Probabilities Of Markov Chain Research Articles

Application of Computer-Aided Technology in Teaching Spoken English

Computer-aided technology has revolutionized the teaching of spoken English by offering innovative tools and resources that enhance the learning experience. Through interactive software and multimedia platforms, learners can engage in immersive language exercises, receive real-time feedback, and access personalized instruction tailored to their proficiency levels. This paper introduces a groundbreaking approach for integrating computer-aided technology into the teaching of spoken English, utilizing Automated Probabilistic Markov Chain Machine Learning (APMC-ML). Recognizing the significance of effective communication skills in the modern world, particularly in the realm of English language proficiency, this research endeavors to enhance the pedagogical process through innovative technological means. The methodology involves the development and implementation of an interactive computer-aided system that leverages APMC-ML algorithms to facilitate language learning. This system encompasses various modules designed to cater to different aspects of spoken English acquisition, including pronunciation, vocabulary, fluency, and conversational skills. Through a user-friendly interface, learners are provided with personalized learning experiences tailored to their individual proficiency levels and learning preferences. The application of APMC-ML in teaching spoken English represents a paradigm shift in language education, offering a data-driven approach that complements traditional teaching methods. By harnessing the power of machine learning and probabilistic modeling, educators can optimize the learning experience, expedite skill acquisition, and promote greater language proficiency among learners.

Electric circuit representation of the human circulatory system to estimate the position of nanosensors in vessels

Nanodevices are the focus of research enhancing the detection and treatment of diseases in the human body. Focusing on the scenario where nanosensors are flowing with the blood in the human circulatory system (HCS), in this work, we investigate a model to predict their distribution along the various vessel segments. Although various approaches report solutions for localizing nanosensors in the body, it is also relevant to derive their stationary distribution along the vessel segments as a prior step to assess their actuation and sensing capabilities in the body. We use a Markov chain formulation to derive the stationary distribution of nanosensors. We evaluate the transition probabilities relying on the representation of vessels with electric circuit components. We implement the electric circuit representation of the left ventricle in the heart and the arteries to find the blood flow at vessel bifurcations and then compute the Markov chain probabilities. Our system also allows to reveal the dynamics of the movement of nanosensors with the human activity. We illustrate results in two regimes, as low and high activity, to mimic the case when being at rest or doing sports.

Steady-state statistical properties and implementation of randomization designs with maximum tolerated imbalance restriction for two-arm equal allocation clinical trials.

In recent decades, several randomization designs have been proposed in the literature as better alternatives to the traditional permuted block design (PBD), providing higher allocation randomness under the same restriction of the maximum tolerated imbalance (MTI). However, PBD remains the most frequently used method for randomizing subjects in clinical trials. This status quo may reflect an inadequate awareness and appreciation of the statistical properties of these randomization designs, and a lack of simple methods for their implementation. This manuscript presents the analytic results of statistical properties for five randomization designs with MTI restriction based on their steady-state probabilities of the treatment imbalance Markov chain and compares them to those of the PBD. A unified framework for randomization sequence generation and real-time on-demand treatment assignment is proposed for the straightforward implementation of randomization algorithms with explicit formulas of conditional allocation probabilities. Topics associated with the evaluation, selection, and implementation of randomization designs are discussed. It is concluded that for two-arm equal allocation trials, several randomization designs offer stronger protection against selection bias than the PBD does, and their implementation is not necessarily more difficult than the implementation of the PBD.

Non-Fragile H∞ Synchronization for Markov Jump Singularly Perturbed Coupled Neural Networks Subject to Double-Layer Switching Regulation.

