Slope Constraints Research Articles

On the density distribution within the Earth

The distribution of density as a function of position within the Earth is much less well constrained than the seismic velocities. The primary information comes from the mass and moment of inertia of the Earth and this information alone requires that there be a concentration of mass towards the centre of the globe. Additional information is to be found in the frequencies of the graver normal modes of the Earth which are sensitive to density through self-gravitation effects induced in deformation. The present generation of density models has been constructed using linearized inversion techniques from earlier models, which ultimately relate back to models developed by Bullen and based in large part on physical arguments. A number of experiments in non-linear inversion have been conducted using the PREM reference model, with fixed velocity and attenuation, but with the density model constrained to lie within fixed bounds on both density and density gradient. A set of models is constructed from a uniform probability density within the bound and slope constraints. Each of the resultant density models is tested against the mass and moment of inertia of the Earth, and for successful models a comparison is made with observed normal mode frequencies. From the misfit properties of the ensemble of models the robustness of the density profile in different portions of the Earth can be assessed, which can help with the design of parametrization for future reference models. In both the lower mantle and the outer core it would be desirable to allow a more flexible representation than the single cubic polynomial employed in PREM.

The MCS/MFNN algorithm for open pit optimization

ABSTRACT Many algorithms and their modifications have been used to design and optimize open pit limits. These algorithms have provided mine planning engineers with pertinent information in designing, optimizing and extracting ore reserves by open pit technology. However, they do not address the random field properties associated with the ore grades and reserves, and thus, fail to yield the truly optimized pit limits in any time horizon. In this paper, a new algorithm, MCS/MFNN, which overcomes these limitations is developed to optimize open pit limits. The random field properties of the ore grade and reserves have been modelled using the modified conditional simulation based on the best linear unbiased estimation and local average subdivision techniques. Artificial neural networks are then used to classify the blocks based on their conditioned economic block values. The error back propagation algorithm, in the neural networks, is used to optimize the pit limits by minimizing the desired and actual outputs error in a multilayer perceptron under the pit wall slope constraints. The MCS/MFNN algorithm is used to optimize a section of the gold deposit of the Sabi Heap Leaching Gold Project in Zimbabwe. The results of this algorithm are the same as that obtained from the Lerchs-Grossman's 2D algorithm, but in random multivariable states, the MCS/MFNN algorithm is the most suitable for pit optimization. The method is also fast since it mimics the operation of the brain in the solution of the pit optimization problem.

Finite element modeling of scattering problems involving infinite domains using drilling degrees of freedom

Scattering of waves involving complex geometries in conjunction with infinite or semi-infinite domains is modeled by introducing a mathematical boundary within which the finite element representation is employed. On the mathematical boundary, the finite element representation is matched with analytical representation in the infinite/sem-infinite domain. The matching has been done with and without slope constraints on the boundary. Drilling degrees of freedom at each of the nodes of the finite element model are introduced to take into account the transverse component of the elastodynamic field more precisely. Use of the slope constraint makes the eigenvalues of the mathematical domain complex and hence reduces the error at those frequencies compared to the use of field continuity only, which would result in real eigenvalues. Use of drilling degrees of freedom improves accuracy. Examples involving elastic and acoustic wave scattering at the interface of fluid-solid half spaces are considered. In the examples involving a fluid-solid interface, a method for using displacement formulation in the irrotational fluid region is also presented. The approach presented here can be applied to acoustic and electromagnetic field problems also.

Effect of different boundary conditions in the finite element modeling of acoustic field problems involving infinite domains—An application to smart structures

In the modeling of structural acoustic problems involving infinite domains, finite element modeling is often used in regions involving complex geometry, material anisotropy, coupled fields, etc. These same problems often involve coupling of the structure with an infinite acoustic fluid. Several methods have been proposed involving infinite elements, Dtn boundary conditions, matching the FEM representation with analytical representations in the infinite domain, to name a few. In modeling the response of embedded sensors and actuators in a structure subject to fluid loading, we have found it convenient to match plane wave solutions in the acoustic fluid with the FEM representation. The matching can be done with and without slope constraints and the matching can also be done using the so-called Dtn (Dirichlet to Neumann) boundary condition that results from the radiation conditions in the infinite domain. A parametric study of convergence and accuracy of numerical results using each of these methods will be presented.

