Relevant Coefficients Research Articles

Nonlinear Kernel Convolutional Neural Network to Find Median Sand Particle Size

Kim, H.; Yoo, H.J., and Lee, J.L., 2021. Nonlinear Kernel Convolutional Neural Network to find median sand particle size. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 1-5. Coconut Creek (Florida), ISSN 0749-0208. Convolutional Neural Network (CNN) has successfully been used in various areas. We focus on predicting various sand particle sizes by applying convolutional neural network with a nonlinear kernel. The nonlinear kernel involves a bias and negative square of subtraction between input image pixel numbers and the kernel coefficients and summation. The convolution layer conform new feature map in Convolutional Neural Network. While using batch gradient descent method to train relevant coefficients and biases, the gradient of the square of subtraction term appears in the whole gradient over each kernel coefficient. The network was examined on regular-sized sands, i.e. 2000, 1000, 500, 250, 125 and 63 micrometer. The network was trained by using various images for each size. It was validated against new images and the absolute error was less than 30 micrometer, respectively, which is satisfactory. The network was applied by using 3 images of sands with size distribution. The results show good validation and satisfactory predictions. In the course of study, several numbers of kernels, kernel sizes, pooling sizes were tried and the optimum architecture for this work was chosen. It is expected that the present network will reduce time and effort in obtaining median sand size in many field projects. The size distribution of sand particles could also be obtained with the present network in the near future.

Comparing the embodied carbon and cost of concrete floor solutions

Multi-objective optimisation of concrete floors for economic and environmental performance is critical in the present context since the building construction sector is responsible for a rising share of the global economy and greenhouse gas emissions. This study explores how the designs with optimum cost and embodied carbon are governed by the selection of a concrete floor system and column spacing. Discrete concrete floor designs were generated parametrically varying the column spacing for eight different construction forms available in practice. Pareto optimal solutions for cost and cradle-to-gate embodied carbon were identified for a range of column spacings. The trends of the sensitivity of the optimum solutions were also investigated due to inherent uncertainty and potential variations in the cost and embodied carbon of different constituents. Column spacings can be increased up to 2 m than the optimum, compromising cost or embodied carbon only up to 10% due to their nonlinear relationship, depending on the slab type. Post-tensioning can reduce embodied carbon of flat slabs for spans longer than 7 m but do not reach Pareto optimality due to available cheaper floor solutions with similar levels of embodied carbon. Flat slabs can be suggested as Pareto optimal for spans within 6 m–8 m when construction time and storey height is considered, due to reduced cost. However, parallelly Pareto optimal two-way slabs on beams have up to only 8% higher cost but up to 37% lower embodied carbon than flat slabs. While the floor designs are optimum for spans within 5–7 m for most of the slab types, two-way slabs on beams and/or hollow-core slabs are the optimum choice for a wide range of spans depending on relevant cost and carbon coefficients.

Boundary equation from a lattice model and modification of the Peierls equation

ABSTRACT The boundary equation establishes the relationship between the displacement and the external force on the boundary of a solid. In the short-range interaction approximation, the boundary equation of a half-infinite lattice can be formally derived in lattice statics. Based on a model of cubic lattice, the boundary matrix as the kernal of the boundary equation is studied and calculated. In particular, the boundary matrix is completely presented for quasi one-dimensional problem and the leading order correction to the results in the elastic continuum theory is explicitly determined. The boundary equation can be used to derive the dislocation equation as a generalisation of classical Peierls equation. As an application, the modification of the Peierls equation is obtained and relevant coefficients are successfully related to bulk properties of solids.

Accurate determination of the peak channel temperature by an electrical method combined with EL mapping technique in In0.17Al0.83N/GaN HEMTs

In this work, an effective electrical method combined with EL mapping technique is developed to evaluate the peak channel temperature (Tp) in lattice-matched InAlN/GaN high electron mobility transistors. Electroluminescence (EL) is observed when devices operate at different dissipated power with Vg = 0 V. EL intensity shows a triangular distribution along the channel and the highest intensity is near the gate edge towards the drain. Assuming a linear relationship between the EL intensity and the channel temperature, a simple triangular resistivity distribution is established. The relevant temperature coefficient is directly obtained by measuring the channel resistance as a function of the temperature. Due to the different physical nature, the resultant Tp values are obviously higher than the average channel temperature derived by the traditional electrical measurements, and are very close to the peak values determined by the Raman spectroscopy. Therefore, our proposed method is more suitable for practical large-scale production.

