In the present work, we evaluate the prediction capability of six Pedotransfer functions (PTFs), reported in the literature, for the saturated hydraulic conductivity estimations (Ks). We used a database with 900 measured samples obtained from the Irrigation District 023, in San Juan del Rio, Queretaro, Mexico. Additionally, six new PTFs were construct for Ks from clay percentage, bulk density and saturation water content data. The results show, for the evaluated models, that one model present an overestimation for Ks>0.5 cm h-1 values, three models have a underestimation for Ks>1.0 cm h-1 and two models have a good correlation (R2>0.98) but are necessary more than three parameters. Nevertheless, the last two models requires from three to four parameters in order to get the optimization. By other hand, the models proposed in this work have a similar correlation with a less number of parameters: the fit is seen to be much better than using the existing ones, achieving a correlation of R2 = 0.9822 with only one variable and a R2 = 0.9901 when we use two.

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem

Often, when solving forward, inverse or data assimilation problems, only a part of the solution is needed. As a model, we consider the stationary diffusion problem. We demonstrate an algorithm that can compute only a part or a functional of the solution, without calculating the full inversion operator and the complete solution. It is a well-known fact about partial differential equations that the solution at each discretisation point depends on the solutions at all other discretisation points. Therefore, it is impossible to compute the solution only at one point, without calculating the solution at all other points. The standard numerical methods like a conjugate gradient or Gauss elimination compute the whole solution and/or the complete inverse operator. We suggest a method which can compute the solution of the given partial differential equation 1) at a point; 2) at few points; 3) on an interface; or a functional of the solution, without computing the solution at all points. The required storage cost and computational resources will be lower as in the standard approach. With this new method, we can speed up, for instance, computation of the innovation in filtering or the likelihood distribution, which measures the data misfit (mismatch). Further, we can speed up the solution of the regression, Bayesian inversion, data assimilation, and Kalman filter update problems. Applying additionally the hierarchical matrix approximation, we reduce the cubic computational cost to almost linear $\mathcal{O}(k^2n \log^2 n)$, where $k\ll n$ and $n$ is the number of degrees of freedom. Up to the hierarchical matrix approximation error, the computed solution is exact. One of the disadvantages of this method is the need to modify the existing deterministic solver.

As many if not most ligands at G protein-coupled receptor antagonists are inverse agonists, we have systematically reviewed inverse agonism at the nine adrenoceptor subtypes. Except for β3-adrenoceptors, inverse agonism has been reported for each of the adrenoceptor subtypes, most often for β2-adrenoceptors, including endogenously expressed receptors in human tissues. As with other receptors, detection and degree of inverse agonism depends on the cells and tissues under investigation, i.e. is greatest when the model has a high intrinsic tone/constitutive activity for the response being studied. Accordingly, it may differ between parts of a tissue, for instance atria vs. ventricles of the heart, and within a cell type between cellular responses. The basal tone of endogenously expressed receptors often is low, leading to less consistent detection and smaller extent of observed inverse agonism. The extent inverse agonism depends on specific molecular properties of a compound but clusters by chemical class. While inverse agonism is a fascinating facet in attempts to mechanistically understand observed drug effects, we are skeptical whether an a priori definition of extent of inverse agonism in the target product profile of a developmental candidate is a meaningful option in drug discovery and development.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.

The application of instrumented indentation to assess material properties like Young’s modulus and micro-hardness has become a standard method. In recent developments, indentation experiments and simulations have been combined to inverse methods, from which further material parameters as yield strength, work hardening rate, and tensile strength can be determined. In this work, an inverse method is introduced by which material parameters for cyclic plasticity, i.e. kinematic hardening parameters, can be determined. To accomplish this, cyclic Vickers indentation experiments are combined with finite element simulations of the indentation with unknown material properties, which are then determined by inverse analysis. To validate the proposed method, these parameters are subsequently applied to predict the uniaxial stress-strain response of a material with success. The method has been validated successfully for a quenched and tempered martensitic steel and for technically pure copper, where an excellent agreement between measured and predicted cyclic stress-strain-curves has been achieved. Hence, the proposed inverse method based on cyclic nanoindentation, as a quasi-non-destructive method, could complement or even substitute the resource-intensive conventional fatigue testing in the future for some applications.

