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

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.

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Atmospheric blocking types: Frequencies and transitions

10.5194/wcd-2020-62 ◽

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.

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Predicting diameter distributions: a test of the stationary Markov model

Canadian Journal of Forest Research ◽

10.1139/x86-022 ◽

1986 ◽

Vol 16 (1) ◽

pp. 130-135 ◽

Cited By ~ 18

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.

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

Jurnal Teknologi ◽

10.11113/jt.v52.123 ◽

2012 ◽

Cited By ~ 2

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

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

ASM Science Journal ◽

10.32802/asmscj.2020.553 ◽

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.

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Postpartum depression symptoms in survey-based research: a structural equation analysis

BMC Public Health ◽

10.1186/s12889-020-09999-2 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Che Wan Jasimah Bt Wan Mohamed Radzi ◽

Hashem Salarzadeh Jenatabadi ◽

Nadia Samsudin

Keyword(s):

Postpartum Depression ◽

Latent Variable ◽

Structural Equation ◽

Depression Scale ◽

Public Health Problem ◽

Equation Modeling ◽

Depression Symptoms ◽

Postpartum Women ◽

Unhealthy Food ◽

High Level

Abstract Background Since the last decade, postpartum depression (PPD) has been recognized as a significant public health problem, and several factors have been linked to PPD. Mothers at risk are rarely undetected and underdiagnosed. Our study aims to determine the factors leading to symptoms of depression using Structural Equation Modeling (SEM) analysis. In this research, we introduced a new framework for postpartum depression modeling for women. Methods We structured the model of this research to take into consideration the Malaysian culture in particular. A total of 387 postpartum women have completed the questionnaire. The symptoms of postpartum depression were examined using the Edinburgh Postnatal Depression Scale (EPDS), and they act as a dependent variable in this research model. Results Four hundred fifty mothers were invited to participate in this research. 86% of the total distributed questionnaire received feedback. The majority of 79.6% of respondents were having depression symptoms. The highest coefficients of factor loading analysis obtained in every latent variable indicator were income (β = 0.77), screen time (β = 0.83), chips (β = 0.85), and anxiety (β = 0.88). Lifestyle, unhealthy food, and BMI variables were directly affected by the dependent variable. Based on the output, respondents with a high level of depression symptoms tended to consume more unhealthy food and had a high level of body mass indexes (BMI). The highest significant impact on depression level among postpartum women was unhealthy food consumption. Based on our model, the findings indicated that 76% of the variances stemmed from a variety of factors: socio-demographics, lifestyle, healthy food, unhealthy food, and BMI. The strength of the exogenous and endogenous variables in this research framework is strong. Conclusion The prevalence of postpartum women with depression symptoms in this study is considerably high. It is, therefore, imperative that postpartum women seek medical help to prevent postpartum depressive symptoms from worsening.

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Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

Journal of Vibration and Control ◽

10.1177/1077546321989202 ◽

2021 ◽

pp. 107754632198920

Author(s):

Zeinab Fallah ◽

Mahdi Baradarannia ◽

Hamed Kharrati ◽

Farzad Hashemzadeh

Keyword(s):

Transition Probabilities ◽

Sliding Mode ◽

Transition Probability ◽

Transition Probability Matrix ◽

Linear Matrix ◽

Sliding Mode Controller ◽

Sliding Surface ◽

Markovian Jump ◽

Markovian Jump System ◽

Singular Markovian Jump Systems

This study considers the designing of the H ∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H ∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.

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Infinitely divisible random transition probabilities with application to dependent Markov chains

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000004215 ◽

1984 ◽

Vol 25 (4) ◽

pp. 463-472

Author(s):

Peter L. Chesson

Keyword(s):

Markov Chain ◽

Markov Chains ◽

White Noise ◽

Transition Probabilities ◽

Transition Probability ◽

Transition Rates ◽

Infinitely Divisible ◽

Random Transition ◽

Transition Probability Matrices ◽

Probability Matrices

AbstractRandom transition probability matrices with stationary independent factors define “white noise” environment processes for Markov chains. Two examples are considered in detail. Such environment processes can be used to construct several Markov chains which are dependent, have the same transition probabilities and are jointly a Markov chain. Transition rates for such processes are evaluated. These results have application to the study of animal movements.

