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Purpose\ud \ud The apparent propagator anisotropy (APA) is a new diffusion MRI metric that, while drawing on the benefits of the ensemble averaged propagator anisotropy (PA) compared to the fractional anisotropy (FA), can be estimated from single‐shell data.\ud Theory and Methods\ud \ud Computation of the full PA requires acquisition of large datasets with many diffusion directions and different b‐values, and results in extremely long processing times. This has hindered adoption of the PA by the community, despite evidence that it provides meaningful information beyond the FA. Calculation of the complete propagator can be avoided under the hypothesis that a similar sensitivity/specificity may be achieved from apparent measurements at a given shell. Assuming that diffusion anisotropy (DiA) is nondependent on the b‐value, a closed‐form expression using information from one single shell (ie, b‐value) is reported.\ud Results\ud \ud Publicly available databases with healthy and diseased subjects are used to compare the APA against other anisotropy measures. The structural information provided by the APA correlates with that provided by the PA for healthy subjects, while it also reveals statistically relevant differences in white matter regions for two pathologies, with a higher reliability than the FA. Additionally, APA has a computational complexity similar to the FA, with processing‐times several orders of magnitude below the PA.\ud Conclusions\ud \ud The APA can extract more relevant white matter information than the FA, without any additional demands on data acquisition. This makes APA an attractive option for adoption into existing diffusion MRI analysis pipelines.

The article deals with the analysis of the fractional COVID‐19 epidemic model (FCEM) with a convex incidence rate. Keeping in view the fading memory and crossover behavior found in many biological phenomena, we study the coronavirus disease by using the noninteger Caputo derivative (CD). Under the Caputo operator (CO), existence and uniqueness for the solutions of the FCEM have been analyzed using fixed point theorems. We study all the basic properties and results including local and global stability. We show the global stability of disease‐free equilibrium using the method of Castillo‐Chavez, while for disease endemic, we use the method of geometrical approach. Sensitivity analysis is carried out to highlight the most sensitive parameters corresponding to basic reproduction number. Simulations are performed via first‐order convergent numerical technique to determine how changes in parameters affect the dynamical behavior of the system.

This paper studies optimal control and stabilization problems for continuous‐time mean‐field systems with input delay, which are the fundamental development of control and stabilization problems for mean‐field systems. There are two main contributions: (1) To the best of the authors' knowledge, the present paper is the first to establish the necessary and sufficient solvability condition for this kind of optimal control problem with input delay, and to derive the analytical form of an optimal controller through overcoming the obstacle that separation principle no longer holds for multiplicative‐noise systems. (2) For the stabilization problem, under the assumption of exact observability, it is strictly proven that the system is stabilizable if and only if the algebraic Riccati equation has a unique positive definite solution.

In this paper a thorough analysis is carried out of the type of order reduction that Lawson methods exhibit when used to integrate nonlinear initial boundary value problems. In particular, we focus on nonlinear reaction-diffusion problems, and therefore, this study is important in a large number of practical applications modeled by this type of nonlinear equations. A theoretical study of the local and global error of the total discretization of the problem is carried out, taking into account both, the error coming from the space discretization and that due to the integration in time. These results are also corroborated by the numerical experiments performed in this paper., Ministerio de Ciencia e Innovación and Regional Development European Funds, Grant/Award Number: PGC2018-101443-B-I00; Junta de Castilla y León and Feder, Grant/Award Number: VA169P20

In this paper we solve $m$-parameter eigenvalue problems ($m$EPs), with $m$ any natural number by representing the problem using Tensor-Trains (TT) and designing a method based on this format. $m$EPs typically arise when separation of variables is applied to separable boundary value problems. Often, methods for solving $m$EP are restricted to $m = 3$, due to the fact that, to the best of our knowledge, no available solvers exist for $m>3$ and reasonable size of the involved matrices. In this paper, we prove that computing the eigenvalues of a $m$EP can be recast into computing the eigenvalues of TT-operators. We adapted the algorithm in \cite{Dolgov2014a} for symmetric eigenvalue problems in TT-format to an algorithm for solving generic $m$EPs. This leads to a subspace method whose subspace dimension does not depend on $m$, in contrast to other subspace methods for $m$EPS. This allows us to tackle $m$EPs with $m > 3$ and reasonable size of the matrices. We provide theoretical results and report numerical experiments. The MATLAB code is publicly available., 17 pages, 14 figures

