Smaller Maximum Error Research Articles

Ultrafast Electronic Coupling Estimators: Neural Networks versus Physics-Based Approaches.

Fast and accurate estimation of electronic coupling matrix elements between molecules is essential for the simulation of charge transfer phenomena in chemistry, materials science, and biology. Here we investigate neural-network-based coupling estimators combined with different protocols for sampling reference data (random, farthest point, and query by committee) and compare their performance to the physics-based analytic overlap method (AOM), introduced previously. We find that neural network approaches can give smaller errors than AOM, in particular smaller maximum errors, while they require an order of magnitude more reference data than AOM, typically one hundred to several hundred training points, down from several thousand required in previous ML works. A Δ-ML approach taking AOM as a baseline is found to give the best overall performance at a relatively small computational overhead of about a factor of 2. Highly flexible π-conjugated organic molecules like non-fullerene acceptors are found to be a particularly challenging case for ML because of the varying (de)localization of the frontier orbitals for different intramolecular geometries sampled along molecular dynamics trajectories. Here the local symmetry functions used in ML are insufficient, and long-range descriptors are expected to give improved performance.

Improved Approximations to Wagner Function Using Sparse Identification of Nonlinear Dynamics

The Wagner function represents the response in lift on an airfoil that is subject to a sudden change in conditions. While it plays a fundamental role in the development and application of unsteady aerodynamic methods, explicit expressions for this function are difficult to obtain. This has led to numerous proposed approximations that facilitate convenient and rapid computations. While these approximations can be sufficient for many purposes, their behavior is often noticeably different from the true Wagner function, especially for long-time asymptotic behavior. In particular, while many approximations have small maximum absolute error across all times, the relative error of the asymptotic behavior can be substantial. Here, we propose an alternative approximation methodology that is accurate for all times, for a variety of accuracy measures. This methodology casts the Wagner function as the solution of a nonlinear scalar ordinary differential equation, which is identified using a variant of the sparse identification of nonlinear dynamics algorithm. We show that this approach yields accurate approximations using either first- or second-order differential equations. We additionally demonstrate that this method can be applied to model the lift response for a more realistic aerodynamic system, featuring a finite thickness airfoil and nonplanar wake.

Scattered Data Interpolation Using Quartic Triangular Patch for Shape-Preserving Interpolation and Comparison with Mesh-Free Methods

Scattered data interpolation is important in sciences, engineering, and medical-based problems. Quartic Bézier triangular patches with 15 control points (ordinates) can also be used for scattered data interpolation. However, this method has a weakness; that is, in order to achieve C 1 continuity, the three inner points can only be determined using an optimization method. Thus, we cannot obtain the exact Bézier ordinates, and the quartic scheme is global and not local. Therefore, the quartic Bézier triangular has received less attention. In this work, we use Zhu and Han’s quartic spline with ten control points (ordinates). Since there are only ten control points (as for cubic Bézier triangular cases), all control points can be determined exactly, and the optimization problem can be avoided. This will improve the presentation of the surface, and the process to construct the scattered surface is local. We also apply the proposed scheme for the purpose of positivity-preserving scattered data interpolation. The sufficient conditions for the positivity of the quartic triangular patches are derived on seven ordinates. We obtain nonlinear equations that can be solved using the regula-falsi method. To produce the interpolated surface for scattered data, we employ four stages of an algorithm: (a) triangulate the scattered data using Delaunay triangulation; (b) assign the first derivative at the respective data; (c) form a triangular surface via convex combination from three local schemes with C 1 continuity along all adjacent triangles; and (d) construct the scattered data surface using the proposed quartic spline. Numerical results, including some comparisons with some existing mesh-free schemes, are presented in detail. Overall, the proposed quartic triangular spline scheme gives good results in terms of a higher coefficient of determination (R2) and smaller maximum error (Max Error), requires about 12.5% of the CPU time of the quartic Bézier triangular, and is on par with Shepard triangular-based schemes. Therefore, the proposed scheme is significant for use in visualizing large and irregular scattered data sets. Finally, we tested the proposed positivity-preserving interpolation scheme to visualize coronavirus disease 2019 (COVID-19) cases in Malaysia.

