Recursos de colección
Caltech Authors (138.832 recursos)
Repository of works by Caltech published authors.
Type = Report or Paper
Repository of works by Caltech published authors.
Type = Report or Paper
Barna, Arpad
Transient responses, input and output impedances have been derived for the use of the circuit designer. A hybrid equivalent circuit was assumed to be correct and has been used as the basis of the derived relationships.
Grounded emitter, grounded base, grounded collector and emitter degenerated configurations are discussed.
Tollestrup, A. V.
If a low energy synchrotron is to be used as an injector for a 300 Bev machine, the problem may arise of synchronizing the two R.F. systems at transfer time in order that a bunch of protons in the injector may be transferred to a bucket in the main machine without loss of particles. A possible synchronization scheme is proposed and investigated here.
Gell-Mann, Murray; Zachariasen, Fredrik
There is no question that broken symmetries are of the highest importance in particle physics. We are familiar with the conservation of the isotopic spin current, which is violated by electromagnetism, and the conservation of the strangeness or hypercharge current, which is violated by the weak interactions. In both of these cases, the violations are small.
Barna, Arpad; Marshall, J. Howard
In the past, linear gate circuits for gating pulses of photomultiplier tubes have been mostly based on semiconductor diodes. Using diffused base transistors as a gate in an emitter input configuration provides favorable linearity and feedthrough properties. The circuit described here is an improved version of one developed by A. V. Tollestrup.
Matranga, M.; Di Salvo, T.; Iaria, R.; Gambino, A. F.; Burderi, L.; Riggio, A.; Sanna, A.
Context: Ser X-1 is a well studied LMXB which clearly shows a broad iron
line. Recently, Miller et al. (2103) have presented broad-band, high quality
NuSTAR data of SerX-1.Using relativistically smeared self-consistent reflection
models, they find a value of R_in close to 1.0 R_ISCO (corresponding to 6 R_g),
and a low inclination angle, less than 10 deg. Aims: The aim of this paper is
to probe to what extent the choice of reflection and continuum models (and
uncertainties therein) can affect the conclusions about the disk parameters
inferred from the reflection component. To this aim we re-analyze all the
available public NuSTAR and XMM-Newton. Ser X-1 is a...
Sun, Qiming
Orbital optimization procedure is widely called in electronic structure simulation. To efficiently find the orbital optimization solution, we developed a new second order orbital optimization algorithm, co-iteration augmented Hessian (CIAH) method. In this method, the orbital optimization is embedded in the diagonalization procedure for augmented Hessian (AH) eigenvalue equation. Hessian approximations can be easily employed in this method to improve the computational costs. We numerically performed the CIAH algorithm with SCF convergence of 20 challenging systems and Boys localization of C60 molecule. We found that CIAH algorithm has better SCF convergence and less computational costs than direct inversion iterative subspace...
Vakilzadeh, Majid K.; Beck, James L.; Abrahamsson, Thomas
Approximate Bayesian Computation (ABC) methods have gained in their popularity over the last decade because they expand the horizon of Bayesian parameter inference methods to the range of models for which only forward simulation is available. The majority of the ABC methods rely on the choice of a set of summary statistics to reduce the dimension of the data. However, as has been noted in the ABC literature, the lack of convergence guarantees that is induced by the absence of a vector of sufficient summary statistics that assures inter-model sufficiency over the set of competing models, hinders the use of...
Filippidis, Ioannis; Murray, Richard M.
This report proposes a TLA+ definition for the problem of constructing a strategy that implements a temporal property. It is based on a note by Lamport [1] that outlines a formalization of realizability in TLA. The modified definition proposed here is expressed axiomatically in TLA+. Specifying what function is acceptable as a strategy requires care, so that a function with empty domain be avoided, while ensuring that the strategy will not need to have a domain too large to be a set.
We prove that initial conditions should appear in assumptions only, unless an initial predicate is added to the...
Lu, Yulong; Stuart, Andrew M.; Weber, Hendrik
This paper concerns the approximation of probability measures on R^d with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the existence of the best approximation, with respect to this divergence, from certain sets of Gaussian measures and Gaussian mixtures. The asymptotic behavior of such best approximations is then studied in the small parameter limit where the measure concentrates; this asymptotic behaviour is characterized using Γ-convergence. The theory developed is then applied to understanding the frequentist consistency of Bayesian inverse problems. For a fixed realization of noise, we show the asymptotic normality of the posterior measure in...
Kelly, David; Stuart, Andrew M.
Data assimilation refers to the methodology of combining dynamical models and observed data with the objective of improving state estimation. Most data assimilation algorithms are viewed as approximations of the Bayesian posterior (filtering distribution) on the signal given the observations. Some of these approximations are controlled, such as particle filters which may be refined to produce the true filtering distribution in the large particle number limit, and some are uncontrolled, such as ensemble Kalman filter methods which do not recover the true filtering distribution in the large ensemble limit. Other data assimilation algorithms, such as cycled 3DVAR methods, may be...
