Experiments with Active-Set LP Algorithms Allowing Basis Deficiency

n interesting question for linear programming (LP) algorithms is how to deal with solutions in which the number of nonzero variables is less than the number of rows of the matrix in standard form. An approach is that of basis deficiency-allowing (BDA) simplex variations, which work with a subset of independent columns of the coefficient matrix in standard form, wherein the basis is not necessarily represented by a square matrix. We describe one such algorithm with several variants. The research question deals with studying the computational behaviour by using small, extreme cases. For these instances, we must wonder which parameter setting or variants are more appropriate. We compare the setting of two nonsimplex active-set methods with Holmström’s TomLab LpSimplex v3.0 commercial sparse primal simplex commercial implementation. All of them update a sparse QR factorization in Matlab. The first two implementations require fewer iterations and provide better solution quality and running time.This work has been funded by grant PID2021-123278OB-I00 from the Spanish Ministry of Science and Innovation. Partial funding for open access charge: Universidad de Málag

Row generation techniques for approximate solution of linear programming problems

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Science of Bilkent University, 2010.Thesis (Master's) -- Bilkent University, 2010.Includes bibliographical references leaves 69-77.In this study, row generation techniques are applied on general linear programming problems with a very large number of constraints with respect to the problem dimension. A lower bound is obtained for the change in the objective value caused by the generation of a specific row. To achieve row selection that results in a large shift in the feasible region and the objective value at each row generation iteration, the lower bound is used in the comparison of row generation candidates. For a warm-start to the solution procedure, an effective selection of the subset of constraints that constitutes the initial LP is considered. Several strategies are discussed to form such a small subset of constraints so as to obtain an initial solution close to the feasible region of the original LP. Approximation schemes are designed and compared to make possible the termination of row generation at a solution in the proximity of an optimal solution of the input LP. The row generation algorithm presented in this study, which is enhanced with a warm-start strategy and an approximation scheme is implemented and tested for computation time and the number of rows generated. Two efficient primal simplex method variants are used for benchmarking computation times, and the row generation algorithm appears to perform better than at least one of them especially when number of constraints is large.Paç, A BurakM.S

A phase-1 approach for the generalized simplex algorithm

AbstractA new simplex variant allowing basis deficiency has recently been proposed to attack the degeneracy [1]. As a generalization of the simplex algorithm, it uses a Phase-1 procedure, solving an auxiliary problem with piecewise-linear sums of infeasibilities as its objective. In this paper, we develop another Phase-1 approach that only introduces a single artificial variable. Unlike the former, which needs a crash procedure to supply an initial basis, the proposed Phase-1 is able to get itself started from scratch, with an artificial basis having a single column. Computational results with a set of standard test problems from NETLIB are also reported

Radial Basis Functions: Biomedical Applications and Parallelization

Radial basis function (RBF) is a real-valued function whose values depend only on the distances between an interpolation point and a set of user-specified points called centers. RBF interpolation is one of the primary methods to reconstruct functions from multi-dimensional scattered data. Its abilities to generalize arbitrary space dimensions and to provide spectral accuracy have made it particularly popular in different application areas, including but not limited to: finding numerical solutions of partial differential equations (PDEs), image processing, computer vision and graphics, deep learning and neural networks, etc. The present thesis discusses three applications of RBF interpolation in biomedical engineering areas: (1) Calcium dynamics modeling, in which we numerically solve a set of PDEs by using meshless numerical methods and RBF-based interpolation techniques; (2) Image restoration and transformation, where an image is restored from its triangular mesh representation or transformed under translation, rotation, and scaling, etc. from its original form; (3) Porous structure design, in which the RBF interpolation used to reconstruct a 3D volume containing porous structures from a set of regularly or randomly placed points inside a user-provided surface shape. All these three applications have been investigated and their effectiveness has been supported with numerous experimental results. In particular, we innovatively utilize anisotropic distance metrics to define the distance in RBF interpolation and apply them to the aforementioned second and third applications, which show significant improvement in preserving image features or capturing connected porous structures over the isotropic distance-based RBF method. Beside the algorithm designs and their applications in biomedical areas, we also explore several common parallelization techniques (including OpenMP and CUDA-based GPU programming) to accelerate the performance of the present algorithms. In particular, we analyze how parallel programming can help RBF interpolation to speed up the meshless PDE solver as well as image processing. While RBF has been widely used in various science and engineering fields, the current thesis is expected to trigger some more interest from computational scientists or students into this fast-growing area and specifically apply these techniques to biomedical problems such as the ones investigated in the present work

Nonlinear control of an industrial robot

The precise control of a robot manipulator travelling at high speed constitutes a major research challenge. This is due to the nonlinear nature of the dynamics of the arm which make many traditional, linear control methodologies inappropriate. An alternative approach is to adopt controllers which are themselves nonlinear. Variable structure control systems provide the possibility of imposing dynamic characteristics upon a poorly modelled and time varying system by means of a discontinuous control signal. The basic algorithm overcomes some nonlinear effects but is sensitive to Coulomb friction andactuator saturation. By augmenting this controller with compensation terms, these effects may largely be eliminated.In order to investigate these ideas, a number of variable structure control systems ~re applied to a low cost industrial robot having a highly nonlinear and flexible drive system. By a combination of hardware enhancements and control system developments, an improvement in speed by a factor of approximately three was achieved while the trajectory tracking accuracy was improved by a factor of ten, compared with the manufacturer's control system.In order to achieve these improvements, it was necessary to develop a dynamic model of the arm including the effects of drive system flexibility and nonlinearities. The development of this model is reported in this thesis, as is work carried out on a comparison of numerical algorithms for the solution of differential equations with discontinuous right hand sides, required in the computer aided design of variable structure control systems

