Incoherence-based optimal selection of independent measurements in diffuse optical tomography

An optimal measurement selection strategy based on incoherence among rows (corresponding to measurements) of the sensitivity (or weight) matrix for the near infrared diffuse optical tomography is proposed. As incoherence among the measurements can be seen as providing maximum independent information into the estimation of optical properties, this provides high level of optimization required for knowing the independency of a particular measurement on its counterparts. The proposed method was compared with the recently established data-resolution matrix-based approach for optimal choice of independent measurements and shown, using simulated and experimental gelatin phantom data sets, to be superior as it does not require an optimal regularization parameter for providing the same information. (C) 2014 Society of Photo-Optical Instrumentation Engineers (SPIE)

Optimal control of information epidemics modeled as Maki Thompson rumors

We model the spread of information in a homogeneously mixed population using the Maki Thompson rumor model. We formulate an optimal control problem, from the perspective of single campaigner, to maximize the spread of information when the campaign budget is fixed. Control signals, such as advertising in the mass media, attempt to convert ignorants and stiflers into spreaders. We show the existence of a solution to the optimal control problem when the campaigning incurs non-linear costs under the isoperimetric budget constraint. The solution employs Pontryagin's Minimum Principle and a modified version of forward backward sweep technique for numerical computation to accommodate the isoperimetric budget constraint. The techniques developed in this paper are general and can be applied to similar optimal control problems in other areas. We have allowed the spreading rate of the information epidemic to vary over the campaign duration to model practical situations when the interest level of the population in the subject of the campaign changes with time. The shape of the optimal control signal is studied for different model parameters and spreading rate profiles. We have also studied the variation of the optimal campaigning costs with respect to various model parameters. Results indicate that, for some model parameters, significant improvements can be achieved by the optimal strategy compared to the static control strategy. The static strategy respects the same budget constraint as the optimal strategy and has a constant value throughout the campaign horizon. This work finds application in election and social awareness campaigns, product advertising, movie promotion and crowdfunding campaigns. (C) 2014 Elsevier B.V. All rights reserved.

A Stochastic Chemical Dynamic Approach to Correlate Autoimmunity and Optimal Vitamin-D Range

Motivated by several recent experimental observations that vitamin-D could interact with antigen presenting cells (APCs) and T-lymphocyte cells (T-cells) to promote and to regulate different stages of immune response, we developed a coarse grained but general kinetic model in an attempt to capture the role of vitamin-D in immunomodulatory responses. Our kinetic model, developed using the ideas of chemical network theory, leads to a system of nine coupled equations that we solve both by direct and by stochastic (Gillespie) methods. Both the analyses consistently provide detail information on the dependence of immune response to the variation of critical rate parameters. We find that although vitamin-D plays a negligible role in the initial immune response, it exerts a profound influence in the long term, especially in helping the system to achieve a new, stable steady state. The study explores the role of vitamin-D in preserving an observed bistability in the phase diagram (spanned by system parameters) of immune regulation, thus allowing the response to tolerate a wide range of pathogenic stimulation which could help in resisting autoimmune diseases. We also study how vitamin-D affects the time dependent population of dendritic cells that connect between innate and adaptive immune responses. Variations in dose dependent response of anti-inflammatory and pro-inflammatory T-cell populations to vitamin-D correlate well with recent experimental results. Our kinetic model allows for an estimation of the range of optimum level of vitamin-D required for smooth functioning of the immune system and for control of both hyper-regulation and inflammation. Most importantly, the present study reveals that an overdose or toxic level of vitamin-D or any steroid analogue could give rise to too large a tolerant response, leading to an inefficacy in adaptive immune function.

