Accurate Parameter Estimation of Contaminant Transport Inverse Problem using Particle Swarm Optimization

Swarm Intelligence techniques such as particle swarm optimization (PSO) are shown to be incompetent for an accurate estimation of global solutions in several engineering applications. This problem is more severe in case of inverse optimization problems where fitness calculations are computationally expensive. In this work, a novel strategy is introduced to alleviate this problem. The proposed inverse model based on modified particle swarm optimization algorithm is applied for a contaminant transport inverse model. The inverse models based on standard-PSO and proposed-PSO are validated to estimate the accuracy of the models. The proposed model is shown to be out performing the standard one in terms of accuracy in parameter estimation. The preliminary results obtained using the proposed model is presented in this work.

Agents Based Algorithms for Design Parameter Estimation in Contaminant Transport Inverse Problems

A considerable amount of work has been dedicated on the development of analytical solutions for flow of chemical contaminants through soils. Most of the analytical solutions for complex transport problems are closed-form series solutions. The convergence of these solutions depends on the eigen values obtained from a corresponding transcendental equation. Thus, the difficulty in obtaining exact solutions from analytical models encourages the use of numerical solutions for the parameter estimation even though, the later models are computationally expensive. In this paper a combination of two swarm intelligence based algorithms are used for accurate estimation of design transport parameters from the closed-form analytical solutions. Estimation of eigen values from a transcendental equation is treated as a multimodal discontinuous function optimization problem. The eigen values are estimated using an algorithm derived based on glowworm swarm strategy. Parameter estimation of the inverse problem is handled using standard PSO algorithm. Integration of these two algorithms enables an accurate estimation of design parameters using closed-form analytical solutions. The present solver is applied to a real world inverse problem in environmental engineering. The inverse model based on swarm intelligence techniques is validated and the accuracy in parameter estimation is shown. The proposed solver quickly estimates the design parameters with a great precision.

Optimum design of cantilever sheet pile walls in sandy soils using inverse reliability approach

In this paper an approach for obtaining depth and section modulus of the cantilever sheet pile wall using inverse reliability method is described. The proposed procedure employs inverse first order reliability method to obtain the design penetration depth and section modulus of the steel sheet pile wall in order that the reliability of the wall against failure modes must meet a desired level of safety. Sensitivity analysis is conducted to assess the effect of uncertainties in design parameters on the reliability of cantilever sheet pile walls. The analysis is performed by treating back fill soil properties, depth of the water table from the top of the sheet pile wall, yield strength of steel and section modulus of steel pile as random variables. Two limit states, viz., rotational and flexural failure of sheet pile wall are considered. The results using this approach are used to develop a set of reliability based design charts for different coefficients of variation of friction angle of the backfill (5%, 10% and 15%). System reliability considerations in terms of series and parallel systems are also studied.

Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

Solving MDPs using two-timescale simulated annealing with multiplicative weights

We develop extensions of the Simulated Annealing with Multiplicative Weights (SAMW) algorithm that proposed a method of solution of Finite-Horizon Markov Decision Processes (FH-MDPs). The extensions developed are in three directions: a) Use of the dynamic programming principle in the policy update step of SAMW b) A two-timescale actor-critic algorithm that uses simulated transitions alone, and c) Extending the algorithm to the infinite-horizon discounted-reward scenario. In particular, a) reduces the storage required from exponential to linear in the number of actions per stage-state pair. On the faster timescale, a 'critic' recursion performs policy evaluation while on the slower timescale an 'actor' recursion performs policy improvement using SAMW. We give a proof outlining convergence w.p. 1 and show experimental results on two settings: semiconductor fabrication and flow control in communication networks.

Adaptive dendron: A bile acid oligomer behaving as both normal and inverse micellar mimic

The normal and inverse micellar property of a bile-acid-based dendritic structure was established through dye solubilization studies in both polar and nonpolar media.

Composite signal decomposition by digital inverse filtering

Inverse filters are conventionally used for resolving overlapping signals of identical waveshape. However, the inverse filtering approach is shown to be useful for resolving overlapping signals, identical or otherwise, of unknown waveshapes. Digital inverse filter design based on autocorrelation formulation of linear prediction is known to perform optimum spectral flattening of the input signal for which the filter is designed. This property of the inverse filter is used to accomplish composite signal decomposition. The theory has been presented assuming constituent signals to be responses of all-pole filters. However, the approach may be used for a general situation.

An integer arithmetic method to compute generalized matrix inverse and solve linear equations exactly

An algorithm that uses integer arithmetic is suggested. It transforms anm ×n matrix to a diagonal form (of the structure of Smith Normal Form). Then it computes a reflexive generalized inverse of the matrix exactly and hence solves a system of linear equations error-free.

