Today, mechanical tracking systems have been downsized to allow them to be used in the field of airborne laser communications and in the military domain. Risley systems are used for this purpose, which work by directing a beam of light to a given target point, this procedure is commonly known as the inverse problem. In this paper, an analytical method, the geometric method, has been designed and developed to determine the beam steering in a Risley system and solve the inverse problem. The method focuses on different geometric shapes, like circumference or ellipse, that are described when the beam passes through the second prism. The accuracy and efficiency of the geometric method has been analysed and found to be faster than the two-step method. Furthermore, the geometric method has been implemented in an iterative process and an accuracy of up to 1 pm has been achieved. This high accuracy would allow the geometric method to be applied in fields such as lithography, stereolithography or 3D printers.

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.

Inverse problems of recovering surface fluxes on the boundary of a domain from pointwise observations are considered. Sharp conditions on the data ensuring existence and uniqueness of solutions in Sobolev classes are exposed. They are smoothness conditions on the data, geometric conditions on the location of measurement points, and the boundary of a domain. The proof relies on asymptotics of fundamental solutions to the corresponding elliptic problems and the Laplace transform. The problem is reduced to a linear algebraic system with a nondegerate matrix.

This paper proposes a non-extensive entropy econometric technique to predict energy efficiency at province (NUT-2) level based on imperfect knowledge of the national overall efficiency in the sectors of industry, transport, households and services. The model is applied to the polish case. As acknowledged in recent literature, non-extensive entropy model should remain a valuable device for econometric modelling even in the case of low frequency series since outputs provided by the Gibbs-Shannon entropy approach correspond to the Tsallis entropy limiting case of the Gaussian law when the Tsallis q-parameter converges to unity. Therefore, we set up a q-Tsallis-Kullback-Leibler entropy criterion function with a priori consistency moment and model data constraints, including province energy intensity (known with uncertainty), regional climate differentiation and regular conditions. The model outputs continue to conform to empirical expectations. In spite of the close to unity q-Tsallis parameter, this Tsallis related approach reflects higher stability for parameter computation in comparison with the Shannon-Gibbs entropy econometrics technique. The proposed technique can be applied in different EU countries and elsewhere for example in the context of experimental official statistics.

This work implements a stable algorithm in Field-Programmable Gate Arrays (FPGAs) for which two architectures (unrolling the loop) were developed and analyzed. The algorithm recovers sources located at the boundary separating two homogeneous media that make up a two-dimensional non-homogeneous region from measurements on the boundary of such region. The problem of recovering these sources is an ill-posed inverse problem as small errors in the measurement can produce important changes in the source location. Inverse source problems have many applications in different areas, such as engineering and medicine, making the proposed implementation important. The first architecture (mode one) allows considering different operating speeds, which is an advantage depending on whether we work with fast or slow signals. The second one (mode two) reduces resource consumption by exploiting the characteristics of the source identification algorithm, which is an advantage for multichannel problems such as inverse electrocardiography or electroencephalography. The architectures were tested on four FPGAs of the 7 Series of Xilinx: Spartan-7 xc7s100fgga484, Virtex-7 xc7v585tffg1157, Kintex-7 xc7k70tfbg484, and Artix-7 xc7a35tcpg236. The two FPGA implementations of the algorithm were validated using synthetic examples implemented in MATLAB. The results presented here can be extended to concentric spheres and complex geometries.

In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.

This article shows how to establish expansion formulas for calculating the mixed operations $(A^{\dag})^{\#}$, $(A^{\#})^{\dag}$, $((A^{\dag})^{\#})^{\dag}$, $((A^{\#})^{\dag})^{\#}$, $\ldots$ of generalized inverses, where $(\cdot)^{\dag}$ denotes the Moore--Penrose inverse of a matrix and $(\cdot)^{\#}$ denotes the group inverse of a square matrix. As applications of the formulas obtained, the author constructs and classifies some groups of matrix equalities involving the above mixed operations, and derives necessary and sufficient conditions for them to hold.

Given a square matrix $A$, we are able to construct numerous equalities that involve reasonable mixed operations of $A$ and its conjugate transpose $A^{\ast}$, Moore--Penrose inverse $A^{\dag}$, and group inverse $A^{\#}$. Such kind of equalities can be generally represented in the equation form $f(A, \, A^{\ast}, A^{\dag}, A^{\#}) =0$. In this article, the author constructs a series of simple or complicated matrix equalities, as well as matrix rank equalities involving the mixed operations of the four matrices. As applications, we give a sequence of necessary and sufficient conditions for a square matrix to be range-Hermitian.

It is a classic topic in algebras to construct and verify equalities that are composed of various algebraic operations of elements and their inverses or generalized inverses. In this note, the author constructs a matrix equality $(AB)^{\dag} = B^{\ast}(A^{\ast}ABB^{\ast})^{\#}A^{\ast}$ (called a mixed reverse-order law), where $A$ and $B$ are two matrices of appropriate sizes, $(\cdot)^{\ast}$, $(\cdot)^{\dag}$, and $(\cdot)^{\#}$ denote the conjugate transpose, the Moore--Penrose inverse, and the group inverse of a matrix, respectively, and shows that the mixed reverse-order law always holds. A list of variation forms of this matrix equality are also given, and necessary and sufficient conditions are obtained for them to hold. Especially, we show a remarkable fact that the two reverse-order laws $(AB)^{\dag} = B^{\dag}A^{\dag}$ and $(A^{\ast}ABB^{\ast})^{\#} = (BB^{\ast})^{\#}(A^{\ast}A)^{\#}$ are equivalent.

Subglottal Impedance-Based Inverse Filtering (IBIF) allows for the continuous, non-invasive estimation of glottal airflow from a surface accelerometer placed over the anterior neck skin below the larynx, which has been shown to be advantageous for the ambulatory monitoring of vocal function. However, during long-term ambulatory recordings over several days, conditions may drift from the laboratory environment where the IBIF parameters were initially estimated due to sensor positioning, skin attachment, and temperature, among other factors. Observation uncertainties and model mismatch may result in significant deviations in the glottal airflow estimates, but are very difficult to quantify in ambulatory conditions due to a lack of a reference signal. To address this issue, we propose a Kalman filter implementation of the IBIF filter, which allows for both estimating the model uncertainty and adapting the airflow estimates to correct for signal deviations. One-way ANOVA results from laboratory experiments using the Rainbow Passage indicate a an improvement on amplitude-based measures for PVH subjects compared to IBIF which shows a statistically difference with respect to the reference oral airflow (p=0.02,F=4.1). MFDR from PVH subjects is slightly different to the oral airflow when compared to IBIF (p=0.04, F=3.3). Other measures did not have significant differences with either Kalman or IBIF, with the exception of H1H2, whose performance deteriorates for both methods. Overall, both methods show similar flottal airflow measures, with the advantage of Kalman by improving amplitude estimation. Moreover, Kalman filter deviations from the IBIF output airflow might suggest a better representation of some fine details in the ground-truth glottal airflow signal. Other applications may take more advantage from the adaptation offered by the Kalman filter implementation.