Chiral excitations of open-beauty systems

We study the scattering of open-beauty mesons and Goldstone bosons as predicted by the chiral SU(3) Lagrangian. The impact of subleading order chiral interactions to systems with $J^P= 0^+$ and $J^P=1^+$ quantum numbers is worked out. We estimate the relevant low-energy coefficients from the open-charm sector, for which their values have been determined previously from sets of QCD lattice data. The leading order heavy-quark symmetry breaking effects are estimated by matching the $B$-meson ground-state chiral mass formula to the mass formula from the heavy-quark effective theory. We make refined predictions for the flavor anti-triplet and sextet resonances that are generated dynamically by coupled-channel interactions.

Modelling the trade balance between the northern and southern eurozone using an intertemporal approach

We use an intertemporal model to examine the division of the Eurozone area into countries with persistent trade account surpluses and those with persistent deficits. This is done by examining the trade account balances between a Northern group of countries that are in persistent trade account surplus and a Southern group of countries that have persistent deficits over the period 2001–2018. The theoretical model highlights the interaction of consumption, portfolio optimization between holdings of domestic and foreign bonds, fiscal balances, changes in the demand to hold money balances and changes in the pricing of risk in financial markets as reflected in changes in the interest rate differentials. We test the model using both the ARDL and Fully Modified OLS methodologies and find that it performs well empirically with relevant coefficients being both right signed and significant.

Study on Air Pollution Behavior of VOCs with Photochemical Monitoring Stations Using EGARCH Model in Southern Taiwan

This study adopted the exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model to examine the 10 ozone precursors of the highest concentrations among the 54 that were assessed over a number of years at the four photochemical assessment monitoring stations (PAMSs) in the Kaohsiung–Pingtung Area in Taiwan. First, the 10 ozone precursors, which were all volatile organic compounds (VOCs), were analyzed using the factor analyses in multiple statistical analyses that had the most significant impact on the area’s ozone formation: mobile pollution factor, which included 1,2,4-Trimethylbenzene (C9H12), toluene (C7H8), and Isopropyl benzene (C9H12). Then, taking into consideration that the number sequences might be affected by standardized residuals, this study applied the vector autoregressive moving average-EGARCH (VARMA-EGARCH) model to analyze the correlation between the three VOCs under different polluting activities. The VARMA-EGARCH model in this research included dummy variables representing changing points of variance structures in the variance formula to predict the conditional variance. This process proved able to effectively estimate the relevant coefficients of the three VOCs’ dynamic conditions that changed with time. The model also helped to prevent errors from occurring when estimating the conditional variance. Based on the testing results, this study determined the VARMA(2,1)-EGARCH(1,0) as the most suitable model for exploring the correlation between the three VOCs and meteorological phenomena, as well as the interplay between them in regard to interaction and formation. With the most representative of the three, toluene (TU), as the dependent variable and 1,2,4-Trimethylbenzene (TB) and Isopropyl benzene (IB) as the independent variables, this study found it impossible to calculate the TU concentration with TB and IB concentrations in the same period; estimations of TB and IB concentrations with a period of lag time were required because TU was mainly contributed by automobiles and motorcycles in Kaohsiung. TB and IB resulted from other stationary pollution sources in the region besides cars and motorbikes. When TU was evenly distributed and stayed longer in the atmosphere, the TB and IB concentrations were lower, so distribution conditions and concentrations could not be used to effectively estimate the concentration of toluene. This study had to wait until the next period, or when stationary pollution sources started producing TB and IB of higher concentrations during the daytime, in order to estimate the TU concentrations in a better photochemical situation.