Automatic control to any of robot manipulators, some kind of issues are being observed. A numerical method for solution generation to the inverse kinematics problem of redundant robotic manipulators is presented to obtain the smoothest algorithm as possible, leading to a robust iterative method. After the primary objective of the reachability of end-effectors to the target point is achieved, the aim is set to resolve the redundant degrees of freedom of redundant manipulator. This method is numerically stable since it converges to the correct answer with virtually any initial approximation, and it is not sensitive to the singular configurations of the manipulator. In addition, this technique is computationally effective and able to apply for serial manipulators with any DOF applications. A planar 3R-DOF serial link redundant manipulator is considered as exemplar problem for solving. Also, the continuum approach for resolving more complex structure with variable DoF is illustrated here and their brief applicability to support surgeries and adaptive use of artificial linkage moments is also calculated.

One of the typical forms of linear matrix expressions (linear matrix-valued functions) is given by $A + B_1X_1C_1 + \cdots + B_kX_kC_k$, where $X_1, \ldots, X_k$ are independent variable matrices of appropriate sizes, which include almost all matrices with unknown entries as its special cases. The domain of the matrix expression is defined to be all possible values of the matrix expressions with respect to $X_1, \ldots, X_k$. I this article, we approach some problems on the relationships between the domains of two linear matrix expressions by means of the block matrix method (BMM), the matrix rank method (MRM), and the matrix equation method (MEM). As application, we discuss some topics on the relationships among general solutions of some linear matrix equations and their reduced equations.

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.

Spiral galaxies and their rotation curves have key characteristics of differentially spinning objects. Oblate spheroid shapes are a consequence of spin and reasonably describe galaxies, indicating that their matter is distributed in gravitationally interacting homeoidal shells. Previously published equations describing differentially spinning oblate spheroids with radially varying density are here applied to 51 galaxies, mostly spirals. A constant volumetric density (rho, kg m-3) is assumed for each thin homeoid in these formulae, after Newton, which is consistent with RC being reported simply as a function of equatorial radius r. We construct parameter-free inverse models that uniquely specify mass inside any given r, and thus directly constrain rho vs. r solely from velocity v(r) and galactic aspect ratios (assumed as 1:10 when data are unavailable). Except for their innermost zones, rho is proven to be closely proportional to rn, where n for all 36 spirals studied equals -1.80±0.40. Our values for interior densities compare closely with independently measured baryon density in appropriate astronomical environments: for example, calculated rho at galactic edges agrees with estimated rho of intergalactic media (IGM). Our finding that central densities increase with galaxy size is consistent with behavior exhibited by diverse self-gravitating entities. Our calculated mass distributions are consistent with visible luminosity and require no non-baryonic component. Empirical luminosity-velocity relationships for galaxies, such as the Tully-Fisher rule, originate in Newtonian physics.

Helmholtz energy of ice VII-X is determined in a pressure regime extending to 450 GPa at 300 K using local basis functions in the form of b splines. The new representation for the equation of state is embedded in a physics-based inverse theory framework of parameter estimation. Selected pressures as a function of volume from 14 prior experimental studies and two theoretical studies constrain the behavior of Helmholtz energy. Separately measured bulk moduli, not used to construct the representation, are accurately replicated below about 20 GPa and above 60 GPa. In the intermediate range of pressure, the experimentally determined moduli are larger and have greater scatter than values predicted using the Helmholtz representation. Although systematic experimental error in the experimental elastic moduli is possible and likely, the alternative hypothesis is a slow relaxation time associated with changes in proton mobility or the ice VII to X transition. A correlation is observed between anomalies in the pressure derivative of the predicted bulk modulus and previously suggested higher-order phase transitions. Improved determinations of elastic properties at high pressure would allow refinement of the current equation of state. More generally, the current method of data assimilation is broadly applicable to other materials in high-pressure studies.

