Search

In this paper we introduce the modelwise interpolation property of a logic that states that whenever \(\models\phi\to\psi\) holds for two formulas \(\phi\) and \(\psi\), then for every model \(\mathfrak{M}\) there is an interpolant formula \(\chi\) formulated in the intersection of the vocabularies of \(\phi\) and \(\psi\), such that \(\mathfrak{M}\models\phi\to\chi\) and \(\mathfrak{M}\models\chi\to\psi\), that is, the interpolant formula in Craig interpolation may vary from model to model. We compare the modelwise interpolation property with the standard Craig interpolation and with the local interpolation property by discussing examples, most notably the finite variable fragments of first order logic, and difference logic. As an application we connect the modelwise interpolation property with the local Beth definability, and we prove that the modelwise interpolation property of an algebraizable logic can be characterized by a weak form of the superamalgamation property of the class of algebras corresponding to the models of the logic.

The extension of the (ordinary) institution theory of Goguen and Burstall, known as the theory of stratified institutions, is a general axiomatic approach to model theories where the satisfaction is parameterized by states of models. Stratified institutions cover a uniformly wide range of applications from various Kripke semantics to various automata theories and even model theories with partial signature morphisms. In this paper, we introduce two natural concepts of logical interpolation at the abstract level of stratified institutions and we provide some sufficient technical conditions in order to establish a causality relationship between them. In essence, these conditions amount to the existence of nominals structures, which are considered fully and abstractly.

International audience; An interpolation problem is defined by a set of linear forms on the (multivariate) polynomial ring and values to be achieved by an interpolant. For Lagrange interpolation the linear forms consist of evaluations at some nodes,while Hermite interpolation also considers the values of successive derivatives. Both are examples of ideal interpolation in that the kernels of the linear forms intersect into an ideal. For an ideal interpolation problem with symmetry, we address the simultaneous computation of a symmetry adapted basis of the least interpolation space and the symmetry adapted H-basis of the ideal. Beside its manifest presence in the output, symmetry is exploited computationally at all stages of the algorithm. For an ideal invariant, under a group action, defined by a Groebner basis, the algorithm allows to obtain a symmetry adapted basis of the quotient and of the generators. We shall also note how it applies surprisingly but straightforwardly to compute fundamental invariants and equivariants of a reflection group.

Digital security in modern systems very often uses biometric, and increasingly new implementations appear. Such applications can be found everywhere, even when picking up the package from courier, we certify its receipt through our signature on tablet. However, verification of this form is not one of the simplest elements in information processing systems. Given the different sizes, angles, or writing conditions that may affect its stability new methods to evaluate signatures are constantly needed. In this article, we propose the use of spline interpolation and two types of artificial neural networks to verify the identity of a person based on selected local and global features extracted from the image of a signature. Global features are extracted concerning interpolation and graphic processing methods, while local features are verified using Convolutional Neural Networks. Both sets of features are used in the identity verification process. The article presents the model of operation together with experiments, taking into account various parameters of the proposed extraction. We have reached an accuracy of 87.7% on the SVC2004 database.

Projection techniques are often used to visualize high-dimensional data, allowing users to better understand the overall structure of multi-dimensional spaces on a 2D screen. Although many such methods exist, comparably little work has been done on generalizable methods of inverse-projection -- the process of mapping the projected points, or more generally, the projection space back to the original high-dimensional space. In this paper we present NNInv, a deep learning technique with the ability to approximate the inverse of any projection or mapping. NNInv learns to reconstruct high-dimensional data from any arbitrary point on a 2D projection space, giving users the ability to interact with the learned high-dimensional representation in a visual analytics system. We provide an analysis of the parameter space of NNInv, and offer guidance in selecting these parameters. We extend validation of the effectiveness of NNInv through a series of quantitative and qualitative analyses. We then demonstrate the method's utility by applying it to three visualization tasks: interactive instance interpolation, classifier agreement, and gradient visualization.

Different discretization and trust-region methods are compared for the low-thrust fuel-optimal trajectory optimization problem using successive convex programming. In particular, the differential and integral formulations of the adaptive pseudospectral Legendre–Gauss–Radau method, an arbitrary-order Legendre–Gauss–Lobatto technique based on Hermite interpolation, and a first-order-hold discretization are considered. The number of discretization points and segments is varied. Moreover, two hard-trust-region methods and a soft-trust-region strategy are compared. It is briefly discussed whether these methods, if implemented on relevant hardware, would fulfill the general requirements for onboard guidance. A perturbed cubic interpolation and the propagation of the nonlinear dynamics are used to generate initial guesses of varying quality. Interplanetary transfers to a near-Earth asteroid, Venus, and asteroid Dionysus are chosen to assess the overall performance.

The mortar finite element method is a well-established method for the numerical solution of partial differential equations on domains displaying non-conforming interfaces. The method is known for its application in computational contact mechanics. However, its implementation remains challenging as it relies on geometrical projections and unconventional quadrature rules. The INTERNODES (INTERpolation for NOn-conforming DEcompositionS) method, instead, could overcome the implementation difficulties thanks to flexible interpolation techniques. Moreover, it was shown to be at least as accurate as the mortar method making it a very promising alternative for solving problems in contact mechanics. Unfortunately, in such situations the method requires solving a sequence of ill-conditioned linear systems. In this paper, preconditioning techniques are designed and implemented for the efficient solution of those linear systems.

This paper presents a set of newly constructed polynomials valid in interval [-1, 1] with respect to weight function w(x) = x + 1. For applicability sake, the polynomials shall be employed as trial function to develop a fast, efficient and reliable block algorithm for the numerical solution of ordinary differential equations with application to second order initial value problems. Collocation and interpolation techniques were adopted for the formulation of self-starting continuous hybrid schemes. Findings from the analysis of the basic properties of the method using appropriate existing theorems show that the developed schemes are consistent, zero-stable and hence convergent. On implementation, the superiority of the scheme over the existing method is established numerically. Further investigation of the properties of these polynomials is ongoing as we hope to discuss this in the future paper.

