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This paper considers maximum likelihood (ML) estimation in a large class of models with hidden Markov regimes. We investigate consistency of the ML estimator and local asymptotic normality for the models under general conditions, which allow for autoregressive dynamics in the observable process, Markov regime sequences with covariatedependent transition matrices, and possible model misspecification. A Monte Carlo study examines the finite-sample properties of the ML estimator in correctly specified and misspecified models. An empirical application is also discussed.

DNA-binding proteins (DBPs) participate in various biological processes including DNA replication, recombination, and repair. In the human genome, about 6–7% of these proteins are utilized for genes encoding. DBPs shape the DNA into a compact structure known chromatin while some of these proteins regulate the chromosome packaging and transcription process. In the pharmaceutical industry, DBPs are used as a key component of antibiotics, steroids, and cancer drugs. These proteins also involve in biophysical, biological, and biochemical studies of DNA. Due to the crucial role in various biological activities, identification of DBPs is a hot issue in protein science. A series of experimental and computational methods have been proposed, however, some methods didn’t achieve the desired results while some are inadequate in its accuracy and authenticity. Still, it is highly desired to present more intelligent computational predictors. In this work, we introduce an innovative computational method namely DP-BINDER based on physicochemical and evolutionary information. We captured local highly decisive features from physicochemical properties of primary protein sequences via normalized Moreau-Broto autocorrelation (NMBAC) and evolutionary information by position specific scoring matrix-transition probability composition (PSSM-TPC) and pseudo-position specific scoring matrix (PsePSSM) using training and independent datasets. The optimal features were selected by the support vector machine-recursive feature elimination and correlation bias reduction (SVM-RFE + CBR) from fused features and were fed into random forest (RF) and support vector machine (SVM). Our method attained 92.46% and 89.58% accuracy with jackknife and ten-fold cross-validation, respectively on the training dataset, while 81.17% accuracy on the independent dataset for prediction of DBPs. These results demonstrate that our method attained the highest success rate in the literature. The superiority of DP-BINDER over existing approaches due to several reasons including abstraction of local dominant features via effective feature descriptors, utilization of appropriate feature selection algorithms and effective classifier.

In this article, the tracking control problem for discrete-time singularly perturbed systems with a piecewise-homogeneous Markov chain subject to the effect of quantization and packet dropout is addressed based on Takagi–Sugeno (T–S) fuzzy-approximation. Firstly, the stochastic variation of mode transition probabilities with time-varying peculiarities is considered in a finite set, which is dominated by a higher-level homogeneous Markov chain. Moreover, partially unknown information in higher-level transition probabilities (HTPs) matrix is resolved by constructing a unified framework, which covers the stochastic switching and arbitrary switching as special cases, simultaneously. Secondly, considering the burden of network communication between components, the quantization impact and packet dropout caused by network network-induced constraints are integrated into the co-design of fuzzy tracking controller, which is mode-dependent and variation-dependent. Several criteria for the stochastic stability and H ∞ performance of the augmented system are deduced by establishing a series of linear matrix inequalities. Ultimately, two simulation examples are given to verify the practicability and effectiveness of the proposed control design schemes.

We consider a discrete-time population growth system called the Bienaymé–Galton–Watson stochastic branching system. We deal with a noncritical case, in which the per capita offspring mean $m\\neq1$ . The famous Kolmogorov theorem asserts that the expectation of the population size in the subcritical case $m<1$ on positive trajectories of the system asymptotically stabilizes and approaches ${1}/\\mathcal{K}$ , where $\\mathcal{K}$ is called the Kolmogorov constant. The paper is devoted to the search for an explicit expression of this constant depending on the structural parameters of the system. Our argumentation is essentially based on the basic lemma describing the asymptotic expansion of the probability-generating function of the number of individuals. We state this lemma for the noncritical case. Subsequently, we find an extended analogue of the Kolmogorov constant in the noncritical case. An important role in our discussion is also played by the asymptotic properties of transition probabilities of the Q-process and their convergence to invariant measures. Obtaining the explicit form of the extended Kolmogorov constant, we refine several limit theorems of the theory of noncritical branching systems, showing explicit leading terms in the asymptotic expansions.

On-farm adoption of individual and groups of precision agriculture technologies has grown in the past 15 years. Based on a sample of 545 farm observations collected by the Kansas Farm Management Association, farm adoption of bundles of embodied knowledge and information intensive technologies was analyzed using a Markov transition approach. Three separate analyses estimated transition probabilities to show the adoption of bundles of embodied knowledge technologies, the adoption of bundles of information intensive technologies, and the adoption of variable rate technologies contingent on prior adoption of embodied knowledge and/or information intensive technologies. Each analysis was estimated for two separate time periods (2009–2012) and (2013–2016). The probability that farms retain the same bundle or transition to a different bundle by the next time period are reported. The results indicate that persistence with the same technology bundle is the predominant behavior and that this behavior has strengthened in the study’s most recent time period.