As is well-know, on an Arens regular Banach algebra all continuous functionals are weakly almost periodic. In this paper we show that $\ell^1$-bases which approximate upper and lower triangles of products of elements in the algebra produce large sets of functionals that are not weakly almost periodic. This leads to criteria for extreme non-Arens regularity of Banach algebras in the sense of Granirer. We find in particular that bounded approximate identities (bai's) and bounded nets converging to invariance (TI-nets) both fall into this approach, suggesting that this is indeed the main tool behind most known constructions of non-Arens regular algebras. These criteria can be applied to the main algebras in harmonic analysis such as the group algebra, the measure algebra, the semigroup algebra (with certain weights) and the Fourier algebra. In this paper, we apply our criteria to the Lebesgue-Fourier algebra, the 1-Segal Fourier algebra and the Fig\`a-Talamanca Herz algebra., Comment: 23 pages. Third version. The proof of Theorem 5.5 had to be corrected to include locally compact groups that are not unimodular. Definition 3.1 had to adapted to match its use in Theorem 3.9

This paper considers tests and confidence sets (CSs) concerning the coefficient on the endogenous variable in the linear IV regression model with homoskedastic normal errors and one right‐hand side endogenous variable. The paper derives a finite‐sample lower bound function for the probability that a CS constructed using a two‐sided invariant similar test has infinite length and shows numerically that the conditional likelihood ratio (CLR) CS of Moreira (2003) is not always “very close,” say 0.005 or less, to this lower bound function. This implies that the CLR test is not always very close to the two‐sided asymptotically‐efficient (AE) power envelope for invariant similar tests of Andrews, Moreira, and Stock (2006) (AMS). On the other hand, the paper establishes the finite‐sample optimality of the CLR test when the correlation between the structural and reduced‐form errors, or between the two reduced‐form errors, goes to 1 or −1 and other parameters are held constant, where optimality means achievement of the two‐sided AE power envelope of AMS. These results cover the full range of (nonzero) IV strength. The paper investigates in detail scenarios in which the CLR test is not on the two‐sided AE power envelope of AMS. Also, theory and numerical results indicate that the CLR test is close to having the greatest average power, where the average is over a specified grid of concentration parameter values and over a pair of alternative hypothesis values of the parameter of interest, uniformly over all such pairs of alternative hypothesis values and uniformly over the correlation between the structural and reduced‐form errors. Here, “close” means 0.015 or less for k ≤ 20, where k denotes the number of IVs, and 0.025 or less for 0

The present paper first establishes that an identity involving generalized fractional integrals is proved for differentiable functions by using two parameters. By utilizing this identity, we obtain several parameterized inequalities for the functions whose derivatives in absolute value are convex. Finally, we show that our main inequalities reduce to Ostrowski type inequalities, Simpson type inequalities and trapezoid type inequalities which are proved in earlier published papers. WOS:000655362700001 2-s2.0-85106753378

In this present paper, we introduce the idea and concept of n-polynomial s-type preinvex functions. We elaborate and investigate the algebraic properties of the newly introduced definition and discuss their connections and relations with convex functions. We find the new sort of Hermite-Hadamard inequality via a newly introduced definition. Furthermore, some refinements of Hermite-Hadamard inequality are given. Finally, we investigated some applications via this newly introduced definition. The results obtained in this paper can be viewed as significant improvement of previously known results. H.E.C. Pakistan under NRPU project [7906] The research of the author Saad Ihsan Butt has been fully supported by H.E.C. Pakistan under NRPU project 7906. WOS:000649589100001 2-s2.0-85105631491

In this paper, we present some new integral and series representations for the eigenfunctions of the multidimensional time‐fractional diffusion‐wave operator with the time‐fractional derivative of order β ∈]1, 2[ defined in the Caputo sense. The integral representations are obtained in form of the inverse Fourier–Bessel transform and as a double contour integrals of the Mellin–Barnes type. Concerning series expansions, the eigenfunctions are expressed as the double generalized hypergeometric series for any β ∈]1, 2[ and as Kampé de Fériet and Lauricella series in two variables for the rational values of β. The limit cases 𝛽=1 (diffusion operator) and 𝛽=2 (wave operator) as well as an intermediate case 𝛽=32 are studied in detail. Finally, we provide several plots of the eigenfunctions to some selected eigenvalues for different particular values of the fractional derivative order β and the spatial dimension n. In this paper, we present some new integral and series representations for the eigenfunctions of the multidimensional time-fractional diffusion-wave operator with the time-fractional derivative of order $\beta \in ]1,2[$ defined in the Caputo sense. The integral representations are obtained in form of the inverse Fourier-Bessel transform and as a double contour integrals of the Mellin-Barnes type. Concerning series expansions, the eigenfunctions are expressed as the double generalized hypergeometric series for any $\beta \in ]1,2[$ and as Kamp\'{e} de F\'{e}riet and Lauricella series in two variables for the rational values of $\beta$. The limit cases $\beta=1$ (diffusion operator) and $\beta=2$ (wave operator) as well as an intermediate case $\beta=\frac{3}{2}$ are studied in detail. Finally, we provide several plots of the eigenfunctions to some selected eigenvalues for different particular values of the fractional derivative order $\beta$ and the spatial dimension $n$. published