Effects of Wingwall Configurations on the Behavior of Integral Abutment Bridges

This research includes parametric studies performed with the use of three-dimensional nonlinear finite element models in order to investigate the effects of cantilever wingwall configurations on the behavior of integral abutment bridges located on straight alignment and zero skew. The parametric studies include all three types of cantilever wingwalls; inline, flared, and U-shaped wingwalls. Bridges analyzed vary in length from 100 to 1200 feet. Soil-structure and soil-pile interaction are included in the analysis. Loadings include dead load in combination with temperature loads in both rising and falling temperatures. Plasticity in the integral abutment piles is investigated by means of nonlinear plasticity models. Cracking in the abutments and stresses in the reinforcing steel are investigated by means of nonlinear concrete models. The effects of wingwall configurations are assessed in terms of stresses in the integral abutment piles, cracking in the abutment walls, stresses in the reinforcing steel of abutment walls, and axial forces induced in the steel girders. The models developed are analyzed for three types of soil behind the abutments and wingwalls; dense sand, medium dense sand, and loose sand. In addition, the models consider both the case of presence and absence of predrilled holes at the top nine feet of piles. The soil around the piles below the predrilled holes consists of very stiff clay. The results indicate that for the stresses in the piles, the critical load is temperature contraction and the most critical parameter is the use of predrilled holes. However, for both the stresses in the reinforcing steel and the axial forces induced in the girders, the critical load is temperature expansion and the critical parameter is the bridge length. In addition, the results indicate that the use of cantilever wingwalls in integral abutment bridges results in an increase in the magnitude of axial forces in the steel girders during temperature expansion and generation of pile plasticity at shorter bridge lengths compared to bridges built without cantilever wingwalls

Damping at Every Turn: Maneuvers and Stability in the Free Flight of Hawkmoth Manduca sexta

Here I identify novel stability features in flapping flight. Implications may shift the current scientific consensus that flying animals, particularly insects, must actively monitor and respond to even slight perturbations to maintain control in pitch and roll, and allow engineers to recreate these capabilities in flying robots. Results are consistent with co-directional inertial and viscous effects working together to damp rotations. This could explain flight stability across a broad range of body sizes, speeds, and flapping frequencies. I propose a previously undescribed, likely ubiquitous class of passive “inertio-viscous” damping. Flapping wings move, so rotational perturbations on the time scale of halfstrokes manifest as wing position/orientation changes later in the flapping cycle. My novel results show these (at least partially) passive (inertia-based) kinematic responses push on the air to produce torques that oppose the initial perturbation. I then identify key design elements which future flapping-wing micro air vehicles could employ to exploit these stability effects. This emerges from a series of three experiments exploring roll and pitch dynamics in hawkmoth Manduca sexta. In the first, I coaxed moths to follow a light and described their lateral maneuver mechanics. I concluded roll is heavily damped, and positive coupling between roll and lateral acceleration, negative coupling between roll and lateral velocity, and countertorque from wing motion around the roll axis, are relevant (viscous/velocity) damping factors. In the second, I launched miniature cannonballs at moths and described their pitch recovery mechanics. I concluded inertial (and viscous) resistance of wing stroke plane to the pitch impulse (and rotational velocity) helps create pendular stability in mid-air. Gyroscopic (and viscous) reactions to pitch impulses (and rotational velocity) manifest as deviations to wing kinematics that further damp pitch, indicating reinforcing roles for inertia and drag in flapping flight stability. In the third, I glued T-bars on moths to create weight imbalances during hover. Results reinforce my conclusions about damping and roll/pitch-associated wing kinematics, show flexibility helps compensate for off-axis loads, and associate a novel wing kinematic with roll torque that suggests gyroscopic and pendular damping mechanisms also complement viscous/velocity-based damping in roll.Doctor of Philosoph

Distribution and regulation of ion channels in neurons: Quantitative studies of global ion channel transport and homeostatic synaptic scaling

A healthy neuron must continually produce millions of proteins and distribute them to function-specific regions of the cell. Among these proteins are ion channels that modulate neuronal excitability, allowing neurons to fulfill their primary role of information transfer. Neurons are unique among cells in their morphology, with projections that extend hundreds to thousands of microns. Neuron size and asymmetry pose a challenge for autoregulation of properties that require cargo transport across the cell. Homeostasis of ion channel localization has strong implications for neural excitability. This thesis concerns the intracellular distribution of ion channels in the context of longitudinal transport and global neuron regulation. The principal contributions are experimental measurements, data analysis, and modeling in the study of longitudinal neurite transport. Empirical investigations focus on the distribution and trafficking kinetics of ion channel Kv4.2, including quantitative measurements of both passive diffusion and active microtubule-based transport in both axons and dendrites (Chapters 3 and 5). Mass action models reveal that measured transport profiles corroborate discrepancies in Kv4.2 localization both between neurite types and along the somatodendritic axis (Chapter 4). Exchange between mobile and immobile fractions, inferred from analysis of repeated photobleaching, shapes intracellular distribution of Kv4.2 (Chapter 5). Further, the ensuing theoretical study surveys global regulation of ion channels, specifically for synaptic scaling, which requires cell-wide modulation of AMPA receptors for normalization of neural excitability. A unified model of synaptic potentiation, transport, and feedback reveals limitations imposed on synaptic scaling by neuron morphology. A neuron balances the stability, accuracy, and efficiency of synaptic scaling (Chapter 6).National Institutes of Health Oxford-Cambridge Scholars Gates Cambridge University of North Carolina Medical Scientist Training Progra