Sequential recommendation has achieved remarkable progress with self-attentive architectures such as SASRec (Self-Attentive Sequential Recommendation), yet existing approaches often underutilize semantic relationships among items and fail to model temporal dynamics effectively. These limitations reduce the ability of existing systems to capture nuanced user preferences in real-world settings. To address these issues, this work introduces two novel frameworks: one for effective semantic integration and another for a semantic and temporal-aware hybrid embedding generation that enhances the representational capacity of SASRec. These frameworks construct a semantically rich hybrid matrix utilizing M arkov State Transition probabilities, C osine similarity, P ersonalized PageRank(PPR) based normalization and additionally T ime-weighted decay information for the temporal variant. The constructed hybrid matrix is smoothed using a graph convolutional network (GCN) to generate item embeddings, which are then passed to the transformer-based sequential recommendation model SASRec for next-item prediction. Evaluated on three real-world benchmark datasets (MovieLens, Yelp and Amazon Beauty), our proposed temporal variant achieves up to 10.4% improvement in HR@10 and 8.2% in NDCG@10 over SASRec, while maintaining competitive efficiency. Our studies confirm the effectiveness of each component, including semantic graph construction, temporal weighting, and contrastive alignment. These results demonstrate that incorporating semantic and temporal signals into sequential recommenders substantially enhances both accuracy and relevancy of recommendations.

We provide sufficient conditions for the uniqueness of an invariant measure of a Markov process as well as for the weak convergence of transition probabilities to the invariant measure. Our conditions are formulated in terms of generalized couplings. We apply our results to several SPDEs for which unique ergodicity has been proven in a recent paper by Glatt-Holtz, Mattingly, and Richards and show that under essentially the same assumptions the weak convergence of transition probabilities actually holds true.

Modeling radionuclide reactive transport in host rocks is one of the major challenges with respect to the performance and safety assessment of high-level radioactive repositories. The rock heterogeneity has a significant impact on the scale effects of flow and solute-transport parameters such as the sorption coefficient. The scaling of the radionuclide sorption coefficient is related to the reactive mineral facies (RMF) distributions in fractured rocks, which can be simulated with transition probability-based geostatistical methods. Geostatistical and geochemical analyses of the RMF distributions are performed on granite samples taken from the Beishan site in northwest China. This paper presents an approach to identifying RMF by using a deep-learning-based mineral identification model. The volume proportions and mean lengths of the RMF are accurately estimated in this way compared to the results of X-ray diffraction analysis. This approach overcomes the limitations of traditional methods which are subjective and have lower accuracy. The results show that the composite covariance model of sorption coefficients is related to the volume proportion and mean length of the RMF. The effective sorption coefficient obtained by the upscaling model is greater than the geometric average and smaller than the arithmetic average. Furthermore, through global sensitivity analysis, it is found that mean retardation factors have the most significant effect on the effective sorption coefficient. The results of this study provide substantial information that contributes to improving understanding of radionuclide transport in fractured granite.

The whale optimization algorithm (WOA) has been widely used in different applications. It has simple control parameters and novel population updating mechanism. However, there is few theoretical analysis of WOA and the convergence property of WOA is ambiguity. This paper analyzes the convergence property of WOA by using the Markov chain of the stochastic process theory. The Markov chain model of the WOA algorithm is established. The one step transition probabilities and convergence properties of different population updating mechanisms in WOA are given. It's proved that the convergence property of WOA is determined by its shrinking encircling mechanism. Finally, three algorithms with different population updating mechanisms are tested with thirteen benchmark functions on accuracy and convergence speed. The simulation results on benchmark functions verify the validity of the theoretical analysis of WOA.

In conventional interacting multiple model (IMM) systems, the transition probability matrix (TPM) is predetermined using prior information. However, this fixed configuration can lead to errors in state estimation, which has led to research focused on adaptively adjusting the transition probabilities. While IMM with adaptive transition probability improves estimation accuracy, the robustness of TPM is not guaranteed in systems with more than two models when sub-models switch. To solve this problem, this paper proposes a polynomial function-based correction function and a feedback structure to adjust the transition probabilities. The polynomial function-based correction function increases the probability of sub-models that match the current situation or stabilizes probabilities by suppressing noise. The feedback structure employs a first-order infinite impulse response filter, combining current and previous information to adaptively adjust and prevent rapid declines in transition probabilities. The proposed algorithm is integrated into the IMM algorithm to enhance performance. Simulation for three-model system comparing the proposed algorithm with other adaptive IMM algorithms shows improved robustness of the transition probabilities and the state estimation accuracy.