Data interpolation – construction of new data points within range of a discrete set of known data point – is an important modeling activity in geographical studies. In this study, three commonly applied interpolation methods (nearest point, kriging and moving average) were examined in an assessment of the varying dispersion of selected physical and chemical parameters of stream-borne effluents from palm oil processing area in a growing commercial centre in Ife South local government area in Nigeria. Specific objectives were to examine selected physiochemical properties of a stream that receives palm oil effluent, and compare results of a kriging interpolation using derived variogram values with that which was based on the accepted parametric default in a popular geographical information system. The study also presents visualised results of interpolation of selected parameters based on ordinary kriging, moving average and nearest point interpolation. Analysis were achieved using PAST 3 and ILWIS GIS software. Result showed that although the stream is vulnerable to contamination by the palm oil processing activities around the area, it also receives contaminants from other non-source points that were not investigated in this study. It also indicated that the different point interpolation methods did not produce similar results. Whereas the values of conductivity were interpolated to vary as 120.1 – 219.5 μScm-1 with kriging interpolation, it varied as 105.6 – 220.0 μScm-1 and 135.0 – 173.9 μScm-1, with nearest point and moving average interpolations, respectively. Also, whereas the computed variogram model produced the best fit lines with Gaussian model, the Spherical model was assumed default for all the distributions in selected GIS software, such that the value of Nugget was assumed as 0.00, when it actually varies with data locations distribution. Conclusively, procedure of estimating spatial variation always produce results that are influenced by data distribution and model assumptions, and as such the data characteristics rather than GIS software’s defaults are appropriate for consideration in geospatial evaluation.

Resumo Dados espacializados de precipitação diária são úteis para diversas aplicações relacionadas à meteorologia aplicada e à hidrologia, tais como a detecção de mudanças climáticas, estudo de inundações, e compreensão da interação do clima com os processos hidrológicos e biogeoquímicos. Contudo, cada espacialização da chuva deve ser avaliada para uma determinada região específica antes de sua ampla utilização. Nesse sentido, o presente trabalho objetivou, para as bacias hidrográficas do sul do Espírito Santo (bioma Mata Atlântica), a avaliação de métodos de interpolação espacial, a criação de uma base de dados espaciais de precipitação diária em formato grid, e a comparação desta base com outras bases de dados de precipitação diária em formato grid. A avaliação dos interpoladores foi feita por meio de validação cruzada, na qual o método da Distância Angular Ponderada (ADW) apresentou melhor desempenho. A aplicação do ADW, para todos os dias do período entre 1980 e 2018, originou uma base de dados de precipitação diária em formato grid com resolução espacial de 0,01°. A base de dados criada teve desempenho semelhante à de XAVIER para a representação espacial das chuvas na região, sendo melhor que as demais avaliadas. Abstract Spacialized daily precipitation data are useful for several applications related to Applied meteorology and hydrology, such as detecting climate change, studying floods, and understanding the interaction of climate with hydrological and biogeochemical processes. In addition, each spatialization of rain must be analyzed for a given region. In this sense, the work aimed for the hydrographic basins of the South of Espírito Santo, the evaluation of spatial interpolation methods, the creation of a spatial database of daily precipitation in a grid format, and the comparison of this base with other daily precipitation databases in a grid format. The hydrographic basins were chosen because they are located within the Atlantic Forest biome. The evaluation of the interpolators was carried using means of cross-validation, in which the Weighted Angular Distance (ADW) method presented the best performance. The application of ADW for every day of the period between 1980 and 2018, originated a database of daily precipitation in a grid format and with a spatial resolution of 0.01 °. The database created had a performance similar to that of XAVIER for the spatial representation of rainfall in the region, being better than others also evaluated.

We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the now-standard conformal prediction for uncertainty quantification, with novel theoretical insights and computational advantages. The data-adaptive prediction band is universally applicable with minimal distributional assumptions, has strong non-asymptotic coverage properties, and is easy to implement using standard convex programs. Our approach can be viewed as a novel variance interpolation with confidence and further leverages techniques from semi-definite programming and sum-of-squares optimization. Theoretical and numerical performances for the proposed approach for uncertainty quantification are analyzed., 21 pages, 4 figures

Advection of trace species (tracers), also called tracer transport, in models of the atmosphere and other physical domains is an important and potentially computationally expensive part of a model's dynamical core (dycore). Semi-Lagrangian (SL) advection methods are efficient because they permit a time step much larger than the advective stability limit for explicit Eulerian methods. Thus, to reduce the computational expense of tracer transport, dycores often use SL methods to advect passive tracers. The class of interpolation semi-Lagrangian (ISL) methods contains potentially extremely efficient SL methods. We describe a set of ISL bases for element-based transport, such as for use with atmosphere models discretized using the spectral element (SE) method. An ISL method that uses the natural polynomial interpolant on Gauss-Legendre-Lobatto (GLL) SE nodes of degree at least three is unstable on the test problem of periodic translational flow on a uniform element grid. We derive new alternative bases of up to order of accuracy nine that are stable on this test problem; we call these the Islet bases. Then we describe an atmosphere tracer transport method, the Islet method, that uses three grids that share an element grid: a dynamics grid supporting, for example, the GLL basis of degree three; a physics grid with a configurable number of finite-volume subcells per element; and a tracer grid supporting use of our Islet bases, with particular basis again configurable. This method provides extremely accurate tracer transport and excellent diagnostic values in a number of validation problems. We conclude with performance results that use up to 27,600 NVIDIA V100 GPUs on the Summit supercomputer.

Hard landing is a typical flight safety incident, and interpretability plays an important role in flight safety research. However, existing studies failed to provide good interpretability of the reasons for hard landing incidents and suffer from low prediction accuracy. To address the above problems, in this paper we propose CurveCluster+, a curve clustering method based on quick access recorder (QAR) data for hard landing risk evaluation. Specifically, we first conduct an in-depth analysis on hard landing flights by comparing key QAR parameter curves with the group behavior, based on which we establish a two-level hierarchical classification of hard landing incidents according to the hard landing patterns. Then we extract curve-level features from key QAR parameters through interpolation and resampling. After that we turn the classic K-means clustering into a semi-supervised algorithm by incorporating some expert experience and apply it on the curve-level features to automatically recognize the hard landing patterns. Finally, we propose a risk evaluation model based on the clustering results to discover high-risk flights from normal ones. We evaluate our method on a QAR dataset of 37,943 Airbus 320 aircraft flights. The results show that compared with other state-of-the-art data-driven methods, CurveCluster+ provides strong interpretability of hard landing incidents and exhibits good performance in recognizing hard landing patterns (the overall accuracy of our method reaches up to 92.99%). Moreover, it only requires a handful of hard landing samples to discover high-risk flights from tremendous normal landing flights, which is critical for flight safety warnings.

