Unknown Point Research Articles

Assessing Spatial Variation and Driving Factors of Available Phosphorus in a Hilly Area (Gaozhou, South China) Using Modeling Approaches and Digital Soil Mapping

Soil fertility plays a crucial role in crop growth, so it is important to study the spatial distribution and variation of soil fertility for agricultural management and decision-making. However, traditional methods for assessing soil fertility are time-consuming and economically burdensome. Moreover, it is hard to capture the spatial variation of soil properties across continuous geographic space using the conventional methods. As key techniques of digital soil mapping (DSM), spatial interpolation techniques have been widely applied in soil surveys and analysis in recent years, since they can predict soil properties at unknown points in continuous space based on limited sample points. However, further research is needed on spatial interpolation models for DSM in regions with variable climates and complex terrains, which are characterized by strong spatial variation in both environmental variables and soil fertility. In this study, taking a typical hilly area in a subtropical monsoon climate, i.e., Gaozhou, Guangdong Province, China, as an example, the performances of four popular spatial interpolation models (Random Forest (RF), Ordinary Kriging, Inverse Distance Weighting, and Radial Basis Function) for digital soil mapping on available phosphorus (AP) are compared. Based on RF, the spatial variation and its driving factors of the AP of Gaozhou are then analyzed. Furthermore, by selecting three typical truncation lines from different directions, the correlations between environmental variables and AP in different spatial positions are demonstrated. The root mean square error (RMSE) results of the above four models are 32.01, 32.08, 32.74, and 33.08, respectively, which indicate that the RF has a higher interpolation accuracy. Based on the mapping results of RF, the minimum, maximum, and mean values of AP in the study area are 38.90, 95.24, and 64.96 mg/kg, respectively. The high-value areas of AP are mainly distributed in forested and orchard areas, while the low-value areas are primarily found in urban and cultivated areas in the eastern and western regions. Vegetation and topography are identified as the key factors shaping the spatial variations of AP in the study area. Furthermore, the spatial heterogeneity of the influence strength of altitude and EVI is revealed, providing a new direction for further research on DSM in the future, i.e., spatial interpolation models considering the spatial heterogeneity of the influence of environmental variables.

‘I am watching you. Are you watching yourself in me?1’: reflection as an act of triangulation

This paper approaches the process of ‘reflection’ as an interpersonal and intra-personal creative act. As commonly used, the word ‘reflection’ appears to reference two seemingly different processes; the returning of a mirror image and the process of reflective thought. Examining the intersection of these two definitions – from infant development, through attachment theory to post-Kleinian thinking and Lacan – this paper finds that the act of ‘reflection’ can be conceived of as an act of triangulation, in a mathematical sense, whereby a pre-existing but unknown point is found/made using two known points as the vertices.

Anti-noise twin-hyperspheres with density fuzzy for binary classification to imbalanced data with noise

This paper presents twin-hyperspheres of resisting noise for binary classification to imbalanced data with noise. First, employing the decision of evaluating the contributions created by points for the training of the hyperspheres, then the label density estimator is introduced into the fuzzy membership to quantize the provided contributions, and finally, unknown points can be assigned into corresponding classes. Utilizing the decision, the interference created by the noise hidden in the data is suppressed. Experiment results show that when noise ratio reaches 90%, classification accuracies of the model are 0.802, 0.611 on the synthetic datasets and UCI datasets containing Gaussian noise, respectively. Classification results of the model outperform these of the competitors, and these boundaries learned by the model to separate noise from majority classes and minority classes are superior to these learned by the competitors. Moreover, efforts gained by the proposed density fuzzy are effectiveness in noise resistance; meanwhile, the density fuzzy does not rely on specific classifiers or specific scenarios.