Scaling behavior of deposition models with limited downward mobility.

We have studied the interface-width scaling behavior of deposition models in which limited downward mobility is introduced. In all the models studied here, there is a maximum allowed slope for the interface at which the growth velocity is zero. The Kardar-Parisi-Zhang equation is resummed in order to show explicitly this slope constraint, but still incorporates parameters \ensuremath{\lambda} measuring the slope dependence of the growth velocity, \ensuremath{\nu} measuring the surface tension, and D measuring the noise amplitude. Increasing mobility naturally smooths the interface, and is associated with a decrease in the magnitude of ${\ensuremath{\lambda}}_{\mathrm{eff}}$=\ensuremath{\lambda}${\mathit{D}}^{1/2}$/${\ensuremath{\nu}}^{3/2}$. A detailed study of a bridge-site deposition model, with one hop of probability p, shows that \ensuremath{\Vert}\ensuremath{\lambda}\ensuremath{\Vert} increases with p. From an independent assessment of noise-amplitude behavior, we can conclude that \ensuremath{\nu} must also increase with p to ensure the required ${\ensuremath{\lambda}}_{\mathrm{eff}}$ behavior. Direct determination of \ensuremath{\nu} via the Wolf-Tang procedure of imposing inhomogeneity on some length scale L supports this conclusion. (However \ensuremath{\nu} depends on the inhomogeneity strength, which should be chosen small, and on L.) We comment on anticipated behavior of similar limited-mobility models in d\ensuremath{\ge}2 dimensions, and compare with behavior of limited-mobility ballistic deposition and noise-reduced deposition models.

Short utterance recognition using a network with minimum training

A feedforward network is used to recognize short, digitized, isolated utterances. A high, multispeaker recognition rate is achieved with a small vocabulary with a single training utterance. This approach makes use of the pattern recognition property of the network architecture to classify different temporal patterns in the multidimensional feature space. The network recognizes the utterances without the need of segmentation, phoneme identification, or time alignment. We train the network with four words spoken by one single speaker. The network is then able to recognize 20 tokens spoken by 5 other speakers. We repeat the above training and testing procedure using a different speaker's utterances for training each time. The overall accuracy is 97.5%. We compare this approach to the traditional dynamic programming (DP) approach, and find that DP with slope constraints of 0 and 1 achieve 98.5% and 85% accuracies respectively. Finally we validate out statistics by training and testing the network of a four-word subset of the Texas Instruments (Tl) isolated word database. The accuracy with this vocabulary exceeds 96%. By doubling the size of the training set, the accuracy is raised to 98%. Using a suitable threshold, we are able to raise the accuracy of one network from 87% to 98.5%. Thresholding applied to all networks would then raise the overall accuracy to well over 99%. This technique is especially promising because of the low overhead and computational requirements, which make it suitable for a low cost, portable, command recognition type of application.

On the use of speech recognition in articulation training

Computer processing of speech has been used in many ways as an aid to clinicians in various types of speech therapy. In this work, use of speech recognition for detecting articulation errors, such as a lisp or a phoneme deletion, is investigated. The main features of this approach are (1) the use of a time‐dependent score in template matching and (2) the adjustment of dynamic time‐warping slope constraints according to the type of articulation error (deletions versus substitutions). The use of a time‐dependent score is particularly important because it allows the clinician to target a particular portion of a word for correct pronunciation. The algorithm was implemented in near real time on a PC with a DSP processor. Speaker‐dependent and ‐independent performance was investigated for simulated and actual articulation errors. [Work supported by Design Automation, Inc., through an SBIR grant for the National Institute for Deafness and Other Communications Disorders.]