This work explores the H∞ synchronization issue for singularly perturbed coupled neural networks (SPCNNs) affected by both nonlinear constraints and gain uncertainties, in which a novel double-layer switching regulation containing Markov chain and persistent dwell-time switching regulation (PDTSR) is used. The first layer of switching regulation is the Markov chain to characterize the switching stochastic properties of the systems suffering from random component failures and sudden environmental disturbances. Meanwhile, PDTSR, as the second-layer switching regulation, is used to depict the variations in the transition probability of the aforementioned Markov chain. For systems under double-layer switching regulation, the purpose of the addressed issue is to design a mode-dependent synchronization controller for the network with the desired controller gains calculated by solving convex optimization problems. As such, new sufficient conditions are established to ensure that the synchronization error systems are mean-square exponentially stable with a specified level of the H∞ performance. Eventually, the solvability and validity of the proposed control scheme are illustrated through a numerical simulation.

Computation of the steady-state probability of Markov chain evolving on a mixed state space

Abstract The partitioning algorithm is an iterative procedure that computes explicitly the steady-state probability of a finite Markov chain 𝑋. In this paper, we propose to adapt this algorithm to the case where the state space E := C ∪ D E:=C\cup D is composed of a continuous part 𝐶 and a finite part 𝐷 such that C ∩ D = ∅ C\cap D=\emptyset . In this case, the steady-state probability 𝜋 of 𝑋 is a convex combination of two steady-state probabilities π C \pi_{C} and π D \pi_{D} of two Markov chains on 𝐶 and 𝐷 respectively. The obtained algorithm allows to compute explicitly π D \pi_{D} . If π C \pi_{C} cannot be computed explicitly, our algorithm approximates it by numerical resolution of successive integral equations. Some numerical examples are studied to show the usefulness and proper functioning of our proposal.

A Wavelet-Based Computational Framework for a Block-Structured Markov Chain with a Continuous Phase Variable

We consider the computing issues of the steady probabilities for block-structured discrete-time Markov chains that are of upper-Hessenberg or lower-Hessenberg transition kernels with a continuous phase set. An effective computational framework is proposed based on the wavelet transform, which extends and modifies the arguments in the literature for quasi-birth-death (QBD) processes. A numerical procedure is developed for computing the steady probabilities based on the fast discrete wavelet transform, and several examples are presented to illustrate its effectiveness.

Stochastic paths controlling speed and dissipation.

Natural processes occur in a finite amount of time and dissipate energy, entropy, and matter. Near equilibrium, thermodynamic intuition suggests that fast irreversible processes will dissipate more energy and entropy than slow quasistatic processes connecting the same initial and final states. For small systems, recently discovered thermodynamic speed limits suggest that faster processes will dissipate more than slower processes. Here, we test the hypothesis that this relationship between speed and dissipation holds for stochastic paths far from equilibrium. To analyze stochastic paths on finite timescales, we derive an exact expression for the path probabilities of continuous-time Markov chains from the path summation solution to the master equation. We present a minimal model for a driven system in which relative energies of the initial and target states control the speed, and the nonequilibrium currents of a cycle control the dissipation. Although the hypothesis holds near equilibrium, we find that faster processes can dissipate less under far-from-equilibrium conditions because of strong currents. This model serves as a minimal prototype for designing kinetics to sculpt the nonequilibrium path space so that faster paths produce less dissipation.

Different Markov chains modulate visual stimuli processing in a Go-Go experiment in 2D, 3D, and augmented reality.

The introduction of Augmented Reality (AR) has attracted several developments, although the people's experience of AR has not been clearly studied or contrasted with the human experience in 2D and 3D environments. Here, the directional task was applied in 2D, 3D, and AR using simplified stimulus in video games to determine whether there is a difference in human answer reaction time prediction using context stimulus. Testing of the directional task adapted was also done. Research question: Are the main differences between 2D, 3D, and AR able to be predicted using Markov chains? Methods: A computer was fitted with a digital acquisition card in order to record, test and validate the reaction time (RT) of participants attached to the arranged RT for the theory of Markov chain probability. A Markov chain analysis was performed on the participants' data. Subsequently, the way certain factors influenced participants RT amongst the three tasks time on the accuracy of the participants was sought in the three tasks (environments) were statistically tested using ANOVA. Results: Markov chains of order 1 and 2 successfully reproduced the average reaction time by participants in 3D and AR tasks, having only 2D tasks with the variance predicted with the current state. Moreover, a clear explanation of delayed RT in every environment was done. Mood and coffee did not show significant differences in RTs on a simplified videogame. Gender differences were found in 3D, where endogenous directional goals are in 3D, but no gender differences appeared in AR where exogenous AR buttons can explain the larger RT that compensate for the gender difference. Our results suggest that unconscious preparation of selective choices is not restricted to current motor preparation. Instead, decisions in different environments and gender evolve from the dynamics of preceding cognitive activity can fit and improve neurocomputational models.