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.

This paper addresses the Collatz Conjecture, an open question in mathematics that postulates all positive integers will eventually reach one when a pair of specific operations are repeatedly applied. Despite its apparent simplicity, the conjecture lacks a formal proof. To tackle this enigma, we introduce Algebraic Inverse Trees (AITs), data structures that trace inverse operations of the Collatz sequence. This new approach not only elaborates our unique methodology but also sheds light on the underlying complexities of the Collatz Conjecture.

The Collatz conjecture (or 3n+1 problem) has been explored for about 86 years. In this article, we prove the Collatz conjecture. We will show that this conjecture holds for all positive integers by applying the Collatz inverse operation to the numbers that satisfy the rules of the Collatz conjecture. Finally, we will prove that there are no positive integers that do not satisfy this conjecture.

In this paper, the author derives an explicit form of Heaviside Step Function, which evidently constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics.In particular, this special function is exhibited in a very simple manner as a summation of four inverse tangent functions. The novelty of this work is that the proposed exact formulae are not performed in terms of miscellaneous special functions, e.g. Bessel functions, Error function, Beta function etc and also are neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence.Hence, this formula may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

Karst aquifers show dissolution/precipitation processes of the minerals present in the carbonate rocks. The Ring of Cenotes (RC) extends along the edge of the Chicxulub crater, in the limestone platform of the Yucatan Peninsula (YP), where groundwater shows preferential flow paths toward the coast near Celestun and Dzilam Bravo towns. This study aimed to describe the regional hydrogeochemical evolution of groundwater of the RC, and its association with the dissolution/precipitation of the minerals present along its path to the ocean. To achieve this aim, we: a) characterized groundwater's hydrogeochemistry; b) determined the calcite, dolomite, and gypsum saturation indexes (reaction phases with the groundwater) in the study area; c) proposed a hydrogeochemical model developed through PHREEQC using an inverse modelling approach. The model predictions confirmed that there are two evolution pathways of the groundwater consistent with the preferential flow paths suggested in a previous regionalization of the RC. On the western path, where groundwater flows towards Celestun, an important marine intrusion influences the hydrogeochemical processes and represents a risk for the prevalence of freshwater. On the eastern path, where groundwater flows toward Dzilam Bravo, the hydrogeochemistry in the sinkholes correlates well with rainfall, suggesting a higher vulnerability during droughts than during rainy periods.

This paper describes the development of a controller that enables trajectory control and vibration control. The controller performance was verified the using a 3D 2-link, flexible manipulator. On trajectory control using inverse kinematics, it was confirmed that the deflection due to its own weight deteriorated the track following performance. The vibration component of the resonance frequency of the flexible manipulator was generated, and the tip position accuracy is deteriorated. Using the results of control experiments based on the inverse kinematics, the system is identified and then created an inverse system for simultaneous control of trajectory control and vibration control. The target trajectories were the three joint angles. Finally, it was demonstrated through experiments on actual manipulator, that the system could sufficiently follow the ideal trajectory and suppress link vibrations.

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 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.

Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geometric means finally help to systematically derive handy formulas that approximate the inverse error function. Our approach can be used for applications in e.g. high-speed Monte Carlo simulations where this function is used extensively.

Diffuse optical tomography (DOT) is a medical imaging procedure using light to measure the geometric and working properties of cells, for instance, oxygen consumption, water content, and fat percentage in the tissue by performing three-dimensional visualization of the tissue. This paper aims to explain the theory behind diffuse optical tomography imaging and how the technology works. The paper explains how photon migration techniques based on diffusion theory can be used to image the optical properties of tissue. There are several reasons why near-infrared (NIR) imaging is the most effective method in terms of recovering optical parameters quantitatively in the near-infrared region. The author discusses the methods in detail. This research also presents various advantages, practical uses, and potential problems that have been related to DOT in this work. There is also a brief discussion of current research developments in medical imaging using near-infrared wavelengths, and what the future holds for that area.

Sometimes a pavement deflects only because of seasonal volume change of expansive soils in the pavement subgrade. Engineering practitioners expect an implementable and straightforward analysis method for a geosynthetic-reinforced pavement subjected to the swelling/shrinkage issue of expansive clayey subgrade, in an effort to find the bending moment, shear force and tension force distributions through the reinforced pavement, which are induced from the volumetric changes of subgrade soils. The virtual load method (VLM) was proposed in the past following the Timoshenko beam theory to analyze geosynthetic-reinforced pavement on expansive soils. In the VLM, the unknown virtual distributed load was obtained in the way by applying the inverse theory for the identification of material parameters of the pavement-foundation system. It was seen that the selection of the number of material parameters to obtain virtual load significantly affects the accuracy of the structural properties of the pavement and tensile properties of the geosynthetics if the linear least square method is used. In this paper, a unique numerical scheme was proposed in the hopes of solving the issue. After a forward problem was solved numerically, the Timoshenko beam deflection was taken as a start-up for the inverse problem to back analyze the load applied to the pavement. Solutions from forward/backward examples have explicitly shown the accuracy achieved related to the bending moment in the pavement and tension in the geosynthetic reinforcements. The proposed methodology can be applied for an in-depth understanding of the geosynthetic function for the mitigation of longitudinal cracks on pavements caused by heave/shrinkage of expansive soils.

We propose a deep reinforcement learning based manipulator path tracking method to solve the computationally difficult and non-unique problem of manipulator path tracking methods based on inverse kinematics. By transforming the path tracking task into a sequence decision problem, our method adopts an end-to-end learning method for closed-loop control and avoids the process of finding the inverse solution. We first explored the feasibility of the deep reinforcement learning method in the path tracking of the manipulator. After verifying the feasibility, the path tracking of the multi-degree-of-freedom(multi-DOF) manipulator was realized by combining the maximum entropy deep reinforcement learning algorithm. The experimental results show that our method has a good effect on the path tracking of the manipulator, which not only avoids the process of finding the inverse kinematics solution, but also requires no dynamic model. Therefore, we believe that our method has great significance in the study of manipulator path tracking.

