or internal damage whose impact must be predicted or minimized, and such perturbations are then mimicked in the models by altering nodes or edges. This leads to the broad issue of how to best quantify changes in a model network after some type of perturbation. In the case of node removal there are many centrality metrics which associate a scalar quantity with the removed node, but it can be difficult to associate the quantities with some intuitive aspect of physical behavior in the network. This presents a serious hurdle to the application of network theory: real-world utility networks are rarely altered according to theoretic principles unless the kinetic impact on the network's users are fully appreciated beforehand. In pursuit of a kinetically interpretable centrality score, we discuss the f-score, or frustration score. Each f-score quantifies whether a selected node accelerates or inhibits global mean first passage times to a second, independently selected target node. We show that this is a natural way of revealing the dynamical importance of a node in some networks. After discussing merits of the f-score metric, we combine spectral and Laplacian matrix theory in order to quickly approximate the exact f-score values, which can otherwise be expensive to compute. Following tests on both synthetic and real medium-sized networks, we report f-score runtime improvements over exact brute force approaches in the range of 0 to 400 % with low error (<3 % ).
Adaptive control using neural networks and approximate models.
Narendra, K S; Mukhopadhyay, S
1997-01-01
The NARMA model is an exact representation of the input-output behavior of finite-dimensional nonlinear discrete-time dynamical systems in a neighborhood of the equilibrium state. However, it is not convenient for purposes of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate methods are used for realizing the neural controllers to overcome computational complexity. In this paper, we introduce two classes of models which are approximations to the NARMA model, and which are linear in the control input. The latter fact substantially simplifies both the theoretical analysis as well as the practical implementation of the controller. Extensive simulation studies have shown that the neural controllers designed using the proposed approximate models perform very well, and in many cases even better than an approximate controller designed using the exact NARMA model. In view of their mathematical tractability as well as their success in simulation studies, a case is made in this paper that such approximate input-output models warrant a detailed study in their own right.
Approximating frustration scores in complex networks via perturbed Laplacian spectra
Savol, Andrej J.; Chennubhotla, Chakra S.
2016-01-01
Systems of many interacting components, as found in physics, biology, infrastructure, and the social sciences, are often modeled by simple networks of nodes and edges. The real-world systems frequently confront outside intervention or internal damage whose impact must be predicted or minimized, and such perturbations are then mimicked in the models by altering nodes or edges. This leads to the broad issue of how to best quantify changes in a model network after some type of perturbation. In the case of node removal there are many centrality metrics which associate a scalar quantity with the removed node, but it can be difficult to associate the quantities with some intuitive aspect of physical behavior in the network. This presents a serious hurdle to the application of network theory: real-world utility networks are rarely altered according to theoretic principles unless the kinetic impact on the network’s users are fully appreciated beforehand. In pursuit of a kinetically-interpretable centrality score, we discuss the f-score, or frustration score. Each f-score quantifies whether a selected node accelerates or inhibits global mean first passage times to a second, independently-selected target node. We show that this is a natural way of revealing the dynamical importance of a node in some networks. After discussing merits of the f-score metric, we combine spectral and Laplacian matrix theory in order to quickly approximate the exact f-score values, which can otherwise be expensive to compute. Following tests on both synthetic and real medium-sized networks, we report f-score runtime improvements over exact brute force approaches in the range of 0 to 400% with low error (< 3%). PMID:26764743
A Multithreaded Algorithm for Network Alignment Via Approximate Matching
Khan, Arif; Gleich, David F.; Pothen, Alex; Halappanavar, Mahantesh
2012-11-16
Network alignment is an optimization problem to find the best one-to-one map between the vertices of a pair of graphs that overlaps in as many edges as possible. It is a relaxation of the graph isomorphism problem and is closely related to the subgraph isomorphism problem. The best current approaches are entirely heuristic, and are iterative in nature. They generate real-valued heuristic approximations that must be rounded to find integer solutions. This rounding requires solving a bipartite maximum weight matching problem at each step in order to avoid missing high quality solutions. We investigate substituting a parallel, half-approximation for maximum weight matching instead of an exact computation. Our experiments show that the resulting difference in solution quality is negligible. We demonstrate almost a 20-fold speedup using 40 threads on an 8 processor Intel Xeon E7-8870 system (from 10 minutes to 36 seconds).
Stochastic analysis of Chemical Reaction Networks using Linear Noise Approximation.
Cardelli, Luca; Kwiatkowska, Marta; Laurenti, Luca
2016-11-01
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analyzed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approximate model checking algorithm based on the Linear Noise Approximation (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order polynomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on four case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deterministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN.
Stochastic Analysis of Chemical Reaction Networks Using Linear Noise Approximation.
Cardelli, Luca; Kwiatkowska, Marta; Laurenti, Luca
2016-10-28
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approximate model checking algorithm based on the Linear Noise Approximation (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order polynomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on four case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deterministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN. Copyright © 2016. Published by Elsevier Ireland Ltd.
Convergence and Rate Analysis of Neural Networks for Sparse Approximation
Balavoine, Aurèle; Romberg, Justin; Rozell, Christopher J.
2013-01-01
We present an analysis of the Locally Competitive Algotihm (LCA), which is a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few nonzero coefficients). This class of problems plays a significant role in both theories of neural coding and applications in signal processing. However, the LCA lacks analysis of its convergence properties, and previous results on neural networks for nonsmooth optimization do not apply to the specifics of the LCA architecture. We show that the LCA has desirable convergence properties, such as stability and global convergence to the optimum of the objective function when it is unique. Under some mild conditions, the support of the solution is also proven to be reached in finite time. Furthermore, some restrictions on the problem specifics allow us to characterize the convergence rate of the system by showing that the LCA converges exponentially fast with an analytically bounded convergence rate. We support our analysis with several illustrative simulations. PMID:24199030
Convergence and rate analysis of neural networks for sparse approximation.
Balavoine, Aurèle; Romberg, Justin; Rozell, Christopher J
2012-09-01
We present an analysis of the Locally Competitive Algorithm (LCA), which is a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few nonzero coefficients). This class of problems plays a significant role in both theories of neural coding and applications in signal processing. However, the LCA lacks analysis of its convergence properties, and previous results on neural networks for nonsmooth optimization do not apply to the specifics of the LCA architecture. We show that the LCA has desirable convergence properties, such as stability and global convergence to the optimum of the objective function when it is unique. Under some mild conditions, the support of the solution is also proven to be reached in finite time. Furthermore, some restrictions on the problem specifics allow us to characterize the convergence rate of the system by showing that the LCA converges exponentially fast with an analytically bounded convergence rate. We support our analysis with several illustrative simulations.
NASA Astrophysics Data System (ADS)
Sugimoto, S.; Ueno, H.; Hoshi, N.
2016-12-01
Repeated hydrographic surveys at 155°E conducted by the T/S Oshoro-maru of Hokkaido University of Japan in spring (May/June) of 1989-2010 reveal a dominant decadal-scale ( 10 years) variation of core-layer temperature and salinity of the North Pacific Transition Region Mode Water (TRMW), a water mass with core characterized by potential temperature of 4-8°C, salinity of 33.5-34.0, and potential density of 26.4-26.7 kg m-3. An ocean heat content budget analysis based on historical temperature profiles and atmospheric reanalysis data shows that the observed decadal-scale variation of the core-layer temperature is not explained by variations in air-sea heat exchange and Ekman heat advection. The satellite-derived dataset and historical temperature-salinity profiles reveal that changes in the Kuroshio Extension (KE) path state, that is, stable state with the two quasi-stationary meanders and unstable state characterized by a convoluted path, are responsible for the formation of temperature-salinity anomalies in the TRMW formation region (40-44°N, 153-162°E). Meso-scale eddies that detach northward from the KE in the unstable path state form warmer-saltier conditions in the Kuroshio-Oyashio Confluence region. The warm-salty water is transported northward into the transition region by the quasi-stationary jet flowing from the subtropics to the subarctic, which induces an increase in temperature and salinity in the TRMW formation region, and this results in a peak in temperature and salinity a few years after the arrival of the warm-salty water in the formation region.
Mobile calibration based on laser metrology and approximation networks.
Muñoz-Rodriguez, J Apolinar
2010-01-01
A mobile calibration technique for three-dimensional vision is presented. In this method, vision parameters are computed automatically by approximation networks built based on the position of a camera and image processing of a laser line. The networks also perform three-dimensional visualization. In the proposed system, the setup geometry can be modified online, whereby an online re-calibration is performed based on data provided by the network and the required modifications of extrinsic and intrinsic parameters are thus determined, overcoming any calibration limitations caused by the modification procedure. The mobile calibration also avoids procedures involving references, which are used in traditional online re-calibration methods. The proposed mobile calibration thus improves the accuracy and performance of the three-dimensional vision because online data of calibrated references are not passed on to the vision system. This work represents a contribution to the field of online re-calibration, as verified by a comparison with the results based on lighting methods, which are calibrated and re-calibrated via perspective projection. Processing time is also studied.
Mobile Calibration Based on Laser Metrology and Approximation Networks
Muñoz-Rodriguez, J. Apolinar
2010-01-01
A mobile calibration technique for three-dimensional vision is presented. In this method, vision parameters are computed automatically by approximation networks built based on the position of a camera and image processing of a laser line. The networks also perform three-dimensional visualization. In the proposed system, the setup geometry can be modified online, whereby an online re-calibration is performed based on data provided by the network and the required modifications of extrinsic and intrinsic parameters are thus determined, overcoming any calibration limitations caused by the modification procedure. The mobile calibration also avoids procedures involving references, which are used in traditional online re-calibration methods. The proposed mobile calibration thus improves the accuracy and performance of the three-dimensional vision because online data of calibrated references are not passed on to the vision system. This work represents a contribution to the field of online re-calibration, as verified by a comparison with the results based on lighting methods, which are calibrated and re-calibrated via perspective projection. Processing time is also studied. PMID:22163622
Locally supervised neural networks for approximating terramechanics models
NASA Astrophysics Data System (ADS)
Song, Xingguo; Gao, Haibo; Ding, Liang; Spanos, Pol D.; Deng, Zongquan; Li, Zhijun
2016-06-01
Neural networks (NNs) have been widely implemented for identifying nonlinear models, and predicting the distribution of targets, due to their ability to store and learn training samples. However, for highly complex systems, it is difficult to build a robust global network model, and efficiently managing the large amounts of experimental data is often required in real-time applications. In this paper, an effective method for building local models is proposed to enhance robustness and learning speed in globally supervised NNs. Unlike NNs, Gaussian processes (GP) produce predictions that capture the uncertainty inherent in actual systems, and typically provides superior results. Therefore, in this study, each local NN is learned in the same manner as a Gaussian process. A mixture of local model NNs is created and then augmented using weighted regression. This proposed method, referred to as locally supervised NN for weighted regression like GP, is abbreviated as ;LGPN;, is utilized for approximating a wheel-terrain interaction model under fixed soil parameters. The prediction results show that the proposed method yields significant robustness, modeling accuracy, and rapid learning speed.
Approximating Some Network Design Problems with Node Costs
NASA Astrophysics Data System (ADS)
Kortsarz, Guy; Nutov, Zeev
We study several multi-criteria undirected network design problems with node costs and lengths with all problems related to the node costs Multicommodity Buy at Bulk ( mbb) problem in which we are given a graph G = (V,E), demands {d st : s,t ∈ V}, and a family {c v : v ∈ V} of subadditive cost functions. For every s,t ∈ V we seek to send d st flow units from s to t on a single path, so that ∑ v c v (f v ) is minimized, where f v the total amount of flow through v. In the Multicommodity Cost-Distance ( mcd) problem we are also given lengths {ℓ(v):v ∈ V}, and seek a subgraph H of G that minimizes c(H) + ∑ s,t ∈ V d st ·ℓ H (s,t), where ℓ H (s,t) is the minimum ℓ-length of an st-path in H. The approximation for these two problems is equivalent up to a factor arbitrarily close to 2. We give an O(log3 n)-approximation algorithm for both problems for the case of demands polynomial in n. The previously best known approximation ratio for these problems was O(log4 n) [Chekuri et al., FOCS 2006] and [Chekuri et al., SODA 2007]. This technique seems quite robust and was already used in order to improve the ratio of Buy-at-bulk with protection (Antonakopoulos et al FOCS 2007) from log3 h to log2 h. See ?.
NASA Astrophysics Data System (ADS)
Sweeney, R.; Choi, W.; La Haye, R. J.; Mao, S.; Olofsson, K. E. J.; Volpe, F. A.; The DIII-D Team
2017-01-01
A database has been developed to study the evolution, the nonlinear effects on equilibria, and the disruptivity of locked and quasi-stationary modes with poloidal and toroidal mode numbers m = 2 and n = 1 at DIII-D. The analysis of 22500 discharges shows that more than 18% of disruptions are due to locked or quasi-stationary modes with rotating precursors (not including born locked modes). A parameter formulated by the plasma internal inductance l i divided by the safety factor at 95% of the poloidal flux, q 95, is found to exhibit predictive capability over whether a locked mode will cause a disruption or not, and does so up to hundreds of milliseconds before the disruption. Within 20 ms of the disruption, the shortest distance between the island separatrix and the unperturbed last closed flux surface, referred to as d edge, performs comparably to {{l}i}/{{q}95} in its ability to discriminate disruptive locked modes. Out of all parameters considered, d edge also correlates best with the duration of the locked mode. Disruptivity following a m/n = 2/1 locked mode as a function of the normalized beta, {β\\text{N}} , is observed to peak at an intermediate value, and decrease for high values. The decrease is attributed to the correlation between {β\\text{N}} and q 95 in the DIII-D operational space. Within 50 ms of a locked mode disruption, average behavior includes exponential growth of the n = 1 perturbed field, which might be due to the 2/1 locked mode. Surprisingly, even assuming the aforementioned 2/1 growth, disruptivity following a locked mode shows little dependence on island width up to 20 ms before the disruption. Separately, greater deceleration of the rotating precursor is observed when the wall torque is large. At locking, modes are often observed to align at a particular phase, which is likely related to a residual error field. Timescales associated with the mode evolution are also studied and dictate the
Sweeney, Ryan Myles; Choi, W.; La Haye, R. J.; Mao, S.; Olofsson, K. E. J.; Volpe, F. A.
2016-11-01
A database has been developed to study the evolution, the nonlinear effects on equilibria, and the disruptivity of locked and quasi-stationary modes with poloidal and toroidal mode numbers m = 2 and n = 1 at DIII-D. The analysis of 22500 discharges shows that more than 18% of disruptions are due to locked or quasi-stationary modes with rotating precursors (not including born locked modes). A parameter formulated by the plasma internal inductance l i divided by the safety factor at 95% of the poloidal flux, q 95, is found to exhibit predictive capability over whether a locked mode will cause a disruption or not, and does so up to hundreds of milliseconds before the disruption. Within 20 ms of the disruption, the shortest distance between the island separatrix and the unperturbed last closed flux surface, referred to as d edge, performs comparably to ${{l}_{i}}/{{q}_{95}}$ in its ability to discriminate disruptive locked modes. Out of all parameters considered, d edge also correlates best with the duration of the locked mode. Disruptivity following a m/n = 2/1 locked mode as a function of the normalized beta, ${{\\beta}_{\\text{N}}}$ , is observed to peak at an intermediate value, and decrease for high values. The decrease is attributed to the correlation between ${{\\beta}_{\\text{N}}}$ and q _{95} in the DIII-D operational space. Within 50 ms of a locked mode disruption, average behavior includes exponential growth of the n = 1 perturbed field, which might be due to the 2/1 locked mode. Surprisingly, even assuming the aforementioned 2/1 growth, disruptivity following a locked mode shows little dependence on island width up to 20 ms before the disruption. Separately, greater deceleration of the rotating precursor is observed when the wall torque is large. At locking, modes are often observed to align at a particular phase, which is likely related to a residual error field. Timescales associated with the mode evolution are also studied and dictate the
Sweeney, Ryan Myles; Choi, W.; La Haye, R. J.; ...
2016-11-01
A database has been developed to study the evolution, the nonlinear effects on equilibria, and the disruptivity of locked and quasi-stationary modes with poloidal and toroidal mode numbers m = 2 and n = 1 at DIII-D. The analysis of 22500 discharges shows that more than 18% of disruptions are due to locked or quasi-stationary modes with rotating precursors (not including born locked modes). A parameter formulated by the plasma internal inductance l i divided by the safety factor at 95% of the poloidal flux, q 95, is found to exhibit predictive capability over whether a locked mode will cause a disruption or not, and does so up to hundreds of milliseconds before the disruption. Within 20 ms of the disruption, the shortest distance between the island separatrix and the unperturbed last closed flux surface, referred to as d edge, performs comparably tomore » $${{l}_{i}}/{{q}_{95}}$$ in its ability to discriminate disruptive locked modes. Out of all parameters considered, d edge also correlates best with the duration of the locked mode. Disruptivity following a m/n = 2/1 locked mode as a function of the normalized beta, $${{\\beta}_{\\text{N}}}$$ , is observed to peak at an intermediate value, and decrease for high values. The decrease is attributed to the correlation between $${{\\beta}_{\\text{N}}}$$ and q 95 in the DIII-D operational space. Within 50 ms of a locked mode disruption, average behavior includes exponential growth of the n = 1 perturbed field, which might be due to the 2/1 locked mode. Surprisingly, even assuming the aforementioned 2/1 growth, disruptivity following a locked mode shows little dependence on island width up to 20 ms before the disruption. Separately, greater deceleration of the rotating precursor is observed when the wall torque is large. At locking, modes are often observed to align at a particular phase, which is likely related to a residual error field. Timescales associated with the mode evolution are also studied and dictate the
Sub-problem Optimization With Regression and Neural Network Approximators
NASA Technical Reports Server (NTRS)
Guptill, James D.; Hopkins, Dale A.; Patnaik, Surya N.
2003-01-01
Design optimization of large systems can be attempted through a sub-problem strategy. In this strategy, the original problem is divided into a number of smaller problems that are clustered together to obtain a sequence of sub-problems. Solution to the large problem is attempted iteratively through repeated solutions to the modest sub-problems. This strategy is applicable to structures and to multidisciplinary systems. For structures, clustering the substructures generates the sequence of sub-problems. For a multidisciplinary system, individual disciplines, accounting for coupling, can be considered as sub-problems. A sub-problem, if required, can be further broken down to accommodate sub-disciplines. The sub-problem strategy is being implemented into the NASA design optimization test bed, referred to as "CometBoards." Neural network and regression approximators are employed for reanalysis and sensitivity analysis calculations at the sub-problem level. The strategy has been implemented in sequential as well as parallel computational environments. This strategy, which attempts to alleviate algorithmic and reanalysis deficiencies, has the potential to become a powerful design tool. However, several issues have to be addressed before its full potential can be harnessed. This paper illustrates the strategy and addresses some issues.
Functional approximation using artificial neural networks in structural mechanics
NASA Technical Reports Server (NTRS)
Alam, Javed; Berke, Laszlo
1993-01-01
The artificial neural networks (ANN) methodology is an outgrowth of research in artificial intelligence. In this study, the feed-forward network model that was proposed by Rumelhart, Hinton, and Williams was applied to the mapping of functions that are encountered in structural mechanics problems. Several different network configurations were chosen to train the available data for problems in materials characterization and structural analysis of plates and shells. By using the recall process, the accuracy of these trained networks was assessed.
NASA Astrophysics Data System (ADS)
Song, Y.; Lysak, R. L.
2015-12-01
Parallel E-fields play a crucial role for the acceleration of charged particles, creating discrete aurorae. However, once the parallel electric fields are produced, they will disappear right away, unless the electric fields can be continuously generated and sustained for a fairly long time. Thus, the crucial question in auroral physics is how to generate such a powerful and self-sustained parallel electric fields which can effectively accelerate charge particles to high energy during a fairly long time. We propose that nonlinear interaction of incident and reflected Alfven wave packets in inhomogeneous auroral acceleration region can produce quasi-stationary non-propagating electromagnetic plasma structures, such as Alfvenic double layers (DLs) and Charge Holes. Such Alfvenic quasi-static structures often constitute powerful high energy particle accelerators. The Alfvenic DL consists of localized self-sustained powerful electrostatic electric fields nested in a low density cavity and surrounded by enhanced magnetic and mechanical stresses. The enhanced magnetic and velocity fields carrying the free energy serve as a local dynamo, which continuously create the electrostatic parallel electric field for a fairly long time. The generated parallel electric fields will deepen the seed low density cavity, which then further quickly boosts the stronger parallel electric fields creating both Alfvenic and quasi-static discrete aurorae. The parallel electrostatic electric field can also cause ion outflow, perpendicular ion acceleration and heating, and may excite Auroral Kilometric Radiation.
Leo, Mario; Leo, Rosario Antonio; Tempesta, Piergiulio
2013-06-15
In a recent paper [M. Leo, R.A. Leo, P. Tempesta, C. Tsallis, Phys. Rev. E 85 (2012) 031149], the existence of quasi-stationary states for the Fermi–Pasta–Ulam β system has been shown numerically, by analyzing the stability properties of the N/4-mode exact nonlinear solution. Here we study the energy distribution of the modes N/4, N/3 and N/2, when they are unstable, as a function of N and of the initial excitation energy. We observe that the classical Boltzmann weight is replaced by a different weight, expressed by a q-exponential function. -- Highlights: ► New statistical properties of the Fermi–Pasta–Ulam beta system are found. ► The energy distribution of specific observables are studied: a deviation from the standard Boltzmann behavior is found. ► A q-exponential weight should be used instead. ► The classical exponential weight is restored in the large particle limit (mesoscopic nature of the phenomenon)
S-curve networks and an approximate method for estimating degree distributions of complex networks
NASA Astrophysics Data System (ADS)
Guo, Jin-Li
2010-12-01
In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 (Internet Protocol version 4) addresses, this paper proposes a forecasting model by using S curve (logistic curve). The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions (i.e., Barabási-Albert method) is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabási-Albert method commonly used in current network research.
Nonlinear functional approximation with networks using adaptive neurons
NASA Technical Reports Server (NTRS)
Tawel, Raoul
1992-01-01
A novel mathematical framework for the rapid learning of nonlinear mappings and topological transformations is presented. It is based on allowing the neuron's parameters to adapt as a function of learning. This fully recurrent adaptive neuron model (ANM) has been successfully applied to complex nonlinear function approximation problems such as the highly degenerate inverse kinematics problem in robotics.
High-Dimensional Function Approximation With Neural Networks for Large Volumes of Data.
Andras, Peter
2017-01-25
Approximation of high-dimensional functions is a challenge for neural networks due to the curse of dimensionality. Often the data for which the approximated function is defined resides on a low-dimensional manifold and in principle the approximation of the function over this manifold should improve the approximation performance. It has been show that projecting the data manifold into a lower dimensional space, followed by the neural network approximation of the function over this space, provides a more precise approximation of the function than the approximation of the function with neural networks in the original data space. However, if the data volume is very large, the projection into the low-dimensional space has to be based on a limited sample of the data. Here, we investigate the nature of the approximation error of neural networks trained over the projection space. We show that such neural networks should have better approximation performance than neural networks trained on high-dimensional data even if the projection is based on a relatively sparse sample of the data manifold. We also find that it is preferable to use a uniformly distributed sparse sample of the data for the purpose of the generation of the low-dimensional projection. We illustrate these results considering the practical neural network approximation of a set of functions defined on high-dimensional data including real world data as well.
Approximation bounds for smooth functions in C(IRd) by neural and mixture networks.
Maiorov, V; Meir, R S
1998-01-01
We consider the approximation of smooth multivariate functions in C(IRd) by feedforward neural networks with a single hidden layer of nonlinear ridge functions. Under certain assumptions on the smoothness of the functions being approximated and on the activation functions in the neural network, we present upper bounds on the degree of approximation achieved over the domain IRd, thereby generalizing available results for compact domains. We extend the approximation results to the so-called mixture of expert architecture, which has received considerable attention in recent years, showing that the same type of approximation bound may be achieved.
Adaptive hybrid simulations for multiscale stochastic reaction networks
Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa
2015-01-21
The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.
Adaptive hybrid simulations for multiscale stochastic reaction networks.
Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa
2015-01-21
The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.
A Subsonic Aircraft Design Optimization With Neural Network and Regression Approximators
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Coroneos, Rula M.; Guptill, James D.; Hopkins, Dale A.; Haller, William J.
2004-01-01
The Flight-Optimization-System (FLOPS) code encountered difficulty in analyzing a subsonic aircraft. The limitation made the design optimization problematic. The deficiencies have been alleviated through use of neural network and regression approximations. The insight gained from using the approximators is discussed in this paper. The FLOPS code is reviewed. Analysis models are developed and validated for each approximator. The regression method appears to hug the data points, while the neural network approximation follows a mean path. For an analysis cycle, the approximate model required milliseconds of central processing unit (CPU) time versus seconds by the FLOPS code. Performance of the approximators was satisfactory for aircraft analysis. A design optimization capability has been created by coupling the derived analyzers to the optimization test bed CometBoards. The approximators were efficient reanalysis tools in the aircraft design optimization. Instability encountered in the FLOPS analyzer was eliminated. The convergence characteristics were improved for the design optimization. The CPU time required to calculate the optimum solution, measured in hours with the FLOPS code was reduced to minutes with the neural network approximation and to seconds with the regression method. Generation of the approximators required the manipulation of a very large quantity of data. Design sensitivity with respect to the bounds of aircraft constraints is easily generated.
Application of Neurocomputing for Data Approximation and Classification in Wireless Sensor Networks
Jabbari, Amir; Jedermann, Reiner; Muthuraman, Ramanan; Lang, Walter
2009-01-01
A new application of neurocomputing for data approximation and classification is introduced to process data in a wireless sensor network. For this purpose, a simplified dynamic sliding backpropagation algorithm is implemented on a wireless sensor network for transportation applications. It is able to approximate temperature and humidity in sensor nodes. In addition, two architectures of “radial basis function” (RBF) classifiers are introduced with probabilistic features for data classification in sensor nodes. The applied approximation and classification algorithms could be used in similar applications for data processing in embedded systems. PMID:22574062
Fast approximation of average shortest path length of directed BA networks
NASA Astrophysics Data System (ADS)
Mao, Guoyong; Zhang, Ning
2017-01-01
The average shortest path length is an important feature for complex networks. However, for large networks, it is very difficult to compute it due to the limitation of computing power. By analyzing the node reachability from several real BA networks as the example, we brought forward the concept of Global Reachable Nodes and Local Reachable Nodes. We found that the average shortest path length of a BA network is determined by the Global Reachable Nodes. From the mechanism of the BA network we illustrated this feature and hereby presented a randomized approximation algorithm for computing the average shortest path length. We verified the accuracy of this algorithm using 8 different networks. For large-scale BA network with millions of nodes, the experiments indicate that our method can estimate its ASPL with high accuracy using only several hundreds of Global Reachable Nodes.
NASA Astrophysics Data System (ADS)
Liu, Qiang; Van Mieghem, Piet
2017-04-01
One of the most important quantities of the exact Markovian SIS epidemic process is the time-dependent prevalence, which is the average fraction of infected nodes. Unfortunately, the Markovian SIS epidemic model features an exponentially increasing computational complexity with growing network size N. In this paper, we evaluate a recently proposed analytic approximate prevalence function introduced in Van Mieghem (2016). We compare the approximate function with the N-Intertwined Mean-Field Approximation (NIMFA) and with simulation of the Markovian SIS epidemic process. The results show that the new analytic prevalence function is comparable with other approximate methods.
NASA Technical Reports Server (NTRS)
Patniak, Surya N.; Guptill, James D.; Hopkins, Dale A.; Lavelle, Thomas M.
1998-01-01
Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.
Pair approximation for the q -voter model with independence on complex networks
NASA Astrophysics Data System (ADS)
Jedrzejewski, Arkadiusz
2017-01-01
We investigate the q -voter model with stochastic noise arising from independence on complex networks. Using the pair approximation, we provide a comprehensive, mathematical description of its behavior and derive a formula for the critical point. The analytical results are validated by carrying out Monte Carlo experiments. The pair approximation prediction exhibits substantial agreement with simulations, especially for networks with weak clustering and large average degree. Nonetheless, for the average degree close to q , some discrepancies originate. It is the first time we are aware of that the presented approach has been applied to the nonlinear voter dynamics with noise. Up till now, the analytical results have been obtained only for a complete graph. We show that in the limiting case the prediction of pair approximation coincides with the known solution on a fully connected network.
Universal approximation depth and errors of narrow belief networks with discrete units.
Montúfar, Guido F
2014-07-01
We generalize recent theoretical work on the minimal number of layers of narrow deep belief networks that can approximate any probability distribution on the states of their visible units arbitrarily well. We relax the setting of binary units (Sutskever & Hinton, 2008 ; Le Roux & Bengio, 2008 , 2010 ; Montúfar & Ay, 2011 ) to units with arbitrary finite state spaces and the vanishing approximation error to an arbitrary approximation error tolerance. For example, we show that a q-ary deep belief network with L > or = 2 + (q[m-delta]-1 / (q-1)) layers of width n < or = + log(q) (m) + 1 for some [Formula : see text] can approximate any probability distribution on {0, 1, ... , q-1}n without exceeding a Kullback-Leibler divergence of delta. Our analysis covers discrete restricted Boltzmann machines and naive Bayes models as special cases.
NASA Astrophysics Data System (ADS)
Staszczuk, Anna
2017-03-01
The paper provides comparative results of calculations of heat exchange between ground and typical residential buildings using simplified (quasi-stationary) and more accurate (transient, three-dimensional) methods. Such characteristics as building's geometry, basement hollow and construction of ground touching assemblies were considered including intermittent and reduced heating mode. The calculations with simplified methods were conducted in accordance with currently valid norm: PN-EN ISO 13370:2008. Thermal performance of buildings. Heat transfer via the ground. Calculation methods. Comparative estimates concerning transient, 3-D, heat flow were performed with computer software WUFI®plus. The differences of heat exchange obtained using more exact and simplified methods have been specified as a result of the analysis.
Costarelli, Danilo; Vinti, Gianluca
2016-09-01
In this article, the theory of multivariate max-product neural network (NN) and quasi-interpolation operators has been introduced. Pointwise and uniform approximation results have been proved, together with estimates concerning the rate of convergence. At the end, several examples of sigmoidal activation functions have been provided.
Approximate-master-equation approach for the Kinouchi-Copelli neural model on networks.
Wang, Chong-Yang; Wu, Zhi-Xi; Chen, Michael Z Q
2017-01-01
In this work, we use the approximate-master-equation approach to study the dynamics of the Kinouchi-Copelli neural model on various networks. By categorizing each neuron in terms of its state and also the states of its neighbors, we are able to uncover how the coupled system evolves with respective to time by directly solving a set of ordinary differential equations. In particular, we can easily calculate the statistical properties of the time evolution of the network instantaneous response, the network response curve, the dynamic range, and the critical point in the framework of the approximate-master-equation approach. The possible usage of the proposed theoretical approach to other spreading phenomena is briefly discussed.
Approximate-master-equation approach for the Kinouchi-Copelli neural model on networks
NASA Astrophysics Data System (ADS)
Wang, Chong-Yang; Wu, Zhi-Xi; Chen, Michael Z. Q.
2017-01-01
In this work, we use the approximate-master-equation approach to study the dynamics of the Kinouchi-Copelli neural model on various networks. By categorizing each neuron in terms of its state and also the states of its neighbors, we are able to uncover how the coupled system evolves with respective to time by directly solving a set of ordinary differential equations. In particular, we can easily calculate the statistical properties of the time evolution of the network instantaneous response, the network response curve, the dynamic range, and the critical point in the framework of the approximate-master-equation approach. The possible usage of the proposed theoretical approach to other spreading phenomena is briefly discussed.
NASA Astrophysics Data System (ADS)
Hod, Shahar
2015-10-01
Rotating black holes can support quasi-stationary (unstable) bound-state resonances of massive scalar fields in their exterior regions. These spatially regular scalar configurations are characterized by instability timescales which are much longer than the timescale M set by the geometric size (mass) of the central black hole. It is well-known that, in the small-mass limit α ≡ Mμ ≪ 1 (here μ is the mass of the scalar field), these quasi-stationary scalar resonances are characterized by the familiar hydrogenic oscillation spectrum: ωR / μ = 1 -α2 / 2 nbar02, where the integer nbar0 (l , n ; α → 0) = l + n + 1 is the principal quantum number of the bound-state resonance (here the integers l = 1 , 2 , 3 , … and n = 0 , 1 , 2 , … are the spheroidal harmonic index and the resonance parameter of the field mode, respectively). As it depends only on the principal resonance parameter nbar0, this small-mass (α ≪ 1) hydrogenic spectrum is obviously degenerate. In this paper we go beyond the small-mass approximation and analyze the quasi-stationary bound-state resonances of massive scalar fields in rapidly-spinning Kerr black-hole spacetimes in the regime α = O (1). In particular, we derive the non-hydrogenic (and, in general, non-degenerate) resonance oscillation spectrum ωR / μ =√{ 1 -(α / n bar) 2 }, where n bar (l , n ; α) =√{(l + 1 / 2) 2 - 2 mα + 2α2 } + 1 / 2 + n is the generalized principal quantum number of the quasi-stationary resonances. This analytically derived formula for the characteristic oscillation frequencies of the composed black-hole-massive-scalar-field system is shown to agree with direct numerical computations of the quasi-stationary bound-state resonances.
NASA Astrophysics Data System (ADS)
Barreiro, Andrea K.; Ly, Cheng
2017-08-01
Rapid experimental advances now enable simultaneous electrophysiological recording of neural activity at single-cell resolution across large regions of the nervous system. Models of this neural network activity will necessarily increase in size and complexity, thus increasing the computational cost of simulating them and the challenge of analyzing them. Here we present a method to approximate the activity and firing statistics of a general firing rate network model (of the Wilson-Cowan type) subject to noisy correlated background inputs. The method requires solving a system of transcendental equations and is fast compared to Monte Carlo simulations of coupled stochastic differential equations. We implement the method with several examples of coupled neural networks and show that the results are quantitatively accurate even with moderate coupling strengths and an appreciable amount of heterogeneity in many parameters. This work should be useful for investigating how various neural attributes qualitatively affect the spiking statistics of coupled neural networks.
NASA Astrophysics Data System (ADS)
Van Ende, K. T. R.; Schaare, D.; Kaste, J.; Küçükay, F.; Henze, R.; Kallmeyer, F. K.
2016-10-01
For steer-by-wire systems, the steering feedback must be generated artificially due to the system characteristics. Classical control concepts require operating-point driven optimisations as well as increased calibration efforts in order to adequately simulate the steering torque in all driving states. Artificial neural networks (ANNs) are an innovative control concept; they are capable of learning arbitrary non-linear correlations without complex knowledge of physical dependencies. The present study investigates the suitability of neural networks for approximating unknown steering torques. To ensure robust processing of arbitrary data, network training with a sufficient volume of training data is required, that represents the relation between the input and target values in a wide range. The data were recorded in the course of various test drives. In this research, a variety of network topologies were trained, analysed and evaluated. Though the fundamental suitability of ANNs for the present control task was demonstrated.
