Improving Simulation Efficiency of MCMC for Inverse Modeling of Hydrologic Systems with a Kalman-Inspired Proposal Distribution

Bayesian analysis is widely used in science and engineering for real-time forecasting, decision making, and to help unravel the processes that explain the observed data. These data are some deterministic and/or stochastic transformations of the underlying parameters. A key task is then to summarize the posterior distribution of these parameters. When models become too difficult to analyze analytically, Monte Carlo methods can be used to approximate the target distribution. Of these, Markov chain Monte Carlo (MCMC) methods are particularly powerful. Such methods generate a random walk through the parameter space and, under strict conditions of reversibility and ergodicity, will successively visit solutions with frequency proportional to the underlying target density. This requires a proposal distribution that generates candidate solutions starting from an arbitrary initial state. The speed of the sampled chains converging to the target distribution deteriorates rapidly, however, with increasing parameter dimensionality. In this paper, we introduce a new proposal distribution that enhances significantly the efficiency of MCMC simulation for highly parameterized models. This proposal distribution exploits the cross-covariance of model parameters, measurements and model outputs, and generates candidate states much alike the analysis step in the Kalman filter. We embed the Kalman-inspired proposal distribution in the DREAM algorithm during burn-in, and present several numerical experiments with complex, high-dimensional or multi-modal target distributions. Results demonstrate that this new proposal distribution can greatly improve simulation efficiency of MCMC. Specifically, we observe a speed-up on the order of 10-30 times for groundwater models with more than one-hundred parameters

3β-Hydroxy­friedelan-17β-carboxylic acid

The title compound, C30H50O3, which was isolated from a marine endophytic fungus, is a new friedelan derivative. The mol­ecule contains five six-membered rings, which exhibit boat (ring A), distorted boat (ring B) and chair (rings C–E) conformations. The crystal structure is stabilized by inter­molecular O—H⋯O hydrogen bonds, which link neighbouring mol­ecules into 12-membered rings

The investigations of the PP-wave BsB_s states combining quark model and lattice QCD in the coupled channel framework

Combining the quark model, the quark-pair-creation mechanism and $B^{(*)}K$ interaction, we have investigated the near-threshold $P$-wave $B_s$ states in the framework of the Hamiltonian effective field theory. With the heavy quark flavor symmetry, all the parameters are determined in the $D_s$ sector by fitting the lattice data. The masses of the bottom-strange partners of the $D^{*}_{s0}(2317)$ and $D^{*}_{s1}(2460)$ are predicted to be $M_{B^{*}_{s0}}=5730.2_{-1.5}^{+2.4}$ MeV and $M_{B^{*}_{s1}}= 5769.6_{-1.6}^{+2.4}$ MeV, respectively, which are well consistent with the lattice QCD simulation. The two P-wave $B_s$ states are the mixtures of the bare $b\bar s$ core and $B^{(*)}K$ component. Moreover, we find a crossing point between the energy levels with and without the interaction Hamiltonian in the finite volume spectrum in the $0^+$ case, which corresponds to a CDD (Castillejo-Dalitz-Dyson) zero in the $T$-matrix of the $BK$ scattering. This CDD zero will help deepen the insights of the near-threshold states and can be examined by the future lattice calculation.Comment: 20 pages, 4 figure

Optimal estimation and control for lossy network: stability, convergence, and performance

In this paper, we study the problems of optimal estimation and control, i.e., the linear quadratic Gaussian (LQG) control, for systems with packet losses but without acknowledgment. Such acknowledgment is a signal sent by the actuator to inform the estimator of the incidence of control packet losses. For such system, which is usually called as a user datagram protocol (UDP)-like system, the optimal estimation is nonlinear and its calculation is time-consuming, making its corresponding optimal LQG problem complicated. We first propose two conditions: 1) the sensor has some computation abilities; and 2) the control command, exerted to the plant, is known to the sensor. For a UDP-like system satisfying these two conditions, we derive the optimal estimation. By constructing the finite and infinite product probability measure spaces for the estimation error covariances (EEC), we give the stability condition for the expected EEC, and show the existence of a measurable function to which the EEC converges in distribution, and propose some practical methods to evaluate the estimation performance. Finally, the LQG controllers are derived, and the conditions for the mean square stability of the closed-loop system are established

Experimental Decoy Quantum Key Distribution Up To 130KM Fiber

Decoy State Quantum Key Distribution (QKD), being capable of beating PNS attack and uncon- ditionally secure, have become an attractive one recently. But, in many QKD systems, disturbances of transmission channel make quantum bit error rate (QBER) increase which limits both security distance and key bit rate of real-life decoy state QKD systems. We demonstrate the two-intensity decoy QKD with one-way Faraday-Michelson phase modulation system, which is free of channel dis- turbance and keeps interference fringe visibility (99%) long period, near 130KM single mode optical fiber in telecom (1550 nm) wavelength. This is longest distance fiber decoy state QKD system based on two intensity protocol.Comment: 4 pages, 2figure