Interpolation is procedure that depends on spatial and/or statistical properties of analysed variable(s). It is special challenging task for data that included low number of samples, like dataset with less than 20 data. This problem is especially emphasized in the subsurface geological mapping, i.e. in the cases where data are taken solely from wells. Successful solutions of such mapping problems ask for knowledge about interpolation methods designed primarily for small datasets and dataset itself. Here are compared two methods, namely Inverse Distance Weighting and Modified Shepard’s Method, applied for three variables (porosity, permeability, thickness) measured in the Neogene sandstone hydrocarbon reservoirs (Northern Croatia). The results showed that pure cross-validation is not enough condition for appropriate map selection, but also geometrical features need to be considered, for datasets with less than 20 points.

We present an improved algorithm for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithm is much more accurate than the famous fast inverse square root algorithm and has a similar computational cost. The presented modification concern Newton-Raphson corrections and can be applied when the distribution of these corrections is not symmetric (for instance, in our case they are always negative).

This paper investigates an inverse problem of option pricing in the extended Black--Scholes model. We identify the model coefficients from the measured data and attempt to find arbitrage opportunities in financial markets using a Bayesian inference approach. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by Markov Chain Monte Carlo (MCMC), which explores the posterior state space. The efficient sampling strategy of MCMC enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown drift and volatility coefficients from the measured data.

This paper investigates the inverse option problems (IOP) in the extended Black--Scholes model arising in financial markets. We identify the volatility and the drift coefficient from the measured data in financial markets using a Bayesian inference approach, which is presented as an IOP solution. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC) algorithm, which exploits the posterior state space. The efficient sampling strategy of the MCMC algorithm enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown trend and volatility coefficients from the measured data.

In this research, a novel method to investigation the transient heat transfer coefficient in a channel is suggested experimentally, in which the water flow, itself, is considered both just liquid phase and liquid-vapor phase. The experiments were designed to predict the temporal and spatial resolution of Nusselt number. The inverse technique method is non-intrusive, in which time history of temperature is measured, using some thermocouples within the wall to provide input data for the inverse algorithm. The conjugate gradient method is used mostly as an inverse method. The temporal and spatial changes of heat flux, Nusselt number, vapor quality, convection number, and boiling number have all been estimated, showing that the estimated local Nusselt numbers of flow for without and with phase change are close to those predicted from the correlations of Churchill and Ozoe (1973) and Kandlikar (1990), respectively. This study suggests that the extended inverse technique can be successfully utilized to calculate the local time-dependent heat transfer coefficient of boiling flow.

Despite their obvious differences, biological systems at different scales tend to exhibit common organizational patterns. Unfortunately, these commonalities are usually obscured by the parcelled terminology employed by various scientific sub-disciplines. To explore these commonalities, this papers a comparative study of diverse applications of the maximum entropy principle, ranging from amino acids up to societies. By presenting these studies under a common language, this paper establishes a unified view over seemingly highly heterogeneous biological scenarios.

This paper describes a new approach that can be used to determine the mechanical properties of unknown materials and complex material systems. The approach uses inverse finite element modelling (FEM) accompanied with a designed algorithm to obtain the modulus of elasticity, yield stress and strain hardening material constants of an isotropic hardening material model, as well as the material constants of the Drucker-Prager material model (modulus of elasticity, cap yield stress and angle of friction). The algorithm automatically feeds the input material properties data to finite element software and automatically runs simulations to establish a convergence between the numerical loading-unloading curve and the target data obtained from continuous indentation tests using common indenter geometries. A further module was developed to optimise convergence using an inverse FEM analysis interfaced with a non-linear MATLAB algorithm. A sensitivity analysis determined that the dual Spherical and Berkovich (S&B) approach delivered better results than other dual indentation methods such as Berkovich and Vickers (B&V) and Vickers and Spherical (V&S). It was found that better convergence values can be achieved despite a large variation in the starting parameter values and / or material constitutive model and such behaviour reflects the uniqueness of the dual S&B indentation in predicting complex material systems. The study has shown that a robust optimization method based on a non-linear least-squares curve fitting function (LSQNONLIN) within MATLAB and ABAQUS can be used to accurately predict a unique set of elastic plastic material properties and Drucker-Prager material properties. This is of benefit to the scientific investigation of properties of new materials or obtaining the material properties at different location of a part which might be not be similar due to manufacturing processes (e.g. different heating and cooling rates at different locations).

