Inverse Coefficient Research Articles

An approximate method for solving the inverse coefficient problem

An approximate method for solving the inverse coefficient problem

Direct method for solving the inverse coefficient problem

Direct method for solving the inverse coefficient problem

Quantifying Mobility and Mixing Propensity in the Spatiotemporal Context of a Pandemic Spread.

COVID-19 is the most acute global public health crisis of this century. Current trends in the global infected and death numbers suggest that human mobility leading to high social mixing are key players in infection spread, making it imperative to incorporate the spatiotemporal and mobility contexts to future prediction models. In this work, we present a generalized spatiotemporal model that quantifies the role of human social mixing propensity and mobility in pandemic spread through a composite latent factor. The proposed model calculates the exposed population count by utilizing a nonlinear least-squares optimization that exploits the intrinsic linearity in SEIR (Susceptible, Exposed, Infectious, or Recovered). We also present inverse coefficient of variation of the daily exposed curve as a measure for infection duration and spread. We carry out experiments on the mobility and COVID-19 infected and death curves of New York City to show that boroughs with high inter-zone mobility indeed exhibit synchronicity in peaks of the daily exposed curve as well as similar social mixing patterns. Furthermore, we demonstrate that several nations with high inverse coefficient of variations in daily exposed numbers are amongst the worst COVID-19 affected places. Our insights on the effects of lockdown on human mobility motivate future research in the identification of hotspots, design of intelligent mobility strategies and quarantine procedures to curb infection spread.

Identifying a time-dependent zeroth-order coefficient in a time-fractional diffusion-wave equation by using the measured data at a boundary point

In this paper, we investigate a nonlinear inverse problem of identifying a time-dependent zeroth-order coefficient in a time-fractional diffusion-wave equation by using the measured data at a boundary point. We firstly prove the existence, uniqueness and regularity of the solution for the corresponding direct problem by using the contraction mapping principle. Then we try to give a conditional stability estimate for the inverse zeroth-order coefficient problem and propose a simple condition for the initial value and zeroth-order coefficient such that the uniqueness of the inverse coefficient problem is obtained. The Levenberg–Marquardt regularization method is applied to obtain a regularized solution. Based on the piecewise linear finite elements approximation, we find an approximate minimizer at each iteration by solving a linear system of algebraic equations in which the Fréchet derivative is obtained by solving a sensitive problem. Two numerical examples in one-dimensional case and two examples in two-dimensional case are provided to show the effectiveness of the proposed method.

An Introduction to Finite Element Methods for Inverse Coefficient Problems in Elliptic PDEs

Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the unknown coefficient is often assumed to be piecewise constant on a given pixel partition (corresponding to the desired resolution), and only finitely many measurement can be made. This leads to the problem of inverting a finite-dimensional non-linear forward operator mathcal{F}: mathcal{D}(mathcal{F})subseteq mathbb{R}^{n}to mathbb{R}^{m}, where evaluating ℱ requires one or several PDE solutions.Numerical inversion methods require the implementation of this forward operator and its Jacobian. We show how to efficiently implement both using a standard FEM package and prove convergence of the FEM approximations against their true-solution counterparts. We present simple example codes for Comsol with the Matlab Livelink package, and numerically demonstrate the challenges that arise from non-uniqueness, non-linearity and instability issues. We also discuss monotonicity and convexity properties of the forward operator that arise for symmetric measurement settings.This text assumes the reader to have a basic knowledge on Finite Element Methods, including the variational formulation of elliptic PDEs, the Lax-Milgram-theorem, and the Céa-Lemma. Section 3 also assumes that the reader is familiar with the concept of Fréchet differentiability.

Conditional stability for an inverse coefficient problem of a weakly coupled time-fractional diffusion system with half order by Carleman estimate

Abstract Under a priori boundedness conditions of solutions and coefficients, we prove a Hölder stability estimate for an inverse problem of determining two spatially varying zeroth order non-diagonal elements of a coefficient matrix in a one-dimensional fractional diffusion system of half order in time. The proof relies on the conversion of the fractional diffusion system to a system of order 4 in the space variable and the Carleman estimate.

