scholarly journals A Markovian Approach To The Modeling Of Sound Propagation In Urban Streets

2012 ◽  
Author(s):  
Zaiton Haron ◽  
David Oldham
Keyword(s):  
Markov Process ◽  
Markov Model ◽  
Diffuse Reflection ◽  
Sound Propagation ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Multiple Reflections ◽  
Urban Streets ◽  
Novel Approach ◽  
Markovian Approach

Kertas kerja ini menguji kaedah novel, iaitu Markov untuk tujuan simulasi pengorakan bunyi di jalan raya. Kaedah ini menganggap deretan bangunan di tepi jalan menyerap dan memantulkan bunyi secara berserak. Proses simulasi menganggap proses pengorakan bunyi sebagai proses Markov jujukan pertama bercirikan matrix kebarangkalian perpindahan pancaran bunyi di antara permukaan–permukaan. Keputusan simulasi menggunakan kaedah Markov dibandingkan dengan keputusan diperolehi dari model kommersial RAYNOISE dengan menggunakan pilihan pantulan berserak. Hasil keputusan menunjukkan paras tekanan bunyi di jalan raya yang diramal oleh kaedah Markov mempunyai kesepadanan yang baik dengan ramalan diperolehi dari model RAYNOISE. Ini menunjukkan kaedah Markov mempunyai potensi untuk meramal pantulan berganda bagi keadaan sempadan berserak. Kesan agihan serapan permukaan bangunan juga dikaji, dan dengan skop dan anggapan kajian didapati jalan raya yang mempunyai deretan bangunan berpermukaan menyerap bunyi berupaya menghasilkan pengurangan bunyi kurang dari 1 dB. Kata kunci: Pantulan berserak; proses Markov; kebarangkalian perpindahan; pengorakan bunyi; kawalan bunyi bising This paper examined the capability of the novel approach called Markov in the simulation of sound propagation in streets. The approach assumes that the facades lining the streets absorb and reflect sound diffusely. The simulation process treated the sound propagation process as first order Markov process characterised by a matrix of transition probabilities relating to sound radiation between surfaces. The results of simulation using Markov model were compared with the results obtained from a commercial model, RAYNOISE using the diffuse reflection option. The results showed that sound pressure level in a street predicted by the Markov model was in good agreement with predictions obtained using RAYNOISE model. This suggest that the Markov model has the potential to predict multiple reflections for diffuse boundary conditions. The effects of distribution absorption of building facades were also investigated and within the scope and assumptions in this study; it is shown streets with absorbent building facade result in sound reductions typically less than 1 dB. Key words: Diffuse reflection; Markov process; transition probability; sound propagation; noise control

scholarly journals States Transitions Inference of Postpartum Depression Based on Multi-State Markov Model

2021 ◽  
Vol 18 (14) ◽  
pp. 7449
Author(s):  
Juan Xiong ◽  
Qiyu Fang ◽  
Jialing Chen ◽  
Yingxin Li ◽  
Huiyi Li ◽  
...  
Keyword(s):  
Postpartum Depression ◽  
Markov Model ◽  
Normal State ◽  
Sojourn Time ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Public Health Problem ◽  
Mental States ◽  
Hazard Ratio ◽  
Multiple Time

Background: Postpartum depression (PPD) has been recognized as a severe public health problem worldwide due to its high incidence and the detrimental consequences not only for the mother but for the infant and the family. However, the pattern of natural transition trajectories of PPD has rarely been explored. Methods: In this research, a quantitative longitudinal study was conducted to explore the PPD progression process, providing information on the transition probability, hazard ratio, and the mean sojourn time in the three postnatal mental states, namely normal state, mild PPD, and severe PPD. The multi-state Markov model was built based on 912 depression status assessments in 304 Chinese primiparous women over multiple time points of six weeks postpartum, three months postpartum, and six months postpartum. Results: Among the 608 PPD status transitions from one visit to the next visit, 6.2% (38/608) showed deterioration of mental status from the level at the previous visit; while 40.0% (243/608) showed improvement at the next visit. A subject in normal state who does transition then has a probability of 49.8% of worsening to mild PPD, and 50.2% to severe PPD. A subject with mild PPD who does transition has a 20.0% chance of worsening to severe PPD. A subject with severe PPD is more likely to improve to mild PPD than developing to the normal state. On average, the sojourn time in the normal state, mild PPD, and severe PPD was 64.12, 6.29, and 9.37 weeks, respectively. Women in normal state had 6.0%, 8.5%, 8.7%, and 8.8% chances of progress to severe PPD within three months, nine months, one year, and three years, respectively. Increased all kinds of supports were associated with decreased risk of deterioration from normal state to severe PPD (hazard ratio, HR: 0.42–0.65); and increased informational supports, evaluation of support, and maternal age were associated with alleviation from severe PPD to normal state (HR: 1.46–2.27). Conclusions: The PPD state transition probabilities caused more attention and awareness about the regular PPD screening for postnatal women and the timely intervention for women with mild or severe PPD. The preventive actions on PPD should be conducted at the early stages, and three yearly; at least one yearly screening is strongly recommended. Emotional support, material support, informational support, and evaluation of support had significant positive associations with the prevention of PPD progression transitions. The derived transition probabilities and sojourn time can serve as an importance reference for health professionals to make proactive plans and target interventions for PPD.

