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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.
NASA Technical Reports Server (NTRS)
Adamczyk, J. L.
1974-01-01
An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.
Perturbations of linear delay differential equations at the verge of instability.
Lingala, N; Namachchivaya, N Sri
2016-06-01
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.
Majorization Minimization by Coordinate Descent for Concave Penalized Generalized Linear Models
Jiang, Dingfeng; Huang, Jian
2013-01-01
Recent studies have demonstrated theoretical attractiveness of a class of concave penalties in variable selection, including the smoothly clipped absolute deviation and minimax concave penalties. The computation of the concave penalized solutions in high-dimensional models, however, is a difficult task. We propose a majorization minimization by coordinate descent (MMCD) algorithm for computing the concave penalized solutions in generalized linear models. In contrast to the existing algorithms that use local quadratic or local linear approximation to the penalty function, the MMCD seeks to majorize the negative log-likelihood by a quadratic loss, but does not use any approximation to the penalty. This strategy makes it possible to avoid the computation of a scaling factor in each update of the solutions, which improves the efficiency of coordinate descent. Under certain regularity conditions, we establish theoretical convergence property of the MMCD. We implement this algorithm for a penalized logistic regression model using the SCAD and MCP penalties. Simulation studies and a data example demonstrate that the MMCD works sufficiently fast for the penalized logistic regression in high-dimensional settings where the number of covariates is much larger than the sample size. PMID:25309048
MIDAS: Regionally linear multivariate discriminative statistical mapping.
Varol, Erdem; Sotiras, Aristeidis; Davatzikos, Christos
2018-07-01
Statistical parametric maps formed via voxel-wise mass-univariate tests, such as the general linear model, are commonly used to test hypotheses about regionally specific effects in neuroimaging cross-sectional studies where each subject is represented by a single image. Despite being informative, these techniques remain limited as they ignore multivariate relationships in the data. Most importantly, the commonly employed local Gaussian smoothing, which is important for accounting for registration errors and making the data follow Gaussian distributions, is usually chosen in an ad hoc fashion. Thus, it is often suboptimal for the task of detecting group differences and correlations with non-imaging variables. Information mapping techniques, such as searchlight, which use pattern classifiers to exploit multivariate information and obtain more powerful statistical maps, have become increasingly popular in recent years. However, existing methods may lead to important interpretation errors in practice (i.e., misidentifying a cluster as informative, or failing to detect truly informative voxels), while often being computationally expensive. To address these issues, we introduce a novel efficient multivariate statistical framework for cross-sectional studies, termed MIDAS, seeking highly sensitive and specific voxel-wise brain maps, while leveraging the power of regional discriminant analysis. In MIDAS, locally linear discriminative learning is applied to estimate the pattern that best discriminates between two groups, or predicts a variable of interest. This pattern is equivalent to local filtering by an optimal kernel whose coefficients are the weights of the linear discriminant. By composing information from all neighborhoods that contain a given voxel, MIDAS produces a statistic that collectively reflects the contribution of the voxel to the regional classifiers as well as the discriminative power of the classifiers. Critically, MIDAS efficiently assesses the
Ultrasonic Linear Motor with Two Independent Vibrations
NASA Astrophysics Data System (ADS)
Muneishi, Takeshi; Tomikawa, Yoshiro
2004-09-01
We propose a new structure of an ultrasonic linear motor in order to solve the problems of high-power ultrasonic linear motors that drive the XY-stage for electron beam equipment and to expand the application fields of the motor. We pay special attention to the following three points: (1) the vibration in two directions of the ultrasonic linear motor should not influence mutually each other, (2) the vibration in two directions should be divided into the stage traveling direction and the pressing direction of the ultrasonic linear motor, and (3) the rigidity of the stage traveling direction of the ultrasonic linear motor should be increased. As a result, the supporting method of ultrasonic linear motors is simplified. The efficiency of the motor is improved and temperature rise is reduced. The stage position drift is also improved.
On the linear programming bound for linear Lee codes.
