Determining Top K Nodes in Social Networks using the Shapley Value

In this paper, we consider the problem of selecting, for any given positive integer k, the top-k nodes in a social network, based on a certain measure appropriate for the social network. This problem is relevant in many settings such as analysis of co-authorship networks, diffusion of information, viral marketing, etc. However, in most situations, this problem turns out to be NP-hard. The existing approaches for solving this problem are based on approximation algorithms and assume that the objective function is sub-modular. In this paper, we propose a novel and intuitive algorithm based on the Shapley value, for efficiently computing an approximate solution to this problem. Our proposed algorithm does not use the sub-modularity of the underlying objective function and hence it is a general approach. We demonstrate the efficacy of the algorithm using a co-authorship data set from e-print arXiv (www.arxiv.org), having 8361 authors.

A Shapley Value Analysis to Coordinate the Formation of Procurement Networks

In this paper we address the problem of forming procurement networks for items with value adding stages that are linearly arranged. Formation of such procurement networks involves a bottom-up assembly of complex production, assembly, and exchange relationships through supplier selection and contracting decisions. Research in supply chain management has emphasized that such decisions need to take into account the fact that suppliers and buyers are intelligent and rational agents who act strategically. In this paper, we view the problem of procurement network formation (PNF) for multiple units of a single item as a cooperative game where agents cooperate to form a surplus maximizing procurement network and then share the surplus in a fair manner. We study the implications of using the Shapley value as a solution concept for forming such procurement networks. We also present a protocol, based on the extensive form game realization of the Shapley value, for forming these networks.

Optimised form of acceleration correction algorithm within SPH-based simulations of impact mechanics

In the context of SPH-based simulations of impact dynamics, an optimised and automated form of the acceleration correction algorithm (Shaw and Reid, 2009a) is developed so as to remove spurious high frequency oscillations in computed responses whilst retaining the stabilizing characteristics of the artificial viscosity in the presence of shocks and layers with sharp gradients. A rational framework for an insightful characterisation of the erstwhile acceleration correction method is first set up. This is followed by the proposal of an optimised version of the method, wherein the strength of the correction term in the momentum balance and energy equations is optimised. For the first time, this leads to an automated procedure to arrive at the artificial viscosity term. In particular, this is achieved by taking a spatially varying response-dependent support size for the kernel function through which the correction term is computed. The optimum value of the support size is deduced by minimising the (spatially localised) total variation of the high oscillation in the acceleration term with respect to its (local) mean. The derivation of the method, its advantages over the heuristic method and issues related to its numerical implementation are discussed in detail. (C) 2011 Elsevier Ltd. All rights reserved.

Aerodynamic Load Measurements at Hypersonic Speeds Using Internally Mounted Fiber-Optic Balance System

This paper describes the measurement of aerodynamic loads using fiber-optic strain gauge sensors and associated signal processors at hypersonic speeds in the 300mm hypersonic wind tunnel. at the Department of Aerospace Engineering, Indian Institute of Science. Fiber-optic sensors have been developed in USA since 1990, for variety of applications in experimental stress analysis, skin friction measurement in fluid flows, smart structures, smart materials, sensing of acoustic emission and more recently in the development of compact devices for measurement of displacement, stress/strain, pressure, temperature, acceleration etc. Our group at llSc has been playing a lead role in the use of these fiber - optic sensors for successful measurement of aerodynamic loads in wind tunnels and the first ever six-component wind tunnel strain gauge balance in the world based on fiber optic sensors was built at the Indian Institute of Science in the year 1999. We report here the results of our efforts in the development of an internal strain gauge balance for high-speed wind tunnel applications.

On the solution of bivariate population balance equations for aggregation: X-discretization of space for expansion and contraction of computational domain

A new structured discretization of 2D space, named X-discretization, is proposed to solve bivariate population balance equations using the framework of minimal internal consistency of discretization of Chakraborty and Kumar [2007, A new framework for solution of multidimensional population balance equations. Chem. Eng. Sci. 62, 4112-4125] for breakup and aggregation of particles. The 2D space of particle constituents (internal attributes) is discretized into bins by using arbitrarily spaced constant composition radial lines and constant mass lines of slope -1. The quadrilaterals are triangulated by using straight lines pointing towards the mean composition line. The monotonicity of the new discretization makes is quite easy to implement, like a rectangular grid but with significantly reduced numerical dispersion. We use the new discretization of space to automate the expansion and contraction of the computational domain for the aggregation process, corresponding to the formation of larger particles and the disappearance of smaller particles by adding and removing the constant mass lines at the boundaries. The results show that the predictions of particle size distribution on fixed X-grid are in better agreement with the analytical solution than those obtained with the earlier techniques. The simulations carried out with expansion and/or contraction of the computational domain as population evolves show that the proposed strategy of evolving the computational domain with the aggregation process brings down the computational effort quite substantially; larger the extent of evolution, greater is the reduction in computational effort. (C) 2011 Elsevier Ltd. All rights reserved.

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

Force measurements on hypersonic waveriders in the IISc hypersonic shock tunnel HST2

The drag and lift coefficients for a viscous optimized Mach 6 conical waverider has been measured using an accelerometer force balance system in the IISc hypersonic shock tunnel. A rubber bush placed in between the waverider model and the steel sting ensures unrestrained motion to the model during shock tunnel testing (500 mu s). Two accelerometers mounted on the model are used to measure the model accelerations in the axial and normal directions. The measured value of lift to drag ratio at zero angle of incidence for the IISc conical waverider with viscous optimized leading edge is 2.149, which compares well with the value reported in the open literature (Anderson et al 1991) for similar class of waveriders designed for a flight Mach number of 6. The details of the experimental study along with illustrative numerical results are discussed in this paper.

A new 6-component accelerometer force balance for short duration ground testing facilities

A new six-component accelerometer force balance is developed and used in the HST2 shock tunnel of Indian Institute of Science. Aerodynamic forces and moments for a hypersonic slender body measured using this balance system at a free stream Mach number of 5.75 and Reynolds number of 1.5 million and stagnation enthalpy of 1.5 and 2 MJ/kg are presented. These measured values compare well with the theoretical values estimated using modified Newtonian theory.

A novel free floating accelerometer force balance system for shock tunnel applications

In order to overcome the interference of the model mounting system with the external aerodynamics of the body during shock tunnel testing, a new free floating internally mountable balance system that ensures unrestrained model motion during testing has been designed, fabricated and tested. Minimal friction ball bearings are used for ensuring the free floating condition of the model during tunnel testing. The drag force acting on a blunt leading edge flat plate at hypersonic Mach number has been measured using the new balance system. Finite element model (FEM) and CFD are exhaustively used in the design as well as for calibrating the new balance system. The experimentally measured drag force on the blunt leading edge flat plate at stagnation enthalpy of 0.7 and 1.2 MJ/kg and nominal Mach number of 5.75 matches well with FEM results. The concept can also be extended for measuring all the three fundamental aerodynamic forces in short duration test facilities like free piston driven shock tunnels.