NASA Astrophysics Data System (ADS)
Jones, Jeff
The single celled organism Physarum polycephalum efficiently constructs and minimises dynamical nutrient transport networks resembling proximity graphs. We present a model multi-agent population which collectively approximates the network behaviours of Physarum. We demonstrate spontaneous transport network formation and evolution and show that the collective population also exhibits quasi-physical emergent properties, allowing the collective population to be considered as a virtual computing material - a synthetic plasmodium. This material is used as an unconventional method to approximate spatially represented geometry problems. We demonstrate three different methods for the construction, evolution and minimisation of Physarum-like transport networks which approximate Steiner trees, relative neighbourhood graphs, convex hulls and concave hulls. The results span the Toussaint hierarchy of proximity graphs, suggesting that the foraging and minimising behaviours of Physarum reflect interplay between maximising foraging area and minimising transport distance. The properties and behaviours of the synthetic virtual plasmodium may be useful in future physical instances of unconventional computing devices, and may also provide clues to the generation of emergent computation behaviours by Physarum.
Artificial neural networks and approximate reasoning for intelligent control in space
NASA Technical Reports Server (NTRS)
Berenji, Hamid R.
1991-01-01
A method is introduced for learning to refine the control rules of approximate reasoning-based controllers. A reinforcement-learning technique is used in conjunction with a multi-layer neural network model of an approximate reasoning-based controller. The model learns by updating its prediction of the physical system's behavior. The model can use the control knowledge of an experienced operator and fine-tune it through the process of learning. Some of the space domains suitable for applications of the model such as rendezvous and docking, camera tracking, and tethered systems control are discussed.
Artificial neural networks and approximate reasoning for intelligent control in space
NASA Technical Reports Server (NTRS)
Berenji, Hamid R.
1991-01-01
A method is introduced for learning to refine the control rules of approximate reasoning-based controllers. A reinforcement-learning technique is used in conjunction with a multi-layer neural network model of an approximate reasoning-based controller. The model learns by updating its prediction of the physical system's behavior. The model can use the control knowledge of an experienced operator and fine-tune it through the process of learning. Some of the space domains suitable for applications of the model such as rendezvous and docking, camera tracking, and tethered systems control are discussed.
Mean-field approximation for the Sznajd model in complex networks
NASA Astrophysics Data System (ADS)
Araújo, Maycon S.; Vannucchi, Fabio S.; Timpanaro, André M.; Prado, Carmen P. C.
2015-02-01
This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field approximation. Although quite simple, this approximation allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The analytical prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong approximations involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.
Mean field approximation for biased diffusion on Japanese inter-firm trading network.
Watanabe, Hayafumi
2014-01-01
By analysing the financial data of firms across Japan, a nonlinear power law with an exponent of 1.3 was observed between the number of business partners (i.e. the degree of the inter-firm trading network) and sales. In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this nonlinear scaling and the network structure by applying mean-field approximation of the diffusion in a complex network to this money-transport model. Using theoretical analysis, we obtained the mean-field solution of the model and found that, in the case of the Japanese firms, the scaling exponent of 1.3 can be determined from the power law of the average degree of the nearest neighbours of the network with an exponent of -0.7.
Fast Evaluation of Fluctuations in Biochemical Networks With the Linear Noise Approximation
Elf, Johan; Ehrenberg, Måns
2003-01-01
Biochemical networks in single cells can display large fluctuations in molecule numbers, making mesoscopic approaches necessary for correct system descriptions. We present a general method that allows rapid characterization of the stochastic properties of intracellular networks. The starting point is a macroscopic description that identifies the system's elementary reactions in terms of rate laws and stoichiometries. From this formulation follows directly the stationary solution of the linear noise approximation (LNA) of the Master equation for all the components in the network. The method complements bifurcation studies of the system's parameter dependence by providing estimates of sizes, correlations, and time scales of stochastic fluctuations. We describe how the LNA can give precise system descriptions also near macroscopic instabilities by suitable variable changes and elimination of fast variables. PMID:14597656
NASA Astrophysics Data System (ADS)
Shimelevich, M. I.; Obornev, E. A.; Obornev, I. E.; Rodionov, E. A.
2017-07-01
The iterative approximation neural network method for solving conditionally well-posed nonlinear inverse problems of geophysics is presented. The method is based on the neural network approximation of the inverse operator. The inverse problem is solved in the class of grid (block) models of the medium on a regularized parameterization grid. The construction principle of this grid relies on using the calculated values of the continuity modulus of the inverse operator and its modifications determining the degree of ambiguity of the solutions. The method provides approximate solutions of inverse problems with the maximal degree of detail given the specified degree of ambiguity with the total number of the sought parameters n × 103 of the medium. The a priori and a posteriori estimates of the degree of ambiguity of the approximated solutions are calculated. The work of the method is illustrated by the example of the three-dimensional (3D) inversion of the synthesized 2D areal geoelectrical (audio magnetotelluric sounding, AMTS) data corresponding to the schematic model of a kimberlite pipe.
Montufar, Guido; Ay, Nihat
2011-05-01
We improve recently published results about resources of restricted Boltzmann machines (RBM) and deep belief networks (DBN)required to make them universal approximators. We show that any distribution pon the set {0,1}(n) of binary vectors of length n can be arbitrarily well approximated by an RBM with k-1 hidden units, where k is the minimal number of pairs of binary vectors differing in only one entry such that their union contains the support set of p. In important cases this number is half the cardinality of the support set of p (given in Le Roux & Bengio, 2008). We construct a DBN with 2n/ 2(n-b) , b ∼ log n, hidden layers of width n that is capable of approximating any distribution on {0,1}(n) arbitrarily well. This confirms a conjecture presented in Le Roux and Bengio (2010).
A Neural Network Correction to the Scalar Approximation in Radiative Transfer
NASA Astrophysics Data System (ADS)
Castellanos, P.; da Silva, A. M., Jr.
2016-12-01
Radiative transfer models (RTMs) are essential tools in a wide range of applications that help us understand atmospheric processes and atmosphere-land interactions. RTMs are often used to generate artificial scenes as would be observed by an optical sensor. These instrument simulators function as a virtual laboratory, often referred to as an observing system simulation experiment (OSSE), during the development of remote sensing missions. Advanced detailed RTMs are computationally intensive, and the next generation of remote sensing instruments will have increasingly high spatial, temporal, and spectral resolutions. This can make using detailed RTMs in instrument simulators unfeasible in a practical sense. To overcome this, often the scalar approximation is used in radiative transfer calculations. However, this approximation, which neglects polarization, can produce errors in top of the atmosphere (TOA) radiance calculations as large as 10%, depending on the optical depth, atmospheric composition, and scattering geometry. These errors are particularly important in the UV-Vis where polarized light scattering is significant. Concentrations of air quality and climate relevant trace gases as well as aerosol optical properties are retrieved at these wavelengths. We will present an approach for correcting the errors in TOA radiances calculated with the scalar approximation that utilizes an artificial neural network. The neural network is used as an empirical statistical technique for fast and accurate approximation between RTM input parameters and the scalar error. Our results show that with just a few basic input parameters, a neural network can represent the complex nonlinear relationships between the errors in the scalar approximation and solar-sensor geometry, surface reflectance, and atmospheric composition. Our validation results indicate that the neural network is able to correct the scalar radiance to within 1% of the vector radiance, comparable to the error in
Winkler, David A; Le, Tu C
2017-01-01
Neural networks have generated valuable Quantitative Structure-Activity/Property Relationships (QSAR/QSPR) models for a wide variety of small molecules and materials properties. They have grown in sophistication and many of their initial problems have been overcome by modern mathematical techniques. QSAR studies have almost always used so-called "shallow" neural networks in which there is a single hidden layer between the input and output layers. Recently, a new and potentially paradigm-shifting type of neural network based on Deep Learning has appeared. Deep learning methods have generated impressive improvements in image and voice recognition, and are now being applied to QSAR and QSAR modelling. This paper describes the differences in approach between deep and shallow neural networks, compares their abilities to predict the properties of test sets for 15 large drug data sets (the kaggle set), discusses the results in terms of the Universal Approximation theorem for neural networks, and describes how DNN may ameliorate or remove troublesome "activity cliffs" in QSAR data sets. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Diffusion in random networks: Asymptotic properties, and numerical and engineering approximations
NASA Astrophysics Data System (ADS)
Padrino, Juan C.; Zhang, Duan Z.
2016-11-01
The ensemble phase averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of a set of pockets connected by tortuous channels. Inside a channel, we assume that fluid transport is governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pores mass density. The so-called dual porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain, whose solution is sought numerically. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt- 1 / 4 rather than xt- 1 / 2 as in the traditional theory. This early time sub-diffusive similarity can be explained by random walk theory through the network. In addition, by applying concepts of fractional calculus, we show that, for small time, the governing equation reduces to a fractional diffusion equation with known solution. We recast this solution in terms of special functions easier to compute. Comparison of the numerical and exact solutions shows excellent agreement.
Linear noise approximation for oscillations in a stochastic inhibitory network with delay
NASA Astrophysics Data System (ADS)
Dumont, Grégory; Northoff, Georg; Longtin, André
2014-07-01
Understanding neural variability is currently one of the biggest challenges in neuroscience. Using theory and computational modeling, we study the behavior of a globally coupled inhibitory neural network, in which each neuron follows a purely stochastic two-state spiking process. We investigate the role of both this intrinsic randomness and the conduction delay on the emergence of fast (e.g., gamma) oscillations. Toward that end, we expand the recently proposed linear noise approximation (LNA) technique to this non-Markovian "delay" case. The analysis first leads to a nonlinear delay-differential equation (DDE) with multiplicative noise for the mean activity. The LNA then yields two coupled DDEs, one of which is driven by additive Gaussian white noise. These equations on their own provide an excellent approximation to the full network dynamics, which are much longer to integrate. They further allow us to compute a theoretical expression for the power spectrum of the population activity. Our analytical result is in good agreement with the power spectrum obtained via numerical simulations of the full network dynamics, for the large range of parameters where both the intrinsic stochasticity and the conduction delay are necessary for the occurrence of oscillations. The intrinsic noise arises from the probabilistic description of each neuron, yet it is expressed at the system activity level, and it can only be controlled by the system size. In fact, its effect on the fluctuations in system activity disappears in the infinite network size limit, but the characteristics of the oscillatory activity depend on all model parameters including the system size. Using the Hilbert transform, we further show that the intrinsic noise causes sporadic strong fluctuations in the phase of the gamma rhythm.
Complete hierarchies of SIR models on arbitrary networks with exact and approximate moment closure.
Sharkey, Kieran J; Wilkinson, Robert R
2015-06-01
We first generalise ideas discussed by Kiss et al. (2015) to prove a theorem for generating exact closures (here expressing joint probabilities in terms of their constituent marginal probabilities) for susceptible-infectious-removed (SIR) dynamics on arbitrary graphs (networks). For Poisson transmission and removal processes, this enables us to obtain a systematic reduction in the number of differential equations needed for an exact 'moment closure' representation of the underlying stochastic model. We define 'transmission blocks' as a possible extension of the block concept in graph theory and show that the order at which the exact moment closure representation is curtailed is the size of the largest transmission block. More generally, approximate closures of the hierarchy of moment equations for these dynamics are typically defined for the first and second order yielding mean-field and pairwise models respectively. It is frequently implied that, in principle, closed models can be written down at arbitrary order if only we had the time and patience to do this. However, for epidemic dynamics on networks, these higher-order models have not been defined explicitly. Here we unambiguously define hierarchies of approximate closed models that can utilise subsystem states of any order, and show how well-known models are special cases of these hierarchies.
NASA Technical Reports Server (NTRS)
Hopkins, Dale A.; Patnaik, Surya N.
2000-01-01
A preliminary aircraft engine design methodology is being developed that utilizes a cascade optimization strategy together with neural network and regression approximation methods. The cascade strategy employs different optimization algorithms in a specified sequence. The neural network and regression methods are used to approximate solutions obtained from the NASA Engine Performance Program (NEPP), which implements engine thermodynamic cycle and performance analysis models. The new methodology is proving to be more robust and computationally efficient than the conventional optimization approach of using a single optimization algorithm with direct reanalysis. The methodology has been demonstrated on a preliminary design problem for a novel subsonic turbofan engine concept that incorporates a wave rotor as a cycle-topping device. Computations of maximum thrust were obtained for a specific design point in the engine mission profile. The results (depicted in the figure) show a significant improvement in the maximum thrust obtained using the new methodology in comparison to benchmark solutions obtained using NEPP in a manual design mode.
Development of neural networks for exact and approximate calculation: a FMRI study.
Kucian, Karin; von Aster, Michael; Loenneker, Thomas; Dietrich, Thomas; Martin, Ernst
2008-01-01
Neuroimaging findings in adults suggest exact and approximate number processing relying on distinct neural circuits. In the present study we are investigating whether this cortical specialization is already established in 9- and 12-year-old children. Using fMRI, brain activation was measured in 10 third- and 10 sixth-grade school children and 20 adults during trials of symbolic approximate (AP) and exact (EX) calculation, as well as non-symbolic magnitude comparison (MC) of objects. Children activated similar networks like adults, denoting an availability and a similar spatial extent of specified networks as early as third grade. However, brain areas related to number processing become further specialized with schooling. Children showed weaker activation in the intraparietal sulcus during all three tasks, in the left inferior frontal gyrus during EX and in occipital areas during MC. In contrast, activation in the anterior cingulate gyrus, a region associated with attentional effort and working memory load, was enhanced in children. Moreover, children revealed reduced or absent deactivation of regions involved in the so-called default network during symbolic calculation, suggesting a rather general developmental effect. No difference in brain activation patterns between AP and EX was found. Behavioral results indicated major differences between children and adults in AP and EX, but not in MC. Reaction time and accuracy rate were not correlated to brain activation in regions showing developmental changes suggesting rather effects of development than performance differences between children and adults. In conclusion, increasing expertise with age may lead to more automated processing of mental arithmetic, which is reflected by improved performance and by increased brain activation in regions related to number processing and decreased activation in supporting areas.
Impaired neural networks for approximate calculation in dyscalculic children: a functional MRI study
Kucian, Karin; Loenneker, Thomas; Dietrich, Thomas; Dosch, Mengia; Martin, Ernst; von Aster, Michael
2006-01-01
Background Developmental dyscalculia (DD) is a specific learning disability affecting the acquisition of mathematical skills in children with otherwise normal general intelligence. The goal of the present study was to examine cerebral mechanisms underlying DD. Methods Eighteen children with DD aged 11.2 ± 1.3 years and twenty age-matched typically achieving schoolchildren were investigated using functional magnetic resonance imaging (fMRI) during trials testing approximate and exact mathematical calculation, as well as magnitude comparison. Results Children with DD showed greater inter-individual variability and had weaker activation in almost the entire neuronal network for approximate calculation including the intraparietal sulcus, and the middle and inferior frontal gyrus of both hemispheres. In particular, the left intraparietal sulcus, the left inferior frontal gyrus and the right middle frontal gyrus seem to play crucial roles in correct approximate calculation, since brain activation correlated with accuracy rate in these regions. In contrast, no differences between groups could be found for exact calculation and magnitude comparison. In general, fMRI revealed similar parietal and prefrontal activation patterns in DD children compared to controls for all conditions. Conclusion In conclusion, there is evidence for a deficient recruitment of neural resources in children with DD when processing analog magnitudes of numbers. PMID:16953876
Cluster-variation approximation for a network-forming lattice-fluid model.
Buzano, C; De Stefanis, E; Pretti, M
2008-07-14
We consider a three-dimensional lattice model of a network-forming fluid, which has been recently investigated by Girardi et al. by means of Monte Carlo simulations [J. Chem. Phys. 126, 064503 (2007)], with the aim of describing water anomalies. We develop an approximate semianalytical calculation, based on a cluster-variation technique, which turns out to reproduce almost quantitatively different thermodynamic properties and phase transitions determined by the Monte Carlo method. Nevertheless, our calculation points out the existence of two different phases characterized by long-range orientational order, and of critical transitions between them and to a high-temperature orientationally disordered phase. Also, the existence of such critical lines allows us to explain certain "kinks" in the isotherms and isobars determined by the Monte Carlo analysis. The picture of the phase diagram becomes much more complex and richer, though unfortunately less suitable to describe real water.
NASA Astrophysics Data System (ADS)
Hamacher, Kay
2011-07-01
Biomolecular simulations have become a major tool in understanding biomolecules and their complexes. However, one can typically only investigate a few mutants or scenarios due to the severe computational demands of such simulations, leading to a great interest in method development to overcome this restriction. One way to achieve this is to reduce the complexity of the systems by an approximation of the forces acting upon the constituents of the molecule. The harmonic approximation used in elastic network models simplifies the physical complexity to the most reduced dynamics of these molecular systems. The reduced polymer modeled this way is typically comprised of mass points representing coarse-grained versions of, e.g., amino acids. In this work, we show how the computation of free energy contributions of contacts between two residues within the molecule can be reduced to a simple lookup operation in a precomputable matrix. Being able to compute such contributions is of great importance: protein design or molecular evolution changes introduce perturbations to these pair interactions, so we need to understand their impact. Perturbation to the interactions occurs due to randomized and fixated changes (in molecular evolution) or designed modifications of the protein structures (in bioengineering). These perturbations are modifications in the topology and the strength of the interactions modeled by the elastic network models. We apply the new algorithm to (1) the bovine trypsin inhibitor, a well-known enzyme in biomedicine, and show the connection to folding properties and the hydrophobic collapse hypothesis and (2) the serine proteinase inhibitor CI-2 and show the correlation to Φ values to characterize folding importance. Furthermore, we discuss the computational complexity and show empirical results for the average case, sampled over a library of 77 structurally diverse proteins. We found a relative speedup of up to 10 000-fold for large proteins with respect to
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Guptill, James D.; Hopkins, Dale A.; Lavelle, Thomas M.
2000-01-01
The NASA Engine Performance Program (NEPP) can configure and analyze almost any type of gas turbine engine that can be generated through the interconnection of a set of standard physical components. In addition, the code can optimize engine performance by changing adjustable variables under a set of constraints. However, for engine cycle problems at certain operating points, the NEPP code can encounter difficulties: nonconvergence in the currently implemented Powell's optimization algorithm and deficiencies in the Newton-Raphson solver during engine balancing. A project was undertaken to correct these deficiencies. Nonconvergence was avoided through a cascade optimization strategy, and deficiencies associated with engine balancing were eliminated through neural network and linear regression methods. An approximation-interspersed cascade strategy was used to optimize the engine's operation over its flight envelope. Replacement of Powell's algorithm by the cascade strategy improved the optimization segment of the NEPP code. The performance of the linear regression and neural network methods as alternative engine analyzers was found to be satisfactory. This report considers two examples-a supersonic mixed-flow turbofan engine and a subsonic waverotor-topped engine-to illustrate the results, and it discusses insights gained from the improved version of the NEPP code.
Perfect plastic approximation revisited: a flowline network model for calving glaciers
NASA Astrophysics Data System (ADS)
Ultee, E.; Bassis, J. N.
2015-12-01
Accurate modeling of outlet glacier dynamics requires knowledge of many factors—ice thickness, bed topography, air/ocean temperature, precipitation rate—specific to individual glaciers, and for which only limited data exists. Furthermore, key processes such as iceberg calving remain poorly understood and difficult to include in models. In light of these challenges to even the most sophisticated models, there is great value in simple, computationally efficient models that can capture first-order effects. Many of the simplest models currently in use produce glacier profiles along a central flowline, either ignoring the contribution of tributaries or relying on a measure of "equivalent width" to handle those contributions. Here, we present a simple model that generalizes Nye's 1953 perfect plastic approximation so that it also predicts the position of the glacier terminus based on the yield strength. Moreover, our model simulates not only a central flowline, but the interactions of a network of tributaries. The model requires only minimal information: glacier geometry (network structure and bed topography, available from observation for select glaciers) and basal shear strength (a reasonably-constrained parameter). We apply the model to Columbia Glacier, Alaska and show that, despite its simplicity, the model is able to reproduce observed centerline profiles and terminus retreat for the main branch as well as selected tributaries. Finally, we illustrate how our model can be applied to constrain the calving contribution of individual glaciers to 21st century sea level rise.
NASA Astrophysics Data System (ADS)
Chtioui, Younes; Panigrahi, Suranjan; Marsh, Ronald A.
1998-11-01
The probabilistic neural network (PNN) is based on the estimation of the probability density functions. The estimation of these density functions uses smoothing parameters that represent the width of the activation functions. A two-step numerical procedure is developed for the optimization of the smoothing parameters of the PNN: a rough optimization by the conjugate gradient method and a fine optimization by the approximate Newton method. The thrust is to compare the classification performances of the improved PNN and the standard back-propagation neural network (BPNN). Comparisons are performed on a food quality problem: french fry classification into three different color classes (light, normal, and dark). The optimized PNN correctly classifies 96.19% of the test data, whereas the BPNN classifies only 93.27% of the same data. Moreover, the PNN is more stable than the BPNN with regard to the random initialization. The optimized PNN requires 1464 s for training compared to only 71 s required by the BPNN.
Mayorga, René V; Arriaga, Mariano
2007-10-01
In this article, a novel technique for non-linear global optimization is presented. The main goal is to find the optimal global solution of non-linear problems avoiding sub-optimal local solutions or inflection points. The proposed technique is based on a two steps concept: properly keep decreasing the value of the objective function, and calculating the corresponding independent variables by approximating its inverse function. The decreasing process can continue even after reaching local minima and, in general, the algorithm stops when converging to solutions near the global minimum. The implementation of the proposed technique by conventional numerical methods may require a considerable computational effort on the approximation of the inverse function. Thus, here a novel Artificial Neural Network (ANN) approach is implemented to reduce the computational requirements of the proposed optimization technique. This approach is successfully tested on some highly non-linear functions possessing several local minima. The results obtained demonstrate that the proposed approach compares favorably over some current conventional numerical (Matlab functions) methods, and other non-conventional (Evolutionary Algorithms, Simulated Annealing) optimization methods.
Feng, Ruibin; Leung, Chi-Sing; Constantinides, Anthony G; Zeng, Wen-Jun
2016-07-27
The major limitation of the Lagrange programming neural network (LPNN) approach is that the objective function and the constraints should be twice differentiable. Since sparse approximation involves nondifferentiable functions, the original LPNN approach is not suitable for recovering sparse signals. This paper proposes a new formulation of the LPNN approach based on the concept of the locally competitive algorithm (LCA). Unlike the classical LCA approach which is able to solve unconstrained optimization problems only, the proposed LPNN approach is able to solve the constrained optimization problems. Two problems in sparse approximation are considered. They are basis pursuit (BP) and constrained BP denoise (CBPDN). We propose two LPNN models, namely, BP-LPNN and CBPDN-LPNN, to solve these two problems. For these two models, we show that the equilibrium points of the models are the optimal solutions of the two problems, and that the optimal solutions of the two problems are the equilibrium points of the two models. Besides, the equilibrium points are stable. Simulations are carried out to verify the effectiveness of these two LPNN models.
Transition modes in Ising networks: an approximate theory for macromolecular recognition.
Keating, S; Di Cera, E
1993-01-01
For a statistical lattice, or Ising network, composed of N identical units existing in two possible states, 0 and 1, and interacting according to a given geometry, a set of values can be found for the mean free energy of the 0-->1 transition of a single unit. Each value defines a transition mode in an ensemble of nu N = 3N - 2N possible values and reflects the role played by intermediate states in shaping the energetics of the system as a whole. The distribution of transition modes has a number of intriguing properties. Some of them apply quite generally to any Ising network, regardless of its dimension, while others are specific for each interaction geometry and dimensional embedding and bear on fundamental aspects of analytical number theory. The landscape of transition modes encapsulates all of the important thermodynamic properties of the network. The free energy terms defining the partition function of the system can be derived from the modes by simple transformations. Classical mean-field expressions can be obtained from consideration of the properties of transition modes in a rather straightforward way. The results obtained in the analysis of the transition mode distributions have been used to develop an approximate treatment of the problem of macromolecular recognition. This phenomenon is modeled as a cooperative process that involves a number of recognition subsites across an interface generated by the binding of two macromolecular components. The distribution of allowed binding free energies for the system is shown to be a superposition of Gaussian terms with mean and variance determined a priori by the theory. Application to the analysis of the biologically interaction of thrombin with hirudin has provided some useful information on basic aspects of the interaction, such as the number of recognition subsites involved and the energy balance for binding and cooperative coupling among them. Our results agree quite well with information derived independently
Transition modes in Ising networks: an approximate theory for macromolecular recognition.
Keating, S; Di Cera, E
1993-07-01
For a statistical lattice, or Ising network, composed of N identical units existing in two possible states, 0 and 1, and interacting according to a given geometry, a set of values can be found for the mean free energy of the 0-->1 transition of a single unit. Each value defines a transition mode in an ensemble of nu N = 3N - 2N possible values and reflects the role played by intermediate states in shaping the energetics of the system as a whole. The distribution of transition modes has a number of intriguing properties. Some of them apply quite generally to any Ising network, regardless of its dimension, while others are specific for each interaction geometry and dimensional embedding and bear on fundamental aspects of analytical number theory. The landscape of transition modes encapsulates all of the important thermodynamic properties of the network. The free energy terms defining the partition function of the system can be derived from the modes by simple transformations. Classical mean-field expressions can be obtained from consideration of the properties of transition modes in a rather straightforward way. The results obtained in the analysis of the transition mode distributions have been used to develop an approximate treatment of the problem of macromolecular recognition. This phenomenon is modeled as a cooperative process that involves a number of recognition subsites across an interface generated by the binding of two macromolecular components. The distribution of allowed binding free energies for the system is shown to be a superposition of Gaussian terms with mean and variance determined a priori by the theory. Application to the analysis of the biologically interaction of thrombin with hirudin has provided some useful information on basic aspects of the interaction, such as the number of recognition subsites involved and the energy balance for binding and cooperative coupling among them. Our results agree quite well with information derived independently
Binary-State Dynamics on Complex Networks: Pair Approximation and Beyond
NASA Astrophysics Data System (ADS)
Gleeson, James P.
2013-04-01
A wide class of binary-state dynamics on networks—including, for example, the voter model, the Bass diffusion model, and threshold models—can be described in terms of transition rates (spin-flip probabilities) that depend on the number of nearest neighbors in each of the two possible states. High-accuracy approximations for the emergent dynamics of such models on uncorrelated, infinite networks are given by recently developed compartmental models or approximate master equations (AMEs). Pair approximations (PAs) and mean-field theories can be systematically derived from the AME. We show that PA and AME solutions can coincide under certain circumstances, and numerical simulations confirm that PA is highly accurate in these cases. For monotone dynamics (where transitions out of one nodal state are impossible, e.g., susceptible-infected disease spread or Bass diffusion), PA and the AME give identical results for the fraction of nodes in the infected (active) state for all time, provided that the rate of infection depends linearly on the number of infected neighbors. In the more general nonmonotone case, we derive a condition—that proves to be equivalent to a detailed balance condition on the dynamics—for PA and AME solutions to coincide in the limit t→∞. This equivalence permits bifurcation analysis, yielding explicit expressions for the critical (ferromagnetic or paramagnetic transition) point of such dynamics, that is closely analogous to the critical temperature of the Ising spin model. Finally, the AME for threshold models of propagation is shown to reduce to just two differential equations and to give excellent agreement with numerical simulations. As part of this work, the Octave or Matlab code for implementing and solving the differential-equation systems is made available for download.
Variability of quasi-stationary planetary waves
NASA Technical Reports Server (NTRS)
Krivolutsky, A. A.; Petushkov, N. D.; Tarasenko, D. A.
1989-01-01
The results of the analysis of nonzonal perturbations (m = 1, 2, 3) of the geopotential field at a 30 mb level are presented. A long period modulation of the harmonics' amplitude is discovered. Calculations of eigenfunctions and eigennumbers of the Laplace tidal equation are carried out for a real latitudinal wind profile. The observed first zonal harmonic in different years is caused by the same mode. Thus, the difference in the wave amplitudes could not be accounted for by the difference in stratospheric zonal circulation in different years and should be related to tropospheric processes.
Sorribas, Albert; Hernández-Bermejo, Benito; Vilaprinyo, Ester; Alves, Rui
2007-08-01
Cooperative and saturable systems are common in molecular biology. Nevertheless, common canonical formalisms for kinetic modeling that are theoretically well justified do not have a saturable form. Modeling and fitting data from saturable systems are widely done using Hill-like equations. In practice, there is no theoretical justification for the generalized use of these equations, other than their ability to fit experimental data. Thus it is important to find a canonical formalism that is (a) theoretically well supported, (b) has a saturable functional form, and (c) can be justifiably applicable to any biochemical network. Here we derive such a formalism using Taylor approximations in a special transformation space defined by power-inverses and logarithms of power-inverses. This formalism is generalized for processes with n-variables, leading to a useful mathematical representation for molecular biology: the Saturable and Cooperative Formalism (SC formalism). This formalism provides an appropriate representation that can be used for modeling processes with cooperativity and saturation. We also show that the Hill equation can be seen as a special case within this formalism. Parameter estimation for the SC formalism requires information that is also necessary to build Power-Law models, Metabolic Control Analysis descriptions or (log)linear and Lin-log models. In addition, the saturation fraction of the relevant processes at the operating point needs to be considered. The practical use of the SC formalism for modeling is illustrated with a few examples. Similar models are built using different formalisms and compared to emphasize advantages and limitations of the different approaches.
Vuković, Najdan; Miljković, Zoran
2013-10-01
Radial basis function (RBF) neural network is constructed of certain number of RBF neurons, and these networks are among the most used neural networks for modeling of various nonlinear problems in engineering. Conventional RBF neuron is usually based on Gaussian type of activation function with single width for each activation function. This feature restricts neuron performance for modeling the complex nonlinear problems. To accommodate limitation of a single scale, this paper presents neural network with similar but yet different activation function-hyper basis function (HBF). The HBF allows different scaling of input dimensions to provide better generalization property when dealing with complex nonlinear problems in engineering practice. The HBF is based on generalization of Gaussian type of neuron that applies Mahalanobis-like distance as a distance metrics between input training sample and prototype vector. Compared to the RBF, the HBF neuron has more parameters to optimize, but HBF neural network needs less number of HBF neurons to memorize relationship between input and output sets in order to achieve good generalization property. However, recent research results of HBF neural network performance have shown that optimal way of constructing this type of neural network is needed; this paper addresses this issue and modifies sequential learning algorithm for HBF neural network that exploits the concept of neuron's significance and allows growing and pruning of HBF neuron during learning process. Extensive experimental study shows that HBF neural network, trained with developed learning algorithm, achieves lower prediction error and more compact neural network.
NASA Astrophysics Data System (ADS)
Hisamatu, Hiroyuki; Ohsaki, Hiroyuki; Murata, Masayuki
2003-08-01
In the current Internet, most of the traffic is transmitted by TCP (Transmission Control Protocol). In our previous work, we have proposed a modeling approach for the entire network, including TCP congestion control mechanisms operating at source hosts and the network seen by TCP connections, as a single feedback system. However, our analytic model is limited to a simple network, where TCP connections have the identical propagation delay. In this paper, we therefore extend our analytic approach to a more generic network, where multiple TCP connections are allowed to have different propagation delays. We derive the packet loss probability in the network, the throughput and the average round-trip time of each TCP connection in steady state. By presenting several numerical examples, we quantitatively investigate how the fairness among TCP connections is degraded when multiple TCP connections with different propagation delays share the single bottleneck link.
Characteristics of pattern formation and evolution in approximations of Physarum transport networks.
Jones, Jeff
2010-01-01
Most studies of pattern formation place particular emphasis on its role in the development of complex multicellular body plans. In simpler organisms, however, pattern formation is intrinsic to growth and behavior. Inspired by one such organism, the true slime mold Physarum polycephalum, we present examples of complex emergent pattern formation and evolution formed by a population of simple particle-like agents. Using simple local behaviors based on chemotaxis, the mobile agent population spontaneously forms complex and dynamic transport networks. By adjusting simple model parameters, maps of characteristic patterning are obtained. Certain areas of the parameter mapping yield particularly complex long term behaviors, including the circular contraction of network lacunae and bifurcation of network paths to maintain network connectivity. We demonstrate the formation of irregular spots and labyrinthine and reticulated patterns by chemoattraction. Other Turing-like patterning schemes were obtained by using chemorepulsion behaviors, including the self-organization of regular periodic arrays of spots, and striped patterns. We show that complex pattern types can be produced without resorting to the hierarchical coupling of reaction-diffusion mechanisms. We also present network behaviors arising from simple pre-patterning cues, giving simple examples of how the emergent pattern formation processes evolve into networks with functional and quasi-physical properties including tensionlike effects, network minimization behavior, and repair to network damage. The results are interpreted in relation to classical theories of biological pattern formation in natural systems, and we suggest mechanisms by which emergent pattern formation processes may be used as a method for spatially represented unconventional computation.
Peron, Thomas Kauê Dal'maso; Rodrigues, Francisco A
2012-11-01
An explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. The present paper reports on mean-field approximations to determine the critical coupling of such explosive synchronization. It has been verified that the equation obtained for the critical coupling has an inverse dependence on the network average degree. This expression differs from those whose frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. Numerical simulations were also conducted to verify our analytical results.
An adaptive fuzzy neural network for MIMO system model approximation in high-dimensional spaces.
Chak, C K; Feng, G; Ma, J
1998-01-01
An adaptive fuzzy system implemented within the framework of neural network is proposed. The integration of the fuzzy system into a neural network enables the new fuzzy system to have learning and adaptive capabilities. The proposed fuzzy neural network can locate its rules and optimize its membership functions by competitive learning, Kalman filter algorithm and extended Kalman filter algorithms. A key feature of the new architecture is that a high dimensional fuzzy system can be implemented with fewer number of rules than the Takagi-Sugeno fuzzy systems. A number of simulations are presented to demonstrate the performance of the proposed system including modeling nonlinear function, operator's control of chemical plant, stock prices and bioreactor (multioutput dynamical system).
An efficient approximation algorithm for finding a maximum clique using Hopfield network learning.
Wang, Rong Long; Tang, Zheng; Cao, Qi Ping
2003-07-01
In this article, we present a solution to the maximum clique problem using a gradient-ascent learning algorithm of the Hopfield neural network. This method provides a near-optimum parallel algorithm for finding a maximum clique. To do this, we use the Hopfield neural network to generate a near-maximum clique and then modify weights in a gradient-ascent direction to allow the network to escape from the state of near-maximum clique to maximum clique or better. The proposed parallel algorithm is tested on two types of random graphs and some benchmark graphs from the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS). The simulation results show that the proposed learning algorithm can find good solutions in reasonable computation time.