Knowledge-Driven Ultrasonic Three-Dimensional Organ Modeling

A representation is described for nonstructured biologic objects which are single-valued distortions of a sphere. The representation is implemented in a model-driven system for extracting three-dimensional (3-D) organ reconstructions from a series of arbitrarily oriented ultrasound slices. A training set of ultrasonic reconstructions of similarly shaped objects is used to give the computer generic knowledge of a given shape class. This knowledge is in the form of local slope constraints defined on an object coordinate system. The combination of constraints, interacting together via a relaxation process on continuous label sets, attempts to capture the essential shape and range of variation for an organ class. An initial tolerance region and ``bestguess'' organ surface are established by the interaction of the learned shape knowledge with manually input organ landmarks. A hypothesize-verify paradigm is employed to alternately request new data and to update the tolerance region and bestguess surface. Examples from runs on two balloon classes are presented. These examples show: 1) the local constraints interact to produce a reasonable global depiction of the essential shape and range of variation, 2) the use of shape knowledge permits accurate results from only one third of the available data, and 3) the 3-D shape knowledge provides a two-dimensional (2-D) tolerance region for plan-guided edge detection.

Minimum bandwidth signals with various combinations of specified waveform parameters

For each of four separate conditions placed on a waveform (amplitudes at certain epochs and slopes at those epochs), constraints on the corresponding spectra are obtained for a system of any bandwidth. Waveforms which satisfy certain combinations of amplitude and slope constraints, within a minimum bandwidth, are shown to have unique spectra. The method confirms that Nyquist's first and second conditions are satisfied by the raised-cosine frequency spectrum, and spectra are obtained for other waveform conditions. The results are of interest in practical systems where constraints are placed on intersymbol interference and telegraph distortion, or as design targets in theoretical systems.

Ellipse, arc of ellipse and elliptic spline

A general method for generating ellipses by using conjugate radii is presented. Elliptical arcs are then defined based on this method for generating ellipses. A 90° arc of ellipse is then used to generate a number of curves with slope constraints. Other arc of ellipse interpolations are then discussed. Three of these interpolations are used to define local elliptic splines with first order derivative continuity.

Minimum bandwidth signals with some specified waveform parameters

For each of four separate conditions placed on a waveform (amplitudes at certain epochs, and slopes at those epochs) constraints on the corresponding spectra are obtained for a system of any bandwidth. Waveforms which satisfy certain combinations of amplitude and slope constraints, within a minimum bandwidth, are shown to have unique spectra. The method confirms that Nyquist's first and second conditions are satisfied by the raised-cosine frequency spectrum, and spectra are obtained for other waveform conditions. The new results are of interest in practical systems where constraints are placed on intersymbol interference and telegraph distortion or in theoretical systems as design targets.

A modification over Sakoe and Chiba's dynamic time warping algorithm for isolated word recognition

A modification over Sakoe and Chiba's dynamic time warping algorithm for isolated word recognition is proposed. It is shown that this modified algorithm works better without any slope constraint. Also, this algorithm not only consumes less computation time but also improves the word recognition accuracy.

Dynamic programming algorithm optimization for spoken word recognition

This paper reports on an optimum dynamic progxamming (DP) based time-normalization algorithm for spoken word recognition. First, a general principle of time-normalization is given using time-warping function. Then, two time-normalized distance definitions, called symmetric and asymmetric forms, are derived from the principle. These two forms are compared with each other through theoretical discussions and experimental studies. The symmetric form algorithm superiority is established. A new technique, called slope constraint, is successfully introduced, in which the warping function slope is restricted so as to improve discrimination between words in different categories. The effective slope constraint characteristic is qualitatively analyzed, and the optimum slope constraint condition is determined through experiments. The optimized algorithm is then extensively subjected to experimental comparison with various DP-algorithms, previously applied to spoken word recognition by different research groups. The experiment shows that the present algorithm gives no more than about two-thirds errors, even compared to the best conventional algorithm.

On the Response of Linear Systems to Inputs with Limited Amplitudes and Slopes

The necessary and sufficient conditions for an input vector, whose components satisfy amplitude and slope constraints, to be the unique input vector which maximizes (minimizes) any specified linear combination of the elements of the output vector of a linear system are given. The existence of a singular case in which many input vectors give the same result is established. In either case, the derived conditions permit the construction of the desired extremal inputs.