Approximate Map Research Articles

Effect of substrate thickness and metallization thickness on dispersion characteristics of CPW

Approximate conformal mapping techniques have been used for analysing the effect of finite substrate thickness on coplanar wave guide (CPW). Calculations for impedance and effective dielectric constant are presented for CPW's with finite substrate thicknesses. Analytical formulation are presented for calculations. Network analytical methods of electromagnetic fields are employed to evaluate the effect of thick metal coating on CPW. Dispersion characteristics of CPW have been plotted for various metallization thicknesses. Effect of thick metal coating on guide wavelength is also plotted. Increase in metallization thickness of CPW causes an increase in wavelength. Due to this fact characteristic impedance and effective dielectric constant decreases.

Mapping Datalog program execution to networks of processors

The problem of mapping the parallel bottom up execution of Datalog programs to an interconnected network of processors is studied. The parallelization is achieved by using hash functions that partition the set of instantiations for the rules. We first examine this problem in an environment where the number of processors and the interconnection topology is known, and communication between program segments residing at non-adjacent processors is not permitted. An algorithm is presented that decides whether a given Datalog program can be mapped onto such an architecture. We then relax the constraint on the architecture by allowing program segments residing at non-adjacent processors to communicate, A theory of approximate mappings is developed, and an algorithm to obtain the closest approximate mapping of a given Datalog program onto a given architecture is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Structure, Organization, and Chromosomal Location of the Gene Encoding a Form of Rice Soluble Starch Synthase

A rice (Oryza sativa L.) genomic clone encoding the gene for a form of soluble starch synthase (SSS1) and its 5'- and 3'-flanking regions has been isolated and sequenced. The SSS1 gene contained 15 exons interrupted by 14 introns. The exon/intron organization of the SSS1 gene was divergent from that of the rice Waxy gene coding for granule-bound starch synthase, thus suggesting that the SSS1 and granule-bound starch synthase genes have evolved from an ancestral gene in a different way or that the two genes are products of different ancestral genes that have converged during evolution. However, these two genes were closely located to each other on rice chromosome 6 at an approximate map distance of 5 centimorgans. The nucleotide sequence of the 5'-end region of the gene is unique because of the presence of some repetitive sequences.

A wavelet neural network with network optimizing function

AbstractA new mapping network combining wavelets and neural networks is proposed. The proposed network has three major characteristics, namely, self‐construction of neural networks, partial retrieval of the approximate mapping, and efficient learning. The network learning algorithm can be divided roughly into the self‐construction process and the error minimization process. In the first process, hidden units are appended serially in such a way that the network structure sufficiently approximates the approximation target. Simultaneously, network parameters are updated by competitive learning. In the second process, network parameters are updated by a localized backpropagation algorithm until the desired approximation accuracy is attained. The effectiveness of the proposed network is demonstrated through computer simulations.

The Franklands Village landslide

Between 23 December 1993 and 5 January 1994 a major landslip movement developed in Franklands Village which is situated on the eastern side of Haywards Heath, West Sussex. The approximate Ordnance Survey map reference is TQ 342/236. The site of the landslide is set on the eastern slopes of a north-south trending valley. The existing development comprises blocks of two-storey fiats and semi-detached houses. The development for the Franklands Village Housing Association (FVHA) was constructed in the 1930s. A development comprising a block of two-storey sheltered housing (Charles Bennett Court) was constructed by the Hanover Housing Association between 1991 and 1992, on the higher valley slopes to the southeast of the landslide. Southern Testing Laboratories Limited (STL) were called in by Messrs K. A. Marshall &amp; Partners, Consulting Engineers to the FVHA, to investigate cracking and foundation movement that had been developing in the Franklands Village properties during December 1992. In general terms the valley slopes fall towards a small stream, towards the northwest at overall slopes of between 13 and 16° . Terracing, carried out to facilitate the initial development, steepened locally to between 30 and 45°. An investigation comprising hand-excavated trial holes, shell and auger boreholes (using a specially adapted restricted access rig), piezometers, slip indicator and monitoring of surface reference stakes, laboratory testing and geological and engineering analysis was undertaken by STL between January and April 1993. The solid geology comprises the Upper Tunbridge Wells Sands at the crest of the slope, overlying the clays of the

Approximate map labeling is in Ω ( n log n)

Given n real numbers, the ε-CLOSENESS problem consists in deciding whether any two of them are within ε of each other, where ε is a fixed parameter of the problem. This is a basic problems with an Ω ( n log n) lower bound on the running time in the algebraic computation tree model. In this paper we show that for a natural approximation version thereof the same lower bound holds. The main tool used is a lower bound theorem of Ben-Or. We introduce a new interpolation method relating the approximation version of the problem to two corresponding exact versions. Using this result, we are able to prove the optimality of the running time of a cartographic algorithm, that determines an approximate solution to the so-called MAP LABELING problem. MAP LABELING was shown to be NP-complete. The approximation algorithm discussed here is of provably optimal approximation quality. Our result is the first n log n lower bound for an approximate problem. The proof method is general enough to be potentially helpful for further results of this type.