Low-Power Unsigned Divider and Square Root Circuit Designs Using Adaptive Approximation

In this paper, an adaptive approximation approach is proposed for the design of a divider and a square root (SQR) circuit. In this design, the division/SQR is computed by using a reduced-width divider/SQR circuit and a shifter by adaptively pruning some insignificant input bits. Specifically, for a $2n/n$2n/n division, $2k$2k and $k$k ($k<n$k<n) consecutive bits are selected starting from the most significant ‘1’ in the dividend and divisor, respectively. At the same time, redundant least significant bits (LSBs) are truncated or if the number of remaining bits after pruning is smaller than the number of bits to be kept, ‘0's are appended to the LSBs of the inputs. To avoid overflow, a $2(k+1)/(k+1)$2(k+1)/(k+1) divider is used to compute the $2k/k$2k/k division. Finally, an error correction circuit is proposed to recover the error caused by the shifter using OR gates. For a $2n$2n-bit approximate SQR circuit, similar pruning schemes are used to obtain a $2k$2k-bit radicand. A $2k$2k-bit SQR circuit and a shifter are then utilized to compute the SQR. This adaptive operation leads to very small maximum error distances of the approximate divider and SQR circuits, as shown by a theoretical error analysis. The proposed 16/8 approximate divider using an 8/4 exact array divider is $2.5\times$2.5× as fast but only consumes 34.42 percent of the power of the accurate design. Compared to the accurate 16-bit array SQR circuit, the approximate design with a 6-bit radicand is $3.9\times$3.9× as fast and consumes 20.66 percent of the power. The approximate SQR circuit using a 6-bit lookup table-based SQR circuit consumes 7.15 percent of the power of its corresponding accurate design. The proposed designs outperform other approximate designs in image processing applications including change detection (for the divider), envelope detection (for the SQR circuit) and image reconstruction (for both designs).

DeltaComp: Fast and efficient compression of astronomical timelines

Astronomical instruments commonly generate large data series in tabular format. To efficiently store and transmit these data series, carefully designed compression formats are welcome. We propose DeltaComp, a free open-source program suited for (relatively) smooth streams of data. DeltaComp is based on rather simple mechanisms; essentially it is a tailored combination of delta coding and context-based modeling. Following the methodology of the preceding work presenting Polycomp (Tomasi, 2016), we compress (i) the ephemeris table of Ganymede, and (ii) the publicly available timelines recorded by LFI, an array of microwave radiometers aboard the ESA Planck spacecraft. In the former case (with small data) the compression ratio advantage of DeltaComp over Polycomp is by a factor of about 1.4. For the Planck data, of size 4.24TB, the archives produced by DeltaComp are almost six times smaller than those from Polycomp, at somewhat smaller median quantization error (and much smaller maximum error), which translates to only 66GB of required storage. Importantly, DeltaComp is over three orders of magnitude faster than Polycomp.

Analysis of Large‐Strain Consolidation Behavior of Soil with High Water Content in Consideration of Self‐Weight

Based on the axisymmetric large‐strain consolidation (ALSC) model with the void ratio as the variable under equal strain condition, difference schemes of model’s equation, initial condition, and boundary condition were given. Taking phosphatic clay in Florida as a research object, the consolidation behaviors of soil with high water content by axisymmetric large‐strain theory and one‐dimensional large‐strain theory were analyzed. The effect of different kinds of consolidation theories and self‐weight stress on an average degree of consolidation was evaluated. The development of the void ratio and excess pore water pressure along the soil layer was clarified. The results show that the theoretical value of Terzaghi’s consolidation degree is always less than that of ALSC (Us, the average degree of consolidation defined by strain)‐vertical drainage in the consolidation process. Terzaghi’s solution overestimates the dissipation rate of excess pore water pressure during the earlier consolidation period but underestimates it during the later consolidation period. The degree of consolidation calculated by Hansbo develops faster than ALSC (Up, the average degree of consolidation defined by stress)‐radial drainage, but slower than ALSC (Us)‐radial drainage. In the ALSC model, Us is always been faster than Up. The effect of self‐weight on the consolidation degree of axisymmetric large‐strain consolidation theory is relatively small (maximum error is less than 16%), while it can accelerate the consolidation rate of soil in one‐dimensional large‐strain consolidation theory largely. When only the vertical drainage occurs, the consolidation rate in the middle of the soil is obviously lagging the upper and lower parts, while the radial drainage can reduce the void ratio and the excess pore water pressure along the soil layer uniformly and more rapidly.

Validation of biplane high-speed fluoroscopy combined with two different noninvasive tracking methodologies for measuring invivo distal limb kinematics of the horse.

