Traditional Approximation Research Articles

Leveraging Automatic High-Level Synthesis Resource Sharing to Maximize Dynamical Voltage Overscaling with Error Control

Approximate Computing has emerged as an alternative way to further reduce the power consumption of integrated circuits (ICs) by trading off errors at the output with simpler, more efficient logic. So far the main approaches in approximate computing have been to simplify the hardware circuit by pruning the circuit until the maximum error threshold is met. One of the critical issues, though, is the training data used to prune the circuit. The output error can significantly exceed the maximum error if the final workload does not match the training data. Thus, most previous work typically assumes that training data matches with the workload data distribution. In this work, we present a method that dynamically overscales the supply voltage based on different workload distribution at runtime. This allows to adaptively select the supply voltage that leads to the largest power savings while ensuring that the error will never exceed the maximum error threshold. This approach also allows restoring of the original error-free circuit if no matching workload distribution is found. The proposed method also leverages the ability of High-Level Synthesis (HLS) to automatically generate circuits with different properties by setting different synthesis constraints to maximize the available timing slack and, hence, maximize the power savings. Experimental results show that our proposed method works very well, saving on average 47.08% of power as compared to the exact output circuit and 20.25% more than a traditional approximation method.

The modification of turbulent thermal wind balance by non-traditional effects

The meridional component of the earth's rotation is often neglected in geophysical contexts. This is referred to as the ‘traditional approximation’ and is justified by the typically small vertical velocity and aspect ratio of such problems. Ocean fronts are regions of strong horizontal buoyancy gradient and are associated with strong vertical transport of tracers and nutrients. Given these comparatively large vertical velocities, non-traditional rotation may play a role in governing frontal dynamics. Here the effects of non-traditional rotation on a front in turbulent thermal wind balance are considered using an asymptotic approach. Solutions are presented for a general horizontal buoyancy profile and examined in the simple case of a straight front. Non-traditional effects are found to depend strongly on the direction of the front and may lead to the generation of jets and the modification of the frontal circulation and vertical transport.

Streamer inception thresholds derived from a statistical electron transport model

The aim of this article is to review a statistical description of electron transport in gases based on transport parameter theory, and to derive expressions for streamer inception thresholds in quasi-homogeneous electrical fields within this description. The critical average number of electrons required to induce avalanche-to-streamer transition is derived for arbitrary gases as a function of the gap electric field and the relevant gas parameters. The model is then evaluated for synthetic air. Significant deviations from the traditional approximation are found for small gaps ( 1 mm). Moreover, the minimal necessary number of electrons for avalanche-to-streamer transition is found to scale approximately with the inverse of gas pressure. The application of the adapted streamer inception criterion to the calculation of the partial discharge inception voltage for twisted enamelled wires, where discharges are incepted in gaps with 1 mm, is discussed. Our results support the conclusion that space charges generated by sub-critical avalanche processes play a determining role for streamer onset in such configurations, i.e. that their partial discharge inception cannot be reliably quantified by applying the streamer criterion in the Laplacian electrode field. Finally, the streamer inception probability is compared to the deterministic streamer inception criterion. In particular, the problem of non-exponential growth in the early stages of the electron avalanche development is argued to be properly addressed within the applied statistical interpretation of transport parameters.