Astola, Helena; Tabus, Ioan
2016-01-01
Based on an invariance-type property of the Lee-compositions of a linear Lee code, additional equality constraints can be introduced to the linear programming problem of linear Lee codes. In this paper, we formulate this property in terms of an action of the multiplicative group of the field [Formula: see text] on the set of Lee-compositions. We show some useful properties of certain sums of Lee-numbers, which are the eigenvalues of the Lee association scheme, appearing in the linear programming problem of linear Lee codes. Using the additional equality constraints, we formulate the linear programming problem of linear Lee codes in a very compact form, leading to a fast execution, which allows to efficiently compute the bounds for large parameter values of the linear codes.
NASA Astrophysics Data System (ADS)
Pusok, Adina E.; Kaus, Boris; Popov, Anton
2017-04-01
It is commonly accepted that slab detachment results from the development of extensional stresses within the subducting slab. Subduction slowdown due to arrival of buoyant continental material at the trench is considered to cause such stress build up in the slab. Following slab detachment, slab pull partially or completely loses its strength and hot asthenosphere may flow through the slab window, which can have major consequences for continental collision. The dynamics of slab detachment has been extensively studied in 2D (i.e. analytical and numerical), but 3D models of slab detachment during continental collision remain largely unexplored. Some of the previous 3D models have investigated the role of an asymmetric margin on the propagation of slab detachment (van Hunen and Allen, 2011), the impact of slab detachment on the curvature of orogenic belts (Capitanio and Replumaz, 2013), the role of the collision rate on slab detachment depth (Li et al., 2013) or the effect of along-trench variations on slab detachment (Duretz et al., 2014). However, rheology of mantle and lithosphere is known to have a major influence on the dynamics of subduction. Here, we explore a range of different rheological approximations to understand their sensitivity on the possible scenarios. We employ the code LaMEM (Kaus et al., 2016) to perform 3D simulations of subduction/continental collision in an integrated lithospheric and upper-mantle scale model. The models exhibit a wide range of behaviours depending on the rheological law employed: from linear, to temperature-dependent visco-elasto-plastic rheology that takes into account both diffusion and dislocation creep. For example, we find that slab dynamics varies drastically between end member models: in viscous approximations, slab detachment is slow, dominated by viscous thinning, while for a non-linear visco-elasto-plastic rheology, slab detachment is relatively fast, dominated by plastic breaking and inducing strong mantle flow in
Pandiselvi, S; Raja, R; Cao, Jinde; Rajchakit, G; Ahmad, Bashir
2018-01-01
This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.
NASA Astrophysics Data System (ADS)
Yesilgul, U.; Al, E. B.; Martínez-Orozco, J. C.; Restrepo, R. L.; Mora-Ramos, M. E.; Duque, C. A.; Ungan, F.; Kasapoglu, E.
2016-08-01
In the present study, the effects of electric and magnetic fields on the linear and third-order nonlinear optical absorption coefficients and relative change of the refractive index in asymmetric GaAs/GaAlAs double quantum wells under intense laser fields are theoretically investigated. The electric field is oriented along the growth direction of the heterostructure while the magnetic field is taken in-plane. The intense laser field is linear polarization along the growth direction. Our calculations are made using the effective-mass approximation and the compact density-matrix approach. Intense laser effects on the system are investigated with the use of the Floquet method with the consequent change in the confinement potential of heterostructures. Our results show that the increase of the electric and magnetic fields blue-shifts the peak positions of the total absorption coefficient and of the total refractive index while the increase of the intense laser field firstly blue-shifts the peak positions and later results in their red-shifting.
On some Approximation Schemes for Steady Compressible Viscous Flow
NASA Astrophysics Data System (ADS)
Bause, M.; Heywood, J. G.; Novotny, A.; Padula, M.
This paper continues our development of approximation schemes for steady compressible viscous flow based on an iteration between a Stokes like problem for the velocity and a transport equation for the density, with the aim of improving their suitability for computations. Such schemes seem attractive for computations because they offer a reduction to standard problems for which there is already highly refined software, and because of the guidance that can be drawn from an existence theory based on them. Our objective here is to modify a recent scheme of Heywood and Padula [12], to improve its convergence properties. This scheme improved upon an earlier scheme of Padula [21], [23] through the use of a special “effective pressure” in linking the Stokes and transport problems. However, its convergence is limited for several reasons. Firstly, the steady transport equation itself is only solvable for general velocity fields if they satisfy certain smallness conditions. These conditions are met here by using a rescaled variant of the steady transport equation based on a pseudo time step for the equation of continuity. Another matter limiting the convergence of the scheme in [12] is that the Stokes linearization, which is a linearization about zero, has an inevitably small range of convergence. We replace it here with an Oseen or Newton linearization, either of which has a wider range of convergence, and converges more rapidly. The simplicity of the scheme offered in [12] was conducive to a relatively simple and clearly organized proof of its convergence. The proofs of convergence for the more complicated schemes proposed here are structured along the same lines. They strengthen the theorems of existence and uniqueness in [12] by weakening the smallness conditions that are needed. The expected improvement in the computational performance of the modified schemes has been confirmed by Bause [2], in an ongoing investigation.