The Magnetic Field Analytical Calculation in a Novel Double Air-Gaps Permanent Magnet Vernier Synchronous Motor

A novel double air-gaps permanent magnet vernier synchronous motor (PMVSM) is proposed in this article. Because of the unique slotted structure of the outer stator, the motor has the characteristics of low speed and large torque. The rotating magnetic field of the inner and outer double air gaps simultaneously drags the rotor to move. The parameterized outer stator slotted double air-gaps PMVSM has a 22.5% higher torque than the same structure single air-gap motor. Use a magnetic field analytical calculation to analyze the motor. By establishing the Laplace and Poisson equations, the general solution and the relevant coefficients in the analytical solution of each part of the motor are solved. The parametric study of the outer stator slot angle γ and the inner stator notch angle β increases the torque and reduces the torque ripple. The comparison between the analytical calculation results and the finite-element method (FEM) results confirms the effectiveness of the magnetic field analytical calculation and parametric study.

3D printing fluorescent material with tunable optical properties

The 3D printing of fluorescent materials could help develop, validate, and translate imaging technologies, including systems for fluorescence-guided surgery. Despite advances in 3D printing techniques for optical targets, no comprehensive method has been demonstrated for the simultaneous incorporation of fluorophores and fine-tuning of absorption and scattering properties. Here, we introduce a photopolymer-based 3D printing method for manufacturing fluorescent material with tunable optical properties. The results demonstrate the ability to 3D print various individual fluorophores at reasonably high fluorescence yields, including IR-125, quantum dots, methylene blue, and rhodamine 590. Furthermore, tuning of the absorption and reduced scattering coefficients is demonstrated within the relevant mamalian soft tissue coefficient ranges of 0.005–0.05 mm−1 and 0.2–1.5 mm−1, respectively. Fabrication of fluorophore-doped biomimicking and complex geometric structures validated the ability to print feature sizes less than 200 μm. The presented methods and optical characterization techniques provide the foundation for the manufacturing of solid 3D printed fluorescent structures, with direct relevance to biomedical optics and the broad adoption of fast manufacturing methods in fluorescence imaging.

The Mediated Role of Credibility on Information Sources and Patient Awareness toward Patient Rights.

Although patient rights are an important issue, this remains an understudied research area. Patients are unaware of their rights, lacking control of health care treatments they might deserve. This can contribute to sustaining inequality as well as failure in achieving welfare policy goals. Drawing on channel complementarity theory, the current study explored patients’ awareness toward their rights, and the credibility of information sources related to patient rights. In a web-based survey, 994 Israeli participants, suffering from chronic illness and using health services, were recruited. To examine the study’s theoretical framework and relationships among the constructs and test the hypotheses, a path analysis was conducted using Structural Equation Modeling. The research model depicts direct and indirect relationships between constructs, and the relevant coefficients. The results show a direct and positive interaction between information credibility and patient rights awareness (β = 0.10, p = 0.019). Information credibility partially mediates the relationship between public service information sources and patient rights awareness (bootstrap with 95% CI: 0.01–0.07; p = 0.015). The mass media information sources construct is directly and positively related to information credibility (β = 0.36, p = 0.000). Age was found as a moderator, indicating that information credibility is a factor only at lower ages. Therefore, patient rights should be systematically and reliably accessible in order to raise the awareness and trust of chronic patients regarding information about patient rights. Using planned health communication campaigns mainly via public service sources that are perceived as trustworthy can help contribute to approach patients more effectively and provide them with accessible and detailed information about their rights.

Impact of Updated OECD/NEA Thermodynamic Database on the Safety Assessment of Radioactive Waste Repository Studied Using RESRAD-OFFSITE Code

A RESRAD-OFFISTE computational code for the safety assessment model of a radioactive waste repository was utilized to evaluate the influence of the updated OECD/NEA thermodynamic database on the safety assessment model in terms of exposure dose. The solubility data as the input parameter for the RESRAD-OFFSITE code obtained with two different sets of chemical thermodynamic databases such as JAEA-TDB and amended JAEA-TDB reflecting the updates of the OECD/NEA thermodynamic database were calculated and compared with each other. As a result, almost identical exposure doses were obtained due to the remarkable similarity between the solubility data of various radionuclides for both chemical thermodynamic databases. In contrast, dramatic changes in exposure dose were observed with varying distribution coefficients. Thermodynamic calculations indicated that the aqueous species distribution can be significantly changed by the selection of a chemical thermodynamic database and thus the relevant distribution coefficient can also be influenced as a consequence. Accordingly, the result obtained in the present work indicated that (i) the impact of the updated chemical thermodynamic data was somewhat minor from the viewpoint of the solubility and (ii) the distribution coefficient, which can be sensitively influenced by the predominant chemical species, produced a remarkable change in the exposure dose. This work provided an insight into the precise exposure dose calculation in terms of the reliable estimation of the distribution coefficient by means of a surface complexation model, which can predict the distribution coefficient as a function of groundwater composition coupled with a chemical speciation calculation based on up to date chemical thermodynamic data.