The traditional approximation of rotation for rapidly rotating stars and planets

Context. The traditional approximation of rotation (TAR) is a treatment of the hydrodynamic equations of rotating and stably stratified fluids in which the action of the Coriolis acceleration along the direction of the entropy and chemical stratifications is neglected because it is weak in comparison with the buoyancy Archimedean force. This leads to the neglect of the horizontal projection of the rotation vector in the equations for the dynamics of gravito-inertial waves (GIWs). The dependent variables in those equations then become separable into radial and horizontal parts as in the non-rotating case. The TAR is built on the assumptions that the star is spherical (i.e., its centrifugal deformation is neglected) and uniformly rotating. However, it has recently been generalised to include the effects of a moderate centrifugal deformation using a perturbative approach. Aims. We study the feasibility of carrying out a new generalisation to account for the centrifugal acceleration in the case of strongly deformed uniformly and rapidly rotating stars (and planets), and to identify the validity domain of this approximation. Methods. We built a complete formalism analytically that allows the study of the dynamics of GIWs in spheroidal coordinates which take the flattening of uniformly and rapidly rotating stars into account by assuming the hierarchies of frequencies adopted within the TAR in the spherical case. Results. Using 2D stellar models, we determine the validity domain of the generalised TAR as a function of the rotation rate of the star normalised by its critical angular velocity and its pseudo-radius. Assuming the anelastic and the two-dimensional Jeffreys-Wentzel-Kramers-Brillouin approximations, we derive a generalised Laplace tidal equation for the horizontal eigenfunctions of the GIWs and their asymptotic wave periods, which can be used to probe the structure and dynamics of rotating deformed stars with asteroseismology. The generalised TAR where the centrifugal deformation of a star (or planet) is taken into account non-perturbatively allows us to identify, within the framework of 2D Evolution STEllaire en Rotation models, the validity domain of this approximation which is reduced by increasing the rate of rotation. We can affirm with a level of confidence of 90% that the TAR remains applicable in all the space domain of deformed stars rotating at a rotation rate lower than 20% of the critical rotation rate. Conclusions. A new generalisation of the TAR, which takes the centrifugal acceleration into account in a non-perturbative way, is derived. This generalisation allows us to study the detectability and the signature of the centrifugal effects on GIWs in rapidly rotating deformed stars (and planets). We found that the effects of the centrifugal acceleration in rapidly rotating early-type stars on GIWs are theoretically detectable in modern space photometry using observations from Kepler. We found also, by comparing the period spacing pattern computed with the standard and the generalised TAR, that the centrifugal acceleration affects the period spacing by increasing its values for low radial orders and by decreasing them slightly for high radial orders.

Learning graph edit distance by graph neural networks

The emergence of geometric deep learning as a novel framework to deal with graph-based representations has faded away traditional approaches in favor of completely new methodologies. In this paper, we propose a new framework able to combine the advances on deep metric learning with traditional approximations of the graph edit distance. Hence, we propose an efficient graph distance based on the novel field of geometric deep learning. Our method employs a message passing neural network to capture the graph structure, and thus, leveraging this information for its use on a distance computation. The performance of the proposed graph distance is validated on two different scenarios. On the one hand, in a graph retrieval of handwritten words i.e. keyword spotting, showing its superior performance when compared with (approximate) graph edit distance benchmarks. On the other hand, demonstrating competitive results for graph similarity learning when compared with the current state-of-the-art on a recent benchmark dataset.

Variational balance models for the three-dimensional Euler–Boussinesq equations with full Coriolis force

We derive a semi-geostrophic variational balance model for the three-dimensional Euler–Boussinesq equations on the nontraditional f-plane under the rigid lid approximation. The model is obtained by a small Rossby number expansion in the Hamilton principle, with no other approximations made. We allow for a fully non-hydrostatic flow and do not neglect the horizontal components of the Coriolis parameter; that is, we do not make the so-called “traditional approximation.” The resulting balance models have the same structure as the “L1 balance model” for the primitive equations: a kinematic balance relation, the prognostic equation for the three-dimensional tracer field, and an additional prognostic equation for a scalar field over the two-dimensional horizontal domain, which is linked to the undetermined constant of integration in the thermal wind relation. The balance relation is elliptic under the assumption of stable stratification and sufficiently small fluctuations in all prognostic fields.

A linear source scheme for the 2D/1D transport method in SHARK

The 2D/1D transport method has already become the most popular direct transport method these several years considering the balance of efficiency and accuracy. Linear source scheme has been researched and applied in method of characteristics (MOC), which shows great advantages in efficiency and accuracy compared to the traditional flat source approximation. Therefore, to improve the calculation performance of the 2D/1D method further, the linear source scheme is applied in the 2D/1D method with a newly-developed direct transport code SHARK. The equation derivation is conducted and the framework of the linear source scheme in SHARK is introduced. Two macro cases, including C5G7 benchmark and macro BEAVRS benchmark, are adopted to show the performance improvement of the linear source scheme in the 2D/1D method.