This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current Markov chain Monte Carlo methods which simulate a Markov chain whose stationary distribution is the target. We show how to approximate distributions of interest by carefully combining sequential Monte Carlo methods with methodology for the exact simulation of diffusions. The methodology introduced here is particularly promising in that it is applicable to the same class of problems as gradient based Markov chain Monte Carlo algorithms but entirely circumvents the need to conduct Metropolis-Hastings type accept/reject steps whilst retaining exactness: the paper gives theoretical guarantees ensuring the algorithm has the correct limiting target distribution. Furthermore, this methodology is highly amenable to big data problems. By employing a modification to existing na{\"\i}ve sub-sampling and control variate techniques it is possible to obtain an algorithm which is still exact but has sub-linear iterative cost as a function of data size., Comment: Substantially revised with clearer presentation and more extensive simulation study. 59 pages, 6 figures

In this paper we will show the existence of a face $2$-colourable biembedding of the complete graph onto an orientable surface where each face is a cycle of a fixed length $k$, for infinitely many values of $k$. In particular, under certain conditions, we show that there exists at least $(n-2)[(p-2)!]^2/(e^2 kn)$ non-isomorphic face $2$-colourable biembeddings of $K_{2nk+1}$ in which all faces are cycles of length $k=4p+3$. These conditions are: $n\equiv 1\mod 4$, $k\equiv 3\mod 4$ and either $n$ is prime or $n\gg k$ and $n\equiv 0\mod 3$ implies $p\equiv 1\mod 3$. To achieve this result we begin by verifying the existence of $(n-2)[(p-2)!/e]^2$ non-equivalent Heffter arrays, $H(n;k)$, which satisfy the conditions: (1) for each row and each column the sequential partial sums determined by the natural ordering must be distinct modulo $2nk+1$; (2) the composition of the natural orderings of the rows and columns is equivalent to a single cycle permutation on the entries in the array. The existence of Heffter arrays $H(n;k)$ that satisfy condition (1) was established earlier in \cite{BCDY} and in this current paper we vary this construction and show that there are at least $(n-2)[(p-2)!/e]^2$ such non-equivalent $H(n;k)$ that satisfy condition (1) and then show that each of these Heffter arrays also satisfy condition (2) under certain conditions., Comment: arXiv admin note: text overlap with arXiv:1906.07366

Switch-mode power converters are used in various applications to convert between different voltage (or current) levels. They use transistors to switch on and off the input voltage to generate a pulsed voltage whose arithmetic average is the desired output voltage of the converter. After smoothening by filters, the converter output is used to supply devices. The simulation of these switch-mode power converters by conventional time discretization is computationally expensive since a high number of time steps is necessary to properly resolve the unknown state variables and detect switch events of the excitation. This paper proposes a multirate method based on the concept of Multirate Partial Differential Equations (MPDEs), which splits the solution into fast varying and slowly varying parts. The method is developed to work with pulse width modulated (PWM) excitation with a constant switching cycle and varying duty cycle. The important case of varying duty cycles in the MPDE framework is addressed for the first time. Switching event detection is no longer necessary and a much smaller number of time steps for a decent resolution are required, thus leading to a highly efficient method., Comment: This paper has been submitted to and accepted by International Journal of Numerical Modelling: Electronic Networks, Devices and Fields. It is a preprint without reviewer comments taken into account

Incubation represents a life stage of crucial importance for the optimal development of avian embryos. For most birds, incubation poses a trade-off between investing in self-maintenance and offspring care. Furthermore, incubation is affected by environmental temperatures and, therefore, will be likely impacted by climate change. Despite its relevance and readily available temperature logging methods, avian incubation research is hindered by recognised limitations in available software. In this paper, a new quantitative approach to analyse incubation behaviour is presented. This new approach is embedded in a free R package, incR. The flexibility of the R environment eases the analysis, validation and visualisation of incubation temperature data. The core algorithm in incR is validated here and it is shown that the method extracts accurate metrics of incubation behaviour (e.g. number and duration of incubation bouts). This paper also presents a suggested workflow along with detailed R code to aid the practical implementation of incR.