Detecting an intermittent change of unknown duration

Oftentimes, in practice, the observed process changes statistical properties at an unknown point in time and the duration of a change is substantially finite, in which case one says that the change is intermittent or transient. We provide an overview of existing approaches for intermittent change detection and advocate in favor of a particular setting driven by the intermittent nature of the change. We propose a novel optimization criterion that is more appropriate for many applied areas such as the detection of threats in physical computer systems, near-Earth space informatics, epidemiology, pharmacokinetics, etc. We argue that controlling the local conditional probability of a false alarm, rather than the familiar average run length to a false alarm, and maximizing the local conditional probability of detection is a more reasonable approach versus a traditional quickest change detection approach that requires minimizing the expected delay to detection. We adopt the maximum likelihood (ML) approach with respect to the change duration and show that several commonly used detection rules (cumulative sum [CUSUM], window-limited [WL]-CUSUM, and finite moving average [FMA]) are equivalent to the ML-based stopping times. We discuss how to choose design parameters for these rules and provide a comprehensive simulation study to corroborate intuitive expectations.

Assessing ice sheet models against the landform record: The Likelihood of Accordant Lineations Analysis (LALA) tool

AbstractPalaeo‐ice sheets leave behind a rich database regarding their past behaviour, recorded in the landscape in the form of glacial geomorphology. The most numerous landform created by these ice sheets are subglacial lineations, which generate snapshots of the direction of ice flow at fixed (yet typically unknown) points in time. Despite their relative density within the landform record, the information provided by subglacial lineations is currently underutilised in tests of numerical ice sheet models. To some extent, this is a consequence of ongoing debate regarding lineation formation, but predominantly, it reflects the lack of rigorous model‐data comparison techniques that would enable lineation information to be properly integrated. Here, we present the Likelihood of Accordant Lineations Analysis (LALA) tool. LALA provides a statistically rigorous measure of the log‐likelihood of a supplied ice sheet simulation through comparison of simulation output with both the location and direction of observed lineations. Given an ensemble of ice sheet simulations, LALA provides a formal, and statistically underpinned, quantitative assessment of each simulation's quality‐of‐fit to mapped lineations. This enables a comparison of each simulation's relative plausibility, including identification of the most likely ice sheet simulations amongst the ensemble. This is achieved by modelling lineation formation as a marked Poisson point process and comparison of observed to modelled flow directions using the von Mises distribution. LALA is flexible—users can adapt parameters to account for differing assumptions regarding lineation formation, and for variations in the level of precision required for differing model‐data comparison experiments. We provide guidelines and rationale for assigning parameter values, including an assessment of the variability between users when mapping lineations. Finally, we demonstrate the utility of LALA through application to an ensemble of simulations of the last British‐Irish Ice Sheet. This comparison highlights the benefits of LALA over previous tools and demonstrates some of the considerations of experimental design required when identifying the fit between ice sheet model simulations and the landform record.

Quantification of methane emissions in Hamburg using a network of FTIR spectrometers and an inverse modeling approach

Abstract. Methane (CH4) is a potent greenhouse gas, and anthropogenic CH4 emissions contribute significantly to global warming. In this study, the CH4 emissions of the second most populated city in Germany, Hamburg, were quantified with measurements from four solar-viewing Fourier transform infrared (FTIR) spectrometers, mobile in situ measurements, and an inversion framework. For source type attribution, an isotope ratio mass spectrometer was deployed in the city. The urban district hosts an extensive industrial and port area in the south as well as a large conglomerate of residential areas north of the Elbe River. For emission modeling, the TNO GHGco (Netherlands Organisation for Applied Scientific Research greenhouse gas and co-emitted species emission database) inventory was used as a prior for the inversion. In order to improve the inventory, two approaches were followed: (1) the addition of a large natural CH4 source, the Elbe River, which was previously not included in the inventory, and (2) mobile measurements were carried out to update the spatial distribution of emissions in the TNO GHGco gridded inventory and derive two updated versions of the inventory. The addition of the river emissions improved model performance, whereas the correction of the spatial distribution with mobile measurements did not have a significant effect on the total emission estimates for the campaign period. A comparison of the updated inventories with emission estimates from a Gaussian plume model (GPM) showed that the updated versions of the inventory match the GPM emissions estimates well in several cases, revealing the potential of mobile measurements to update the spatial distribution of emission inventories. The mobile measurement survey also revealed a large and, at the time of the study, unknown point source of thermogenic origin with a magnitude of 7.9 ± 5.3 kg h−1 located in a refinery. The isotopic measurements show strong indications that there is a large biogenic CH4 source in Hamburg that produced repeated enhancements of over 1 ppm which correlated with the rising tide of the river estuary. The CH4 emissions (anthropogenic and natural) of the city of Hamburg were quantified as 1600 ± 920 kg h−1, 900 ± 510 kg h−1 of which is of anthropogenic origin. This study reveals that mobile street-level measurements may miss the majority of total methane emissions, potentially due to sources located within buildings, including stoves and boilers operating on natural gas. Similarly, the CH4 enhancements recorded during the mobile survey from large-area sources, such as the Alster lakes, were too small to generate GPM emission estimates with confidence, but they could nevertheless influence the emission estimates based on total column measurements.

