Fast Dating Using Least-Squares Criteria and Algorithms

FindMinimum No code example is currently available or this language may not be supported. FindMinimum Termination Criteria Optimization algorithms in multiple dimensions commonly have two or three criteria that may each signal that an extremum has been found. The ValueTest property returns a SimpleConvergenceTest object that represents the convergence test based on the value of the objective function. The test is successful if the change in the value of the objective function is less than the tolerance. The test returns a value of Divergent if the value of the objective function is infinite, and BadFunction when the value is NaN. There is some danger in using this test, since some algorithms may not return a new best estimate for the extremum on each iteration. For this reason, the test is not active by default. To make it active, its Active property must be set to true. The SolutionTest property returns a VectorConvergenceTest object that represents the convergence test based on the estimated extremum. The test is successful if the change in the approximate extremum is less than the tolerance.

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International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research.

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Graduate School of Business

This article has been cited by other articles in PMC. Abstract Phylogenies provide a useful way to understand the evolutionary history of genetic samples, and data sets with more than a thousand taxa are becoming increasingly common, notably with viruses e. Dating ancestral events is one of the first, essential goals with such data. However, current sophisticated probabilistic approaches struggle to handle data sets of this size. Here, we present very fast dating algorithms, based on a Gaussian model closely related to the Langley—Fitch molecular-clock model.

We show that this model is robust to uncorrelated violations of the molecular clock.

Papers Using Special Mplus Features. References on this page are ordered by topic. References can also be viewed ordered by date.. Bayesian Analysis expand topic.

For descriptions of the algorithms, see Quadratic Programming Algorithms. Medium-Scale Algorithms An optimization algorithm is large scale when it uses linear algebra that does not need to store, nor operate on, full matrices. This may be done internally by storing sparse matrices, and by using sparse linear algebra for computations whenever possible.

Furthermore, the internal algorithms either preserve sparsity, such as a sparse Cholesky decomposition, or do not generate matrices, such as a conjugate gradient method. In contrast, medium-scale methods internally create full matrices and use dense linear algebra. If a problem is sufficiently large, full matrices take up a significant amount of memory, and the dense linear algebra may require a long time to execute.

Furthermore, you do not need to specify any sparse matrices to use a large-scale algorithm. Choose a medium-scale algorithm to access extra functionality, such as additional constraint types, or possibly for better performance. Potential Inaccuracy with Interior-Point Algorithms Interior-point algorithms in fmincon, quadprog, lsqlin, and linprog have many good characteristics, such as low memory usage and the ability to solve large problems quickly.

However, their solutions can be slightly less accurate than those from other algorithms. The reason for this potential inaccuracy is that the internally calculated barrier function keeps iterates away from inequality constraint boundaries.

Mathematical Problems in Engineering

A simple change of variables yields , which is in the same form as the unweighted case. To manually perform this transformation, the residuals and Jacobian should be modified according to For large systems, the user must perform their own weighting. This method is available only for large systems. This choice of makes the problem scale-invariant, so that if the model parameters are each scaled by an arbitrary constant, , then the sequence of iterates produced by the algorithm would be unchanged.


VIPR vastly undersampled isotropic projection reconstruction 2D digital subtraction angiography and a 3D rotational angiography acquisition followed by 3D-DSA reconstruction are the standards for vascular morphology assessment. There is an increasing demand for hemodynamic information, including blood flow rate and velocity for diagnosis, treatment planning, and evaluation. The availability of the geometric and temporal data in a 4D-DSA reconstruction provides the opportunity to estimate velocity and flow more accurately than has previously been possible with 2D DSA.

In this article, a shifted least-squares based technique was used with the 4D-DSA data to estimate blood velocity. The proposed algorithm was first validated using flow phantom studies, in which the velocity could be documented using an ultrasonic flow probe. The rotational acquisition protocol yields x-ray projection images, which are used to automatically reconstruct both 3D-DSA and 4D-DSA with an isotropic spatial resolution of 0. The centerline of each vascular segment was determined from the static 3D volume using an efficient 3D parallel-thinning algorithm.

Shifted Least-Squares Algorithm In an arterial contrast injection, there is a temporal oscillation in iodine concentration that arises from the mixing of contrast medium, which is injected at a fixed rate, and nonopacified blood, which flows at a variable rate driven by the cardiac cycle. This temporal variation in contrast, referred to as pulsatility, appears at points downstream of the injection with a time delay.

The time delay is related to the distance downstream and the blood velocity. Therefore, velocity can be estimated by measuring the distance along the vessel centerline and the time delay. The spatial distance z between the 2 points is calculated from the 3D path length along the vessel centerline. Optimizing Waveform Selection It has been found that the shifted least-squares algorithm provides the most reliable velocity calculation in vessel segments where pulsatility is strong and consistent.

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Advanced Search Abstract Phylogenies provide a useful way to understand the evolutionary history of genetic samples, and data sets with more than a thousand taxa are becoming increasingly common, notably with viruses e. Dating ancestral events is one of the first, essential goals with such data. However, current sophisticated probabilistic approaches struggle to handle data sets of this size. Here, we present very fast dating algorithms, based on a Gaussian model closely related to the Langley—Fitch molecular-clock model.

A3: Accurate, Adaptable, and Accessible Error Metrics for Predictive Models: abbyyR: Access to Abbyy Optical Character Recognition (OCR) API: abc: Tools for.

However, the practical implementation of DVC involves important challenges such as implementation complexity, calculation accuracy and computational efficiency. In this paper, a least-squares framework is presented for 3D internal displacement and strain field measurement using DVC. The proposed DVC combines a practical linear-intensity-change model with an easy-to-implement iterative least-squares ILS algorithm to retrieve 3D internal displacement vector field with sub-voxel accuracy.