Optimal sequential wireless relay placement on a random lattice path

Our work is motivated by impromptu (or ``as-you-go'') deployment of wireless relay nodes along a path, a need that arises in many situations. In this paper, the path is modeled as starting at the origin (where there is the data sink, e.g., the control center), and evolving randomly over a lattice in the positive quadrant. A person walks along the path deploying relay nodes as he goes. At each step, the path can, randomly, either continue in the same direction or take a turn, or come to an end, at which point a data source (e.g., a sensor) has to be placed, that will send packets to the data sink. A decision has to be made at each step whether or not to place a wireless relay node. Assuming that the packet generation rate by the source is very low, and simple link-by-link scheduling, we consider the problem of sequential relay placement so as to minimize the expectation of an end-to-end cost metric (a linear combination of the sum of convex hop costs and the number of relays placed). This impromptu relay placement problem is formulated as a total cost Markov decision process. First, we derive the optimal policy in terms of an optimal placement set and show that this set is characterized by a boundary (with respect to the position of the last placed relay) beyond which it is optimal to place the next relay. Next, based on a simpler one-step-look-ahead characterization of the optimal policy, we propose an algorithm which is proved to converge to the optimal placement set in a finite number of steps and which is faster than value iteration. We show by simulations that the distance threshold based heuristic, usually assumed in the literature, is close to the optimal, provided that the threshold distance is carefully chosen. (C) 2014 Elsevier B.V. All rights reserved.

Multimodal therapy for complete regression of malignant melanoma using constrained nonlinear optimal dynamic inversion

Using a realistic nonlinear mathematical model for melanoma dynamics and the technique of optimal dynamic inversion (exact feedback linearization with static optimization), a multimodal automatic drug dosage strategy is proposed in this paper for complete regression of melanoma cancer in humans. The proposed strategy computes different drug dosages and gives a nonlinear state feedback solution for driving the number of cancer cells to zero. However, it is observed that when tumor is regressed to certain value, then there is no need of external drug dosages as immune system and other therapeutic states are able to regress tumor at a sufficiently fast rate which is more than exponential rate. As model has three different drug dosages, after applying dynamic inversion philosophy, drug dosages can be selected in optimized manner without crossing their toxicity limits. The combination of drug dosages is decided by appropriately selecting the control design parameter values based on physical constraints. The process is automated for all possible combinations of the chemotherapy and immunotherapy drug dosages with preferential emphasis of having maximum possible variety of drug inputs at any given point of time. Simulation study with a standard patient model shows that tumor cells are regressed from 2 x 107 to order of 105 cells because of external drug dosages in 36.93 days. After this no external drug dosages are required as immune system and other therapeutic states are able to regress tumor at greater than exponential rate and hence, tumor goes to zero (less than 0.01) in 48.77 days and healthy immune system of the patient is restored. Study with different chemotherapy drug resistance value is also carried out. (C) 2014 Elsevier Ltd. All rights reserved.

Microstructure Development, Nanomechanical, and Dynamic Compression Properties of Spark Plasma Sintered TiB2-Ti-Based Homogeneous and Bi-layered Composites

The growing threats due to increased use of small-caliber armor piercing projectiles demand the development of new light-weight body armor materials. In this context, TiB2 appears to be a promising ceramic material. However, poor sinterability and low fracture toughness remain two major issues for TiB2. In order to address these issues together, Ti as a sinter-aid is used to develop TiB2-(x wt pct Ti), (x = 10, 20) homogeneous composites and a bi-layered composite (BLC) with each layer having Ti content of 10 and 20 wt pct. The present study uniquely demonstrates the efficacy of two-stage spark plasma sintering route to develop dense TiB2-Ti composites with an excellent combination of nanoscale hardness (similar to 36 GPa) and indentation fracture toughness (similar to 12 MPa m(1/2)). In case of BLC, these properties are not compromised w.r.t. homogeneous composites, suggesting the retention of baseline material properties even in the bi-layer design due to optimal relief of residual stresses. The better indentation toughness of TiB2-(10 wt pct Ti) and TiB2-(20 wt pct Ti) composites can be attributed to the observed crack deflection/arrest, indicating better damage tolerance. Transmission electron microscope investigation reveals the presence of dense dislocation networks and deformation twins in alpha-Ti at the grain boundaries and triple pockets, surrounded by TiB2 grains. The dynamic strength of around 4 GPa has been measured using Split Hopkinson Pressure Bar tests in a reproducible manner at strain rates of the order of 600 s(-1). The damage progression under high strain rate has been investigated by acquiring real time images for the entire test duration using ultra-high speed imaging. An attempt has been made to establish microstructure-property correlation and a simple analysis based on Mohr-Coulomb theory is used to rationalize the measured strength properties.