Vertical deformation analysis based on combined adjustment for GNSS and leveling data

A method is proposed to fuse the velocity data of the global navigation satellite system (GNSS) and leveling height via combined adjustment with constraints. First, stable GNSS–leveling points are uniformly selected, and the constraints of the geodetic height change velocity and normal height change velocity are given. Then, the GNSS vertical velocities and leveling height difference are used as observations of combined adjustment, and robust least-squares estimation are used to estimate the velocities of the unknown points. Finally, a vertical movement model is established with the GNSS vertical velocities and leveling vertical velocities obtained via combined adjustment. Data from the second-order leveling network and GNSS control points in Shandong Province are taken as test data, and eight calculation schemes are used for discussion. One of the schemes, the bifactor robust combined adjustment method based on variance component estimation with two kinds of vertical velocity constraints achieves the optimal results. The method applied in the scheme can be recommended for data fusion of GNSS and leveling, further improving the reliability of vertical crustal movement in Shandong Province.

Multivariate super-resolution without separation

Abstract In this paper, we study the high-dimensional super-resolution imaging problem. Here, we are given an image of a number of point sources of light whose locations and intensities are unknown. The image is pixelized and is blurred by a known point-spread function arising from the imaging device. We encode the unknown point sources and their intensities via a non-negative measure and we propose a convex optimization program to find it. Assuming the device’s point-spread function is componentwise decomposable, we show that the optimal solution is the true measure in the noiseless case, and it approximates the true measure well in the noisy case with respect to the generalized Wasserstein distance. Our main assumption is that the components of the point-spread function form a Tchebychev system ($T$-system) in the noiseless case and a $T^{*}$-system in the noisy case, mild conditions that are satisfied by Gaussian point-spread functions. Our work is a generalization to all dimensions of the work [14] where the same analysis is carried out in two dimensions. We also extend results in [27] to the high-dimensional case when the point-spread function decomposes.

Detection and Estimation of Change Point in Volatility Function of Foreign Exchange Rate Returns

This work aims at detection and estimation of a change point in conditional variance function of a Nonparametric Auto-Regressive Conditional Heteroscedastic model. The conditional mean and conditional variance functions are not specified a priori but estimated using Nadaraya Watson kernel. This is because inferences based on nonparametric approaches are robust against misspecification of the conditional mean function and the conditional variance function of returns. The squared residuals obtained after estimating the regression function of the returns are used in estimating the conditional variance function. Further, the squared residuals are used in developing a test statistic for unknown abrupt change point in volatility of the exchange rate returns. The test statistic takes into consideration the conditional heteroskedasticity of the disturbances, dependence of the returns, heterogeneity and fourth moment of returns. This does not require prior knowledge of the marginal or the conditional densities of the returns as opposed to maximum likelihood estimation methods. The estimator for change point is considered as the augmented maximum of the test statistic. The consistency of the estimator is stated as a theorem. The asymptotic distribution associated with the test for unknown break points is the Bessel process distribution. The Bessel process distributions have no known simple closed-form expression for the distribution function which makes it difficult to compute exact p-values. Also, the Bessel process distributions depend on two parameters which makes it hard to tabulate the critical values hence one needs to simulate them. After simulating the critical values, hypothesis testing is done in the presence and absence of a change point in volatility of a simulated time series and the test is shown to reject the null hypothesis in the presence of a change point at alpha level of significance. Further, the test fails to reject the null hypothesis in the absence of a change point at alpha level of significance. An application to United States Dollar/Kenya Shilling historical exchange rates returns is made from 1^st January 2010 to 27^th November 2020 where the sample size n = 2839 is done. Through binary segmentation method, three change points are detected, estimated and accounted for. A significant improvement in describing a time series is expected if a point in time for volatility change has been detected and estimated.

