Planar and Grid Graph Reachability Problems

We study the complexity of restricted versions of s-t-connectivity, which is the standard complete problem for . In particular, we focus on different classes of planar graphs, of which grid graphs are an important special case. Our main results are:

Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs

We present a deterministic Logspace procedure, which, given a bipartite planar graph on n vertices, assigns O(log n) bits long weights to its edges so that the minimum weight perfect matching in the graph becomes unique. The Isolation Lemma as described in Mulmuley et al. (Combinatorica 7(1):105–131, 1987) achieves the same for general graphs using randomness, whereas we can do it deterministically when restricted to bipartite planar graphs. As a consequence, we reduce both decision and construction versions of the perfect matching problem in bipartite planar graphs to testing whether a matrix is singular, under the promise that its determinant is 0 or 1, thus obtaining a highly parallel SPL\mathsf{SPL} algorithm for both decision and construction versions of the bipartite perfect matching problem. This improves the earlier known bounds of non-uniform SPL\mathsf{SPL} by Allender et al. (J. Comput. Syst. Sci. 59(2):164–181, 1999) and NC\mathsf{NC} ² by Miller and Naor (SIAM J. Comput. 24:1002–1017, 1995), and by Mahajan and Varadarajan (Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing (STOC), pp. 351–357, 2000). It also rekindles the hope of obtaining a deterministic parallel algorithm for constructing a perfect matching in non-bipartite planar graphs, which has been open for a long time. Further we try to find the lower bound on the number of bits needed for deterministically isolating a perfect matching. We show that our particular method for isolation will require Ω(log n) bits. Our techniques are elementary.     

Application of entropy measurement technique in grey based Taguchi method for solution of correlated multiple response optimization problems: A case study in welding

In the present work, an attempt has been made to apply an efficient technique, in order to solve correlated multiple response optimization problems, in the field of submerged arc welding. The traditional grey based Taguchi approach has been extended to tackle correlated multi-objective optimization problems. The Taguchi optimization technique is based on the assumption that the quality indices (i.e. responses) are independent or uncorrelated. But, in practical cases, the assumption may not be valid always. However, the common trend in the solution of multi-objective optimization problems is to initially convert these multi-objectives into an equivalent single objective function. While deriving this equivalent objective function, different priority weights are assigned to different responses, according to their relative importance. But, there is no specific guideline for assigning these response weights. In this context, the present study aims to apply the entropy measurement technique in order to calculate the relative response weights from the analysis of entropy of the entire process. Principal Component Analysis (PCA) has been adopted to eliminate correlation that exists among the responses and to convert correlated responses into uncorrelated and independent quality indices, called principal components. These have been accumulated to calculate the overall grey relational grade, using the theory of grey relational analysis. Finally, the grey based Taguchi method has been used to derive an optimal process environment capable of producing the desired weld quality. The previously mentioned method has been applied to optimize bead geometry parameters of submerged arc bead-on-plate weldment. The paper highlights a detailed methodology of the proposed technique and its effectiveness.     

Monolithic fabrication of electro-fluidic polymer microchips

Integration of electronic wiring with microfluidic chips is an important process as it allows electrical interactions with the fluidic media, for example required for resistive and capacitive sensing. It is also necessary in order to implement various actuation and control mechanisms such as pumping, electrophoresis and temperature control. Typically electrical wire traces are added to microfabricated fluidic chips using metal deposition processes that are carried out after the fluidic chip has been fabricated. The process for adding the wiring is complicated and is limited to select metals that can be deposited by evaporation or sputtering. We present a single step method for integrating electrical wires into polymer microfluidic chips that are fabricated by a hot embossing process. This process can flexibly embed any kind of commercially available metal wire with a microfluidic chip and the wiring may be integrated to come into surface contact with the fluid or may be embedded in close proximity to (but insulated from)the fluid paths for example for local heating purposes. This method significantly reduces total processing time and is thus a valuable method for wire integration into polymer chips. We demonstrate two applications—a microelectrolysis chip and a heater chip that were fabricated using this methodology. The design, fabrication process and the initial test results are presented.     

LMA: A generic and efficient implementation of the Levenberg–Marquardt Algorithm

This paper presents an open‐source, generic and efficient implementation of a very popular nonlinear optimization method: the Levenberg–Marquardt algorithm (LMA). This minimization algorithm is well known and hundreds of implementations have already been released. However, none of them offer at the same time a high level of genericity, a friendly syntax and a high computational performance. In this paper, we propose a solution to gather all those advantages in one library named LMA. The main challenge is to implement an efficient solver for every encounter problem. To overcome this difficulty, LMA uses compile time algorithms to design a code specific to the given optimization problem. The features of LMA are presented and the performances are compared with the state‐of‐the‐art best alternatives through extensive benchmarks on different kind of problems. Copyright © 2017 John Wiley & Sons, Ltd.     