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Fermions on wobbling kinks: normal versus quasinormal modes

Journal of High Energy Physics ◽

10.1007/jhep09(2021)103 ◽

2021 ◽

Vol 2021 (9) ◽

Author(s):

João G. F. Campos ◽

Azadeh Mohammadi

Keyword(s):

Transition Probabilities ◽

Transition Probability ◽

Quasinormal Modes ◽

Golden Rule ◽

Coupling Constants ◽

Large Coupling ◽

Constant Rate ◽

Fermi's Golden Rule ◽

The Impact ◽

Fermi’S Golden Rule

Abstract The system consisting of a fermion in the background of a wobbling kink is studied in this paper. To investigate the impact of the wobbling on the fermion-kink interaction, we employ the time-dependent perturbation theory formalism in quantum mechanics. To do so, we compute the transition probabilities between states given in terms of the Bogoliubov coefficients. We derive Fermi’s golden rule for the model, which allows the transition to the continuum at a constant rate if the fermion-kink coupling constant is smaller than the wobbling frequency. Moreover, we study the system replacing the shape mode with a quasinormal mode. In this case, the transition rate to continuum decays in time due to the leakage of the mode, and the final transition probability decreases sharply for large coupling constants in a way that is analogous to Fermi’s golden rule. Throughout the paper, we compare the perturbative results with numerical simulations and show that they are in good agreement.

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The Temporal Dynamics of EEG Microstate Reveals the Neuromodulation Effect of Acupuncture With Deqi

Frontiers in Neuroscience ◽

10.3389/fnins.2021.715512 ◽

2021 ◽

Vol 15 ◽

Author(s):

Xiaopeng Si ◽

Shunli Han ◽

Kuo Zhang ◽

Ludan Zhang ◽

Yulin Sun ◽

...

Keyword(s):

Human Brain ◽

Temporal Dynamics ◽

Transition Probabilities ◽

Transition Probability ◽

Therapeutic Effects ◽

Dynamic Feature ◽

Correlation Relationship ◽

External Stimulation ◽

Positive Correlation ◽

Mapping Tool

The electroencephalography (EEG) microstate has recently emerged as a new whole-brain mapping tool for studying the temporal dynamics of the human brain. Meanwhile, the neuromodulation effect of external stimulation on the human brain is of increasing interest to neuroscientists. Acupuncture, which originated in ancient China, is recognized as an external neuromodulation method with therapeutic effects. Effective acupuncture could elicit the deqi effect, which is a combination of multiple sensations. However, whether the EEG microstate could be used to reveal the neuromodulation effect of acupuncture with deqi remains largely unclear. In this study, multichannel EEG data were recorded from 16 healthy subjects during acupuncture manipulation, as well as during pre- and post-manipulation tactile controls and pre- and post-acupuncture rest controls. As the basic acupuncture unit for regulating the central nervous system, the Hegu acupoint was used in this study, and each subject’s acupuncture deqi behavior scores were collected. To reveal the neuroimaging evidence of acupuncture with deqi, EEG microstate analysis was conducted to obtain the microstate maps and microstate parameters for different conditions. Furthermore, Pearson’s correlation was analyzed to investigate the correlation relationship between microstate parameters and deqi behavioral scores. Results showed that: (1) compared with tactile controls, acupuncture manipulation caused significantly increased deqi behavioral scores. (2) Acupuncture manipulation significantly increased the duration, occurrence, and contribution parameters of microstate C, whereas it decreased those parameters of microstate D. (3) Microstate C’s duration parameter showed a significantly positive correlation with acupuncture deqi behavior scores. (4) Acupuncture manipulation significantly increased the transition probabilities with microstate C as node, whereas it reduced the transition probabilities with microstate D as node. (5) Microstate B→C’s transition probability also showed a significantly positive correlation with acupuncture deqi behavior scores. Taken together, the temporal dynamic feature of EEG microstate could be used as objective neuroimaging evidence to reveal the neuromodulation effect of acupuncture with deqi.

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Large Scale Shell Model Calculations of the Negative-Parity States Structure in 24Mg Nucleus

Ukrainian Journal of Physics ◽

10.15407/ujpe66.4.293 ◽

2021 ◽

Vol 66 (4) ◽

pp. 293

Author(s):

A.A. Al-Sammarraie ◽

F.A. Ahmed ◽

A.A. Okhunov

Keyword(s):

Shell Model ◽

Large Scale ◽

Transition Probabilities ◽

Transition Probability ◽

Energy Levels ◽

Form Factors ◽

Model Space ◽

Negative Parity ◽

Matrix Elements ◽

Model Calculations

The negative-parity states of 24Mg nucleus are investigated within the shell model. We are based on the calculations of energy levels, total squared form factors, and transition probability using the p-sd-pf (PSDPF) Hamiltonian in a large model space (0 + 1) hW. The comparison between the experimental and theoretical states showed a good agreement within a truncated model space. The PSDPF-based calculations successfully reproduced the data on the total squared form factors and transition probabilities of the negative-parity states in 24Mg nucleus. These quantities depend on the one-body density matrix elements that are obtained from the PSDPF Hamiltonian. The wave functions of radial one-particle matrix elements calculated with the harmonic-oscillator potential are suitable to predict experimental data by changing the center-of-mass corrections.

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