Interpolation Research Articles

Consistent operator semigroups and their interpolation

Under a mild regularity condition we prove that the generator of the interpolation of two C0-semigroups is the interpolation of the two generators.

PRIVACY-PRESERVING K-NEAREST NEIGHBOUR INTERPOLATION METHOD IN AN OUTSOURCED ENVIRONMENT

One
 of the most emerging computer technologies of this decade is cloud computing
 that allows data owners to outsource their storage and computing requirements.
 It enables data owners to avoid the costs of building and maintaining a private
 storage infrastructure. While outsourcing data to cloud promises significant
 benefits, it possesses substantial security and privacy concerns, especially
 when data stored in the cloud is sensitive and confidential, like a business
 plan. Encrypting the data before outsourcing can ensure privacy. However, it
 will be very difficult to process the cipher text created by the traditional
 encryption method. Considering this fact, we propose an efficient protocol that
 allows a query owner to retrieve the interpolation of the top k records from two
 different databases that are closest to a query point. Note that the databases
 are stored in two different cloud service providers in encrypted form. We also
 show that the proposed protocol ensures the privacy and the security of the
 data and the query point.

A Semi-empirical Model for Estimation of Pressure Drop Coefficient of a Conical Diffuser

Diffusers are widely used in technical practice in order to make the transition from a tube/pipe or duct of smaller section to a larger one. Low pressure drop across a diffuser is highly required to save pumping or ventilation work. Diffuser pressure drop is caused by enhanced turbulence of the flow, separation of the boundary layer from the diffuser walls and violent vortex formation. As a result, the precise pressure drop coefficient estimation is of high importance. The pressure drop coefficient (?d) of a diffuser depends on diffuser geometry and flow parameters. Traditionally, a number of models must be combined and used with the data obtained from tables (with 2-D interpolation) and charts in a series of steps to obtain ?d. This approach is not suitable for computer-based simulations. Consequently, in this study, a semi-empirical model, for estimating ?d of a conical diffuser, as an explicit function of the flow parameters and the diffuser geometry, is developed. The model was validated using literature data. The performance indices which were obtained as high R2=0.9942, low mean absolute relative error (MeARE)=4.04%, low root mean squared error (RMSE)=0.0192 are an indication that the proposed model is accurate enough for computer-based simulations and performance evaluation of a conical diffuser over a wide range of operating conditions.

Análise Comparativa de Metodologias de Determinação de Valores de Referência para Sedimentos de Corrente

A definicao de valores de referencia em series de dados geoquimicos tem sido um dos principais desafios nos estudos relativos a geoquimica ambiental. Antigas metodologias eram fundamentadas em parâmetros estatisticos, na construcao de tabelas, graficos e histogramas. Contudo, estas tecnicas nao definem estes valores de maneira correta ou apresentam valores muito diferentes para a mesma regiao. Desta forma, o presente trabalho testou diferentes metodologias de determinacao de valores de referencia para sedimentos de corrente: media +2 desvio padrao, mediana +2 MAD, boxplot UIF, analise fractal, analise espacial com a interpolacao pelo modelo IDW e as metodologias associadas, o que foi feito na regiao do Quadrilatero Ferrifero – Brasil, conhecida mundialmente por sua diversidade de minerios e tipos litologicos. Os resultados indicam que as tecnicas mais antigas de determinacao de valores de referencia, notadamente a “Media + 2x desvio padrao e a Mediana + 2x MAD” demonstraram nao serem efetivas para a separacao das anomalias, pois superestimam ou subestimam a faixa de referencia, podendo causar erros consideraveis quando sao discutidos aspectos relativos a legislacao ambiental. Ja as metodologias “Analise fractal” e “Boxplot UIF” apresentaram, para a grande maioria dos elementos, valores bem proximos, confirmando que o intervalo de referencia esta correto e, demonstrando que ambas sao as mais adequadas para ambientes geologicos complexos. Contudo, foram verificados para alguns elementos (Cu, Fe, Pb e Ti) valores discrepantes de 30 a 46 % entre as metodologias. No entanto, sempre que ocorreram divergencias, os valores obtidos via Analise fractal demonstraram ser mais condizentes com a distribuicao espacial dos elementos, alem de ter apresentado os outliers em locais onde notadamente sao observados litotipos ricos no elemento e impactos ambientais capazes de disponibiliza-lo para o meio.

