Stochastically ordered subpopulations and optimal burn-in procedure

Burn-in is a widely used engineering method which is adopted to eliminate defective items before they are shipped to customers or put into the field operation. In the studies of burn-in, the assumption of bathtub shaped failure rate function is usually employed and optimal burn-in procedures are investigated. In this paper, however, we assume that the population is composed of two ordered subpopulations and optimal burn-in procedures are studied in this context. Two types of risks are defined and an optimal burn-in procedure, which minimizes the weighted risks is studied. The joint optimal solutions for the optimal burn-in procedure, which minimizes the mean number of repairs during the field operation, are also investigated.

L1L^1-Minimization for Mechanical Systems

Second order systems whose drift is defined by the gradient of a given potential are considered, and minimization of the $L^1$-norm of the control is addressed. An analysis of the extremal flow emphasizes the role of singular trajectories of order two [25,29]; the case of the two-body potential is treated in detail. In $L^1$-minimization, regular extremals are associated with controls whose norm is bang-bang; in order to assess their optimality properties, sufficient conditions are given for broken extremals and related to the no-fold conditions of [20]. An example of numerical verification of these conditions is proposed on a problem coming from space mechanics

Hamiltonian Monte Carlo Acceleration Using Surrogate Functions with Random Bases

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov Chain Monte Carlo (MCMC) methods, namely, Hamiltonian Monte Carlo (HMC). The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the art methods

Commercial objectives, technology transfer, and systems analysis for fusion power development

Fusion is an inexhaustible source of energy that has the potential for economic commercial applications with excellent safety and environmental characteristics. The primary focus for the fusion energy development program is the generation of central station electricity. Fusion has the potential, however, for many other applications. The fact that a large fraction of the energy released in a DT fusion reaction is carried by high energy neutrons suggests potentially unique applications. In addition, fusion R and D will lead to new products and new markets. Each fusion application must meet certain standards of economic and safety and environmental attractiveness. For this reason, economics on the one hand, and safety and environment and licensing on the other, are the two primary criteria for setting long range commercial fusion objectives. A major function of systems analysis is to evaluate the potential of fusion against these objectives and to help guide the fusion R and D program toward practical applications. The transfer of fusion technology and skills from the national labs and universities to industry is the key to achieving the long range objective of commercial fusion applications

The Copernicus project

The Copernicus spacecraft, to be launched on May 4, 2009, is designed for scientific exploration of the planet Pluto. The main objectives of this exploration is to accurately determine the mass, density, and composition of the two bodies in the Pluto-Charon system. A further goal of the exploration is to obtain precise images of the system. The spacecraft will be designed for three axis stability control. It will use the latest technological advances to optimize the performance, reliability, and cost of the spacecraft. Due to the long duration of the mission, nominally 12.6 years, the spacecraft will be powered by a long lasting radioactive power source. Although this type of power may have some environmental drawbacks, currently it is the only available source that is suitable for this mission. The planned trajectory provides flybys of Jupiter and Saturn. These flybys provide an opportunity for scientific study of these planets in addition to Pluto. The information obtained on these flybys will supplement the data obtained by the Voyager and Galileo missions. The topics covered include: (1) scientific instrumentation; (2) mission management, planning, and costing; (3) power and propulsion system; (4) structural subsystem; (5) command, control, and communication; and (6) attitude and articulation control

TRIDEnT: Building Decentralized Incentives for Collaborative Security

Sophisticated mass attacks, especially when exploiting zero-day vulnerabilities, have the potential to cause destructive damage to organizations and critical infrastructure. To timely detect and contain such attacks, collaboration among the defenders is critical. By correlating real-time detection information (alerts) from multiple sources (collaborative intrusion detection), defenders can detect attacks and take the appropriate defensive measures in time. However, although the technical tools to facilitate collaboration exist, real-world adoption of such collaborative security mechanisms is still underwhelming. This is largely due to a lack of trust and participation incentives for companies and organizations. This paper proposes TRIDEnT, a novel collaborative platform that aims to enable and incentivize parties to exchange network alert data, thus increasing their overall detection capabilities. TRIDEnT allows parties that may be in a competitive relationship, to selectively advertise, sell and acquire security alerts in the form of (near) real-time peer-to-peer streams. To validate the basic principles behind TRIDEnT, we present an intuitive game-theoretic model of alert sharing, that is of independent interest, and show that collaboration is bound to take place infinitely often. Furthermore, to demonstrate the feasibility of our approach, we instantiate our design in a decentralized manner using Ethereum smart contracts and provide a fully functional prototype.Comment: 28 page

Parameter estimation by implicit sampling

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use implicit sampling in parameter estimation problems, where the goal is to find parameters of a numerical model, e.g.~a partial differential equation (PDE), such that the output of the numerical model is compatible with (noisy) data. We use the Bayesian approach to parameter estimation, in which a posterior probability density describes the probability of the parameter conditioned on data and compute an empirical estimate of this posterior with implicit sampling. Our approach generates independent samples, so that some of the practical difficulties one encounters with Markov Chain Monte Carlo methods, e.g.~burn-in time or correlations among dependent samples, are avoided. We describe a new implementation of implicit sampling for parameter estimation problems that makes use of multiple grids (coarse to fine) and BFGS optimization coupled to adjoint equations for the required gradient calculations. The implementation is "dimension independent", in the sense that a well-defined finite dimensional subspace is sampled as the mesh used for discretization of the PDE is refined. We illustrate the algorithm with an example where we estimate a diffusion coefficient in an elliptic equation from sparse and noisy pressure measurements. In the example, dimension\slash mesh-independence is achieved via Karhunen-Lo\`{e}ve expansions

A General Framework for Updating Belief Distributions

We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the traditional likelihood function, which is recovered under the special case of using self information loss. Modern application areas make it is increasingly challenging for Bayesians to attempt to model the true data generating mechanism. Moreover, when the object of interest is low dimensional, such as a mean or median, it is cumbersome to have to achieve this via a complete model for the whole data distribution. More importantly, there are settings where the parameter of interest does not directly index a family of density functions and thus the Bayesian approach to learning about such parameters is currently regarded as problematic. Our proposed framework uses loss-functions to connect information in the data to functionals of interest. The updating of beliefs then follows from a decision theoretic approach involving cumulative loss functions. Importantly, the procedure coincides with Bayesian updating when a true likelihood is known, yet provides coherent subjective inference in much more general settings. Connections to other inference frameworks are highlighted.Comment: This is the pre-peer reviewed version of the article "A General Framework for Updating Belief Distributions", which has been accepted for publication in the Journal of Statistical Society - Series B. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archivin