Investigation of spectral (collocation or Galerkin) methods for the solution approximation of different classes of optimal control problems have had been increased in recent years. In this research work, we proposed and analyzed an applicable Legendre spectral collocation approach, based on an efficient space of fractional basis functions, to compute numerically the solution of fractional optimal control problems. We first introduce a fractional Lagrange interpolation and then approximate the unknown control and state by this new set of fractional interpolation functions. The problem is discretized in terms of shifted Legendre–Gauss collocation points and two approaches are suggested to calculate the exact fractional differentiation matrix. Also, we prove that the approximate solutions of the obtained discretized problem converge to the optimal solution of the main problem by assuming some mild conditions. The method is implemented for three numerical test problems to show the claimed efficiency and capability.

Numerical approach of two-derivative Runge-Kutta type method with three-stage fifth-order (TDRKT3(5)) is developed and proposed for solving a special type of third-order delay differential equations (DDEs) with constant delay. An algorithm based on Newton interpolation and hybrid with the TDRKT method is built to approximate the solution of third-order DDEs. In this paper, three-stage fifth-order called TDRKT3(5) method with single third derivative and multiple evaluations of the fourth derivative is highlighted to solve third-order pantograph type delay differential equations directly with the aid of the Newton interpolation method. Stability analysis of TDRKT3(5) method is investigated. The numerical experiments illustrate high efficiency and validity of the new method for solving a special class of third-order DDEs and some future works are recommended by extending proposed method to solve fractional and singularly perturbed delay differential equations.

Mapping of geological variables in the Croatian part of the Pannonian Basin System (CPBS) is mostly based on small input datasets. In the case of the analyzed hydrocarbon field "B", reservoir "K", due to the complex geological structure and pronounced tectonics, the interpretations are restricted on several blocks, where each has very limited dataset. The porosity (19 data) and permeability (18 data) variables were analyzed. The applied interpolation methods are the Inverse Distance Weighting (IDW) and the Moving Average (MA). They were compared and analyzed by visual inspection of the obtained maps, comparison of mathematical background and by calculation of cross-validation (CV). The cross-validation value for the porosity of the "K" reservoir in the case of IDW application is 0.0011, and in the case of MA 0.0010; while in the case of permeability the IDW is 480.84, and in the case of MA 1346.41. According to the visual review of maps, the values of descriptive statistics of estimated values and the results of cross-validation, the IDW method is recommended for mapping the porosity and permeability of reservoirs blocks in the Sava Depression., Kartiranje geoloških spremenljivk v hrvaškem delu Panonskega bazena temelji večinoma na majhnih vhodnih podatkovnih nizih. V primeru preučevanega polja ogljikovodikov »B«, rezervoarja »K« je zaradi kompleksne geološke zgradbe in močno izražene tektonike, interpretacija omejena na nekaj blokov, od katerih ima vsak zelo omejen nabor podatkov. Analizirane spremenljivke so bile poroznost (19 podatkov) in prepustnost (18 podatkov). Kot interpolacijski metodi sta bili uporabljeni metoda inverzne utežene razdalje (IUR) in metoda drsečega povprečja (DP). Metodi smo primerjali in analizirali s pomočjo vizualnega pregleda dobljenih kart, primerjavo matematičnega ozadja in z izračunom navzkrižne validacije. Vrednost navzkrižne validacije za poroznost rezervoarja »K« pri uporabi IDW je 0,0011, v primeru uporabe DP pa 0,0010. Vrednost navzkrižne validacije v primeru prepustnosti pa je bila pri uporabi IDW 480,84 in pri uporabi DP 1346,41. Glede na vizualni pregled kart, vrednosti opisne statistike ocenjenih vrednosti in rezultate navzkrižne validacije, se je metoda IDW izkazala za priporočljivo metodo pri kartiranju poroznosti in prepustnosti rezervoarskih blokov v Savski depresiji.

Image upscaling aims to increase the resolution and size of a low resolution (LR) image in order to generate a high resolution (HR) image of high frequency (HF). There are several polynomial methods for obtaining a sharpened, upscaled HR image. The interpolated pixel is measured using a weighted average of the neighboring pixels within the image grid that blur at HF regions in these methods. Edge degradation is also caused by other edge-directed and learning-based upscaling methods, which produce blurring artifacts. A novel approach is proposed to fill these gaps. Using the concept of unsharp masking (USM), the LR image is blurred adaptively based on the region’s local variance. The sharpened high pass filtered (HPF) image is then obtained by subtracting the adaptively blurred image from the LR image. According to USM, the HPF image is combined with the LR image via a gain factor optimized using the cuckoo search (CS) algorithm. To compensate for the loss caused by upscaling, this pre-processing step is performed prior to interpolation. Aside from that, the edge of the B-spline interpolated image is detected and expanded. Edge expansion of the upscaled image is performed to further restore the HF details and reduce zigzag artifacts introduced by upscaling while also preserving the edge boundary. The proposed method outperforms the Lanczos, Bicubic, and Bilinear schemes in terms of peak signal to noise ratio (PSNR) gain of 3.475, 8.3839, and 8.075 dB, respectively. In terms of performance, this method outperforms state-of-the-art techniques both objectively (PSNR and SSIM) and subjectively (visual quality).

Vehicle trajectory collection usually faces challenges such as inaccurate and incomplete trajectory data, mainly due to missing trajectories caused by Global Navigation Satellite System (GNSS) outages. In this paper, a novel ensemble transfer regression framework is proposed for urban environments with transfer learning as the primary solution for constructing a fine-grained trajectory dataset during GNSS outages. First, GNSS and motion information are fused for the training process. Then, a regression-to-classification (R2C) process is employed to implement incremental training to adapt to dynamically changing environments. Third, to account for GNSS outages, transfer learning is integrated to construct a data filtering strategy that minimizes negative sample weights during the current scenario. Finally, a more accurate classification-type loss function for ensemble learning is designed to obtain the ensemble transfer regression model. We utilize real-world datasets to verify the accuracy of the comparative methods and the proposed framework in trajectory interpolation prediction. The experimental results show that our framework is significantly superior to the comparative methods.