Walking interpolated flaps - history revisited

Walking interpolated flaps - history revisited

The role of geological uncertainty in developing combined geological and potential field inversions

Recently, implicit model building techniques have been developed which use, for example, geo-statistical methods to interpolate boundary orientations as a scalar field. Boundaries are implicitly formulated as iso-values of that field. Using more than one potential allows modelling for intrusion and unconformities. This technique is attractive because it makes 3D geological modeling a repeatable task and model uncertainty can be estimated from the geostatistical estimators. However, this uncertainty does not take into account the error on field measurements, nor estimates of how relevant are the measurements to the modelled structures. Lastly, this uncertainty does not take into account possible variation in the knowledge based information which is very often interpretative, such as structural evolution history, fault network, and overprinting relationships with themselves and the different formations. We present an innovative method that will simulate numerous (millions of) geological models from a single initial structural dataset, taking into account these variables. These models are used to estimate geological uncertainty, highlighting future areas of research or data collection. A series of best models are then assessed against potential field inversions and modified to better fit potential field data. In the end, the models that both better fit geological input data and potential field data will be retained. A best probable model will be proposed that will satisfy geophysical data as well as geological data. To assess the models against the initial geological data input, we develop geological objective functions based on (e.g.) locations and gradients of boundaries. It is our intent to combine these objectives functions with classical geophysical objective functions to provide a new method for combined geological and potential field inversions.

An initial acoustic impedance modeling method based on seismic attributes

It is common that an initial impedance model should be created first, while performing acoustic impedance inversion. The traditional modeling is horizontally interpolated using inverse distance power method for multiple wells, and vertically controlled by seismic horizons. This method was relatively simple, and could not reflect the seismic facies changes in complex geological conditions, inversion accuracy was not high.

DISCover - Broadband Towed Streamer Acquisition

In this paper we present a new method for broadband marine acquisition and processing capable of imaging deep targets while maintaining full high frequency bandwidth data. The method uses a deep interpolated streamer coverage approach (DISCover), which comprises a conventional 3D shallow towed-streamer spread, and a deep streamer spread which is more sparsely sampled in the crossline direction. The measurement from the shallow streamer plane is complemented with a low frequency limited measurement from the deep streamer plane; In essence boosting the low frequencies of the shallow streamer measurement, which are heavily attenuated by the shallow tow ghost response. Because the deep streamers are only going to provide the low-frequency part of the bandwidth, we can more sparsely sample these data thus enabling efficient acquisition scenarios as fewer streamers are required. The data are combined in processing, optimizing the signal-to-noise ratio over the entire bandwidth. The resulting data exhibit both high resolution and deep penetration, characteristics suitable for deep imaging below attenuative overburdens. Velocity model building, imaging and impedance inversion also benefit from the broadband result. In addition, data acquired in this way are more robust to poor weather conditions than conventionally acquired data. Data from a 3D case study using this new acquisition method were acquired off the NW Shelf of Australia. The streamer spread consisted of six shallow streamers towed at a depth of 6 m and two deeper streamers (below shallow streamers 2 and 5) towed at a depth of 20 m. The correct relative position of the streamers was controlled by means of streamer steering. A novel over/under source design was also used to bias source output toward low frequencies and further enhance the low-frequency signal-to-noise ratio of the acquired data.