Interdependency and hierarchy of exact and approximate epidemic models on networks.
Taylor, Timothy J; Kiss, Istvan Z
2014-07-01
Over the years numerous models of S I S (susceptible --> infected --> susceptible) disease dynamics unfolding on networks have been proposed. Here, we discuss the links between many of these models and how they can be viewed as more general motif-based models. We illustrate how the different models can be derived from one another and, where this is not possible, discuss extensions to established models that enables this derivation. We also derive a general result for the exact differential equations for the expected number of an arbitrary motif directly from the Kolmogorov/master equations and conclude with a comparison of the performance of the different closed systems of equations on networks of varying structure.
Luo, Biao; Wu, Huai-Ning
2012-12-01
This paper addresses the approximate optimal control problem for a class of parabolic partial differential equation (PDE) systems with nonlinear spatial differential operators. An approximate optimal control design method is proposed on the basis of the empirical eigenfunctions (EEFs) and neural network (NN). First, based on the data collected from the PDE system, the Karhunen-Loève decomposition is used to compute the EEFs. With those EEFs, the PDE system is formulated as a high-order ordinary differential equation (ODE) system. To further reduce its dimension, the singular perturbation (SP) technique is employed to derive a reduced-order model (ROM), which can accurately describe the dominant dynamics of the PDE system. Second, the Hamilton-Jacobi-Bellman (HJB) method is applied to synthesize an optimal controller based on the ROM, where the closed-loop asymptotic stability of the high-order ODE system can be guaranteed by the SP theory. By dividing the optimal control law into two parts, the linear part is obtained by solving an algebraic Riccati equation, and a new type of HJB-like equation is derived for designing the nonlinear part. Third, a control update strategy based on successive approximation is proposed to solve the HJB-like equation, and its convergence is proved. Furthermore, an NN approach is used to approximate the cost function. Finally, we apply the developed approximate optimal control method to a diffusion-reaction process with a nonlinear spatial operator, and the simulation results illustrate its effectiveness.
Phase patterns in finite oscillator networks with insights from the piecewise linear approximation
NASA Astrophysics Data System (ADS)
Goldstein, Daniel
2015-03-01
Recent experiments on spatially extend arrays of droplets containing Belousov-Zhabotinsky reactants have shown a rich variety of spatio-temporal patterns. Motivated by this experimental set up, we study a simple model of chemical oscillators in the highly nonlinear excitable regime in order to gain insight into the mechanism giving rise to the observed multistable attractors. When coupled, these two attractors have different preferred phase synchronizations, leading to complex behavior. We study rings of coupled oscillators and observe a rich array of oscillating patterns. We combine Turing analysis and a piecewise linear approximation to better understand the observed patterns.
Kostarigka, Artemis K; Rovithakis, George A
2009-10-01
An adaptive output feedback neural network controller is designed, which is capable of rendering affine-in-the-control uncertain multi-input-multi-output nonlinear systems strictly passive with respect to an appropriately defined set. Consequently, a simple output feedback is employed to stabilize the system. The controlled system need not be in normal form or have a well-defined relative degree. Without requiring a zero-state detectability assumption, uniform ultimate boundedness, with respect to an arbitrarily small set, of both the system's state and the output is guaranteed, along with boundedness of all other signals in the closed loop. To effectively avoid possible division by zero, the proposed adaptive controller is of switching type. However, its continuity is guaranteed, thus alleviating drawbacks connected to existence of solutions and chattering phenomena. Simulations illustrate the approach.
Buy-at-bulk network design: Approximating the single-sink edge installation problem
Salman, F.S.; Ravi, R.; Cheriyan, J.
1997-06-01
We initiate the algorithmic study of an important but NP-hard problem that arises commonly in network design. The input consists of (1) An undirected graph with one sink node and multiple source nodes, a specified length for each edge, and a specified demand, dem{sub v}, for each source node v. (2) A small set of cable types, where each cable type is specified by its capacity and its cost per unit length. The cost per unit capacity per unit length of a high-capacity cable may be significantly less than that of a low-capacity cable, reflecting an economy of scale, i.e., the payoff for buying at bulk may be very high.
NASA Astrophysics Data System (ADS)
Van Mieghem, P.
2016-05-01
Based on a recent exact differential equation, the time dependence of the SIS prevalence, the average fraction of infected nodes, in any graph is first studied and then upper and lower bounded by an explicit analytic function of time. That new approximate "tanh formula" obeys a Riccati differential equation and bears resemblance to the classical expression in epidemiology of Kermack and McKendrick [Proc. R. Soc. London A 115, 700 (1927), 10.1098/rspa.1927.0118] but enhanced with graph specific properties, such as the algebraic connectivity, the second smallest eigenvalue of the Laplacian of the graph. We further revisit the challenge of finding tight upper bounds for the SIS (and SIR) epidemic threshold for all graphs. We propose two new upper bounds and show the importance of the variance of the number of infected nodes. Finally, a formula for the epidemic threshold in the cycle (or ring graph) is presented.
NASA Astrophysics Data System (ADS)
Müller, Lucas O.; Blanco, Pablo J.
2015-11-01
We present a methodology for the high order approximation of hyperbolic conservation laws in networks by using the Dumbser-Enaux-Toro solver and exact solvers for the classical Riemann problem at junctions. The proposed strategy can be applied to any hyperbolic system, conservative or non-conservative, and possibly with flux functions containing discontinuous parameters, as long as an exact or approximate Riemann problem solver is available. The methodology is implemented for a one-dimensional blood flow model that considers discontinuous variations of mechanical and geometrical properties of vessels. The achievement of formal order of accuracy, as well as the robustness of the resulting numerical scheme, is verified through the simulation of both, academic tests and physiological flows.
Whittington, James C. R.; Bogacz, Rafal
2017-01-01
To efficiently learn from feedback, cortical networks need to update synaptic weights on multiple levels of cortical hierarchy. An effective and well-known algorithm for computing such changes in synaptic weights is the error backpropagation algorithm. However, in this algorithm, the change in synaptic weights is a complex function of weights and activities of neurons not directly connected with the synapse being modified, whereas the changes in biological synapses are determined only by the activity of presynaptic and postsynaptic neurons. Several models have been proposed that approximate the backpropagation algorithm with local synaptic plasticity, but these models require complex external control over the network or relatively complex plasticity rules. Here we show that a network developed in the predictive coding framework can efficiently perform supervised learning fully autonomously, employing only simple local Hebbian plasticity. Furthermore, for certain parameters, the weight change in the predictive coding model converges to that of the backpropagation algorithm. This suggests that it is possible for cortical networks with simple Hebbian synaptic plasticity to implement efficient learning algorithms in which synapses in areas on multiple levels of hierarchy are modified to minimize the error on the output. PMID:28333583
2012-01-01
Background It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA). The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions. Results We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA), as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations. Conclusions A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions. The ssLNA provides a
Cotter, Simon L.
2016-10-15
Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement to the constrained approach, which is a method for computing effective dynamics of slowly changing quantities in these systems, but which does not rely on the quasi-steady-state assumption (QSSA). The QSSA can cause errors in the estimation of effective dynamics for systems where the difference in timescales between the “fast” and “slow” variables is not so pronounced. This new application of the constrained approach allows us to compute the effective generator of the slow variables, without the need for expensive stochastic simulations. This is achieved by finding the null space of the generator of the constrained system. For complex systems where this is not possible, or where the constrained subsystem is itself multiscale, the constrained approach can then be applied iteratively. This results in breaking the problem down into finding the solutions to many small eigenvalue problems, which can be efficiently solved using standard methods. Since this methodology does not rely on the quasi steady-state assumption, the effective dynamics that are approximated are highly accurate, and in the case of systems with only monomolecular reactions, are exact. We will demonstrate this with some numerics, and also use the effective generators to sample paths of the slow variables which are conditioned on their endpoints, a task which would be computationally intractable for the generator of the full system.
L(p) approximation capabilities of sum-of-product and sigma-pi-sigma neural networks.
Long, Jinling; Wu, Wei; Nan, Dong
2007-10-01
This paper studies the L(p) approximation capabilities of sum-of-product (SOPNN) and sigma-pi-sigma (SPSNN) neural networks. It is proved that the set of functions that are generated by the SOPNN with its activation function in $L_{loc};p(\\mathcal{R})$ is dense in $L;p(\\mathcal{K})$ for any compact set $\\mathcal{K}\\subset \\mathcal{R};N$, if and only if the activation function is not a polynomial almost everywhere. It is also shown that if the activation function of the SPSNN is in ${L_{loc};\\infty(\\mathcal{R})}$, then the functions generated by the SPSNN are dense in $L;p(\\mathcal{K})$ if and only if the activation function is not a constant (a.e.).
NASA Technical Reports Server (NTRS)
Peck, Charles C.; Dhawan, Atam P.; Meyer, Claudia M.
1991-01-01
A genetic algorithm is used to select the inputs to a neural network function approximator. In the application considered, modeling critical parameters of the space shuttle main engine (SSME), the functional relationship between measured parameters is unknown and complex. Furthermore, the number of possible input parameters is quite large. Many approaches have been used for input selection, but they are either subjective or do not consider the complex multivariate relationships between parameters. Due to the optimization and space searching capabilities of genetic algorithms they were employed to systematize the input selection process. The results suggest that the genetic algorithm can generate parameter lists of high quality without the explicit use of problem domain knowledge. Suggestions for improving the performance of the input selection process are also provided.
Costa, Rafael S; Machado, Daniel; Rocha, Isabel; Ferreira, Eugénio C
2010-05-01
The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis-Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action, convenience kinetics, lin-log and power-law). Using the mechanistic model for Escherichia coli central carbon metabolism as a benchmark, we investigate the alternative modeling approaches through comparative simulations analyses. The good dynamic behavior and the powerful predictive capabilities obtained using the hybrid model composed of Michaelis-Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown.
Fuchs, Erich; Gruber, Christian; Reitmaier, Tobias; Sick, Bernhard
2009-09-01
Neural networks are often used to process temporal information, i.e., any kind of information related to time series. In many cases, time series contain short-term and long-term trends or behavior. This paper presents a new approach to capture temporal information with various reference periods simultaneously. A least squares approximation of the time series with orthogonal polynomials will be used to describe short-term trends contained in a signal (average, increase, curvature, etc.). Long-term behavior will be modeled with the tapped delay lines of a time-delay neural network (TDNN). This network takes the coefficients of the orthogonal expansion of the approximating polynomial as inputs such considering short-term and long-term information efficiently. The advantages of the method will be demonstrated by means of artificial data and two real-world application examples, the prediction of the user number in a computer network and online tool wear classification in turning.
De Bartolo, Samuele; Dell'Accio, Francesco; Veltri, Massimo
2009-02-01
A network analysis is used to investigate the low connections of natural river channels. At the basin scale, the river networks are analyzed according to the Horton-Strahler hierarchy. We propose a quantitative criterion for the average junction degree as a function of a fixed hierarchical order of the network and independent of the usual scaling laws. The numerical results of this analysis are compared with exact results of the Peano river network, showing differences of the order of 10(-3). This aspect is especially relevant for the characterization of transport and diffusion processes at the basin scale.
2008-01-01
10 A ve re ge li fe tim e (m in .) ε Fig. 7. Impact of ǫ on lifetime C. Computation time We measured the computation time of our algorithm. Our...allocation in wireless sensor networks with network lifetime requirement,” in Proc. of MOBI-HOC, 2004. [9] J. Gehrke and S. Madden, “Query Processing In
NASA Astrophysics Data System (ADS)
Malshe, M.; Narulkar, R.; Raff, L. M.; Hagan, M.; Bukkapatnam, S.; Agrawal, P. M.; Komanduri, R.
2009-05-01
A general method for the development of potential-energy hypersurfaces is presented. The method combines a many-body expansion to represent the potential-energy surface with two-layer neural networks (NN) for each M-body term in the summations. The total number of NNs required is significantly reduced by employing a moiety energy approximation. An algorithm is presented that efficiently adjusts all the coupled NN parameters to the database for the surface. Application of the method to four different systems of increasing complexity shows that the fitting accuracy of the method is good to excellent. For some cases, it exceeds that available by other methods currently in literature. The method is illustrated by fitting large databases of ab initio energies for Sin(n =3,4,…,7) clusters obtained from density functional theory calculations and for vinyl bromide (C2H3Br) and all products for dissociation into six open reaction channels (12 if the reverse reactions are counted as separate open channels) that include C-H and C-Br bond scissions, three-center HBr dissociation, and three-center H2 dissociation. The vinyl bromide database comprises the ab initio energies of 71 969 configurations computed at MP4(SDQ) level with a 6-31G(d,p) basis set for the carbon and hydrogen atoms and Huzinaga's (4333/433/4) basis set augmented with split outer s and p orbitals (43321/4321/4) and a polarization f orbital with an exponent of 0.5 for the bromine atom. It is found that an expansion truncated after the three-body terms is sufficient to fit the Si5 system with a mean absolute testing set error of 5.693×10-4 eV. Expansions truncated after the four-body terms for Sin(n =3,4,5) and Sin(n =3,4,…,7) provide fits whose mean absolute testing set errors are 0.0056 and 0.0212 eV, respectively. For vinyl bromide, a many-body expansion truncated after the four-body terms provides fitting accuracy with mean absolute testing set errors that range between 0.0782 and 0.0808 eV. These
Stanescu-Cosson, R; Pinel, P; van De Moortele, P F; Le Bihan, D; Cohen, L; Dehaene, S
2000-11-01
Neuropsychological studies have revealed different subtypes of dyscalculia, including dissociations between exact calculation and approximation abilities, and an impact of number size on performance. To understand the origins of these effects, we measured cerebral activity with functional MRI at 3 Tesla and event-related potentials while healthy volunteers performed exact and approximate calculation tasks with small and large numbers. Bilateral intraparietal, precentral, dorsolateral and superior prefrontal regions showed greater activation during approximation, while the left inferior prefrontal cortex and the bilateral angular regions were more activated during exact calculation. Increasing number size during exact calculation led to increased activation in the same bilateral intraparietal regions as during approximation, as well the left inferior and superior frontal gyri. Event-related potentials gave access to the temporal dynamics of calculation processes, showing that effects of task and of number size could be found as early as 200-300 ms following problem presentation. Altogether, the results reveal two cerebral networks for number processing. Rote arithmetic operations with small numbers have a greater reliance on left-lateralized regions, presumably encoding numbers in verbal format. Approximation and exact calculation with large numbers, however, put heavier emphasis on the left and right parietal cortices, which may encode numbers in a non-verbal quantity format. Subtypes of dyscalculia can be explained by lesions disproportionately affecting only one of these networks.
Dynamics of quasi-stationary systems: Finance as an example
NASA Astrophysics Data System (ADS)
Rinn, Philip; Stepanov, Yuriy; Peinke, Joachim; Guhr, Thomas; Schäfer, Rudi
2015-06-01
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical stability as well as transitions between different stable states are found. This combined method allows especially to set up new criteria for merging clusters to uncover dynamically distinct states. The low-dimensional approach allows to recover the high-dimensional fixed points of the system by means of an optimization procedure.
Quasi-Stationary Global Auroral Ionospheric Model: E-layer
NASA Astrophysics Data System (ADS)
Nikolaeva, Vera; Gordeev, Evgeny; Kotikov, Andrey; Makarova, Ludmila; Shirochkov, Aleksander
2014-05-01
E-layer Auroral Ionospheric Model (E-AIM) is developed to provide temporal and spatial density distribution of the main ionosphere neutral species (NO, N(4S),N(2D)), and ions (N2+, NO+,O2+,O+) in the altitude range from 90 to 150 km. NRLMSISE-00 model [Picone et al., JGR 2003] is used for neutral atmosphere content and temperature determination, that is the input for the E-AIM model. The E-AIM model based on chemical equilibrium state in E-layer that reaches in chemical reactions between ionospheric species considering solar radiation ionization source, superposed with sporadic precipitation of magnetospheric electrons. The chemical equilibrium state in each location under specific solar and geomagnetic activity conditions reaches during numerical solution of the continuity equations for the neutrals and ions using the high-performance Gear method [Gear, 1971] for ordinary differential equation (ODE) systems. Applying the Gear method for solving stiff ODE system strongly reduce the computation time and machine resources comparing to widely used methods and provide an opportunity to calculate the global spatial E-layer ion content distribution. In contrast to the mid-latitude ionosphere, structure and dynamics of the auroral zone ionosphere (φ ≡ 60-75° MLat) associated not only with shortwave solar radiation. Precipitating magnetospheric particle flux is the most important ionization source and is the main cause of E-layer disturbances. Precipitated electrons with initial energies of 1 - 30 keV influence the auroral ionosphere E-layer. E-AIM model can estimate ionization rate corresponds to auroral electron precipitation in two different ways: 1. with direct electron flux satellite data; 2. with differential energy spectrum reconstructed from OVATION-Prime empirical model [Newell, JGR 2009] average values, that allows to estimate ionosphere ion content for any time and location in the auroral zone. Comparison of E-AIM results with direct ionospheric observations (ionosonde, incoherent scatter radar) show good agreement of electron concentration vertical distribution values.
The quasi-stationary electromagnetic field in the solar wind
NASA Astrophysics Data System (ADS)
Alekseev, I. I.; Veselovskii, I. S.; Kropotkin, A. P.
1982-02-01
Parker's (1958, 1963) kinematic model of the interplanetary field with ideal conductivity is examined. It is shown that Parker's assumption of the absence of the meridional component (Btheta = 0) is not a necessary one. Instead, in the general case the interplanetary magnetic field can have three components (Br, Btheta, and B sub phi).
The theory of pattern formation on directed networks.
Asllani, Malbor; Challenger, Joseph D; Pavone, Francesco Saverio; Sacconi, Leonardo; Fanelli, Duccio
2014-07-31
Dynamical processes on networks have generated widespread interest in recent years. The theory of pattern formation in reaction-diffusion systems defined on symmetric networks has often been investigated, due to its applications in a wide range of disciplines. Here we extend the theory to the case of directed networks, which are found in a number of different fields, such as neuroscience, computer networks and traffic systems. Owing to the structure of the network Laplacian, the dispersion relation has both real and imaginary parts, at variance with the case for a symmetric, undirected network. The homogeneous fixed point can become unstable due to the topology of the network, resulting in a new class of instabilities, which cannot be induced on undirected graphs. Results from a linear stability analysis allow the instability region to be analytically traced. Numerical simulations show travelling waves, or quasi-stationary patterns, depending on the characteristics of the underlying graph.
2001-09-01
Coniglio Sergio The Sukhoi Su Combat Aircraft Family Military Tech nology Special Supplement Conte SD and de Boor Carl ...Technical Report CF RAND Santa Monica CA deBoor Carl A Practical Guide to Splines SpringerVerlag New York Decision...Sigal C E Pritsker AAB and Solberg JJ The Use of Cutsets in Monte Carlo Analysis of Stochastic Networks Mathematics and Computers in Simu
NASA Astrophysics Data System (ADS)
Mello, M. M.; Ventura, L.
2015-03-01
A method using different light sources and sensors have already been used to approximate weighting functions to calculate light transmittance in sunglasses. Although it made possible a low cost equipment that inform the user about its sunglasses, each transmittance test is still dependent of its components. We tested two methods, using polynomial approximation and artificial neural network, that would open the possibility for the use of a fixed light source and sensor for all light transmittance tests from the standard. Spectrophotometry, visible transmittance and traffic light transmittance was calculated in 45 lenses of sunglasses, used as samples for testing the methodologies. The tests included a white LED, a RGB sensor, and electronic for control and signal acquisition. Bland - Altman analysis tool was used to calculate the agreement between the method and the transmittances calculated in the spectrophotometer. Both methods, had an approximation within the deviation limit required by NBR15111. The system with the polynomial regression showed lower deviations than artificial neural networks. A larger number of samples can improve the methods in order to obtain an optimal calibration that includes all sunglasses. No meter in the market can calculate accurately all light transmittances measurements required for the sunglasses. The methodology was applied only for the visible light, while UV and infrared spectrum remains to be tested. The methodology tested presented a way for simple low-cost equipment for all light transmittance tests in sunglasses.
Nguyen, Hieu T T; Le, Hung M
2012-05-10
The classical interchange (permutation) of atoms of similar identity does not have an effect on the overall potential energy. In this study, we present feed-forward neural network structures that provide permutation symmetry to the potential energy surfaces of molecules. The new feed-forward neural network structures are employed to fit the potential energy surfaces for two illustrative molecules, which are H(2)O and ClOOCl. Modifications are made to describe the symmetric interchange (permutation) of atoms of similar identity (or mathematically, the permutation of symmetric input parameters). The combined-function-derivative approximation algorithm (J. Chem. Phys. 2009, 130, 134101) is also implemented to fit the neural-network potential energy surfaces accurately. The combination of our symmetric neural networks and the function-derivative fitting effectively produces PES fits using fewer numbers of training data points. For H(2)O, only 282 configurations are employed as the training set; the testing root-mean-squared and mean-absolute energy errors are respectively reported as 0.0103 eV (0.236 kcal/mol) and 0.0078 eV (0.179 kcal/mol). In the ClOOCl case, 1693 configurations are required to construct the training set; the root-mean-squared and mean-absolute energy errors for the ClOOCl testing set are 0.0409 eV (0.943 kcal/mol) and 0.0269 eV (0.620 kcal/mol), respectively. Overall, we find good agreements between ab initio and NN prediction in term of energy and gradient errors, and conclude that the new feed-forward neural-network models advantageously describe the molecules with excellent accuracy.
Stochastic analysis of biochemical reaction networks with absolute concentration robustness
Anderson, David F.; Enciso, Germán A.; Johnston, Matthew D.
2014-01-01
It has recently been shown that structural conditions on the reaction network, rather than a ‘fine-tuning’ of system parameters, often suffice to impart ‘absolute concentration robustness’ (ACR) on a wide class of biologically relevant, deterministically modelled mass-action systems. We show here that fundamentally different conclusions about the long-term behaviour of such systems are reached if the systems are instead modelled with stochastic dynamics and a discrete state space. Specifically, we characterize a large class of models that exhibit convergence to a positive robust equilibrium in the deterministic setting, whereas trajectories of the corresponding stochastic models are necessarily absorbed by a set of states that reside on the boundary of the state space, i.e. the system undergoes an extinction event. If the time to extinction is large relative to the relevant timescales of the system, the process will appear to settle down to a stationary distribution long before the inevitable extinction will occur. This quasi-stationary distribution is considered for two systems taken from the literature, and results consistent with ACR are recovered by showing that the quasi-stationary distribution of the robust species approaches a Poisson distribution. PMID:24522780
Schulz, Andreas S.; Shmoys, David B.; Williamson, David P.
1997-01-01
Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science. PMID:9370525
Network Games and Approximation Algorithms
2008-01-03
I also spend time during the last three years writing a textbook on Algorithm Design (with Jon Kleinberg) that had now been adopted by a number of...Minimum-Size Bounded-Capacity Cut (MSBCC) problem, in which we are given a graph with an identified source and seek to find a cut minimizing the number ...Distributed Computing (Special Issue PODC 05) Volume 19, Number 4, 2007, 255-266. http://www.springerlink.com/content/x 148746507861 np7/ ?p
Thorn, Graeme J; King, John R
2016-01-01
The Gram-positive bacterium Clostridium acetobutylicum is an anaerobic endospore-forming species which produces acetone, butanol and ethanol via the acetone-butanol (AB) fermentation process, leading to biofuels including butanol. In previous work we looked to estimate the parameters in an ordinary differential equation model of the glucose metabolism network using data from pH-controlled continuous culture experiments. Here we combine two approaches, namely the approximate Bayesian computation via an existing sequential Monte Carlo (ABC-SMC) method (to compute credible intervals for the parameters), and the profile likelihood estimation (PLE) (to improve the calculation of confidence intervals for the same parameters), the parameters in both cases being derived from experimental data from forward shift experiments. We also apply the ABC-SMC method to investigate which of the models introduced previously (one non-sporulation and four sporulation models) have the greatest strength of evidence. We find that the joint approximate posterior distribution of the parameters determines the same parameters as previously, including all of the basal and increased enzyme production rates and enzyme reaction activity parameters, as well as the Michaelis-Menten kinetic parameters for glucose ingestion, while other parameters are not as well-determined, particularly those connected with the internal metabolites acetyl-CoA, acetoacetyl-CoA and butyryl-CoA. We also find that the approximate posterior is strongly non-Gaussian, indicating that our previous assumption of elliptical contours of the distribution is not valid, which has the effect of reducing the numbers of pairs of parameters that are (linearly) correlated with each other. Calculations of confidence intervals using the PLE method back this up. Finally, we find that all five of our models are equally likely, given the data available at present. Copyright © 2015 Elsevier Inc. All rights reserved.
De la Fuente, Ildefonso M.; Cortes, Jesus M.; Pelta, David A.; Veguillas, Juan
2013-01-01
Background The experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a Systemic Metabolic Structure in the cell, characterized by a set of different enzymatic reactions always locked into active states (metabolic core) while the rest of the catalytic processes are only intermittently active. This global metabolic structure was verified for Escherichia coli, Helicobacter pylori and Saccharomyces cerevisiae, and it seems to be a common key feature to all cellular organisms. In concordance with these observations, the cell can be considered a complex metabolic network which mainly integrates a large ensemble of self-organized multienzymatic complexes interconnected by substrate fluxes and regulatory signals, where multiple autonomous oscillatory and quasi-stationary catalytic patterns simultaneously emerge. The network adjusts the internal metabolic activities to the external change by means of flux plasticity and structural plasticity. Methodology/Principal Findings In order to research the systemic mechanisms involved in the regulation of the cellular enzymatic activity we have studied different catalytic activities of a dissipative metabolic network under different external stimuli. The emergent biochemical data have been analysed using statistical mechanic tools, studying some macroscopic properties such as the global information and the energy of the system. We have also obtained an equivalent Hopfield network using a Boltzmann machine. Our main result shows that the dissipative metabolic network can behave as an attractor metabolic network. Conclusions/Significance We have found that the systemic enzymatic activities are governed by attractors with capacity to store functional metabolic patterns which can be correctly recovered from specific input stimuli. The network attractors regulate the catalytic patterns, modify the efficiency
Approximation techniques for neuromimetic calculus.
Vigneron, V; Barret, C
1999-06-01
Approximation Theory plays a central part in modern statistical methods, in particular in Neural Network modeling. These models are able to approximate a large amount of metric data structures in their entire range of definition or at least piecewise. We survey most of the known results for networks of neurone-like units. The connections to classical statistical ideas such as ordinary least squares (LS) are emphasized.
Multicriteria approximation through decomposition
Burch, C.; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E.
1998-06-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of their technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. Their method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) the authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing; (2) they also show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
Multicriteria approximation through decomposition
Burch, C. |; Krumke, S.; Marathe, M.; Phillips, C.; Sundberg, E. |
1997-12-01
The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) The authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing. (2) They show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.
Networks based on collisions among mobile agents
NASA Astrophysics Data System (ADS)
González, Marta C.; Lind, Pedro G.; Herrmann, Hans J.
2006-12-01
We investigate in detail a recent model of colliding mobile agents [M.C. González, P.G. Lind, H.J. Herrmann, Phys. Rev. Lett. 96 (2006) 088702. cond-mat/0602091], used as an alternative approach for constructing evolving networks of interactions formed by collisions governed by suitable dynamical rules. The system of mobile agents evolves towards a quasi-stationary state which is, apart from small fluctuations, well characterized by the density of the system and the residence time of the agents. The residence time defines a collision rate, and by varying this collision rate, the system percolates at a critical value, with the emergence of a giant cluster whose critical exponents are the ones of two-dimensional percolation. Further, the degree and clustering coefficient distributions, and the average path length, show that the network associated with such a system presents non-trivial features which, depending on the collision rules, enables one not only to recover the main properties of standard networks, such as exponential, random and scale-free networks, but also to obtain other topological structures. To illustrate, we show a specific example where the obtained structure has topological features which characterize the structure and evolution of social networks accurately in different contexts, ranging from networks of acquaintances to networks of sexual contacts.
El-Melegy, Moumen T
2013-07-01
This paper addresses the problem of fitting a functional model to data corrupted with outliers using a multilayered feed-forward neural network. Although it is of high importance in practical applications, this problem has not received careful attention from the neural network research community. One recent approach to solving this problem is to use a neural network training algorithm based on the random sample consensus (RANSAC) framework. This paper proposes a new algorithm that offers two enhancements over the original RANSAC algorithm. The first one improves the algorithm accuracy and robustness by employing an M-estimator cost function to decide on the best estimated model from the randomly selected samples. The other one improves the time performance of the algorithm by utilizing a statistical pretest based on Wald's sequential probability ratio test. The proposed algorithm is successfully evaluated on synthetic and real data, contaminated with varying degrees of outliers, and compared with existing neural network training algorithms.
NASA Astrophysics Data System (ADS)
Opanowicz, A.
2007-08-01
Thermally stimulated luminescence (TSL) and conductivity (TSC) are considered using the classical insulator model that assumes one kind of active trap, one kind of inactive deep trap and one kind of recombination centre. Kinetic equations describing the model are solved numerically without and with the use of quasi-equilibrium (QE) approximation. The QE state is characterized by the parameter qI = (dnc/dt)/Ie, where dnc/dt is the rate of change of free electron density, and Ie is the TSL intensity. The QE state parameter qI, the relative recombination probability γ = Ie/(Ie + It) (It is the trapping intensity) and a new parameter called a quasi-stationary (QS) state parameter q* = qIγ = (dnc/dt)/(Ie + It) are used for the analysis of the TSL and TSC. The QE and QS states are determined by conditions |qI| Lt 1 and, respectively, |q*| Lt 1. The TSL and TSC curves and the temperature dependences of qI, q*, γ the recombination lifetime and the occupancies of active traps and recombination centres are numerically calculated for five sets of kinetic parameters and different heating rates. These calculation results show that (1) the upper limit of the heating rate for the presence of the QS state appears at a higher heating rate than that for the QE state when the retrapping process is present, and (2) the TSL (TSC) curves in the QS state have properties similar to those for the TSL (TSC) curves in the QE state. Approximate formulae for calculation of the parameters qI and q* in the initial range of the TSL and TSC curves are derived and used in the heating-rate methods, proposed in this work, for determination of those parameters from the calculated TSL curves.
Interpolation and Approximation Theory.
ERIC Educational Resources Information Center
Kaijser, Sten
1991-01-01
Introduced are the basic ideas of interpolation and approximation theory through a combination of theory and exercises written for extramural education at the university level. Topics treated are spline methods, Lagrange interpolation, trigonometric approximation, Fourier series, and polynomial approximation. (MDH)
Noctilucent clouds: modern ground-based photographic observations by a digital camera network.
Dubietis, Audrius; Dalin, Peter; Balčiūnas, Ričardas; Černis, Kazimieras; Pertsev, Nikolay; Sukhodoev, Vladimir; Perminov, Vladimir; Zalcik, Mark; Zadorozhny, Alexander; Connors, Martin; Schofield, Ian; McEwan, Tom; McEachran, Iain; Frandsen, Soeren; Hansen, Ole; Andersen, Holger; Grønne, Jesper; Melnikov, Dmitry; Manevich, Alexander; Romejko, Vitaly
2011-10-01
Noctilucent, or "night-shining," clouds (NLCs) are a spectacular optical nighttime phenomenon that is very often neglected in the context of atmospheric optics. This paper gives a brief overview of current understanding of NLCs by providing a simple physical picture of their formation, relevant observational characteristics, and scientific challenges of NLC research. Modern ground-based photographic NLC observations, carried out in the framework of automated digital camera networks around the globe, are outlined. In particular, the obtained results refer to studies of single quasi-stationary waves in the NLC field. These waves exhibit specific propagation properties--high localization, robustness, and long lifetime--that are the essential requisites of solitary waves.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
NASA Astrophysics Data System (ADS)
Niiniluoto, Ilkka
2014-03-01
Approximation of laws is an important theme in the philosophy of science. If we can make sense of the idea that two scientific laws are "close" to each other, then we can also analyze such methodological notions as approximate explanation of laws, approximate reduction of theories, approximate empirical success of theories, and approximate truth of laws. Proposals for measuring the distance between quantitative scientific laws were given in Niiniluoto (1982, 1987). In this paper, these definitions are reconsidered as a response to the interesting critical remarks by Liu (1999).
Matrix product approximations to conformal field theories
NASA Astrophysics Data System (ADS)
König, Robert; Scholz, Volkher B.
2017-07-01
We establish rigorous error bounds for approximating correlation functions of conformal field theories (CFTs) by certain finite-dimensional tensor networks. For chiral CFTs, the approximation takes the form of a matrix product state. For full CFTs consisting of a chiral and an anti-chiral part, the approximation is given by a finitely correlated state. We show that the bond dimension scales polynomially in the inverse of the approximation error and sub-exponentially in inverse of the minimal distance between insertion points. We illustrate our findings using Wess-Zumino-Witten models, and show that there is a one-to-one correspondence between group-covariant MPS and our approximation.
Approximate symmetries of Hamiltonians
NASA Astrophysics Data System (ADS)
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
Networks and the Best Approximation Property
1989-10-01
problems and the regularization method. Soviet Math. Dokl., 4:1035-1038, 1963. 21 [281 A. N. Tikhonov and V. Y. Arsenin . Solutions of il- posed ...reconstruction is given by regularization theory ( Tikhonov and Arsenin , 1977 ; Bertero et al. 8 1988). Poggio and Girosi (1989) have shown that the solution ...set of data that we want to ap- proximate by means of a function f. The regularization approach ( Tikhonov , 1963; Tikhonov and Arsenin , 1977
Ocean tides and quasi-stationary departures from the marine geoid investigation
NASA Technical Reports Server (NTRS)
Siry, J. W.; Kahn, W. D.; Bryan, J. W.; Vonbun, F. O.
1973-01-01
The detection of tides and/or currents through the analysis of data generated in connection with the Ocean Geoid Determination Investigation is presented. A discussion of the detailed objectives and approach are included.
Quasi-Stationary Zonally Asymmetric Circulations in the Equatorial Lower Mesosphere.
NASA Astrophysics Data System (ADS)
Hitchman, Matthew H.; Leovy, Conway B.; Gille, John C.; Bailey, Paul L.
1987-08-01
Data from the Limb Infrared Monitor of the Stratosphere (LIMS) are used to identify a new type of planetary scale disturbance in the equatorial lower mesosphere during northern winter 1978/79. The disturbances consist of two or three vertically stacked temperature extrema of alternating sign. They persist for as long as two weeks and do not propagate. Their occurrence is confined to regions of very weak or negative inertial stability, and their meridional to vertical aspect ratio, meridional structure and zonal spectrum are consistent with disturbances predicted by inertial instability theory. However, they are found only when there is strong forcing of the subtropical mesosphere by zonal wavenumber one and two Rossby waves. This fact, together with the absence of zonal propagation, suggests that stationary Rossby waves determine their occurrence and longitudinal structure. These structures can significantly modify the zonal mean flow and should be taken into account in dynamical models of the equatorial mesosphere.