Applying the Virtual Input-Output Method to the Identification of Key Nodes in Busy Traffic Network

How to identify the key nodes effectively in urban traffic networks to achieve the equitable resource allocation face to the complex traffic network? This issue needs to be solved in current traffic management. This study considered the urban traffic network topology and network traffic status, put forward an improved model based on the economics of the input-output method by introducing a virtual node to the selected network set up with the flow of urban traffic network, sensor nodes by Leontief inverse matrix calculation coefficient to determine node importance, according to the node importance to deliberate attack traffic network to analyze its robustness, to test the accuracy and practicability of the method. The results show that this improved method adopted to measure the importance of traffic nodes from the global scope has the advantages of fast calculation and simple process and provides a more reliable basis for rational allocation of transport resources.

A Direct Method for Solving the Inverse Coefficient Problem for an Elliptic Equation with Piecewise Constant Coefficients

A Direct Method for Solving the Inverse Coefficient Problem for an Elliptic Equation with Piecewise Constant Coefficients

An Approximate Method for Solving an Inverse Coefficient Problem for the Heat Equation

An Approximate Method for Solving an Inverse Coefficient Problem for the Heat Equation

Identification of the permeability field for three-dimensional reservoir using the results of geophysical well survey

A model problem of the permeability field identification for a three-dimensional reservoir opened by a large number of wells in the conditions of stationary single-phase fluid filtration is considered. The permeability field is determined in the process of solving the inverse coefficient problem by on known values of bottomhole pressure. The solving problem algorithm is constructed so that the proportionality coefficients of the layers permeability on wells obtained from the results of geophysical well survey are preserved. The influence of various types of errors on the identification results is studied.

Morphometric analysis to characterize the soil erosion susceptibility in the western part of lower Gangetic River basin, India

The present study is an attempt to identify the morphometric parameters for determining the soil erosion susceptibility (SES) in upper plateau fringe catchment and lower undulating plain catchment of Kangsabati basin using of multi-criteria decision model as compound factor (CF) and hydrological model as revised universal soil loss equation (RUSLE) under GIS platform. In this research, twenty morphometric parameters of three aspects, namely, linear, areal, and relief were taken from twenty-seven sub-basins to compute the morphometric priority rank using CF model. In contrary, soil erosion factors like rainfall, soil character, slope, and land cover management were taken to measure the potential annual soil erosion using RUSLE. The result showed that fourteen sub-basins in upper catchment (UC) with low compound value represent high morphometric priority rank whereas thirteen sub-basins in lower catchment (LC) with high compound value indicate lower morphometric priority rank. RUSLE estimated that higher rate of mean soil erosion (225 t ha−1 year−1) occurred in UC, whereas low rate of mean soil erosion (74 t ha−1 year−1) occurred in LC. Stepwise least regression of Akaike information criteria (AIC) showed that mean bifurcation ratio (p > 0.013), ruggedness index (p 0.034) are the best positive coefficient of erosion susceptibility (ES), but gradient ratio (p > 0.003) and elongation ratio (p > 0.024) have perfect inverse coefficient of high ES in LC. Gradient ratio (p > 0.044) is the only best inverse coefficient parameter of ES in LC due to presence of several conservative practices. Moreover, proper management strategy, effective morphometric, and erosion factors play vital role to determine the ES.

The Correlation Among Land Cover Spectral Indices and Surface Temperature Using Remote Sensing Techniques

Land cover explains the physical nature of the Earth’s surface in a specific area. Land cover is a reflection of the Earth’s surface’s observable spatial cover comprising complex classes such as agricultural areas, built-up areas, barren lands, forests, water bodies, as well as wetlands. change detection and monitoring of the land cover assist decision-makers to understand the dynamics of the environmental change to assure sustainability development. Hence land cover feature classification has appeared as a serious research aspect and thus, an accurate methodology for land cover categorizing it became an urgent necessity at this time. This study focuses to find the association between surface temperature and the spectral indices of the land cover. The spectral indices of the land cover such as (NDVI, NDBI, NDBAI, and NDWI) were compared with land surface temperature (LST) and computed the correlation coefficient, just using three images on March 18, July 24 as well as 31 December in 2018, indicating a high positive correlation coefficient among (NDBI, NDBAI) and (LST) and recorded (by built-up areas R= 0.99, R= 0.97 and R= 0.98) ) and (with bare areas R= 0.94, R= 0.98 and R= 0.99), respectively. An inverse correlation coefficient among (NDVI, NDWI) and (LST) where the results recorded a correlation coefficient with (the agricultural areas R= - 0.97, R= - 0.96 and R= - 0.95) and the correlation coefficient with (water bodies R = - 0.93, R= - 0.90 and R= - 0.58) respectively.