Biplane high-speed fluoroscopy is a new method for gait analysis of the equine distal extremity. This is the first study validating the noninvasive tracking possibilities (Autoscoping and Scientific Rotoscoping) taking equine anatomy into account. To determine the resolution with which Autoscoping and Scientific Rotoscoping depict motion of the equine phalanges in comparison to the invasive gold standard marker-based registration. Comparative exvivo study. In 5 distal extremities of slaughtered ponies, 3 or 4 tantalum beads with 1mm diameter were implanted in each of the proximal, middle and distal phalangeal bones. Three-dimensional models of the bones were reconstructed using computed tomographic data (120kV, 50mA, slice thickness 1mm, increment 0.5). The beads were digitally removed from the bone models. Biplane fluoroscopic videos were taken at 69.5±3.5kV, 102.5±22.5mA, 500frames/s and 0.5ms shutter speed. The 5 specimens were moved in the trial field of the biplane fluoroscopic setup in a step-like motion (simulation of landing, main stance phase, lift-off). Marker-based registration, Autoscoping and Scientific Rotoscoping were carried out. For statistical analysis agreement was computed as percentiles, mean and s.d. The medians of Scientific Rotoscoping ranged from 0.16 to 0.66mm in translations and 0.43 to 2.78° in rotations, while values for Autoscoping were 0.13-0.70mm and 0.28-2.39° respectively. With 2 exceptions, all differences between methods were statistically significant. Scientific Rotoscoping is more time efficient than Autoscoping and results in smaller maximum errors. The experimental set-up was specifically designed to accommodate invivo requirements. Autoscoping was not manually corrected but rather expected to work automatically. It is possible to noninvasively apply both Autoscoping and Scientific Rotoscoping for gait analysis of the equine phalanges with high precision. The summary is available in Chinese - see supporting information.

High-accuracy variable-phase filter design utilising iterative linear-programming strategy

ABSTRACTThis paper proposes an iterative strategy employing the linear programming (LP) method for the design of an all-pass variable-phase (AP-VP) digital filter in the minimax error sense. Mathematically, designing an AP-VP digital filter belongs to a non-linear optimisation problem. The novel LP design method first reduces this non-linear minimisation problem to a linear minimisation problem and then solves the linearised optimisation problem iteratively via using the LP method. The iterative LP-solving scheme is able to reduce the largest design errors significantly and thus can get a considerable accuracy improvement as compared to the noniterative one. We will utilise three design examples to show that this iterative scheme can get much better design results (much smaller maximum errors) than the noniterative method in the literature. Therefore, this iterative LP design strategy can significantly enhance the performance of the AP-VP digital filter.

Trajic: An Effective Compression System for Trajectory Data

The need to store vast amounts of trajectory data becomes more problematic as GPS-based tracking devices become increasingly prevalent. There are two commonly used approaches for compressing trajectory data. The first is the line generalisation approach which aims to fit the trajectory using a series of line segments. The second is to store the initial data point and then store the remaining data points as a sequence of successive deltas. The line generalisation approach is only effective when given a large error margin, and existing delta compression algorithms do not permit lossy compression. Consequently there is an uncovered gap in which users expect a good compression ratio by giving away only a small error margin. This paper fills this gap by extending the delta compression approach to allow users to trade a small maximum error margin for large improvements to the compression ratio. In addition, alternative techniques are extensively studied for the following two key components of any delta-based approach: predicting the value of the next data point and encoding leading zeros. We propose a new trajectory compression system called Trajic based on the results of the study. Experimental results show that Trajic produces 1.5 times smaller compressed data than a straight-forward delta compression algorithm for lossless compression and produces 9.4 times smaller compressed data than a state-of-the-art line generalisation algorithm when using a small maximum error bound of 1 meter.

Estimation of semolina dough rheological parameters by inversion of a finite elements model

The description of the rheological properties of food material plays an important role in food engineering. Particularly for the optimisation of pasta manufacturing process (extrusion) is needful to know the rheological properties of semolina dough. Unfortunately characterisation of non-Newtonian fluids, such as food doughs, requires a notable time effort, especially in terms of number of tests to be carried out. The present work proposes an alternative method, based on the combination of laboratory measurement, made with a simplified tool, with the inversion of a finite elements numerical model. To determine the rheological parameters, an objective function, defined as the distance between simulation and experimental data, was considered and the well-known Levenberg-Marqard optimisation algorithm was used. In order to verify the feasibility of the method, the rheological characterisation of the dough was carried also by a traditional procedure. Results shown that the difference between measurements of rheological parameters of the semolina dough made with traditional procedure and inverse methods are very small (maximum percentage error equal to 3.6%). This agreement supports the coherence of the inverse method that, in general, may be used to characterise many non-Newtonian materials.