Firefighting Equipment Arrangement Optimization for an Offshore Platform Considering Travel Distances

The offshore plant, due to its characteristics, is subject to many restrictions on the material and design of the pipes. Because the design of the firefighting piping depends on the pre-set fire protection design, it is possible to reduce the cost of the piping design by optimizing the arrangement of the firefighting equipment. Existing studies have low accuracy in obtaining service areas under these conditions. In addition, the arrangement optimization problem is generally modeled as a set cover problem (SCP). However, except for the traditional greedy approximation, this problem is not well researched for general solutions. In this paper, first, a modified iterative-deepening search (MIDS), which accurately obtains a service area according to the travel distance in the grid space, is proposed before optimization. Additionally, this paper seeks to define a set cover problem by combining the subsets obtained by MIDS. Second, by using the traditional greedy algorithm, we obtained the initial arrangement of the firefighting equipment. Then, we proposed a method to obtain an approximate optimization solution using a modified greedy method including rearrangement. The validity of the proposed coverage area acquisition and arrangement optimization method is verified by comparing the performance with other algorithms. Finally, this study was applied to the drawings of an actual offshore platform.

Границы применимости теории Элиашберга и ограничения на температуру сверхпроводящего перехода

The discovery of record - breaking values of superconducting transition temperature $T_c$ in quite a number of hydrides under high pressure was an impressive demonstration of capabilities of electron - phonon mechanism of Cooper pairing. This lead to an increased interest to foundations and limitations of Eliashberg - McMillan theory as the main theory describing superconductivity in a system of electrons and phonons. Below we shall consider both elementary basics of this theory and a number of new results derived only recently. We shall discuss limitations on the value of the coupling constant related to lattice instability and a phase transition to another phase (CDW, bipolarons). Within the stable metallic phase the effective pairing constant may acquire arbitrary values. We consider extensions beyond the traditional adiabatic approximation. It is shown that Eliasberg - McMillan theory is also applicable in the strong antiadiabatic limit. The limit of very strong coupling, being most relevant for the physics of hydrides, is analyzed in details. We also discuss the bounds for $T_c$ appearing in this limit.

Neural network approximation

Neural networks (NNs) are the method of choice for building learning algorithms. They are now being investigated for other numerical tasks such as solving high-dimensional partial differential equations. Their popularity stems from their empirical success on several challenging learning problems (computer chess/Go, autonomous navigation, face recognition). However, most scholars agree that a convincing theoretical explanation for this success is still lacking. Since these applications revolve around approximating an unknown function from data observations, part of the answer must involve the ability of NNs to produce accurate approximations.This article surveys the known approximation properties of the outputs of NNs with the aim of uncovering the properties that are not present in the more traditional methods of approximation used in numerical analysis, such as approximations using polynomials, wavelets, rational functions and splines. Comparisons are made with traditional approximation methods from the viewpoint of rate distortion, i.e. error versus the number of parameters used to create the approximant. Another major component in the analysis of numerical approximation is the computational time needed to construct the approximation, and this in turn is intimately connected with the stability of the approximation algorithm. So the stability of numerical approximation using NNs is a large part of the analysis put forward.The survey, for the most part, is concerned with NNs using the popular ReLU activation function. In this case the outputs of the NNs are piecewise linear functions on rather complicated partitions of the domain of f into cells that are convex polytopes. When the architecture of the NN is fixed and the parameters are allowed to vary, the set of output functions of the NN is a parametrized nonlinear manifold. It is shown that this manifold has certain space-filling properties leading to an increased ability to approximate (better rate distortion) but at the expense of numerical stability. The space filling creates the challenge to the numerical method of finding best or good parameter choices when trying to approximate.