Analysis of dry and wet weeks of rainfall by using Markov Chain - A case study at Jorhat (Assam), India

Knowledge of the weekly dry and wet spell rainfall analysis is an important aspect for successful agricultural planning as well as water conservation techniques. The rainfall data during the period 1996-2018 from Jorhat station has been analyzed and the average, maximum, minimum, standard deviation and co-efficient of variation for each 52 Standard Meteorological Weeks (SMWs) were calculated. The initial and conditional probabilities of dry and wet weeks were investigated by employing Markov Chain probability model. It was observed that, during the first 12 SMWs, the chance of two and three consecutive dry weeks was ranged from 40 to 100% and from 15 to 96%, respectively, while the chance of two and three consecutive wet weeks was ranged from 0 to 20% and 0 to 16%, respectively. The 20th SMW (14th to 20th May) is the earliest and the 23rd SMW (4th to 10th June) is the most delayed week of the onset of rainy season. Also, the 40th SMW (1st to 7th Oct) is the earliest and the 47th SMW (19th to 25th Nov) is the latest of withdrawal of southwest monsoon. The length of the rainy season is 161 days (21st May to 28th Oct). The 41st to 43rd SMWs were vulnerable to 50% probability for dryness. The monthly effective rainfall (ER) of the station was calculated and it was observed that, the total annual ER accounts only 47% of the average annual rainfall of this region.

Predictive performance and clinical application of COV50, a urinary proteomic biomarker in early COVID-19 infection: a prospective multicentre cohort study

BackgroundThe SARS-CoV-2 pandemic is a worldwide challenge. The CRIT-CoV-U pilot study generated a urinary proteomic biomarker consisting of 50 peptides (COV50), which predicted death and disease progression from SARS-CoV-2. After the interim analysis presented for the German Government, here, we aimed to analyse the full dataset to consolidate the findings and propose potential clinical applications of this biomarker.MethodsCRIT-CoV-U was a prospective multicentre cohort study. In eight European countries (Austria, France, Germany, Greece, North Macedonia, Poland, Spain, and Sweden), 1012 adults with PCR-confirmed COVID-19 were followed up for death and progression along the 8-point WHO scale. Capillary electrophoresis coupled with mass spectrometry was used for urinary proteomic profiling. Statistical methods included logistic regression and receiver operating characteristic curve analysis with a comparison of the area under curve (AUC) between nested models. Hospitalisation costs were derived from the care facility corresponding with the Markov chain probability of reaching WHO scores ranging from 3 to 8 and flat-rate hospitalisation costs adjusted for the gross per capita domestic product of each country.FindingsFrom June 30 to Nov 19, 2020, 228 participants were recruited, and from April 30, 2020, to April 14, 2021, 784 participants were recruited, resulting in a total of 1012 participants. The entry WHO scores were 1–3 in 445 (44%) participants, 4–5 in 529 (52%) participants, and 6 in 38 (4%) participants; and of all participants, 119 died and 271 had disease progression. The odds ratio (OR) associated with COV50 in all 1012 participants for death was 2·44 (95% CI 2·05–2·92) unadjusted and 1·67 (1·34–2·07) when adjusted for sex, age, BMI, comorbidities, and baseline WHO score; and for disease progression, the OR was 1·79 (1·60–2·01) when unadjusted and 1·63 (1·41–1·91) when adjusted (p<0·0001 for all). The predictive accuracy of the optimised COV50 thresholds was 74·4% (71·6–77·1%) for mortality (threshold 0·47) and 67·4% (64·4–70·3%) for disease progression (threshold 0·04). When adjusted for covariables and the baseline WHO score, these thresholds improved AUCs from 0·835 to 0·853 (p=0·033) for death and from 0·697 to 0·730 (p=0·0008) for progression. Of 196 participants who received ambulatory care, 194 (99%) did not reach the 0·04 threshold. The cost reductions associated with 1 day less hospitalisation per 1000 participants were million Euro (M€) 0·887 (5–95% percentile interval 0·730–1·039) in participants at a low risk (COV50 <0·04) and M€2·098 (1·839-2·365) in participants at a high risk (COV50 ≥0·04).InterpretationThe urinary proteomic COV50 marker might be predictive of adverse COVID-19 outcomes. Even in people with mild-to-moderate PCR-confirmed infections (WHO scores 1–4), the 0·04 COV50 threshold justifies earlier drug treatment, thereby potentially reducing the number of days in hospital and associated costs.FundingGerman Federal Ministry of Health.