Copyright © 2018 John Wiley & Sons, Ltd. The concept of full commutativity of displacements in the expression for strain energy density for the geometrically nonlinear problem has been introduced for the first time and fully established in this paper. Its consequences for the FEM formulation have been demonstrated. As a result, the strain energy, equilibrium equation, and incremental equilibrium equation for the geometrically nonlinear problem can all be presented in a unified manner involving various stiffness matrices that are all symmetric, unique, and explicitly expressed. As an important application, the framework has been employed in the FEM implementation of Koiter's initial postbuckling theory, which has been handicapped by its mesh sensitivity in evaluating one of the initial postbuckling coefficients. This has largely prevented it from being incorporated in mainstream commercial FEM codes. Based on the outcomes of this paper, the mesh sensitivity problem has been completely resolved without the need to use any specially formulated element. As a result, Koiter's theory can be practically and straightforwardly implemented in any FEM code. The results have been verified against those found in the literature.

Spatial statistical analyses are often used to study the link between environmental factors and the incidence of diseases. In modelling spatial data, the existence of spatial correlation between observations must be considered. However, in many situations, the exact form of the spatial correlation is unknown. This paper studies environmental factors that might influence the incidence of malaria in Afghanistan. We assume that spatial correlation may be induced by multiple latent sources. Our method is based on a generalized estimating equation of the marginal mean of disease incidence, as a function of the geographical factors and the spatial correlation. Instead of using one set of generalized estimating equations, we embed a series of generalized estimating equations, each reflecting a particular source of spatial correlation, into a larger system of estimating equations. To estimate the spatial correlation parameters, we set up a supplementary set of estimating equations based on the correlation structures that are induced from the various sources. Simultaneous estimation of the mean and correlation parameters is performed by alternating between the two systems of equations. 2017 Royal Statistical Society We thank the Associate Editor and the referees for their perceptive comments and suggestions, that have led to a greatly improved version of this paper. Denis Leung�s research is funded by the Research Center at Singapore Management University. You-Gan Wang�s research is funded by Australian Research Council discovery grant DP130100766 and project DP160104292. Scopus

This paper investigates a bumpless transfer control problem for uncertain switched positive linear time‐delay systems (SPLTDSs) with discrete and distributed delays. The innovation of this study is to develop a linear feedback controller and design a switching law that ensures lower controller signal bumps due to the switches of the SPLTDSs and also guarantee the L1–gain performance of the system. To this end, a bumpless transfer performance is proposed, and stabilisation constraints for SPLTDSs with synchronous switching are developed. Dwell time criteria are utilised in the stability analysis. Also, the results are improved to cover the uncertain SPLTDSs with interval or polytopic uncertainties. Then, asynchronous switching is considered, and the proposed method is extended to deals with asynchronous switching mode. Asynchronous switching means switches of the controller have lagged behind the subsystem switches. All the stability conditions are derived by multiple co‐positive Lyapunov–Krasovskii functional for synchronous and asynchronous switching conditions. At last, two numerical examples are presented to show the effectiveness of the proposed method compared with the leading existing solutions.

Nowadays, the deterministic construction of sensing matrices is a hot topic in compressed sensing. The coherence of the measurement matrix is an important research area in the design of deterministic compressed sensing. To solve this problem, this paper proposes a novel sparse deterministic measurement matrix, which basically accesses the optimal low coherence of the measurement matrix. Firstly, a class of sparse square matrix is constructed based on finite fields' arithmetic. Then, the Hadamard matrix, or (discrete Fourier transform) DFT matrix, is nestled into the square matrix to construct an asymptotically optimal deterministic measurement matrix. That is, the relevant column vectors have orthogonal characteristics. Using this feature, the measurement matrix can be further optimized to reduce its mutual coherence, almost achieving the lower bound of the coherence (Welch bound). The two types of deterministic measurement matrices proposed are sparse with low mutual coherence and flexible measurement sizes. So, the proposed deterministic measurement matrices require less memory and time for the recovery as well as reducing the complexity due to their sparse structure. The simulation results show that compared with the existing (several typical) random matrices, the proposed method can reduce the mutual coherence and computational complexity of the measurement matrix.