In the process industry, it is essential to establish a data-driven soft sensor to predict the key variable that is difficult to online measure directly. The accuracy performance of data-driven soft sensors relies heavily on data. Unfortunately, it is hard to acquire sufficient and informative data from the samples with limited number, which is called as the small sample problem. For handling the small sample problem, it is a good solution to generating virtual samples according to the distribution of original data. This paper proposes an enhanced method of virtual sample generation utilizing manifold features to develop soft sensors using small data. First, T-Distribution Stochastic Neighbor Embedding (t-SNE) is utilized to extract the features of input data. The main idea of generating virtual samples is to use the interpolation algorithm to obtain virtual t-SNE input features and then the random forest algorithm is utilized to get the virtual outputs using virtual t-SNE input features. Finally, virtual samples using the proposed t-SNE based virtual sample generation (t-SNE-VSG) can be achieved. For the sake of confirming the effectiveness and feasibility of the presented t-SNE-VSG, a standard data set is first used. What is more, a small data set from an actual industrial process of Purified Terephthalic Acid is used to establish a soft sensor model. The results from simulations show that the accuracy performance of the soft sensor established with small data can be effectively improved by adding the virtual samples generated by t-SNE-VSG. In addition, t-SNE-VSG achieves superior accuracy to state-of-the-art virtual sample generation methods.

MixUp is an effective data augmentation method to regularize deep neural networks via random linear interpolations between pairs of samples and their labels. It plays an important role in model regularization, semisupervised learning (SSL), and domain adaption. However, despite its empirical success, its deficiency of randomly mixing samples has poorly been studied. Since deep networks are capable of memorizing the entire data set, the corrupted samples generated by vanilla MixUp with a badly chosen interpolation policy will degrade the performance of networks. To overcome overfitting to corrupted samples, inspired by metalearning (learning to learn), we propose a novel technique of learning to a mixup in this work, namely, MetaMixUp. Unlike the vanilla MixUp that samples interpolation policy from a predefined distribution, this article introduces a metalearning-based online optimization approach to dynamically learn the interpolation policy in a data-adaptive way (learning to learn better). The validation set performance via metalearning captures the noisy degree, which provides optimal directions for interpolation policy learning. Furthermore, we adapt our method for pseudolabel-based SSL along with a refined pseudolabeling strategy. In our experiments, our method achieves better performance than vanilla MixUp and its variants under SL configuration. In particular, extensive experiments show that our MetaMixUp adapted SSL greatly outperforms MixUp and many state-of-the-art methods on CIFAR-10 and SVHN benchmarks under the SSL configuration.

In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and time-consuming. We propose a new algorithm that accelerates the CS-based reconstruction by using a fast pseudopolar Fourier based Radon transform and rebinning the diverging fan beams to parallel beams. The reconstruction process is analyzed using a maximum-a-posterior approach, which is transformed into a weighted CS problem. The weights involved in the proposed model are calculated based on the statistical characteristics of the reconstruction process, which is formulated in terms of the measurement noise and rebinning interpolation error. Therefore, the proposed method not only accelerates the reconstruction, but also removes the rebinning and interpolation errors. Simulation results are shown for phantoms and a patient. For example, a 512 × 512 Shepp-Logan phantom when reconstructed from 128 rebinned projections using a conventional CS method had 10% error, whereas with the proposed method the reconstruction error was less than 1%. Moreover, computation times of less than 30 sec were obtained using a standard desktop computer without numerical optimization.

A robust algorithm to solve the low-thrust fuel-optimal trajectory optimization problem for interplanetary spacecraft is developed in this paper. The original nonlinear optimal control problem is convexified and transformed into a parameter optimization problem using an arbitrary-order Gauss-Lobatto discretization scheme with nonlinear control interpolation. A homotopic approach that considers the energy-to-fuel smoothing path is combined with an adaptive second-order trust-region mechanism to increase the convergence rate. The overall robustness is assessed in several fuel-optimal transfers with poor initial guesses. The results show a superior performance in terms of convergence compared to standard convex programming approaches in the literature.

Establishing correct correspondences between two images should consider both local and global spatial context. Given putative correspondences of feature points in two views, in this paper, we propose Order-Aware Network, which infers the probabilities of correspondences being inliers and regresses the relative pose encoded by the essential or fundamental matrix. Specifically, this proposed network is built hierarchically and comprises three operations. First, to capture the local context of sparse correspondences, the network clusters unordered input correspondences by learning a soft assignment matrix. These clusters are in canonical order and invariant to input permutations. Next, the clusters are spatially correlated to encode the global context of correspondences. After that, the context-encoded clusters are interpolated back to the original size and position to build a hierarchical architecture. We intensively experiment on both outdoor and indoor datasets. The accuracy of the two-view geometry and correspondences are significantly improved over the state-of-the-arts. Besides, based on the proposed method and advanced local feature, we won the first place in CVPR 2019 image matching workshop challenge and also achieve state-of-the-art results in the Visual Localization benchmark. Code is available at https://github.com/zjhthu/OANet.

We propose a generic and scalable method for computing global solutions of nonlinear, high-dimensional dynamic stochastic economic models. First, within an MPI–TBB parallel time-iteration framework, we approximate economic policy functions using an adaptive, high-dimensional model representation scheme, combined with adaptive sparse grids. With increasing dimensions, the number of points in this efficiently-chosen combination of low-dimensional grids grows much more slowly than standard tensor product grids, sparse grids, or even adaptive sparse grids. Moreover, the adaptivity within the individual component functions adds an additional layer of sparsity, since grid points are added only where they are most needed — that is to say, in regions of the computational domain with steep gradients or at non-differentiabilities. Second, we introduce a performant vectorization scheme of the interpolation compute kernel. Third, we validate our claims with numerical experiments conducted on “Piz Daint" (Cray XC50) at the Swiss National Super-computing Center. We observe significant speedups over the state-of-the-art techniques, and almost ideal strong scaling up to at least 1, 000 compute nodes. Fourth, to demonstrate the broad applicability of our method, we compute global solutions to two different versions of a dynamic stochastic economic model: a high-dimensional international real business cycle model with capital adjustment costs, and with or without irreversible investment. We solve these models up to 300 continuous state variables globally.