Fictitious time integration method for seeking periodic orbits of nonlinear dynamical systems

In the paper, we compute the period and periodic orbit of an n-dimensional nonlinear dynamical system by developing two iterative algorithms based on the fictitious time integration method (FTIM). Periodicity condition, also known as the Poincaré map, is a necessary condition for the existence of a periodic motion in the state space, which consists of n implicit nonlinear algebraic equations (NAEs). Instead of solving the NAEs by the Newton–Raphson method, we derive an equivalent nonlinear scalar equation to determine unknown period by using the FTIM. The resulting sequence of the iterated periods monotonically converges to a desired period, wherein the unknown initial point on the periodic orbit is determined simultaneously. We find that the second iterative algorithm using the matrix shape function to convert the periodic problem into a corresponding initial value problem is convergent faster than the first iterative algorithm. A key point is that the periodicity condition is satisfied automatically by the second iterative algorithm when the terminal values of the new variables are convergent. Numerical examples exhibit some major advantages of these two iterative algorithms.

Modeling a nonlinear biophysical trend followed by long-memory equilibrium with unknown change point

Measurements of many biological processes are characterized by an initial trend period followed by an equilibrium period. Scientists may wish to quantify features of the two periods as well as the timing of the change point. Specifically, we are motivated by problems in the study of electrical cell-substrate impedance sensing (ECIS) data. ECIS is a popular new technology which measures cell behavior noninvasively. Previous studies using ECIS data have found that different cell types can be classified by their equilibrium behavior. However, it can be challenging to identify when equilibrium has been reached and to quantify the relevant features of cells’ equilibrium behavior. In this paper we assume that measurements during the trend period are independent deviations from a smooth nonlinear function of time, and that measurements during the equilibrium period are characterized by a simple long memory model. We propose a method to simultaneously estimate the parameters of the trend and equilibrium processes and locate the change point between the two. We find that this method performs well in simulations and in practice. When applied to ECIS data, it produces estimates of change points and measures of cell equilibrium behavior which offer improved classification of infected and uninfected cells.

The origin and evolution of emerged swine acute diarrhea syndrome coronavirus with zoonotic potential.

Swine acute diarrhea syndrome coronavirus (SADS-CoV) is a newly discovered alphacoronavirus with zoonotic potential that causes diarrhea and vomiting mainly in piglets. Having emerged suddenly in 2017, the prevailing opinion is that the virus originated from HKU2, an alphacoronavirus whose primary host is bats, and at some unknown point achieved interspecies transmission via some intermediate. Here, we further explore the evolutionary history and possible cross-species transmission event for SADS-CoV. Coevolutionary analysis demonstrated that HKU2 may have achieved host switch via SADS-related (SADSr)-CoV, which was isolated from the genus Rhinolophus in 2017. SADS-CoV, HKU2 and SADSr-CoV share similar codon usage patterns and showed a lower tendency to use CpG, which may reflect a method of immune escape. The analyses of virus-host coevolution and recombination support SADSr-CoV is the direct source of SADS-CoV that may have undergone recombination events during its formation. Structure-based spike glycoprotein variance analysis revealed a more nuanced evolutionary pathway to receptor recognition for host switch. We did not find a possible positive selection site, and the dN/dS of the S gene was only 0.29, which indicates that the current SADS-CoV is slowly evolving. These results provide new insights that may help predict future cross-species transmission, and possibly surveil future zoonotic outbreaks and associated public health emergencies. This article is protected by copyright. All rights reserved.