The very weak solution for the Stokes, Oseen and Navier-Stokes equations has been studied by several authors in the last decades in domains of Rn, n ≥ 2. The authors studied the Oseen and Navier-Stokes problems assuming a solenoidal convective velocity in a bounded domain Ω ⊂ R3 of class C1,1 for v ∈ Ls (Ω) for s ≥ 3 in some previous papers. The results for the Navier-Stokes equations were obtained by using a fixed-point argument over the Oseen problem. These results improve those of Galdi et al. , Farwig et al. and Kim for the Navier-Stokes equations, because a less regular domain Ω ⊂ R3 and more general hypothesis on the data are considered. In particular, the external forces must not be small. In this work, existence of weak, strong, regularised and very weak solution for the Oseen problem are proved, mainly assuming that v ∈ L3(Ω) and its divergence ∇ · v is sufficiently small in the W−1,3(Ω)-norm. In this sense, one extends the analysis made by the authors for a given solenoidal v in some previous papers. As a consequence, the existence of very weak solution for the Navier-Stokes problem (u, π) ∈ L3(Ω) × W−1,3(Ω)/R for a non-zero divergence condition is obtained in the 3D case. Ministerio de Ciencia e Innovación (España) MTM2009-12927 Ministerio de Economía y Competitividad MTM2012-32325

Adaptive search is one of the fastest fractal compression algorithms and has gained great success in many industrial applications. By substituting the luminance offset by the range block mean, the authors create a completely new version for both the encoding and decoding algorithms. In this paper, theoretically, they prove that the proposed decoding algorithm converges at least as fast as the existing decoding algorithms using the luminance offset. In addition, they prove that the attractor of the decoding algorithm can be represented by a linear combination of range-averaged images. These theorems are very important contributions to the theory and applications of fractal image compression. As a result, the decoding image can be represented as the sum of the DC and AC component images, which is similar with discrete cosine transform or wavelet transform. To further speed up this algorithm and reduce the complexity of range and domain blocks matching, they propose two improvements in this paper, that is, employing the post-quantisation and geometric neighbouring local search to replace the currently used pre-quantisation and the global search, respectively. The corresponding experimental results show the proposed encoding and decoding algorithms can provide a better performance compared with the existing algorithms.

In this paper, we forecast EU-area inflation with many predictors using time-varying parameter models. The facts that time-varying parameter models are parameter-rich and the time span of our data is relatively short motivate a desire for shrinkage. In constant coefficient regression models, the Bayesian Lasso is gaining increasing popularity as an effective tool for achieving such shrinkage. In this paper, we develop econometric methods for using the Bayesian Lasso with time-varying parameter models. Our approach allows for the coefficient on each predictor to be: i) time varying, ii) constant over time or iii) shrunk to zero. The econometric methodology decides automatically which category each coefficient belongs in. Our empirical results indicate the benefits of such an approach.

A number of different fundamental problems in fault detection and fault identification are formulated in this paper. The fundamental problems include exact, almost, generic and class-wise fault detection and identification. Necessary and sufficient conditions for the solvability of the fundamental problems are derived. These conditions are weaker than the ones found in the literature since we do not assume any particular structure for the residual generator. At the end of the paper, a time domain synthesis procedure based on state-space methods to construct appropriate residual generators is given. Copyright © 2000 John Wiley & Sons, Ltd.

This paper concentrates on the stability problem of systems with two additive time‐varying delay components. For the construction of Lyapunov–Krasovskii functional (LKF), in the case that the introduced augmented vector contains the double integral term of the state vector, a special form of the binary quadratic function with respect to two time‐varying delays has often been introduced into the derivative of the LKF. In order to determine the negative definiteness of such function, by making full use of the idea of partial differential, the convex/concave property and the slope characteristic of tangent lines of the binary quadratic function, a binary quadratic function negative‐determination lemma is proposed in the case of the pluses or minuses of quadratic coefficients are unknown. Then, the obtained stability criterion in the form of linear matrix inequality shows a greater advantage than the previous criteria since not only some advanced techniques are employed to treat some integral terms, but also the proposed lemma is employed to deal with quadratic terms in functional derivative. Finally, a typical example is given to verify the superiority of the derived criterion.

