Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\it a-priori}. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201

Bayesian inference with optimal maps

We present a new approach to Bayesian inference that entirely avoids Markov chain simulation, by constructing a map that pushes forward the prior measure to the posterior measure. Existence and uniqueness of a suitable measure-preserving map is established by formulating the problem in the context of optimal transport theory. We discuss various means of explicitly parameterizing the map and computing it efficiently through solution of an optimization problem, exploiting gradient information from the forward model when possible. The resulting algorithm overcomes many of the computational bottlenecks associated with Markov chain Monte Carlo. Advantages of a map-based representation of the posterior include analytical expressions for posterior moments and the ability to generate arbitrary numbers of independent posterior samples without additional likelihood evaluations or forward solves. The optimization approach also provides clear convergence criteria for posterior approximation and facilitates model selection through automatic evaluation of the marginal likelihood. We demonstrate the accuracy and efficiency of the approach on nonlinear inverse problems of varying dimension, involving the inference of parameters appearing in ordinary and partial differential equations.United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Grant DE-SC0002517)United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Grant DE-SC0003908

Hepatocyte Lysosomal Membrane Stabilization by Olive Leaves against Chemically Induced Hepatocellular Neoplasia in Rats

Extensive efforts are exerted looking for safe and effective chemotherapy for hepatocellular carcinoma (HCC). Specific and sensitive early biomarkers for HCC still in query. Present work to study proteolytic activity and lysosomal membrane integrity by hepatocarcinogen, trichloroacetic acid (TCA), in Wistar rats against aqueous olive leaf extract (AOLE).TCA showed neoplastic changes as oval- or irregular-shaped hepatocytes and transformed, vesiculated, and binucleated liver cells. The nuclei were pleomorphic and hyperchromatic. These changes were considerably reduced by AOLE. The results added, probably for the first time, that TCA-induced HCC through disruption of hepatocellular proteolytic enzymes as upregulation of papain, free cathepsin-D and nonsignificant destabilization of lysosomal membrane integrity, a prerequisite for cancer invasion and metastasis. AOLE introduced a promising therapeutic value in liver cancer, mostly through elevating lysosomal membrane integrity. The study substantiated four main points: (1) the usefulness of proteolysis and lysosomalmembrane integrity in early prediction of HCC. (2) TCA carcinogenesis is possibly mediated by lysosomal membrane destabilization, through cathepsin-D disruption, which could be reversed by AOLE administration. (3) A new strategy for management of HCC, using dietary olive leaf system may be a helpful phytotherapeutic trend. (4) A prospective study on serum proteolytic enzyme activity may introduce novel diagnostic tools

Resonant Energy Transfer From Argon Dimers to Atomic Oxygen in Microhollow Cathode Discharges

The emission of atomic oxygen lines at 130.2 and 130.5 nm from a microhollow cathode discharge in argon with oxygen added indicates resonant energy transfer from argon dimers to oxygen atoms. The internal efficiency of the vacuum-ultraviolet (VUV) radiation was measured as 0.7% for a discharge in 1100 Torr argon with 0.1% oxygen added. The direct current VUV point source operates at voltages below 300 V and at current levels of milliamperes

Xenon Excimer Emission From Pulsed Microhollow Cathode Discharges

By applying electrical pulses of 20 ns duration to xenon microplasmas, generated by direct current microhollow cathode discharges, we were able to increase the xenon excimer emission by more than an order of magnitude over direct current discharge excimer emission. For pulsed voltages in excess of 500 V, the optical power at 172 nm was found to increase exponentially with voltage. Largest values obtained were 2.75 W of vacuum-ultraviolet optical power emitted from a single microhollow cathode discharge in 400 Torr xenon with a 750 V pulse applied to a discharge. Highest radiative emittance was 15.2 W/cm2. The efficiency for excimer emission was found to increase linearly with pulsed voltages above 500 V reaching values of 20% at 750 V

Stochastic Testing Method for Transistor-Level Uncertainty Quantification Based on Generalized Polynomial Chaos

Uncertainties have become a major concern in integrated circuit design. In order to avoid the huge number of repeated simulations in conventional Monte Carlo flows, this paper presents an intrusive spectral simulator for statistical circuit analysis. Our simulator employs the recently developed generalized polynomial chaos expansion to perform uncertainty quantification of nonlinear transistor circuits with both Gaussian and non-Gaussian random parameters. We modify the nonintrusive stochastic collocation (SC) method and develop an intrusive variant called stochastic testing (ST) method. Compared with the popular intrusive stochastic Galerkin (SG) method, the coupled deterministic equations resulting from our proposed ST method can be solved in a decoupled manner at each time point. At the same time, ST requires fewer samples and allows more flexible time step size controls than directly using a nonintrusive SC solver. These two properties make ST more efficient than SG and than existing SC methods, and more suitable for time-domain circuit simulation. Simulation results of several digital, analog and RF circuits are reported. Since our algorithm is based on generic mathematical models, the proposed ST algorithm can be applied to many other engineering problems

Biochemical markers as diagnostic/prognostic indicators for ischemic disease

Objective: The use of a biomarker was extremely useful in clinical emergencies such as stroke to aid in triage and early management of cases. The diagnostic accuracy of laboratory biomarkers is run to approve the identification of easy, cheap and fast tests associated with cerebral ischemia and intracranial hemorrhage. The present study was designed to screen serum enolase activity, activities of CK-BB, LDH and lipid profile in patients with ischemic or related diseases as good diagnostic/ prognostic indicator for ischemic diseases. Methods: Sixty male subjects in the age range of (45 ±2years) were divided into four groups each with 15 participants: Group (I) normal . Group (II) patients recently diagnosed as ischemic disease; Group (III) hypertensive patients and Group (IV); diabetic patients enolase activity (p<0.001) and CK-BB (p<0.01) in ischemic and hypertensive patients compared with control and diabetic groups. LDH level was significantly elevated in ischemic, hypertensive and diabetic patients compared with controls (p<0.001). The cut -off value for serum enolase was 62.5 nmol/l showing 90% sensitivity and 93% specificity for differentiation of ischemic disease. Positive correlations were observed between serum enolase (r = 0.56), and CK-BB (r = 0.53). Conclusion: Serum enolase can be considered as a more sensitive and specific marker and used as a sensitive diagnostic or prognostic marker for ischemic related diseases.Keywords: Serum enolase, ischemia, hypertension, diagnosis, prognostic

Efficient Uncertainty Quantification for the Periodic Steady State of Forced and Autonomous Circuits

This brief proposes an uncertainty quantification method for the periodic steady-state (PSS) analysis with both Gaussian and non-Gaussian variations. Our stochastic testing formulation for the PSS problem provides superior efficiency over both Monte Carlo methods and existing spectral methods. The numerical implementation of a stochastic shooting Newton solver is presented for both forced and autonomous circuits. Simulation results on some analog/RF circuits are reported to show the effectiveness of our proposed algorithms