Practical strategies for the solution of large‐scale electromagnetic inverse problems

Nonlinear inverse problems in electromagnetics are typically solved by dividing the Earth into cells of constant conductivity, linearizing the equations about a current model, computing the sensitivities, and then solving an optimization problem to obtain an updated estimate of the conductivity. In principle, this procedure can be implemented for any size problem, but in practice the computations involved may be too large for the available computing hardware. In electromagnetics this is currently the situation irrespective of whether the interpreter has access to a workstation or a supercomputer. In addition to the demands imposed by the need to compute the predicted responses from a specified model (i.e., invoking a forward mapping) there are two computational roadblocks encountered when solving an inverse problem: (1) calculation of the sensitivity matrix and (2) solution of the resultant large system of equations. If either of these operations cannot be carried out in reasonable time then an alternate strategy is required. Such strategies include generalized subspace methods, conjugate gradient methods, or approximate inverse mapping (AIM) procedures. The theoretical foundations and computational details of these strategies are explored in this paper with the ultimate goal that the inversionist, after assessing his/her computing power and knowing the time required to perform forward modeling, can generate a methodology by which to solve the problem. The methodologies are compared quantitatively by considering an archetypal inversion problem in electromagnetics, the inversion of dc potential data to recover the electrical conductivity.

An analytical study of chaotic stirring in tidal areas

Chaotic advection is studied in a flow representative of tidal areas. The flow consists of a residual flow, represented by a lattice of eddies, perturbed by a tidal flow. The physical background of the flow is given by means of a dynamical model for tide-topography interaction. Lagrangian advection in this flow can be described in terms of perturbed Hamiltonian systems. For small perturbations analytical techniques, like Melnikov's method, provide mixing coefficients. But also in the limit of large perturbations analytical results can be achieved. In this paper the method of orbit expansion is presented. The coordinates are transformed into a system, moving with the perturbation. By integration over the period of the perturbation, one obtains an (first-order) approximation of the Poincaré map. The next order can be obtained by a new coordinate transformation, this time moving with both the perturbation and the lower-order displacement. Again the moving system is integrated over a period of the perturbation. In this way an analytical approximation of the Poincaré map can be constructed. Using this approximate map one can find analytical expressions for the mixing coefficients. This method is applied successfully to a model of a tidal area. It can explain the non-monotonic dependence of the mixing on the topographic wavenumber.

Antigenic specificities of human CD4+ T-cell clones recovered from recurrent genital herpes simplex virus type 2 lesions.

Lesions resulting from recurrent genital herpes simplex virus (HSV) infection are characterized by infiltration of CD4+ lymphocytes. We have investigated the antigenic specificity of 47 HSV-specific CD4+ T-cell clones recovered from the HSV-2 buttock and thigh lesions of five patients. Clones with proliferative responses to recombinant truncated glycoprotein B (gB) or gD of HSV-2 or purified natural gC of HSV-2 comprised a minority of the total number of HSV-specific clones isolated from lesions. The gC2- and gD2-specific CD4+ clones had cytotoxic activity. The approximate locations of the HSV-2 genes encoding HSV-2 type-specific CD4+ antigens have been determined by using HSV-1 x HSV-2 intertypic recombinant virus and include the approximate map regions 0.30 to 0.46, 0.59 to 0.67, 0.67 to 0.73, and 0.82 to 1.0 units. The antigenic specificity of an HLA DQ2-restricted, HSV-2 type-specific T-cell clone was mapped to amino acids 425 to 444 of VP16 of HSV-2 by sequential use of an intertypic recombinant virus containing VP16 of HSV-2 in an HSV-1 background, recombinant VP16 fusion proteins, and synthetic peptides. Each of the remaining four patients also yielded at least one type-specific T-cell clone reactive with an HSV-2 epitope mapping to approximately 0.67 to 0.73 map units. The antigenic specificities of lesion-derived CD4+ T-cell clones are quite diverse and include at least 10 epitopes. Human T-cell clones reactive with gC and VP16 are reported here for the first time.

Point Monotonicity and Radial Convexity of First Order Approximation Mappings

In non‐smooth optimization a central role is performed by the concept which replaces the gradient. Several notions of generalized differentiability have been introduced and, within these frameworks, some attempts have been made to characterize non‐differentiable functions, by different concepts of generalized monotonicity related to the generalized convexity of the functions. Our purpose is to approach this topic by some kinds of generalized monotonicity and convexity of the first order approximation mappings for the functions, suitable from theoretical and computational points of view.