Effect of port gas injection on in-cylinder stratification in a CNG fuelled SI engine

The concept of barrel stratification of air-fuel mixture is evaluated for a port gas injection (PGI) single cylinder spark ignition (SI) internal combustion (IC) engine using a transient three-dimensional computational fluid dynamic (CFD) model. The gaseous fuel used in the study is compressed natural gas (CNG). It is observed that compared to the premixed gas carburettor case, a substantial amount of in-cylinder stratification can be achieved with port gas injection system. A detailed parametric study is reported to understand the effect of the various injection parameters such as injection location, injection orientation, start of injection (SOT) and its duration, and injection rate. Furthermore, the best injection timing is evaluated for various load and speed cases. It is observed that the best stratification pattern can be achieved at 50% engine load. The injection location is observed to have a profound effect on the in-cylinder stratification pattern, and injection towards the side of the spark plug is observed to give a rich fuel-air mixture near the spark plug. It is also shown that there exists an optimal injection pressure.

Single network adaptive critic aided dynamic inversion for optimal regulation and command tracking with online adaptation for enhanced robustness

To combine the advantages of both stability and optimality-based designs, a single network adaptive critic (SNAC) aided nonlinear dynamic inversion approach is presented in this paper. Here, the gains of a dynamic inversion controller are selected in such a way that the resulting controller behaves very close to a pre-synthesized SNAC controller in the output regulation sense. Because SNAC is based on optimal control theory, it makes the dynamic inversion controller operate nearly optimal. More important, it retains the two major benefits of dynamic inversion, namely (i) a closed-form expression of the controller and (ii) easy scalability to command tracking applications without knowing the reference commands a priori. An extended architecture is also presented in this paper that adapts online to system modeling and inversion errors, as well as reduced control effectiveness, thereby leading to enhanced robustness. The strengths of this hybrid method of applying SNAC to optimize an nonlinear dynamic inversion controller is demonstrated by considering a benchmark problem in robotics, that is, a two-link robotic manipulator system. Copyright (C) 2013 John Wiley & Sons, Ltd.

A simulation-based algorithm for optimal pricing policy under demand uncertainty

We propose a simulation-based algorithm for computing the optimal pricing policy for a product under uncertain demand dynamics. We consider a parameterized stochastic differential equation (SDE) model for the uncertain demand dynamics of the product over the planning horizon. In particular, we consider a dynamic model that is an extension of the Bass model. The performance of our algorithm is compared to that of a myopic pricing policy and is shown to give better results. Two significant advantages with our algorithm are as follows: (a) it does not require information on the system model parameters if the SDE system state is known via either a simulation device or real data, and (b) as it works efficiently even for high-dimensional parameters, it uses the efficient smoothed functional gradient estimator.

Interference-Constrained Optimal Power-Adaptive Amplify-and-Forward Relaying and Selection for Underlay Cognitive Radios

In an underlay cognitive radio (CR) system, a secondary user can transmit when the primary is transmitting but is subject to tight constraints on the interference it causes to the primary receiver. Amplify-and-forward (AF) relaying is an effective technique that significantly improves the performance of a CR by providing an alternate path for the secondary transmitter's signal to reach the secondary receiver. We present and analyze a novel optimal relay gain adaptation policy (ORGAP) in which the relay is interference aware and optimally adapts both its gain and transmit power as a function of its local channel gains. ORGAP minimizes the symbol error probability at the secondary receiver subject to constraints on the average relay transmit power and on the average interference caused to the primary. It is different from ad hoc AF relaying policies and serves as a new and fundamental theoretical benchmark for relaying in an underlay CR. We also develop a near-optimal and simpler relay gain adaptation policy that is easy to implement. An extension to a multirelay scenario with selection is also developed. Our extensive numerical results for single and multiple relay systems quantify the power savings achieved over several ad hoc policies for both MPSK and MQAM constellations.

BELIEF PROPAGATION FOR OPTIMAL EDGE COVER IN THE RANDOM COMPLETE GRAPH

We apply the objective method of Aldous to the problem of finding the minimum-cost edge cover of the complete graph with random independent and identically distributed edge costs. The limit, as the number of vertices goes to infinity, of the expected minimum cost for this problem is known via a combinatorial approach of Hessler and Wastlund. We provide a proof of this result using the machinery of the objective method and local weak convergence, which was used to prove the (2) limit of the random assignment problem. A proof via the objective method is useful because it provides us with more information on the nature of the edge's incident on a typical root in the minimum-cost edge cover. We further show that a belief propagation algorithm converges asymptotically to the optimal solution. This can be applied in a computational linguistics problem of semantic projection. The belief propagation algorithm yields a near optimal solution with lesser complexity than the known best algorithms designed for optimality in worst-case settings.