Land use and land cover change in a tropical mountain landscape of northern Ecuador: Altitudinal patterns and driving forces

Tropical mountain ecosystems are threatened by land use pressures, compromising their capacity to provide ecosystem services. Although local patterns and interactions among anthropogenic and biophysical factors shape these socio-ecological systems, the analysis of landscape changes and their driving forces is often qualitative and sector oriented. Using the Driver-Pressure-State-Impact-Response (DPSIR) framework, we characterized land use land cover (LULC) dynamics using Markov chain probabilities by elevation and geographic settings and then integrated them with a variety of publicly available geospatial and temporal data into a Generalized Additive Model (GAM) to evaluate factors driving such landscape dynamics in a sensitive region of the northern Ecuadorian Andes. In previous agricultural land located at lower elevations to the east of the studied territory, we found a significant expansion of floriculture (13 times) and urban areas (25 times), reaching together almost 10% of the territory from 1990 to 2014. Our findings also revealed an unexpected trend of páramo stability (0.75-0.90), but also a 40% reduction of montane forests, with the lowest probability (<0.50) of persistence in the elevation band of 2800-3300 m; agricultural land is replacing this LULC classes at higher elevation. These trends highlight the increasing threat of permanently losing the already vulnerable native mountain biodiversity. GAMs of socio-economic factors, demographic, infrastructure variables, and environmental parameters explained between 21 to 42% of the variation of LULC transitions observed in the study region, where topographic factors was the main drivers of change. The conceptual and methodological approach of our findings demonstrate how dynamic patterns through space and time and their explanatory drivers can assist local authorities and decision makers to improve sustainable resource land management in vulnerable landscapes such as the tropical Andes in northern Ecuador.

Markov Chain Probability Models to Describe Bi-modal Rainfall Pattern in Sri Lanka

Purpose: Sri Lanka is a tropical island with prominent four monsoonal seasons. The rainfall pattern of the country follows a bi-modal distribution with two peaks centred on two growing seasons. Model the bimodel rainfall distribution of Sri Lanka using the Markov probability chain model was the objective of this study. Research Method: Both first and second-order Markov probability models were developed for Anuradhapura, Badulla, Hambanthota and Katunayake using daily rainfall data for 1981–2011 period and the locations were selected to cover the major parts of the country. The model fit was done using Instat Statistical Programme. Findings: Both first and second-order Markov models successfully described bi-modal distribution of rainfall. In general, both transitional probabilities in the first order (p_rd and p_rr) and three transitional probabilities of second-order except rainfall after dry day and rainy day (p_rrd) followed a bi-modal pattern with two peaks. The sum of the logs of the rainfall amount (lr) and the amount of rainfall on rainy days (r_mean) also showed two peaks for two growing seasons. In both models, stations in the dry zone showed higher agreement in the simulated rainfall. Research Limitations: Lack of continuous long-term rainfall data is one of the major limitations. Originality/ Value: It is evident that both first and second-order Markov chain probability models are very much capable to explain the bi-modal rainfall distribution in Sri Lanka.