We propose an algorithm for generating a panoramic image of a pipe’s inner surface based on inverse perspective mapping (IPM). For efficient crack detection, we used only perspective images of the pipe interior that can be obtained with a single lens camera instead of those taken with a 360-degree camera or a 3D depth camera. Frontal images taken while passing through the pipe were converted to images of the inner surface of the pipe using IPM. We derived a generalized IPM formula that considers the slope of the image plane to correct image distortion caused by the tilt of the plane; this IPM formula was derived based on the vanishing point of the perspective image, which was detected using optical flow techniques. Finally, the multiple transformed images with overlapping areas were combined via image stitching to create a panoramic image of the inner pipe surface. To validate our proposed algorithm, we restored images of pipe inner surface using a 3D pipe model and used these images for crack detection.

In this paper, an analytical form of the Unit Step Function (or Heaviside Step function) is presented. This important function constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics. In particular, Heaviside Step Function is performed in a very simple manner by the use of a finite number of standard operations, as the summation of six inverse tangent functions. The novelty of this work when compared with other analytical expressions, is that the proposed exact formula contains two arbitrary single - valued continuous functions which satisfy only one restriction. In addition, the proposed representation is not exhibited in terms of miscellaneous special functions, e.g. Bessel functions, Beta function, Logistic function. Besides, it is neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence. Hence, this formula may be much more practical, flexible and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

Ultrasound based haptic feedback is a potential technology for human-computer interaction (HCI) with the advantages of low cost, low power consumption and controlled force. In this paper, the phase optimization for multipoint haptic feedback based on ultrasound array is investigated and the corresponding experimental verification is provided. A mathematical model of acoustic pressure is established for the ultrasound array and then a phase optimization model for an ultrasound transducer is constructed. We propose a pseudo-inverse (PINV) algorithm to accurately determine the phase contribution of each transducer in the ultrasound array. By controlling the phase difference of the ultrasound array, the multipoint focusing forces are formed leading to various shapes such as geometries and letters that can be visualized. Because the unconstrained PINV solution results in unequal amplitudes for each transducer, a weighted amplitude iterative optimization is deployed to further optimize the phase solution, by which the uniform amplitude distributions of each transducer are obtained. For the purpose of experimental verifications, a platform of ultrasound haptic feedback consisting of a Field Programmable Gate Array (FPGA), an electrical circuit and an ultrasound transducer array is prototyped. The haptic performances of single point, multiple points and dynamic trajectory were verified by controlling the ultrasound force exerted on the liquid surface. The experimental results demonstrate that the proposed phase optimization model and theoretical results are effective and feasible, and the acoustic pressure distribution is consistent with the simulation results.

In this note we generalize the regularity concept for semigroups in two ways simultaneously: to higher regularity and to higher arity. We show that the one-relational and multi-relational formulations of higher regularity do not coincide, and each element has several inverses. The higher idempotents are introduced, and their commutation leads to unique inverses in the multi-relational formulation, and then further to the higher inverse semigroups. For polyadic semigroups we introduce several types of higher regularity which satisfy the arity invariance principle as introduced: the expressions should not depend of the numerical arity values, which allows us to provide natural and correct binary limits. In the first definition no idempotents can be defined, analogously to the binary semigroups, and therefore the uniqueness of inverses can be governed by shifts. In the second definition called sandwich higher regularity, we are able to introduce the higher polyadic idempotents, but their commutation does not provide uniqueness of inverses, because of the middle terms in the higher polyadic regularity conditions.

Accurate monthly runoff estimation is fundamental in water resources management, planning, and development, resulting in preventing and reducing water-related problems, such as flooding and drought. This article evaluates the performance of the monthly hydrological rainfall-runoff model, GR2M model, in Thailand's southern basins. The GR2M model requires only two parameters, and no prior research has been reported on its application in this region. The 37 runoff stations, which are distributively located in three sub-watersheds of Thailand's southern region, namely; Thale Sap Songkhla, Peninsular-East Coast, and Peninsular-West Coast, were selected as study cases. The available monthly hydrological data of runoff, rainfall, air temperature from the Royal Irrigation Department (RID) and the Thai Meteorological Department (TMD) were collected and analyzed. Thornthwaite method was utilized for the determination of evapotranspiration. The model's performance was conducted using three statistical indices: Nash-Sutcliffe Efficiency (NSE), Correlation Coefficient (r), and Overall Index (OPI). The model's calibration results for 37 runoff stations gave the average of NSE, r, and OPI of 0.637, 0.825, and 0.757, and those values for verification of 0.465, 0.750, and 0.639, respectively. It indicated a model's acceptable performance and could apply the GR2M model for determining monthly runoff variation in this region. The spatial distribution of X1 and X2 values was conducted by using IDW method. It was susceptible to the X1 value and X2 value of approximately more than 0.90 gave the higher model's performance.

We consider the inverse function $z=g(w)$ of a (normalized) starlike function $w=f(z)$ of order $\alpha$ on the unit disk of the complex plane with $0<\alpha<1.$ Krzy{\. z}, Libera and Z\l otkiewicz obtained sharp estimates of the second and the third coefficients of $g(w)$ in their 1979 paper. Prokhorov and Szynal gave sharp estimates of the fourth coefficient of $g(w)$ as a consequence of the solution to an extremal problem in 1981. We give a straightforward proof of the estimate of the fourth coefficient of $g(w)$ together with explicit forms of the extremal functions.

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.

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.

A human eye has about 120 million rod cells and 6 million cone cells. This huge number of light sensing cells inside a human eye will continuously produce a huge quantity of visual signals which flow into a human brain for daily processing. However, the real-time processing of these visual signals does not cause any fatigue to a human brain. This fact tells us the truth which is to say that human-like vision processes do not rely on complicated formulas to compute depth, displacement, and colors, etc. On the other hand, a human eye is like a PTZ camera. Here, PTZ stands for pan, tilt and zoom. We all know that in computer vision, each set of PTZ parameters (i.e., coefficients of pan, tilt and zoom) requires a dedicated calibration to determine a camera’s projection matrix. Since there is an infinite number of PTZ parameters which could be produced by a human eye, it is unlikely that a human brain stores an infinite number of calibration matrices for each human eye. Therefore, it is an interesting question for us to answer, which is to say whether simpler formulas of computing depth and displacement exist or not. Moreover, these formulas must be calibration friendly (i.e., easy process on the fly or on the go). In this paper, we disclose an important discovery of a new solution to 3D projection in a human-like binocular vision system. The purpose of doing 3D projection in binocular vision is to undertake forward and inverse transformations (or mappings) between coordinates in 2D digital images and coordinates in a 3D analogue scene. The formulas underlying the new solution are accurate, easily computable, easily tunable (i.e., to be calibrated on the fly or on the go) and could be easily implemented by a neural system (i.e., a network of neurons). Experimental results have validated the discovered formulas.

