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.

An experimental study on cracking evolution in concrete and cement mortar by the b-value analysis of acoustic emission technique

Notched three point bend (TPB) specimens made with plain concrete and cement mortar were tested under crack mouth opening displacement (CMOD) control at a rate of 0.0004 mm/s and simultaneously acoustic emissions (AE) released were recorded during the experiments. Amplitude distribution analysis of AE released during concrete was carried out to study the development of fracture process in concrete and mortar specimens. The slope of the log-linear frequency-amplitude distribution of AE is known as the AE based b-value. The AE based b-value was computed in terms of physical process of time varying applied load using cumulative frequency distribution (Gutenberg-Richter relationship) and discrete frequency distribution (Aki's method) of AE released during concrete fracture. AE characteristics of plain concrete and cement mortar were studied and discussed and it was observed that the AE based b-value analysis serves as a tool to identify the damage in concrete structural members. (C) 2012 Elsevier Ltd. All rights reserved.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

A QUADRATIC C degrees INTERIOR PENALTY METHOD FOR LINEAR FOURTH ORDER BOUNDARY VALUE PROBLEMS WITH BOUNDARY CONDITIONS OF THE CAHN-HILLIARD TYPE

We develop a quadratic C degrees interior penalty method for linear fourth order boundary value problems with essential and natural boundary conditions of the Cahn-Hilliard type. Both a priori and a posteriori error estimates are derived. The performance of the method is illustrated by numerical experiments.

Influence limitation in multi-campaign social networks: A Shapley value based approach

We investigate the problem of influence limitation in the presence of competing campaigns in a social network. Given a negative campaign which starts propagating from a specified source and a positive/counter campaign that is initiated, after a certain time delay, to limit the the influence or spread of misinformation by the negative campaign, we are interested in finding the top k influential nodes at which the positive campaign may be triggered. This problem has numerous applications in situations such as limiting the propagation of rumor, arresting the spread of virus through inoculation, initiating a counter-campaign against malicious propaganda, etc. The influence function for the generic influence limitation problem is non-submodular. Restricted versions of the influence limitation problem, reported in the literature, assume submodularity of the influence function and do not capture the problem in a realistic setting. In this paper, we propose a novel computational approach for the influence limitation problem based on Shapley value, a solution concept in cooperative game theory. Our approach works equally effectively for both submodular and non-submodular influence functions. Experiments on standard real world social network datasets reveal that the proposed approach outperforms existing heuristics in the literature. As a non-trivial extension, we also address the problem of influence limitation in the presence of multiple competing campaigns.

Seismic site classification and correlation between standard penetration test N value and shear wave velocity for Lucknow city in Indo-Gangetic basin

Subsurface lithology and seismic site classification of Lucknow urban center located in the central part of the Indo-Gangetic Basin (IGB) are presented based on detailed shallow subsurface investigations and borehole analysis. These are done by carrying out 47 seismic surface wave tests using multichannel analysis of surface waves (MASW) and 23 boreholes drilled up to 30 m with standard penetration test (SPT) N values. Subsurface lithology profiles drawn from the drilled boreholes show low- to medium-compressibility clay and silty to poorly graded sand available till depth of 30 m. In addition, deeper boreholes (depth >150 m) were collected from the Lucknow Jal Nigam (Water Corporation), Government of Uttar Pradesh to understand deeper subsoil stratification. Deeper boreholes in this paper refer to those with depth over 150 m. These reports show the presence of clay mix with sand and Kankar at some locations till a depth of 150 m, followed by layers of sand, clay, and Kankar up to 400 m. Based on the available details, shallow and deeper cross-sections through Lucknow are presented. Shear wave velocity (SWV) and N-SPT values were measured for the study area using MASW and SPT testing. Measured SWV and N-SPT values for the same locations were found to be comparable. These values were used to estimate 30 m average values of N-SPT (N-30) and SWV (V-s(30)) for seismic site classification of the study area as per the National Earthquake Hazards Reduction Program (NEHRP) soil classification system. Based on the NEHRP classification, the entire study area is classified into site class C and D based on V-s(30) and site class D and E based on N-30. The issue of larger amplification during future seismic events is highlighted for a major part of the study area which comes under site class D and E. Also, the mismatch of site classes based on N-30 and V-s(30) raises the question of the suitability of the NEHRP classification system for the study region. Further, 17 sets of SPT and SWV data are used to develop a correlation between N-SPT and SWV. This represents a first attempt of seismic site classification and correlation between N-SPT and SWV in the Indo-Gangetic Basin.

Evaluation of document binarization using eigen value decomposition

A necessary step for the recognition of scanned documents is binarization, which is essentially the segmentation of the document. In order to binarize a scanned document, we can find several algorithms in the literature. What is the best binarization result for a given document image? To answer this question, a user needs to check different binarization algorithms for suitability, since different algorithms may work better for different type of documents. Manually choosing the best from a set of binarized documents is time consuming. To automate the selection of the best segmented document, either we need to use ground-truth of the document or propose an evaluation metric. If ground-truth is available, then precision and recall can be used to choose the best binarized document. What is the case, when ground-truth is not available? Can we come up with a metric which evaluates these binarized documents? Hence, we propose a metric to evaluate binarized document images using eigen value decomposition. We have evaluated this measure on DIBCO and H-DIBCO datasets. The proposed method chooses the best binarized document that is close to the ground-truth of the document.

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.

High Value of Proton Relaxivity Achieved by Graphene Oxide-Cobalt Ferrite Nanoparticle Composite: A Potential Contrast Agent in Magnetic Resonance Imaging

This work investigates the potential of graphene oxide-cobalt ferrite nanoparticle (GO-CoFe2O4) composite as image contrast enhancing material in Magnetic Resonance Imaging (MRI). In the preset work, GO-CoFe2O4 composites were produced by a two-step synthesis process. In the first step, graphene oxide (GO) was synthesized, and in the second step CoFe2O4 nanoparticles were synthesized in a reaction mixture containing GO to yield graphene GO-CoFe2O4 composite. Proton relaxivity value obtained from the composite was 361 mM(-1)s(-1). This value of proton relaxivity is higher than a majority of reported relaxivity values obtained using several ferrite based contrast agents.

Graphene oxide-Fe3O4 nanoparticle composite with high transverse proton relaxivity value for magnetic resonance imaging

The potential of graphene oxide-Fe3O4 nanoparticle (GO-Fe3O4) composite as an image contrast enhancing material in magnetic resonance imaging has been investigated. Proton relaxivity values were obtained in three different homogeneous dispersions of GO-Fe3O4 composites synthesized by precipitating Fe3O4 nanoparticles in three different reaction mixtures containing 0.01 g, 0.1 g, and 0.2 g of graphene oxide. A noticeable difference in proton relaxivity values was observed between the three cases. A comprehensive structural and magnetic characterization revealed discrete differences in the extent of reduction of the graphene oxide and spacing between the graphene oxide sheets in the three composites. The GO-Fe3O4 composite framework that contained graphene oxide with least extent of reduction of the carboxyl groups and largest spacing between the graphene oxide sheets provided the optimum structure for yielding a very high transverse proton relaxivity value. It was found that the GO-Fe3O4 composites possessed good biocompatibility with normal cell lines, whereas they exhibited considerable toxicity towards breast cancer cells. (C) 2015 AIP Publishing LLC.