Lee, Won-Ho; Lee, Se-Hee; Lee, Sangyoup; Lee, Jong-Chul
2018-09-01
Nanoparticles and nanofluids have been implemented in energy harvesting devices, and energy harvesting based on magnetic nanofluid flow was recently achieved by using a layer-built magnet and micro-bubble injection to induce a voltage on the order of 10-1 mV. However, this is not yet suitable for some commercial purpose. In order to further increase the amount of electric voltage and current from this energy harvesting the air bubbles must be segmented in the base fluid, and the magnetic flux of the segmented flow should be materially altered over time. The focus of this research is on the development of a segmented ferrofluid flow linear generator that would scavenge electrical power from waste heat. Experiments were conducted to obtain the induced voltage, which was generated by moving a ferrofluid-filled capsule inside a multi-turn coil. Computations were then performed to explain the fundamental physical basis of the motion of the segmented flow of the ferrofluids and the air-layers.
Linear summation of outputs in a balanced network model of motor cortex
Capaday, Charles; van Vreeswijk, Carl
2015-01-01
Given the non-linearities of the neural circuitry’s elements, we would expect cortical circuits to respond non-linearly when activated. Surprisingly, when two points in the motor cortex are activated simultaneously, the EMG responses are the linear sum of the responses evoked by each of the points activated separately. Additionally, the corticospinal transfer function is close to linear, implying that the synaptic interactions in motor cortex must be effectively linear. To account for this, here we develop a model of motor cortex composed of multiple interconnected points, each comprised of reciprocally connected excitatory and inhibitory neurons. We show how non-linearities in neuronal transfer functions are eschewed by strong synaptic interactions within each point. Consequently, the simultaneous activation of multiple points results in a linear summation of their respective outputs. We also consider the effects of reduction of inhibition at a cortical point when one or more surrounding points are active. The network response in this condition is linear over an approximately two- to three-fold decrease of inhibitory feedback strength. This result supports the idea that focal disinhibition allows linear coupling of motor cortical points to generate movement related muscle activation patterns; albeit with a limitation on gain control. The model also explains why neural activity does not spread as far out as the axonal connectivity allows, whilst also explaining why distant cortical points can be, nonetheless, functionally coupled by focal disinhibition. Finally, we discuss the advantages that linear interactions at the cortical level afford to motor command synthesis. PMID:26097452
Linear summation of outputs in a balanced network model of motor cortex.
Capaday, Charles; van Vreeswijk, Carl
2015-01-01
Given the non-linearities of the neural circuitry’s elements, we would expect cortical circuits to respond non-linearly when activated. Surprisingly, when two points in the motor cortex are activated simultaneously, the EMG responses are the linear sum of the responses evoked by each of the points activated separately. Additionally, the corticospinal transfer function is close to linear, implying that the synaptic interactions in motor cortex must be effectively linear. To account for this, here we develop a model of motor cortex composed of multiple interconnected points, each comprised of reciprocally connected excitatory and inhibitory neurons. We show how non-linearities in neuronal transfer functions are eschewed by strong synaptic interactions within each point. Consequently, the simultaneous activation of multiple points results in a linear summation of their respective outputs. We also consider the effects of reduction of inhibition at a cortical point when one or more surrounding points are active. The network response in this condition is linear over an approximately two- to three-fold decrease of inhibitory feedback strength. This result supports the idea that focal disinhibition allows linear coupling of motor cortical points to generate movement related muscle activation patterns; albeit with a limitation on gain control. The model also explains why neural activity does not spread as far out as the axonal connectivity allows, whilst also explaining why distant cortical points can be, nonetheless, functionally coupled by focal disinhibition. Finally, we discuss the advantages that linear interactions at the cortical level afford to motor command synthesis.