Nanoparticles are of great importance for various scientific and technological applications, drug discovery, ecology, molecular biology, etc. Size is a basic characteristic of any particle, and dynamic light scattering is beyond competition when measuring particle size in dispersions ranging from nanometers to micrometers. Unfortunately, this method has a serious problem in processing and interpreting experimental data. Instrument noise and polydispersity of the sample lead to the situation when one initial autocorrelation function corresponds to several different particle size distributions. Sometimes these different solutions of the inverse task can be found by changing parameters in the software. Sometimes the scientist cannot be suspicious of possible other solutions, having one result from the program. In this article I demonstrate the problem on model and experimental data using three known programs: CONTIN, the Malvern Zetasizer and DynaLS. I also present my own free program Autocor, which allows to test our own hypotheses about the modality and shape of the particle size distribution by optimizing the parameters of our own models with a small number of degrees of freedom.

Mercury (Hg (II)) contamination is indefatigable global hazard which causes severe permanent damages to human health. Extensive research has been carried out to produce mercury adsorbents however they are still facing certain challenges limiting their upscaling. Herein we reported the synthesis of novel amine impregnated inverse vulcanized copolymer for effective mercury removal. Poly(S-MA) was prepared using sulfur and methacrylic acid employing inverse vulcanization method following by functionalization. The polyethylenime (PEI) was impregnated on poly(S-MA) to increase the adsorption active sites. The developed adsorbent was then characterized using Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM). FTIR confirmed formation of copolymer and successful impregnation of PEI and SEM revealed composite porous morphology of the copolymer. Amine impregnated copolymer (amine@poly(S-MA)) outperformed poly(S-MA) in mercury as it showed 20 % superior performance with 44.7 mg/g maximum adsorption capacity. The adsorption data best fits the pseudo second order which indicates that the chemisorption is most influential mechanism in this case indicating the involvement of NH2 in mercury removal. The adsorption is mainly monolayer on homogenous surface as indicated by 0.76 value of Redlich-Peterson exponent (g) which describes the adsorption nature advent from R2 value of 0.99.

This article proposes application of a new mathematical model of spots for solving inverse problems using a learning method, which is similar to using the deep learning. In general, the spots represent vague figures in abstract “information spaces” or crisp figures with lack of in-formation about their shapes and are adequate for representation human mental images and reasoning in Artificial Intelligence (AI). However, crisp figures are regarded as a special and limiting case of spots. A basic mathematical apparatus, basing on L4 numbers, has been developed for the representation and processing of qualitative information of elementary spatial relations between spots. Also, we defined L4 vectors, L4 matrices, and mathematical operations on them. Developed apparatus can be used in AI, in particular, for knowledge representation and for modeling qualitative reasoning and learning. Another application area is the solution of inverse problems by learning. For example, this can be applied to image reconstruction using ultrasound, X-ray, magnetic resonance, or radar scan data. The introduced apparatus was verified by solving problems of reconstruction of images, utilizing only qualitative data of its elementary relations with some scanning figures. This article also demonstrates application of spot-based inverse Radon algorithm for binary image reconstruction.

Model predictive control (MPC) is a multi-objective control technique that can handle 2 system constraints. However, the performance of an MPC controller highly relies on a proper 3 prioritization weight for each objective, which highlights the need for a precise weight tuning 4 technique. In this paper, we propose an analytical tuning technique by matching the MPC 5 controller performance with the performance of a linear quadratic regulator (LQR) controller. The 6 proposedmethodology derives the transformation of LQRweightingmatrixwith a fixedweighting 7 factor using discrete algebraic Riccati equation (DARE) and designs MPC controller using the 8 idea of discrete time linear quadratic tracking problem (LQT) in the presence of constraints. 9 The proposed methodology ensures the optimal performance between unconstrained MPC and 10 LQR controller and provides a sub-optimal solution while the constraints are active during 11 transient operations. The resultingMPC behaves as the discrete time LQR by selecting appropriate 12 weighting matrix in the MPC control problem and ensures the asymptotic stability of the system. 13 In this paper, the effectiveness of the proposed technique is investigated in the application of 14 a novel vehicle collision avoidance system which is designed in the form of linear inequality 15 constraints within MPC. The simulation results confirm the potency of the proposed MPC control 16 technique in performing a safe, feasible and collision free path while respecting the inputs, states 17 and collision avoidance constraints.

This note addresses a fundamental problem in matrix theory on establishing and characterizing range equalities for matrix expressions that involve generalized inverses. We first establish a group of necessary and sufficient conditions for the matrix range equality ${\rm range}(D_1 - C_1A_1^{\dag}B_1) = {\rm range}(D_2 - C_2A_2^{\dag}B_2)$ to hold, where $(\cdot)^{\dag}$ denotes the Moore--Penrose inverse of matrix. We then give several groups of range equalities with extrusion properties for multiple matrix products associated with two matrices and their conjugate transposes and Moore--Penrose inverses.

Crystallization is a significant procedure in the manufacturing of many pharmaceutical and solid food products. In-situ Electrical Resistance Tomography (ERT) is a novel Process Analytical Tool (PAT) to provide a cheap and quick way to test, visualize, and evaluate the progress of crystallization processes. In this work, the spatial accuracy of the non-conductive phantoms in low conductivity solutions was evaluated. Gauss-Newton, Linear Back Projection, and iterative Total Variation reconstruction algorithms were used to compare the phantom reconstructions for tap water, industrial-grade saturated sucrose solution, and demineralized water. Cylindrical phantom measuring 10 mm in diameter and a cross-section area of 1.5 % of the total beaker area was detected at the center of the beaker. Two phantoms with a 10 mm diameter were visualized separately in non-central locations. The quantitative evaluations were done for the phantoms with radii ranging from 10 mm to 50 mm in demineralized water. Multiple factors such as ERT device and sensor development, FEM mesh density and simulations, image reconstruction algorithms, number of iterations, segmentation methods, and morphological image processing methods were discussed and analyzed to achieve spatial accuracy. The development of ERT imaging modality for the purpose of monitoring crystallization in low conductivity solutions was performed satisfactorily.

This note shows that the well-known reverse order law $(AB)^{\dag} = B^{\dag}A^{\dag}$ for the Moore--Penrose inverse of matrix product is equivalent to many other equalities for that are composed of multiple products $(AB)^{\dag}$ and $B^{\dag}A^{\dag}$ by means of the definition of the Moore--Penrose inverse and orthogonal projector theory.

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.

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.

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.

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 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.

