Extreme self-organization in networks constructed from gene expression data

We study networks constructed from gene expression data obtained from many types of cancers. The networks are constructed by connecting vertices that belong to each others' list of K-nearest-neighbors, with K being an a priori selected non-negative integer. We introduce an order parameter for characterizing the homogeneity of the networks. On minimizing the order parameter with respect to K, degree distribution of the networks shows power-law behavior in the tails with an exponent of unity. Analysis of the eigenvalue spectrum of the networks confirms the presence of the power-law and small-world behavior. We discuss the significance of these findings in the context of evolutionary biological processes.Comment: 4 pages including 3 eps figures, revtex. Revisions as in published versio

Effective Test Pattern Generation using LFSR for Memory Testing

Volume 2 Issue 3 (March 2014

Assessment of Poisson's Ratio for Hydroxy-terminated Polybutadine-based Solid Rocket Propellants

Poisson's ratio of hydroxy-terminated polybutadine (HTPB)-based composite propellant is estimated from uni-axial tensile testing. Double dumbbell specimens as per ASTM D638 type IV standard were used and Poisson's ratio at break, obtained by change in volume of specimen, was calculated as approximately 0.25. It was also observed that Poisson's ratio is different along different lateral directions of the propellant specimen. Poisson's ratios in two orthogonal directions perpendicular to longitudinal axis were calculated as 0.17 and 0.30. As ASTM specimen has rectangular cross-section of approximate size 6 mm x 4 mm, the directional behaviour of Poisson's ratio may be attributed to initial dimensions. Prismatic propellant specimen with square cross-section and of 115 mm x 6 mm x 6 mm dimension do not show any variation wrt Young's modulus,tensile strength, and percentage elongation as compared to ASTM specimen. Directional behaviour of Poisson's ratio with almost similar numerical value was again observed, thus ruling out dependence of this behaviour on different initial dimensions of propellant cross-section. Further, Poisson's ratio varies linearly with strain even in linear portion of stress-strain curve in uni-axial tensile testing. The rate of reduction of Poisson's ratio with increase in strain is slower in linear region and it accelerates after dewetting due to formation of vacuoles. Variation of Poisson's ratio with strain has two different slopes in linear (slope = 0.3165) and nonlinear regions (slope = 0.61364). Numerical value of slope for variation of Poisson's ratio with strain almost doubles after dewetting. It must be noted that no change in volume does not necessarily indicate constant Poisson's ratioequal to 0.5. Composite propellants behave as compressible material in most of the regions and near-failure region or at higher strains; Poisson's ratio is not anywhere near to 0.5, instead it is near 0.25.Defence Science Journal, 2010, 60(5), pp.497-501, DOI:http://dx.doi.org/10.14429/dsj.60.57

Physics-Informed Polynomial Chaos Expansions

Surrogate modeling of costly mathematical models representing physical systems is challenging since it is typically not possible to create a large experimental design. Thus, it is beneficial to constrain the approximation to adhere to the known physics of the model. This paper presents a novel methodology for the construction of physics-informed polynomial chaos expansions (PCE) that combines the conventional experimental design with additional constraints from the physics of the model. Physical constraints investigated in this paper are represented by a set of differential equations and specified boundary conditions. A computationally efficient means for construction of physically constrained PCE is proposed and compared to standard sparse PCE. It is shown that the proposed algorithms lead to superior accuracy of the approximation and does not add significant computational burden. Although the main purpose of the proposed method lies in combining data and physical constraints, we show that physically constrained PCEs can be constructed from differential equations and boundary conditions alone without requiring evaluations of the original model. We further show that the constrained PCEs can be easily applied for uncertainty quantification through analytical post-processing of a reduced PCE filtering out the influence of all deterministic space-time variables. Several deterministic examples of increasing complexity are provided and the proposed method is applied for uncertainty quantification

Efficiency of Indian Commodity Market: A Survey of Brokers’ Perception

The present study documents the finding of a survey of brokers’ perception pertaining to the recently introduced commodity derivatives market in India. The survey results show the brokers’ assessment about trading/marketing activities and their perception of the benefits and concerns about commodity derivatives. It also throw some light on the perception of brokers about the efficiency of Indian commodity derivatives in performing the functions of price discovery, hedging effectiveness and volatility dynamics. The survey results show that high net worth individual are contributing significantly in the trade volume of commodity derivatives. Interestingly, retail investors are also emerged as the significant contributor in total turnover of brokers. Survey results exhibit that price discovery and hedging effectiveness functions are well performed by all the commodity futures except the energy commodities futures. Energy commodities, being the most volatile commodities, are perceived as having less hedging effectiveness as compared to others. Brokers are assenting on the high to moderate impact of open interest, volume and time to maturity on the volatility of the commodity futures derivatives

Transfer Operator Theoretic Framework for Monitoring Building Indoor Environment in Uncertain Operating Conditions

Dynamical system-based linear transfer Perron- Frobenius (P-F) operator framework is developed to address analysis and design problems in the building system. In particular, the problems of fast contaminant propagation and optimal placement of sensors in uncertain operating conditions of indoor building environment are addressed. The linear nature of transfer P-F operator is exploited to develop a computationally efficient numerical scheme based on the finite dimensional approximation of P-F operator for fast propagation of contaminants. The proposed scheme is an order of magnitude faster than existing methods that rely on simulation of an advection-diffusion partial differential equation for contami- nant transport. Furthermore, the system-theoretic notion of observability gramian is generalized to nonlinear flow fields using the transfer P-F operator. This developed notion of observability gramian for nonlinear flow field combined with the finite dimensional approximation of P-F operator is used to provide a systematic procedure for optimal placement of sensors under uncertain operating conditions. Simulation results are presented to demonstrate the applicability of the developed framework on the IEA-annex 2D benchmark problem

Learning thermodynamically constrained equations of state with uncertainty

Numerical simulations of high energy-density experiments require equation of state (EOS) models that relate a material's thermodynamic state variables -- specifically pressure, volume/density, energy, and temperature. EOS models are typically constructed using a semi-empirical parametric methodology, which assumes a physics-informed functional form with many tunable parameters calibrated using experimental/simulation data. Since there are inherent uncertainties in the calibration data (parametric uncertainty) and the assumed functional EOS form (model uncertainty), it is essential to perform uncertainty quantification (UQ) to improve confidence in the EOS predictions. Model uncertainty is challenging for UQ studies since it requires exploring the space of all possible physically consistent functional forms. Thus, it is often neglected in favor of parametric uncertainty, which is easier to quantify without violating thermodynamic laws. This work presents a data-driven machine learning approach to constructing EOS models that naturally captures model uncertainty while satisfying the necessary thermodynamic consistency and stability constraints. We propose a novel framework based on physics-informed Gaussian process regression (GPR) that automatically captures total uncertainty in the EOS and can be jointly trained on both simulation and experimental data sources. A GPR model for the shock Hugoniot is derived and its uncertainties are quantified using the proposed framework. We apply the proposed model to learn the EOS for the diamond solid state of carbon, using both density functional theory data and experimental shock Hugoniot data to train the model and show that the prediction uncertainty reduces by considering the thermodynamic constraints.Comment: 26 pages, 7 figure