A mixed effects changepoint quantile regression model for longitudinal data with application on COVID-19 data

IntroductionLongitudinal individual response profiles could exhibit a mixture of two or more phases of increase or decrease in trend throughout the follow-up period, with one or more unknown transition points (changepoints). The detection and estimation of these changepoints is crucial. Most of the proposed statistical methods for detecting and estimating changepoints in literature rely on distributional assumptions that may not hold. In this case, a good alternative is to use a robust approach; the quantile regression model. There are methods in the literature to deal with quantile regression models with a changepoint. These methods ignore the within-subject dependence of longitudinal data.MethodsWe propose a mixed effects quantile regression model with changepoints to account for dependence structure in the longitudinal data. Fixed effects parameters, in addition to the location of the changepoint, are estimated using the profile estimation method. The stochastic approximation EM algorithm is proposed to estimate the fixed effects parameters exploiting the link between an asymmetric Laplace distribution and the quantile regression. In addition, the location of the changepoint is estimated using the usual optimization methods.Results and discussionA simulation study shows that the proposed estimation and inferential procedures perform reasonably well in finite samples. The practical use of the proposed model is illustrated using COVID-19 data. The data focus on the effect of global economic and health factors on the monthly death rate due to COVID-19 from 1 April 2020 to 30th April 2021. the results show a positive effect on the monthly number of patients with COVID-19 in intensive care units (ICUs) for both 0.5th and 0.8th quantiles of new monthly deaths per million. The stringency index, hospital beds, and diabetes prevalence have no significant effect on both 0.5th and 0.8th quantiles of new monthly deaths per million.

On-Line Monitoring of Shunt Capacitor Bank Based on Relay Protection Device

In modern power systems, the installation of a shunt capacitor bank is one of the cheapest and most widely used methods for improving the voltage profile. One shunt capacitor bank is composed of mass capacitor units and have ground, ungrounded, delta, wye connections that make configuration of capacitor banks is various. In the case of long-term operation, the failure of a single capacitor unit of a capacitor bank is likely to cause uneven voltage, which will lead to the breakdown and burning of the whole group, resulting in huge losses. The relay protection device can detect the simultaneous voltage and current of the capacitor. By utilizing these data from the relay, the abnormal state of the shunt capacitor banks at the initial stage of the fault can be found through monitoring the slight change in capacitance. Timely and early maintenance and repair would avoid capacitor bank faults and potentially greater economic losses. Capacitor banks have different connection modes. For ungrounded wye-connected capacitor banks with an unknown neutral point voltage, the capacitance parameters of each branch cannot be calculated. A parameter symmetry based on the calculation method for capacitor parameters is proposed. For long-term monitoring and observation of the capacitor capacitance value, the fault state and abnormal state of the capacitor are identified based on statistical methods. The simulation established by PSCAD verified that a relay protection device can realized an effective monitoring of the early abnormal state of the capacitor bank.

Sequential Detection of an Arbitrary Transient Change Profile by the FMA Test

This article addresses the sequential detection of transient changes by using the finite moving average (FMA) test. It is assumed that a change occurs at an unknown (but nonrandom) change point and the duration of postchange period is finite and known. We relax the assumption that the profile of a transient change is chosen so that the log-likelihood ratios of the observations are associated random variables (r.v.s) in the prechange mode. Hence, the profile of the transient change is arbitrary and it is not necessarily of constant sign for a distribution with monotone likelihood ratio. A new upper bound for the worst-case probability of false alarm is proposed. It is shown that the optimization of the window-limited cumulative sum (CUSUM) test again leads to the FMA test. Three particular transient changes are considered: in the Gaussian mean, in the Gaussian variance, and in the parameter of exponential distribution. In the first case, a comparison between the bounds for the FMA test operating characteristics and the exact operating characteristics calculated by numerical integration is used to estimate the sharpness of the bounds. In the second and third cases, special attention is paid to the calculation of the FMA distribution in the case of arbitrary profile. The method of convolution is used to solve the problem.

A self-gelling powder based on polyacrylic acid/polyacrylamide/quaternate chitosan for rapid hemostasis