scholarly journals Atmospheric blocking types: Frequencies and transitions

2020 ◽  
Author(s):  
Carola Detring ◽  
Annette Müller ◽  
Lisa Schielicke ◽  
Peter Névir ◽  
Henning W. Rust
Keyword(s):  
Markov Model ◽  
Northern Hemisphere ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Time Step ◽  
Pressure System ◽  
Monthly Basis ◽  
Atlantic Sector ◽  
Weather Patterns ◽  
Significant Difference

Abstract. Stationary, long-lasting blocked weather patterns can lead to extreme conditions such as very high temperatures or heavy rainfall. They are defined by a persistent high pressure system in combination with one or two low pressure systems. The mechanisms for the onset of such weather patterns are still not fully understood. Using a novel method based on the kinematic vorticity number we distinguish between two blocking types, namely High-over-Low and Omega block, in previously-identified blocking periods. Our main goal of this work is to study the temporal evolution of the occurrence probability and the onset, offset, and transition probabilities of blocking on the northern hemisphere. We analyze NCEP-DOE Reanalysis 2 data over the30 year period from 1990 to 2019 in two regions: Euro-Atlantic sector (40° W–30° E) and half northern hemisphere (90° W–90° E). First, we use logistic regression to investigate the temporal development of blocking probabilities depending on years, seasons and months. We find no significant difference in blocking numbers over the 30 year period. But we find large differences in the occurrence probabilities on a monthly basis with strongest increases over the 30 year period in February and March that are compensated by a decrease in December and autumn. Second, we use a Markov model to calculate the transition probabilities for two models: One is composed of two states blocking and no blocking, and another Markov model (three states) that additionally distinguishes between the specific blocking types High-over-Low and Omega blocking as well as of the state no blocking. The description with Markov theory reduces the probability to change from one weather regime to another or to stay within the same regime to a dependency only on the previous time step. Over the 30 year period, we found the largest changes in transition probabilities in the summer season, where the transition probability to Omega blocks increase strongly, while the unblocked state becomes less probable. Hence, Omega blocks become more frequent and stable in summer at the expense of the other states. As a main result, we show that Omega blocking is more likely to occur and more persistent than the High-over-Low blocking pattern.

Transition Probabilities for Markov Process on a Line Segment Located within a Quarter-Plane

2021 ◽  
pp. 4-24
Author(s):  
A.V. Kalinkin
Keyword(s):  
Markov Process ◽  
Random Process ◽  
Generating Function ◽  
Line Segment ◽  
Transition Probabilities ◽  
Special Functions ◽  
Transition Probability ◽  
Separation Of Variables ◽  
Two Dimensional ◽  
Quarter Plane

The paper considers a quadratic birth-death Markov process. The points on a line segment located within a quarter-plane represent the states of the random process. We designate the set of vectors that have integer non-negative coordinates as our quarter plane. The process is defined by infinitesimal characteristics, or transition probability densities. These characteristics are determined by a quadratic function of the coordinates at the segment points with integer coordinates. The boundary points of the segment are absorbing; at these points, the random process stops. We investigated a critical case when process jumps are equally probable at the moment of exiting a point. We derived expressions describing transition probabilities of the Markov process as a spectral series. We used a two-dimensional exponential generating function of transition probabilities and a two-dimensional generating function of transition probabilities. The first and second systems of ordinary differential Kolmogorov equations for Markov process transition probabilities are reduced to second-order mixed type partial differential equations for a double generating function. We solve the resulting system of linear equations using separation of variables. The spectrum obtained is discrete. The eigen-functions are expressed in terms of hypergeometric functions. The particular solution constructed is a Fourier series, whose coefficients are derived by means of expo-nential expansion. We employed sums of functional series known in the theory of special functions to construct the exponential expansion required

Predicting diameter distributions: a test of the stationary Markov model

1986 ◽  
Vol 16 (1) ◽  
pp. 130-135 ◽  
Author(s):  
Mark R. Roberts ◽  
Allan J. Hruska
Keyword(s):  
Markov Model ◽  
Growth Rates ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Diameter Distribution ◽  
Stand Age ◽  
Growth Data ◽  
Diameter Class ◽  
Average Growth ◽  
Diameter Classes