Point monotonicity and radial convexity of first order approximation mappings

In non-smooth optimization a central role is performed by the concept which replaces the gradient. Several notions of generalized differentiability have been introduced and, within these frameworks, some attempts have been made to characterize non-differentiable functions, by different concepts of generalized monotonicity related to the generalized convexity of the functions. Our purpose is to approach this topic by some kinds of generalized monotonicity and convexity of the first order approximation mappings for the functions, suitable from theoretical and computational points of view.

Inversion of 3-D DC resistivity data using an approximate inverse mapping

SUMMARY We present an iterative algorithm for inverting 3-D pole-pole DC resistivity data. The algorithm utilizes an AIM (approximate inverse mapping) formalism and iterative inversions are carried out by performing updates in both model space (AIM—MS) and data space (AIM—DS) by using an approximate inverse mapping with an exact forward mapping. In the approximate inverse mapping, the potential anomaly is expressed as a depth integral of the logarithmic conductivity perturbation convolved horizontally with a known kernel. Fourier transforming the data equation decouples wavenumber components and the Fourier transform of the conductivity anomaly is recovered by performing 1-D linear inversions at each wavenumber. Inverse Fourier transforming the 1-D inversion results produces the sought conductivity. The AIM methodology avoids the generation and inversion of a full 3-D sensitivity matrix and is consequently fast and efficient. Only one forward modelling is performed at each iteration. The algorithm is tested with synthetic data and a field data set from an epithermal region.

Frustration and Quantum Fluctuation in Spin-1 Antiferromagnetic Chains with Competing Interactions

Ground-state phase diagram and low-lying excitation spectrum of the one-dimensional S =1 anisotropic Heisenberg antiferromagnetic chain with nearest neighbor and next nearest neighbor interactions are studied by means of an approximate mapping of the original S =1 spin Hamiltonian to the effective fermion Hamiltonian, which describes the dynamics of spin zero defects in antiferromagnetic environments (domain walls in the Neel state). We find that the frustration due to the next nearest neighbor interactions works cooperatively with quantum fluctuation in the Haldane state and stabilizes it. This is naturally explained in terms of the spin zero defect. In addition, we discuss characteristic features of the excitation spectrum in connection with its ground-state properties.

Tip lengths and whiskering in noise-reduced diffusion-limited aggregation

The authors examine the nature of the tunable family of patterns obtained from the discrete eta -DLA model in the deterministic zero-noise limit. The eta -DLA model is a variant of the standard diffusion-limited aggregation (DLA) model in which the DLA growth probabilities are raised to the power eta . The observed morphologies, which range from compact Eden clusters for eta =0 through to sharp needle-like clusters with increasing eta , can be characterized by a sequence of step lengths in a stable staircase structure proceeding back from the tip. Side-branch whiskers, which are found on the triangular lattice but not on the square lattice, occur closer to the tip as eta is increased. Beyond a value eta c, whiskers are found immediately behind the tip. They derive the length of the exposed tip as a function of eta using a stationary contour approximation and conformal mapping methods. A theoretical estimate for eta c is derived by refining this approach to incorporate the possible shielding of surface sites by aggregate sites. Their theoretical results are in excellent agreement with the numerical results on both lattices.

Periodic Motions of a Hopping Robot With Vertical and Forward Motion

This article analyzes the global dynamical behavior of sim plified hopping robot models that are analogous to Raibert's experimental machines. We first review a one-dimensional ver tical hopping model that captures both the vertical hopping dynamics and nonlinear control algorithm. Second, we present a more complicated two-dimensional model that includes both forward and vertical hopping dynamics and a foot placement algorithm. These systems are analyzed using a Poincare return map. In this approach, issues of stability and global dynamical behavior are reduced to the study of the fixed points of this map. For the one-dimensional model, a closed-form return map is obtained. For the two-dimensional model, we derive an exact return map based on the first integrals of motion. Because this map can only be constructed numerically, we also derive an analytical approximation to the return map based on perturba tion methods. The approximate return map is shown to closely predict the behavior of the exact map for small forward run ning velocities. In addition, the approximate return map can be used to quantitatively explore the coupling of vertical and lat eral dynamics and to determine the effect of the foot placement algorithm on dynamical behavior The bifurcation diagrams, which capture variations in dy namical behavior with respect to the variations in system and control parameters, are also constructed. The bifurcation dia grams exhibit a period-doubling cascade. In other words, for certain system parameter values, Raibert's control algorithm can lead to an anomalous nonuniform, but stable, hopping be havior. Using the vertical model results as a guide, we interpret the interesting dynamical behavior of this system.