Dissimilar friction stir welding between aluminum alloy and magnesium alloy at a low rotational speed

A sound weld was obtained between 2024-T3 Al alloy and AZ31B-O Mg alloy dissimilar metal plates of 5 mm thickness, at a rotational speed of 300 rev min(-1) and at a welding speed of 50 mm min(-1). One of the parameter studied was, the effect of interface offset variation, on the quality and properties of the welded samples and on the thickness of intermetallic layer formed in the welded samples. The intermetallic layer at the midst of the weld volume contains intermetallic compounds Al12Mg17 and Al3Mg2. Highest tensile strength of 106.86 MPa, corresponding tensile joint efficiency of 44.52% and corresponding elongation 1.33% were obtained for the tensile sample, with interface offset of 0.66 mm from zero interface offset in retreating side and with approximate least intermetallic thickness of 1.2 mu m. Dissimilar friction stir welded joint samples had failed completely in brittle fracture mode; the position of tensile fracture was located at the midst of intermetallic layer, which had maximum hardness and minimum ductility. The nano hardness values fluctuate in the weld nugget owing to dynamic recrystallization of alloy materials and formation of brittle intermetallic compounds of alloy materials in the weld nugget; maximum hardness of 10.74 GPa occurred for the sample with least intermetallic thickness of 1.2 mu m. (C) 2014 Elsevier B.V. All rights reserved.

Optimal Binary Power Control for Underlay CR With Different Interference Constraints and Impact of Channel Estimation Errors

Adapting the power of secondary users (SUs) while adhering to constraints on the interference caused to primary receivers (PRxs) is a critical issue in underlay cognitive radio (CR). This adaptation is driven by the interference and transmit power constraints imposed on the secondary transmitter (STx). Its performance also depends on the quality of channel state information (CSI) available at the STx of the links from the STx to the secondary receiver and to the PRxs. For a system in which an STx is subject to an average interference constraint or an interference outage probability constraint at each of the PRxs, we derive novel symbol error probability (SEP)-optimal, practically motivated binary transmit power control policies. As a reference, we also present the corresponding SEP-optimal continuous transmit power control policies for one PRx. We then analyze the robustness of the optimal policies when the STx knows noisy channel estimates of the links between the SU and the PRxs. Altogether, our work develops a holistic understanding of the critical role played by different transmit and interference constraints in driving power control in underlay CR and the impact of CSI on its performance.

Capturability Analysis of a 3-D Retro-PN Guidance Law for Higher Speed Nonmaneuvering Targets

This brief presents the capturability analysis of a 3-D Retro-proportional navigation (Retro-PN) guidance law, which uses a negative navigation constant (as against the usual positive one), for intercepting targets having higher speeds than interceptors. This modification makes it possible to achieve collision conditions that were inaccessible to the standard PN law. A modified polar coordinate system, that makes the model more compact, is used in this brief for capturability analysis. In addition to the ratio of the target to interceptor speeds, the directional cosines of the interceptor, and target velocity vectors play a crucial role in the capturability. The existence of nontrivial capture zone of the Retro-PN guidance law and necessary and sufficient conditions, for capturing the target in finite time, are presented. A sufficient condition on the navigation constant is derived to ensure finiteness of the line-of-sight turn rate. The results are more extensive than those available for 2-D engagements, which can be obtained as special cases of this brief. Simulation results are given to support the analytical results.

Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems

In this article, we study the problem of determining an appropriate grading of meshes for a system of coupled singularly perturbed reaction-diffusion problems having diffusion parameters with different magnitudes. The central difference scheme is used to discretize the problem on adaptively generated mesh where the mesh equation is derived using an equidistribution principle. An a priori monitor function is obtained from the error estimate. A suitable a posteriori analogue of this monitor function is also derived for the mesh construction which will lead to an optimal second-order parameter uniform convergence. We present the results of numerical experiments for linear and semilinear reaction-diffusion systems to support the effectiveness of our preferred monitor function obtained from theoretical analysis. (C) 2014 Elsevier Inc. All rights reserved.