The effect of the centrifugal acceleration on period spacings of gravito-inertial modes in intermediate-mass stars

Context. The Kepler and Transiting Exoplanet Survey Satellite (TESS) space telescopes delivered high-precision, long-duration photometric time series for hundreds of main-sequence stars, revealing their numerous gravito-inertial (g) pulsation modes. This high precision allows us to evaluate increasingly detailed theoretical stellar models. Recent theoretical work extended the traditional approximation of rotation, a framework to evaluate the effect of the Coriolis acceleration on g modes, to include the effects of the centrifugal acceleration in the approximation of slightly deformed stars, which so far have mostly been neglected in asteroseismology. This extension of the traditional approximation was conceived by re-deriving the traditional approximation in a centrifugally-deformed, spheroidal coordinate system. Aims. We explore the effect of the centrifugal acceleration on g modes and assess its detectability in space-based photometric observations. Methods. We implemented the new theoretical framework to calculate the centrifugal deformation of pre-computed 1D spherical stellar structure models and computed the corresponding g-mode frequencies, assuming uniform rotation. The framework was evaluated for a grid of stellar structure models covering a relevant parameter space for observed g-mode pulsators. Results. The centrifugal acceleration modifies the effect of the Coriolis acceleration on g modes, narrowing the equatorial band in which they are trapped. Furthermore, the centrifugal acceleration causes the pulsation periods and period spacings of the most common g modes (prograde dipole modes and r modes) to increase with values similar to the observational uncertainties of the measured period spacing values in Kepler and TESS data. Conclusions. The effect of the centrifugal acceleration on g modes is formally detectable in modern space photometry. The implementation of the used theoretical framework in stellar structure and pulsation codes will allow for more precise asteroseismic modelling of centrifugally deformed stars in order to assess its effect on mode excitation, trapping, and damping.

Large-offset P-wave traveltime in layered transversely isotropic media

Large-offset seismic data processing, imaging, and velocity estimation require an accurate traveltime approximation over a wide range of offsets. In layered transversely isotropic media with a vertical symmetry axis, the accuracy of traditional traveltime approximations is limited to near offsets. We have developed a new traveltime approximation that maintains the accuracy of classic equations around the zero offset and exhibits the correct curvilinear asymptote at infinitely large offsets. Our approximation is based on the conventional acoustic assumption. Its equation incorporates six parameters. To define them, we use the Taylor series expansion of the exact traveltime around the zero offset and a new asymptotic series for the infinite offset. Our asymptotic equation indicates that the traveltime behavior at infinitely large offsets is dominated by the properties of the layer with the maximum horizontal velocity in the sequence. The parameters of our approximation depend on the effective zero-offset traveltime, the normal moveout velocity, the anellipticity, a new large-offset heterogeneity parameter, and the properties of the layer with the maximum horizontal velocity in the sequence. We have applied our traveltime approximation (1) to directly calculate traveltime and ray parameter at given offsets, as analytical forward modeling, and (2) to estimate the first four of the aforementioned parameters for the layers beneath a known high-velocity layer. Our large-offset heterogeneity parameter includes the layering effect on the reflections’ traveltime.

Variability of newly identified B-type stars observed by Kepler

ABSTRACT Recent re-determination of stellar atmospheric parameters for a sample of stars observed during the Kepler mission allowed to enlarge the number of Kepler B-type stars. We present the detailed frequency analysis for all these objects. All stars exhibit pulsational variability with maximum amplitudes at frequencies corresponding to high-order g modes. Peaks that could be identified with low-order p/g modes are also extracted for a few stars. We identified some patters in the oscillation spectra that can be associated with the period spacings that can results from the asymptotic nature of the detected pulsational modes. We also tentatively confront the observed oscillation characteristics with predictions from linear non-adiabatic computations of stellar pulsations. For high-order g modes the traditional approximation was employed to include the effects of rotation on the frequency values and mode instability.