Industrial manipulators and parallel robots are often used for tasks like drilling or milling, that require three translational, but only two rotational degrees of freedom (“3T2R”). While kinematic models for specific mechanisms for these tasks exist, a general kinematic model for parallel robots is still missing. This paper presents the definition of the rotational component of kinematic constraints equations for parallel robots based on two reciprocal sets of Euler angles for the end-effector orientation and the orientation residual. The method allows to completely remove the redundant coordinate in 3T2R tasks and to solve the inverse kinematics for general serial and parallel robots with the gradient-descent algorithm. The functional redundancy of robots with full mobility is exploited using nullspace projection.

In laser-assisted milling, higher temperature in shear zone softens the material potentially resulting in a shift of mean residual stress, which significantly affects the damage tolerance and fatigue performance of product. In order to guide the selection of laser and cutting parameters based on the preferred mean residual stress, inverse analysis is conducted by predicting residual stress based on guessed process parameters, which is defined as the forward problem, and applying iterative gradient search to find process parameters for next iteration, which is defined as the inverse problem. An analytical inverse analysis is therefore proposed for the mean residual stress in laser-assisted milling. The forward problem is solved by analytical prediction of mean residual stress after laser-assisted milling. The residual stress profile is predicted through the calculation of thermal stress, by treating laser beam as heat source, and plastic stress by first assuming pure elastic stress in loading process, then obtaining true stress with kinematic hardening followed by the stress relaxation. The variance-based recursive method is applied to solve inverse problem by updating process parameters to match the measured mean residual stress. Three cutting parameters including depth of cut, feed per tooth, and cutting speed, and two laser parameters including laser-tool distance and laser power, are updated with respected to the minimization of resulting residual stress and measurement in each iteration. Experimental measurements are referred on the laser-assisted milling of Ti-6Al-4V grade 5 and ELI. The percentage difference between experiments and predictions is less than 5% for both materials, and the selection is completed within 50 loops.

Here are analysed data taken in two hydrocarbon fields ("A" and "B"), located in the western part of Sava Depression (North Croatia). They are in the secondary phase of production. The selected reservoirs "L" (in the “A” Field) and "K" (“B”) are of the Lower Pontian (Upper Miocene) age and belong to Kloštar-Ivanić Formation. Due to strong tectonics, there are numerous tectonic block, relatively rarely sampled with well and laboratory tests. Here are selected two variables for interpolation - reservoirs permeabilities and the injected volumes of field water. The following interpolation methods are described, compared and applied: Nearest Neighbourhood, Natural Neighbour (the first time in the Sava Depression) and Inverse Distance Weighting. The last one has been proven as the most appropriate for datasets with size lower than 20 points.

Based on the Graph Model of Conflict Resolution (GMCR), a two-stage decision framework is developed to reveal the essence of brownfield incidents and facilitate the resolution of brownfield conflicts caused by the incidents. More particularly, the forward GMCR is utilized in Stage I, the negotiation stage, to simulate the evolution of a brownfield conflict (BC) and predict its potential resolution via stability analysis. If no acceptable equilibrium can be obtained, the BC progresses into Stage II, the third-party-intervention stage, where the inverse GMCR is used to assist a third party in intervening the conflict to achieve a desirable outcome. To illustrate the practicality of this framework, a recent BC occurred in Changzhou, China, is taken as a case study. Invaluable insights are provided through the computation and investigation of the corresponding preference relationships.