Quasi-stationary convection in a periodic-pulsed optical discharge in high pressure rare gas
NASA Astrophysics Data System (ADS)
Zimakov, V. P.; Kuznetsov, V. A.; Solovyov, N. G.; Shemyakin, A. N.; Shilov, A. O.; Yakimov, M. Yu
2017-02-01
Unusual convection flows were observed in stabilized pre-breakdown phase of the periodic-pulsed optical discharge (POD) called “quiet” POD. The discharge was a relatively weakly glowing plasma filament sustained by focused λ = 1.064 μm laser pulses with repetition rate of fr = 50÷100 kHz at the intensity several times below than that required for the optical breakdown to occur. No strong shock waves or irregular turbulence around the discharge were observed, in contrast to breakdown types of POD. Significant laser beam refraction measured in the beam cross-section behind the discharge zone was explained by the gas heating in the discharge up to 10 kK, providing high gradients of gas density and refraction index. Intense convective flow was detected on the schlieren images as thermal traces of the laser-induced gas streams flowing from the discharge zone, directed mainly normally to the optical axis. Repeated relaxation of the gas expanding after being rapidly heated by the laser pulse is proposed to explain the effect. The periodic-pulsed discharge located in the elongated beam waist generates an anisotropic heated region with gas streams and vortices, which may form the observed regular convective flow at the late stages of expanding.
Quasi-stationary parameters of small bodies in the solar system
NASA Astrophysics Data System (ADS)
Kramer, E. N.; Shestaka, I. S.
1987-03-01
The following quasistationary parameters of small bodies in the solar system are introduced: P = 0.6/a-[a(1-e2)]cos2i-2, Q = 0.4+(2a-1)(1-e2)cos2i- e2(0.4-sin2ωmsin2i). These are investigated on the basis of data of photographic and radar observations of meteors, comets and Apollo-Amor asteroids. From the quasistationary parameters P and Q one can infer the genetic relations between the bodies studied, specify the probabilities of their encounters with planets and the meteor matter influx on the planets of our solar system.
On the formation of a quasi-stationary twisted disc after a tidal disruption event
NASA Astrophysics Data System (ADS)
Xiang-Gruess, M.; Ivanov, P. B.; Papaloizou, J. C. B.
2016-12-01
We investigate misaligned accretion discs formed after tidal disruption events that occur when a star encounters a supermassive black hole. We employ the linear theory of warped accretion discs to find the shape of a disc for which the stream arising from the disrupted star provides a source of angular momentum that is misaligned with that of the black hole. For quasi-steady configurations, we find that when the warp diffusion or propagation time is large compared to the local mass accretion time and/or the natural disc alignment radius is small, misalignment is favoured. These results have been verified using smoothed particle hydrodynamics simulations. We also simulated 1D model discs including gas and radiation pressure. As accretion rates initially exceed the Eddington limit, the disc is initially advection dominated. Assuming the α model for the disc, where it can be thermally unstable, it subsequently undergoes cyclic transitions between high and low states. During these transitions, the aspect ratio varies from ˜1 to ˜10-3 which is reflected in changes in the degree of disc misalignment at the stream impact location. For maximal black hole rotation and sufficiently large values of viscosity parameter α > ˜0.01-0.1, the ratio of the disc inclination to that of the initial stellar orbit is estimated to be 0.1-0.2 in the advection-dominated state, while reaching of order unity in the low state. Misalignment decreases with decrease of α, but increases as the black hole rotation parameter decreases. Thus, it is always significant when the latter is small.
Water formation in early solar nebula: I. Quasi-stationary cloud core
NASA Astrophysics Data System (ADS)
Tornow, C.; Gast, P.; Pelivan, I.; Kupper, S.; Kührt, E.; Motschmann, U.
2014-08-01
An important condition for the habitability of rocky planets is the existence of water in or on their upper lithospheric layer. We will show that the available amount of this water depends on the conditions in the parental cloud the planetary system has formed from. These clouds can be giant gas clusters with a complex structure associated with bright nebulae or smaller gas aggregations appearing as quiescent dark regions. It has been observed that in both cloud types young stars are formed in dense cores consisting mainly of molecular hydrogen. We assume that the physical and chemical state of these cores, which defines the initial conditions of star formation, is also representative for the initial state of the solar nebula 4.6 Giga years ago. Based on this assumption, we have developed a radial symmetric model to study the physical and chemical evolution of the earliest period of the solar nebula described by a cloud core with 1.01 solar mass and a radius of about 104 AU. The evolution of this core is simulated for a few Mega years, while its molecular gas being in a hydrostatic equilibrium. The related radial distributions of the gas and dust temperature can be calculated from thermal balance equations. These equations depend on the radial profile of the dust to gas density which follows from the continuity equation of the dust phase. The velocity of the dust grains is influenced by the radiation pressure of the local interstellar radiation field and the gas drag. The resulting temperature and dust profiles derived from our model depend on the grain size distribution of the dust. These profiles determine the chemical evolution of the cloud core. It is shown that in the dust phase about 106 to 107 times more water is produced than in the gas phase. Further, the total mass of the water formed in the core varies only marginally between 0.11 and 0.12 wt% for a life time of the core between 1 and 6.5 Mega years, respectively. Roughly 84% of the oxygen atoms are incorporated into water molecules, if the intensity of the radiation field is about 1 Habing. The number of oxygen atoms decreases to 77% if this intensity triples. The water amount produced in the gas phase depends stronger on the interstellar radiation field and the living time of the core than the water amount formed on dust. For the 1 Habing radiation intensity the size distribution of the dust grains has nearly no influence. Finally, a number of species representing compounds mainly formed in the dust or in the gas phase was selected (H2O, CO, etc.) in order to use them for a validation of our model. Thereto, we have compared the abundances of these compounds simulated with the model to the related data from observations published in the literature. For almost all cases except N2H+ a sufficient agreement was found.
Characterisation of quasi-stationary planetary waves in the Northern MLT during summer
NASA Astrophysics Data System (ADS)
Stray, Nora H.; Espy, Patrick J.; Limpasuvan, Varavut; Hibbins, Robert E.
2015-05-01
Observations of planetary wave (PW) activity in the northern hemisphere, polar summer mesosphere and lower thermosphere (MLT) are presented. Meteor winds from a northern hemisphere chain of SuperDARN radars have been used to monitor the meridional wind along a latitude band (51-66°N) in the MLT. A stationary PW-like longitudinal structure with a strong zonal PW number 1 characteristic is persistently observed year-to-year during summer. Here we characterize the amplitude and the phase structure of this wave in the MLT. The Modern-Era Retrospective Analysis for Research and Application (MERRA) of the NASA Global Modelling and Assimilation Office has been used to evaluate possible sources of the observed longitudinal perturbation in the mesospheric meridional wind by investigating the amplitudes and phases of PWs in the underlying atmosphere. The investigation shows that neither gravity wave modulation by lower atmospheric PWs nor direct propagation of PWs from the lower atmosphere are a significant cause of the observed longitudinal perturbation. However, the data are not of sufficient scope to investigate longitudinal differences in gravity wave sources, or to separate the effects of instabilities and inter-hemispheric propagation as possible causes for the large PW present in the summer MLT.
A Case Study of a Quasi-Stationary Tropical Convective Line
1989-08-01
G Scialom, and J. Testud , 1987: A tropical squall line observed during the COPT 81 experiment in West Africa. Part 1: Kinematic structure inferred...mesosynoptic analysis of the thunderstorms on 28 August 1958. Brit. Meteor. Office, Geophys. Memo., No. 106, 74 pp. Rcux, F., J. Testud , M. Payen and B. Pinty
ERIC Educational Resources Information Center
Maughan, George R.; Petitto, Karen R.; McLaughlin, Don
2001-01-01
Describes the connectivity features and options of modern campus communication and information system networks, including signal transmission (wire-based and wireless), signal switching, convergence of networks, and network assessment variables, to enable campus leaders to make sound future-oriented decisions. (EV)
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning.
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
A model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment is presented. Algorithms are developed which can be used to reason about spatial information expressed in the form of approximate linguistic descriptions similar to the kind of spatial information processed by humans. Particular attention is given to static spatial reasoning.
NASA Astrophysics Data System (ADS)
Barry, D. A.; Parlange, J.-Y.; Li, L.; Jeng, D.-S.; Crapper, M.
2005-10-01
The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of asymptotic expansions to W-1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green-Ampt infiltration with immediate ponding), a method is presented for approximating W-1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green-Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 × 10 -5%. This error is orders of magnitude lower than any existing analytical approximations.
Transient selection in multicellular immune networks
NASA Astrophysics Data System (ADS)
Ivanchenko, M. V.
2011-03-01
We analyze the dynamics of a multi-clonotype naive T-cell population competing for survival signals from antigen-presenting cells. We find that this competition provides with an efficacious selection of clonotypes, making the less able and more repetitive get extinct. We uncover the scaling principles for large systems the extinction rate obeys and calibrate the model parameters to their experimental counterparts. For the first time, we estimate the physiological values of the T-cell receptor-antigen presentation profile recognition probability and T-cell clonotypes niche overlap. We demonstrate that, while the ultimate state is a stable fixed point, sequential transients dominate the dynamics over large timescales that may span over years, if not decades, in real time. We argue that what is currently viewed as "homeostasis" is a complex sequential transient process, while being quasi-stationary in the total number of T-cells only. The discovered type of sequential transient dynamics in large random networks is a novel alternative to the stable heteroclinic channel mechanism.
Intrinsic Nilpotent Approximation.
1985-06-01
RD-A1II58 265 INTRINSIC NILPOTENT APPROXIMATION(U) MASSACHUSETTS INST 1/2 OF TECH CAMBRIDGE LAB FOR INFORMATION AND, DECISION UMCLRSSI SYSTEMS C...TYPE OF REPORT & PERIOD COVERED Intrinsic Nilpotent Approximation Technical Report 6. PERFORMING ORG. REPORT NUMBER LIDS-R-1482 7. AUTHOR(.) S...certain infinite-dimensional filtered Lie algebras L by (finite-dimensional) graded nilpotent Lie algebras or g . where x E M, (x,,Z) E T*M/O. It
Anomalous diffraction approximation limits
NASA Astrophysics Data System (ADS)
Videen, Gorden; Chýlek, Petr
It has been reported in a recent article [Liu, C., Jonas, P.R., Saunders, C.P.R., 1996. Accuracy of the anomalous diffraction approximation to light scattering by column-like ice crystals. Atmos. Res., 41, pp. 63-69] that the anomalous diffraction approximation (ADA) accuracy does not depend on particle refractive index, but instead is dependent on the particle size parameter. Since this is at odds with previous research, we thought these results warranted further discussion.
NASA Technical Reports Server (NTRS)
Dutta, Soumitra
1988-01-01
Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.
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.
SIR model on a dynamical network and the endemic state of an infectious disease
NASA Astrophysics Data System (ADS)
Dottori, M.; Fabricius, G.
2015-09-01
In this work we performed a numerical study of an epidemic model that mimics the endemic state of whooping cough in the pre-vaccine era. We considered a stochastic SIR model on dynamical networks that involve local and global contacts among individuals and analysed the influence of the network properties on the characterization of the quasi-stationary state. We computed probability density functions (PDF) for infected fraction of individuals and found that they are well fitted by gamma functions, excepted the tails of the distributions that are q-exponentials. We also computed the fluctuation power spectra of infective time series for different networks. We found that network effects can be partially absorbed by rescaling the rate of infective contacts of the model. An explicit relation between the effective transmission rate of the disease and the correlation of susceptible individuals with their infective nearest neighbours was obtained. This relation quantifies the known screening of infective individuals observed in these networks. We finally discuss the goodness and limitations of the SIR model with homogeneous mixing and parameters taken from epidemiological data to describe the dynamic behaviour observed in the networks studied.
ERIC Educational Resources Information Center
Duvall, Betty
Networking is an information giving and receiving system, a support system, and a means whereby women can get ahead in careers--either in new jobs or in current positions. Networking information can create many opportunities: women can talk about how other women handle situations and tasks, and previously established contacts can be used in…
Covariant approximation averaging
NASA Astrophysics Data System (ADS)
Shintani, Eigo; Arthur, Rudy; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2015-06-01
We present a new class of statistical error reduction techniques for Monte Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in Nf=2 +1 lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte Carlo calculations over conventional methods for the same cost.
Approximate Bayesian Computation
NASA Astrophysics Data System (ADS)
Cisewski, Jessi
2015-08-01
Explicitly specifying a likelihood function is becoming increasingly difficult for many problems in astronomy. Astronomers often specify a simpler approximate likelihood - leaving out important aspects of a more realistic model. Approximate Bayesian computation (ABC) provides a framework for performing inference in cases where the likelihood is not available or intractable. I will introduce ABC and explain how it can be a useful tool for astronomers. In particular, I will focus on the eccentricity distribution for a sample of exoplanets with multiple sub-populations.
ERIC Educational Resources Information Center
Wolff, Hans
This paper deals with a stochastic process for the approximation of the root of a regression equation. This process was first suggested by Robbins and Monro. The main result here is a necessary and sufficient condition on the iteration coefficients for convergence of the process (convergence with probability one and convergence in the quadratic…
Approximating Integrals Using Probability
ERIC Educational Resources Information Center
Maruszewski, Richard F., Jr.; Caudle, Kyle A.
2005-01-01
As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…
Approximating Integrals Using Probability
ERIC Educational Resources Information Center
Maruszewski, Richard F., Jr.; Caudle, Kyle A.
2005-01-01
As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…
Optimizing the Zeldovich approximation
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Pellman, Todd F.; Shandarin, Sergei F.
1994-01-01
We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1993, hereafter CMS) we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that what we called the 'truncated Zeldovich approximation' (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear (sigma approximately 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k(sub nl), where k(sub nl) marks the transition to the nonlinear regime. Here, we study the cross correlation of generalized TZA with a group of n-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a tophat in coordinate space, or a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window e(exp(-k(exp 2)/2k(exp 2, sub G))) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation in those cases which most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of kG for the Gaussian window is (a somewhat spectrum-dependent) 1 to 1.5 times k(sub nl). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, the agreement of the phases of the Fourier components with the n-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment
NASA Technical Reports Server (NTRS)
Merrill, W. C.
1978-01-01
The Routh approximation technique for reducing the complexity of system models was applied in the frequency domain to a 16th order, state variable model of the F100 engine and to a 43d order, transfer function model of a launch vehicle boost pump pressure regulator. The results motivate extending the frequency domain formulation of the Routh method to the time domain in order to handle the state variable formulation directly. The time domain formulation was derived and a characterization that specifies all possible Routh similarity transformations was given. The characterization was computed by solving two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described, and some results are given. Additional computational problems are discussed, including an optimization procedure that can improve the approximation accuracy by taking advantage of the transformation characterization.
Topics in Metric Approximation
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Little, Charles D.
2007-03-01
Taking advantage of wide-field, time-lapse microscopy we examined the assembly of vascular polygonal networks in whole bird embryos and in explanted embryonic mouse tissue (allantois). Primary vasculogenesis assembly steps range from cellular (1-10 μm) to tissue (100μm-1mm) level events: Individual vascular endothelial cells extend protrusions and move with respect to the extracellular matrix/surrounding tissue. Consequently, long-range, tissue-level, deformations directly influence the vascular pattern. Experimental perturbation of endothelial-specific cell-cell adhesions (VE-cadherin), during mouse vasculogenesis, permitted dissection of the cellular motion required for sprout formation. In particular, cells are shown to move actively onto vascular cords that are subject to strain via tissue deformations. Based on the empirical data we propose a simple model of preferential migration along stretched cells. Numerical simulations reveal that the model evolves into a quasi-stationary pattern containing linear segments, which interconnect above a critical volume fraction. In the quasi-stationary state the generation of new branches offsets the coarsening driven by surface tension. In agreement with empirical data, the characteristic size of the resulting polygonal pattern is density-independent within a wide range of volume fractions. These data underscore the potential of combining physical studies with experimental embryology as a means of studying complex morphogenetic systems. In collaboration with Brenda J. Rongish^1, Andr'as Czir'ok^1,2, Erica D. Perryn^1, Cheng Cui^1, and Evan A. Zamir^1 ^1Department of Anatomy and Cell Biology, the University of Kansas Medical Center, Kansas City, KS ^2Department of Biological Physics, E"otv"os Lor'and University, Budapest, Hungary.
Chalasani, P.; Saias, I.; Jha, S.
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.
Beyond the Kirchhoff approximation
NASA Technical Reports Server (NTRS)
Rodriguez, Ernesto
1989-01-01
The three most successful models for describing scattering from random rough surfaces are the Kirchhoff approximation (KA), the small-perturbation method (SPM), and the two-scale-roughness (or composite roughness) surface-scattering (TSR) models. In this paper it is shown how these three models can be derived rigorously from one perturbation expansion based on the extinction theorem for scalar waves scattering from perfectly rigid surface. It is also shown how corrections to the KA proportional to the surface curvature and higher-order derivatives may be obtained. Using these results, the scattering cross section is derived for various surface models.
The Cell Cycle Switch Computes Approximate Majority
NASA Astrophysics Data System (ADS)
Cardelli, Luca; Csikász-Nagy, Attila
2012-09-01
Both computational and biological systems have to make decisions about switching from one state to another. The `Approximate Majority' computational algorithm provides the asymptotically fastest way to reach a common decision by all members of a population between two possible outcomes, where the decision approximately matches the initial relative majority. The network that regulates the mitotic entry of the cell-cycle in eukaryotes also makes a decision before it induces early mitotic processes. Here we show that the switch from inactive to active forms of the mitosis promoting Cyclin Dependent Kinases is driven by a system that is related to both the structure and the dynamics of the Approximate Majority computation. We investigate the behavior of these two switches by deterministic, stochastic and probabilistic methods and show that the steady states and temporal dynamics of the two systems are similar and they are exchangeable as components of oscillatory networks.
Hierarchical Approximate Bayesian Computation
Turner, Brandon M.; Van Zandt, Trisha
2013-01-01
Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model’s parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function. PMID:24297436
Roy, Swapnoneel; Thakur, Ashok Kumar
2008-01-01
Genome rearrangements have been modelled by a variety of primitives such as reversals, transpositions, block moves and block interchanges. We consider such a genome rearrangement primitive Strip Exchanges. Given a permutation, the challenge is to sort it by using minimum number of strip exchanges. A strip exchanging move interchanges the positions of two chosen strips so that they merge with other strips. The strip exchange problem is to sort a permutation using minimum number of strip exchanges. We present here the first non-trivial 2-approximation algorithm to this problem. We also observe that sorting by strip-exchanges is fixed-parameter-tractable. Lastly we discuss the application of strip exchanges in a different area Optical Character Recognition (OCR) with an example.
Hybrid Approximate Message Passing
NASA Astrophysics Data System (ADS)
Rangan, Sundeep; Fletcher, Alyson K.; Goyal, Vivek K.; Byrne, Evan; Schniter, Philip
2017-09-01
The standard linear regression (SLR) problem is to recover a vector $\\mathbf{x}^0$ from noisy linear observations $\\mathbf{y}=\\mathbf{Ax}^0+\\mathbf{w}$. The approximate message passing (AMP) algorithm recently proposed by Donoho, Maleki, and Montanari is a computationally efficient iterative approach to SLR that has a remarkable property: for large i.i.d.\\ sub-Gaussian matrices $\\mathbf{A}$, its per-iteration behavior is rigorously characterized by a scalar state-evolution whose fixed points, when unique, are Bayes optimal. AMP, however, is fragile in that even small deviations from the i.i.d.\\ sub-Gaussian model can cause the algorithm to diverge. This paper considers a "vector AMP" (VAMP) algorithm and shows that VAMP has a rigorous scalar state-evolution that holds under a much broader class of large random matrices $\\mathbf{A}$: those that are right-rotationally invariant. After performing an initial singular value decomposition (SVD) of $\\mathbf{A}$, the per-iteration complexity of VAMP can be made similar to that of AMP. In addition, the fixed points of VAMP's state evolution are consistent with the replica prediction of the minimum mean-squared error recently derived by Tulino, Caire, Verd\\'u, and Shamai. The effectiveness and state evolution predictions of VAMP are confirmed in numerical experiments.
Countably QC-Approximating Posets
Mao, Xuxin; Xu, Luoshan
2014-01-01
As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σc(L)op of all σ-Scott-closed subsets of L is weakly generalized countably approximating. PMID:25165730
Function approximation using combined unsupervised and supervised learning.
Andras, Peter
2014-03-01
Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.
Estimation of distribution algorithms with Kikuchi approximations.
Santana, Roberto
2005-01-01
The question of finding feasible ways for estimating probability distributions is one of the main challenges for Estimation of Distribution Algorithms (EDAs). To estimate the distribution of the selected solutions, EDAs use factorizations constructed according to graphical models. The class of factorizations that can be obtained from these probability models is highly constrained. Expanding the class of factorizations that could be employed for probability approximation is a necessary step for the conception of more robust EDAs. In this paper we introduce a method for learning a more general class of probability factorizations. The method combines a reformulation of a probability approximation procedure known in statistical physics as the Kikuchi approximation of energy, with a novel approach for finding graph decompositions. We present the Markov Network Estimation of Distribution Algorithm (MN-EDA), an EDA that uses Kikuchi approximations to estimate the distribution, and Gibbs Sampling (GS) to generate new points. A systematic empirical evaluation of MN-EDA is done in comparison with different Bayesian network based EDAs. From our experiments we conclude that the algorithm can outperform other EDAs that use traditional methods of probability approximation in the optimization of functions with strong interactions among their variables.
Fast approximate stochastic tractography.
Iglesias, Juan Eugenio; Thompson, Paul M; Liu, Cheng-Yi; Tu, Zhuowen
2012-01-01
Many different probabilistic tractography methods have been proposed in the literature to overcome the limitations of classical deterministic tractography: (i) lack of quantitative connectivity information; and (ii) robustness to noise, partial volume effects and selection of seed region. However, these methods rely on Monte Carlo sampling techniques that are computationally very demanding. This study presents an approximate stochastic tractography algorithm (FAST) that can be used interactively, as opposed to having to wait several minutes to obtain the output after marking a seed region. In FAST, tractography is formulated as a Markov chain that relies on a transition tensor. The tensor is designed to mimic the features of a well-known probabilistic tractography method based on a random walk model and Monte-Carlo sampling, but can also accommodate other propagation rules. Compared to the baseline algorithm, our method circumvents the sampling process and provides a deterministic solution at the expense of partially sacrificing sub-voxel accuracy. Therefore, the method is strictly speaking not stochastic, but provides a probabilistic output in the spirit of stochastic tractography methods. FAST was compared with the random walk model using real data from 10 patients in two different ways: 1. the probability maps produced by the two methods on five well-known fiber tracts were directly compared using metrics from the image registration literature; and 2. the connectivity measurements between different regions of the brain given by the two methods were compared using the correlation coefficient ρ. The results show that the connectivity measures provided by the two algorithms are well-correlated (ρ = 0.83), and so are the probability maps (normalized cross correlation 0.818 ± 0.081). The maps are also qualitatively (i.e., visually) very similar. The proposed method achieves a 60x speed-up (7 s vs. 7 min) over the Monte Carlo sampling scheme, therefore
Approximating centrality in evolving graphs: toward sublinearity
NASA Astrophysics Data System (ADS)
Priest, Benjamin W.; Cybenko, George
2017-05-01
The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.
DALI: Derivative Approximation for LIkelihoods
NASA Astrophysics Data System (ADS)
Sellentin, Elena
2015-07-01
DALI (Derivative Approximation for LIkelihoods) is a fast approximation of non-Gaussian likelihoods. It extends the Fisher Matrix in a straightforward way and allows for a wider range of posterior shapes. The code is written in C/C++.
Taylor Approximations and Definite Integrals
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2007-01-01
We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)
Taylor Approximations and Definite Integrals
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2007-01-01
We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)
Approximate equilibria for Bayesian games
NASA Astrophysics Data System (ADS)
Mallozzi, Lina; Pusillo, Lucia; Tijs, Stef
2008-07-01
In this paper the problem of the existence of approximate equilibria in mixed strategies is central. Sufficient conditions are given under which approximate equilibria exist for non-finite Bayesian games. Further one possible approach is suggested to the problem of the existence of approximate equilibria for the class of multicriteria Bayesian games.
Combining global and local approximations
NASA Technical Reports Server (NTRS)
Haftka, Raphael T.
1991-01-01
A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.
Combining global and local approximations
Haftka, R.T. )
1991-09-01
A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model. 6 refs.
Phenomenological applications of rational approximants
NASA Astrophysics Data System (ADS)
Gonzàlez-Solís, Sergi; Masjuan, Pere
2016-08-01
We illustrate the powerfulness of Padé approximants (PAs) as a summation method and explore one of their extensions, the so-called quadratic approximant (QAs), to access both space- and (low-energy) time-like (TL) regions. As an introductory and pedagogical exercise, the function 1 zln(1 + z) is approximated by both kind of approximants. Then, PAs are applied to predict pseudoscalar meson Dalitz decays and to extract Vub from the semileptonic B → πℓνℓ decays. Finally, the π vector form factor in the TL region is explored using QAs.
Approximating Functions with Exponential Functions
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2005-01-01
The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…
Structural optimization with approximate sensitivities
NASA Technical Reports Server (NTRS)
Patnaik, S. N.; Hopkins, D. A.; Coroneos, R.
1994-01-01
Computational efficiency in structural optimization can be enhanced if the intensive computations associated with the calculation of the sensitivities, that is, gradients of the behavior constraints, are reduced. Approximation to gradients of the behavior constraints that can be generated with small amount of numerical calculations is proposed. Structural optimization with these approximate sensitivities produced correct optimum solution. Approximate gradients performed well for different nonlinear programming methods, such as the sequence of unconstrained minimization technique, method of feasible directions, sequence of quadratic programming, and sequence of linear programming. Structural optimization with approximate gradients can reduce by one third the CPU time that would otherwise be required to solve the problem with explicit closed-form gradients. The proposed gradient approximation shows potential to reduce intensive computation that has been associated with traditional structural optimization.
Approximate circuits for increased reliability
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
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.
Approximating subtree distances between phylogenies.
Bonet, Maria Luisa; St John, Katherine; Mahindru, Ruchi; Amenta, Nina
2006-10-01
We give a 5-approximation algorithm to the rooted Subtree-Prune-and-Regraft (rSPR) distance between two phylogenies, which was recently shown to be NP-complete. This paper presents the first approximation result for this important tree distance. The algorithm follows a standard format for tree distances. The novel ideas are in the analysis. In the analysis, the cost of the algorithm uses a "cascading" scheme that accounts for possible wrong moves. This accounting is missing from previous analysis of tree distance approximation algorithms. Further, we show how all algorithms of this type can be implemented in linear time and give experimental results.
NASA Technical Reports Server (NTRS)
Yao, M.-S.
1980-01-01
A study of the maintenance of the quasistationary waves forced by topography using a truncated two-level quasigeostrophic spectral model in a zonal channel on a beta-plane is presented. The model's motion contains wavenumbers 0, n, and 2n in the zonal direction, where n is the lowest eddy wavenumber and also the wavenumber of the topography. The study covered the two cases defined by n=2 and n=3; the spectral mode was integrated by initially perturbing the stationary solution of the equations governing the spectral coefficients, and a detailed energetics study was made of the quasiequilibrium state to study the maintenance of the quasistationary waves. The energy conversions required for maintaining these waves when n=3 imply that they are generated mainly by baroclinic stability of the forced waves; this type of baroclinic wave tends to become stationary to draw efficiently on the available energy of the forced wave.
NASA Astrophysics Data System (ADS)
Kumar, Umesh; Thatipamula, Shekar G.; Ganesh, R.; Saxena, Y. C.; Raju, D.
2016-10-01
In a simple toroidal device, the plasma profiles and properties depend on toroidal magnetic field topology. For example, the toroidal connection length crucially controls the adiabatic or non-adiabatic nature of electron dynamics, which in turn governs the nature of instabilities, fluctuations, and transport, the latter of which governs the plasma mean profiles. We present the results of extensive experiments in a simple toroidal device obtained by controlling the mean parallel connection length L ¯ c , by application of external vertical component of magnetic field Bv, where B v ≤ 2 % of toroidal magnetic field BT. Interestingly, for nearly closed field lines, which are characterized by large values of L ¯ c , it is found that flute like coherent modes are observed to be dominant and is accompanied by large poloidal flows. For small values of L ¯ c , the mean density on the high field side is seen to increase and the net poloidal flow reduces while a turbulent broad band in fluctuation spectrum is observed. Upon a gradual variation of L ¯ c from large to small values, continuous changes in mean plasma potential and density profiles, fluctuation, and poloidal flows demonstrate that in a simple toroidal device there exists a strong relationship between Lc, flows, and fluctuations. The net flow measured is found independent of the direction of Bv, but an asymmetry in the magnitude of the flow is found. The observed imbalance between the mean flow, fluctuation driven flow, and net flow is also discussed.
Lapshin, V. I.; Tarasov, I. K.; Tkachenko, I. V.; Tkachenko, V. I.
2006-01-15
Results of investigations of collective trap formation for a tubular electron beam which propagates in the conducting cylinder with a longitudinal magnetic field are submitted. It is shown that collective trap forms due to the double potential sag occurrence. Long lived particles accumulation may be theoretically described in the terms of shearless electron tubular beam rotation.
Rytov approximation in electron scattering
NASA Astrophysics Data System (ADS)
Krehl, Jonas; Lubk, Axel
2017-06-01
In this work we introduce the Rytov approximation in the scope of high-energy electron scattering with the motivation of developing better linear models for electron scattering. Such linear models play an important role in tomography and similar reconstruction techniques. Conventional linear models, such as the phase grating approximation, have reached their limits in current and foreseeable applications, most importantly in achieving three-dimensional atomic resolution using electron holographic tomography. The Rytov approximation incorporates propagation effects which are the most pressing limitation of conventional models. While predominately used in the weak-scattering regime of light microscopy, we show that the Rytov approximation can give reasonable results in the inherently strong-scattering regime of transmission electron microscopy.
Dual approximations in optimal control
NASA Technical Reports Server (NTRS)
Hager, W. W.; Ianculescu, G. D.
1984-01-01
A dual approximation for the solution to an optimal control problem is analyzed. The differential equation is handled with a Lagrange multiplier while other constraints are treated explicitly. An algorithm for solving the dual problem is presented.
Exponential approximations in optimal design
NASA Technical Reports Server (NTRS)
Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.
1990-01-01
One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.
Mathematical algorithms for approximate reasoning
NASA Technical Reports Server (NTRS)
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
Approximating random quantum optimization problems
NASA Astrophysics Data System (ADS)
Hsu, B.; Laumann, C. R.; Läuchli, A. M.; Moessner, R.; Sondhi, S. L.
2013-06-01
We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem k-body quantum satisfiability (k-QSAT) on large random graphs. As an approximation strategy, we optimize the solution space over “classical” product states, which in turn introduces a novel autonomous classical optimization problem, PSAT, over a space of continuous degrees of freedom rather than discrete bits. Our central results are (i) the derivation of a set of bounds and approximations in various limits of the problem, several of which we believe may be amenable to a rigorous treatment; (ii) a demonstration that an approximation based on a greedy algorithm borrowed from the study of frustrated magnetism performs well over a wide range in parameter space, and its performance reflects the structure of the solution space of random k-QSAT. Simulated annealing exhibits metastability in similar “hard” regions of parameter space; and (iii) a generalization of belief propagation algorithms introduced for classical problems to the case of continuous spins. This yields both approximate solutions, as well as insights into the free energy “landscape” of the approximation problem, including a so-called dynamical transition near the satisfiability threshold. Taken together, these results allow us to elucidate the phase diagram of random k-QSAT in a two-dimensional energy-density-clause-density space.
Function approximation using adaptive and overlapping intervals
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.
Wavelet Sparse Approximate Inverse Preconditioners
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Tang, W.-P.; Wan, W. L.
1996-01-01
There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.
Gadgets, approximation, and linear programming
Trevisan, L.; Sudan, M.; Sorkin, G.B.; Williamson, D.P.
1996-12-31
We present a linear-programming based method for finding {open_quotes}gadgets{close_quotes}, i.e., combinatorial structures reducing constraints of one optimization problems to constraints of another. A key step in this method is a simple observation which limits the search space to a finite one. Using this new method we present a number of new, computer-constructed gadgets for several different reductions. This method also answers a question posed by on how to prove the optimality of gadgets-we show how LP duality gives such proofs. The new gadgets improve hardness results for MAX CUT and MAX DICUT, showing that approximating these problems to within factors of 60/61 and 44/45 respectively is N P-hard. We also use the gadgets to obtain an improved approximation algorithm for MAX 3SAT which guarantees an approximation ratio of .801. This improves upon the previous best bound of .7704.
Rational approximations for tomographic reconstructions
NASA Astrophysics Data System (ADS)
Reynolds, Matthew; Beylkin, Gregory; Monzón, Lucas
2013-06-01
We use optimal rational approximations of projection data collected in x-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the measured data, i.e., double the number of available samples in each projection or, equivalently, extend (double) the domain of their Fourier transform. We also develop a new, fast, polar coordinate Fourier domain algorithm which uses our nonlinear approximation of projection data in a natural way. Using augmented projections of the Shepp-Logan phantom, we provide a comparison between the new algorithm and the standard filtered back-projection algorithm. We demonstrate that the reconstructed image has improved resolution without additional artifacts near sharp transitions in the image.
Heat pipe transient response approximation.
Reid, R. S.
2001-01-01
A simple and concise routine that approximates the response of an alkali metal heat pipe to changes in evaporator heat transfer rate is described. This analytically based routine is compared with data from a cylindrical heat pipe with a crescent-annular wick that undergoes gradual (quasi-steady) transitions through the viscous and condenser boundary heat transfer limits. The sonic heat transfer limit can also be incorporated into this routine for heat pipes with more closely coupled condensers. The advantages and obvious limitations of this approach are discussed. For reference, a source code listing for the approximation appears at the end of this paper.
Adaptive approximation models in optimization
Voronin, A.N.
1995-05-01
The paper proposes a method for optimization of functions of several variables that substantially reduces the number of objective function evaluations compared to traditional methods. The method is based on the property of iterative refinement of approximation models of the optimand function in approximation domains that contract to the extremum point. It does not require subjective specification of the starting point, step length, or other parameters of the search procedure. The method is designed for efficient optimization of unimodal functions of several (not more than 10-15) variables and can be applied to find the global extremum of polymodal functions and also for optimization of scalarized forms of vector objective functions.
Approximating spatially exclusive invasion processes.