Precise Modeling of Mutual Inductance for Planar Spiral Coils in Wireless Power Transfer and Its Application

In magnetic coupling resonant wireless power transfer devices, planar spiral coils are often used as the coupling mechanism. In such application area, the coils are often wound sparsely with wide screw pitches and often under complex relative position. An accurate model of mutual inductance for planar spiral coils wound either densely or sparsely is established in this article. Utilizing Euler Angles, an exact expression of mutual inductance for a couple of planar spiral coils under arbitrary relative position is proposed. Based on this expression and geometric mean distance principle, a self-inductance expression for planar spiral coils is derived. Based on numerical calculation of the expressions proposed in this article, the influence of precession and spin angle on mutual inductance is studied; the method of determining radius of each turn when using traditional concentric circular filaments cluster approximation model for self- and mutual inductance calculation is studied; the difference of calculation results between the accurate model and the traditional approximation model is compared. Finite element simulation and experimental results verify the correctness of the proposed models.

Horizontal shear instabilities in rotating stellar radiation zones

Context. Stellar interiors are the seat of efficient transport of angular momentum all along their evolution. In this context, understanding the dependence of the turbulent transport triggered by the instabilities of the vertical and horizontal shears of the differential rotation in stellar radiation zones as a function of their rotation, stratification, and thermal diffusivity is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory, which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. Aims. We investigate horizontal shear instabilities in rotating stellar radiation zones by considering the full Coriolis acceleration with both the dimensionless horizontal Coriolis component f̃ and the vertical component f. Methods. We performed a linear stability analysis using linearized equations derived from the Navier-Stokes and heat transport equations in the rotating nontraditional f-plane. We considered a horizontal shear flow with a hyperbolic tangent profile as the base flow. The linear stability was analyzed numerically in wide ranges of parameters, and we performed an asymptotic analysis for large vertical wavenumbers using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation for nondiffusive and highly-diffusive fluids. Results. As in the traditional f-plane approximation, we identify two types of instabilities: the inflectional and inertial instabilities. The inflectional instability is destabilized as f̃ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is also extended in the nondiffusive limit as 0 < f < 1 + f̃ 2/N2, where N is the dimensionless Brunt-Väisälä frequency. More strikingly, in the high thermal diffusivity limit, it is always inertially unstable at any colatitude θ except at the poles (i.e., 0° < θ < 180°). We also derived the critical Reynolds numbers for the inertial instability using the asymptotic dispersion relations obtained from the WKBJ analysis. Using the asymptotic and numerical results, we propose a prescription for the effective turbulent viscosities induced by the inertial and inflectional instabilities that can be possibly used in stellar evolution models. The characteristic time of this turbulence is short enough so that it is efficient to redistribute angular momentum and to mix chemicals in stellar radiation zones.

Unsupervised Balanced Covariance Learning for Visual-Inertial Sensor Fusion

Incorporating multi-sensor, in filter-based as well as graph-based simultaneous localization and mapping (SLAM), relies on the uncertainties involved in each measurement. Proper covariance estimation is thus critical to balance confidence levels among sensors. Despite its importance, traditional covariance approximation mostly relied on first order derivative or fixed measurement covariance and therefore tended to be error-prone, and even heuristic. Recently, deep learning for uncertainty estimation yielded meaningful performance, but applied to a single sensor in a supervised manner. Unlike the traditional supervised manner, we introduce an unsupervised loss for uncertainty modeling, to learn uncertainty without needing ground truth covariance as a label. Most important, we overcome the limitation of learning a single sensor's uncertainty by introducing a way of balancing uncertainty between different sensor modalities. In doing so, we alleviate the uncertainty balancing issue between sensors that has often been encountered in the multi-sensor SLAM application. Targeting covariance learning for visual odometry, particularly with regard to the integration of inertial sensors, the proposed uncertainty learning method was validated in a visual-inertial odometry application over the public datasets under artificial visual and inertial degradations to mimic harsh environment.