Generation of Flat and Curved Membranes by Inverse-BAR Domain Proteins

Biological membranes are tightly linked to the evolution of life, because they provide a way to concentrate molecules into partially closed compartments. The dynamic shaping of cellular membranes is essential for many physiological processes, including cell morphogenesis, motility, cytokinesis, endocytosis, and secretion. It is therefore essential to understand the structure of the membrane and recognize the players that directly sculpt the membrane and enable it to adopt different shapes. The actin cytoskeleton provides the force to push eukaryotic plasma membrane in order to form different protrusions or/and invaginations. It has now became evident that actin directly co-operates with many membrane sculptors, including BAR domain proteins, in these important events. However, the molecular mechanisms behind BAR domain function and the differences between the members of this large protein family remain largely unresolved. In this thesis, the structure and functions of the I-BAR domain family members IRSp53 and MIM were thoroughly analyzed. By using several methods such as electron microscopy and systematic mutagenesis, we showed that these I-BAR domain proteins bind to PI(4,5)P2-rich membranes, generate negative membrane curvature and are involved in the formation of plasma membrane protrusions in cells e.g. filopodia. Importantly, we characterized a novel member of the BAR-domain superfamily which we named Pinkbar. We revealed that Pinkbar is specifically expressed in kidney and epithelial cells, and it localizes to Rab13-positive vesicles in intestinal epithelial cells. Remarkably, we learned that the I-BAR domain of Pinkbar does not generate membrane curvature but instead stabilizes planar membranes. Based on structural, mutagenesis and biochemical work we present a model for the mechanism of the novel membrane deforming activity of Pinkbar. Collectively, this work describes the mechanism by which I-BAR domain proteins deform membranes and provides new information about the biological roles of these proteins. Intriguingly, this work also gives evidence that significant functional plasticity exists within the I-BAR domain family. I-BAR proteins can either generate negative membrane curvature or stabilize planar membrane sheets, depending on the specific structural properties of their I-BAR domains. The results presented in this thesis expand our knowledge on membrane sculpting mechanisms and shows for the first time how flat membranes can be generated in cells.

Inverse problem for the wave equation : partial data and novel boundary sources

An inverse problem for the wave equation is a mathematical formulation of the problem to convert measurements of sound waves to information about the wave speed governing the propagation of the waves. This doctoral thesis extends the theory on the inverse problems for the wave equation in cases with partial measurement data and also considers detection of discontinuous interfaces in the wave speed. A possible application of the theory is obstetric sonography in which ultrasound measurements are transformed into an image of the fetus in its mother's uterus. The wave speed inside the body can not be directly observed but sound waves can be produced outside the body and their echoes from the body can be recorded. The present work contains five research articles. In the first and the fifth articles we show that it is possible to determine the wave speed uniquely by using far apart sound sources and receivers. This extends a previously known result which requires the sound waves to be produced and recorded in the same place. Our result is motivated by a possible application to reflection seismology which seeks to create an image of the Earth s crust from recording of echoes stimulated for example by explosions. For this purpose, the receivers can not typically lie near the powerful sound sources. In the second article we present a sound source that allows us to recover many essential features of the wave speed from the echo produced by the source. Moreover, these features are known to determine the wave speed under certain geometric assumptions. Previously known results permitted the same features to be recovered only by sequential measurement of echoes produced by multiple different sources. The reduced number of measurements could increase the number possible applications of acoustic probing. In the third and fourth articles we develop an acoustic probing method to locate discontinuous interfaces in the wave speed. These interfaces typically correspond to interfaces between different materials and their locations are of interest in many applications. There are many previous approaches to this problem but none of them exploits sound sources varying freely in time. Our use of more variable sources could allow more robust implementation of the probing.

Inverse relationship of the dehydrogenase and ADP-ribosylation activities in sodium-nitroprusside-treated glyceraldehyde-3-phosphate dehydrogenase is coincidental

Incubation of glyceraldehyde-3-phosphate dehydrogenase (GAPD) with sodium nitroprusside (SNP) decreased its activity in concentration- and time-dependent fashion in the presence of a thiol compounds, with DTT being more effective than GSH. Both forward and backward reactions were effected. Coinciding with this, HgCl2-sensitive labelling of the protein by [32P]NAD+ also increased, indicating the stimulation of ADP-ribosylation. Treatment with SNP of GAPD samples from rabbit muscle, sheep brain and yeast inactivated the dehydrogenase activity of the three, but only the mammalian proteins showed ADP-ribosylation activity. The SNP-modified protein of rabbit muscle GAPD, freed from the reagent by Sephadex filtration showed a concentration-dependent restoration of the dehydrogenase activity on preincubation with DTT and GSH. Such thiol-treated preparations also gave increased ADP-ribosylation activity with DTT, and to a lesser extent with GSH. The SNP-modified protein was unable to catalyze this activity with the native yeast enzyme and native and heat-inactivated muscle enzyme. It was possible to generate the ADP-ribosylation activity in muscle GAPD, by an NO-independent mechanism, on dialysis in Tris buffer under aerobic conditions , and on incubating with NADPH, but not NADH, in muscle and brain, but not yeast, enzymes. The results suggest that the inverse relationship of the dehydrogenase and ADP-ribosylation activities is coincidental but not correlated

Flat rotation curves: A result of the helical inverse cascade in turbulent media

We have modeled the rotation curves of 21 galaxies observed by Amram et al. (1992), by combining the effects of rigid rotation, gravity, and turbulence. The main motivation behind such modeling is to study the formation of coherent structures in turbulent media and explore its role in the large-scale structures of the universe. The values of the parameters such as mass, turbulent velocity, and angular velocity derived from the rotation curve fits are in good agreement with those derived from the prevalent models.

Boson Inverse Operators and a New Family of Two-photon Annihilation Operators

We introduce the inverse of the Hermitian operator (acircacirc†) and express the Boson inverse operators acirc-1 and acirc†-1 in terms of the operators acirc, acirc† and (acircacirc†)-1. We show that these Boson inverse operators may be realized by Susskind-Glogower phase operators. In this way, we find a new two-photon annihilation operator and denote it as acirc2(acircacirc†)-1. We show that the eigenstates of this operator have interesting non-classical properties. We find that the eigenstates of the operators (acircacirc†)-1 acirc2, acirc(acircacirc†)-1 acirc and acirc2(acircacirc†)-1 have many similar properties and thus they constitute a family of two-photon annihilation operators.