IDENTIFICACIÓN DE LAS ZONAS CONTAMINADAS CON METALES PESADOS EN EL POLVO URBANO DE LA CIUDAD DE MÉXICO

Siete millones de personas mueren al ano por cancer relacionado con la contaminacion ambiental. El polvo urbano (PU) contiene particulas < 10 µm que afectan la salud humana. En la Ciudad de Mexico (CDMX) existe solo un estudio de PU. El objetivo de este estudio fue identificar las zonas de la CDMX con mayor probabilidad de contaminacion por metales pesados (MP) en el PU. Se recolectaron 89 muestras de PU y se midio la concentracion de MP por fluorescencia de rayos X. El analisis espacial se realizo mediante interpolacion con kriging indicador. El porcentaje de la superficie con mayor probabilidad de que los MP superen los limites maximos permitidos (LMP) fueron: Cr (LMP 280 mg/kg), 0.55 %, suroeste; Cr (LMP 64 mg/kg), 89 %, toda la CDMX y la mayoria de las areas conurbadas (AC); Cu, 17 %, 11 delegaciones y AC del norte; Ni, 13 %, centro y suroeste; Pb (LMP 140 mg/kg), 17.5 %, delegaciones centricas y AC del noroeste; Pb (LMP 400 mg/kg), 2.2 %, delegaciones centricas y AC del noroeste; V, 26 %, delegaciones centricas y del sur, asi como AC del noreste; Zn, 21 %, delegaciones centricas y AC del norte. Los elementos con mayor numero de sitios y superficie contaminada son: Cr, Zn, Cu y Pb. Los sitios con mayor superficie de sobreposicion de MP son aquellos con asociaciones entre Cu y Zn (15 %), y Cu y Pb (13 %). Las delegaciones Cuauhtemoc, Venustiano Carranza y Gustavo A. Madero son las mas contaminadas con metales pesados.

A Spark-based Distributed Implementation of Interpolating MODIS LST over Qinghai-Tibetan Plateau

A Spark-based Distributed Implementation of Interpolating MODIS LST over Qinghai-Tibetan Plateau

BLOCK PROCEDURE WITH IMPLICIT SIXTH ORDER LINEAR MULTISTEP METHOD USING LEGENDRE POLYNOMIALS FOR SOLVING STIFF INITIAL VALUE PROBLEMS

In this paper, a discrete implicit linear multistep method in block form of uniform step size for the solution of first-order ordinary differential equations is presented using the power series as a basis function. To improve the accuracy of the method, a perturbation term is added to the approximated solution. The method is based on collocation of the differential equation and interpolation of the approximate solution using power series at the grid points. The procedure yields four linear multistep schemes which are combined as simultaneous numerical integrators to form block method. The method is found to be consistent and zero-stable, and hence convergent. The accuracy of the method is tested with some standard stiff first order initial value problems. The results are compared with the two point implicit block backward difference formula and two point implicit block extended backward difference formula. All numerical examples show that our proposed method has a better accuracy than the existing literature.

Combining radial point interpolation meshless method with a new homogenization technique for trabecular bone multiscale structural analyses.

Bone tissue is a dynamic tissue, possessing different functional requirements at different scales. This layered organization indicates the existence of a hierarchical structure, which can be characterized to distinguish macro-scale from micro-scale levels. Structurally, both scales can be linked by the use of classic multiscale homogenization techniques. Since in bone tissue each micro-scale domain is distinct form its neighbour, applying a classic multiscale homogenization technique to a complete bone structure could represent an inadmissible computational cost. Thus, this work proposes a homogenization methodology that is computationally efficient, presenting a reduced computational cost, and is capable to define the homogenized microscale mechanical properties of the trabecular bone highly heterogeneous medium. The methodology uses the fabric tensor concept in order to define the material principal directions. Then, using an anisotropic phenomenological law for bone tissue correlating the local apparent density with directional elasticity moduli, the anisotropic homogenized material properties of the micro-scale patch are fully defined. To validate the developed methodology, several numerical tests were performed, measuring the sensitivity of the technique to changes in the micro-patch size and preferential orientation. The results show that the developed technique is robust and capable to provide a consistent material homogenization. Additionally, the technique was combined with two discrete numerical techniques: the finite element method and radial point interpolation meshless method. Structural analyses were performed using real trabecular patches, showing that the proposed methodology is capable to accurately predict the micro-scale patch mechanical behavior in a fraction of the time required by classic homogenization techniques.