Preceding Vehicle Detection Based on Optimized Faster R-CNN Algorithm

Preceding vehicle detection is still a challenge for unmanned driving technology. Deep learning has achieved great success in target detection. Among them, the Faster R-CNN algorithm is a classic representative. However, the algorithm still has some room for improvement in detection accuracy. By analyzing the problems of Faster R-CNN in the detection of occluded vehicles, taking the target detection post-processing algorithm Soft-NMS as the research object, two new penalty coefficients, inverse proportional penalty coefficient and exponential penalty coefficient, were proposed. It further improves the algorithm’s detection accuracy of the blocked vehicle in front.

Incremental holistic controller

The trace of inverse coefficient matrix method in state space is used to implement and simplify an iterative design of a control system with main interest in increasing dynamical performance quality or to check if stability danger exists. The tau -locus is a helpful design element. Various applications and examples are presented for illustration.

LSTM and CNN based ensemble approach for spoof detection task in automatic speaker verification systems

Nowadays, fingerprint and retina scans are the most reliable and widely used biometric authentication systems. Another emerging biometric approach for authentication, though vulnerable, is speech-based systems. However, speech-based systems are more prone to spoofing attacks. Through such malicious attacks, an unauthentic person tries to present himself as legitimate user, in order to acquire illegitimate advantage. Therefore, these attacks, created by synthesis or conversion of speech, pose an enormous threat to the reliable functioning of automatic speaker verification (ASV) authentication systems. The work presented in this paper tries to address this problem by using deep learning (DL) methods and ensemble of different neural networks. The first model is a combination of time-distributed dense layers and long short-term memory (LSTM) layers. The other two deep neural networks (DNNs) are based on temporal convolution (TC) and spatial convolution (SC). Finally, an ensemble model comprising of these three DNNs has also been analysed. All these models are analysed with Mel frequency cepstral coefficients (MFCC), inverse Mel frequency cepstral coefficients (IMFCC) and constant Q cepstral coefficients (CQCC) at the frontend, where the proposed ensemble performs best with CQCC features. The proposed work uses ASVspoof 2015 and ASVspoof 2019 datasets for training and testing, with the evaluation set having speech synthesis (SS) and voice conversion (VC) attacked utterances. Performance of proposed system trained with ASVspoof 2015 dataset degrades with evaluation set of ASVspoof 2019 dataset, whereas performance of the same system improves when training is also done with the ASVspoof 2019 dataset. Also, a joint ASVspoof 1519 dataset is created to add more variations into the single dataset, and it has been observed that the trained ensemble with this joint dataset performs even better, while performing evaluation using single datasets. This research promotes the development of systems that can cope with completely unknown data in testing. It has been further observed that the models can reach promising results, paving the way for future research in this domain using DL.

Stable numerical solution of an inverse coefficient problem for a time fractional reaction-diffusion equation

‎In this paper‎, ‎an inverse problem of determining an unknown reaction coefficient in a one-dimensional time-fractional reaction-diffusion equation is considered‎. ‎This inverse problem is generally ill-posed‎. ‎For this reason‎, ‎the mollification regularization technique with the generalized cross-validation criteria will be employed to find an equivalent stable problem‎. ‎Afterward‎, ‎a finite difference marching scheme is introduced to solve this regularized problem‎. ‎The stability and convergence of the numerical solution are investigated‎. ‎In the end‎, ‎some numerical examples are presented to verify the ability and effectiveness of the proposed algorithm‎.