In this paper, at first, a color image of a car is taken. Then the image is transformed into a grayscale image. After that, the motion blurring effect is applied to that image according to the image degradation model described in equation 3. The blurring effect can be controlled by a and b components of the model. Then random noise is added in the image via Matlab programming. Many methods can restore the noisy and motion blurred image; particularly in this paper Inverse filtering as well as Wiener filtering are implemented for the restoration purpose. Consequently, both motion blurred and noisy motion blurred images are restored via Inverse filtering as well as Wiener filtering techniques and the comparison is made among them.

Deep Learning is a recent and important addition to the computational toolbox available for image reconstruction in fluorescence microscopy. We review state-of-the-art applications such as image restoration, super-resolution, and light-field imaging, and discuss how the latest Deep Learning research can be applied to other image reconstruction tasks such as structured illumination, spectral deconvolution, and sample stabilisation. Despite its successes, Deep Learning also poses significant challenges, has often misunderstood capabilities, and overlooked limits. We will address key questions, such as: What are the challenges in obtaining training data? Can we discover structures not present in the training data? And, what is the danger of inferring unsubstantiated image details?

Background: Underreporting of Visceral Leishmaniasis (VL) in India remains a problem to public health controls. Effective and reliable surveillance systems are critical for monitoring disease outbreaks and public health control programs. However, in India, government surveillance systems are affected by levels of scarcity in resources and therefore, uncertainty surrounds the true incidence of asymptomatic and clinical cases, affecting morbidity and mortality rates. The State of Bihar alone contributes up to the 40\% of the worldwide VL cases. The inefficiency of surveillance systems occurs because of multiple reasons including delay in seeking health care, accessing non-authentic health care clinics, and existence of significant asymptomatic self healing infectious cases. This results in a failure of the system to adequately report true transmission rates and number of symptomatic cases that have sought medical advice (thus, high underreporting of cases). Objectives and Methods: There are several methods to estimate the extent of underreporting in the surveillance system. In this research, we use a mathematical dynamic model and two different types of data sets, namely, monthly incidence for 2003-2005 and yearly incidence from 2006-2012 from the Bihar's 21 most VL affected districts out of its 38 districts. The goals of the study are to estimate critical metrics to measure level of transmission and to evaluate the estimation process between the two data sets and 21 districts. In particularly, our focus is on (i) estimating infection transmission potential, underreporting level in incidence and proportion of self-healing cases, (ii) quantifying reproduction number of the$R_0$, and (iii) comparing underreporting incidence levels and proportion of self-healing cases between the two periods 2003-2005 and 2006-2012 and between 21 districts. Results: Our research suggests that the number of asymptomatic individuals in the population who eventually self-heal may have a significant effect on the dynamics of VL spread. The estimated mean self-healing proportion (out of all infected) is found to be $\sim 0.6$ with only 7 out of 21 affected districts having self-healing proportion less than $0.5$ for both data sets. The estimated mean underreporting level is at least $64$\% for the state of Bihar. The estimates of the basic reproduction numbers obtained are similar in magnitude for most of the districts, being in the range of (0.88, 2.79) and (0.98, 1.01) for 2003-2005 and 2006-2012, respectively. Conclusions: The estimates for the two types (monthly and yearly) of temporal data suggest that monthly data are better for estimation if less number of data points are available, however, in general, using such data set results in larger variances in parameters as compared to estimates obtained through aggregated yearly data. Estimated values of transmission related metrics are lower than those obtained from earlier analyses in the literature, and the implications of this for VL control are discussed. The spatial heterogeneity in these control metrics increases the risk of epidemics and makes the control strategies more complex.