Nonlocal geometrically nonlinear dynamic analysis of nanobeam using a meshless method

In the present paper, the element free Galerkin (EFG) method is developed for geometrically nonlinear analysis of deep beams considering small scale effect. To interpret the behavior of structure at the nano scale, the higher-order gradient elasticity nonlocal theory is taken into account. The radial point interpolation method with high order of continuity is used to construct the shape functions. The nonlinear equation of motion is derived using the principle of the minimization of total potential energy based on total Lagrangian approach. The Newmark method with the small time steps is used to solve the time dependent equations. At each time step, the iterative Newton-Raphson technique is applied to minimize the residential forces caused by the nonlinearity of the equations. The effects of nonlocal parameter and aspect ratio on stiffness and dynamic parameters are discussed by numerical examples. This paper furnishes a ground to develop the EFG method for large deformation analysis of structures considering small scale effects.

Modellazione di superfici di età romana nel centro urbano di Treviso per lo studio del paesaggio antico e la tutela archeologica

Treviso, as many other historical towns in Italy, is a large and multi-stratified site occupied since the Bronze Age to the present time. This study was oriented to model trend surfaces, representative of the ground level of the city in Roman Age, on the basis of stratigraphic data. GIS spatial analyses were performed to select a reliable dataset. DTM was obtained by the interpolation of elevation points related to significant features, with the aim to contribute to the study of the ancient landscape and to support the evaluation of risks connected with public works that may impact local archaeological heritage.

Spatial Estimation of Forest Species Diversity Index by Applying Spatial Interpolation Method - Based on 1 st Forest Health Management data-

Spatial Estimation of Forest Species Diversity Index by Applying Spatial Interpolation Method - Based on 1 st Forest Health Management data-

An iterative approach to barycentric rational Hermite interpolation

In this paper we study an iterative approach to the Hermite interpolation problem, which first constructs an interpolant of the function values at $$n+1$$n+1 nodes and then successively adds m corr...

Optimizing the use of interpolated tests: The influence of interpolated test lag.

Optimizing the use of interpolated tests: The influence of interpolated test lag.

Metal Artifact Reduction of Dental Fillings in Head and Neck CT Images

Introduction: The issue of metal artifact and its reduction is as old as the clinical use of computed tomography itself. When metal objects such as dental fillings, hip prostheses or surgical clips are present in the computed tomography (CT) field of view (FOV), make severe artifacts that reduce the image quality and accuracy of CT numbers. They can lead to unreliable clinical results due to inability in true tumor volume delineation and uncertainty in dose calculation of treatment planning software. So far, no generally accepted solution to this problem, especially for small size dental fillings, has been found. Herein, an approach is presented to reduce the dental filling artifacts in CT images of head and neck patients with multiple dental fillings. The proposed approach is compared with the commercial orthopedic metal artifact reduction (O-MAR) algorithm by Philips company. Materials and Methods: Our algorithm consists of six steps: 1) metallic object segmentation by thresholding, 2) obtaining the prior image by multi thresholding of the initial image, 3) normalization of the original image sinogram by prior image, 4) interpolation (replacing the affected projection data by previous slice unaffected projection data, 5) denormalization of the corrected sinogram and 6) application of a two dimensional adaptive filter to the final image. The forth step can be implemented by substitution of affected projections with opposite view projections. Both methods were tested and previous slice substitution was superior. Quantitative evaluation of the commercial and proposed algorithms was done in terms of peak signal-to-noise ratio (PSNR), signal-to- noise ratio (SNR) and structural similarity index (SSIM) on a CT image of a head and neck patient with four dental fillings. The posterior part of the head in original image was considered as the reference image. Also two uniform regions of interest (ROI) were considered in the image. ROI1 was posterior region of the head away from dental fillings, while ROI2 was restricted to the tongue region near to the dental fillings. Results: The PSNR, SNR, SSIM values obtained by the proposed method and O-MAR algorithm were 37.05, 36.13, 22.29, 21.37, 0.93 and 0.84, respectively. Using our approach, the standard deviation of CT numbers in ROI1 was 27 times less than the original image and 7% better than the commercial competitor. However, for ROI2 the commercial algorithm was 36% more successful in reduction of variations due to metal artifact. Conclusion: The proposed approach can be applied successfully for dental filling artifact reduction in head and neck patients. Although the performance of the commercial method was superior to ours in near dental regions, for the farther regions with more critical organs was vice versa. However, weighting the interpolation and adaptive filtering steps may result in even better results.