Applications of gradient method for nonlinear optimization in development of Gradient Neural Network (GNN) and Zhang Neural Network (ZNN) are investigated. Particularly, the solution of the matrix equation AXB=D which changes over time is studied using the novel GNN model, termed as GGNN(A,B,D). The GGNN model is developed applying GNN dynamics on the gradient of the error matrix used in the development of the GNN model. The convergence analysis shows that the neural state matrix of the GGNN(A,B,D) design converges asymptotically to the solution of the matrix equation AXB=D, for any initial state matrix. It is also shown that the convergence result is the least square solution which is defined depending on the selected initial matrix. A hybridization of GGNN with analogous modification GZNN of the ZNN dynamics is considered. The Simulink implementation of presented GGNN models is carried out on the set of real matrices.

Application of the Ramsey Theory to the set of the points placed in the plane is discussed. Consider a set of N points located in the same plane. The straight lines connecting these points are yikx=αikx+βik i,k=1...N. Listed below values of slopes αik are possible: αik&gt;0; αik=0; αik is not defined; αik&lt;0. Following coloring procedure is introduced: we connect the pairs of points for which αik&gt;0, αik=0 or αik is not defined, with the red links, and the pairs of points for which αik&lt;0 place with green links. The suggested coloring procedure enables building of the complete bi-colored graph for any set containing N points located in the same plane. We apply the Ramsey theorem to the complete graph emerging from the suggested coloring. For the set containing N=6 points at least one monochromatic triangle will necessarily appear in the graph. The values of the slopes αik depend on the chosen coordinate system. The rotation of coordinate axes changes the coloring of the graph; however, at least one monochromatic triangle will be present for N=6. The introduced coloring procedure diminishes the order of the symmetry group of the regular hexagon, irrespectively to the orientation of the coordinate axes. We hypothesized that this will be true for arbitrary regular n-polygon, independently on the orientation of coordinate axes. The inverse bi-color Ramsey graphs arise, when we replace red links appearing in the source graph with red ones, and vice versa. The total number of triangles in the “direct” and “inverse” Ramsey graphs is the same. We considered the particular case of the set of points for which αik&gt;0 or αik&lt;0 is true in the given coordinates. In this particular case, the rotation of the Cartesian coordinate axes to the angle θ=π2 yields the inverse complete graph. Generalization of this coloring for an arbitrary number and arbitrary location of the source points is introduced.

In this note we study the computation of the minimum polynomial of a matrix $A$ and how we can use it for the computation of the matrix $A^n$. We also describe the form of the elements of the matrix $A^{-n}$ and we will see that it is closely related with the computation of the Drazin generalized inverse of $A$. Next we study the computation of the exponential matrix and finally we give a simple proof of the Leverrier - Faddeev algorithm for the computation of the characteristic polynomial.

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).

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.

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.

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.

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.

Diffuse optical tomography (DOT) is an optical medical imaging method that can assess the structural properties of tissues and their functional characteristics, such as hemoglobin concentration, water content, as well as lipid concentration, via three-dimensional image reconstruction. This paper presents the theoretical basis and working principle of diffuse optical tomography. The paper explains how the optical properties of tissue can be imaged by photon migration techniques based on diffusion theory. The author presents the reasoning for near-infrared (NIR) imaging as the most effective technique in terms of quantitative recovery of spectroscopic optical parameters. This work also listed various advantages, applications, and challenges of DOT. The paper also briefly discusses current progress in near-infrared medical imaging and its future direction.

One of matrix equalities composed of multiple products of matrices and their generalized inverses is given by $A_1B_1^{-}A_2B_2^{-} \cdots A_kB_k^{-}A_{k+1}= A$ where $A_1$, $B_1$, $A_2$, $B_2$, $\ldots$, $A_k$, $B_k$, $A_{k+1}$, and $A$ are given matrices of appropriate sizes, and $B_1^{-}$, $B_2^{-}$, $\cdots$, $B_k^{-}$ are generalized inverses of matrices. The cases for $k = 1, 2$ and their special forms were properly approached in the theory of generalized inverses of matrices. In this note, the author presents an algebraic procedure to derive explicit necessary and sufficient conditions for the equality with $k = 3$ to always hold using certain rank equalities for the block matrices constructed by the given matrices, and then mention a key step of extending the previous work to a general situation.

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.

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.

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.

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.

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.

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.

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.

The available direct gas dynamic tables provide the area ratio and the Prandtl-Meyer(P-M) angle of isentropic expansion of gas as functions of the Mach number. But finding the value of the Mach number in terms of area ratio or P-M angle requires an inverse function. Currently, the Mach number is determined by either interpolation from the direct gas dynamics tables, or the application of non-linear equation solvers using numerical methods. Both methods are approximate. In this paper inverse functions for Mach number in the form of Taylor’s series expansions are reported to develop the so-called inverse tables. The advantage of this approach is that the Mach number with a greater accuracy, referred to as nearly exact can be obtained by reading from the inverse table. In the presentation, the necessary equations and new tables that can be used by the scientific community will be disseminated. The data and computer programs are made available on GitHub through https://github.com/anillals/Inverse-gas-dynamic-tables- and-codes. A paper describing the complete mathematical steps in the derivation of the equations can be found at https://rdcu.be/dgrlf

In this paper, we introduce as a pedagogical strategy an internal division-free, straightforward, and symmetrically progressing algorithm in manually computing matrix inverse and solving systems of linear equations by revisiting the application of elementary row operations in the Gauss-Jordan reduction method and connecting it to the determinant method. The proposed cross-multiplication-flip (CMF) algorithm employs cross-multiplication similar to the butterfly movement in computing determinants as a strategic application of elementary row operations to efficiently reduce the rows and then applies flipping of rows and entries to put an upper triangular matrix into lower triangular form to continue the reduction process.

In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy is used to solve likelihood equation. In addition, the approximation confidence interval is given by the Delta method. Because the form of estimation results is more complex in the Bayesian estimation, the Lindley approximation method is used to achieve the numerical calculation. Finally, Monte Carlo simulations and a real data set are used to illustrate the results derived. By comparing the mean square error between the estimated value and the real value, it can be found that the performance of ML estimation of Shannon entropy is better than that of Bayesian estimation, and there is no significant difference between the performance of ML estimation of Rényi entropy and that of Bayesian estimation.