In this paper, some mixed type bounds on the spectral radius $\rho(A\circ B)$ for the Hadamard product of two nonnegative matrices ($A$ and $B$) and the minimum eigenvalue $\tau(C\star D)$ of the Fan product of two $M$-matrices ($C$ and $D$) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several $M$-matrices is also presented: $$ \tau(A_{1}\star A_{2}\cdots\star A_{m})\geq \min_{1\leq i\leq n}\{\prod^{m}_{k=1}A_{k}(i,i)-\prod^{m}_{k=1}[A_{k}(i,i)^{P_{k}}-\tau(A_{k}^{(P_{k})})]^\frac{1}{P_{k}}\}, $$ where $A_{1},\ldots, A_{k}$ are $n\times n$ $M$-matrices and $P_{1},\ldots, P_{k}>0$ satisfy $\sum^{m}_{k=1}\frac{1}{P_{k}}\geq 1$. Some special cases of the above result and numerical examples show that this new bound improves some existing results.

The development and generalization of Digital Volume Correlation (DVC) on X-ray computed tomography data highlight the issue of long term storage. The present paper proposes a new model-free method for pruning the DVC data. The size of the remaining sampled data can be user-defined, depending on the needs concerning storage space. The data pruning procedure is deeply linked to hyper-reduction techniques. The DVC data of a resin-bonded sand tested in uniaxial compression is used as an illustrating example. The relevance of the pruned data is tested afterwards for model calibration. A new Finite Element Model Updating (FEMU) technique coupled with an hybrid hyper-reduction method is used to successfully calibrate a constitutive model of the resin bonded sand with the pruned data only.

Model-based image reconstruction has brought improvements in terms of contrast and spatial resolution to imaging applications such as magnetic resonance imaging and emission computed tomography. However, their use for pulse-echo techniques like ultrasound imaging is limited by the fact that model-based algorithms assume a finite grid of possible locations of scatterers in a medium -- which does not reflect the continuous nature of real world objects and creates a problem known as off-grid deviation. To cope with this problem, we present a method of dictionary expansion and constrained reconstruction that approximates the continuous manifold of all possible scatterer locations within a region of interest. The expanded dictionary is created using a highly coherent sampling of the region of interest, followed by a rank reduction procedure based on a truncated singular value decomposition. We develop a greedy algorithm, based on the Orthogonal Matching Pursuit (OMP), that uses a correlation-based non-convex constraint set that allows for the division of the region of interest into cells of any size. To evaluate the performance of the method, we present results of 2-dimensional ultrasound image reconstructions with simulated data in a nondestructive testing application. Our method succeeds in the reconstructions of sparse images from noisy measurements, providing higher accuracy than previous approaches based on regular discrete models.

Let G[F,Vk, Huv] be the graph with k pockets, where F is a simple graph of order n ≥ 1,Vk= {v1,v2,··· ,vk} is a subset of the vertex set of F and Hvis a simple graph of order m ≥ 2,v is a specified vertex of Hv. Also let G[F,Ek, Huv] be the graph with k edge pockets, where F is a simple graph of order n ≥ 2, Ek= {e1,e2,···ek} is a subset of the edge set of F and Huvis a simple graph of order m ≥ 3, uv is a specified edge of Huvsuch that Huv− u is isomorphic to Huv− v. In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of G[F,Vk, Hv] and G[F,Ek, Huv] in terms of the resistance distance and Kirchhoff index F, Hv and F, Huv, respectively.

We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions when using different numbers of width-optimized IMQ functions. The effects of the ratio of the number of collocation points to the number of basis functions and of the choice of the IMQ exponent are studied. We show that the IMQ basis can be used with parameters where the IMQ function is not integrable. We find that the quality of the spectrum with IMQ basis functions is somewhat lower that that with a Gaussian basis when the basis size is large and for a range of IMQ exponents. The IMQ functions are, however, advantageous when a small number of functions is used or with a small number of collocation points e.g. when using square collocation.

