Fast Sampling and Counting k -SAT Solutions in the Local Lemma Regime

We give new algorithms based on Markov chains to sample and approximately count satisfying assignments to k -uniform CNF formulas where each variable appears at most d times. For any k and d satisfying kd < n o(1) and k ≥ 20 log k + 20 log d + 60, the new sampling algorithm runs in close to linear time, and the counting algorithm runs in close to quadratic time. Our approach is inspired by Moitra (JACM, 2019), which remarkably utilizes the Lovász local lemma in approximate counting. Our main technical contribution is to use the local lemma to bypass the connectivity barrier in traditional Markov chain approaches, which makes the well-developed MCMC method applicable on disconnected state spaces such as SAT solutions. The benefit of our approach is to avoid the enumeration of local structures and obtain fixed polynomial running times, even if k = ω (1) or d = ω (1).

A Spatial Nonhomogeneous Poisson Process Model Using Bayesian Approach on a Space-Time Geostatistical Data

In this research, we propose the nonhomogeneous Poisson process on geostatistical data by adding a time component to be applied in the study case of air pollution in the Special Region of Yogyakarta. We use the Bayesian approach to inference the model using the MCMC method. And to generate samples of the posterior distribution, we wield the Metropolis-Hastings algorithm, and we obtained it has good convergence for this case. And to show the goodness of fit of this model, we had the value of DIC.

Opinion mining for user experience evaluation model using kernel-naive bayes classification algorithm

User experience evaluation approach is the major key to adapt the new trends and technology. The product launch is based on the various opinions of users and availability of product. The first impression about the product makes successful sales, which is analysed with UX (User eXperience) design. Before developing / launching the product, have to evaluate the user experience model by online sources. The opinion/sentimental analysis are the way to capture the people’s opinion about the product. Rating, page session, website page views, and number of buyers or users are evaluated as a graph model and predict the requirement of the product. This process makes the product’s benefits. The previous work utilizes the Markov Chain Monte Carlo (MCMC) Method to model the UX design. In this proposed research work, the opinion mining approach is used to get the dataset from Google analytics. This dataset is model using Kernel based Naïve Bayes Classification algorithm and the prior & posterior probability is calculated by MCMC (Markov Chain Monte Carlo) techniques. Classification approach takes the training and testing data. Here the confusion matrix is used to create the UX evaluation model’s accuracy. By this proposed algorithm, it summarized the positive and negative opinion then we can calculate the accuracy of the system and it easily identifies the user opinion. This proposed UX design model improves the result as compared to the previous MCMC method. The data mining based sentimental classification is done with the help of MATLAB 2018a tool.

Moving the epidemic tipping point through topologically targeted social distancing

The epidemic threshold of a social system is the ratio of infection and recovery rate above which a disease spreading in it becomes an epidemic. In the absence of pharmaceutical interventions (i.e. vaccines), the only way to control a given disease is to move this threshold by non-pharmaceutical interventions like social distancing, past the epidemic threshold corresponding to the disease, thereby tipping the system from epidemic into a non-epidemic regime. Modeling the disease as a spreading process on a social graph, social distancing can be modeled by removing some of the graphs links. It has been conjectured that the largest eigenvalue of the adjacency matrix of the resulting graph corresponds to the systems epidemic threshold. Here we use a Markov chain Monte Carlo (MCMC) method to study those link removals that do well at reducing the largest eigenvalue of the adjacency matrix. The MCMC method generates samples from the relative canonical network ensemble with a defined expectation value of $$\lambda _{\text {max}}$$ λ max . We call this the “well-controlling network ensemble” (WCNE) and compare its structure to randomly thinned networks with the same link density. We observe that networks in the WCNE tend to be more homogeneous in the degree distribution and use this insight to define two ad-hoc removal strategies, which also substantially reduce the largest eigenvalue. A targeted removal of 80% of links can be as effective as a random removal of 90%, leaving individuals with twice as many contacts. Finally, by simulating epidemic spreading via either an SIS or an SIR model on network ensembles created with different link removal strategies (random, WCNE, or degree-homogenizing), we show that tipping from an epidemic to a non-epidemic state happens at a larger critical ratio between infection rate and recovery rate for WCNE and degree-homogenized networks than for those obtained by random removals.