Parametric appraisal and optimization in machining of CFRP composites by using TLBO (teaching–learning based optimization algorithm)

The present paper focuses on machining (turning) aspects of CFRP (epoxy) composites by using single point HSS cutting tool. The optimal setting i.e. the most favourable combination of process parameters (such as spindle speed, feed rate, depth of cut and fibre orientation angle) has been derived in view of multiple and conflicting requirements of machining performance yields viz. material removal rate, surface roughness, SR \((\hbox {R}_{\mathrm{a}})\) (of the turned product) and cutting force. This study initially derives mathematical models (objective functions) by using statistics of nonlinear regression for correlating various process parameters with respect to the output responses. In the next phase, the study utilizes a recently developed advanced optimization algorithm teaching–learning based optimization (TLBO) in order to determine the optimal machining condition for achieving satisfactory machining performances. Application potential of TLBO algorithm has been compared to that of genetic algorithm (GA). It has been observed that exploration of TLBO appears more fruitful in contrast to GA in the context of this case experimental research focused on machining of CFRP composites.     

The economics and psychology of consumer trust in intermediaries in electronic markets: the EM-Trust Framework

The rise of electronic markets (EM) and e-commerce came with the promise of disintermediation. Yet, from aggregators to authenticators, the online landscape today is scattered with intermediaries such as EBay and Verisign, aiming to streamline e-commerce transactions and building consumer trust in EM. The central theme of this paper is to understand the contextual factors that lead to consumers’ need to trust intermediaries. In developing our arguments, the paper synthesizes perspectives from information economics, transaction cost economics, and literature on institution-based trust to develop the EM-Trust Framework. Drawing from information economics, the paper contends that EM embody certain inefficiencies, which in turn contribute towards heightening consumer uncertainty, especially under conditions of high information specificity. Heightened consumer uncertainty subsequently reduces consumer trust in EM. It is only in the face of uncertainty and a loss of trust in EM that consumers transfer their need to trust in intermediaries. However, the transference of trust is complete only if agency costs from intermediation lie within consumer thresholds. A mini-case of online mortgage marketplaces is used to illustrate the EM-Trust Framework, thus creating threads for more insightful investigations in the future.     

Energy Efficient Layered Cluster Head Rotation Based Routing Protocol for Underwater Wireless Sensor Networks

Energy efficiency is of paramount concern in underwater sensor networks. The very nature of underwater environment makes it difficult to deploy an energy efficient network that enhances network lifetime. The existing protocols of terrestrial networks cannot be implemented directly to underwater scenarios and as such new protocols have to be designed because of speed of signal propagation under water. Improving the energy efficiency in UWSNs is an active area of research and many protocols to that end have been proposed. The routing protocol that this paper proposes is Energy Efficient Layered Cluster Head Rotation (EE-LCHR) routing protocol. This protocol makes use of the multi sink architecture and creates virtual layers containing a number of sensor nodes such that the hop count from the sensor nodes in a particular layer to the surface sink is the same. Also each layer has a number of clusters with a cluster head that keeps on rotating depending on the fitness value of the sensor nodes. The proposed protocol as compared to other extant protocols like EE-DBR and DBR improves network lifetime. The presence of virtual layers and rotation of cluster heads together ensure that energy balance is better achieved in our proposed protocol which leads to an enhanced network lifetime.

     

Boundary layer flow of a dusty fluid over a semi-infinite flat plate

Summary Both the drag force due to slip and the transverse force due to slip-shear have been considered in boundary layer equations. The solution has been found in a power series of non-dimensionalx, x being the distance in the down-stream direction. Solutions for high slip region and small slip region characterised byx1 andx1 respectively, have been found separately. In the high slip region the effect of increase in concentration parameter of the dust particles is to increase the magnitude of the longitudinal fluid phase velocityu. Also the magnitude of the longitudinal particle slip velocityu _p -u is becoming maximum on the plate and decreasing along the plate withx. The transverse particle velocityv _p is independent of but it is directly proportional to , the transverse force coefficient. An interesting result is thatv _p is assuming small positive value on the plate. The transverse force has taken an important role in migration of particles away from the plate. In the small slip region the flow of dust particles is mainly governed by the fluid-phase. The effect of on the flow field in this region is to decrease the boundary layer thickness. In this region the particles are having some tendency to accumulate near the plate. Lastly, it has been found that the shearing stress, skinfriction and the dimensionless drag-coefficient on the plate increase with increase of .With 5 Figures