The article presents a cyber-physical system for acquiring, processing and reconstructing images from measurement data. The technology was based on process tomography, intelligent measurement sensors, machine learning, Big Data, Cloud Computing, Internet of Things as a solution for Industry 4.0. Industrial tomography enables observation of physical and chemical phenomena without the need of internal penetration and allows real-time monitoring of production processes. The application includes specialized intelligent devices for tomographic measurements and dedicated algorithms for solving the inverse problem. The work focuses mainly on electrical tomography and image reconstruction using deterministic methods and machine learning, the reconstruction results were compared, different measurement models were used. The researches were carried out for synthetic data and laboratory measurements. The main advantage of the proposed system is the possibility of spatial data analysis and their high processing speed. The presented research results show that the process tomography gives the possibility to analyse the processes taking place inside the facility without disturbing the production, analysis and detection of obstacles, defects and various anomalies. Knowing the characteristics of a given solution, the application allows you to choose the appropriate method to reconstruct the image.

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densi- ties and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on dierent set of true values. Some real data sets were employed to show the usefulness and exibility of the model which serves as generalization to many sub-models in the elds of engineering, medical, survival and reliability analysis.

The article presents a non-destructive test system based on electrical impedance tomography for monitoring flood embankments. The technology of cyber-physical systems and the Internet of Things with the use of electrical impedance tomography enables real-time monitoring of flood embankments. This solution provides a visual analysis of damage and leaks, which allows for quick and effective intervention and possible prevention of danger. A dedicated solution based on the IT structure, dedicated laboratory models and a dedicated measurement system with various types of sensors and machine learning algorithms for image reconstruction has been developed. The system includes specialized intelligent devices for tomographic measurements. The application contains the analysis of anomalies occurring in the structure of the object as a result of damage or danger and breaking the shaft during the flood. The presented solution enables ongoing monitoring of objects by collecting measurement results, forecasts and simulations. The main advantage of the proposed system is the spatial ability to analyse shafts, high accuracy of imaging and high speed of data processing. The use of tomographic techniques in conjunction with image reconstruction algorithms allow for non-invasive and very accurate spatial assessment of humidity and damages of flood embankments. The presented results show the effectiveness of the presented research.

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densities and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on different set of true values. Some real data sets were employed to show the usefulness and flexibility of the model which serves as generalization to many sub-models in the field of engineering, medical, survival and reliability analysis.

Different process parameters can alter the temperature during machining. Consequently, selecting process parameters that lead to a desirable cutting temperature would help to increase the tool life, decrease the tensile residual stress, and controls the microstructure evolution of the workpiece. An inverse computational methodology is proposed to design the process parameters for specific cutting temperature. A physics-based analytical model is used to predict the temperature induced by cutting forces. To calculate the temperature induced by the deformation in the shear zone, a moving point heat source approach is used. The shear deformation and chip formation model is implemented to calculate machining forces as functions of process parameters, material properties, and etc. The proposed model uses the analytical model to predict the cutting temperatures and applies a variance-based recursive method to guide the inverse analysis. In order to achieve the cutting process parameters, an iterative gradient search is used to adaptively approach the specific temperature by the optimization of process parameters such that an inverse reasoning can be achieved. Experimental data are used to illustrate the implementation and validate the viability of the computational methodology.

Synthetic Aperture RADAR (SAR) is a radar imaging technique in which the relative motion of the sensor is used to synthesize a very long antenna and obtain high spatial resolution. Standard SAR raw data processing techniques assume uniform motion of the satellite (or aerial vehicle) and a fixed antenna beam pointing sideway orthogonally to the motion path, assumed rectilinear. Despite SAR data processing is a well established imaging technology that has become fundamental in several fields and applications, in this paper a novel approach has been used to exploit coherent illumination, demonstrating the possibility of extracting a large part of the ancillary data information from the raw data itself, to be used in the focusing procedure. In this work an effort has been carried out to try to focus the raw SAR complex data matrix without the knowledge of anyof the parameters needed in standard focusing procedures as Range Doppler (RD) algorithm, ω - K algorithm and Chirp Scaling (CS) algorithm. All the literature references regarding the algorithms needed to obtain a precise image from raw data use such parameters that refer both to the SAR system acquisition geometry and its radiometric specific parameters. In [12], authors introduced a preliminary work dealing with this problem and able to obtain, in the presence of a strong point scatterer in the observed scene, good quality images, if compared to the standard processing techniques. In this work the proposed technique is described and performances parameters are extracted to compare the proposed approach to RD.