Internal calibration of Gaia BP/RP low-resolution spectra

Context. The full third Gaia data release will provide, for the first time, the calibrated spectra obtained with the blue and red Gaia slitless spectrophotometers (BP and RP, respectively). Gaia is a very complex mission and cannot be considered as a single instrument, but rather as many instruments. The two lines of sight with wide fields of view introduce strong variations of the observations across the large focal plane with more than one hundred different detectors. The main challenge when facing Gaia spectral calibration is that no lamp spectra or flat fields are available during the mission. Also, the significant size of the line spread function with respect to the dispersion of the prisms produces alien photons contaminating neighbouring positions of the spectra. This makes the calibration special and different from standard approaches. Aims. This work gives a detailed description of the internal calibration model for the spectrophotometric data used to obtain the content of the Gaia catalogue. The main purpose of the internal calibration is to bring all the epoch spectra onto a common flux and pixel (pseudo-wavelength) scale, taking into account variations over the focal plane and with time, producing a mean spectrum from all the observations of the same source. Methods. In order to describe all observations on a common mean flux and pseudo-wavelength scale, we constructed a suitable representation of the internally calibrated mean spectra via basis functions, and we described the transformation between non-calibrated epoch spectra and calibrated mean spectra via a discrete convolution, parametrising the convolution kernel to recover the relevant coefficients. Results. The model proposed here for the internal calibration of the Gaia spectrophotometric observations is able to combine all observations into a mean instrument to allow the comparison of different sources and observations obtained with different instrumental conditions along the mission and the generation of mean spectra from a number of observations of the same source. We derived a calibration model that can handle the self-calibrating nature of the problem. The output of this model provides the internal mean spectra, not as a sampled function (flux and wavelength), but as a linear combination of basis functions, although sampled spectra can easily be derived from them.

Tailoring the microstructure of an oriented graphite flake/Al composite produced by powder metallurgy for achieving high thermal conductivity

An Al matrix composite reinforced with 40 vol% graphite flake (Gf) was developed by powder metallurgy as a promising candidate for thermal management applications. Thermal conductivity (TC) along the orientation direction of the composite sintered at 640 °C was measured to be 452 W/m K, which is approximate to the highest TC value theoretically predicted by effective medium approximation model. The three underlying mechanisms responsible for such TC enhancement were clarified in terms of microstructure characterization. First, heat treatment of as-received Gf under Ar + H2 atmosphere resulted in reduction of defects on the edge contributing to improvement of interface thermal exchange efficiency between Al and Gf. Second, image analysis quantitatively confirmed that a step-by-step die filling process using the spherical powder ensures the perfect orientation of Gf in the Al matrix. Third, it was found that the TC of the composite increases with the sintering temperature from 580 to 640 °C. The formation of a small amount of fine platelet-like Al4C3 at the interface between the side surface of Gf and Al matrix indicates the desirable bonding state for minimizing interfacial thermal resistance, beneficial for the overall TC enhancement. Besides, the relevant coefficient of thermal expansion and bending strength were discussed.

A Novel Design Method of Heat Sink with Conjugate Heat Transfer by Free-Shape Channel Modeling

Heat sink is an indispensable and even hard-core device which ensures the reliability and lifespan of most electronic equipment. Geometry factor plays a crucial role in the heat sink design. This paper proposes a novel geometric modeling method for heat sink with conjugate heat transfer properties, which involves parametric design of the flow passage patterns and cross-sections. Two assumed serpentine cooling plates with round and quadrilateral cross-sections are utilized to validate the proposed method respectively. During modeling, the fixed geometry dimensions are divided into several degrees of freedom to promote the flexibility of geometry factor with regard to heat sink design. The Bernstein-Bézier function is utilized to define these degrees of freedom. The numerical simulations based on the orthogonal experimental design are carried out, and then the results are analyzed and compared. The experimental results revealed that the optimised design can be obtained by adjusting the relevant control coefficients, which further improves the performance of cooling plate effectively. This paper guides the heat sink design and provides an insight into the structure problems from the perspective of geometry parameterization.