We tested the null hypothesis that diameter class transitions over a 40-year period (1940–1980) in an even-aged mixed Pinusresinosa Ait. – Pinusstrobus L. stand represent a stationary Markov process. Transition probabilities were constructed from growth data on 202 trees ≥ 5.1 cm DBH in a 0.4-ha permanent plot. For each species, a diameter distribution in 1980 was predicted with the stationary Markov model using the 1940–1950 transition probability matrix. The predicted and observed 1980 distributions were significantly different for P. resinosa (χ2 = 31.67, p < 0.01), but not P. strobus (χ2 = 7.86, not significant). In P. resinosa, growth rates of trees in the same diameter class at different points in time declined with increasing stand age. This violates the assumption of stationarity. Growth did not decline in most diameter classes in P. strobus. The model also assumes that differences in the competitive histories of trees of the same size do not affect transition probabilities. The average growth rates of trees in different crown classes within two diameter classes were significantly different for P. resinosa, but not for P. strobus. Both assumptions of the model were violated in the case of P. resinosa. The.model was not rejected for P. strobus because it is a midtolerant species capable of relatively constant growth in the understory. However, this study included only the middle period of stand development when growth rates are relatively constant. These results indicate that more biologically realistic modelling approaches which incorporate growth declines with stand age and past competitive effects should be pursued.

scholarly journals Transition Probabilities of Disablement for Malaysian Population in Need of Long-Term Care

2020 ◽  
Vol 13 ◽  
pp. 1-10
Author(s):  
Syazreen Niza Shair
Keyword(s):  
Markov Model ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Age Groups ◽  
Prevalence Rates ◽  
Cross Sectional ◽  
Term Care ◽  
Data Limitations ◽  
Multiple State ◽  
Almost All

This research aims to estimate the transition probabilities of lives becoming disabled and the extent to which they are disabled using the approach of functional Markov model. The transition probability from one disabled state to a more or less severely disabled state is best estimated using longitudinal data in which the change in the health status of each respondent can be monitored over one or more years. Such data are limited in Malaysia, typically covering only a smaller area of the nation. The functional Markov model overcomes such data limitations, using cross-sectional data which measures the disability status of individuals only at one point in time and build a functional form for the transition probabilities in a multiple state model. Results suggested that multiple state model's prevalence rates replicated the Malaysian prevalence rates quite well, indicating that the parameters of the probability of deterioration had been estimated accurately with sum squared of errors less than 5% for almost all age groups and disability levels. Furthermore, severely disabled elderlies, especially among the oldest age group, have the highest probability to die compared to less severely disabled elderlies.

scholarly journals Predicting the natural history of metabolic syndrome with a Markov-system dynamic model: a novel approach

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Abbas Rezaianzadeh ◽  
Esmaeil Khedmati Morasae ◽  
Davood Khalili ◽  
Mozhgan Seif ◽  
Ehsan Bahramali ◽  
...  
Keyword(s):  
Metabolic Syndrome ◽  
Natural History ◽  
Markov Model ◽  
Transition Probabilities ◽  
Model Fitting ◽  
System Dynamic ◽  
Markov System ◽  
Novel Approach ◽  
Kolmogorov Smirnov ◽  
Mean Differences

Abstract Background Markov system dynamic (MSD) model has rarely been used in medical studies. The aim of this study was to evaluate the performance of MSD model in prediction of metabolic syndrome (MetS) natural history. Methods Data gathered by Tehran Lipid & Glucose Study (TLGS) over a 16-year period from a cohort of 12,882 people was used to conduct the analyses. First, transition probabilities (TPs) between 12 components of MetS by Markov as well as control and failure rates of relevant interventions were calculated. Then, the risk of developing each component by 2036 was predicted once by a Markov model and then by a MSD model. Finally, the two models were validated and compared to assess their performance and advantages by using mean differences, mean SE of matrices, fit of the graphs, and Kolmogorov-Smirnov two-sample test as well as R2 index as model fitting index. Results Both Markov and MSD models were shown to be adequate for prediction of MetS trends. But the MSD model predictions were closer to the real trends when comparing the output graphs. The MSD model was also, comparatively speaking, more successful in the assessment of mean differences (less overestimation) and SE of the general matrix. Moreover, the Kolmogorov-Smirnov two-sample showed that the MSD model produced equal distributions of real and predicted samples (p = 0.808 for MSD model and p = 0.023 for Markov model). Finally, R2 for the MSD model was higher than Markov model (73% for the Markov model and 85% for the MSD model). Conclusion The MSD model showed a more realistic natural history than the Markov model which highlights the importance of paying attention to this method in therapeutic and preventive procedures.