Ross, Joshua V; Binder, Benjamin J
2014-05-01
A number of biological processes, such as invasive plant species and cell migration, are composed of two key mechanisms: motility and reproduction. Due to the spatially exclusive interacting behavior of these processes a cellular automata (CA) model is specified to simulate a one-dimensional invasion process. Three (independence, Poisson, and 2D-Markov chain) approximations are considered that attempt to capture the average behavior of the CA. We show that our 2D-Markov chain approximation accurately predicts the state of the CA for a wide range of motility and reproduction rates.
Galerkin approximations for dissipative magnetohydrodynamics
NASA Technical Reports Server (NTRS)
Chen, Hudong; Shan, Xiaowen; Montgomery, David
1990-01-01
A Galerkin approximation scheme is proposed for voltage-driven, dissipative magnetohydrodynamics. The trial functions are exact eigenfunctions of the linearized continuum equations and represent helical deformations of the axisymmetric, zero-flow, driven steady state. The lowest nontrivial truncation is explored: one axisymmetric trial function and one helical trial function each for the magnetic and velocity fields. The system resembles the Lorenz approximation to Benard convection, but in the region of believed applicability, its dynamical behavior is rather different, including relaxation to a helically deformed state similar to those that have emerged in the much higher resolution computations of Dahlburg et al.
Second Approximation to Conical Flows
1950-12-01
Public Release WRIGHT AIR DEVELOPMENT CENTER AF-WP-(B)-O-29 JUL 53 100 NOTICES ’When Government drawings, specifications, or other data are used V...so that the X, the approximation always depends on the ( "/)th, etc. Here the second approximation, i.e., the terms in C and 62, are computed and...the scheme shown in Fig. 1, the isentropic equations of motion are (cV-X2) +~X~C 6 +- 4= -x- 1 It is assumed that + Ux !E . $O’/ + (8) Introducing Eqs
Approximation methods for stochastic petri nets
NASA Technical Reports Server (NTRS)
Jungnitz, Hauke Joerg
1992-01-01
Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay
Pythagorean Approximations and Continued Fractions
ERIC Educational Resources Information Center
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…
Pythagorean Approximations and Continued Fractions
ERIC Educational Resources Information Center
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…
Singularly Perturbed Lie Bracket Approximation
Durr, Hans-Bernd; Krstic, Miroslav; Scheinker, Alexander; Ebenbauer, Christian
2015-03-27
Here, we consider the interconnection of two dynamical systems where one has an input-affine vector field. We show that by employing a singular perturbation analysis and the Lie bracket approximation technique, the stability of the overall system can be analyzed by regarding the stability properties of two reduced, uncoupled systems.
On stochastic approximation algorithms for classes of PAC learning problems
Rao, N.S.V.; Uppuluri, V.R.R.; Oblow, E.M.
1994-03-01
The classical stochastic approximation methods are shown to yield algorithms to solve several formulations of the PAC learning problem defined on the domain [o,1]{sup d}. Under some assumptions on different ability of the probability measure functions, simple algorithms to solve some PAC learning problems are proposed based on networks of non-polynomial units (e.g. artificial neural networks). Conditions on the sizes of these samples required to ensure the error bounds are derived using martingale inequalities.
Approximate Sensory Data Collection: A Survey.
Cheng, Siyao; Cai, Zhipeng; Li, Jianzhong
2017-03-10
With the rapid development of the Internet of Things (IoTs), wireless sensor networks (WSNs) and related techniques, the amount of sensory data manifests an explosive growth. In some applications of IoTs and WSNs, the size of sensory data has already exceeded several petabytes annually, which brings too many troubles and challenges for the data collection, which is a primary operation in IoTs and WSNs. Since the exact data collection is not affordable for many WSN and IoT systems due to the limitations on bandwidth and energy, many approximate data collection algorithms have been proposed in the last decade. This survey reviews the state of the art of approximatedatacollectionalgorithms. Weclassifythemintothreecategories: themodel-basedones, the compressive sensing based ones, and the query-driven ones. For each category of algorithms, the advantages and disadvantages are elaborated, some challenges and unsolved problems are pointed out, and the research prospects are forecasted.
Ab initio dynamical vertex approximation
NASA Astrophysics Data System (ADS)
Galler, Anna; Thunström, Patrik; Gunacker, Patrik; Tomczak, Jan M.; Held, Karsten
2017-03-01
Diagrammatic extensions of dynamical mean-field theory (DMFT) such as the dynamical vertex approximation (DΓ A) allow us to include nonlocal correlations beyond DMFT on all length scales and proved their worth for model calculations. Here, we develop and implement an Ab initio DΓ A approach (AbinitioDΓ A ) for electronic structure calculations of materials. The starting point is the two-particle irreducible vertex in the two particle-hole channels which is approximated by the bare nonlocal Coulomb interaction and all local vertex corrections. From this, we calculate the full nonlocal vertex and the nonlocal self-energy through the Bethe-Salpeter equation. The AbinitioDΓ A approach naturally generates all local DMFT correlations and all nonlocal G W contributions, but also further nonlocal correlations beyond: mixed terms of the former two and nonlocal spin fluctuations. We apply this new methodology to the prototypical correlated metal SrVO3.
Random-Phase Approximation Methods
NASA Astrophysics Data System (ADS)
Chen, Guo P.; Voora, Vamsee K.; Agee, Matthew M.; Balasubramani, Sree Ganesh; Furche, Filipp
2017-05-01
Random-phase approximation (RPA) methods are rapidly emerging as cost-effective validation tools for semilocal density functional computations. We present the theoretical background of RPA in an intuitive rather than formal fashion, focusing on the physical picture of screening and simple diagrammatic analysis. A new decomposition of the RPA correlation energy into plasmonic modes leads to an appealing visualization of electron correlation in terms of charge density fluctuations. Recent developments in the areas of beyond-RPA methods, RPA correlation potentials, and efficient algorithms for RPA energy and property calculations are reviewed. The ability of RPA to approximately capture static correlation in molecules is quantified by an analysis of RPA natural occupation numbers. We illustrate the use of RPA methods in applications to small-gap systems such as open-shell d- and f-element compounds, radicals, and weakly bound complexes, where semilocal density functional results exhibit strong functional dependence.
Testing the frozen flow approximation
NASA Technical Reports Server (NTRS)
Lucchin, Francesco; Matarrese, Sabino; Melott, Adrian L.; Moscardini, Lauro
1993-01-01
We investigate the accuracy of the frozen-flow approximation (FFA), recently proposed by Matarrese, et al. (1992), for following the nonlinear evolution of cosmological density fluctuations under gravitational instability. We compare a number of statistics between results of the FFA and n-body simulations, including those used by Melott, Pellman & Shandarin (1993) to test the Zel'dovich approximation. The FFA performs reasonably well in a statistical sense, e.g. in reproducing the counts-in-cell distribution, at small scales, but it does poorly in the crosscorrelation with n-body which means it is generally not moving mass to the right place, especially in models with high small-scale power.
Potential of the approximation method
Amano, K.; Maruoka, A.
1996-12-31
Developing some techniques for the approximation method, we establish precise versions of the following statements concerning lower bounds for circuits that detect cliques of size s in a graph with m vertices: For 5 {le} s {le} m/4, a monotone circuit computing CLIQUE(m, s) contains at least (1/2)1.8{sup min}({radical}s-1/2,m/(4s)) gates: If a non-monotone circuit computes CLIQUE using a {open_quotes}small{close_quotes} amount of negation, then the circuit contains an exponential number of gates. The former is proved very simply using so called bottleneck counting argument within the framework of approximation, whereas the latter is verified introducing a notion of restricting negation and generalizing the sunflower contraction.
Nonlinear Filtering and Approximation Techniques
1991-09-01
Shwartz), Academic Press (1991). [191 M.Cl. ROUTBAUD, Fiting lindairc par morceaux avec petit bruit d’obserration, These. Universit6 de Provence ( 1990...Kernel System (GKS), Academic Press (1983). 181 H.J. KUSHNER, Probability methods for approximations in stochastic control and for elliptic equations... Academic Press (1977). [9] F. LE GLAND, Time discretization of nonlinear filtering equations, in: 28th. IEEE CDC, Tampa, pp. 2601-2606. IEEE Press (1989
Analytical solution approximation for bearing
NASA Astrophysics Data System (ADS)
Hanafi, Lukman; Mufid, M. Syifaul
2017-08-01
The purpose of lubrication is to separate two surfaces sliding past each other with a film of some material which can be sheared without causing any damage to the surfaces. Reynolds equation is a basic equation for fluid lubrication which is applied in the bearing problem. This equation can be derived from Navier-Stokes equation and continuity equation. In this paper Reynolds equation is solved using analytical approximation by making simplification to obtain pressure distribution.
Ultrafast approximation for phylogenetic bootstrap.
Minh, Bui Quang; Nguyen, Minh Anh Thi; von Haeseler, Arndt
2013-05-01
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and the Shimodaira-Hasegawa-like approximate likelihood ratio test have been introduced to speed up the bootstrap. Here, we suggest an ultrafast bootstrap approximation approach (UFBoot) to compute the support of phylogenetic groups in maximum likelihood (ML) based trees. To achieve this, we combine the resampling estimated log-likelihood method with a simple but effective collection scheme of candidate trees. We also propose a stopping rule that assesses the convergence of branch support values to automatically determine when to stop collecting candidate trees. UFBoot achieves a median speed up of 3.1 (range: 0.66-33.3) to 10.2 (range: 1.32-41.4) compared with RAxML RBS for real DNA and amino acid alignments, respectively. Moreover, our extensive simulations show that UFBoot is robust against moderate model violations and the support values obtained appear to be relatively unbiased compared with the conservative standard bootstrap. This provides a more direct interpretation of the bootstrap support. We offer an efficient and easy-to-use software (available at http://www.cibiv.at/software/iqtree) to perform the UFBoot analysis with ML tree inference.
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
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. PMID:26161994
Computer Experiments for Function Approximations
Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C
2007-10-15
This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative.
Approximate reasoning using terminological models
NASA Technical Reports Server (NTRS)
Yen, John; Vaidya, Nitin
1992-01-01
Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved.
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.
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
Neighbourhood approximation using randomized forests.
Konukoglu, Ender; Glocker, Ben; Zikic, Darko; Criminisi, Antonio
2013-10-01
Leveraging available annotated data is an essential component of many modern methods for medical image analysis. In particular, approaches making use of the "neighbourhood" structure between images for this purpose have shown significant potential. Such techniques achieve high accuracy in analysing an image by propagating information from its immediate "neighbours" within an annotated database. Despite their success in certain applications, wide use of these methods is limited due to the challenging task of determining the neighbours for an out-of-sample image. This task is either computationally expensive due to large database sizes and costly distance evaluations, or infeasible due to distance definitions over semantic information, such as ground truth annotations, which is not available for out-of-sample images. This article introduces Neighbourhood Approximation Forests (NAFs), a supervised learning algorithm providing a general and efficient approach for the task of approximate nearest neighbour retrieval for arbitrary distances. Starting from an image training database and a user-defined distance between images, the algorithm learns to use appearance-based features to cluster images approximating the neighbourhood structured induced by the distance. NAF is able to efficiently infer nearest neighbours of an out-of-sample image, even when the original distance is based on semantic information. We perform experimental evaluation in two different scenarios: (i) age prediction from brain MRI and (ii) patch-based segmentation of unregistered, arbitrary field of view CT images. The results demonstrate the performance, computational benefits, and potential of NAF for different image analysis applications. Copyright © 2013 Elsevier B.V. All rights reserved.
Topics in Multivariate Approximation Theory.
1982-05-01
of the Bramble -Hilbert lemma (see Bramble & Hhert (13ŕ). Kergin’s scheme raises some questions. In .ontrast £.t its univar- iate antecedent, it...J. R. Rice (19791# An adaptive algorithm for multivariate approximation giving optimal convergence rates, J.Approx. Theory 25, 337-359. J. H. Bramble ...J.Numer.Anal. 7, 112-124. J. H. Bramble & S. R. Hilbert (19711, BoUnds for a class of linear functionals with applications to Hermite interpolation
Approximate transferability in conjugated polyalkenes
NASA Astrophysics Data System (ADS)
Eskandari, Keiamars; Mandado, Marcos; Mosquera, Ricardo A.
2007-03-01
QTAIM computed atomic and bond properties, as well as delocalization indices (obtained from electron densities computed at HF, MP2 and B3LYP levels) of several linear and branched conjugated polyalkenes and O- and N-containing conjugated polyenes have been employed to assess approximate transferable CH groups. The values of these properties indicate the effects of the functional group extend to four CH groups, whereas those of the terminal carbon affect up to three carbons. Ternary carbons also modify significantly the properties of atoms in α, β and γ.
Improved non-approximability results
Bellare, M.; Sudan, M.
1994-12-31
We indicate strong non-approximability factors for central problems: N{sup 1/4} for Max Clique; N{sup 1/10} for Chromatic Number; and 66/65 for Max 3SAT. Underlying the Max Clique result is a proof system in which the verifier examines only three {open_quotes}free bits{close_quotes} to attain an error of 1/2. Underlying the Chromatic Number result is a reduction from Max Clique which is more efficient than previous ones.
Approximation for Bayesian Ability Estimation.
1987-02-18
posterior pdfs of ande are given by p(-[Y) p(F) F P((y lei’ j)P )d. SiiJ i (4) a r~d p(e Iy) - p(t0) 1 J i P(Yij ei, (5) As shown in Tsutakawa and Lin...inverse A Hessian of the log of (27) with respect to , evaulatedat a Then, under regularity conditions, the marginal posterior pdf of O is...two-way contingency tables. Journal of Educational Statistics, 11, 33-56. Lindley, D.V. (1980). Approximate Bayesian methods. Trabajos Estadistica , 31
Fermion tunneling beyond semiclassical approximation
Majhi, Bibhas Ranjan
2009-02-15
Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in R. Banerjee and B. R. Majhi, J. High Energy Phys. 06 (2008) 095 for the scalar particle, Hawking radiation as tunneling of the Dirac particle through an event horizon is analyzed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly.
Generalized Gradient Approximation Made Simple
Perdew, J.P.; Burke, K.; Ernzerhof, M.
1996-10-01
Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}
Approximate Matrix Diagonalization for Use in Distributed Control Networks
1999-01-01
2, 3, . . . , L, Pi = Po for i oddPe for i even (3.32) This process is depicted graphically in Figure 3.1. The resulting transform Q1 is of the...smart sensors. where, for i = 2, 3, . . . , L, Pi = Po for i oddPe for i even (3.61) Hence, we have constructed a transform of the form Q1 = ΘLPL
Head Related Transfer Function Approximation Using Neural Networks.
1994-12-01
start at the very top. No one deserves more credit for this work than my Lord and Savior- Jesus Christ. My thesis committee, composed of Dr. Steve Rogers...to the right (23:3). Binaural mixing console is an electronic device that contains filters which con- vert a monophonic signal to a binaural signal
A Production Network Model and Its Diffusion Approximation.
1982-09-01
Buffers. 3 .....................-............ 9, - ’*** * ** ** *-- . 8 4 . . . . . . . . . . . * sheet metal , or the cooling of hot liquid Input in a...Appear. ;4 (71 Xglebart, D. and Whitt, W., -Multiple Channel Queue in Havy Traffic I,- Advances In Applied Probability, Vol. 2, 1970, pp. 150-177. (81 Ito
Laguerre approximation of random foams
NASA Astrophysics Data System (ADS)
Liebscher, André
2015-09-01
Stochastic models for the microstructure of foams are valuable tools to study the relations between microstructure characteristics and macroscopic properties. Owing to the physical laws behind the formation of foams, Laguerre tessellations have turned out to be suitable models for foams. Laguerre tessellations are weighted generalizations of Voronoi tessellations, where polyhedral cells are formed through the interaction of weighted generator points. While both share the same topology, the cell curvature of foams allows only an approximation by Laguerre tessellations. This makes the model fitting a challenging task, especially when the preservation of the local topology is required. In this work, we propose an inversion-based approach to fit a Laguerre tessellation model to a foam. The idea is to find a set of generator points whose tessellation best fits the foam's cell system. For this purpose, we transform the model fitting into a minimization problem that can be solved by gradient descent-based optimization. The proposed algorithm restores the generators of a tessellation if it is known to be Laguerre. If, as in the case of foams, no exact solution is possible, an approximative solution is obtained that maintains the local topology.
Wavelet Approximation in Data Assimilation
NASA Technical Reports Server (NTRS)
Tangborn, Andrew; Atlas, Robert (Technical Monitor)
2002-01-01
Estimation of the state of the atmosphere with the Kalman filter remains a distant goal because of high computational cost of evolving the error covariance for both linear and nonlinear systems. Wavelet approximation is presented here as a possible solution that efficiently compresses both global and local covariance information. We demonstrate the compression characteristics on the the error correlation field from a global two-dimensional chemical constituent assimilation, and implement an adaptive wavelet approximation scheme on the assimilation of the one-dimensional Burger's equation. In the former problem, we show that 99%, of the error correlation can be represented by just 3% of the wavelet coefficients, with good representation of localized features. In the Burger's equation assimilation, the discrete linearized equations (tangent linear model) and analysis covariance are projected onto a wavelet basis and truncated to just 6%, of the coefficients. A nearly optimal forecast is achieved and we show that errors due to truncation of the dynamics are no greater than the errors due to covariance truncation.
Rational approximations to fluid properties
Kincaid, J.M.
1990-05-01
The purpose of this report is to summarize some results that were presented at the Spring AIChE meeting in Orlando, Florida (20 March 1990). We report on recent attempts to develop a systematic method, based on the technique of rational approximation, for creating mathematical models of real-fluid equations of state and related properties. Equation-of-state models for real fluids are usually created by selecting a function {tilde p} (T,{rho}) that contains a set of parameters {l brace}{gamma}{sub i}{r brace}; the {l brace}{gamma}{sub i}{r brace} is chosen such that {tilde p}(T,{rho}) provides a good fit to the experimental data. (Here p is the pressure, T the temperature and {rho} is the density). In most cases a nonlinear least-squares numerical method is used to determine {l brace}{gamma}{sub i}{r brace}. There are several drawbacks to this method: one has essentially to guess what {tilde p}(T,{rho}) should be; the critical region is seldom fit very well and nonlinear numerical methods are time consuming and sometimes not very stable. The rational approximation approach we describe may eliminate all of these drawbacks. In particular it lets the data choose the function {tilde p}(T,{rho}) and its numerical implementation involves only linear algorithms. 27 refs., 5 figs.
Analytical approximations for spiral waves
Löber, Jakob Engel, Harald
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.
Interplay of approximate planning strategies.
Huys, Quentin J M; Lally, Níall; Faulkner, Paul; Eshel, Neir; Seifritz, Erich; Gershman, Samuel J; Dayan, Peter; Roiser, Jonathan P
2015-03-10
Humans routinely formulate plans in domains so complex that even the most powerful computers are taxed. To do so, they seem to avail themselves of many strategies and heuristics that efficiently simplify, approximate, and hierarchically decompose hard tasks into simpler subtasks. Theoretical and cognitive research has revealed several such strategies; however, little is known about their establishment, interaction, and efficiency. Here, we use model-based behavioral analysis to provide a detailed examination of the performance of human subjects in a moderately deep planning task. We find that subjects exploit the structure of the domain to establish subgoals in a way that achieves a nearly maximal reduction in the cost of computing values of choices, but then combine partial searches with greedy local steps to solve subtasks, and maladaptively prune the decision trees of subtasks in a reflexive manner upon encountering salient losses. Subjects come idiosyncratically to favor particular sequences of actions to achieve subgoals, creating novel complex actions or "options."
Indexing the approximate number system.
Inglis, Matthew; Gilmore, Camilla
2014-01-01
Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects.
Approximating metal-insulator transitions
NASA Astrophysics Data System (ADS)
Danieli, Carlo; Rayanov, Kristian; Pavlov, Boris; Martin, Gaven; Flach, Sergej
2015-12-01
We consider quantum wave propagation in one-dimensional quasiperiodic lattices. We propose an iterative construction of quasiperiodic potentials from sequences of potentials with increasing spatial period. At each finite iteration step, the eigenstates reflect the properties of the limiting quasiperiodic potential properties up to a controlled maximum system size. We then observe approximate Metal-Insulator Transitions (MIT) at the finite iteration steps. We also report evidence on mobility edges, which are at variance to the celebrated Aubry-André model. The dynamics near the MIT shows a critical slowing down of the ballistic group velocity in the metallic phase, similar to the divergence of the localization length in the insulating phase.
Analytical approximations for spiral waves.
Löber, Jakob; Engel, Harald
2013-12-01
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(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(+)) dependence improves the result by Keener and Tyson for spiral waves pinned to a circular defect of radius R(+) 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.
IONIS: Approximate atomic photoionization intensities
NASA Astrophysics Data System (ADS)
Heinäsmäki, Sami
2012-02-01
A program to compute relative atomic photoionization cross sections is presented. The code applies the output of the multiconfiguration Dirac-Fock method for atoms in the single active electron scheme, by computing the overlap of the bound electron states in the initial and final states. The contribution from the single-particle ionization matrix elements is assumed to be the same for each final state. This method gives rather accurate relative ionization probabilities provided the single-electron ionization matrix elements do not depend strongly on energy in the region considered. The method is especially suited for open shell atoms where electronic correlation in the ionic states is large. Program summaryProgram title: IONIS Catalogue identifier: AEKK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1149 No. of bytes in distributed program, including test data, etc.: 12 877 Distribution format: tar.gz Programming language: Fortran 95 Computer: Workstations Operating system: GNU/Linux, Unix Classification: 2.2, 2.5 Nature of problem: Photoionization intensities for atoms. Solution method: The code applies the output of the multiconfiguration Dirac-Fock codes Grasp92 [1] or Grasp2K [2], to compute approximate photoionization intensities. The intensity is computed within the one-electron transition approximation and by assuming that the sum of the single-particle ionization probabilities is the same for all final ionic states. Restrictions: The program gives nonzero intensities for those transitions where only one electron is removed from the initial configuration(s). Shake-type many-electron transitions are not computed. The ionized shell must be closed in the initial state. Running time: Few seconds for a
Approximate analytic solutions to the NPDD: Short exposure approximations
NASA Astrophysics Data System (ADS)
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.
A new approximate solution for chlorine concentration decay in pipes.
Yeh, Hund-Der; Wen, Shi-Bin; Chang, Ya-Chi; Lu, Chung-Sying
2008-05-01
Biswas et al. (1993. A model for chlorine concentration decay in pipes. Water Res. 27(12), 1715-1724) presented an analytical solution of a two-dimensional (2-D) steady-state chlorine transport equation in a pipe under the turbulent condition and employed fractional error function and regression technique to develop an approximate solution. However, their approximate solution may not give a good result if the wall decay parameter is large. This paper provides a more accurate approximate solution of the 2-D steady-state chlorine transport equation under the turbulent condition. This new approximate solution has advantages of easy evaluation and good accuracy when compared with the approximate solution given by Biswas et al. (1993). In addition, this paper also develops a methodology that combines simulated annealing (SA) with this new approximate solution to determine the wall decay parameter. Two cases are chosen to demonstrate the application of the present approximate solution and methodology. The first case is to use this new approximate solution in simulating chlorine decay in pipes with the experiment-observed data given by Rossman (2006. The effect of advanced treatment on chlorine decay in metallic pipes. Water Res. 40(13), 2493-2502), while the second case presents the determination of the wall consumption at the end of the pipe network.
The Casimir Energy for the Riemann Caps
NASA Astrophysics Data System (ADS)
Palesheva, E. V.; Pecheritsyn, A. A.
2017-03-01
The Casimir energy of a massive scalar field on a Riemann cap with the Dirichlet boundary conditions is calculated. The problem is considered in the quasi-stationary approximation. Formulas are derived which are suitable for numerical calculations.
The Casimir Energy for the Riemann Caps
NASA Astrophysics Data System (ADS)
Palesheva, E. V.; Pecheritsyn, A. A.
2017-03-01
The Casimir energy of a massive scalar field on a Riemann cap with the Dirichlet boundary conditions is calculated. The problem is considered in the quasi-stationary approximation. Formulas are derived which are suitable for numerical calculations.
B-term approximation using tree-structured Haar transforms
NASA Astrophysics Data System (ADS)
Ho, Hsin-Han; Egiazarian, Karen O.; Mitra, Sanjit K.
2009-02-01
We present a heuristic solution for B-term approximation using Tree-Structured Haar (TSH) transforms. Our solution consists of two main stages: best basis selection and greedy approximation. In addition, when approximating the same signal with different B constraint or error metric, our solution also provides the flexibility of having less overall running time at expense of more storage space. We adopted lattice structure to index basis vectors, so that one index value can fully specify a basis vector. Based on the concept of fast computation of TSH transform by butterfly network, we also developed an algorithm for directly deriving butterfly parameters and incorporated it into our solution. Results show that, when the error metric is normalized l1-norm and normalized l2-norm, our solution has comparable (sometimes better) approximation quality with prior data synopsis algorithms.
Multidimensional stochastic approximation Monte Carlo
NASA Astrophysics Data System (ADS)
Zablotskiy, Sergey V.; Ivanov, Victor A.; Paul, Wolfgang
2016-06-01
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g (E ) , of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g (E1,E2) . We show when and why care has to be exercised when obtaining the microcanonical density of states g (E1+E2) from g (E1,E2) .
Randomized approximate nearest neighbors algorithm
Jones, Peter Wilcox; Osipov, Andrei; Rokhlin, Vladimir
2011-01-01
We present a randomized algorithm for the approximate nearest neighbor problem in d-dimensional Euclidean space. Given N points {xj} in , the algorithm attempts to find k nearest neighbors for each of xj, 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·k2·(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 {xj} for an arbitrary point . 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 {xj} and illustrate its performance via several numerical examples. PMID:21885738
Interplay of approximate planning strategies
Huys, Quentin J. M.; Lally, Níall; Faulkner, Paul; Eshel, Neir; Seifritz, Erich; Gershman, Samuel J.; Dayan, Peter; Roiser, Jonathan P.
2015-01-01
Humans routinely formulate plans in domains so complex that even the most powerful computers are taxed. To do so, they seem to avail themselves of many strategies and heuristics that efficiently simplify, approximate, and hierarchically decompose hard tasks into simpler subtasks. Theoretical and cognitive research has revealed several such strategies; however, little is known about their establishment, interaction, and efficiency. Here, we use model-based behavioral analysis to provide a detailed examination of the performance of human subjects in a moderately deep planning task. We find that subjects exploit the structure of the domain to establish subgoals in a way that achieves a nearly maximal reduction in the cost of computing values of choices, but then combine partial searches with greedy local steps to solve subtasks, and maladaptively prune the decision trees of subtasks in a reflexive manner upon encountering salient losses. Subjects come idiosyncratically to favor particular sequences of actions to achieve subgoals, creating novel complex actions or “options.” PMID:25675480
Femtolensing: Beyond the semiclassical approximation
NASA Technical Reports Server (NTRS)
Ulmer, Andrew; Goodman, Jeremy
1995-01-01
Femtolensoing is a gravitational lensing effect in which the magnification is a function not only of the position and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of 10(exp -13) - 10(exp -16) solar mass) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculation in general potentials. The physical optics results presented here differ at low frequencies from the semiclassical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semicalssical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10(exp -11) solar mass, much larger than previously believed. Additionally, we discuss the possibility of a search femtolensing of white dwarfs in the Large Magellanic Cloud at optical wavelengths.
Kohsokabe, Takahiro; Kaneko, Kunihiko
2016-01-01
Search for possible relationships between phylogeny and ontogeny is important in evolutionary-developmental biology. Here we uncover such relationships by numerical evolution and unveil their origin in terms of dynamical systems theory. By representing developmental dynamics of spatially located cells with gene expression dynamics with cell-to-cell interaction under external morphogen gradient, gene regulation networks are evolved under mutation and selection with the fitness to approach a prescribed spatial pattern of expressed genes. For most numerical evolution experiments, evolution of pattern over generations and development of pattern by an evolved network exhibit remarkable congruence. Both in the evolution and development pattern changes consist of several epochs where stripes are formed in a short time, while for other temporal regimes, pattern hardly changes. In evolution, these quasi-stationary regimes are generations needed to hit relevant mutations, while in development, they are due to some gene expression that varies slowly and controls the pattern change. The morphogenesis is regulated by combinations of feedback or feedforward regulations, where the upstream feedforward network reads the external morphogen gradient, and generates a pattern used as a boundary condition for the later patterns. The ordering from up to downstream is common in evolution and development, while the successive epochal changes in development and evolution are represented as common bifurcations in dynamical-systems theory, which lead to the evolution-development congruence. Mechanism of exceptional violation of the congruence is also unveiled. Our results provide a new look on developmental stages, punctuated equilibrium, developmental bottlenecks, and evolutionary acquisition of novelty in morphogenesis. © 2015 The Authors. Journal of Experimental Zoology Part B: Molecular and Developmental Evolution Published by Wiley Periodicals, Inc.
[Complex systems variability analysis using approximate entropy].
Cuestas, Eduardo
2010-01-01
Biological systems are highly complex systems, both spatially and temporally. They are rooted in an interdependent, redundant and pleiotropic interconnected dynamic network. The properties of a system are different from those of their parts, and they depend on the integrity of the whole. The systemic properties vanish when the system breaks down, while the properties of its components are maintained. The disease can be understood as a systemic functional alteration of the human body, which present with a varying severity, stability and durability. Biological systems are characterized by measurable complex rhythms, abnormal rhythms are associated with disease and may be involved in its pathogenesis, they are been termed "dynamic disease." Physicians have long time recognized that alterations of physiological rhythms are associated with disease. Measuring absolute values of clinical parameters yields highly significant, clinically useful information, however evaluating clinical parameters the variability provides additionally useful clinical information. The aim of this review was to study one of the most recent advances in the measurement and characterization of biological variability made possible by the development of mathematical models based on chaos theory and nonlinear dynamics, as approximate entropy, has provided us with greater ability to discern meaningful distinctions between biological signals from clinically distinct groups of patients.
Producing approximate answers to database queries
NASA Technical Reports Server (NTRS)
Vrbsky, Susan V.; Liu, Jane W. S.
1993-01-01
We have designed and implemented a query processor, called APPROXIMATE, that makes approximate answers available if part of the database is unavailable or if there is not enough time to produce an exact answer. The accuracy of the approximate answers produced improves monotonically with the amount of data retrieved to produce the result. The exact answer is produced if all of the needed data are available and query processing is allowed to continue until completion. The monotone query processing algorithm of APPROXIMATE works within the standard relational algebra framework and can be implemented on a relational database system with little change to the relational architecture. We describe here the approximation semantics of APPROXIMATE that serves as the basis for meaningful approximations of both set-valued and single-valued queries. We show how APPROXIMATE is implemented to make effective use of semantic information, provided by an object-oriented view of the database, and describe the additional overhead required by APPROXIMATE.
Rough Set Approximations in Formal Concept Analysis
NASA Astrophysics Data System (ADS)
Yamaguchi, Daisuke; Murata, Atsuo; Li, Guo-Dong; Nagai, Masatake
Conventional set approximations are based on a set of attributes; however, these approximations cannot relate an object to the corresponding attribute. In this study, a new model for set approximation based on individual attributes is proposed for interval-valued data. Defining an indiscernibility relation is omitted since each attribute value itself has a set of values. Two types of approximations, single- and multiattribute approximations, are presented. A multi-attribute approximation has two solutions: a maximum and a minimum solution. A maximum solution is a set of objects that satisfy the condition of approximation for at least one attribute. A minimum solution is a set of objects that satisfy the condition for all attributes. The proposed set approximation is helpful in finding the features of objects relating to condition attributes when interval-valued data are given. The proposed model contributes to feature extraction in interval-valued information systems.
An approximation technique for jet impingement flow
Najafi, Mahmoud; Fincher, Donald; Rahni, Taeibi; Javadi, KH.; Massah, H.
2015-03-10
The analytical approximate solution of a non-linear jet impingement flow model will be demonstrated. We will show that this is an improvement over the series approximation obtained via the Adomian decomposition method, which is itself, a powerful method for analysing non-linear differential equations. The results of these approximations will be compared to the Runge-Kutta approximation in order to demonstrate their validity.
Energy conservation - A test for scattering approximations
NASA Technical Reports Server (NTRS)
Acquista, C.; Holland, A. C.
1980-01-01
The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method.
Approximation method for the kinetic Boltzmann equation
NASA Technical Reports Server (NTRS)
Shakhov, Y. M.
1972-01-01
The further development of a method for approximating the Boltzmann equation is considered and a case of pseudo-Maxwellian molecules is treated in detail. A method of approximating the collision frequency is discussed along with a method for approximating the moments of the Boltzmann collision integral. Since the return collisions integral and the collision frequency are expressed through the distribution function moments, use of the proposed methods make it possible to reduce the Boltzmann equation to a series of approximating equations.
Energy conservation - A test for scattering approximations
NASA Technical Reports Server (NTRS)
Acquista, C.; Holland, A. C.
1980-01-01
The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method.
Compressive Imaging via Approximate Message Passing
2015-09-04
We propose novel compressive imaging algorithms that employ approximate message passing (AMP), which is an iterative signal estimation algorithm that...Approved for Public Release; Distribution Unlimited Final Report: Compressive Imaging via Approximate Message Passing The views, opinions and/or findings...Research Triangle Park, NC 27709-2211 approximate message passing , compressive imaging, compressive sensing, hyperspectral imaging, signal reconstruction
Fractal Trigonometric Polynomials for Restricted Range Approximation
NASA Astrophysics Data System (ADS)
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.
On Approximation of Distribution and Density Functions.
ERIC Educational Resources Information Center
Wolff, Hans
Stochastic approximation algorithms for least square error approximation to density and distribution functions are considered. The main results are necessary and sufficient parameter conditions for the convergence of the approximation processes and a generalization to some time-dependent density and distribution functions. (Author)
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.
A unified approach to the Darwin approximation
Krause, Todd B.; Apte, A.; Morrison, P. J.
2007-10-15
There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting.
Approximation error in PDE-based modelling of vehicular platoons
NASA Astrophysics Data System (ADS)
Hao, He; Barooah, Prabir
2012-08-01
We study the problem of how much error is introduced in approximating the dynamics of a large vehicular platoon by using a partial differential equation, as was done in Barooah, Mehta, and Hespanha [Barooah, P., Mehta, P.G., and Hespanha, J.P. (2009), 'Mistuning-based Decentralised Control of Vehicular Platoons for Improved Closed Loop Stability', IEEE Transactions on Automatic Control, 54, 2100-2113], Hao, Barooah, and Mehta [Hao, H., Barooah, P., and Mehta, P.G. (2011), 'Stability Margin Scaling Laws of Distributed Formation Control as a Function of Network Structure', IEEE Transactions on Automatic Control, 56, 923-929]. In particular, we examine the difference between the stability margins of the coupled-ordinary differential equations (ODE) model and its partial differential equation (PDE) approximation, which we call the approximation error. The stability margin is defined as the absolute value of the real part of the least stable pole. The PDE model has proved useful in the design of distributed control schemes (Barooah et al. 2009; Hao et al. 2011); it provides insight into the effect of gains of local controllers on the closed-loop stability margin that is lacking in the coupled-ODE model. Here we show that the ratio of the approximation error to the stability margin is O(1/N), where N is the number of vehicles. Thus, the PDE model is an accurate approximation of the coupled-ODE model when N is large. Numerical computations are provided to corroborate the analysis.