With the increased proliferation of smart devices, the transit passengers of today expect a higher quality of service in the form of real-time traffic updates, accurate expected time-of-arrival (ETA) predictions. Providing these services requires public transit agencies and private transportation players to maintain full situational awareness of the city-wide traffic. However, most such agencies and companies are resource-constrained and do not have access to city-wide traffic data. The availability of sparsely sampled and outlier-corrupted traffic data renders the resulting traffic maps patchy and unreliable and necessitates the use of sophisticated real-time traffic interpolation and prediction algorithms. Moreover, since the traffic data is measured and collected in a sequential manner, the estimations must also be generated online. Thankfully, the traffic matrices are spatially and temporally structured, allowing the use of time-series and matrix/tensor completion algorithms. This work puts forth a generative model for the traffic density and subsequently uses a variational Bayesian formalism to learn the parameters of the model. Specifically, we consider low-rank traffic matrices whose subspace evolves according to a state-space model with possible sparse outliers. Unlike most matrix/tensor completion algorithms, the proposed model is equipped with automatic relevance determination priors that allow it to learn the parameters in an entirely data-driven manner. A forward-backward algorithm is proposed that enables the updates to be carried out at low-complexity. Simulations carried out on real traffic speed data demonstrate that the proposed algorithm better predicts the future traffic densities as compared to the state-of-the-art matrix/tensor completion algorithms.

This article presents a 9-bit 500-MS/s 2-bit/cycle successive approximation register (SAR) analog-to-digital converter (ADC) with an error-tolerant interpolation technique. The proposed interpolation technique uses flip-flops to implement a 2-bit/cycle operation in the SAR ADC. By taking advantage of the metastable region of the flip-flop, the proposed interpolator can defer the bit decision when a decision error occurs with a high probability. Because the SAR ADC approximates the signal range step by step, the deferred decisions proceed to the next conversion cycles without any increase in quantization noise. The deferring-decision characteristic increases the error tolerance in the presence of comparator mismatches and increases the inherent linearity of the interpolation technique compared to conventional latch interpolation. A prototype ADC was designed using the 28-nm CMOS technology to verify the effectiveness of the proposed interpolation technique. The measured signal-to-noise-and-distortion ratio (SNDR) and spurious-free dynamic range (SFDR) at the Nyquist rate are 50.6 and 61.4 dB, respectively. The power consumption is 1.87 mW at a sampling frequency of 500 MS/s. The proposed ADC achieves a Walden figure of merit (FoM) of 13.5 fJ/conversion-step.

This paper proposed an innovative approach for reversible data hiding (RDH) within images in such a way that the image can be accurately recovered after extracting the data. The work presented a challenging task due to the need to compromise between the quality of the stego-image and the capacity of the hidden data. It is used in applications that need to reconstruct the original images without any distortion, such as medical diagnosis, remote sensing images and military maps. The aim of this paper is to study improving RDH methods using interpolation-based scheme. The proposed interpolation-based RDH (IRDH) scheme improves the embedding capacity and security over state-of-the-art schemes. We investigated the interpolation techniques improving the parabolic interpolation (PI) method to scale-up the original image, then embedding within it the secret data using newly proposed embedding technique. The experimental results demonstrate that the proposed quadratic Bezier interpolation (QBI) technique reduced the computational complexity of PI with same quality of the produced image. Additionally, the proposed cubic interpolation techniques improved the image quality of PI but with more computational complexity. On the other hand, the proposed circle interpolation (CIRI) achieved less PSNR value than PI showing interesting remarks. The general steps of this scheme are generation of the interpolated image, data embedding, data extraction and image recovery showing attractive promising research contribution.

Assembly interfaces, the joint surfaces between the vertical tail and rear fuselage of a large aircraft, are thin-wall components. Their machining quality are seriously restricted by the machining vibration. To address this problem, an in-process adaptive milling method is proposed for the large-scale assembly interface driven by real-time machining vibration data. Within this context, the milling operation is first divided into several process steps, and the machining vibration data in each process step is separated into some data segments. Second, based on the real-time machining vibration data in each data segment, a finite-element-unit-force approach and an optimized space–time domain method are adopted to estimate the time-varying in-operation frequency response functions of the assembly interface. These FRFs are in turn employed to calculate stability lobe diagrams. Thus, the three-dimensional stability lobe diagram considering material removal is acquired via interpolation of all stability lobe diagrams. Third, to restrain milling chatter and resonance, the cutting parameters for next process step, e.g., spindle speed and axial cutting depth, are optimized by genetic algorithm. Finally, the proposed method is validated by a milling test of the assembly interface on a vertical tail, and the experimental results demonstrate that the proposed method can improve the machining quality and efficiency of the assembly interface, i.e., the surface roughness reduced from 3.2 μm to 1.6 μm and the machining efficiency improved by 33%.

In this paper, a simple scheme is constructed for finding approximate solution of the nonlinear Fredholm integral equation of the second kind. To this end, the Lagrange interpolation polynomials together with the Gauss-Legendre quadrature rule are used to transform the source problem to a system of nonlinear algebraic equations. Afterwards, the resulting system can be solved by the Newton method. The basic idea is to choose the Lagrange interpolation points to be the same as the points for the Gauss-Legendre integration. This facilitates the evaluation of the integral part of the equation. We prove that the approximate solution converges uniformly to the exact solution. Also, stability of the approximate solution is investigated. The advantages of the method are simplicity, fastness and accuracy which enhance its applicability in practical situations. Finally, we provide some test examples.

We present a systematic way to implement higher order Whitney forms in numerical methods based on discrete exterior calculus. Given a simplicial mesh, we first refine the mesh into smaller simplices which can be used to define higher order Whitney forms. Cochains on this refined mesh can then be interpolated using higher order Whitney forms. Hence, when the refined mesh is used with methods based on discrete exterior calculus, the solution can be expressed as a higher order Whitney form. We present algorithms for the three required steps: refining the mesh, solving the coefficients of the interpolant, and evaluating the interpolant at a given point. With our algorithms, the order of the Whitney forms one wishes to use can be given as a parameter so that the same code covers all orders, which is a significant improvement on previous implementations. Our algorithms are applicable with all methods in which the degrees of freedom are integrals over mesh simplices — that is, when the solution is a cochain on a simplicial mesh. They can also be used when one simply wishes to approximate differential forms in finite-dimensional spaces. Numerical examples validate the generality of our algorithms.