A comparative analysis of pre- and post-industrial spatiotemporal drought trends and patterns of Tibet Plateau using Sen slope estimator and steady-state probabilities of Markov Chain

A comparative analysis of pre- and post-industrial spatiotemporal drought trends and patterns of Tibet Plateau using Sen slope estimator and steady-state probabilities of Markov Chain

Spatio-Temporal Extraction of Surface Waterbody and Its Response of Extreme Climate along the Upper Huaihe River

The upper Huaihe River is the water-producing area of the Huaihe River Basin and the major grain and oil-producing area in China. The changing global climate over the recent years has increased the frequency of extreme weather in the upper reaches of the Huaihe River. Research on the responses of surface water bodies to extreme climates has become increasingly important. Based on all utilizable Landsat 4–8 T1–SR data and frequency mapping, the spatio-temporal extraction of surface water and its response to extreme climate were studied. We generated high-precision frequency maps of surface water, and a comparison of cartographic accuracy evaluation indices and spatial consistency was also carried out. The high-precision interpretation of small waterbodies constructs a surface water distribution with better continuity and integrity. Furthermore, we investigated the effect of El Niño/La Niña events on precipitation, temperature, and surface water along the upper Huaihe River, using the Mann–Kendall mutation tests. The results show: in 1987–2018, periods of abrupt changes in precipitation coincide with EI Niño/La Niña events, indicating that the precipitation was sensitive to EI Niño/La Niña events, which also strongly correlated with surface water area during wet and dry years. The effect of extreme events on seasonal water was smaller than permanent water. Surface water area showed an insignificant declining trend after 1999 and a significant drop in 2012. The phenomenon of topographic enhancement of precipitation controlled the spatial distribution of permanent water, with human activities having a substantial effect on the landscape pattern of seasonal water. Finally, discussions and applications related to the Markov Chain probability calculation theory in the paper contributed to enriching the theories on frequency mapping. The relevant results provide a theoretical basis and case support for the formulation of long-term water resources utilization and allocation policies.

Analysis of Consecutive Days Maximum Rainfall Together With Dry, Wet Spell Rainfall for Crop Planning at Jorhat (Assam), India

In this study, frequency analyses of 1 to 6 consecutive days maximum rainfalls have been carried out. For this purpose, the daily rainfall data for 23 years has been collected from the Indian Meteorological Department (IMD), Guwahati for Jorhat Station. Based on L-moment, we consider the probability distributions like Log Normal (LN), Pearson Type III (P III), Log-Pearson Type III (LP III), and Extreme Value Type I (EVI). The best-fitting probability distribution for consecutive days maximum rainfall is discussed for estimating the rainfall in different return periods such as 2 to 100 years. Also, the daily rainfall data are converted to 52 standard meteorological weeks (SMW) to use the Markov Chain Probability model. Then average, maximum, minimum, standard deviation, and covariance of rainfall are calculated. By using this model, initial and conditional probabilities of dry and wet weeks are calculated. The probability of onset and withdrawal rainy season are calculated which are 95.83% chance during 23rd and 47th weeks. And, we find a relation of average rainfall and effective rainfall (ER) of the station.

Predict and Simulate Sustainable Urban Growth by Using GIS and MCE Based CA. Case of Famagusta in Northern Cyprus

The research study utilizes Multi Criteria Evaluation (MCE) method in geographic information systems (GIS) environment and uses MCE suitability maps with Cellular Automata (CA) for predicting and simulating sustainable urban development scenarios in Famagusta City. It represents first scenario-based simulations of the future growth of Famagusta as “do-nothing” and “sustainable”. Under the do-nothing scenario, Markov Chain probability analysis with CA models is used with temporal land-use/cover datasets based on the images from 2002 and 2011. It shows that, Famagusta City is moving away from sustainable development. Future expansion of both medium-density and low-density urban zones are always located around existing built-up urban area along transportation lines. A similar model is employed by applying sustainable urban development policies by the policy driven scenario. As a main goal, sustainable urban development includes three main criteria, compactness, environmental protection, and social equity. Additionally, brownfield development, distance from center, soil characteristics, soil productivity, vegetation, environmental protection areas (EPA), distance from local services, distance from open space are used as criteria with Analytical Hierarchy Process (AHP). Having such a simulation with the combination of MCE, GIS, and CA has several advantages. Prediction of urban growth presents possible alternative development in the future; visualization of decision making easier for town planners and supports the spatial planning process; and creates more realistic results of our choices related to urban growth.