Experimental testing of relativistic effects, variability of the gravitational constant and topography of Mercury surface from radar observations 1964?1989

The new analysis of radar observations of inner planets for the time span 1964–1989 is described. The residuals show that Mercury topography is an important source of systematic errors which have not been taken into account up to now. The longitudinal and latitudinal variations of heights of Mercury surface were found and an approximate map of equatorial zone |ϕ|≤120° was constructed. Including three values characterizing global nonsphericity of Mercury surface into the set of parameters under determination allowed to improve essentially all estimates. In particular, the variability of the gravitational constantG was evaluated: $$\dot G/G = (0.47 \pm 0.47) \times 10^{ - 11} yr^{ - 1} $$ . The correction to Mercury perihelion motion: $$\Delta \dot \pi = - 0''.017 \pm 0''.052 cy^{ - 1} $$ and linear combination of the parameters of PPN formalism: $$\upsilon = (2 + 2\gamma - \beta )/3 = 0.9995 \pm 0.0013$$ were determined; they are in a good agreement with General Relativity predictions. The obtained values Δ.π and ν correspond to the negligible solar oblateness, the estimate of solar quadrupole moment being: $$J_2 = ( - 0.13 \pm 0.41) \times 10^{ - 6} $$ .

Approximate seniority-dictated boson-quasifermion mapping and derivation of the interacting boson fermion model.

We derive an approximate boson-quasifermion mapping of a single-j shell-model algebra, applicable to the seniority classification scheme, as an expansion in the ratio of the seniority quantum number to the level degeneracy, with selective summation of higher order terms. The procedure used is an extension of the algebraic technique first applied to the purely bosonic part of the mapping by Bonatsos, Klein, and Li. Only the maps of the generators are needed to derive a Hamiltonian for the interacting boson fermion model (IBFM), and these can be obtained in Hermitian form without having to go through the intermediary of a mapping of the fermion operators. Application of the results is illustrated by a fresh discussion of the so-called exchange interaction of the IBFM. A consistent mapping of the single fermion in terms of bosons and quasifermions is also derived that includes a consideration of the unusual properties of the quasifermions.

Approximate Inverse Mapping Inversion of the COPROD2 Data.

The results of the inversion of the COPROD2 magnetotelluric data set are presented using two implementations of the AIM inverse method. The two algorithms invert magnetotelluric data over 2D conductivity structures. Both algorithms use an approximate inverse mapping based on approximate sensitivities that arise from the 1D conductivity profile beneath each station; this avoids the large computations normally required to approximate the exact inverse mapping, for example, by using the full 2D Jacobian. The primary difference between the algorithms is that the first algorithm minimizes the l1 norm of the data misfit with regularization provided by minimizing the l1 norm of the conductivity. This problem is solved with standard linear programming techniques. The second algorithm uses the l2 norm in place of the l1 norm and is solved using a subspace approach., Both algorithms produce models with predicted data in satisfactory agreement with the COPROD2 data. The difference between the final models is evidence of the well known nonuniqueness in geophysical inverse problems; the similarities of the final models give a suggestion of that which might be common to all models which fit the data.

Growth and form in the zero-noise limit of discrete Laplacian growth processes with inherent surface tension: I. The square lattice

Laplacian growth models that include surface tension in a lowest approximation are simulated on the square lattice in the deterministic zero-noise limit. The models include the dielectric breakdown model with exponent η and a generalized diffusion-limited aggregation (DLA) model with local sticking probability s = α 3− B , where B is the number of neighbouring aggregate sites and α is a parameter. We identify two morphological transitions in the zero-noise limit for these models as the effective surface tension is increased; (i) a transition from a stable needle staircase to tip-splitting and (ii) a transition from axial growth to diagonal growth. We use a stationary contour approximation and conformal mapping methods to obtain theoretical estimates for the step lengths in the stable needle staircase for the DLA model with zero surface tension ( α = 1). We further extend this formalism to describe the collapse of the needle and subsequent tip-splitting in the generalized DLA model.

The effect of high modulus single and double layer coatings on contact stresses

Abstract The elastic stress distributions arising from spherical indentation of high modulus single and double layer coatings of different thicknesses on a lower modulus substrate are investigated using finite element methods. It was found that the shape of the pressure distribution under the indenter is approximately the same as the Hertzian pressure distribution except for the thickest coatings. As a consequence, maximum radial tensile stresses obtained from this study agreed with the results of Van der Zwaag and Field, and Van der Zwaag, Dear, and Field for the thinnest coatings. However, the stresses were different for the thicker coatings where the pressure distribution under the indenter differed from the parabolic distribution. An approximate map giving the interface location of the maximum radial tensile and shear stresses as a function of coating moduli and total coating thickness is presented. The map shows that increasing the total thickness or increasing the modulus of the top layer moves the ...