scholarly journals Markov Chain Models for the Stochastic Modeling of Pitting Corrosion

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
A. Valor ◽  
F. Caleyo ◽  
L. Alfonso ◽  
J. C. Velázquez ◽  
J. M. Hallen
Keyword(s):  
Markov Process ◽  
Pitting Corrosion ◽  
Probability Function ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Closed Form Solution ◽  
Form Solution ◽  
Extreme Value Statistics ◽  
Pit Depth ◽  
Transition Probability Function

The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth) Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.

scholarly journals The Markov model as a pattern for earthquakes recurrence in South America

2001 ◽  
Vol 34 (4) ◽  
pp. 1611 ◽  
Author(s):  
T. M. TSAPANOS
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Markov Process ◽  
South America ◽  
Markov Chains ◽  
Stochastic Model ◽  
Markov Model ◽  
Transition Matrix ◽  
Transition Probabilities ◽  
Large Earthquakes

The well known stochastic model of the Markov chains is applied in south America, in order to search for pattern of great earthquakes recurrence. The model defines a process in which successive state occupancies are governed by the transition probabilities pij, of the Markov process and are presented as a transition matrix say P, which has NxN dimensions. We considered as states in the present study the predefined seismic zones of south America. Thus the visits from zone to zone, which is from state to state, carry with them the number of the zone in which they occurred. If these visits are considered to be earthquake occurrences we can inspect their migration between the zones (states) and estimate their genesis in a statistical way, through the transition probabilities. Attention is given in zones where very large earthquakes with Ms>7.8 have occurred. A pattern is revealed which is suggested migration of these large shocks from south towards north. The use of Monte Carlo simulation verify the defined pattern.

scholarly journals Deep Learning for Transient Image Reconstruction from ToF Data

Sensors ◽  
2021 ◽  
Vol 21 (6) ◽  
pp. 1962
Author(s):  
Enrico Buratto ◽  
Adriano Simonetto ◽  
Gianluca Agresti ◽  
Henrik Schäfer ◽  
Pietro Zanuttigh
Keyword(s):  
Deep Learning ◽  
State Of The Art ◽  
Light Response ◽  
Real Data ◽  
Depth Image ◽  
Learning Approach ◽  
Multiple Reflections ◽  
Noisy Input ◽  
Novel Approach ◽  
Incoming Light

In this work, we propose a novel approach for correcting multi-path interference (MPI) in Time-of-Flight (ToF) cameras by estimating the direct and global components of the incoming light. MPI is an error source linked to the multiple reflections of light inside a scene; each sensor pixel receives information coming from different light paths which generally leads to an overestimation of the depth. We introduce a novel deep learning approach, which estimates the structure of the time-dependent scene impulse response and from it recovers a depth image with a reduced amount of MPI. The model consists of two main blocks: a predictive model that learns a compact encoded representation of the backscattering vector from the noisy input data and a fixed backscattering model which translates the encoded representation into the high dimensional light response. Experimental results on real data show the effectiveness of the proposed approach, which reaches state-of-the-art performances.

scholarly journals A MARKOV PROCESS OF GENE FREQUENCY CHANGE IN A GEOGRAPHICALLY STRUCTURED POPULATION

Genetics ◽  
1974 ◽  
Vol 76 (2) ◽  
pp. 367-377
Author(s):  
Takeo Maruyama
Keyword(s):  
Genetic Variation ◽  
Markov Process ◽  
Diffusion Process ◽  
Gene Frequency ◽  
Transition Probabilities ◽  
Large Population ◽  
Sample Path ◽  
Time Parameter ◽  
Frequency Change ◽  
Structured Population

ABSTRACT A Markov process (chain) of gene frequency change is derived for a geographically-structured model of a population. The population consists of colonies which are connected by migration. Selection operates in each colony independently. It is shown that there exists a stochastic clock that transforms the originally complicated process of gene frequency change to a random walk which is independent of the geographical structure of the population. The time parameter is a local random time that is dependent on the sample path. In fact, if the alleles are selectively neutral, the time parameter is exactly equal to the sum of the average local genetic variation appearing in the population, and otherwise they are approximately equal. The Kolmogorov forward and backward equations of the process are obtained. As a limit of large population size, a diffusion process is derived. The transition probabilities of the Markov chain and of the diffusion process are obtained explicitly. Certain quantities of biological interest are shown to be independent of the population structure. The quantities are the fixation probability of a mutant, the sum of the average local genetic variation and the variation summed over the generations in which the gene frequency in the whole population assumes a specified value.

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