Traditionally, reduced hair simulation methods are either restricted to heuristic approximations or bound to specific hairstyles. We introduce the first CNN-integrated framework for simulating various hairstyles. The approach produces visually realistic hairs with an interactive speed. To address the technical challenges, our hair simulation pipeline is designed as a two-stage process. First, we present a fully-convolutional neural interpolator as the backbone generator to compute dynamic weights for guide hair interpolation. Then, we adopt a second generator to produce fine-scale displacements to enhance the hair details. We train the neural interpolator with a dedicated loss function and the displacement generator with an adversarial discriminator. Experimental results demonstrate that our method is effective, efficient, and superior to the state-of-the-art on a wide variety of hairstyles. We further propose a performance-driven digital avatar system and an interactive hairstyle editing tool to illustrate the practical applications.

This paper proposes an open-loop based demodulation technique for the instantaneous phase angle estimation of three phase voltage systems. The proposed demodulation-based method relies on the Clarke transform, finite-impulse-response filters and algorithms for phase angle and frequency deviation estimation. When compared to a frequency-locked loop (FLL) based on dual second-order generalized integrators and a phase-locked loop (PLL) relying on adaptive delayed signal cancellation operator, the proposed one does not use any integrators, recursive signals and feedback of frequency or phase angle, thus unconditionally stable and relatively simple tuning is achieved. In addition, the proposed method is computationally efficient due to avoiding interpolation, square-root, trigonometric functions or their inverse operations. Moreover, under equal dynamic condition, the proposed one generates improved accuracy at steady-state in a range of the frequency deviation specified by standard and grid code. Simulated and experimental results are presented to verify the efficacy of the proposed method.

The description of a physical problem through a model necessarily involves the introduction of parameters. Hence, one wishes to have a solution of the problem that is a function of all these parameters: a parametric solution. However, the construction of such parametric solutions exhibiting localization in space is only ensured by costly and time-consuming tests, which can be both numerical or experimental. Numerical methodologies used classically imply enormous computational efforts for exploring the design space. Therefore, parametric solutions obtained using advanced nonlinear regressions are an essential tool to address this challenge. However, classical regression techniques, even the most advanced ones, can lead to non physical interpolation in some fields such as fluid dynamics, where the solution localizes in different regions depending on the problem parameters choice. In this context, Optimal Transport (OT) offers a mathematical approach to measure distances and interpolate between general objects in a, sometimes, more physical way than the classical interpolation approach. Thus, OT has become fundamental in some fields such as statistics or computer vision, and it is being increasingly used in fields such as computational mechanics. However, the OT problem is usually computationally costly to solve and not adapted to be accessed in an online manner. Therefore, the aim of this paper is combining advanced nonlinear regressions with Optimal Transport in order to implement a parametric real-time model based on OT. To this purpose, a parametric model is built offline relying on Model Order Reduction and OT, leading to a real-time interpolation tool following Optimal Transport theory. Such a tool is of major interest in design processes, but also within the digital twin rationale.

Due to recent developments in the additive manufacturing industry, topology optimization is nowadays a powerful computational tool that allows to design feasible lightweight components. Although the Finite Element Method (FEM) is the most applied discretization technique, meshless methods are currently established as accurate numerical methods with relevant advantages in several engineering fields. Nonetheless, the state-of-the-art of meshless methods in topology optimization is still scarce. This work develops the combination of a bi-direction structural optimization (BESO) algorithm with the Natural Neighbour Radial Point Interpolation Method (NNRPIM), a meshless method combining the natural neighbours geometric concept with the RPI shape functions. First, several benchmark examples are solved to evaluate the algorithm capability under several algorithm parameters. The proposed methodology is then implemented to design new automotive lightweight components. The results from the numerical applications demonstrate that the NNRPIM is a solid technique to be incorporated in optimization algorithms. Additionally, innovative automotive industry designs for additive manufacturing can be obtained using the presented approach.

Adaptive-Network-based Fuzzy Inference System, ANFIS, offers a popular and powerful fuzzy inference mechanism. As with many other advanced data driven techniques, developing an effective ANFIS typically requires sufficient training data. However, in many real-world applications it is not always straightforward to obtain a large amount of representative data that covers the entire problem space to accomplish the required training, seriously restricting the performance of a learned ANFIS. This paper introduces a new ANFIS learning approach through an evolutionary process, which is able to generate an ANFIS with only a small number of training data in a certain problem region, by interpolating well trained ANFISs in the neighbouring regions. Such a process works by firstly producing an initial population of candidate fuzzy rules in the region of data shortage, through interpolating a rule dictionary constructed from trained ANFISs in the neighbourhood regions. The crossover and mutation operations over these candidate rules are then executed in an effort to attain candidates of improved performance. When this genetic learning process terminates the chromosomes in the final population either collectively form or each individually represent a learned ANFIS, depending on whether a single fuzzy rule or a set of fuzzy rules representing an entire ANFIS is implemented with a chromosome within the evolving population. Comparative experimental evaluations on both synthetic and real world datasets are carried out, demonstrating that in spite of data shortage, the proposed interpolation approach is able to produce ANFIS models that significantly outperform those trained using existing learning mechanisms.

While the traditional trajectory planning methods are used in robotic belt grinding of blades with an uneven machining allowance distribution, it is hard to obtain the preferable profile accuracy and surface quality to meet the high-performance requirements of aero-engine. To solve this problem, a novel trajectory planning method is proposed in this paper by considering the developed interpolation algorithm and the machining allowance threshold. The residual height error obtained from grinding experiments of titanium alloy sample was compensated to modify the calculation model of row spacing, and a new geometric algorithm was presented to dynamically calculate the cutter contact points based on this revised calculation model and the dichotomy method. Subsequently, the off-line machining program is generated based on a double-vector controlling method to obtain an optimal contact posture. On this basis, three sets of robotic grinding tests of titanium alloy blades were conducted to investigate the advantages of the proposed method. The comparative experimental results revealed that the presented algorithm had improved the surface profile accuracy of blade by 34.2% and 55.1%, respectively. Moreover, the average machined surface roughness was achieved to 0.3 µm and the machining efficiency was obviously promoted. It is concluded that this research work is beneficial to comprehensively improve the machined quality of blades in robotic belt grinding.