Spatial and temporal analysis of the mid-summer dry spells for the summer rainfall region of South Africa

South Africa is frequently subjected to severe droughts and dry spells during the rainy season. As such, rainfall is one of the most significant factors limiting dryland crop production in South Africa. The mid-summer period is particularly important for agriculture since a lack of rain during this period negatively affects crop yields. Dry spell frequency analyses are used to investigate the impacts of sub-seasonal rainfall variability on crop yield, since seasonal rainfall totals alone do not explain the relationship between rainfall and crop yields. This study investigated the spatial and temporal occurrences of the mid-summer dry spells based on magnitude, length and time of occurrence in the major maize growing areas of the summer rainfall region of South Africa. Three thresholds of 5 mm, 10 mm, and 15 mm total rainfall for a pentad were used for the analysis of dry spells. Dry spell analysis showed that dry pentads occur during mid-summer with differing intensity, duration and frequency across the summer rainfall region. Annual frequency of dry pentads for the mid-summer period ranged between 0 and 4 pentads for the 5 mm threshold and 1 to 7 for the 10 mm and 15 mm thresholds. The non-parametric Mann-Kendall trend analysis of the dry pentads indicates that there is no significant trend in the frequency of dry spells at a 95% confidence level. The initial and conditional probabilities of getting a dry spell using the Markov chain model also showed that there is a 32% to 80% probability that a single pentad will be dry using the 15 mm threshold. There is a 5% to 48% probability of experiencing two consecutive dry pentads and 1% to 29% probability of getting three consecutive dry pentads. The duration and intensity of dry spells, as well as the Markov chain probabilities, showed a decrease in dry spells from west to east of the maize-growing areas of the summer rainfall region of South Africa.

Cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noises

This paper focuses on the mean square cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noise via pinning control technique. Network topology can take weaker conditions in each cluster but an extra balanced condition is also needed. A time-varying control gain will be introduced to eliminate the effect of stochastic noise. For the case of fixed topology, if the induced digraph of each cluster has a directed spanning tree, the sufficient conditions for the mean square cluster consensus can be obtained. For the case of Markovian switching topologies, if the induced digraph of union of the Laplacian matrix of each mode has a directed spanning tree, the mean square cluster consensus conclusion can be derived. Particularly, if the elements of transition probability of Markov chain are partly unknown, we can also obtain the same conclusion under the same conditions. Finally, two examples are given to illustrate our results.

A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks

The combination of network sciences, nonlinear dynamics and time series analysis provides novel insights and analogies between the different approaches to complex systems. By combining the considerations behind the Lyapunov exponent of dynamical systems and the average entropy of transition probabilities for Markov chains, we introduce a network measure for characterizing the dynamics on state-transition networks with special focus on differentiating between chaotic and cyclic modes. One important property of this Lyapunov measure consists of its non-monotonous dependence on the cylicity of the dynamics. Motivated by providing proper use cases for studying the new measure, we also lay out a method for mapping time series to state transition networks by phase space coarse graining. Using both discrete time and continuous time dynamical systems the Lyapunov measure extracted from the corresponding state-transition networks exhibits similar behavior to that of the Lyapunov exponent. In addition, it demonstrates a strong sensitivity to boundary crisis suggesting applicability in predicting the collapse of chaos.

Estimates of stability of transition probabilities for non-homogeneous Markov chains in the case of the uniform minorization

Estimates of stability of transition probabilities for non-homogeneous Markov chains in the case of the uniform minorization