A new active position sensing method for ropeless elevator

Traditional cable driven elevators perform poorly in high-rise buildings because the weight of the cable limits the payload, and its elasticity degrades control performance. Further, it is not mechanically possible to include several elevator cars in the same hoistway because of the cable. However such multi-car elevator systems are desirable since they reduce passenger waiting time and reduce the space requirements of the elevator system. A promising solution is to use long armature linear motors spanning the hoistway to directly drive elevator cages. In such applications, the mover position sensing method must be explicitly addressed since most active position sensing methods require traveling cables, which are also an obstacle for multi-car elevator systems.In this paper, the linear-motor active position sensing method is formally introduced and the principle of operation, design and real-time operation methods are presented. The proposed method is used to measure the position of the mover of a long armature permanent magnet linear synchronous motor requiring no active components on the mover, thus traveling cables are eliminated. The principle of operation is inspired by linear variable differential transformer: A magnetic shunt positioned at a fixed distance ahead of the mover deforms the magnetic field created by one of the armature coils. The deformation can be determined by measuring the induced voltages on the neighboring coils, and the position of the shunt, and thus the mover, can be calculated.A design method for the optimal dimensions of the shunt for a given armature to provide long measurement range and small maximum position error is presented, accompanied by a real-time measurement algorithm that will enable the motor to be driven using the method. Finally the method is verified by simulations and experimental results conducted on a full scale linear-motor elevator prototype that was constructed in the laboratory.

Nyquist-Rate Current-Steering Digital-to-Analog Converters With Random Multiple Data-Weighted Averaging Technique and &amp;lt;formula formulatype="inline"&amp;gt;&amp;lt;tex&amp;gt;$Q^{N}$&amp;lt;/tex&amp;gt;&amp;lt;/formula&amp;gt; Rotated Walk Switching Scheme

In this brief, Nyquist-rate current-steering digital-to-analog converters (DACs) applying the random multiple data-weighted averaging (RMDWA) technique and the QN rotated walk switching scheme are proposed such that high spurious-free dynamic range (SFDR) and small maximum output error can be achieved without calibrations, which are area and power consuming. RMDWA suppresses the harmonics caused by element mismatches to gain high SFDR performance. Furthermore, QN rotated walk can lower the maximum output error when RMDWA and Q N rotated walk are employed simultaneously. Because the benefits of both dynamic element matching technique and switching scheme are obtained by the proposed DAC structure, the proposed structure can deliver smaller maximum output errors than traditional randomization techniques even if a low-cost small-area DAC with poor matching property is adopted

Error Bounds for Numerical Inversion of a Probability Characteristic Function

Given the characteristic function of a continuous real random variable, it is possible to construct a finite Fourier series that approximates the density over any specified finite interval. This series converges in mean square if the density decays faster than |x|-1 and the characteristic function decays faster than |t|-1/2; it converges in minimax if the density decays faster than |x|-1 and the characteristic function decays faster than |t|-1. It is also possible to construct a finite Fourier series for the distribution function that has arbitrarily small maximum error over any finite interval provided that the characteristic function decays as $|t|^{-\beta}$ for some $\beta>0$ and that either the distribution or the density decays (to 0 or 1, as appropriate) as $|x|^{-\alpha}$ for some $\alpha>1$; these conditions are weak enough to include most continuous distributions of practical interest. Explicit error bounds can be obtained directly from the characteristic function, without prior knowledge of either the distribution or density, making these series useful for numerical inversion.

Accurate Impedance Determination of Coupled TEM Conductors

A computer-aided finite-difference method is described which can be used to calculate accurately TEM mode impedances of a uniform pair of offset parallel-coupled conductors of arbitrary cross section. The calculated impedance is the average of the lower and upper bounds computed on the mode impedance. For a given computing time, the average impedance is usually found to be more accurate than the one obtainable with either bound alone. The use of a graded mesh is found to provide a smaller separation between the bounds, and hence a smaller maximum error in the average impedance value, in a time much shorter than with the uniform mesh.