An assessment of radio network coverage, usually in the form of a measurement campaign, is essential for multi-base-station (multi-BS) network deployment and maintenance. It can be conducted by a network operator or its served consumers. However, the number of measurement points and their locations may not be known in advance for an efficient and accurate evaluation. The main goal of this study is to propose a new methodology for understanding the selection of measurement points during coverage and signal quality assessment. It is particularly tailored to multi-BS low-power wide-area network (LPWAN) deployments without explicit knowledge of BS locations. To this aim, we first conduct a large-scale measurement campaign for three popular LPWAN technologies, namely, NB-IoT, Sigfox, and LoRaWAN. Utilizing this baseline data, we develop a procedure for identifying the minimum set of measurement points for the coverage assessment with a given accuracy as well as study which interpolation algorithms produce the lowest approximation error. Our results demonstrate that a random choice of measurement points is on par with their deterministic selection. Out of the candidate interpolation algorithms, Kriging method offers attractive performance in terms of the absolute error for NB-IoT deployments. By contrast, for Sigfox and LoRaWAN infrastructures, less complex techniques, such as Natural-neighbor, Linear interpolation, or Inverse-Distance Weighting, can achieve comparable (and occasionally even better) accuracy levels. acceptedVersion

Trajectory similarity computation is a fundamental problem for many intelligent applications such as trip trajectory mining to find the most popular routes and road anomaly detection. Existing similarity computation methods for vehicle trajectory, such as Dynamic Time Wrapping(DTW) and Frechet distance, are dynamic programming problems with a quadratic time complexity in all cases and need to handle local time shifts when computing the distance between trajectories, thus limiting the scalability of these methods. In addition, GPS-based vehicle trajectories usually contain errors such as noise and outliers due to poor satellite visibility in urban regions and non-uniform sampling rates. To this end, we propose an embedding-based method for trajectory similarity computation with linear time complexity, which encodes a trajectory as a vector via deep representation learning and learns the similarity between trajectories with an attention-based learning to rank model. We use an interpolation-based approach to reduce noise and outliers by considering vehicle trajectory is physically constrained to the road network. Experiments on a massive vehicle trajectory dataset show that the proposed approach outperforms state-of-the-art baselines consistently and significantly.

In conventional agricultural production systems, soil management is generally carried out without considering the spatial variability of its properties. This situation generates not only soil degradation but also an increase in production costs associated with the management of this factor. The objective of this research was to evaluate, through geostatistical methods, the spatial variability of soil fertility in Botana Experimental Farm of Universidad de Nariño. Spatial variability maps were estimated using the ArcGIS 10 program, the Kriging interpolation method, and the optimal ranges of soil fertility for the Andean region as projection parameters for making decisions related to land use. The fertility zoning of the farm was established, classifying soil as having high, medium, and low fertility. Most of the experimental farm had low fertility soils (20.7ha), and only 3ha had good conditions. Statistical analysis indicated a high variability in soil chemical properties. Properties such as pH and bulk density showed low variability. RESUMEN En sistemas de producción agrícola convencional, generalmente el manejo de suelos se realiza sin considerar la variabilidad espacial de sus propiedades. Esta situación genera no solo degradación del mismo, sino también incremento en los costos de producción asociados al manejo de este factor. El objetivo de la presente investigación fue evaluar a través de métodos geo estadísticos la variabilidad espacial de la fertilidad de suelos en un área de uso agropecuario (Granja experimental Botana, Universidad de Nariño). Se realizó la estimación de mapas de variabilidad espacial, empleando el programa ArcGIS 10 y el método de interpolación Kriging, teniendo en cuenta los rangos óptimos de fertilidad de los suelos para la región andina como parámetros de proyección en la toma de decisiones relacionadas al uso del suelo en el área estudiada. Se estableció la zonificación de la fertilidad de los suelos seleccionados de la granja, clasificándolos en: suelos de fertilidad alta, media y baja. La mayor parte de la finca experimental presentó suelos de baja fertilidad (20,7ha) y solo 3ha, buenas condiciones al respecto. El análisis estadístico indicó una alta variabilidad en las propiedades químicas del suelo. Las propiedades como el pH y la densidad aparente mostraron una baja variabilidad.

In this paper, we presented a method of minimizing the number of overlapped partial products in the accumulation of four-term Karatsuba multiplication. This method reduced the summation of 13 overlapped partial products to 9 and the summation of 40 overlapped partial products to 24 in the case of four-term Karatsuba multiplication and eight-term Karatsuba multiplication, respectively. Moreover, to deal with the problem of negative multiplicands introduced by the choice in the evaluation of four-term Karatsuba multiplication, we further presented a method of converting negative multiplicands to non-negative multiplicands. In this way, our method would lead to the reduction of summation complexity and not using signed multipliers. Compared to the original Karatsuba multiplication designs, our proposed Karatsuba-like multiplication with optimal interpolation would lead to up to 7.7% reduction in ADP (area-delay-product) in ASIC implementations, and up to 20.2% reduction in ADP compared with built-in designs of Synopsys Design Compiler.

Soil erodibility (K factor) mapping has been accomplished mainly by soil map-linked or geo-statistical interpolation. However, the resulting maps usually have coarse spatial resolution at a regional scale. The objectives of this study were a) to map the K factors using a set of environmental variables and random forest (RF) model, and b) to identify the important environmental variables in the predictive mapping on a regional scale. We collected 101 surface soil samples across southeast China in the summer of 2019. For each sample, we measured the particle size distribution and organic matter content, and calculated the K factors using the nomograph equation. The hyperparameters of RF were optimized through 5-fold cross validation (mtry = 2, ntree = 500, p = 63), and a digital map with 250 m resolution was generated for the K factor. The lower and upper limits of a 90% prediction interval were also produced for uncertainty analysis. It was found that the important environmental variables for the K factor prediction were relief, climate, land surface temperature and vegetation indexes. Since the existing K factor map has an average polygonal area of 6.8 km2, our approach dramatically improves the spatial resolution of the K factor to 0.0625 km2. The new method captures more distinct differences in spatial details, and the spatial distribution of the K factor derived from RF prediction followed a similar pattern with kriging interpolation. This suggests the presented approach in this study is effective for mapping the K factor with limited sampling data.

In this paper, the free vibration of the functionally graded porous (FGP) non-uniform annular-nanoplates lying on Winkler foundation (WF) is studied by using the smoothed finite element method based on the first-order shear deformation theory (FSDT). The combination of the mixed interpolation of the tensorial components for the three-node triangular element (MITC3 element) and the edge-based smoothed finite element method (ES-FEM) creates the ES-MITC3 element. This element is employed to avoid the shear locking problem as well as to improve the accuracy of the original MITC3 element. The small-scale effect is considered based on the nonlocal theory. Applying Hamilton's principle, the governing equation of the FGP non-uniform thickness annular-nanoplate is derived. Material properties of the nanoplate are characterized by two parameters: power-law index ( k ) and maximum porosity distributions ( Ω ) in the forms of cosine functions. The results of the present work are compared with other published work to verify accuracy and reliability. Moreover, the effects of geometry parameters and material properties on the free vibration of FGP non-uniform annular-nanoplates are comprehensively investigated.