The article presents the results of research on a new method of spatial analysis of walls and buildings moisture. Due to the fact that destructive methods are not suitable for historical buildings of great architectural significance, a non-destructive method based on electrical tomography has been adopted. A hybrid tomograph with special sensors was developed for the measurements. This device enables the acquisition of data, which are then reconstructed by appropriately developed methods enabling spatial analysis of wet buildings. Special electrodes that ensure good contact with the surface of porous building materials such as bricks and cement were introduced. During the research, a group of algorithms enabling supervised machine learning was analyzed. They have been used in the process of converting input electrical values into conductance depicted by the output image pixels. The conductance values of individual pixels of the output vector made it possible to obtain images of the interior of building walls, both flat intersections (2D) and spatial (3D) images. The presented group of algorithms has a high application value. The main advantages of the new methods are: high accuracy of imaging, low costs, high processing speed, ease of application to walls of various thickness and irregular surface. By comparing the results of tomographic reconstructions, the most efficient algorithms were identified.

Schrödinger dynamics is a nonlocal process. Not only does local perturbation affect instantaneously the entire space, but the effect decays slowly. When the wavefunction is spectrally bounded, the Schrödinger equation can be written as a universal set of ordinary differential equations, with universal coupling between them, which is related to Euler’s formula. Since every variable represents a different local value of the wave equation, the coupling represents the dynamics’ nonlocality. It is shown that the nonlocal coefficient is inversely proportional to the distance between the centers of these local areas. As far as we know, this is the first time that this inverse square law was formulated.

The active power-assist function greatly expands the potential applications of exoskeleton robots, yet the motion intention estimation (MIE) for active power-assist strategy is quite problematic. Through the analysis of the conduction path and the different stage manifestations of motion intention in human body, we confirmed that the joint torque of human body meets the basic requirements of MIE for the active power-assist that we suggest, namely: (i) it reflects the direction and intensity of the wearer’s efforts; (ii) it precedes the human limb motion; (iii) it generates real-time and continuous output. Thus, an online calculation method of human joint torque was proposed. The sensing system integrated in exoskeleton robots was designed to perceive motion data and foot contact force of a human body. A special inverse dynamics with a parameterized model of the human body was proposed. Contrast experiments were carried out with the motion capture system, which results’ accuracy and similarity were evaluated via the root mean square error and correlation coefficient. The comparative analysis of two synchronous results shows good accuracy of the proposed MIE method, which lays the foundation for the realization of active power-assist.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

An inverse aeroacoustic problem for a helicopter rotor combined with aerodynamic constraint is proposed based on Ffowcs Williams and Hawkings equation in subsonic. The rotor noise includes thickness noise and loading noise when quadrupole noise is neglected. Thickness noise is related to geometry and motion conditions. Loading noise is related to the pressure on the wall. Therefore, the equation between pressure on the wall and far-field noise can be established, thus the pressure on the wall can be obtained by solving this equation. Since this equation is an ill-posed, the singular value decomposition combined with the regulation method is applied and the aerodynamic constraint is taken into account. The direct noise prediction is verify firstly and then the inverse problem is solved. The reconstruction pressure is compared to the input data. The result is in good agreement with the input value. At the same time, the influence of interference noise is also considered. Under low signal-to-noise ratio, the reconstruction result is also reasonable.

In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

In this paper, a new millimeter wave 3D imaging radar is proposed. The user just needs to move the radar along a circular track, a high resolution 3D imaging can be generated. The proposed radar uses the movement of itself to synthesize a large aperture in both the azimuth and elevation directions. It can utilize inverse Radon transform to resolve 3D imaging. To improve the sensing result, compressed sensing approach is further investigated. The simulation and experimental result further illustrated the design. Because a single transceiver circuit is needed, a light, affordable and high resolution 3D mmWave imaging radar is illustrated in the paper.