An asymmetric analysis of the role of exports and imports in consumption-based carbon emissions in the G7 economies: evidence from nonlinear panel autoregressive distributed lag model.

A genuine concern faced by the present world is global warming. Millions of human and animal lives are at risk due to global warming. Therefore, the subject has gained enormous attention from research and academia around the world. Literature shows that the primary cause of global climate change or global warming is carbon (CO2) emissions. Hence, the role of a reliable carbon emission measurement is important for devising a relevant climate policy to deal with environmental problems. Based on trade-adjusted statistics of carbon emissions, a relevant climate policy response can be provided. Unlike the previous studies, this study examines the asymmetric impact of international trade on consumption-based carbon emissions from 1990 to 2017 in the G7 economies. To get empirical estimates, the study applies second-generation co-integration technique and nonlinear panel autoregressive distributive lag (NPARDL) model for estimating the relevant coefficients. The empirical results show that positive growth of exports significantly decreases consumption-based carbon emissions both in the short and long run, whereas the impact of negative growth of exports is insignificant. For imports, the results show that, over time, positive growth of imports significantly increases consumption-based carbon emissions in the long run, while the impact of negative growth of imports is insignificant. Finally, it is recommended for the policymakers to target the export industries for relevant policy interventions, which are less polluting and can generate other economic benefits as well.

COVID-19 and overconfidence bias: the case of developed, emerging and frontier markets

PurposeThe main purpose of the present study is to delve into the overconfidence bias in global stock markets during both pre COVID-19 and COVID-19 phases.Design/methodology/approachThe present study makes use of daily adjusted closing prices and volume of the broad market indices of 46 global stock markets over a period ranging from July 2015 till June 2020. The sample period is split into pre COVID-19 and COVID-19 phases. In order to test the overconfidence fallacy in the chosen stock markets, bivariate market-wide vector auto regression (VAR) models and impulse response functions (IRFs) have been employed in both phases.FindingsA highly significant contemporaneous relationship between market return and volume appears to be more pronounced in the Japanese, US, Chinese and Vietnamese stock markets in the pre COVID-19 era for the relevant coefficients are positive and highly significant for most lags. Coming to the period of turbulence, the present study discovers strong overconfident behavior in the Chinese, Taiwanese, Turkish, Jordanian and Vietnamese stock markets during COVID-19 phase.Practical implicationsA stark finding is that none of the developed stock markets reveal strong overconfidence bias during pandemic, suggesting a loss or decline in the investors' confidence. Therefore, the regulators should try to regain the investors' trust and confidence in the markets by ensuring honest, fair and transparent practices. The money managers should reduce the transaction cost to encourage trading and educate investors to hold a well-diversified portfolio to mitigate risk in the long run. The governments may launch recovery packages focusing on sustaining and improving economic activities. Finally, a better investment culture may be built by the corporate houses through good corporate governance practices to regain lost trust.Originality/valueThe present study appears to be the very first attempt to gauge overconfidence bias in the wake of a recent COVID-19 pandemic.

Analysis of Protein Content on Commercial Protein Supplement in Indonesia

Commercial Protein Supplements that are circulating freely nowadays are consumed not only by athletes but the wider community, especially sports activists who rely upon it to improve performance or merely for aesthetic interests. This study aims to analyze the nutritional content of the five supplements circulating freely in Indonesia to then compare it with the claims on the packaging label. We analyzed five samples of popular supplements in Indonesia obtained online and then tested in three copies for each sample. The actual total protein in the supplement sample is measured using the Kjeldahl method where the appropriate nitrogen material is converted to percentage of protein by multiplying a factor of 6.38 in duplicate. Then the research data processed and analyzed using Microsoft Excel 2016 computer programs then by Statistical Program for Social Sciences (SPSS), consecutively. Relationships between different tests were evaluated by calculating the relevant correlation coefficients (Pearson linear correlation) (p <0.05). Analysis of variance (ANOVA) was used to compare the differences between products with different manufacturing processes (p <0.05). Based on the analysis results, only two of the five samples studied has a minimum of 80% compatibility with the claim on the packaging label. Several main factors including inaccurate analysis, preparation processing on products that triggers protein denaturation, inadequate storage, and regulations that have just been set so that producers are still free to write Nutrition Value Information with a fairly low level of accuracy. This research is expected to be able to help the evaluation for producers and the government (BPOM) to be able to provide correct information to consumers so that maximum physiological benefits can be obtained.