Air pollution, health care use and medical costs: Evidence from China

Using the micro data of China Family Panel Studies, this study quantifies the effect of air pollution on the health care use and medical costs of people in China. To avoid the potential endogenous biases, the thermal inversion and ventilation coefficient are used as instruments. Findings show that PM2.5 increases the medical care costs, hospitalization spending and self-payment costs of people significantly. Besides, the detrimental effect of air pollution is much larger for young people, and the long-term effect of PM2.5 on personal medical costs is much smaller. The evidence of two possible channels through which air pollution is related to medical use and hospital spending of people are found. On the one hand, the decrease of sleep hours caused by ambient air pollution is not beneficial for maintaining fitness, which could increase personal health care use or medical costs. On the other hand, people spend more hours in sedentary activities to avoid the exposure to air pollution, which is also positively associated with personal medical spending. This study implies that the social welfare loss should be considered when the costs and benefits of air pollution are calculated, and reducing air pollution is effective to improve the overall social welfare in the long run.

Determination of the reaction coefficient in a time dependent nonlocal diffusion process

This paper investigates the inverse reaction coefficient problem for a time dependent nonlocal diffusion equation by utilizing the nonlocal flux measurement from an accessible part of region, which is a continuation and an extension of our recent work (Zheng and Ding 2020 Inverse Problems 36 035006). The uniqueness of inverse reaction coefficient problem is proved. The variational regularization method is proposed to overcome the ill-posedness of inverse problem, and an alternating iteration method is adopted to automatically select regularization parameters. Furthermore, we use Laplace approximation method to capture the statistics information of the solution. In particular, we prove the lower bound of confidence width is rigorously estimated to characterize the reliability of the method. Finally, numerical results indicate that the proposed method could yield an accurate estimate and efficient uncertainty quantification of the solution.

Giant piezoelectric coefficient of PNN-PZT-based relaxor piezoelectric ceramics by constructing an R-T MPB

xTa-PNN-PZT piezoelectric ceramics with [0.55 Pb(Ni1/3Nb2/3)O3 - 0.45 Pb(Zr0.3Ti0.7)O3 - xwt%Ta2O5] + 1 wt% PbO composition (0 ≤ x ≤ 0.7) were prepared by conventional solid-state reaction method. Special attention was paid to the effect of Ta2O5 concentration on structural, dielectric, piezoelectric, and ferroelectric properties of these ceramics. In particular, rhombohedral-tetragonal morphotropic phase boundary was observed in PNN-PZT crystal structure near the composition of x = 0.5. At this point, volume fraction of rhombohedral phase was almost equal to that of tetragonal phase. In addition, the ceramic exhibited the optimum values of piezoelectric coefficient, bipolar strain, unipolar strain, and inverse piezoelectric coefficient, i.e., 1090 pC/N, 0.135%, 0.165%, and 1493 pm/V, respectively. Moreover, according to in-situ X-ray diffraction, piezoelectric force microscopy, and in-situ strain measurement results, phase structure of 0.5Ta-PNN-PZT revealed relatively stable piezoelectric behavior at 60 °C.

Low-temperature synthesis of bismuth titanate by modified citrate amorphous method

Bismuth titanate is a lead-free piezoelectric ceramic with outstanding properties that strictly depend on the composition and microstructure. However, bismuth-based materials are difficult to synthesize due to bismuth volatilisation that causes secondary phases and stoichiometry deviations. In this work, we propose a low-temperature chemical route, i.e. a modified amorphous citrate method, that allows a reduction of thermal treatment temperature, when compared with solid-state or other chemical routes, to obtain single-phase bismuth titanate samples. Single-phase powders with particle size under 300 nm are produced by calcination at 700 °C, and prepared into homogeneous dense pellets (density above 95%), with only isolated pores. The pellets show two distinctive features in the electrical behaviours directly associated with their mica-like microstructure: planar oriented boundaries are responsible for oxygen conduction, while the bulk is dominated by electronic conductivity. The samples show a high dielectric constant, around 200 at room temperature, while maintaining a low loss factor. The pellets also achieved a maximum polarisation of 5.85 μC/cm2 and an inverse piezoelectric coefficient of 7.4 pm/V. The dielectric and piezoelectric properties obtained are comparable or superior to the state-of-the-art.