In order to improve the hemostatic effect of the hemostatic dressing for non-compressible wounds, unknown bleeding points and irregularly shaped wounds, a self-gelling hemostasis powder based on polyacrylic acid/polyacrylamide/quaternate chitosan (PAA/PAM/QCS) is prepared in this study. When in contact with water, the PAA/PAM/QCS can fuse and rapidly form a stable hydrogel in a short time (< 0.25 min). The PAA/PAM ratio is the main parameter that modulates the formation of the self-gel. The PAA/PAM self-gel can be formed only when the PAA/PAM ratio is 5:5, and the introduction of QCS does not influence the self-gelling behaviors and hydrogel stability. Moreover, the PAA/PAM/QCS self-gel shows good adhesive properties on wet tissue surfaces. In addition, the introduction of QCS improves the antibacterial activity of the self-gelling hemostasis powder. Furthermore, the prepared PAA/PAM/QCS powder can rapidly adsorb lots of blood, aggregate blood cells and platelets. The hemostatic results in vivo show that PAA/PAM/QCS powder is superior to the control group and commercial product groups (chitosan powder) with performance similar to hemostatic zeolite in terms of the amount of bleeding and hemostatic time. Therefore, the PAA/PAM/QCS self-gelling powder shows great application prospects for rapid hemostasis.

ARSENY: A program for computing inelastic transitions via hidden crossings in one-electron atomic ion–ion collisions with classical description of nuclear motion

The ARSENY program is intended to compute cross-sections of inelastic transitions via hidden crossings upon slow one-electron atomic ion–ion collisions using the approximation of classical description of nuclear motion in the collision energy region E<20 KeV/nucleon. Particular attention is paid to the calculation of the analytical properties of adiabatic potential energy curves of the two-center Coulomb problem for complex values of the internuclear distance. Complex branch points and hidden crossings are calculated and their significance for the dynamics of one-electron collisional systems is revealed. Benchmark calculations of cross sections for charge exchange, excitation, and ionization in slow He2++H(1s) collisions are presented and compared with experimental data. Program summaryProgram Title: ARSENYCPC Library link to program files:https://doi.org/10.17632/n43srxwdnm.1Licensing provisions: CC By 4.0Programming language: FORTRAN 90/95. Compilers: Intel(R) Visual Fortran Compiler 19.0.4.245 [IA-32]Nature of problem: The processes of charge exchange, excitation, and ionization in one-electron atomic ion–ion collisions in a low-temperature plasma are actively studied in astrophysics and tokamak Charge-eXchange Recombination Spectroscopy (CXRS) Edge diagnostics in ITER [1–7]. Numerical calculations of cross sections for charge exchange, excitation, and ionization for slow one-electron atomic ion–ion collisions within the approximation of classical description of nuclear motion have been conventionally implemented, in particular, by the electron-nuclear dynamics approach [8] and the close-coupled channel method using basis functions of the two-center Coulomb problem (see, e.g., [9–13]). However, with real-valued internuclear distance these approaches did not allow for the dynamical structure of discrete-discrete and discrete-continuous transitions in the two-center Coulomb problem. This disadvantage manifests itself in the disagreement between the theoretical and experimental cross-sections at small velocity of ions [13–15]. In a number of papers [1,14,16–20] the dynamical structure of the transitions is considered in terms of hidden crossing of potential curves, when using the analytic continuation to a complex plane of the internuclear distance. This approach is implemented in the ARSENY program aimed at computing cross sections of inelastic discrete-discrete and discrete-continuous transitions via hidden crossings for slow one-electron atomic ion–ion collisions within the approximation of classical description of nuclear motion announced in [1]. Benchmark calculations of cross sections for charge exchange, excitation, and ionization in slow He2++H(1s) collisions are presented and compared with experimental data.Solution method: The potential energy curves E=E(R) and the separation constant λ=λ(R) depending on the real-valued and complex-valued parameter R of the two-center Coulomb problem are calculated from the minimization condition for a quadratic functional corresponding to a pair of nonlinear equations with respect to a pair of unknowns E(R) and λ(R) by iterating three-term recurrent relations [21,22] using a mean least square method [23]. These equations are obtained from the known recurrent relations for the expansion coefficients of quasiradial and quasiangular spheroidal Coulomb functions. The series of branching points Rc sought for in the complex plane of internuclear distance R and the hidden crossings of complex potential energy curves E(R) are calculated by an iterative method using the known analytical behavior in the form of a square root of difference E(R)−E(Rc) in the vicinity of the unknown branch points Rc. Calculations of cross-sections of inelastic transitions via hidden crossings for the slow one-electron atomic ion–ion collisions within the approximation of classical description of nuclear motion are carried out by integration over the impact parameter of the nonadiabatic transition probability expressed in terms of the Stückelberg parameter determined integral of difference of imaginary parts of each pair of complex potential energy curves E(R) by a contour around the branching point Rc [18,19].Additional comments including restrictions and unusual features: In calculations of cross sections and required branch points, about 220 adiabatic states of the lower part of the discrete spectrum of the two-center problem are used.