Gamma-ray shielding properties for silicate glasses containing Bi2O3, PbO, and BaO

Introduction: With the extensive application of radiation sources and radioactive materials in various fields, the study of attenuation and absorption of X-rays and gamma-rays in several materials has become an essential and interesting field of research. Glass materials are possible alternatives of concretes for radiation-shielding materials. Materials and Methods: The mass attenuation coefficients (µm), effective atomic cross section (σa), effective atomic number (Zeff) and effective electron density (Neff) of silicate glasses containing different concentrations of Bi2O3, PbO, and BaO (30–70% by weight) were obtained using MCNP-4C code, XCOM and XMuDat programs, in the energy range of 10 keV–10 MeV. The interpolation method was employed to extract Zeff and Neff. The Auto-Zeff software was used to determine the Zeff as well. Results: The MCNP-4C Code, XCOM and XMuDat programs and Auto-Zeff results were in good agreement. It was found that the µm and σa values decrease with photon energy. Also the results indicate that σa and Zeff of glasses improve by increasing their Bi2O3, PbO and BaO contents, while increasing these contents to the same fraction has no significant effect on µm in the energy range of 0.3–5 MeV, where the Compton Effect takes over as dominant process and Neff do not follow certain rule. Above 0.1 MeV, lead oxide silicate glass showed the highest values of Zeff and σa. Conclusion: Observed good agreement indicates that the chosen Monte Carlo code and computer programs may be useful to calculate the gamma-ray shielding characteristics of different glass systems, particularly in cases where no experimental data exist.

Artifact reduction techniques in Cone Beam Computed Tomography (CBCT) imaging modality

Introduction: Cone beam computed tomography (CBCT) was introduced and became more common based on its low cost, fast image procedure rate and low radiation dose compared to CT. This imaging modality improved diagnostic and treatment-planning procedures by providing three-dimensional information with greatly reduced level of radiation dose compared to 2D dental imaging modalities for investigation of maxillofacial skeleton, dentition and the relationship of anatomical structures. However, CBCT is associated with multiple artifacts like. Extinction artifacts, beam hardening artifacts, partial volume effect, aliasing artifacts, ring artifacts and motion artifacts (misalignment artifacts), Noise and scatter. All of them leads to image quality reduction and have capability of Mistakenly considering as a pathological lesion. This study aimed to investigate Cone Beam Computed Tomography artifacts and their reduction procedures. Materials and Methods: A systematic search of the literature published from 2000 to 2017 in the PubMed, scopus and web of science databases was performed. The following key words combined in different ways: cone beam computed tomography, CBCT Artifacts and artifact reduction. Results: Artifact is caused by several factors containing reconstruction parameters like small field of views (FOVs), presence of metal objects, patient movement, etc. Artifact reduction methods can have divided into two categorize preprocessing in the projection domain and post processing in the image domain. Limitation of field of view, modification of patient head position or separating dental arches for scatter reduction, Application of high KVP in order to beam hardening reduction, iterative method and projection modification method for metal artifacts are recommended. In addition, Filtration, interpolation, iterative reconstruction and filtering algorithms, application of the smaller voxel size and respiratory gating are other suggested items for artifact reduction in CBCT. Conclusion: Multiple artifacts accompany CBCT imaging procedures. There for With the aim of improving the quality of the CBCT images; reducing the artifact caused scatter photons , various software-based and hardware-based correction methods are recommended .