Calculation of Phase Diagrams and First-Principles Study of Germanium Impacts on Phosphorus Distribution in Czochralski Silicon

Phosphorus (P) is one of the most widely used donor dopants for fabricating a low-resistivity silicon (Si) substrate. However, its volatile nature and the relatively small equilibrium segregation coefficient in Si at the melting temperature of Si impede the efficient and effective growth of low-resistivity Czochralski (CZ) Si single crystal. The primary objective of this work is to theoretically perceive the influence of germanium co-doping on the heavily P-doped Si crystal by means of CALculation of PHase Diagrams (CALPHAD) approaches and density functional theory (DFT) calculations. Phase equilibria at the Si-rich corner of the Si-Ge-P system has been thermodynamically extrapolated based on robust thermodynamic descriptions of involved binary systems, where Si-P and Ge-P have been re-assessed in this work. Phase diagram calculation results indicate that at a given P concentration (e.g. 0.33 at.% P) Ge co-doping lowers the solidification temperature of the Si(Ge, P) alloys, as well as the relevant equilibrium segregation coefficients of P in the doped Si. DFT calculations simulated the formation of (i) monovacancy in Si as well as (ii) solutions of Si(P) and Si(Ge) with one dopant substitutionally inserted in 64- and 216-atom Si cubic supercells. Binding energies were calculated and compared for Ge-Ge, Ge-P and P-P bonds positioning at the first nearest-neighbors (1NN) to the third nearest-neighbors (3NN). P-P bonds have the largest bonding energy from 1NN to 3NN configurations. The climbing image nudged elastic band method (CL-NEB) was utilized to calculate the energy barriers of P 1NN jump in the 64-atom Si cubic supercell with/without a neighboring Ge atom. With Ge present, a higher energy barrier for P 1NN jump was obtained than that without involving Ge. This indicates that Ge can impede the P diffusion in Si matrix.

Crossing symmetry for long multiplets in 4D mathcal{N} = 1 SCFTs

In this work we construct the crossing symmetry equations for mixed correlators of two long and two BPS operators in 4D mathcal{N} = 1 SCFTs. The analysis presented here illustrates how our general group theoretic approach to long superblocks and tensor structures of superconformal algebras can be applied to give explicit ready-to-use expressions. In the case at hand, we obtain a system of four crossing symmetry equations for the relevant OPE coefficients. One of these four equations coincides with the equation found and analysed by Li, Meltzer and Stergiou by restricting to the superprimary component of the long multiplets. The other three equations are new and they provide powerful additional constraints on the same OPE data.

In-Plane Shear-Axial Strain Coupling Formulation for Shear-Deformable Composite Thin-Walled Beams

This paper presents an improved description of the in-plane strain coupling in Librescu-type shear-deformable composite thin-walled beams (CTWB). Based on existing descriptions for Euler-type CTWB, an analogous formulation for shear-deformable CTWB is here developed by building, via the Mindlin–Reissner theory and an orthotropic constitutive law of the shell wall, an alternate equation for the in-plane shear force which effectively couples the axial and shear in-plane strains. It is observed that this strain coupling formulation includes some of the transversal (out-of-plane) shear strain terms, thus also functioning as a path for transferring transversal shear energy to the in-plane strain field and therefore improving shear-deformability. The performance of the new CTWB model is compared against that of previously available CWTB (i.e. Euler-type with strain coupling and Timoshenko-type without strain coupling) for several aspect ratios, fibre-orientations and laminate types. Error measures are calculated by comparing several relevant stiffness coefficients and displacement shapes to reference results provided by corresponding 3D shell-based ANSYS finite-element models. Results indicate that for cases involving significant shear energy (i.e. short aspect ratios) and/or in-plane shear-axial strain coupling (i.e. off-axis or asymmetric/unbalanced laminates), the new CTWB model proposed in this work can attain an accuracy level comparable to that associated to more sophisticated models, two to three orders of magnitude larger, at a fraction of the computational cost.