Laboratory experiments and natural phenomena investigations in this research series experimentally revealed the existence of gravitational repulsion force dependent on thermal energy content, pervading our surroundings both microscopically and macroscopically. This paper presents an alternative mathematical model of both gravitational repulsion and attraction forces between two gaseous molecules, validated by experimental data. The model is self-standing and independent of existing models built on idealistic assumptions. While existing models considered gravitational interaction as a single force, the presented experimental model considers it the resultant of two distinct forces: gravitational repulsion and attraction. When established experimental data on nitrogen, hydrogen, oxygen, water vapor, carbon monoxide and carbon dioxide were applied, the model performed, both analytically and experimentally: (1) confirming the existence of both gravitational repulsion and attraction forces among gas molecules, (2) demonstrating that the two forces follow Inverse-Cube relationship with the distance between molecules, (3) revealing that repulsion force is linearly proportional to the absolute temperature, thus filling the critical gap between energy and fundamental forces. Orders of magnitude of gravitational repulsion and attraction forces are very large compared to the gravitational force between gas molecules calculated according to the classical theory, enabling manipulation to achieve hitherto unknown outcomes and developments.

As an implementation of inverse Radon transform, the Second-order Divided-difference Back Projection (SDBP) technique has been proposed in this paper, by which the accurate CT reconstruction can be theoretically realized. A computational model for CT reconstruction filter expressions has been derived on the basis of SDBP technique. The method reveals the correlation between the convolution kernel for data restoration and the filter expression. By substituting kernel functions into the computational model, the amplitude sequences of a variety of filters can be calculated. On the proposed filter construction method, the decomposition form of filters has been discovered, where a series of basic filters have been acquired. The properties of any filter depend on the decomposed basic filters. Basic filters can be used to compose filters in actual needs.

The nonlocal boundary value problem, dtρu(t)+Au(t)=f(t) (0&lt;ρ&lt;1, 0&lt;t≤T), u(ξ)=αu(0)+φ (α is a constant and 0&lt;ξ≤T), in an arbitrary separable Hilbert space H with the strongly positive selfadjoint operator A, is considered. The operator dt on the left hand side of the equation expresses either the Caputo derivative or the Riemann-Liouville derivative; naturally, in the case of the Riemann - Liouville derivatives, the nonlocal boundary condition should be slightly changed. Existence and uniqueness theorems for solutions of the problems under consideration are proved. The influence of the constant α on the existence of a solution to problems is investigated. Inequalities of coercivity type are obtained and it is shown that these inequalities differ depending on the considered type of fractional derivatives. The inverse problems of determining the right-hand side of the equation and the function φ in the boundary conditions are investigated.

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.

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.

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.

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.

Australia is a unique continent surrounded by the ocean and the majority of catchments flow to the coast. Some of these catchments are gauged and others are ungauged. There are 405 gauged catchments covering 2,549,000 km2 across the coastal regions of 12 drainage divisions in Australia. Whereas there are 771 catchments conceptualised as ungauged covering additional 835,000 km2. The mean annual rainfall and PET and its spatial and temporal distribution vary significantly from one drainage division to another. We developed a continuous daily streamflow time series of all gauged and ungauged catchments from 1993 onwards. We applied the GR4J lumped conceptual model to these catchments. The performance of gauged catchments was analysed through (i) visual inspection of daily hydrographs, flow duration curves and daily scatter plots, and (ii) performance metrics including NSE and PBias. Based on the NSE and PBias, performance ratings of 80% and 96% of the models respectively were found 'good'. There was no relationship found between the catchment area and model performance. The ungauged catchments were divided into four categories based on distance from potential donor catchments where observed data are available for GR4J model calibration, and Köppen climate zone. The total ungauged catchments represent 24.7% of the total drainage division areas. The streamflow from ungauged catchments was estimated using GR4J model based on the parameters of their donor catchments. Overall, runoff ratios from ungauged catchments were found to be higher compared to their donor gauged catchments, likely driven by their higher rainfall and less PET. This tendency was particularly evident in two drainage divisions – the Carpentaria Coast (CC) and Tanami-Timor Sea Coast (TTS) where ungauged areas comprised 51% and 43% respectively. The mean gauged annual streamflow varied significantly across drainage divisions – 230 GL from South Australian Gulf (SAG) to 146,150 GL in TTS. The streamflow from all ungauged catchments was estimated at 232,200 GL per year. Overall, the average streamflow from all drainage divisions, including gauged and ungauged areas, across the coastal regions of Australia was estimated at 419,950 GL per year. This nationwide estimate of streamflow dataset could potentially enhance our understanding of coastal processes and improvements of marine modelling systems and tools.

In the broad field of Inverse Analysis and Structural Identification, it is nowadays of a large interest the study of Gaussian Processes, as a reliable and efficient optimisation method, particularly helpful toward the identification of a global optimum point, under the conditions of complicated functions to be optimised. In the present contribution, a specific case study is considered, focusing on a historical road reinforced concrete arched bridge, located in Northern Italy, employing dynamic modal properties, deciphered from in-situ measurements, previously acquired under operational traffic conditions, by a standard wired accelerometer system, placed at the deck level. Aiming at the identification and diagnosis of the bridge structure, three main methodological steps are herein considered: the adoption of a FEM model of the structure (in the linear dynamic framework), the definition of an appropriate discrepancy function, based on measured and numerically computed quantities (natural frequencies and mode shapes of the bridge), and the investigation of such a discrepancy function, toward a consistent selection of an optimisation strategy for the identification of sought parameters (Young’s moduli and mass densities of diverse elements of the structure). The presented developments, within the framework of methodological optimisation approach by Gaussian Processes, and achieved results display a rather efficient perspective, with reference to the considered case study, toward inverse analysis for structural diagnosis, in the context of strategic (historical) infrastructures.

The inverse Finite Element Method (iFEM) is a model-based technique to compute the displacement (and then the strain) field of a structure from strain measurements and a geometrical discretization of the same. Different literature works exploit the error between the numerically reconstructed strains and the experimental measurements to perform damage identification in a Structural Health Monitoring framework. However, only damage detection and localization are performed, without attempting a proper damage size estimation. The latter could be based on machine learning techniques, however, an a priori definition of the damage conditions would be required. To overcome these limitations, the present work proposes a new approach in which the damage is systematically introduced in the iFEM model to minimize its discrepancy with respect to the physical structure. This is performed with a maximum likelihood estimation framework, where the most accurate damage scenario is selected among a series of different models. The proposed approach is experimentally verified on an aluminum plate subjected to fatigue crack propagation, which enables the creation of a Digital-Twin of the structure itself. The strain field fed to the iFEM routine is experimentally measured with an Optical Backscatter Reflectometry fiber and the methodology is validated with independent observations of lasers and the Digital Image Correlation.