MONITORING OF LAND SURFACE DISPLACEMENT BASED ON SBAS-INSAR TIME-SERIES AND GIS TECHNIQUES: A CASE STUDY OVER THE SHIRAZ METROPOLIS, IRAN

Abstract. Nowadays, subsidence as one of the natural disasters, threaten urban environments. Over the past three decades, the small baseline subset (SBAS) InSAR method due to its capability to monitor medium to large-scale deformations, has emerged as an important tool for estimating surface displacements. In densely vegetated environments, however, the SBAS technique is not effective due to the decorrelation effect. Since the SBAS technique can estimate millions of points for subsidence, these data can be used as input to the Kriging method to estimate the unknown points. Therefore, in this study, we identified the subsidence disaster-stricken-urban areas in the Shiraz metropolis over a 4-year period (between 2017 and 2021) based on the fusion of the SBAS technique and geospatial information science (GIS) using Sentinel-1A time-series images. In the GIS part of this research, the ordinary kriging method was used for interpolation of the SBAS data. Also, the kernel estimation density (KED) was used for the preparation of the raster layers of a population and the built-up density. Based on 33 radar images in ascending and descending orbit, a total of 95 interferograms have been computed. In this research, temporal baselines of less than 100 meters and multi-look window dimensions of 200 meters were used. What is more, the amount of coherence was 0.8 in estimating displacements. Based on the results, the highest displacements occurred in districts 2, 4, 7, and 11. The maximum value of the displacement (30 mm per year) was seen in the southeast of the Shiraz metropolis, in district 7. Moreover, the surface displacement was mainly observed in the lands of the Shiraz international airport and some of the agricultural lands located in district 2. The reasons for the displacements in districts 4 and 11 are related to the high density of the building coverages in these regions. Also, the increased population density was another reason for the subsidence in district 4. It can be concluded that the suggested framework is efficient in determining time-series surface movements in extensive urban and non-urban areas.

Reconstruction of pointwise sources in a time-fractional diffusion equation

This paper is concerned with an inverse pointwise source problem for the time-fractional diffusion equation in the two-dimensional case. The source term to be identified models the action of a finite number of small particles. Each particle is assumed to be no larger than a single point, characterized by its location and intensity. Both theoretical and numerical aspects are discussed. In the theoretical part, we analyse the well-posedness of the Dirac time-fractional diffusion problem. For the inverse problem, we establish that the unknown point sources can be uniquely identified from local measured data and we derive a local Lipschitz stability result. In the numerical part, we develop a fast and accurate reconstruction approach. The unknown pointwise sources are characterized as solution to an optimization problem minimizing a tracking-type functional. A noniterative reconstruction algorithm is devised, allowing us to determine the number, locations and intensities of the pointwise sources. The efficiency of the proposed approach is confirmed by some numerical examples.

Minimizing online retailers’ revenue loss under a time-varying willingness-to-pay distribution

We study revenue management for an online retailer that offers a single product to customers with a time-varying willingness-to-pay (WTP) distribution. When the WTP distribution changes at an unknown time point (i.e., the change point), the original price quoted to customers may not be optimal. The retailer’s objective is to minimize his revenue loss by determining when to quote a new price to incoming customers and what the new price is. We formulate the problem as an optimization model, which is challenging to solve due to the presence of the unknown change point. To overcome this challenge, we first characterize the probability distribution of the estimated change point using maximum likelihood estimation. We then develop two pricing algorithms to solve the model by leveraging the characterized distribution. Lastly, through numerical studies, we illustrate the effectiveness of the proposed algorithms in identifying change points and recommending optimal post-change selling prices. The numerical results suggest that the proposed pricing algorithms significantly reduce the frequency of false change detection in the early stages of a selling season. The proposed pricing algorithms also outperform the benchmark pricing algorithm in reducing the retailer’s revenue loss.