Kuntz, J.; Ottobre, M.; Stuart, A. M.
The Random Walk Metropolis (RWM) algorithm is a Metropolis- Hastings MCMC algorithm designed to sample from a given target distribution \pi with Lebesgue density on R^N. RWM constructs a Markov chain by randomly proposing a new position (the "proposal move"), which is then accepted or rejected according to a rule which makes the chain reversible with respect to \pi. When the dimension N is large a key question is to determine the optimal scaling with N of the proposal variance: if the proposal variance is too large, the algorithm will reject the proposed moves too often; if it is too...
Iglesias, Marco A.; Lu, Yulong; Stuart, Andrew M.
We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the object of the inference. Whilst the level set methodology has been widely used for the solution of geometric inverse problems, the Bayesian formulation that we develop here contains two significant advances: firstly it leads to a well-posed inverse problem in which the posterior distribution is Lipschitz with respect to the observed data; and secondly it leads to computationally expedient algorithms in...
Agapiou, Sergios; Papaspiliopoulos, Omiros; Sanz-Alonso, D.; Stuart, A. M.
The basic idea of importance sampling is to use independent samples from one measure in order to approximate expectations with respect to another measure. Understanding how many samples are needed is key to understanding the computational complexity of the method, and hence to understanding when it will be effective and when it will not. It is intuitive that the size of the difference between the measure which is sampled, and the measure against which expectations are to be computed, is key to the computational complexity. An implicit challenge in many of the published works in this area is to find...
Iglesias, Marco A.; Lin, Kui; Stuart, Andrew M.
Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering methods have recently been used to solve inverse problems by introducing an artificial dynamical sys- tem. This opens up the possibility of using a range of other filtering methods, such as 3DVAR and Kalman based methods, to solve inverse problems, again by introducing an artificial dynamical system. The aim of this paper is to analyze such methods in the context of the ill-posed linear inverse problem. Statistical...
Lee, Wongjung; Stuart, Andrew
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those arising in turbulence, in which effective low-dimensional representation of the desired probability distribution is challenging. Nonetheless recent advances have shown considerable success in filtering based on certain carefully chosen simplifications of the underlying system, which allow closed form filters. This leads to filtering algorithms with significant, but judiciously chosen, model error. The purpose of this article is to analyze the effectiveness of these simplified filters, and...
Schillings, Claudia; Stuart, Andrew M.
The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences, and its gradual adoption in many other areas of application, analysis of the method is in its infancy. Furthermore, much of the existing analysis deals with the large ensemble limit, far from the regime in which the method is typically used. The goal of this paper is to analyze the method when applied to inverse problems with fixed ensemble size. A continuous-time limit is derived and...
Bréhier, Charles-Edouard; Hairer, Martin; Stuart, Andrew M.
We consider stochastic semi-linear evolution equations which are driven by additive, spatially correlated, Wiener noise, and in particular consider problems of heat equation (analytic semigroup) and damped-driven wave equations (bounded semigroup) type. We discretize these equations by means of a spectral Galerkin projection, and we study the approximation of the probability distribution of the trajectories: test functions are regular, but depend on the values of the process on the interval [0,T].
We introduce a new approach in the context of quantative weak error analysis for discretization of SPDEs. The weak error is formulated using a deterministic function (It\^o map) of...
Scheichl, R.; Stuart, A. M.; Teckentrup, A. L.
We are interested in computing the expectation of a functional of a PDE solution under a Bayesian posterior distribution. Using Bayes' rule, we reduce the problem to estimating the ratio of two related prior expectations. For a model elliptic problem, we provide a full convergence and complexity analysis of the ratio estimator in the case where Monte Carlo, quasi-Monte Carlo or multilevel Monte Carlo methods are used as estimators for the two prior expectations. We show that the computational complexity of the ratio estimator to achieve a given accuracy is the same as the corresponding complexity of the individual estimators...
Ooguri, Hirosi; Yin, Zheng
These lecture notes are based on a course on string theories given by Hirosi Ooguri in the first week of TASI 96 Summer School at Boulder, Colorado. It is an introductory course designed to provide students with minimum knowledge before they attend more advanced courses on non-perturbative aspects of string theories in the School. The course consists of five lectures: 1. Bosonic String, 2. Toroidal Compactifications, 3. Superstrings, 4. Heterotic Strings, and 5. Orbifold Compactifications.
Stuart, Andrew M.; Teckentrup, Aretha L.
We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior distribution and various approximations based on the Gaussian process emulator. Our analysis includes approximations based on the mean of the predictive process, as well as approximations based on the full Gaussian process emulator. Our results show that the Hellinger distance between the true posterior and its approximations can be bounded by moments of the error in the emulator. Numerical results confirm our theoretical findings.