Ocean surface waves have been utilized as fundamental information in various fields of oceanic research. In this paper, we suggest a simulation and modelling technique for generating an ocean surface wave using an inverse Fast Fourier Transform (iFFT), and we subsequently verify the wave’s accuracy. The conventional method, linear superposition, requires recursive calculation because of the double summation and the time variable; to circumvent this issue, the new algorithm is presented. The Joint North Sea Wave Project (JONSWAP) spectrum is utilized for the ocean surface wave simulation example, and the parameters are the significant wave height (HS) and the zero-crossing wave period (TZ). A coordinate transform for the wavenumber domain was used to apply the inverse FFT algorithm. To verify the accuracy of the simulation result, the relative error between the input condition and the analysis result was calculated. The result for TZ is below 4% relative error, and the maximum relative error for HS is 7%. To avoid the Nyquist frequency for wave-field analysis and simulation, the minimum grid size was calculated by twice applying the maximum wavenumber.

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.

The Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and ensure that the predictions are consistent and stable with the physical laws. PINNs opens up a new approach to address inverse problems in fluid mechanics. Based on the single-relaxation-time lattice Boltzmann method (SRT-LBM) with the Bhatnagar-Gross-Krook (BGK) collision operator, the PINN-SRT-LBM model is proposed in this paper for solving the inverse problem in fluid mechanics. The PINN-SRT-LBM model consists of three components. The first component involves a deep neural network that predicts the equilibrium control equations in different discrete velocity directions within SRT-LBM. The second component employs another deep neural network to predict non-equilibrium control equations, enabling inference of the fluid's non-equilibrium characteristics. The third component, a physics informed function translates the outputs of the first two networks into physical infor-mation. By minimizing the residuals of the physical partial differential equations (PDEs), the physics informed function infers relevant macroscopic quantities of the flow. The model evolves two sub-models applicable to different dimensions, named PINN-SRT-LBM-I and PINN-SRT-LBM-II models according to the construction of the physical informed function. The innovation of this work is the introduction of SRT-LBM and discrete velocity models as physical drivers into the neural network through the interpretation function. Therefore, PINN-SRT-LBM allows the neural network to handle inverse problems of various dimensions and focus on problem-specific solving. Experimental results confirm the accurate prediction of flow infor-mation at different Reynolds numbers within the computational domain. Relying on the PINN-SRT-LBM models, inverse problems in fluid mechanics can be solved efficiently.

In the context of Inverse Analysis in Civil Engineering, parameter identification and model calibration, of a structural system, relying on dynamic measurements, are subjects of a growing research interest. In the present contribution, the topic is tackled with reference both to simplified structural numerical examples and to a specific case study, namely a historical road three-span reinforced concrete arched bridge, with vibrational data previously acquired by standard wired accelerometers on the deck, under operational traffic conditions. In particular, the present work aims at focussing on the identification issues, concerning the definition of a maximum allowable threshold number of sought material parameters (e.g., Young’s moduli and mass densities of different structural components), with respect to the amount of available measurement data, and the investigation of the inverse analysis discrepancy function to be optimised, in order to set the intrinsic issue of multiple “realizations”, in case of a plain use of modal properties, and in view of forming a well–posed optimisation problem. Structural modelling, sensitivity analysis and numerical optimisation approaches are herein combined toward a robust and efficient identification strategy, to be effectively employed in structural assessment and diagnosis, also with respect to originally available or enriched sets of experimental data. The proposed methodology, and collected results, shall outline an efficient identification procedure, in view of automated inverse analysis, practically oriented to the dynamic assessment and structural diagnosis in the Civil Engineering context, as applied e.g. to strategic bridge infrastructures.

Universal gravitation is investigated with principles of foundational classical (Newtonian) physics. The results reveal gravitation an atomic field action; hence, Newton’s law, although absolutely valid, unavoidably misleads in creating the impression of matter rather than waveform action. Six force constants fully define gravitation: (i) a waveform torque field ; (ii) an expansion force field ; (iii) a centripetal force field ; (iv) a matter-wave torque field (the force fields , and constitute gravitational inertial rest frame); (v) a Galilean acceleration field and (vi) nuclear inverse mass-squared centripetal force constant The inertial rest frame force constants sum up to give observational G = 2.266 + 2.61 + 2.61cos46^o) x 10^-11 = 6.689 x 10^-11 m³ kg^-1 s^-2. Notably, the procedure is able to account also for observational inclination of galaxies and their aligned conjunctions. An attempt is made to account for angular momentum quantization and rectilinear, parabolic or elliptic profile of objects in gravitational acceleration. Same quantitative expression, , defines the photon and gravitation thus uniquely unifying gravitation, electricity and magnetism; furthermore, the expression reveals the photon packed with tremendous energy amounting to some . It is argued that: (i) neither mass nor gravitation curves spacetime; (ii) the principles that sustain cosmic time-scale dynamic equilibrium, scale invariance and inertia are incompatible with quantum gravitation; and (iii) the cosmic vacuum field comprises gravitational (photonic) waves, hence the interferometer likely measures shock waves.

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

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).

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.

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.

We introduce a new generalized inverse (i.e., generalized EP element) which is a natural generalization of EP and *-DMP elements in a Banach *-algebra. We present polar-like characterizations of generalized EP elements. The necessary and sufficient conditions under which the sum of two generalized EP elements is a generalized EP element are investigated. Finally, the generalized core-EP orders for generalized EP elements are characterized.

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.

People have long had a problem: the equations of motion that reflect the laws of physics are invariance under time inversion, while there always are irreversible processes for gases compose of microscopic particles. This article solves this problem. The point is that we should distinguish between the concepts of the equation of motion and motion. We also need to distinguish between the concepts of time-inverse motion and reverse motion. The former is anticlockwise, which is a frictional motion, while the latter is clockwise. For the single-particle motions in classical mechanics and in quantum mechanics, we present mathematical expressions for time-inversion motion and reverse motion, respectively. We demonstrate that single-particle motion is irreversible. The definition of the reversibility of two-particle collisions is given. According to the definition, the two-particle collision as a microscopic motion processes is irreversible. Consequently, for a gas consisting of a large number of particles colliding with each other, its movement should be irreversible, unless the condition of detailed balance is met. We give a physical explanation for the detailed balance, which does not concern the meaning of microscopic reversibility. The detailed balance means that after a pair of reciprocal collisions occur, the distribution function of the particles remains unchanged. Therefore, microscopic two-particle collision events are irreversible, but the statistical average of a large number of collision events makes it possible for the macroscopic process of a gas to be reversible. Conclusively, we clarify the microscopic mechanism of the irreversible process of gases.

