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The hitting time, which refers to the time required to find the marked element in the search algorithm, is one of the most interesting properties of quantum walk. In this paper we briefly analyze the hitting time on a finite 2D lattice in the classical case, focusing on the quantum version of the hitting time and give specific expressions for each. It is well known that the quantum hitting time has the same order as the square of the classical case, and our work also happens to verify this particular property. [ABSTRACT FROM AUTHOR]

Aquatic vegetation is an important marker of the change in the lake ecosystem. It plays an important supporting role in the lake ecosystem, and its abundance and cover changes affect the ecosystem balance. Collecting accurate long-term distribution data on aquatic vegetation can help monitor the change in the lake ecosystem, thereby providing scientific support for efforts to maintain the balance of the ecosystem. This work aimed to establish an improved CA-Markov model to reconstruct historical potential distribution of aquatic vegetation in the two typical lakes (Xingkai Lake and Hulun Lake) in Northeast China during 1950s to 1960s. We firstly analyzed remote sensing data on the spatial distribution of aquatic vegetation data in two lakes in six periods from the 1970 to 2015. Then, we built a transfer probability matrix for changes in hydrothermal conditions (temperature and precipitation) based on similar periods, and we designed suitability images using the spatial frequency and temporal continuity of the constraints. Finally, we established an improved CA-Markov model based on the transfer probability matrix and suitability images to reconstruct the potential distributions of aquatic vegetation in the two northeastern lakes during the 1950s and 1960s. The results showed the areas of aquatic vegetation in the 1950s and 1960s were 102.37 km2 and 100.7 km2 for Xingkai Lake and 90.81 km2 and 88.15 km2 for Hulun Lake, respectively. Compared with the traditional CA-Markov model, the overall accuracy of the improved model increased by more than 50%, which proved the improved CA-Markov model can be used to effectively reconstruct the historical potential distribution of aquatic vegetation. This study provides an accurate methodology for simulating the potential historical distributions of aquatic vegetation to enrich the study of the historical evolution of lake ecosystem.

N6-methyladenosine (m6A), the most common posttranscriptional modification in eukaryotic mRNAs, plays an important role in mRNA splicing, editing, stability, degradation, etc. Since the methylation state is dynamic, methylation sequencing needs to be carried out over different time periods, which brings some difficulties to identify the RNA methyladenine sites. Thus, it is necessary to develop a fast and accurate method to identify the RNA N6-methyladenosine sites in the transcriptome. In this study, we use first-order and second-order Markov models to identify RNA N6-methyladenine sites in three species (Saccharomyces cerevisiae, mouse, and Homo sapiens). These two methods can fully consider the correlation between adjacent nucleotides. The results show that the performance of our method is better than that of other existing methods. Furthermore, the codons encoded by three nucleotides have biases in mRNA, and a second-order Markov model can capture this kind of information exactly. This may be the main reason why the performance of the second-order Markov model is better than that of the first-order Markov model in the m6A prediction problem. In addition, we provide a corresponding web tool called MM-m6APred.

N6-methyladenosine (m6A), the most common posttranscriptional modification in eukaryotic mRNAs, plays an important role in mRNA splicing, editing, stability, degradation, etc. Since the methylation state is dynamic, methylation sequencing needs to be carried out over different time periods, which brings some difficulties to identify the RNA methyladenine sites. Thus, it is necessary to develop a fast and accurate method to identify the RNA N6-methyladenosine sites in the transcriptome. In this study, we use first-order and second-order Markov models to identify RNA N6-methyladenine sites in three species (Saccharomyces cerevisiae , mouse, and Homo sapiens). These two methods can fully consider the correlation between adjacent nucleotides. The results show that the performance of our method is better than that of other existing methods. Furthermore, the codons encoded by three nucleotides have biases in mRNA, and a second-order Markov model can capture this kind of information exactly. This may be the main reason why the performance of the second-order Markov model is better than that of the first-order Markov model in the m6A prediction problem. In addition, we provide a corresponding web tool called MM-m6APred. [ABSTRACT FROM AUTHOR]

The existing interacting multiple model (IMM) suffers from two problems when tracking an underwater maneuvering target: 1) the conventional nonlinear filters in IMM cannot work on the condition of delayed measurement, 2) the inefficiency of model switching in IMM may degrade the tracking performance. In order to handle the delayed measurement, a novel Bayesian filter framework under two Gaussian assumptions is proposed. The new extended Kalman filter (EKF) and unscented Kalman filter (UKF) are developed as two variations of the proposed filter. In addition, to solve the problem of low switching efficiency between IMM models, a transfer probability corrected function is designed to adaptively update the transfer probability matrix (TPM) in IMM. The simulation results show that the proposed algorithm outperforms the existing IMM-EKF and IMM-UKF. • This paper investigates the problem of underwater maneuvering target tracking with one-step randomly delayed measurements. • We construct a new augmented state vector including target state and measurement noise information. • Under Gaussian assumptions, a novel Bayesian filter framework with delayed measurement is proposed. • A new extended Klaman filter and unscented Kalman filter with randomly delayed measurements are evaluated. • A new function is proposed to update the transfer probability matrix in interacting multiple model. [ABSTRACT FROM AUTHOR]

A stochastic model was developed to describe the liquid radial dispersion in a trickle-bed reactor, which has conventionally been modeled by the effective diffusion model. To establish the stochastic model, the column was divided into some layers of particles in the axial direction and several annulus rings in each layer in the radial direction. The liquid spreading was regarded as a fluid transport process and the matrix of transfer probability was derived based on the coordinates of the particle network in the cross-section of the column. With this transfer probability matrix and the initial liquid distribution, the liquid distribution in the downstream was predicted. In order to evaluate the model parameters, experimental data of the liquid dispersion were obtained from electrical capacitance tomography images and tracer injection. Good agreement was obtained between the stochastic model and the experimental liquid distribution data. [ABSTRACT FROM AUTHOR]