Ribeiro, Fabiano; Opper, Manfred
2011-04-01
We discuss the expectation propagation (EP) algorithm for approximate Bayesian inference using a factorizing posterior approximation. For neural network models, we use a central limit theorem argument to make EP tractable when the number of parameters is large. For two types of models, we show that EP can achieve optimal generalization performance when data are drawn from a simple distribution.
Cosmological applications of Padé approximant
Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan E-mail: 764644314@qq.com
2014-01-01
As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.
Approximations in the performance evaluation of queueing systems. Final technical report
Knessl, Charles; Tier, Charles
2001-06-06
The research program on this grant was to develop new asymptotic and perturbation methods for approximating the performance of queueing systems. This involved obtaining approximations to complicated equations.The approximations provide accurate formulas for the performance measures. Queueing models of these types arise in the analysis of computer and communications systems such as ATM networks. In addition, the methods developed in the proposal were also found to be applicable to other stochastic and diffusion models.
Approximate dynamic model of a turbojet engine
NASA Technical Reports Server (NTRS)
Artemov, O. A.
1978-01-01
An approximate dynamic nonlinear model of a turbojet engine is elaborated on as a tool in studying the aircraft control loop, with the turbojet engine treated as an actuating component. Approximate relationships linking the basic engine parameters and shaft speed are derived to simplify the problem, and to aid in constructing an approximate nonlinear dynamic model of turbojet engine performance useful for predicting aircraft motion.
The JWKB approximation in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Craig, David; Singh, Parampreet
2017-01-01
We explore the JWKB approximation in loop quantum cosmology in a flat universe with a scalar matter source. Exact solutions of the quantum constraint are studied at small volume in the JWKB approximation in order to assess the probability of tunneling to small or zero volume. Novel features of the approximation are discussed which appear due to the fact that the model is effectively a two-dimensional dynamical system. Based on collaborative work with Parampreet Singh.
Piecewise linear approximation for hereditary control problems
NASA Technical Reports Server (NTRS)
Propst, Georg
1990-01-01
This paper presents finite-dimensional approximations for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems, when a quadratic cost integral must be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in the case where the cost integral ranges over a finite time interval, as well as in the case where it ranges over an infinite time interval. The arguments in the last case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense.
Bent approximations to synchrotron radiation optics
Heald, S.
1981-01-01
Ideal optical elements can be approximated by bending flats or cylinders. This paper considers the applications of these approximate optics to synchrotron radiation. Analytic and raytracing studies are used to compare their optical performance with the corresponding ideal elements. It is found that for many applications the performance is adequate, with the additional advantages of lower cost and greater flexibility. Particular emphasis is placed on obtaining the practical limitations on the use of the approximate elements in typical beamline configurations. Also considered are the possibilities for approximating very long length mirrors using segmented mirrors.
Inversion and approximation of Laplace transforms
NASA Technical Reports Server (NTRS)
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.
Approximate methods for equations of incompressible fluid
NASA Astrophysics Data System (ADS)
Galkin, V. A.; Dubovik, A. O.; Epifanov, A. A.
2017-02-01
Approximate methods on the basis of sequential approximations in the theory of functional solutions to systems of conservation laws is considered, including the model of dynamics of incompressible fluid. Test calculations are performed, and a comparison with exact solutions is carried out.
Quirks of Stirling's Approximation
ERIC Educational Resources Information Center
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…
Spline approximations for nonlinear hereditary control systems
NASA Technical Reports Server (NTRS)
Daniel, P. L.
1982-01-01
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Computing Functions by Approximating the Input
ERIC Educational Resources Information Center
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…
Quirks of Stirling's Approximation
ERIC Educational Resources Information Center
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…
An approximation for inverse Laplace transforms
NASA Technical Reports Server (NTRS)
Lear, W. M.
1981-01-01
Programmable calculator runs simple finite-series approximation for Laplace transform inversions. Utilizing family of orthonormal functions, approximation is used for wide range of transforms, including those encountered in feedback control problems. Method works well as long as F(t) decays to zero as it approaches infinity and so is appliable to most physical systems.
Piecewise linear approximation for hereditary control problems
NASA Technical Reports Server (NTRS)
Propst, Georg
1987-01-01
Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
NASA Technical Reports Server (NTRS)
1974-01-01
The objectives, functions, and organization, of the Deep Space Network are summarized. Deep Space stations, ground communications, and network operations control capabilities are described. The network is designed for two-way communications with unmanned spacecraft traveling approximately 1600 km from earth to the farthest planets in the solar system. It has provided tracking and data acquisition support for the following projects: Ranger, Surveyor, Mariner, Pioneer, Apollo, Helios, Viking, and the Lunar Orbiter.
Albuquerque Basin seismic network
Jaksha, Lawrence H.; Locke, Jerry; Thompson, J.B.; Garcia, Alvin
1977-01-01
The U.S. Geological Survey has recently completed the installation of a seismic network around the Albuquerque Basin in New Mexico. The network consists of two seismometer arrays, a thirteen-station array monitoring an area of approximately 28,000 km 2 and an eight-element array monitoring the area immediately adjacent to the Albuquerque Seismological Laboratory. This report describes the instrumentation deployed in the network.
Three-dimensional inelastic approximate analysis code (MOMM)
NASA Technical Reports Server (NTRS)
Meister, Jeffrey P.
1988-01-01
The Mechanics of Materials Model (MOMM) is one of a series of new stand-alone three dimensional nonlinear structural analysis codes. Incorporation of a general purpose finite element computer code into the hot section design process was severely limited by the high costs involved. MOMM is a stiffness method finite element code that uses an internally generated network of beams to characterize hot section component behavior. The method was proposed as a fast, easy to use, computationally efficient tool for approximate analyses. MOMM incorporates a wide variety of analysis capabilities, material models, and load type specifiers instrumental for the analysis of hot section components.
Approximation algorithms for the min-power symmetric connectivity problem
NASA Astrophysics Data System (ADS)
Plotnikov, Roman; Erzin, Adil; Mladenovic, Nenad
2016-10-01
We consider the NP-hard problem of synthesis of optimal spanning communication subgraph in a given arbitrary simple edge-weighted graph. This problem occurs in the wireless networks while minimizing the total transmission power consumptions. We propose several new heuristics based on the variable neighborhood search metaheuristic for the approximation solution of the problem. We have performed a numerical experiment where all proposed algorithms have been executed on the randomly generated test samples. For these instances, on average, our algorithms outperform the previously known heuristics.
An Examination of New Paradigms for Spline Approximations.
Witzgall, Christoph; Gilsinn, David E; McClain, Marjorie A
2006-01-01
Lavery splines are examined in the univariate and bivariate cases. In both instances relaxation based algorithms for approximate calculation of Lavery splines are proposed. Following previous work Gilsinn, et al. [7] addressing the bivariate case, a rotationally invariant functional is assumed. The version of bivariate splines proposed in this paper also aims at irregularly spaced data and uses Hseih-Clough-Tocher elements based on the triangulated irregular network (TIN) concept. In this paper, the univariate case, however, is investigated in greater detail so as to further the understanding of the bivariate case.
Bahrami, Arash; Assadi, Amir H.; Markley, John L.; Eghbalnia, Hamid R.
2009-01-01
The process of assigning a finite set of tags or labels to a collection of observations, subject to side conditions, is notable for its computational complexity. This labeling paradigm is of theoretical and practical relevance to a wide range of biological applications, including the analysis of data from DNA microarrays, metabolomics experiments, and biomolecular nuclear magnetic resonance (NMR) spectroscopy. We present a novel algorithm, called Probabilistic Interaction Network of Evidence (PINE), that achieves robust, unsupervised probabilistic labeling of data. The computational core of PINE uses estimates of evidence derived from empirical distributions of previously observed data, along with consistency measures, to drive a fictitious system M with Hamiltonian H to a quasi-stationary state that produces probabilistic label assignments for relevant subsets of the data. We demonstrate the successful application of PINE to a key task in protein NMR spectroscopy: that of converting peak lists extracted from various NMR experiments into assignments associated with probabilities for their correctness. This application, called PINE-NMR, is available from a freely accessible computer server (http://pine.nmrfam.wisc.edu). The PINE-NMR server accepts as input the sequence of the protein plus user-specified combinations of data corresponding to an extensive list of NMR experiments; it provides as output a probabilistic assignment of NMR signals (chemical shifts) to sequence-specific backbone and aliphatic side chain atoms plus a probabilistic determination of the protein secondary structure. PINE-NMR can accommodate prior information about assignments or stable isotope labeling schemes. As part of the analysis, PINE-NMR identifies, verifies, and rectifies problems related to chemical shift referencing or erroneous input data. PINE-NMR achieves robust and consistent results that have been shown to be effective in subsequent steps of NMR structure determination. PMID
Bahrami, Arash; Assadi, Amir H; Markley, John L; Eghbalnia, Hamid R
2009-03-01
The process of assigning a finite set of tags or labels to a collection of observations, subject to side conditions, is notable for its computational complexity. This labeling paradigm is of theoretical and practical relevance to a wide range of biological applications, including the analysis of data from DNA microarrays, metabolomics experiments, and biomolecular nuclear magnetic resonance (NMR) spectroscopy. We present a novel algorithm, called Probabilistic Interaction Network of Evidence (PINE), that achieves robust, unsupervised probabilistic labeling of data. The computational core of PINE uses estimates of evidence derived from empirical distributions of previously observed data, along with consistency measures, to drive a fictitious system M with Hamiltonian H to a quasi-stationary state that produces probabilistic label assignments for relevant subsets of the data. We demonstrate the successful application of PINE to a key task in protein NMR spectroscopy: that of converting peak lists extracted from various NMR experiments into assignments associated with probabilities for their correctness. This application, called PINE-NMR, is available from a freely accessible computer server (http://pine.nmrfam.wisc.edu). The PINE-NMR server accepts as input the sequence of the protein plus user-specified combinations of data corresponding to an extensive list of NMR experiments; it provides as output a probabilistic assignment of NMR signals (chemical shifts) to sequence-specific backbone and aliphatic side chain atoms plus a probabilistic determination of the protein secondary structure. PINE-NMR can accommodate prior information about assignments or stable isotope labeling schemes. As part of the analysis, PINE-NMR identifies, verifies, and rectifies problems related to chemical shift referencing or erroneous input data. PINE-NMR achieves robust and consistent results that have been shown to be effective in subsequent steps of NMR structure determination.
Frankenstein's glue: transition functions for approximate solutions
NASA Astrophysics Data System (ADS)
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.
Stochastic population dynamics: The Poisson approximation
NASA Astrophysics Data System (ADS)
Solari, Hernán G.; Natiello, Mario A.
2003-03-01
We introduce an approximation to stochastic population dynamics based on almost independent Poisson processes whose parameters obey a set of coupled ordinary differential equations. The approximation applies to systems that evolve in terms of events such as death, birth, contagion, emission, absorption, etc., and we assume that the event-rates satisfy a generalized mass-action law. The dynamics of the populations is then the result of the projection from the space of events into the space of populations that determine the state of the system (phase space). The properties of the Poisson approximation are studied in detail. Especially, error bounds for the moment generating function and the generating function receive particular attention. The deterministic approximation for the population fractions and the Langevin-type approximation for the fluctuations around the mean value are recovered within the framework of the Poisson approximation as particular limit cases. However, the proposed framework allows to treat other limit cases and general situations with small populations that lie outside the scope of the standard approaches. The Poisson approximation can be viewed as a general (numerical) integration scheme for this family of problems in population dynamics.
Approximating Light Rays in the Schwarzschild Field
NASA Astrophysics Data System (ADS)
Semerák, O.
2015-02-01
A short formula is suggested that 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 behavior is also discussed, important for lensing. An example is attached indicating that the newly suggested approximation is usable—and very accurate—for practically solving the ray-deflection exercise.
Approximate knowledge compilation: The first order case
Val, A. del
1996-12-31
Knowledge compilation procedures make a knowledge base more explicit so as make inference with respect to the compiled knowledge base tractable or at least more efficient. Most work to date in this area has been restricted to the propositional case, despite the importance of first order theories for expressing knowledge concisely. Focusing on (LUB) approximate compilation, our contribution is twofold: (1) We present a new ground algorithm for approximate compilation which can produce exponential savings with respect to the previously known algorithm. (2) We show that both ground algorithms can be lifted to the first order case preserving their correctness for approximate compilation.
Approximate Bruechner orbitals in electron propagator calculations
Ortiz, J.V.
1999-12-01
Orbitals and ground-state correlation amplitudes from the so-called Brueckner doubles approximation of coupled-cluster theory provide a useful reference state for electron propagator calculations. An operator manifold with hold, particle, two-hole-one-particle and two-particle-one-hole components is chosen. The resulting approximation, third-order algebraic diagrammatic construction [2ph-TDA, ADC (3)] and 3+ methods. The enhanced versatility of this approximation is demonstrated through calculations on valence ionization energies, core ionization energies, electron detachment energies of anions, and on a molecule with partial biradical character, ozone.
Alternative approximation concepts for space frame synthesis
NASA Technical Reports Server (NTRS)
Lust, R. V.; Schmit, L. A.
1985-01-01
A method for space frame synthesis based on the application of a full gamut of approximation concepts is presented. It is found that with the thoughtful selection of design space, objective function approximation, constraint approximation and mathematical programming problem formulation options it is possible to obtain near minimum mass designs for a significant class of space frame structural systems while requiring fewer than 10 structural analyses. Example problems are presented which demonstrate the effectiveness of the method for frame structures subjected to multiple static loading conditions with limits on structural stiffness and strength.
APPROXIMATING LIGHT RAYS IN THE SCHWARZSCHILD FIELD
Semerák, O.
2015-02-10
A short formula is suggested that 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 behavior is also discussed, important for lensing. An example is attached indicating that the newly suggested approximation is usable—and very accurate—for practically solving the ray-deflection exercise.
Information geometry of mean-field approximation.
Tanaka, T
2000-08-01
I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models. Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of mean-field approximation of general orders is derived. It includes in a natural way the "naive" mean-field approximation and is consistent with the Thouless-Anderson-Palmer (TAP) approach and the linear response theorem in statistical physics.
A Survey of Techniques for Approximate Computing
Mittal, Sparsh
2016-03-18
Approximate computing trades off computation quality with the effort expended and as rising performance demands confront with plateauing resource budgets, approximate computing has become, not merely attractive, but even imperative. Here, we present a survey of techniques for approximate computing (AC). We discuss strategies for finding approximable program portions and monitoring output quality, techniques for using AC in different processing units (e.g., CPU, GPU and FPGA), processor components, memory technologies etc., and programming frameworks for AC. Moreover, we classify these techniques based on several key characteristics to emphasize their similarities and differences. Finally, the aim of this paper is to provide insights to researchers into working of AC techniques and inspire more efforts in this area to make AC the mainstream computing approach in future systems.
A Survey of Techniques for Approximate Computing
Mittal, Sparsh
2016-03-18
Approximate computing trades off computation quality with the effort expended and as rising performance demands confront with plateauing resource budgets, approximate computing has become, not merely attractive, but even imperative. Here, we present a survey of techniques for approximate computing (AC). We discuss strategies for finding approximable program portions and monitoring output quality, techniques for using AC in different processing units (e.g., CPU, GPU and FPGA), processor components, memory technologies etc., and programming frameworks for AC. Moreover, we classify these techniques based on several key characteristics to emphasize their similarities and differences. Finally, the aim of this paper is tomore » provide insights to researchers into working of AC techniques and inspire more efforts in this area to make AC the mainstream computing approach in future systems.« less
Approximate probability distributions of the master equation.
Thomas, Philipp; Grima, Ramon
2015-07-01
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.
Linear Approximation SAR Azimuth Processing Study
NASA Technical Reports Server (NTRS)
Lindquist, R. B.; Masnaghetti, R. K.; Belland, E.; Hance, H. V.; Weis, W. G.
1979-01-01
A segmented linear approximation of the quadratic phase function that is used to focus the synthetic antenna of a SAR was studied. Ideal focusing, using a quadratic varying phase focusing function during the time radar target histories are gathered, requires a large number of complex multiplications. These can be largely eliminated by using linear approximation techniques. The result is a reduced processor size and chip count relative to ideally focussed processing and a correspondingly increased feasibility for spaceworthy implementation. A preliminary design and sizing for a spaceworthy linear approximation SAR azimuth processor meeting requirements similar to those of the SEASAT-A SAR was developed. The study resulted in a design with approximately 1500 IC's, 1.2 cubic feet of volume, and 350 watts of power for a single look, 4000 range cell azimuth processor with 25 meters resolution.
AN APPROXIMATE EQUATION OF STATE OF SOLIDS.
research. By generalizing experimental data and obtaining unified relations describing the thermodynamic properties of solids, and approximate equation of state is derived which can be applied to a wide class of materials. (Author)
Approximate Controllability Results for Linear Viscoelastic Flows
NASA Astrophysics Data System (ADS)
Chowdhury, Shirshendu; Mitra, Debanjana; Ramaswamy, Mythily; Renardy, Michael
2017-09-01
We consider linear viscoelastic flow of a multimode Maxwell or Jeffreys fluid in a bounded domain with smooth boundary, with a distributed control in the momentum equation. We establish results on approximate and exact controllability.
Approximation concepts for efficient structural synthesis
NASA Technical Reports Server (NTRS)
Schmit, L. A., Jr.; Miura, H.
1976-01-01
It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.
Approximate probability distributions of the master equation
NASA Astrophysics Data System (ADS)
Thomas, Philipp; Grima, Ramon
2015-07-01
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.
Computational aspects of pseudospectral Laguerre approximations
NASA Technical Reports Server (NTRS)
Funaro, Daniele
1989-01-01
Pseudospectral approximations in unbounded domains by Laguerre polynomials lead to ill-conditioned algorithms. Introduced are a scaling function and appropriate numerical procedures in order to limit these unpleasant phenomena.
Polynomial approximation of functions in Sobolev spaces
Dupont, T.; Scott, R.
1980-04-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Computing functions by approximating the input
NASA Astrophysics Data System (ADS)
Goldberg, Mayer
2012-12-01
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 output. Our approach assumes only the most rudimentary knowledge of algebra and trigonometry, and makes no use of calculus.
Approximate String Matching with Reduced Alphabet
NASA Astrophysics Data System (ADS)
Salmela, Leena; Tarhio, Jorma
We present a method to speed up approximate string matching by mapping the factual alphabet to a smaller alphabet. We apply the alphabet reduction scheme to a tuned version of the approximate Boyer-Moore algorithm utilizing the Four-Russians technique. Our experiments show that the alphabet reduction makes the algorithm faster. Especially in the k-mismatch case, the new variation is faster than earlier algorithms for English data with small values of k.
Some Recent Progress for Approximation Algorithms
NASA Astrophysics Data System (ADS)
Kawarabayashi, Ken-ichi
We survey some recent progress on approximation algorithms. Our main focus is the following two problems that have some recent breakthroughs; the edge-disjoint paths problem and the graph coloring problem. These breakthroughs involve the following three ingredients that are quite central in approximation algorithms: (1) Combinatorial (graph theoretical) approach, (2) LP based approach and (3) Semi-definite programming approach. We also sketch how they are used to obtain recent development.
Polynomial approximation of functions in Sobolev spaces
NASA Technical Reports Server (NTRS)
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.
Polynomial approximation of functions in Sobolev spaces
NASA Technical Reports Server (NTRS)
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.
Nonlinear Stochastic PDEs: Analysis and Approximations
2016-05-23
3.4.1 Nonlinear Stochastic PDEs: Analysis and Approximations We compare Wiener chaos and stochastic collocation methods for linear advection-reaction...ADDRESS (ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 nonlinear stochastic PDEs (SPDEs), nonlocal SPDEs, Navier...3.4.1 Nonlinear Stochastic PDEs: Analysis and Approximations Report Title We compare Wiener chaos and stochastic collocation methods for linear
Approximations and Solution Estimates in Optimization
2016-04-06
Approximations and Solution Estimates in Optimization Johannes O. Royset Operations Research Department Naval Postgraduate School joroyset@nps.edu...Abstract. Approximation is central to many optimization problems and the supporting theory pro- vides insight as well as foundation for algorithms. In...functions quantifies epi-convergence, we are able to obtain estimates of optimal solutions and optimal values through estimates of that distance. In
The closure approximation in the hierarchy equations.
NASA Technical Reports Server (NTRS)
Adomian, G.
1971-01-01
The expectation of the solution process in a stochastic operator equation can be obtained from averaged equations only under very special circumstances. Conditions for validity are given and the significance and validity of the approximation in widely used hierarchy methods and the ?self-consistent field' approximation in nonequilibrium statistical mechanics are clarified. The error at any level of the hierarchy can be given and can be avoided by the use of the iterative method.
An improved proximity force approximation for electrostatics
Fosco, Cesar D.; Lombardo, Fernando C.; Mazzitelli, Francisco D.
2012-08-15
A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated with their shapes. Indeed, in the so called 'proximity force approximation' the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contributions of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied in different contexts, ranging from nuclear physics to Casimir effect calculations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy contained between the surfaces. The results obtained could be useful for discussing the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip-sample electrostatic interaction in atomic force microscopes. - Highlights: Black-Right-Pointing-Pointer The proximity force approximation (PFA) has been widely used in different areas. Black-Right-Pointing-Pointer The PFA can be improved using a derivative expansion in the shape of the surfaces. Black-Right-Pointing-Pointer We use the improved PFA to compute electrostatic forces between conductors. Black-Right-Pointing-Pointer The results can be used as an analytic benchmark for numerical calculations in AFM. Black-Right-Pointing-Pointer Insight is provided for people who use the PFA to compute nuclear and Casimir forces.
Configurable hardware integrate and fire neurons for sparse approximation.
Shapero, Samuel; Rozell, Christopher; Hasler, Paul
2013-09-01
Sparse approximation is an important optimization problem in signal and image processing applications. A Hopfield-Network-like system of integrate and fire (IF) neurons is proposed as a solution, using the Locally Competitive Algorithm (LCA) to solve an overcomplete L1 sparse approximation problem. A scalable system architecture is described, including IF neurons with a nonlinear firing function, and current-based synapses to provide linear computation. A network of 18 neurons with 12 inputs is implemented on the RASP 2.9v chip, a Field Programmable Analog Array (FPAA) with directly programmable floating gate elements. Said system uses over 1400 floating gates, the largest system programmed on a FPAA to date. The circuit successfully reproduced the outputs of a digital optimization program, converging to within 4.8% RMS, and an objective cost only 1.7% higher on average. The active circuit consumed 559 μA of current at 2.4 V and converges on solutions in 25 μs, with measurement of the converged spike rate taking an additional 1 ms. Extrapolating the scaling trends to a N=1000 node system, the spiking LCA compares favorably with state-of-the-art digital solutions, and analog solutions using a non-spiking approach. Copyright © 2013 Elsevier Ltd. All rights reserved.
NASA Technical Reports Server (NTRS)
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.
NASA Technical Reports Server (NTRS)
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.
The tendon approximator device in traumatic injuries.
Forootan, Kamal S; Karimi, Hamid; Forootan, Nazilla-Sadat S
2015-01-01
Precise and tension-free approximation of two tendon endings is the key predictor of outcomes following tendon lacerations and repairs. We evaluate the efficacy of a new tendon approximator device in tendon laceration repairs. In a comparative study, we used our new tendon approximator device in 99 consecutive patients with laceration of 266 tendons who attend a university hospital and evaluated the operative time to repair the tendons, surgeons' satisfaction as well as patient's outcomes in a long-term follow-up. Data were compared with the data of control patients undergoing tendon repair by conventional method. Totally 266 tendons were repaired by approximator device and 199 tendons by conventional technique. 78.7% of patients in first group were male and 21.2% were female. In approximator group 38% of patients had secondary repair of cut tendons and 62% had primary repair. Patients were followed for a mean period of 3years (14-60 months). Time required for repair of each tendon was significantly reduced with the approximator device (2 min vs. 5.5 min, p<0.0001). After 3-4 weeks of immobilization, passive and active physiotherapy was started. Functional Results of tendon repair were identical in the two groups and were not significantly different. 1% of tendons in group A and 1.2% in group B had rupture that was not significantly different. The new nerve approximator device is cheap, feasible to use and reduces the time of tendon repair with sustained outcomes comparable to the conventional methods.
On uniform approximation of elliptic functions by Padé approximants
NASA Astrophysics Data System (ADS)
Khristoforov, Denis V.
2009-06-01
Diagonal Padé approximants of elliptic functions are studied. It is known that the absence of uniform convergence of such approximants is related to them having spurious poles that do not correspond to any singularities of the function being approximated. A sequence of piecewise rational functions is proposed, which is constructed from two neighbouring Padé approximants and approximates an elliptic function locally uniformly in the Stahl domain. The proof of the convergence of this sequence is based on deriving strong asymptotic formulae for the remainder function and Padé polynomials and on the analysis of the behaviour of a spurious pole. Bibliography: 23 titles.
Approximation of Bivariate Functions via Smooth Extensions
Zhang, Zhihua
2014-01-01
For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole space. These smooth extensions have simple and clear representations which are determined by this bivariate function and some polynomials. After that, we expand the smooth, periodic function into a Fourier series or a periodic wavelet series or we expand the smooth, compactly supported function into a wavelet series. Since our extensions are smooth, the obtained Fourier coefficients or wavelet coefficients decay very fast. Since our extension tools are polynomials, the moment theorem shows that a lot of wavelet coefficients vanish. From this, with the help of well-known approximation theorems, using our extension methods, the Fourier approximation and the wavelet approximation of the bivariate function on the general domain with small error are obtained. PMID:24683316
Recent advances in discrete dipole approximation
NASA Astrophysics Data System (ADS)
Flatau, P. J.
2012-12-01
I will describe recent advances and results related to Discrete Dipole Approximation. I will concentrate on Discrete Dipole Scattering (DDSCAT) code which has been jointly developed by myself and Bruce T. Draine. Discussion will concentrate on calculation of scattering and absorption by isolated particles (e.g., dust grains, ice crystals), calculations of scattering by periodic structures with applications to studies of scattering and absorption by periodic arrangement of finite cylinders, cubes, etc), very fast near field calculation, ways to display scattering targets and their composition using three dimensional graphical codes. I will discuss possible extensions. References Flatau, P. J. and Draine, B. T., 2012, Fast near field calculations in the discrete dipole approximation for regular rectilinear grids, Optics Express, 20, 1247-1252. Draine B. T. and Flatau P. J., 2008, Discrete-dipole approximation for periodic targets: theory and tests , J. Opt. Soc. Am. A., 25, 2693-2703. Draine BT and Flatau PJ, 2012, User Guide for the Discrete Dipole Approximation Code DDSCAT 7.2, arXiv:1202.3424v3.ear field calculations (Fast near field calculations in the discrete dipole approximation for regular rectilinear grids P. J. Flatau and B. T. Draine, Optics Express, Vol. 20, Issue 2, pp. 1247-1252 (2012))
MACFP: Maximal Approximate Consecutive Frequent Pattern Mining under Edit Distance
Shang, Jingbo; Peng, Jian; Han, Jiawei
2017-01-01
Consecutive pattern mining aiming at finding sequential patterns substrings, is a special case of frequent pattern mining and has been played a crucial role in many real world applications, especially in biological sequence analysis, time series analysis, and network log mining. Approximations, including insertions, deletions, and substitutions, between strings are widely used in biological sequence comparisons. However, most existing string pattern mining methods only consider hamming distance without insertions/deletions (indels). Little attention has been paid to the general approximate consecutive frequent pattern mining under edit distance, potentially due to the high computational complexity, particularly on DNA sequences with billions of base pairs. In this paper, we introduce an efficient solution to this problem. We first formulate the Maximal Approximate Consecutive Frequent Pattern Mining (MACFP) problem that identifies substring patterns under edit distance in a long query sequence. Then, we propose a novel algorithm with linear time complexity to check whether the support of a substring pattern is above a predefined threshold in the query sequence, thus greatly reducing the computational complexity of MACFP. With this fast decision algorithm, we can efficiently solve the original pattern discovery problem with several indexing and searching techniques. Comprehensive experiments on sequence pattern analysis and a study on cancer genomics application demonstrate the effectiveness and efficiency of our algorithm, compared to several existing methods. PMID:28174677
Multi-level methods and approximating distribution functions
NASA Astrophysics Data System (ADS)
Wilson, D.; Baker, R. E.
2016-07-01
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie's direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie's direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146-179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.
Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas
Bedford, Tim; Daneshkhah, Alireza
2015-01-01
Many applications of risk analysis require us to jointly model multiple uncertain quantities. Bayesian networks and copulas are two common approaches to modeling joint uncertainties with probability distributions. This article focuses on new methodologies for copulas by developing work of Cooke, Bedford, Kurowica, and others on vines as a way of constructing higher dimensional distributions that do not suffer from some of the restrictions of alternatives such as the multivariate Gaussian copula. The article provides a fundamental approximation result, demonstrating that we can approximate any density as closely as we like using vines. It further operationalizes this result by showing how minimum information copulas can be used to provide parametric classes of copulas that have such good levels of approximation. We extend previous approaches using vines by considering nonconstant conditional dependencies, which are particularly relevant in financial risk modeling. We discuss how such models may be quantified, in terms of expert judgment or by fitting data, and illustrate the approach by modeling two financial data sets. PMID:26332240
Multi-level methods and approximating distribution functions
Wilson, D. Baker, R. E.
2016-07-15
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie’s direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146–179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.
Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas.
Bedford, Tim; Daneshkhah, Alireza; Wilson, Kevin J
2016-04-01
Many applications of risk analysis require us to jointly model multiple uncertain quantities. Bayesian networks and copulas are two common approaches to modeling joint uncertainties with probability distributions. This article focuses on new methodologies for copulas by developing work of Cooke, Bedford, Kurowica, and others on vines as a way of constructing higher dimensional distributions that do not suffer from some of the restrictions of alternatives such as the multivariate Gaussian copula. The article provides a fundamental approximation result, demonstrating that we can approximate any density as closely as we like using vines. It further operationalizes this result by showing how minimum information copulas can be used to provide parametric classes of copulas that have such good levels of approximation. We extend previous approaches using vines by considering nonconstant conditional dependencies, which are particularly relevant in financial risk modeling. We discuss how such models may be quantified, in terms of expert judgment or by fitting data, and illustrate the approach by modeling two financial data sets.
Ancilla-approximable quantum state transformations
Blass, Andreas; Gurevich, Yuri
2015-04-15
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation.
Separable approximations of two-body interactions
NASA Astrophysics Data System (ADS)
Haidenbauer, J.; Plessas, W.
1983-01-01
We perform a critical discussion of the efficiency of the Ernst-Shakin-Thaler method for a separable approximation of arbitrary two-body interactions by a careful examination of separable 3S1-3D1 N-N potentials that were constructed via this method by Pieper. Not only the on-shell properties of these potentials are considered, but also a comparison is made of their off-shell characteristics relative to the Reid soft-core potential. We point out a peculiarity in Pieper's application of the Ernst-Shakin-Thaler method, which leads to a resonant-like behavior of his potential 3SD1D. It is indicated where care has to be taken in order to circumvent drawbacks inherent in the Ernst-Shakin-Thaler separable approximation scheme. NUCLEAR REACTIONS Critical discussion of the Ernst-Shakin-Thaler separable approximation method. Pieper's separable N-N potentials examined on shell and off shell.
Approximate solutions of the hyperbolic Kepler equation
NASA Astrophysics Data System (ADS)
Avendano, Martín; Martín-Molina, Verónica; Ortigas-Galindo, Jorge
2015-12-01
We provide an approximate zero widetilde{S}(g,L) for the hyperbolic Kepler's equation S-g {{arcsinh}}(S)-L=0 for gin (0,1) and Lin [0,∞ ). We prove, by using Smale's α -theory, that Newton's method starting at our approximate zero produces a sequence that converges to the actual solution S( g, L) at quadratic speed, i.e. if S_n is the value obtained after n iterations, then |S_n-S|≤ 0.5^{2^n-1}|widetilde{S}-S|. The approximate zero widetilde{S}(g,L) is a piecewise-defined function involving several linear expressions and one with cubic and square roots. In bounded regions of (0,1) × [0,∞ ) that exclude a small neighborhood of g=1, L=0, we also provide a method to construct simpler starters involving only constants.
Fast wavelet based sparse approximate inverse preconditioner
Wan, W.L.
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.
Approximation methods in gravitational-radiation theory
NASA Technical Reports Server (NTRS)
Will, C. M.
1986-01-01
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. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, 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 (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
Approximation methods in gravitational-radiation theory
NASA Technical Reports Server (NTRS)
Will, C. M.
1986-01-01
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. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, 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 (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
NASA Astrophysics Data System (ADS)
Tishchenko, V. N.; Shaikhislamov, I. F.
2006-01-01
A merging mechanism of shock waves in a plasma with a magnetic field is considered. The merging criterion is found at which a point source produces low-frequency waves of magnetic and vortex electric fields in the surroundings.
Exponential Approximations Using Fourier Series Partial Sums
NASA Technical Reports Server (NTRS)
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.
Approximating W projection as a separable kernel
NASA Astrophysics Data System (ADS)
Merry, Bruce
2016-02-01
W projection is a commonly used approach to allow interferometric imaging to be accelerated by fast Fourier transforms, but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show that they can be closely approximated by separable kernels. The error scales with the fourth power of the field of view, and so is small enough to be ignored at mid- to high frequencies. We also show that hybrid imaging algorithms combining W projection with either faceting, snapshotting, or W stacking allow the error to be made arbitrarily small, making the approximation suitable even for high-resolution wide-field instruments.
Approximate convective heating equations for hypersonic flows
NASA Technical Reports Server (NTRS)
Zoby, E. V.; Moss, J. N.; Sutton, K.
1979-01-01
Laminar and turbulent heating-rate equations appropriate for engineering predictions of the convective heating rates about blunt reentry spacecraft at hypersonic conditions are developed. The approximate methods are applicable to both nonreacting and reacting gas mixtures for either constant or variable-entropy edge conditions. A procedure which accounts for variable-entropy effects and is not based on mass balancing is presented. Results of the approximate heating methods are in good agreement with existing experimental results as well as boundary-layer and viscous-shock-layer solutions.
