Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models

Global sensitivity analysis aims at quantifying the impact of input variability onto the variation of the response of a computational model. It has been widely applied to deterministic simulators, for which a set of input parameters has a unique corresponding output value. Stochastic simulators, however, have intrinsic randomness due to their use of (pseudo)random numbers, so they give different results when run twice with the same input parameters but non-common random numbers. Due to this random nature, conventional Sobol' indices, used in global sensitivity analysis, can be extended to stochastic simulators in different ways. In this paper, we discuss three possible extensions and focus on those that depend only on the statistical dependence between input and output. This choice ignores the detailed data generating process involving the internal randomness, and can thus be applied to a wider class of problems. We propose to use the generalized lambda model to emulate the response distribution of stochastic simulators. Such a surrogate can be constructed without the need for replications. The proposed method is applied to three examples including two case studies in finance and epidemiology. The results confirm the convergence of the approach for estimating the sensitivity indices even with the presence of strong heteroskedasticity and small signal-to-noise ratio

Local models of Shimura varieties and a conjecture of Kottwitz

We give a group theoretic definition of "local models" as sought after in the theory of Shimura varieties. These are projective schemes over the integers of a $p$-adic local field that are expected to model the singularities of integral models of Shimura varieties with parahoric level structure. Our local models are certain mixed characteristic degenerations of Grassmannian varieties; they are obtained by extending constructions of Beilinson, Drinfeld, Gaitsgory and the second-named author to mixed characteristics and to the case of general (tamely ramified) reductive groups. We study the singularities of local models and hence also of the corresponding integral models of Shimura varieties. In particular, we study the monodromy (inertia) action and show a commutativity property for the sheaves of nearby cycles. As a result, we prove a conjecture of Kottwitz which asserts that the semi-simple trace of Frobenius on the nearby cycles gives a function which is central in the parahoric Hecke algebra.Comment: 88 pages, several corrections and change

Inner product computation for sparse iterative solvers on\ud distributed supercomputer

Recent years have witnessed that iterative Krylov methods without re-designing are not suitable for distribute supercomputers because of intensive global communications. It is well accepted that re-engineering Krylov methods for prescribed computer architecture is necessary and important to achieve higher performance and scalability. The paper focuses on simple and practical ways to re-organize Krylov methods and improve their performance for current heterogeneous distributed supercomputers. In construct with most of current software development of Krylov methods which usually focuses on efficient matrix vector multiplications, the paper focuses on the way to compute inner products on supercomputers and explains why inner product computation on current heterogeneous distributed supercomputers is crucial for scalable Krylov methods. Communication complexity analysis shows that how the inner product computation can be the bottleneck of performance of (inner) product-type iterative solvers on distributed supercomputers due to global communications. Principles of reducing such global communications are discussed. The importance of minimizing communications is demonstrated by experiments using up to 900 processors. The experiments were carried on a Dawning 5000A, one of the fastest and earliest heterogeneous supercomputers in the world. Both the analysis and experiments indicates that inner product computation is very likely to be the most challenging kernel for inner product-based iterative solvers to achieve exascale

Friction on a Quantized Vortex in a Superfluid

We obtain the explicit expression of the friction on a moving quantized vortex, following the formulation of Thouless, Ao and Niu. It is shown that the friction on a moving vortex is sensitive to details but does not change the transverse force. We provide a general thermodynamic interpretation for the mutual independence of the transverse force and the friction. The friction is evaluated for the case of quasiparticle contributions in a clean fermionic superfluid, showing a new feature of logarithmic divergence.Comment: latex, minor change

A 0.18μm CMOS 9mW current-mode FLF linear phase filter with gain boost

“This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder." “Copyright IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.”The design and implementation of a CMOS continuous-time follow-the-leader-feedback (FLF) filter is described. The filter is implemented using a fully-differential linear, low voltage and low power consumption operational transconductance amplifier (OTA) based on a source degeneration topology. PSpice simulations using a standard TSMC 0.18 mum CMOS process with 2 V power supply have shown that the cut-off frequency of the filter ranges from 55 MHz to 160 MHz and dynamic range is about 45 dB. The group delay is less than 5% over the whole tuning range; the power consumption is only 9 mW

Interdecadal variability of winter precipitation in Southeast China

Interdecadal variability of observed winter precipitation in Southeast China (1961–2010) is characterized by the first empirical orthogonal function of the three-monthly Standardized Precipitation Index (SPI) subjected to a 9-year running mean. For interdecadal time scales the dominating spatial modes represent monopole features involving the Arctic Oscillation (AO) and the sea surface temperature (SST) anomalies. Dynamic composite analysis (based on NCEP/NCAR reanalyzes) reveals the following results: (1) Interdecadal SPI-variations show a trend from a dryer state in the 1970s via an increase during the 1980s towards stabilization on wetter conditions commencing with the 1990s. (2) Increasing wetness in Southeast China is attributed to an abnormal anticyclone over south Japan, with northward transport of warm and humid air from the tropical Pacific to South China. (3) In mid-to-high latitudes the weakened southward flow of polar airmasses induces low-level warming over Eurasia due to stronger AO by warmer zonal temperature advection. This indicates that AO is attributed to the Southeast China precipitation increase influenced by circulation anomalies over the mid-to-high latitudes. (4) The abnormal moisture transport along the southwestern boundary of the abnormal anticyclone over south Japan is related to anomalous south-easterlies modulated by the SST anomalies over Western Pacific Ocean; a positive (negative) SST anomaly will strengthen (weaken) warm and humid air transport, leading to abundant (reduced) precipitation in Southeast China. That is both AO and SST anomalies determine the nonlinear trend observed in winter precipitation over Southeast China