Because the linear-intensity-change model is capable of accounting for both the possible intensity changes and the relative geometric transform of the target subvolume, the presented DVC thus provides the highest sub-voxel registration accuracy and widest applicability. Furthermore, as the ILS algorithm uses only first-order spatial derivatives of the deformed volumetric image, the developed DVC thus significantly reduces computational complexity.

To further extract 3D strain distributions from the 3D discrete displacement vectors obtained by the ILS algorithm, the presented DVC employs a pointwise least-squares algorithm to estimate the strain components for each measurement point.

Levenberg-Marquardt algorithm

Structural equation modeling SEM depicts one of the most salient research methods across a variety of disciplines, including hospitality management. While for many researchers, SEM is equivalent to carrying We systematically examine how PLS-SEM has been applied in major hospitality research journals with the aim of providing important guidance and, if necessary, opportunities for realignment in future applications. As PLS-SEM in hospitality research is still in an early stage of development, critically examining its use holds considerable promise in order to counteract misapplications which otherwise might reinforce over time.

Tying in with prior studies in the field, our review covers reasons for using PLS-SEM, data characteristics, model characteristics, the evaluation of the measurement models, the evaluation of the structural model, reporting, and use of advanced analyses. Compared to other fields, our results show that several reporting practices are clearly above standard but still leave room for improvement, particularly regarding the consideration of state-of-the art metrics for measurement and structural model assessment.

1: Offered jointly with the School of Biological Sciences and The Paul Merage School of Business. See School of Biological Sciences section of the Catalogue for information.. 2: Offered jointly with the Donald Bren School of Information and Computer Sciences.

In this context of changing and challenging market requirements, Gas Insulated Substation GIS has found a broad range of applications in power systems for more than two decades because of its high reliability, easy maintenance and small ground space requirement etc. SF6 has been of considerable technological interest as an insulation medium in GIS because of its superior insulating properties, high dielectric strength at relatively low pressure and its thermal and chemical stability. SF6 is generally found to be very sensitive to field perturbations such as those caused by conductor surface imperfections and by conducting particle contaminants.

The presence of contamination can therefore be a problem with gas insulated substations operating at high fields. If the effects of these particles could be eliminated, then this would improve the reliability of compressed gas insulated substation. It would also offer the possibility of operating at higher fields to affect a potential reduction in the GIS size with subsequent savings in the cost of manufacture and installation.

The purpose of this paper is to develop techniques, which will formulate the basic equations that will govern the movement of metallic particles like aluminum, copper in a coated as well as uncoated busduct. In recent years, the areas of industrial application of AC drives, especially Induction machine based on DTC technique has gradually increased due to its advantages over the other techniques of control. However conventional DTC suffers from high torque ripple and variable switching frequency.

PLS (Partial Least Squares) Methods

Advanced Search Abstract The main outcome of molecular dating, the timetree, provides crucial information for understanding the evolutionary history of lineages and is a requirement of several evolutionary analyses. Although essential, the estimation of divergence times from molecular data is frequently regarded as a complicated task. However, establishing biological timescales can be performed in a straightforward manner, even with large, genome-wide data sets.

1. Introduction. Since the early s, the process of deregulation and the introduction of competitive markets have been reshaping the landscape of the traditionally .

However, current sophisticated probabilistic approaches struggle to handle data sets of this size. Here, we present very fast dating algorithms, based on a Gaussian model closely related to the Langley—Fitch molecular-clock model. We show that this model is robust to uncorrelated violations of the molecular clock. Our algorithms apply to serial data, where the tips of the tree have been sampled through times.

They estimate the substitution rate and the dates of all ancestral nodes. When t he input tree is unrooted, they can provide an estimate for the root position, thus representing a new, practical alternative to the standard rooting methods e. Our algorithms exploit the tree recursive structure of the problem at hand, and the close relationships between least- squares and linear algebra. We distinguish between an unconstrained setting and the case where the temporal precedence constraint i.

With rooted trees, the former is solved using linear algebra in linear computing time i. With unrooted trees the computing time becomes nearly quadratic i. Using simulated data, we show that their estimation accuracy is similar to that of the most sophisticated met hods, while their computing time is much faster. Again the results show that these algorithms provide a very fast alternative with results similar to those of other computer programs. These algorithms are implemented in the LSD software least-squares dating , which can be downloaded from http:

Journal of Applied Mathematics

Overview T he Basic FLS Approach Any real-world system that a researcher attempts to model will inevitably behave in a manner that is incompatible to some degree with the theoretical assumptions the researcher has incorporated in the model. Box, These theoretical assumptions typically fall into four conceptually-distinct categories: Discrepancies between the theoretical assumptions 1 – 4 and the actual real-world system of interest are called model specification errors.

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Object containing the optimized parameter and several goodness-of-fit statistics. Changed in version 0. Return value changed to MinimizerResult. Notes The objective function should return the value to be minimized. For the Levenberg-Marquardt algorithm from leastsq , this returned value must be an array, with a length greater than or equal to the number of fitting variables in the model. For the other methods, the return value can either be a scalar or an array.

If an array is returned, the sum of squares of the array will be sent to the underlying fitting method, effectively doing a least-squares optimization of the return values. A common use for and kws would be to pass in other data needed to calculate the residual, including such things as the data array, dependent variable, uncertainties in the data, and other data structures for the model calculation.

On output, params will be unchanged. The best-fit values and, where appropriate, estimated uncertainties and correlations, will all be contained in the returned MinimizerResult. See MinimizerResult — the optimization result for further details. This function is simply a wrapper around Minimizer and is equivalent to:

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