Bronchopulmonary segments approximation using anatomical atlas
NASA Astrophysics Data System (ADS)
Busayarat, Sata; Zrimec, Tatjana
2007-03-01
Bronchopulmonary segments are valuable as they give more accurate localization than lung lobes. Traditionally, determining the segments requires segmentation and identification of segmental bronchi, which, in turn, require volumetric imaging data. In this paper, we present a method for approximating the bronchopulmonary segments for sparse data by effectively using an anatomical atlas. The atlas is constructed from a volumetric data and contains accurate information about bronchopulmonary segments. A new ray-tracing based image registration is used for transferring the information from the atlas to a query image. Results show that the method is able to approximate the segments on sparse HRCT data with slice gap up to 25 millimeters.
Local density approximations from finite systems
NASA Astrophysics Data System (ADS)
Entwistle, M. T.; Hodgson, M. J. P.; Wetherell, J.; Longstaff, B.; Ramsden, J. D.; Godby, R. W.
2016-11-01
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 slablike 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.
Congruence Approximations for Entrophy Endowed Hyperbolic Systems
NASA Technical Reports Server (NTRS)
Barth, Timothy J.; Saini, Subhash (Technical Monitor)
1998-01-01
Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.
Very fast approximate reconstruction of MR images.
Angelidis, P A
1998-11-01
The ultra fast Fourier transform (UFFT) provides the means for a very fast computation of a magnetic resonance (MR) image, because it is implemented using only additions and no multiplications at all. It achieves this by approximating the complex exponential functions involved in the Fourier transform (FT) sum with computationally simpler periodic functions. This approximation introduces erroneous spectrum peaks of small magnitude. We examine the performance of this transform in some typical MRI signals. The results show that this transform can very quickly provide an MR image. It is proposed to be used as a replacement of the classically used FFT whenever a fast general overview of an image is required.
Characterizing inflationary perturbations: The uniform approximation
Habib, Salman; Heinen, Andreas; Heitmann, Katrin; Jungman, Gerard; Molina-Paris, Carmen
2004-10-15
The spectrum of primordial fluctuations from inflation can be obtained using a mathematically controlled, and systematically extendable, uniform approximation. Closed-form expressions for power spectra and spectral indices may be found without making explicit slow-roll assumptions. Here we provide details of our previous calculations, extend the results beyond leading-order in the approximation, and derive general error bounds for power spectra and spectral indices. Already at next-to-leading-order, the errors in calculating the power spectrum are less than a percent. This meets the accuracy requirement for interpreting next-generation cosmic microwave background observations.
An Approximation Scheme for Delay Equations.
1980-06-16
AD-Am" 155 BtO~i UNkIV PROVIDENCE RI LEFSCI4ETZ CENTER FOR DYNAMI-flO F/f 12/ 1 AN APPROXIMATION SCIEME FOR DELAY EQUATIONS (U) JUN 80 F KAPPEL DAA629...for publ.ic release IAM 19.. and 1s aftnaotaton in unhi tea.0 ( f) 1 DDC UtB Distwifeaton A_._il .rd/or 1 . Introduction. In recent years one can see...Banach spaces. Fundamental for our approach is the following approximation theorem for semigroups of type W: Theorem 1 ([10]). Let AN, N - 1,2,..., and A
Approximate learning algorithm in Boltzmann machines.
Yasuda, Muneki; Tanaka, Kazuyuki
2009-11-01
Boltzmann machines can be regarded as Markov random fields. For binary cases, they are equivalent to the Ising spin model in statistical mechanics. Learning systems in Boltzmann machines are one of the NP-hard problems. Thus, in general we have to use approximate methods to construct practical learning algorithms in this context. In this letter, we propose new and practical learning algorithms for Boltzmann machines by using the belief propagation algorithm and the linear response approximation, which are often referred as advanced mean field methods. Finally, we show the validity of our algorithm using numerical experiments.
An approximate classical unimolecular reaction rate theory
NASA Astrophysics Data System (ADS)
Zhao, Meishan; Rice, Stuart A.
1992-05-01
We describe a classical theory of unimolecular reaction rate which is derived from the analysis of Davis and Gray by use of simplifying approximations. These approximations concern the calculation of the locations of, and the fluxes of phase points across, the bottlenecks to fragmentation and to intramolecular energy transfer. The bottleneck to fragment separation is represented as a vibration-rotation state dependent separatrix, which approximation is similar to but extends and improves the approximations for the separatrix introduced by Gray, Rice, and Davis and by Zhao and Rice. The novel feature in our analysis is the representation of the bottlenecks to intramolecular energy transfer as dividing surfaces in phase space; the locations of these dividing surfaces are determined by the same conditions as locate the remnants of robust tori with frequency ratios related to the golden mean (in a two degree of freedom system these are the cantori). The flux of phase points across each dividing surface is calculated with an analytic representation instead of a stroboscopic mapping. The rate of unimolecular reaction is identified with the net rate at which phase points escape from the region of quasiperiodic bounded motion to the region of free fragment motion by consecutively crossing the dividing surfaces for intramolecular energy exchange and the separatrix. This new theory generates predictions of the rates of predissociation of the van der Waals molecules HeI2, NeI2 and ArI2 which are in very good agreement with available experimental data.
Alternative approximation concepts for space frame synthesis
NASA Technical Reports Server (NTRS)
Lust, R. V.; Schmit, L. A.
1985-01-01
A structural synthesis methodology for the minimum mass design of 3-dimensionall frame-truss structures under multiple static loading conditions and subject to limits on displacements, rotations, stresses, local buckling, and element cross-sectional dimensions is presented. A variety of approximation concept options are employed to yield near optimum designs after no more than 10 structural analyses. Available options include: (A) formulation of the nonlinear mathematcal programming problem in either reciprocal section property (RSP) or cross-sectional dimension (CSD) space; (B) two alternative approximate problem structures in each design space; and (C) three distinct assumptions about element end-force variations. Fixed element, design element linking, and temporary constraint deletion features are also included. The solution of each approximate problem, in either its primal or dual form, is obtained using CONMIN, a feasible directions program. The frame-truss synthesis methodology is implemented in the COMPASS computer program and is used to solve a variety of problems. These problems were chosen so that, in addition to exercising the various approximation concepts options, the results could be compared with previously published work.
Approximations For Controls Of Hereditary Systems
NASA Technical Reports Server (NTRS)
Milman, Mark H.
1988-01-01
Convergence properties of controls, trajectories, and feedback kernels analyzed. Report discusses use of factorization techniques to approximate optimal feedback gains in finite-time, linear-regulator/quadratic-cost-function problem of system governed by retarded-functional-difference equations RFDE's with control delays. Presents approach to factorization based on discretization of state penalty leading to simple structure for feedback control law.
Progressive Image Coding by Hierarchical Linear Approximation.
ERIC Educational Resources Information Center
Wu, Xiaolin; Fang, Yonggang
1994-01-01
Proposes a scheme of hierarchical piecewise linear approximation as an adaptive image pyramid. A progressive image coder comes naturally from the proposed image pyramid. The new pyramid is semantically more powerful than regular tessellation but syntactically simpler than free segmentation. This compromise between adaptability and complexity…
Quickly Approximating the Distance Between Two Objects
NASA Technical Reports Server (NTRS)
Hammen, David
2009-01-01
A method of quickly approximating the distance between two objects (one smaller, regarded as a point; the other larger and complexly shaped) has been devised for use in computationally simulating motions of the objects for the purpose of planning the motions to prevent collisions.
Approximate Solution to the Generalized Boussinesq Equation
NASA Astrophysics Data System (ADS)
Telyakovskiy, A. S.; Mortensen, J.
2010-12-01
The traditional Boussinesq equation describes motion of water in groundwater flows. It models unconfined groundwater flow under the Dupuit assumption that the equipotential lines are vertical, making the flowlines horizontal. The Boussinesq equation is a nonlinear diffusion equation with diffusivity depending linearly on water head. Here we analyze a generalization of the Boussinesq equation, when the diffusivity is a power law function of water head. For example polytropic gases moving through porous media obey this equation. Solving this equation usually requires numerical approximations, but for certain classes of initial and boundary conditions an approximate analytical solution can be constructed. This work focuses on the latter approach, using the scaling properties of the equation. We consider one-dimensional semi-infinite initially empty aquifer with boundary conditions at the inlet in case of cylindrical symmetry. Such situation represents the case of an injection well. Solutions would propagate with the finite speed. We construct an approximate scaling function, and we compare the approximate solution with the direct numerical solutions obtained by using the scaling properties of the equations.
Semiclassical Approximations and Predictability in Ocean Acoustics
1999-09-30
the ONR-funded work being performed by P. Worcester (SIO), J. Colosi (WHOI), M. Wolfson (WSU), J. Spiesberger (UPenn), S. 2 Tomsovic (WSU), G...Acoust. Soc. Am. 103, 2232-2235. Tappert, F. D., Spiesberger , J. L., and L. Boden (1995) New full-wave approximation for ocean acoustic travel time
Approximated integrability of the Dicke model
NASA Astrophysics Data System (ADS)
Relaño, A.; Bastarrachea-Magnani, M. A.; Lerma-Hernández, S.
2016-12-01
A very approximate second integral of motion of the Dicke model is identified within a broad energy region above the ground state, and for a wide range of values of the external parameters. This second integral, obtained from a Born-Oppenheimer approximation, classifies the whole regular part of the spectrum in bands, coming from different semi-classical energy surfaces, and labelled by its corresponding eigenvalues. Results obtained from this approximation are compared with exact numerical diagonalization for finite systems in the superradiant phase, obtaining a remarkable accord. The region of validity of our approach in the parameter space, which includes the resonant case, is unveiled. The energy range of validity goes from the ground state up to a certain upper energy where chaos sets in, and extends far beyond the range of applicability of a simple harmonic approximation around the minimal energy configuration. The upper energy validity limit increases for larger values of the coupling constant and the ratio between the level splitting and the frequency of the field. These results show that the Dicke model behaves like a two-degree-of-freedom integrable model for a wide range of energies and values of the external parameters.
Can Distributional Approximations Give Exact Answers?
ERIC Educational Resources Information Center
Griffiths, Martin
2013-01-01
Some mathematical activities and investigations for the classroom or the lecture theatre can appear rather contrived. This cannot, however, be levelled at the idea given here, since it is based on a perfectly sensible question concerning distributional approximations that was posed by an undergraduate student. Out of this simple question, and…
Local discontinuous Galerkin approximations to Richards’ equation
NASA Astrophysics Data System (ADS)
Li, H.; Farthing, M. W.; Dawson, C. N.; Miller, C. T.
2007-03-01
We consider the numerical approximation to Richards' equation because of its hydrological significance and intrinsic merit as a nonlinear parabolic model that admits sharp fronts in space and time that pose a special challenge to conventional numerical methods. We combine a robust and established variable order, variable step-size backward difference method for time integration with an evolving spatial discretization approach based upon the local discontinuous Galerkin (LDG) method. We formulate the approximation using a method of lines approach to uncouple the time integration from the spatial discretization. The spatial discretization is formulated as a set of four differential algebraic equations, which includes a mass conservation constraint. We demonstrate how this system of equations can be reduced to the solution of a single coupled unknown in space and time and a series of local constraint equations. We examine a variety of approximations at discontinuous element boundaries, permeability approximations, and numerical quadrature schemes. We demonstrate an optimal rate of convergence for smooth problems, and compare accuracy and efficiency for a wide variety of approaches applied to a set of common test problems. We obtain robust and efficient results that improve upon existing methods, and we recommend a future path that should yield significant additional improvements.
Approximating a nonlinear MTFDE from physiology
NASA Astrophysics Data System (ADS)
Teodoro, M. Filomena
2016-12-01
This paper describes a numerical scheme which approximates the solution of a nonlinear mixed type functional differential equation from nerve conduction theory. The solution of such equation is defined in all the entire real axis and tends to known values at ±∞. A numerical method extended from linear case is developed and applied to solve a nonlinear equation.
Large Hierarchies from Approximate R Symmetries
Kappl, Rolf; Ratz, Michael; Schmidt-Hoberg, Kai; Nilles, Hans Peter; Ramos-Sanchez, Saul; Vaudrevange, Patrick K. S.
2009-03-27
We show that hierarchically small vacuum expectation values of the superpotential in supersymmetric theories can be a consequence of an approximate R symmetry. We briefly discuss the role of such small constants in moduli stabilization and understanding the huge hierarchy between the Planck and electroweak scales.
Block Addressing Indices for Approximate Text Retrieval.
ERIC Educational Resources Information Center
Baeza-Yates, Ricardo; Navarro, Gonzalo
2000-01-01
Discusses indexing in large text databases, approximate text searching, and space-time tradeoffs for indexed text searching. Studies the space overhead and retrieval times as functions of the text block size, concludes that an index can be sublinear in space overhead and query time, and applies the analysis to the Web. (Author/LRW)
Approximating Confidence Intervals for Factor Loadings.
ERIC Educational Resources Information Center
Lambert, Zarrel V.; And Others
1991-01-01
A method is presented that eliminates some interpretational limitations arising from assumptions implicit in the use of arbitrary rules of thumb to interpret exploratory factor analytic results. The bootstrap method is presented as a way of approximating sampling distributions of estimated factor loadings. Simulated datasets illustrate the…
Curved Finite Elements and Curve Approximation
NASA Technical Reports Server (NTRS)
Baart, M. L.
1985-01-01
The approximation of parameterized curves by segments of parabolas that pass through the endpoints of each curve segment arises naturally in all quadratic isoparametric transformations. While not as popular as cubics in curve design problems, the use of parabolas allows the introduction of a geometric measure of the discrepancy between given and approximating curves. The free parameters of the parabola may be used to optimize the fit, and constraints that prevent overspill and curve degeneracy are introduced. This leads to a constrained optimization problem in two varibles that can be solved quickly and reliably by a simple method that takes advantage of the special structure of the problem. For applications in the field of computer-aided design, the given curves are often cubic polynomials, and the coefficient may be calculated in closed form in terms of polynomial coefficients by using a symbolic machine language so that families of curves can be approximated with no further integration. For general curves, numerical quadrature may be used, as in the implementation where the Romberg quadrature is applied. The coefficient functions C sub 1 (gamma) and C sub 2 (gamma) are expanded as polynomials in gamma, so that for given A(s) and B(s) the integrations need only be done once. The method was used to find optimal constrained parabolic approximation to a wide variety of given curves.
Fostering Formal Commutativity Knowledge with Approximate Arithmetic.
Hansen, Sonja Maria; Haider, Hilde; Eichler, Alexandra; Godau, Claudia; Frensch, Peter A; Gaschler, Robert
2015-01-01
How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school.
Inhomogeneous random phase approximation: A solvable model
Lemm, J.C.
1995-11-15
A recently developed method to include particle-hole correlations into the time-independent mean field theory for scattering (TIMF) by an inhomogeneous random phase approximation (IRPA) is applied to a numerically solvable model. Having adapted the procedure according to numerical requirements, IRPA calculations turn out to be tractable. The obtained results improve TIMF results. 8 refs., 28 figs., 3 tabs.
Block Addressing Indices for Approximate Text Retrieval.
ERIC Educational Resources Information Center
Baeza-Yates, Ricardo; Navarro, Gonzalo
2000-01-01
Discusses indexing in large text databases, approximate text searching, and space-time tradeoffs for indexed text searching. Studies the space overhead and retrieval times as functions of the text block size, concludes that an index can be sublinear in space overhead and query time, and applies the analysis to the Web. (Author/LRW)
Sensing Position With Approximately Constant Contact Force
NASA Technical Reports Server (NTRS)
Sturdevant, Jay
1996-01-01
Computer-controlled electromechanical system uses number of linear variable-differential transformers (LVDTs) to measure axial positions of selected points on surface of lens, mirror, or other precise optical component with high finish. Pressures applied to pneumatically driven LVDTs adjusted to maintain small, approximately constant contact forces as positions of LVDT tips vary.
Padé approximations and diophantine geometry
Chudnovsky, D. V.; Chudnovsky, G. V.
1985-01-01
Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves. PMID:16593552
Can Distributional Approximations Give Exact Answers?
ERIC Educational Resources Information Center
Griffiths, Martin
2013-01-01
Some mathematical activities and investigations for the classroom or the lecture theatre can appear rather contrived. This cannot, however, be levelled at the idea given here, since it is based on a perfectly sensible question concerning distributional approximations that was posed by an undergraduate student. Out of this simple question, and…
Approximate model for laser ablation of carbon
NASA Astrophysics Data System (ADS)
Shusser, Michael
2010-08-01
The paper presents an approximate kinetic theory model of ablation of carbon by a nanosecond laser pulse. The model approximates the process as sublimation and combines conduction heat transfer in the target with the gas dynamics of the ablated plume which are coupled through the boundary conditions at the interface. The ablated mass flux and the temperature of the ablating material are obtained from the assumption that the ablation rate is restricted by the kinetic theory limitation on the maximum mass flux that can be attained in a phase-change process. To account for non-uniform distribution of the laser intensity while keeping the calculation simple the quasi-one-dimensional approximation is used in both gas and solid phases. The results are compared with the predictions of the exact axisymmetric model that uses the conservation relations at the interface derived from the momentum solution of the Boltzmann equation for arbitrary strong evaporation. It is seen that the simpler approximate model provides good accuracy.
Kravchuk functions for the finite oscillator approximation
NASA Technical Reports Server (NTRS)
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.
Variance approximations for assessments of classification accuracy
R. L. Czaplewski
1994-01-01
Variance approximations are derived for the weighted and unweighted kappa statistics, the conditional kappa statistic, and conditional probabilities. These statistics are useful to assess classification accuracy, such as accuracy of remotely sensed classifications in thematic maps when compared to a sample of reference classifications made in the field. Published...
Multidimensional stochastic approximation using locally contractive functions
NASA Technical Reports Server (NTRS)
Lawton, W. M.
1975-01-01
A Robbins-Monro type multidimensional stochastic approximation algorithm which converges in mean square and with probability one to the fixed point of a locally contractive regression function is developed. The algorithm is applied to obtain maximum likelihood estimates of the parameters for a mixture of multivariate normal distributions.
Fostering Formal Commutativity Knowledge with Approximate Arithmetic
Hansen, Sonja Maria; Haider, Hilde; Eichler, Alexandra; Godau, Claudia; Frensch, Peter A.; Gaschler, Robert
2015-01-01
How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school. PMID:26560311
Approximation algorithms for planning and control
NASA Technical Reports Server (NTRS)
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.
Approximating the efficiency characteristics of blade pumps
NASA Astrophysics Data System (ADS)
Shekun, G. D.
2007-11-01
Results from a statistical investigation into the experimental efficiency characteristics of commercial type SD centrifugal pumps and type SDS swirl flow pumps are presented. An exponential function for approximating the efficiency characteristics of blade pumps is given. The versatile nature of this characteristic is confirmed by the fact that the use of different systems of relative units gives identical results.
Counting independent sets using the Bethe approximation
Chertkov, Michael; Chandrasekaran, V; Gamarmik, D; Shah, D; Sin, J
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.
Jiang, Xiaoye; Yao, Yuan; Liu, Han; Guibas, Leonidas
2014-01-01
Modern data acquisition routinely produces massive amounts of network data. Though many methods and models have been proposed to analyze such data, the research of network data is largely disconnected with the classical theory of statistical learning and signal processing. In this paper, we present a new framework for modeling network data, which connects two seemingly different areas: network data analysis and compressed sensing. From a nonparametric perspective, we model an observed network using a large dictionary. In particular, we consider the network clique detection problem and show connections between our formulation with a new algebraic tool, namely Randon basis pursuit in homogeneous spaces. Such a connection allows us to identify rigorous recovery conditions for clique detection problems. Though this paper is mainly conceptual, we also develop practical approximation algorithms for solving empirical problems and demonstrate their usefulness on real-world datasets. PMID:25620806
Jiang, Xiaoye; Yao, Yuan; Liu, Han; Guibas, Leonidas
2014-11-01
Modern data acquisition routinely produces massive amounts of network data. Though many methods and models have been proposed to analyze such data, the research of network data is largely disconnected with the classical theory of statistical learning and signal processing. In this paper, we present a new framework for modeling network data, which connects two seemingly different areas: network data analysis and compressed sensing. From a nonparametric perspective, we model an observed network using a large dictionary. In particular, we consider the network clique detection problem and show connections between our formulation with a new algebraic tool, namely Randon basis pursuit in homogeneous spaces. Such a connection allows us to identify rigorous recovery conditions for clique detection problems. Though this paper is mainly conceptual, we also develop practical approximation algorithms for solving empirical problems and demonstrate their usefulness on real-world datasets.
Finite difference methods for approximating Heaviside functions
NASA Astrophysics Data System (ADS)
Towers, John D.
2009-05-01
We present a finite difference method for discretizing a Heaviside function H(u(x→)), where u is a level set function u:Rn ↦ R that is positive on a bounded region Ω⊂Rn. There are two variants of our algorithm, both of which are adapted from finite difference methods that we proposed for discretizing delta functions in [J.D. Towers, Two methods for discretizing a delta function supported on a level set, J. Comput. Phys. 220 (2007) 915-931; J.D. Towers, Discretizing delta functions via finite differences and gradient normalization, Preprint at http://www.miracosta.edu/home/jtowers/; J.D. Towers, A convergence rate theorem for finite difference approximations to delta functions, J. Comput. Phys. 227 (2008) 6591-6597]. We consider our approximate Heaviside functions as they are used to approximate integrals over Ω. We prove that our first approximate Heaviside function leads to second order accurate quadrature algorithms. Numerical experiments verify this second order accuracy. For our second algorithm, numerical experiments indicate at least third order accuracy if the integrand f and ∂Ω are sufficiently smooth. Numerical experiments also indicate that our approximations are effective when used to discretize certain singular source terms in partial differential equations. We mostly focus on smooth f and u. By this we mean that f is smooth in a neighborhood of Ω, u is smooth in a neighborhood of ∂Ω, and the level set u(x)=0 is a manifold of codimension one. However, our algorithms still give reasonable results if either f or u has jumps in its derivatives. Numerical experiments indicate approximately second order accuracy for both algorithms if the regularity of the data is reduced in this way, assuming that the level set u(x)=0 is a manifold. Numerical experiments indicate that dependence on the placement of Ω with respect to the grid is quite small for our algorithms. Specifically, a grid shift results in an O(hp) change in the computed solution
Iedema, Rick; Verma, Raj; Wutzke, Sonia; Lyons, Nigel; McCaughan, Brian
2017-04-10
Purpose To further our insight into the role of networks in health system reform, the purpose of this paper is to investigate how one agency, the NSW Agency for Clinical Innovation (ACI), and the multiple networks and enabling resources that it encompasses, govern, manage and extend the potential of networks for healthcare practice improvement. Design/methodology/approach This is a case study investigation which took place over ten months through the first author's participation in network activities and discussions with the agency's staff about their main objectives, challenges and achievements, and with selected services around the state of New South Wales to understand the agency's implementation and large system transformation activities. Findings The paper demonstrates that ACI accommodates multiple networks whose oversight structures, self-organisation and systems change approaches combined in dynamic ways, effectively yield a diversity of network governances. Further, ACI bears out a paradox of "centralised decentralisation", co-locating agents of innovation with networks of implementation and evaluation expertise. This arrangement strengthens and legitimates the role of the strategic hybrid - the healthcare professional in pursuit of change and improvement, and enhances their influence and impact on the wider system. Research limitations/implications While focussing the case study on one agency only, this study is unique as it highlights inter-network connections. Contributing to the literature on network governance, this paper identifies ACI as a "network of networks" through which resources, expectations and stakeholder dynamics are dynamically and flexibly mediated and enhanced. Practical implications The co-location of and dynamic interaction among clinical networks may create synergies among networks, nurture "strategic hybrids", and enhance the impact of network activities on health system reform. Social implications Network governance requires more
NASA Astrophysics Data System (ADS)
Gollas, Frank; Tetzlaff, Ronald
2009-05-01
-temporal autoregressive filter models are considered, for a prediction of EEG signal values. Thus Signal features values for successive, short, quasi stationary segments of brain electrical activity can be obtained, with the objective of detecting distinct changes prior to impending epileptic seizures. Furthermore long term recordings gained during presurgical diagnostics in temporal lobe epilepsy are analyzed and the predictive performance of the extracted features is evaluated statistically. Therefore a Receiver Operating Characteristic analysis is considered, assessing the distinguishability between distributions of supposed preictal and interictal periods.
Approximating local observables on projected entangled pair states
NASA Astrophysics Data System (ADS)
Schwarz, M.; Buerschaper, O.; Eisert, J.
2017-06-01
Tensor network states are for good reasons believed to capture ground states of gapped local Hamiltonians arising in the condensed matter context, states which are in turn expected to satisfy an entanglement area law. However, the computational hardness of contracting projected entangled pair states in two- and higher-dimensional systems is often seen as a significant obstacle when devising higher-dimensional variants of the density-matrix renormalization group method. In this work, we show that for those projected entangled pair states that are expected to provide good approximations of such ground states of local Hamiltonians, one can compute local expectation values in quasipolynomial time. We therefore provide a complexity-theoretic justification of why state-of-the-art numerical tools work so well in practice. We finally turn to the computation of local expectation values on quantum computers, providing a meaningful application for a small-scale quantum computer.
Decentralized Bayesian search using approximate dynamic programming methods.
Zhao, Yijia; Patek, Stephen D; Beling, Peter A
2008-08-01
We consider decentralized Bayesian search problems that involve a team of multiple autonomous agents searching for targets on a network of search points operating under the following constraints: 1) interagent communication is limited; 2) the agents do not have the opportunity to agree in advance on how to resolve equivalent but incompatible strategies; and 3) each agent lacks the ability to control or predict with certainty the actions of the other agents. We formulate the multiagent search-path-planning problem as a decentralized optimal control problem and introduce approximate dynamic heuristics that can be implemented in a decentralized fashion. After establishing some analytical properties of the heuristics, we present computational results for a search problem involving two agents on a 5 x 5 grid.
Approximation techniques of a selective ARQ protocol
NASA Astrophysics Data System (ADS)
Kim, B. G.
Approximations to the performance of selective automatic repeat request (ARQ) protocol with lengthy acknowledgement delays are presented. The discussion is limited to packet-switched communication systems in a single-hop environment such as found with satellite systems. It is noted that retransmission of errors after ARQ is a common situation. ARQ techniques, e.g., stop-and-wait and continuous, are outlined. A simplified queueing analysis of the selective ARQ protocol shows that exact solutions with long delays are not feasible. Two approximation models are formulated, based on known exact behavior of a system with short delays. The buffer size requirements at both ends of a communication channel are cited as significant factor for accurate analysis, and further examinations of buffer overflow and buffer lock-out probability and avoidance are recommended.
Approximate inverse preconditioners for general sparse matrices
Chow, E.; Saad, Y.
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.
Approximate gauge symmetry of composite vector bosons
NASA Astrophysics Data System (ADS)
Suzuki, Mahiko
2010-08-01
It can be shown in a solvable field theory model that the couplings of the composite vector bosons 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 a more 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.
Approximated solutions to Born-Infeld dynamics
NASA Astrophysics Data System (ADS)
Ferraro, Rafael; Nigro, Mauro
2016-02-01
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.
Flow past a porous approximate spherical shell
NASA Astrophysics Data System (ADS)
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.
A Varifold Approach to Surface Approximation
NASA Astrophysics Data System (ADS)
Buet, Blanche; Leonardi, Gian Paolo; Masnou, Simon
2017-06-01
We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we introduce the notion of approximate mean curvature and show various convergence results that hold, in particular, for sequences of discrete varifolds associated with point clouds or pixel/voxel-type discretizations of d-surfaces in the Euclidean n-space, without restrictions on dimension and codimension. The variational nature of the approach also allows us to consider surfaces with singularities, and in that case the approximate mean curvature is consistent with the generalized mean curvature of the limit surface. A series of numerical tests are provided in order to illustrate the effectiveness and generality of the method.
Planetary ephemerides approximation for radar astronomy
NASA Technical Reports Server (NTRS)
Sadr, R.; Shahshahani, M.
1991-01-01
The planetary ephemerides approximation for radar astronomy is discussed, and, in particular, the effect of this approximation on the performance of the programmable local oscillator (PLO) used in Goldstone Solar System Radar is presented. Four different approaches are considered and it is shown that the Gram polynomials outperform the commonly used technique based on Chebyshev polynomials. These methods are used to analyze the mean square, the phase error, and the frequency tracking error in the presence of the worst case Doppler shift that one may encounter within the solar system. It is shown that in the worst case the phase error is under one degree and the frequency tracking error less than one hertz when the frequency to the PLO is updated every millisecond.
Smooth polynomial approximation of spiral arcs
NASA Astrophysics Data System (ADS)
Cripps, R. J.; Hussain, M. Z.; Zhu, S.
2010-03-01
Constructing fair curve segments using parametric polynomials is difficult due to the oscillatory nature of polynomials. Even NURBS curves can exhibit unsatisfactory curvature profiles. Curve segments with monotonic curvature profiles, for example spiral arcs, exist but are intrinsically non-polynomial in nature and thus difficult to integrate into existing CAD systems. A method of constructing an approximation to a generalised Cornu spiral (GCS) arc using non-rational quintic Bézier curves matching end points, end slopes and end curvatures is presented. By defining an objective function based on the relative error between the curvature profiles of the GCS and its Bézier approximation, a curve segment is constructed that has a monotonic curvature profile within a specified tolerance.
Flexible least squares for approximately linear systems
NASA Astrophysics Data System (ADS)
Kalaba, Robert; Tesfatsion, Leigh
1990-10-01
A probability-free multicriteria approach is presented to the problem of filtering and smoothing when prior beliefs concerning dynamics and measurements take an approximately linear form. Consideration is given to applications in the social and biological sciences, where obtaining agreement among researchers regarding probability relations for discrepancy terms is difficult. The essence of the proposed flexible-least-squares (FLS) procedure is the cost-efficient frontier, a curve in a two-dimensional cost plane which provides an explicit and systematic way to determine the efficient trade-offs between the separate costs incurred for dynamic and measurement specification errors. The FLS estimates show how the state vector could have evolved over time in a manner minimally incompatible with the prior dynamic and measurement specifications. A FORTRAN program for implementing the FLS filtering and smoothing procedure for approximately linear systems is provided.
Quantum fluctuations beyond the Gutzwiller approximation
NASA Astrophysics Data System (ADS)
Fabrizio, Michele
2017-02-01
We present a simple scheme to evaluate linear response functions including quantum fluctuation corrections on top of the Gutzwiller approximation. The method is derived for a generic multiband lattice Hamiltonian without any assumption about the dynamics of the variational correlation parameters that define the Gutzwiller wave function, and which thus behave as genuine dynamical degrees of freedom that add on those of the variational uncorrelated Slater determinant. We apply the method to the standard half-filled single-band Hubbard model. We are able to recover known results, but, as a by-product, we also obtain a few other results. In particular, we show that quantum fluctuations can reproduce, almost quantitatively, the behavior of the uniform magnetic susceptibility uncovered by dynamical mean-field theory, which, though enhanced by correlations, is found to be smooth across the paramagnetic Mott transition. By contrast, the simple Gutzwiller approximation predicts that susceptibility to diverge at the transition.
Approximate Dynamic Programming for Military Resource Allocation
2014-12-26
UNLIMITED The views expressed in this thesis are those of the author and do not reflect the official policy or position of the United States Air... auction algo- rithm in a greedy fashion to an exact (but computationally expensive) branching and bounding technique. Sahin and Leblebicioglu [62] apply...network architectures. Brown et al. [18] apply a two-sided model to determine the optimal location to pre- position defensive platforms with the objective
JIMWLK evolution in the Gaussian approximation
NASA Astrophysics Data System (ADS)
Iancu, E.; Triantafyllopoulos, D. N.
2012-04-01
We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors N c . This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it re-produces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite N c . Any higher n-point function with n ≥ 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.
Barycentric approximation in financial decision making
Frauendorfer, K.
1994-12-31
We consider dynamic portfolio selection problems which are exposed to interest rate risk and credit risk caused by stochastic cash-flows and interest rates. For maximizing the expected net present value, we apply the barycentric approximation scheme of stochastic programming and discuss its features to be utilized in financial decision making. In particular, we focus on the martingale property, the term structure of interest rates, cash-flow dynamics, and correlations of the later two.
Beyond the Kirchhoff approximation. II - Electromagnetic scattering
NASA Technical Reports Server (NTRS)
Rodriguez, Ernesto
1991-01-01
In a paper by Rodriguez (1981), the momentum transfer expansion was introduced for scalar wave scattering. It was shown that this expansion can be used to obtain wavelength-dependent curvature corrections to the Kirchhoff approximation. This paper extends the momentum transfer perturbation expansion to electromagnetic waves. Curvature corrections to the surface current are obtained. Using these results, the specular field and the backscatter cross section are calculated.
Solving Math Problems Approximately: A Developmental Perspective
Ganor-Stern, Dana
2016-01-01
Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults’ ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner. PMID:27171224
Stochastic approximation boosting for incomplete data problems.
Sexton, Joseph; Laake, Petter
2009-12-01
Boosting is a powerful approach to fitting regression models. This article describes a boosting algorithm for likelihood-based estimation with incomplete data. The algorithm combines boosting with a variant of stochastic approximation that uses Markov chain Monte Carlo to deal with the missing data. Applications to fitting generalized linear and additive models with missing covariates are given. The method is applied to the Pima Indians Diabetes Data where over half of the cases contain missing values.
Nonlinear amplitude approximation for bilinear systems
NASA Astrophysics Data System (ADS)
Jung, Chulwoo; D'Souza, Kiran; Epureanu, Bogdan I.
2014-06-01
An efficient method to predict vibration amplitudes at the resonant frequencies of dynamical systems with piecewise-linear nonlinearity is developed. This technique is referred to as bilinear amplitude approximation (BAA). BAA constructs a single vibration cycle at each resonant frequency to approximate the periodic steady-state response of the system. It is postulated that the steady-state response is piece-wise linear and can be approximated by analyzing the response over two time intervals during which the system behaves linearly. Overall the dynamics is nonlinear, but the system is in a distinct linear state during each of the two time intervals. Thus, the approximated vibration cycle is constructed using linear analyses. The equation of motion for analyzing the vibration of each state is projected along the overlapping space spanned by the linear mode shapes active in each of the states. This overlapping space is where the vibratory energy is transferred from one state to the other when the system switches from one state to the other. The overlapping space can be obtained using singular value decomposition. The space where the energy is transferred is used together with transition conditions of displacement and velocity compatibility to construct a single vibration cycle and to compute the amplitude of the dynamics. Since the BAA method does not require numerical integration of nonlinear models, computational costs are very low. In this paper, the BAA method is first applied to a single-degree-of-freedom system. Then, a three-degree-of-freedom system is introduced to demonstrate a more general application of BAA. Finally, the BAA method is applied to a full bladed disk with a crack. Results comparing numerical solutions from full-order nonlinear analysis and results obtained using BAA are presented for all systems.