Sustainability evaluation for phosphorus mines using a hybrid multi-criteria decision making method

Considering the mounting conflict of economic growth and environmental destruction, promoting sustainable development has become inevitable in many industries, especially for mines. This study focuses on developing suitable approaches to assess the sustainability for phosphorus mines. First, a comprehensive sustainability assessment criteria scheme is designed. For quantitative criteria, real numbers are utilized to signify objective values. For qualitative criteria, triangular fuzzy numbers (TFNs) are used to represent subjective fuzzy cognition of decision makers. Meanwhile, a variable-weight model is built to calculate sub-criteria weights. Thereafter, the traditional multi-attributive border approximation area comparison (MABAC) approach is modified with hybrid assessment data (i.e., real numbers and TFNs) to obtain the final evaluation results. Last, an example of evaluating the sustainability for four phosphorus mines in China is studied to justify the feasibility of the hybrid multi-criteria decision making (MCDM) method. Moreover, the advantages of our approach are revealed by the sensitivity and comparative analyses. The results show that our approach is dependable to deal with such hybrid MCDM problems and can provide effective guidance for sustainable development management.

Communication Modes With Large Intelligent Surfaces in the Near Field

This paper proposes a practical method for the definition of multiple communication modes when antennas operate in the near-field region, by realizing ad-hoc beams exploiting the focusing capability of large antennas. The beamspace modeling proposed to define the communication modes is then exploited to derive expressions for the number of communication modes (i.e., degrees of freedom) in a generic setup, beyond the traditional paraxial approximation, together with closed-form definitions for the basis set at the transmitting and receiving antennas for several cases of interest, such as for the communication between a large antenna and a small antenna. Numerical results indicate that quasi-optimal communication can be obtained starting from focusing functions. This translates into the possibility of a significant enhancement of the channel capacity even in line-of-sight channel condition without the need of resorting to optimal but complex phase/amplitude antenna profiles as well as intensive numerical simulations. Traditional results valid under paraxial approximation are revised in light of the proposed modeling, showing that similar conclusions can be obtained from different perspectives.

Channel Estimation and Pilot Symbol Optimization Based on Intrinsic Interference Utilization for OQAM/FBMC Systems

In this paper, we propose a novel channel estimation method and optimize the pilot symbols based on intrinsic interference utilization for offset quadrature amplitude modulation based filter-bank multicarrier (OQAM/FBMC) systems. Specifically, we firstly propose a line fitting based channel estimation method by analyzing and utilizing the distribution characteristics of the demodulated OQAM symbols, where no guard symbols are needed between pilot symbols and data symbols. Then, we formulate a pilot symbol optimization problem by utilizing the intrinsic interferences to improve the accuracy of the line fitting. Finally, we obtain the optimal solution of the optimization problem and present the corresponding pilot structure. Simulation results demonstrate that the proposed method with the optimized pilot structure performs the best among candidate pilot symbols and outperforms the traditional interference approximation method (IAM) with the optimal pilot structure.

Kakim obrazom okeanicheskiye vikhri mogut byt' stol' dolgozhivushchimi

Purpose. The article is aimed at substantiating theoretically amazing longevity (up to 5 years) of the individual vortices in the World Ocean against the background of strong fluctuations of the ocean currents and regardless of the Rossby wave dispersion features. Methods and Results. Evolution of the baroclinic vortices is considered in a hybrid two-layer ocean model over a topographic slope on the beta-plane. In the upper layer with strong potential vorticity anomalies, the currents are assumed to be balanced; in the lower layer at week potential vorticity anomalies, the currents are described in the traditional quasi-geostrophic approximation. Slow evolving almost circular vortices embedded in a vertically sheared current typical of the subtropical part of the ocean are described analytically. The theory shows how a baroclinic vortex is followed by the lee Rossby waves. The vortex drift across the mean current is conditioned mainly by the baroclinic-dipole structure of the represented solution; at that the vortex energy loss related to the Rossby wave radiation can be compensated by the energy stored in the mean currents. Conclusions. The constructed model provides reasonable estimates of the energy drift and transfer typical of the ocean vortices with strong anomalies of potential vorticity. Direct support of long-lived vortices by the energy of the baroclinic mean flows irrespective of their stability, is of great importance for better understanding the physical mechanisms relating to significant longetivity of the geophysical vortices and the features of their movement.