Schweiger, Regev; Fisher, Eyal; Rahmani, Elior; Shenhav, Liat; Rosset, Saharon; Halperin, Eran
2018-06-22
Estimation of heritability is an important task in genetics. The use of linear mixed models (LMMs) to determine narrow-sense single-nucleotide polymorphism (SNP)-heritability and related quantities has received much recent attention, due of its ability to account for variants with small effect sizes. Typically, heritability estimation under LMMs uses the restricted maximum likelihood (REML) approach. The common way to report the uncertainty in REML estimation uses standard errors (SEs), which rely on asymptotic properties. However, these assumptions are often violated because of the bounded parameter space, statistical dependencies, and limited sample size, leading to biased estimates and inflated or deflated confidence intervals (CIs). In addition, for larger data sets (e.g., tens of thousands of individuals), the construction of SEs itself may require considerable time, as it requires expensive matrix inversions and multiplications. Here, we present FIESTA (Fast confidence IntErvals using STochastic Approximation), a method for constructing accurate CIs. FIESTA is based on parametric bootstrap sampling, and, therefore, avoids unjustified assumptions on the distribution of the heritability estimator. FIESTA uses stochastic approximation techniques, which accelerate the construction of CIs by several orders of magnitude, compared with previous approaches as well as to the analytical approximation used by SEs. FIESTA builds accurate CIs rapidly, for example, requiring only several seconds for data sets of tens of thousands of individuals, making FIESTA a very fast solution to the problem of building accurate CIs for heritability for all data set sizes.
Bounded-Degree Approximations of Stochastic Networks
Quinn, Christopher J.; Pinar, Ali; Kiyavash, Negar
2017-06-01
We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identifymore » the r-best approximations among these classes, enabling robust decision making.« less
NASA Astrophysics Data System (ADS)
MacArt, Jonathan F.; Mueller, Michael E.
2016-12-01
Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport-reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.
Vestibular short latency responses to pulsed linear acceleration in unanesthetized animals
NASA Technical Reports Server (NTRS)
Jones, T. A.
1992-01-01
Linear acceleration transients were used to elicit vestibular compound action potentials in non-invasively prepared, unanesthetized animals for the first time (chicks, Gallus domesticus, n = 33). Responses were composed of a series of up to 8 dominant peaks occurring within 8 msec of the stimulus. Response amplitudes for 1.0 g stimulus ranged from 1 to 10 microV. A late, slow, triphasic, anesthesia-labile component was identified as a dominant response feature in unanesthetized animals. Amplitudes increased and latencies decreased as stimulus intensity was increased (MANOVA P less than 0.05). Linear regression slope ranges were: amplitudes = 1.0-5.0 microV/g; latencies = -300 to -1100 microseconds/g. Thresholds for single polarity stimuli (0.035 +/- 0.022 g, n = 11) were significantly lower than those of alternating polarity (0.074 +/- 0.028 g, n = 18, P less than 0.001). Bilateral labyrinthectomy eliminated responses whereas bilateral extirpation of cochleae did not significantly change response thresholds. Intense acoustic masking (100/104 dB SL) produced no effect in 2 animals, but did produce small to moderate effects on response amplitudes in 7 others. Changes were attributed to effects on vestibular end organs. Results of unilateral labyrinth blockade (tetrodotoxin) suggest that P1 and N1 preferentially reflect ipsilateral eighth nerve compound action potentials whereas components beyond approximately 2 msec reflect activity from vestibular neurons that depend on both labyrinths. The results demonstrate that short latency vestibular compound action potentials can be measured in unanesthetized, non-invasively prepared animals.
Improved Linear-Ion-Trap Frequency Standard
NASA Technical Reports Server (NTRS)
Prestage, John D.
1995-01-01
Improved design concept for linear-ion-trap (LIT) frequency-standard apparatus proposed. Apparatus contains lengthened linear ion trap, and ions processed alternately in two regions: ions prepared in upper region of trap, then transported to lower region for exposure to microwave radiation, then returned to upper region for optical interrogation. Improved design intended to increase long-term frequency stability of apparatus while reducing size, mass, and cost.
NASA Astrophysics Data System (ADS)
Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho
2018-06-01
In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.
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