Development of New Density Functional Approximations
NASA Astrophysics Data System (ADS)
Su, Neil Qiang; Xu, Xin
2017-05-01
Kohn-Sham density functional theory has become the leading electronic structure method for atoms, molecules, and extended systems. It is in principle exact, but any practical application must rely on density functional approximations (DFAs) for the exchange-correlation energy. Here we emphasize four aspects of the subject: (a) philosophies and strategies for developing DFAs; (b) classification of DFAs; (c) major sources of error in existing DFAs; and (d) some recent developments and future directions.
Oscillation of boson star in Newtonian approximation
NASA Astrophysics Data System (ADS)
Jarwal, Bharti; Singh, S. Somorendro
2017-03-01
Boson star (BS) rotation is studied under Newtonian approximation. A Coulombian potential term is added as perturbation to the radial potential of the system without disturbing the angular momentum. The results of the stationary states of these ground state, first and second excited state are analyzed with the correction of Coulombian potential. It is found that the results with correction increased in the amplitude of oscillation of BS in comparison to potential without perturbation correction.
Solving Math Problems Approximately: A Developmental Perspective.
Ganor-Stern, Dana
2016-01-01
Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4th graders, 6th graders and adults' ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner.
Empirical progress and nomic truth approximation revisited.
Kuipers, Theo A F
2014-06-01
In my From Instrumentalism to Constructive Realism (2000) I have shown how an instrumentalist account of empirical progress can be related to nomic truth approximation. However, it was assumed that a strong notion of nomic theories was needed for that analysis. In this paper it is shown, in terms of truth and falsity content, that the analysis already applies when, in line with scientific common sense, nomic theories are merely assumed to exclude certain conceptual possibilities as nomic possibilities.
Numerical quadratures for approximate computation of ERBS
NASA Astrophysics Data System (ADS)
Zanaty, Peter
2013-12-01
In the ground-laying paper [3] on expo-rational B-splines (ERBS), the default numerical method for approximate computation of the integral with C∞-smooth integrand in the definition of ERBS is Romberg integration. In the present work, a variety of alternative numerical quadrature methods for computation of ERBS and other integrals with smooth integrands are studied, and their performance is compared on several benchmark examples.
Numerical Approximation to the Thermodynamic Integrals
NASA Astrophysics Data System (ADS)
Johns, S. M.; Ellis, P. J.; Lattimer, J. M.
1996-12-01
We approximate boson thermodynamic integrals as polynomials in two variables chosen to give the correct limiting expansion and to smoothly interpolate into other regimes. With 10 free parameters, an accuracy of better than 0.009% is achieved for the pressure, internal energy density, and number density. We also revisit the fermion case, originally addressed by Eggleton, Faulkner, & Flannery (1973), and substantially improve the accuracy of their fits.
Coherent population transfer beyond rotating wave approximation
NASA Astrophysics Data System (ADS)
Rhee, Yongjoo; Kwon, Duck-Hee; Han, Jaemin; Park, Hyunmin; Kim, Sunkook
2002-05-01
The mechanism of coherent population transfer in a three-level system of lamda type interacting with strong and ultra-short laser pulses is investigated beyond the rotating wave approximation (RWA). The characteristics of population transfer arising from the consideration without RWA are numerically shown and interpreted in the point of view of dressed states both for the typical Stimulated Raman Adiabatic Passage(STIRAP) and for Optimal Detuning Method(ODM) which uses large wavelength-detuned lasers without time delay.
Three Definitions of Best Linear Approximation
1976-04-01
Three definitions of best (in the least squares sense) linear approximation to given data points are presented. The relationships between these three area discussed along with their relationship to basic statistics such as mean values, the covariance matrix, and the (linear) correlation coefficient . For each of the three definitions, and best line is solved in closed form in terms of the data centroid and the covariance matrix.
Approximate active fault detection and control
NASA Astrophysics Data System (ADS)
Škach, Jan; Punčochář, Ivo; Šimandl, Miroslav
2014-12-01
This paper deals with approximate active fault detection and control for nonlinear discrete-time stochastic systems over an infinite time horizon. Multiple model framework is used to represent fault-free and finitely many faulty models. An imperfect state information problem is reformulated using a hyper-state and dynamic programming is applied to solve the problem numerically. The proposed active fault detector and controller is illustrated in a numerical example of an air handling unit.
Microscopic justification of the equal filling approximation
Perez-Martin, Sara; Robledo, L. M.
2008-07-15
The equal filling approximation, a procedure widely used in mean-field calculations to treat the dynamics of odd nuclei in a time-reversal invariant way, is justified as the consequence of a variational principle over an average energy functional. The ideas of statistical quantum mechanics are employed in the justification. As an illustration of the method, the ground and lowest-lying states of some octupole deformed radium isotopes are computed.
Variational Bayesian Approximation methods for inverse problems
NASA Astrophysics Data System (ADS)
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.
Capacitor-Chain Successive-Approximation ADC
NASA Technical Reports Server (NTRS)
Cunningham, Thomas
2003-01-01
A proposed successive-approximation analog-to-digital converter (ADC) would contain a capacitively terminated chain of identical capacitor cells. Like a conventional successive-approximation ADC containing a bank of binary-scaled capacitors, the proposed ADC would store an input voltage on a sample-and-hold capacitor and would digitize the stored input voltage by finding the closest match between this voltage and a capacitively generated sum of binary fractions of a reference voltage (Vref). However, the proposed capacitor-chain ADC would offer two major advantages over a conventional binary-scaled-capacitor ADC: (1) In a conventional ADC that digitizes to n bits, the largest capacitor (representing the most significant bit) must have 2(exp n-1) times as much capacitance, and hence, approximately 2(exp n-1) times as much area as does the smallest capacitor (representing the least significant bit), so that the total capacitor area must be 2(exp n) times that of the smallest capacitor. In the proposed capacitor-chain ADC, there would be three capacitors per cell, each approximately equal to the smallest capacitor in the conventional ADC, and there would be one cell per bit. Therefore, the total capacitor area would be only about 3(exp n) times that of the smallest capacitor. The net result would be that the proposed ADC could be considerably smaller than the conventional ADC. (2) Because of edge effects, parasitic capacitances, and manufacturing tolerances, it is difficult to make capacitor banks in which the values of capacitance are scaled by powers of 2 to the required precision. In contrast, because all the capacitors in the proposed ADC would be identical, the problem of precise binary scaling would not arise.
Parameter Biases Introduced by Approximate Gravitational Waveforms
NASA Astrophysics Data System (ADS)
Farr, Benjamin; Coughlin, Scott; Le, John; Skeehan, Connor; Kalogera, Vicky
2013-04-01
The production of the most accurate gravitational waveforms from compact binary mergers require Einstein's equations to be solved numerically, a process far too expensive to produce the ˜10^7 waveforms necessary to estimate the parameters of a measured gravitational wave signal. Instead, parameter estimation depends on approximate or phenomenological waveforms to characterize measured signals. As part of the Ninja collaboration, we study the biases introduced by these methods when estimating the parameters of numerically produced waveforms.
Green-Ampt approximations: A comprehensive analysis
NASA Astrophysics Data System (ADS)
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.
CMB-lensing beyond the Born approximation
NASA Astrophysics Data System (ADS)
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.
A coastal ocean model with subgrid approximation
NASA Astrophysics Data System (ADS)
Walters, Roy A.
2016-06-01
A wide variety of coastal ocean models exist, each having attributes that reflect specific application areas. The model presented here is based on finite element methods with unstructured grids containing triangular and quadrilateral elements. The model optimizes robustness, accuracy, and efficiency by using semi-implicit methods in time in order to remove the most restrictive stability constraints, by using a semi-Lagrangian advection approximation to remove Courant number constraints, and by solving a wave equation at the discrete level for enhanced efficiency. An added feature is the approximation of the effects of subgrid objects. Here, the Reynolds-averaged Navier-Stokes equations and the incompressibility constraint are volume averaged over one or more computational cells. This procedure gives rise to new terms which must be approximated as a closure problem. A study of tidal power generation is presented as an example of this method. A problem that arises is specifying appropriate thrust and power coefficients for the volume averaged velocity when they are usually referenced to free stream velocity. A new contribution here is the evaluation of three approaches to this problem: an iteration procedure and two mapping formulations. All three sets of results for thrust (form drag) and power are in reasonable agreement.
An Origami Approximation to the Cosmic Web
NASA Astrophysics Data System (ADS)
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.
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.
Ranking Support Vector Machine with Kernel Approximation
Dou, Yong
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. PMID:28293256
Strong washout approximation to resonant leptogenesis
NASA Astrophysics Data System (ADS)
Garbrecht, Björn; Gautier, Florian; Klaric, Juraj
2014-09-01
We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ɛ=Xsin(2varphi)/(X2+sin2varphi), where X=8πΔ/(|Y1|2+|Y2|2), Δ=4(M1-M2)/(M1+M2), varphi=arg(Y2/Y1), and M1,2, Y1,2 are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where |Y1,2|2gg Δ, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to the case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space.
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.
Using Approximations to Accelerate Engineering Design Optimization
NASA Technical Reports Server (NTRS)
Torczon, Virginia; Trosset, Michael W.
1998-01-01
Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem often are computationally intensive. Within a standard nonlinear optimization algorithm, the computational expense of evaluating the functions that define the problem would necessarily be incurred for each iteration of the optimization algorithm. Faced with such prohibitive computational costs, an attractive alternative is to make use of surrogates within an optimization context since surrogates can be chosen or constructed so that they are typically much less expensive to compute. For the purposes of this paper, we will focus on the use of algebraic approximations as surrogates for the objective. In this paper we introduce the use of so-called merit functions that explicitly recognize the desirability of improving the current approximation to the objective during the course of the optimization. We define and experiment with the use of merit functions chosen to simultaneously improve both the solution to the optimization problem (the objective) and the quality of the approximation. Our goal is to further improve the effectiveness of our general approach without sacrificing any of its rigor.
Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin
2016-01-01
What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright
2014-10-21
networks. With economists Larry Blume and David Easley, and computer scientists Jon Kleinberg and Éva Tardos, we investigated so-called threshold...and Nicole Immorlica [13], we investigated Schelling’s segregation model, a famous model of residential segregation that has been observed, in...approximation ratio achieves the first provable improvement upon the approximation ratio of the famous algorithm introduced by Christofides in 1976 (which
Spacecraft attitude control using neuro-fuzzy approximation of the optimal controllers
NASA Astrophysics Data System (ADS)
Kim, Sung-Woo; Park, Sang-Young; Park, Chandeok
2016-01-01
In this study, a neuro-fuzzy controller (NFC) was developed for spacecraft attitude control to mitigate large computational load of the state-dependent Riccati equation (SDRE) controller. The NFC was developed by training a neuro-fuzzy network to approximate the SDRE controller. The stability of the NFC was numerically verified using a Lyapunov-based method, and the performance of the controller was analyzed in terms of approximation ability, steady-state error, cost, and execution time. The simulations and test results indicate that the developed NFC efficiently approximates the SDRE controller, with asymptotic stability in a bounded region of angular velocity encompassing the operational range of rapid-attitude maneuvers. In addition, it was shown that an approximated optimal feedback controller can be designed successfully through neuro-fuzzy approximation of the optimal open-loop controller.
Bicriteria network design problems
Marathe, M.V.; Ravi, R.; Sundaram, R.; Ravi, S.S.; Rosenkrantz, D.J.; Hunt, H.B. III
1997-11-20
The authors study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a subgraph from a given subgraph class that minimizes the second objective subject to the budget on the first. They consider three different criteria -- the total edge cost, the diameter and the maximum degree of the network. Here, they present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, they develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same they present a black box parametric search technique. This black box takes in as input an (approximation) algorithm for the criterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs they use a cluster based approach to devise approximation algorithms. The solutions violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, they provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. The authors show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.
Photoelectron spectroscopy and the dipole approximation
Hemmers, O.; Hansen, D.L.; Wang, H.
1997-04-01
Photoelectron spectroscopy is a powerful technique because it directly probes, via the measurement of photoelectron kinetic energies, orbital and band structure in valence and core levels in a wide variety of samples. The technique becomes even more powerful when it is performed in an angle-resolved mode, where photoelectrons are distinguished not only by their kinetic energy, but by their direction of emission as well. Determining the probability of electron ejection as a function of angle probes the different quantum-mechanical channels available to a photoemission process, because it is sensitive to phase differences among the channels. As a result, angle-resolved photoemission has been used successfully for many years to provide stringent tests of the understanding of basic physical processes underlying gas-phase and solid-state interactions with radiation. One mainstay in the application of angle-resolved photoelectron spectroscopy is the well-known electric-dipole approximation for photon interactions. In this simplification, all higher-order terms, such as those due to electric-quadrupole and magnetic-dipole interactions, are neglected. As the photon energy increases, however, effects beyond the dipole approximation become important. To best determine the range of validity of the dipole approximation, photoemission measurements on a simple atomic system, neon, where extra-atomic effects cannot play a role, were performed at BL 8.0. The measurements show that deviations from {open_quotes}dipole{close_quotes} expectations in angle-resolved valence photoemission are observable for photon energies down to at least 0.25 keV, and are quite significant at energies around 1 keV. From these results, it is clear that non-dipole angular-distribution effects may need to be considered in any application of angle-resolved photoelectron spectroscopy that uses x-ray photons of energies as low as a few hundred eV.
Product-State Approximations to Quantum States
NASA Astrophysics Data System (ADS)
Brandão, Fernando G. S. L.; Harrow, Aram W.
2016-02-01
We show that for any many-body quantum state there exists an unentangled quantum state such that most of the two-body reduced density matrices are close to those of the original state. This is a statement about the monogamy of entanglement, which cannot be shared without limit in the same way as classical correlation. Our main application is to Hamiltonians that are sums of two-body terms. For such Hamiltonians we show that there exist product states with energy that is close to the ground-state energy whenever the interaction graph of the Hamiltonian has high degree. This proves the validity of mean-field theory and gives an explicitly bounded approximation error. If we allow states that are entangled within small clusters of systems but product across clusters then good approximations exist when the Hamiltonian satisfies one or more of the following properties: (1) high degree, (2) small expansion, or (3) a ground state where the blocks in the partition have sublinear entanglement. Previously this was known only in the case of small expansion or in the regime where the entanglement was close to zero. Our approximations allow an extensive error in energy, which is the scale considered by the quantum PCP (probabilistically checkable proof) and NLTS (no low-energy trivial-state) conjectures. Thus our results put restrictions on the possible Hamiltonians that could be used for a possible proof of the qPCP or NLTS conjectures. By contrast the classical PCP constructions are often based on constraint graphs with high degree. Likewise we show that the parallel repetition that is possible with classical constraint satisfaction problems cannot also be possible for quantum Hamiltonians, unless qPCP is false. The main technical tool behind our results is a collection of new classical and quantum de Finetti theorems which do not make any symmetry assumptions on the underlying states.
An approximate projection method for incompressible flow
NASA Astrophysics Data System (ADS)
Stevens, David E.; Chan, Stevens T.; Gresho, Phil
2002-12-01
This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139-1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40-65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency.A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake.
Approximate protein structural alignment in polynomial time
Kolodny, Rachel; Linial, Nathan
2004-01-01
Alignment of protein structures is a fundamental task in computational molecular biology. Good structural alignments can help detect distant evolutionary relationships that are hard or impossible to discern from protein sequences alone. Here, we study the structural alignment problem as a family of optimization problems and develop an approximate polynomial-time algorithm to solve them. For a commonly used scoring function, the algorithm runs in O(n10/ε6) time, for globular protein of length n, and it detects alignments that score within an additive error of ε from all optima. Thus, we prove that this task is computationally feasible, although the method that we introduce is too slow to be a useful everyday tool. We argue that such approximate solutions are, in fact, of greater interest than exact ones because of the noisy nature of experimentally determined protein coordinates. The measurement of similarity between a pair of protein structures used by our algorithm involves the Euclidean distance between the structures (appropriately rigidly transformed). We show that an alternative approach, which relies on internal distance matrices, must incorporate sophisticated geometric ingredients if it is to guarantee optimality and run in polynomial time. We use these observations to visualize the scoring function for several real instances of the problem. Our investigations yield insights on the computational complexity of protein alignment under various scoring functions. These insights can be used in the design of scoring functions for which the optimum can be approximated efficiently and perhaps in the development of efficient algorithms for the multiple structural alignment problem. PMID:15304646
Strong washout approximation to resonant leptogenesis
Garbrecht, Björn; Gautier, Florian; Klaric, Juraj E-mail: florian.gautier@tum.de
2014-09-01
We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ε=Xsin(2φ)/(X{sup 2}+sin{sup 2}φ), where X=8πΔ/(|Y{sub 1}|{sup 2}+|Y{sub 2}|{sup 2}), Δ=4(M{sub 1}-M{sub 2})/(M{sub 1}+M{sub 2}), φ=arg(Y{sub 2}/Y{sub 1}), and M{sub 1,2}, Y{sub 1,2} are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where |Y{sub 1,2}|{sup 2}>> Δ, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to the case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space.
Relativistic Random Phase Approximation At Finite Temperature
Niu, Y. F.; Paar, N.; Vretenar, D.; Meng, J.
2009-08-26
The fully self-consistent finite temperature relativistic random phase approximation (FTRRPA) has been established in the single-nucleon basis of the temperature dependent Dirac-Hartree model (FTDH) based on effective Lagrangian with density dependent meson-nucleon couplings. Illustrative calculations in the FTRRPA framework show the evolution of multipole responses of {sup 132}Sn with temperature. With increased temperature, in both monopole and dipole strength distributions additional transitions appear in the low energy region due to the new opened particle-particle and hole-hole transition channels.
Analytic Approximation to Randomly Oriented Spheroid Extinction
1993-12-01
104 times faster than by the T - matrix code . Since the T-matrix scales as at least the cube of the optical size whereas the analytic approximation is...coefficient estimate, and with the Rayleigh formula. Since it is difficult estimate the accuracy near the limit of stability of the T - matrix code some...additional error due to the T - matrix code could be present. UNCLASSIFIED 30 Max Ret Error, Analytic vs T-Mat, r= 1/5 0.0 20 25 10 ~ 0.5 100 . 7.5 S-1.0
Relativistic mean field approximation to baryons
Dmitri Diakonov
2005-02-01
We stress the importance of the spontaneous chiral symmetry breaking for understanding the low-energy structure of baryons. The Mean Field Approximation to baryons is formulated, which solves several outstanding paradoxes of the naive quark models, and which allows to compute parton distributions at low virtuality in a consistent way. We explain why this approach to baryons leads to the prediction of relatively light exotic pentaquark baryons, in contrast to the constituent models which do not take seriously the importance of chiral symmetry breaking. We briefly discuss why, to our mind, it is easier to produce exotic pentaquarks at low than at high energies.
Approximation of Dynamical System's Separatrix Curves
NASA Astrophysics Data System (ADS)
Cavoretto, Roberto; Chaudhuri, Sanjay; De Rossi, Alessandra; Menduni, Eleonora; Moretti, Francesca; Rodi, Maria Caterina; Venturino, Ezio
2011-09-01
In dynamical systems saddle points partition the domain into basins of attractions of the remaining locally stable equilibria. This problem is rather common especially in population dynamics models, like prey-predator or competition systems. In this paper we construct programs for the detection of points lying on the separatrix curve, i.e. the curve which partitions the domain. Finally, an efficient algorithm, which is based on the Partition of Unity method with local approximants given by Wendland's functions, is used for reconstructing the separatrix curve.
Optimal Markov approximations and generalized embeddings
NASA Astrophysics Data System (ADS)
Holstein, Detlef; Kantz, Holger
2009-05-01
Based on information theory, we present a method to determine an optimal Markov approximation for modeling and prediction from time series data. The method finds a balance between minimal modeling errors by taking as much as possible memory into account and minimal statistical errors by working in embedding spaces of rather small dimension. A key ingredient is an estimate of the statistical error of entropy estimates. The method is illustrated with several examples, and the consequences for prediction are evaluated by means of the root-mean-squared prediction error for point prediction.
Approximation concepts for numerical airfoil optimization
NASA Technical Reports Server (NTRS)
Vanderplaats, G. N.
1979-01-01
An efficient algorithm for airfoil optimization is presented. The algorithm utilizes approximation concepts to reduce the number of aerodynamic analyses required to reach the optimum design. Examples are presented and compared with previous results. Optimization efficiency improvements of more than a factor of 2 are demonstrated. Improvements in efficiency are demonstrated when analysis data obtained in previous designs are utilized. The method is a general optimization procedure and is not limited to this application. The method is intended for application to a wide range of engineering design problems.
Semiclassical approximations to quantum time correlation functions
NASA Astrophysics Data System (ADS)
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.
Approximation Algorithms for Free-Label Maximization
NASA Astrophysics Data System (ADS)
de Berg, Mark; Gerrits, Dirk H. P.
Inspired by air traffic control and other applications where moving objects have to be labeled, we consider the following (static) point labeling problem: given a set P of n points in the plane and labels that are unit squares, place a label with each point in P in such a way that the number of free labels (labels not intersecting any other label) is maximized. We develop efficient constant-factor approximation algorithms for this problem, as well as PTASs, for various label-placement models.
Shear viscosity in the postquasistatic approximation
Peralta, C.; Rosales, L.; Rodriguez-Mueller, B.; Barreto, W.
2010-05-15
We apply the postquasistatic approximation, an iterative method for the evolution of self-gravitating spheres of matter, to study the evolution of anisotropic nonadiabatic radiating and dissipative distributions in general relativity. Dissipation is described by viscosity and free-streaming radiation, assuming an equation of state to model anisotropy induced by the shear viscosity. We match the interior solution, in noncomoving coordinates, with the Vaidya exterior solution. Two simple models are presented, based on the Schwarzschild and Tolman VI solutions, in the nonadiabatic and adiabatic limit. In both cases, the eventual collapse or expansion of the distribution is mainly controlled by the anisotropy induced by the viscosity.
The monoenergetic approximation in stellarator neoclassical calculations
NASA Astrophysics Data System (ADS)
Landreman, Matt
2011-08-01
In 'monoenergetic' stellarator neoclassical calculations, to expedite computation, ad hoc changes are made to the kinetic equation so speed enters only as a parameter. Here we examine the validity of this approach by considering the effective particle trajectories in a model magnetic field. We find monoenergetic codes systematically under-predict the true trapped particle fraction. The error in the trapped ion fraction can be of order unity for large but experimentally realizable values of the radial electric field, suggesting some results of these codes may be unreliable in this regime. This inaccuracy is independent of any errors introduced by approximation of the collision operator.
Localization and stationary phase approximation on supermanifolds
NASA Astrophysics Data System (ADS)
Zakharevich, Valentin
2017-08-01
Given an odd vector field Q on a supermanifold M and a Q-invariant density μ on M, under certain compactness conditions on Q, the value of the integral ∫Mμ is determined by the value of μ on any neighborhood of the vanishing locus N of Q. We present a formula for the integral in the case where N is a subsupermanifold which is appropriately non-degenerate with respect to Q. In the process, we discuss the linear algebra necessary to express our result in a coordinate independent way. We also extend the stationary phase approximation and the Morse-Bott lemma to supermanifolds.
Approximations of nonlinear systems having outputs
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Su, R.
1985-01-01
For a nonlinear system with output derivative x = f(x) and y = h(x), two types of linearizations about a point x(0) in state space are considered. One is the usual Taylor series approximation, and the other is defined by linearizing the appropriate Lie derivatives of the output with respect to f about x(0). The latter is called the obvservation model and appears to be quite natural for observation. It is noted that there is a coordinate system in which these two kinds of linearizations agree. In this coordinate system, a technique to construct an observer is introduced.
Approximating the maximum weight clique using replicator dynamics.
Bomze, I R; Pelillo, M; Stix, V
2000-01-01
Given an undirected graph with weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having the largest total weight. This is a generalization of the classical problem of finding the maximum cardinality clique of an unweighted graph, which arises as a special case of the MWCP when all the weights associated to the vertices are equal. The problem is known to be NP-hard for arbitrary graphs and, according to recent theoretical results, so is the problem of approximating it within a constant factor. Although there has recently been much interest around neural-network algorithms for the unweighted maximum clique problem, no effort has been directed so far toward its weighted counterpart. In this paper, we present a parallel, distributed heuristic for approximating the MWCP based on dynamics principles developed and studied in various branches of mathematical biology. The proposed framework centers around a recently introduced continuous characterization of the MWCP which generalizes an earlier remarkable result by Motzkin and Straus. This allows us to formulate the MWCP (a purely combinatorial problem) in terms of a continuous quadratic programming problem. One drawback associated with this formulation, however, is the presence of "spurious" solutions, and we present characterizations of these solutions. To avoid them we introduce a new regularized continuous formulation of the MWCP inspired by previous works on the unweighted problem, and show how this approach completely solves the problem. The continuous formulation of the MWCP naturally maps onto a parallel, distributed computational network whose dynamical behavior is governed by the so-called replicator equations. These are dynamical systems introduced in evolutionary game theory and population genetics to model evolutionary processes on a macroscopic scale.We present theoretical results which guarantee that the solutions provided by
Elfwing, Stefan; Uchibe, Eiji; Doya, Kenji
2016-12-01
Free-energy based reinforcement learning (FERL) was proposed for learning in high-dimensional state and action spaces. However, the FERL method does only really work well with binary, or close to binary, state input, where the number of active states is fewer than the number of non-active states. In the FERL method, the value function is approximated by the negative free energy of a restricted Boltzmann machine (RBM). In our earlier study, we demonstrated that the performance and the robustness of the FERL method can be improved by scaling the free energy by a constant that is related to the size of network. In this study, we propose that RBM function approximation can be further improved by approximating the value function by the negative expected energy (EERL), instead of the negative free energy, as well as being able to handle continuous state input. We validate our proposed method by demonstrating that EERL: (1) outperforms FERL, as well as standard neural network and linear function approximation, for three versions of a gridworld task with high-dimensional image state input; (2) achieves new state-of-the-art results in stochastic SZ-Tetris in both model-free and model-based learning settings; and (3) significantly outperforms FERL and standard neural network function approximation for a robot navigation task with raw and noisy RGB images as state input and a large number of actions.
2016-01-01
Three-dimensional Gaussian functions have been shown useful in representing electron microscopy (EM) density maps for studying macromolecular structure and dynamics. Methods that require setting a desired number of Gaussian functions or a maximum number of iterations may result in suboptimal representations of the structure. An alternative is to set a desired error of approximation of the given EM map and then optimize the number of Gaussian functions to achieve this approximation error. In this article, we review different applications of such an approach that uses spherical Gaussian functions of fixed standard deviation, referred to as pseudoatoms. Some of these applications use EM-map normal mode analysis (NMA) with elastic network model (ENM) (applications such as predicting conformational changes of macromolecular complexes or exploring actual conformational changes by normal-mode-based analysis of experimental data) while some other do not use NMA (denoising of EM density maps). In applications based on NMA and ENM, the advantage of using pseudoatoms in EM-map coarse-grain models is that the ENM springs are easily assigned among neighboring grains thanks to their spherical shape and uniformed size. EM-map denoising based on the map coarse-graining was so far only shown using pseudoatoms as grains. PMID:28097146
Analytic approximate radiation effects due to Bremsstrahlung
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.
Optimal Approximation of Quadratic Interval Functions
NASA Technical Reports Server (NTRS)
Koshelev, Misha; Taillibert, Patrick
1997-01-01
Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.
Perturbed kernel approximation on homogeneous manifolds
NASA Astrophysics Data System (ADS)
Levesley, J.; Sun, X.
2007-02-01
Current methods for interpolation and approximation within a native space rely heavily on the strict positive-definiteness of the underlying kernels. If the domains of approximation are the unit spheres in euclidean spaces, then zonal kernels (kernels that are invariant under the orthogonal group action) are strongly favored. In the implementation of these methods to handle real world problems, however, some or all of the symmetries and positive-definiteness may be lost in digitalization due to small random errors that occur unpredictably during various stages of the execution. Perturbation analysis is therefore needed to address the stability problem encountered. In this paper we study two kinds of perturbations of positive-definite kernels: small random perturbations and perturbations by Dunkl's intertwining operators [C. Dunkl, Y. Xu, Orthogonal polynomials of several variables, Encyclopedia of Mathematics and Its Applications, vol. 81, Cambridge University Press, Cambridge, 2001]. We show that with some reasonable assumptions, a small random perturbation of a strictly positive-definite kernel can still provide vehicles for interpolation and enjoy the same error estimates. We examine the actions of the Dunkl intertwining operators on zonal (strictly) positive-definite kernels on spheres. We show that the resulted kernels are (strictly) positive-definite on spheres of lower dimensions.
Fast approximate surface evolution in arbitrary dimension
Malcolm, James; Rathi, Yogesh; Yezzi, Anthony; Tannenbaum, Allen
2013-01-01
The level set method is a popular technique used in medical image segmentation; however, the numerics involved make its use cumbersome. This paper proposes an approximate level set scheme that removes much of the computational burden while maintaining accuracy. Abandoning a floating point representation for the signed distance function, we use integral values to represent the signed distance function. For the cases of 2D and 3D, we detail rules governing the evolution and maintenance of these three regions. Arbitrary energies can be implemented in the framework. This scheme has several desirable properties: computations are only performed along the zero level set; the approximate distance function requires only a few simple integer comparisons for maintenance; smoothness regularization involves only a few integer calculations and may be handled apart from the energy itself; the zero level set is represented exactly removing the need for interpolation off the interface; and evolutions proceed on the order of milliseconds per iteration on conventional uniprocessor workstations. To highlight its accuracy, flexibility and speed, we demonstrate the technique on intensity-based segmentations under various statistical metrics. Results for 3D imagery show the technique is fast even for image volumes. PMID:24392194
Variational extensions of the mean spherical approximation
NASA Astrophysics Data System (ADS)
Blum, L.; Ubriaco, M.
2000-04-01
In a previous work we have proposed a method to study complex systems with objects of arbitrary size. For certain specific forms of the atomic and molecular interactions, surprisingly simple and accurate theories (The Variational Mean Spherical Scaling Approximation, VMSSA) [(Velazquez, Blum J. Chem. Phys. 110 (1990) 10 931; Blum, Velazquez, J. Quantum Chem. (Theochem), in press)] can be obtained. The basic idea is that if the interactions can be expressed in a rapidly converging sum of (complex) exponentials, then the Ornstein-Zernike equation (OZ) has an analytical solution. This analytical solution is used to construct a robust interpolation scheme, the variation mean spherical scaling approximation (VMSSA). The Helmholtz excess free energy Δ A=Δ E- TΔ S is then written as a function of a scaling matrix Γ. Both the excess energy Δ E( Γ) and the excess entropy Δ S( Γ) will be functionals of Γ. In previous work of this series the form of this functional was found for the two- (Blum, Herrera, Mol. Phys. 96 (1999) 821) and three-exponential closures of the OZ equation (Blum, J. Stat. Phys., submitted for publication). In this paper we extend this to M Yukawas, a complete basis set: We obtain a solution for the one-component case and give a closed-form expression for the MSA excess entropy, which is also the VMSSA entropy.
Exact and Approximate Sizes of Convex Datacubes
NASA Astrophysics Data System (ADS)
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.
Adaptive Discontinuous Galerkin Approximation to Richards' Equation
NASA Astrophysics Data System (ADS)
Li, H.; Farthing, M. W.; Miller, C. T.
2006-12-01
Due to the occurrence of large gradients in fluid pressure as a function of space and time resulting from nonlinearities in closure relations, numerical solutions to Richards' equations are notoriously difficult for certain media properties and auxiliary conditions that occur routinely in describing physical systems of interest. These difficulties have motivated a substantial amount of work aimed at improving numerical approximations to this physically important and mathematically rich model. In this work, we build upon recent advances in temporal and spatial discretization methods by developing spatially and temporally adaptive solution approaches based upon the local discontinuous Galerkin method in space and a higher order backward difference method in time. Spatial step-size adaption, h adaption, approaches are evaluated and a so-called hp-adaption strategy is considered as well, which adjusts both the step size and the order of the approximation. Solution algorithms are advanced and performance is evaluated. The spatially and temporally adaptive approaches are shown to be robust and offer significant increases in computational efficiency compared to similar state-of-the-art methods that adapt in time alone. In addition, we extend the proposed methods to two dimensions and provide preliminary numerical results.
Approximation of Failure Probability Using Conditional Sampling
NASA Technical Reports Server (NTRS)
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.
Revisiting approximate dynamic programming and its convergence.
Heydari, Ali
2014-12-01
Value iteration-based approximate/adaptive dynamic programming (ADP) as an approximate solution to infinite-horizon optimal control problems with deterministic dynamics and continuous state and action spaces is investigated. The learning iterations are decomposed into an outer loop and an inner loop. A relatively simple proof for the convergence of the outer-loop iterations to the optimal solution is provided using a novel idea with some new features. It presents an analogy between the value function during the iterations and the value function of a fixed-final-time optimal control problem. The inner loop is utilized to avoid the need for solving a set of nonlinear equations or a nonlinear optimization problem numerically, at each iteration of ADP for the policy update. Sufficient conditions for the uniqueness of the solution to the policy update equation and for the convergence of the inner-loop iterations to the solution are obtained. Afterwards, the results are formed as a learning algorithm for training a neurocontroller or creating a look-up table to be used for optimal control of nonlinear systems with different initial conditions. Finally, some of the features of the investigated method are numerically analyzed.
Investigating Material Approximations in Spacecraft Radiation Analysis
NASA Technical Reports Server (NTRS)
Walker, Steven A.; Slaba, Tony C.; Clowdsley, Martha S.; Blattnig, Steve R.
2011-01-01
During the design process, the configuration of space vehicles and habitats changes frequently and the merits of design changes must be evaluated. Methods for rapidly assessing astronaut exposure are therefore required. Typically, approximations are made to simplify the geometry and speed up the evaluation of each design. In this work, the error associated with two common approximations used to simplify space radiation vehicle analyses, scaling into equivalent materials and material reordering, are investigated. Over thirty materials commonly found in spacesuits, vehicles, and human bodies are considered. Each material is placed in a material group (aluminum, polyethylene, or tissue), and the error associated with scaling and reordering was quantified for each material. Of the scaling methods investigated, range scaling is shown to be the superior method, especially for shields less than 30 g/cm2 exposed to a solar particle event. More complicated, realistic slabs are examined to quantify the separate and combined effects of using equivalent materials and reordering. The error associated with material reordering is shown to be at least comparable to, if not greater than, the error associated with range scaling. In general, scaling and reordering errors were found to grow with the difference between the average nuclear charge of the actual material and average nuclear charge of the equivalent material. Based on this result, a different set of equivalent materials (titanium, aluminum, and tissue) are substituted for the commonly used aluminum, polyethylene, and tissue. The realistic cases are scaled and reordered using the new equivalent materials, and the reduced error is shown.