Damage Evaluation of Bridge Hanger Based on Bayesian Inference: Analytical Model

With the increase of the long-span bridge, the damage of the long-span bridge hanger has attracted more and more attention. Nowadays, the probability statistics method based on Bayes’ theorem is widely used for evaluating the damage of bridge, that is, Bayesian inference. In this study, the damage evaluation model of bridge hanger is established based on Bayesian inference. For the damage evaluation model, the analytical expressions for calculating the weights by finite mixture (FM) method are derived. In order to solve the complex analytical expressions in damage evaluation model, the Metropolis-Hastings (MH) sampling of Markov chain Monte Carlo (MCMC) method was used. Three case studies are adopted to demonstrate the effect of the initial value and the applicability of the proposed model. The result suggests that the proposed model can evaluate the damage of the bridge hanger.

Spatial Origin and Diversification of the Lycocerus fainanus Species Group (Coleoptera, Cantharidae), with Descriptions of Four New Species from China and Vietnam

Five previously known species were attributed to the Lycocerus fainanus species group, including L. inopaciceps (Pic 1926), L. oberthueri (Gorham 1889), L. oudai (Švihla 2004), L. metallipennis (Fairmaire 1887), and L. nigripes (Wittmer, 1995). Four new species of this group were discovered from China and Vietnam, L. binotatus sp. nov., L. testacicollis sp. nov., L. daliensis sp. nov., and L. vietnamensis sp. nov. An updated key to all species was provided. A geographical distribution map is presented, which shows that all the members were located between 18.69041–33.93441° N, and between 98.61413–121.77102° E. The ancestral geographical range was reconstructed based on a phylogeny of morphological data by the Bayesian Binary MCMC method. The result showed that the spatial origin of L. fainanus species group was probably located in northern Vietnam and southwest China. The divergence of the species in southwest China and Taiwan was caused by vicariance about 24 Ma ago, when the latter was separated in the Qinghai-Tibet Plateau, and the remaining species of mainland China all originated from Taiwan after traveling around Southeast Asia and back to China. Nevertheless, this conclusion should be verified when fossil evidence and molecular data are available.

A Novel Hybrid Monte Carlo Algorithm for Sampling Path Space

To sample from complex, high-dimensional distributions, one may choose algorithms based on the Hybrid Monte Carlo (HMC) method. HMC-based algorithms generate nonlocal moves alleviating diffusive behavior. Here, I build on an already defined HMC framework, hybrid Monte Carlo on Hilbert spaces (Beskos, et al. Stoch. Proc. Applic. 2011), that provides finite-dimensional approximations of measures π, which have density with respect to a Gaussian measure on an infinite-dimensional Hilbert (path) space. In all HMC algorithms, one has some freedom to choose the mass operator. The novel feature of the algorithm described in this article lies in the choice of this operator. This new choice defines a Markov Chain Monte Carlo (MCMC) method that is well defined on the Hilbert space itself. As before, the algorithm described herein uses an enlarged phase space Π having the target π as a marginal, together with a Hamiltonian flow that preserves Π. In the previous work, the authors explored a method where the phase space π was augmented with Brownian bridges. With this new choice, π is augmented by Ornstein–Uhlenbeck (OU) bridges. The covariance of Brownian bridges grows with its length, which has negative effects on the acceptance rate in the MCMC method. This contrasts with the covariance of OU bridges, which is independent of the path length. The ingredients of the new algorithm include the definition of the mass operator, the equations for the Hamiltonian flow, the (approximate) numerical integration of the evolution equations, and finally, the Metropolis–Hastings acceptance rule. Taken together, these constitute a robust method for sampling the target distribution in an almost dimension-free manner. The behavior of this novel algorithm is demonstrated by computer experiments for a particle moving in two dimensions, between two free-energy basins separated by an entropic barrier.