The paper deals with the Compound Inverse Rayleigh distribution, shown to constitute a proper model for the characterization of the probability distribution of extreme values of wind-speed, a topic which is gaining growing interest in the field of renewable generation assessment, both in view of wind power production evaluation and the wind-tower mechanical reliability and safety. The first part of the paper illustrates such model starting from its origin as a generalization of the Inverse Rayleigh model - already proven to be a valid model for extreme wind-speeds - by means of a continuous mixture generated by a Gamma distribution on the scale parameter, which gives rise to its name. Moreover, its validity to interpret different field data is illustrated, also by means of numerous numerical examples based upon real wind speed measurements. Then, a novel Bayes approach for the estimation of such extreme wind-speed model is proposed. The method relies upon the assessment of prior information in a practical way, that should be easily available to system engineers. In practice, the method allows to express one’s prior beliefs both in terms of parameters, as customary, and/or in terms of probabilities. The results of a large set of numerical simulations – using typical values of wind-speed parameters - are reported to illustrate the efficiency and the accuracy of the proposed method. The validity of the approach is also verified in terms of its robustness with respect to significant differences compared to the assumed prior information.

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?

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.

One of the possible mechanisms causing significant emissions of methane into the atmosphere within the Arctic shelf may be the decomposition of gas hydrates. Their accumulations within the Arctic shelf formed during Ice Age almost simultaneously with the formation of permafrost, which contributed to the emergence of a zone of stable existence of gas hydrates. The subsequent flooding of the Arctic shelf led to the degradation of the permafrost and the violation of the conditions for the existence of hydrates. To assess the state of the stability zone, methods of mathematical numerical modeling are used. Standard seismic methods are widely used to localize gas hydrates, but monitoring their physical state requires the development of fundamentally new approaches based on solving multiparameter inverse seismic problems. In particular, the degree of attenuation of seismic energy is one of the objective parameters for assessing the consolidation of gas hydrates: the closer they are to the beginning of decomposition, the higher the attenuation, and hence the lower the quality factor. Thus, the methods of seismic monitoring of the state of gas hydrates in order to predict the possibility of developing dangerous scenarios should be based on solving a multi-parameter inverse seismic problem. This publication is devoted to the presentation of this approach.

An adaptive deep neural network is used in an inverse system identification setting to approximate the inverse of a nonlinear plant with the aim of constituting the plant controller by copying to the latter the weights and architecture of the converging deep neural network. This deep learning (DL) approach to the adaptive inverse control (AIC) problem is shown to outperform adaptive filtering techniques and algorithms normally used in adaptive control, especially when the plant is nonlinear. The deeper the controller the better the inverse function approximation, provided that the nonlinear plant have an inverse and that this inverse can be approximated. Simulation results prove the feasibility of this DL-based adaptive inverse control scheme. The DL-based AIC system is robust to parameter change of the nonlinear plant in that, under such change, the plant output reassumes the value of the reference signal considerably faster than with the adaptive filter counterpart of the deep neural network. Settling times and rise times of the step response are shown to improve in the DL-based AIC system.

This paper considers the solution of the equations for ruin probabilities in infinite continuous time. Using the Fourier Transform and certain results from the theory of complex functions, these solutions are obtained as com- plex integrals in a form which may be evaluated numerically by means of the inverse Fourier Transform. In addition the relationship between the re- sults obtained for the continuous time cases, and those in the literature, are compared. Closed form ruin probabilities for the heavy tailed distributions: mixed exponential; Gamma (including Erlang); Lognormal; Weillbull; and Pareto, are derived as a result (or computed to any degree of accuracy, and without the use of simulations).

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.

The inverse finite element method (iFEM) is a novel method for reconstructing the full-field displacement of structures by discrete measurement strain. In practical engineering applications, the accuracy of iFEM is reduced due to the positional offset of strain sensors during installation, and errors in structural installation. Therefore, coarse and fine two-stage calibration (CFTSC) method is proposed to enhance the accuracy of the reconstruction of structures. Firstly, the coarse calibration is based on a single-objective particle swarm optimization algorithm to optimize the displacement-strain transformation matrix related to the sensor position. Secondly, as selecting different training data can affect the training effect of self-constructed fuzzy networks, this paper proposes to screen the appropriate training data based on residual analysis. Finally, the experiments of the wing integrated antenna structure verify the efficient of the method on the reconstruction accuracy of the structural body displacement field.

Classical methods for inverse problems are mainly based on regularization theory. In particular those which are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond, respectively, to the likelihood and prior probability models.

Social distancing is a recommended solution by the World Health Organisation (WHO) to minimise the spread of COVID-19 in public places. The majority of governments and national health authorities have set the 2-meter physical distancing as a mandatory safety measure in shopping centres, schools and other covered areas. In this research, we develop a Deep Neural Network-based Model for automated people detection, tracking, and inter-people distances estimation in the crowd, using common CCTV security cameras. The proposed DNN model along with an inverse perspective mapping technique leads to a very accurate people detection and social distancing monitoring in challenging conditions, including people occlusion, partial visibility, and lighting variations. We also provide an online infection risk assessment scheme by statistical analysis of the Spatio-temporal data from the moving trajectories and the rate of social distancing violations. We identify high-risk zones with the highest possibility of virus spread and infection. This may help authorities to redesign the layout of a public place or to take precaution actions to mitigate high-risk zones. The efficiency of the proposed methodology is evaluated on the Oxford Town Centre dataset, with superior performance in terms of accuracy and speed compared to three state-of-the-art methods.

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.

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.

G-protein-coupled receptors (GPCRs) are ubiquitous sensors and regulators of cellular functions. Each GPCR exists in complex aggregates with multiple resting and active conformations. Designed to detect weak stimuli, GPCRs can also activate spontaneously, resulting in basal ligand-free signaling. Agonists trigger a cascade of events leading to an activate agonist-receptor-G protein complex with high agonist affinity. However, the ensuing signaling process can further remodel the receptor complex to reduce agonist affinity, causing rapid ligand dissociation. The acutely activated ligand-free receptor can continue signaling, as proposed for rhodopsin and  opioid receptors, resulting in robust receptor activation at low agonist occupancy with enhanced agonist potency. Continued receptor stimulation can further modify the receptor complex, regulating sustained ligand-free signaling - proposed to play a role in opioid dependence. Basal, acutely agonist-triggered, and sustained elevated ligand-free signaling could each have distinct functions, reflecting multi-state conformations of GPCRs. This review addresses basal and stimulus-activated ligand-free signaling, its regulation, genetic factors, and pharmacological implications, focusing on opioid and serotonin receptors, and the growth hormone secretagogue receptor (GHSR). Ligand-free signaling of intracellular 5-HT2A receptors could mediate therapeutic effects of psychedelic drugs. Research avenues are suggested to close gaps in our knowledge of ligand-free GPCR signaling.