AIS-BN: An Adaptive Importance Sampling Algorithm for Evidential Reasoning in Large Bayesian Networks

Stochastic sampling algorithms, while an attractive alternative to exact algorithms in very large Bayesian network models, have been observed to perform poorly in evidential reasoning with extremely unlikely evidence. To address this problem, we propose an adaptive importance sampling algorithm, AIS-BN, that shows promising convergence rates even under extreme conditions and seems to outperform the existing sampling algorithms consistently. Three sources of this performance improvement are (1) two heuristics for initialization of the importance function that are based on the theoretical properties of importance sampling in finite-dimensional integrals and the structural advantages of Bayesian networks, (2) a smooth learning method for the importance function, and (3) a dynamic weighting function for combining samples from different stages of the algorithm. We tested the performance of the AIS-BN algorithm along with two state of the art general purpose sampling algorithms, likelihood weighting (Fung and Chang, 1989; Shachter and Peot, 1989) and self-importance sampling (Shachter and Peot, 1989). We used in our tests three large real Bayesian network models available to the scientific community: the CPCS network (Pradhan et al., 1994), the PathFinder network (Heckerman, Horvitz, and Nathwani, 1990), and the ANDES network (Conati, Gertner, VanLehn, and Druzdzel, 1997), with evidence as unlikely as 10^-41. While the AIS-BN algorithm always performed better than the other two algorithms, in the majority of the test cases it achieved orders of magnitude improvement in precision of the results. Improvement in speed given a desired precision is even more dramatic, although we are unable to report numerical results here, as the other algorithms almost never achieved the precision reached even by the first few iterations of the AIS-BN algorithm

MODELING OF HOPPER DISCHARGE

Hoppers are widely used in many engineering processes. The discharging of granular mate- rials from a hopper is a critical topic of industrial importance, and the discharge flow rate from hoppers is the focus of the current work. Many parameters influence the discharge rate including: the hopper outlet width, the angle of the hopper wall, the particle size, and particle friction, and so on. Due to the expensive of examining a large variety of particle types and hopper conditions, computational simulation has been widely studied in an effort to establish an alternative method of determining critical factors impacting hopper flow. In this thesis, the process of hopper discharge has been simulated by the Discrete Element Method (DEM), which is one of the most popular methods for granular flow simulation. To validate against existing experiments, all conditions were matched as closely as possible to those in the experiment. The particles used in our simulation are spheroids with diameters of 0.77 cm. The angles of the hoppers examined range from 0◦ to 90◦, while the opening sizes vary from 2.9 cm to 4.3 cm. Computationally, the friction coefficient has been adjusted several times and finally is set to 0.5 in the simulation in order to fit the experimental resultsas closely as possible. As a quantitative test of the simulation fidelity we compare the hopper empty time t – which is related to the hopper discharge rate – for these different hopper angles and hopper opening size. As a secondary test of the fit, the survival time τ, the normal force profile, the velocity profile, and the probability of jamming Ps are also computed and compared to existing experimental data from collaborators at Duke University. Ultimately, the goal of the work is to establish the degree of model fidelity necessary in order to closely mimic the experimental results obtained

Optimisation of the hydrotesting sequence in tank farm construction using an adaptive genetic algorithm with stochastic preferential logic

In the construction of tank farms there is a requirement for the tanks to be hydro-tested in order to verify that they are leak proof as well as proving the lack of differential settlement in the foundations. The tanks will be required to be filled to a predetermined level and then to maintain this loaded state for a certain period of time before being drained. In areas such as the Middle East water for hydro-testing is not freely available as sea water is often not suitable for this purpose, so fresh water needs to be produced or transported to the construction site for this purpose. It is therefore of major benefit to the project to schedule the hydro-testing of the tanks in such a manner as to minimize the utilization of hydro-test water. This problem is a special case of the Resource Constrained Project Scheduling Problem (RCPSP) and in this research we have modified our previously developed Fitness differential adaptive genetic algorithm [4, 6 & 7] to the solution of this real world problem. The Algorithm has been ported from the original MATLAB code into Microsoft Project using VBA in order to provide a more user friendly, practical interface

Numerical study of the optical nonlinearity of doped and gapped graphene: From weak to strong field excitation

Numerically solving the semiconductor Bloch equations within a phenomenological relaxation time approximation, we extract both the linear and nonlinear optical conductivities of doped graphene and gapped graphene under excitation by a laser pulse. We discuss in detail the dependence of second harmonic generation, third harmonic generation, and the Kerr effects on the doping level, the gap, and the electric field amplitude. The numerical results for weak electric fields agree with those calculated from available analytic perturbation formulas. For strong electric fields when saturation effects are important, all the effective third order nonlinear response coefficients show a strong field dependence.Comment: 12 pages with 9 figure

Third order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature

We investigate the effect of phenomenological relaxation parameters on the third order optical nonlinearity of doped graphene by perturbatively solving the semiconductor Bloch equation around the Dirac points. An analytic expression for the nonlinear conductivity at zero temperature is obtained under the linear dispersion approximation. With this analytic formula as starting point, we construct the conductivity at finite temperature and study the optical response to a laser pulse of finite duration. We illustrate the dependence of several nonlinear optical effects, such as third harmonic generation, Kerr effects and two photon absorption, parametric frequency conversion, and two color coherent current injection, on the relaxation parameters, temperature, and pulse duration. In the special case where one of the electric fields is taken as a dc field, we investigate the dc-current and dc-field induced second order nonlinearities, including dc-current induced second harmonic generation and difference frequency generation.Comment: 23+ pages, 10 figures. In this version we correct a sign typo in Eq. (25), for which we thank the discussion in the work http://arxiv.org/abs/1506.00534v