We find expressions of the polynomials defining the dual varieties of Grassmannians Gr ( 3 , 9 ) and Gr ( 4 , 8 ) both in terms of the fundamental invariants and in terms of a generic semi-simple element. We restrict the polynomial defining the dual of the adjoint orbit of E 8 and obtain the polynomials of interest as factors. To find an expression of the Gr ( 4 , 8 ) discriminant in terms of fundamental invariants, which has 15 , 942 terms, we perform interpolation with mod-p reductions and rational reconstruction. From these expressions for the discriminants of Gr ( 3 , 9 ) and Gr ( 4 , 8 ) we also obtain expressions for well-known hyperdeterminants of formats 3 × 3 × 3 and 2 × 2 × 2 × 2 .

This paper applies a unified process to calculate ”exact” (consistent) finite-element (FE) matrices for framed structures having nonprismatic elements and including shear-deformation and rotational-inertia effects. In this process, the exact expressions for the element stiffness and nodal-load coefficients result from applying the principle of virtual forces (PVF) at the element level. Rigidity values, determined at a certain number of cross sections in the frame element, are employed to describe how the corresponding rigidities vary along its length. For that, interpolation polynomials of different orders are considered. Exact Timoshenko’s shape functions, built under the most general cases of rigidity variation, are used for evaluating the mass matrix coefficients. In the applications, complex 2D frames with nonprismatic elements are considered to simulate bridge structures under seismic excitation and a generic harmonic load. Comparisons with highly accurate response time-histories obtained by employing ANSYS (3D) solid-FE models are effected to verify the robustness of the proposed formulation.

Information sensor can realize the ubiquitous connection between objects and humans by distributed fiber-optic sensor array, i.e., emerging infrastructure for Internet of Things, in which optical frequency domain reflectometry (OFDR) with its high spatial resolution plays an important role in achieving intelligent perception and identification of the objects. However, given a certain fiber length, there are tradeoffs among the processing speed, the spatial resolution, and the strain measurement range. In this paper, a time optimization interpolation method and a distance domain compensation method are reported and experimentally verified to break the aforementioned tradeoffs for the first time. First, a full theoretical analysis on how to reduce the interpolation number and the reason why it is difficult to achieve high spatial resolution and large strain measurement and how to resolve it is made. Second in the proof-of-concept experiment, measurements of large strains up to 10000le are realized along the sensing fiber with a spatial resolution of 2mm using a conventional OFDR system. Also, the processing time is shortened by 76 times compared with the traditional processing method. This paper makes a significant step toward high-performance OFDR system with fast processing, high spatial resolution and wide strain measurement.

In this paper, a novel approach based on C1 finite element (FE) interpolation is used to construct a regional ionospheric grid model (RIGM) with high spatio-temporal resolution over Europe. The spatial resolution of the new model is 0.50 for a longitude and latitude and a temporal resolution is 15 minutes. Observations of 38 GPS stations at different days and seasons with different geomagnetic and solar activity conditions are used to evaluate the new method. All stations are used to discretize the whole domain of the problem into separate triangular patches using a Delaunay triangulation algorithm. In this case, GPS stations would be the vertices of the triangular patches. Also, the position of stations in sun-fixed coordinate system with coordinates of latitude and longitude are chosen in order to consider the temporal variations of vertical total electron content (VTEC). To model the behavior of VTEC in each triangular patch, a particular shape function is defined which is fitted to VTEC values at three vertices of each triangle while it satisfies C1 continuity of VTEC at the common edges of the adjacent triangles. The results of the new model are compared with the VTEC of GPS at 4 control stations as well as global ionosphere map (GIM) and NeQuick models. Statistical parameters, including correlation coefficient, root mean square error (RMSE), standard deviation and dVTEC=|VTECGPS - VTECmodel| have been used to evaluate the error of the models. In low geomagnetic activity (KP 4), they are 1.24, 1.68 and 7.62 TECU, respectively. For further analysis, the accuracy of three models in precise point positioning (PPP) has been also evaluated. In PPP method, there is an improvement of about 1 to 16 mm compared to GIM and NeQuick models at coordinate components of control stations in high geomagnetic activity. The results of the analysis performed in this paper show that the FE model has a very high capability and accuracy in regional VTEC modeling in high and low geomagnetic conditions. The regional accuracy of this model is higher than GIM and NeQuick models and therefore can be considered as a new model for the ionosphere.

Harmonic measured foliation has demonstrated its usefulness for many geometric problems, including conformal parameterization and mesh quadrangulation. Due to the non-linearity and hard constraints for its computation, existing iterative solvers converge very slowly, and so impractical for large meshes. Though the multigrid approach is well-known for speeding up iterative solvers, a general multigrid solver cannot be applied here in a plug-and-play fashion, because the constraints for computing the harmonic measured foliations would be broken. In this article, we design a novel multigrid solver for this problem, where we propose specific multi-resolution mesh hierarchies and interpolation schemes to fulfill the requirements of the harmonic measured foliation. Experimental results show that our multigrid solver converges much faster than the original algorithm on meshes ranging from a few thousands to over one million edges, even by over a hundred times. This would benefit scalable geometry processing using harmonic measured foliations.

A united-reference fractional counter (URFC) is proposed for multi-level time-to-digital converters (TDCs) used in direct time-of-flight (dToF) light detection and ranging (LiDAR) applications. The URFC combines the integer counter and the second-level interpolation in one functional block that derives both the integer part and the fractional part from the same synchronization result. Thus the proposed TDC has a more robust structure to deal with misalignment errors, and measurement results from different levels can be perfectly matched. High linearity and high precision can be guaranteed because of the united reference without calibration. The response time of the URFC decreases to hundreds of picoseconds, which makes it suitable for all output pulses from the avalanche photodiode. A TDC with the proposed URFC was implemented in 65nm standard CMOS technology with a detection range of 2.5μs (~375m) and a single shot precision of 27.63ps (~4.0mm). The power consumption is 51.4mW with a reference clock at 200MHz and a repetition rate at 999kHz. The INL and DNL are ±2.751 LSB and ±1.679 LSB, respectively.