Morphing between 3D objects is a fundamental technique in computer graphics. Traditional methods of shape\ud morphing focus on establishing meaningful correspondences and finding smooth interpolation between shapes.\ud Such methods however only take geometric information as input and thus cannot in general avoid producing\ud unnatural interpolation, in particular for large-scale deformations. This paper proposes a novel data-driven approach\ud for shape morphing. Given a database with various models belonging to the same category, we treat them\ud as data samples in the plausible deformation space. These models are then clustered to form local shape spaces\ud of plausible deformations. We use a simple metric to reasonably represent the closeness between pairs of models.\ud Given source and target models, the morphing problem is casted as a global optimization problem of finding a\ud minimal distance path within the local shape spaces connecting these models. Under the guidance of intermediate\ud models in the path, an extended as-rigid-as-possible interpolation is used to produce the final morphing. By\ud exploiting the knowledge of plausible models, our approach produces realistic morphing for challenging cases as\ud demonstrated by various examples in the paper.

This paper investigates the stability analysis and stabilization of T‐S fuzzy systems with time‐varying delays. First, a new augmented Lyapunov–Krasovskii functional is constructed, delay‐dependent stability criteria in terms of linear matrix inequalities (LMIs) are obtained by combining them with the integral inequality technique and the reciprocally convex combination inequality. Based on the state space decomposition method, some piecewise membership functions are employed to approximate the membership functions. The piecewise membership functions can be locally represented in terms of the convex combinations of the supremum and infimum of some local basis functions. The boundary information of the membership functions is adequately taken into consideration in stability analysis, and then some relaxed membership‐function‐dependent stability results are obtained. Second, state feedback controllers for fuzzy systems with time‐varying delays are presented under the imperfect premise‐matching technique, whose membership functions and the number of fuzzy rules are allowed to be designed freely, consequently, the flexibility of controller design is improved. Finally, four numerical examples are given to demonstrate the effectiveness of the presented approaches.

This paper evaluates the performance of multiple‐input multiple‐output systems with orthogonal space‐time block code transmit diversity technique experiencing over G composite fading channels. Particularly, closed form expressions for ergodic capacity, average symbol error rate and outage probability are presented in high SNR regime. The ergodic capacity of multiple‐input multiple‐output systems with orthogonal space‐time block code is also measured in low signal‐to noise ratio regime. Other essential statistical properties such as variance and probability density function of capacity are also explored for comprehensive analysis. Compared to the exact expressions, the derived analytical formulations are found to be involved with considerably less mathematical exercise and provide additional insights into the implications of model parameters on system performance. The accuracy of G distribution in approximating Nakagami‐m/lognormal over several realistic scenario are examined and simultaneously the efficiency of distribution is compared with that of Nakagami‐m/Gamma distribution. The obtained analytical expressions are corroborated using Monte‐Carlo simulations where it is observed that the approximated results remain notably tight in asymptotically high signal‐to noise ratio regime.

The use of optimised resistivity tomography surveys to acquire field data imposes extra constraints on the design strategy beyond maximising the quality of the resulting tomographic image. In this paper, methods are presented to 1) minimise electrode polarisation effects; 2) make efficient use of parallel measurement channels; and 3) incorporate data noise estimates in the optimisation process. 1) A simulated annealing algorithm is used to rearrange the optimised measurement sequences to minimise polarisation errors. The method is developed using random survey designs, and is demonstrated to be effective for use with single and multi-channel optimised surveys. 2) An optimisation algorithm is developed to design surveys by successive addition of multi-channel groups of measurements rather than individual electrode configurations. The multi-channel surveys are shown to produce results nearly as close to optimal as equivalent single channel surveys, while reducing data collection times by an order of magnitude. 3) Random errors in the data are accounted for by weighting the electrode configurations in the optimisation process according to a simple error model incorporating background and voltage-dependent noise. The use of data weighting produces optimised surveys that are more robust in the presence of noise, while maintaining as much of the image resolution of the noise-free designs as possible. All the new methods described in this paper are demonstrated using both synthetic and real data, the latter having been measured on an active landslide using a permanently installed geoelectrical monitoring system.

This paper studies Frobenius maps on injective hulls of residue fields of complete local rings with a view toward providing constructive descriptions of objects originating from the theory of tight closure. Specifically, the paper describes algorithms for computing parameter test ideals, and tight closure of certain submodules of the injective hull of residue fields of a class of well-behaved rings which includes all quasi-Gorenstein complete local rings., Comment: Minor corrections, an example added. To appear in the Journal of the London Mathematical Society