Eigenanalysis for the Kolmogorov backward equation for the neutral multi-allelic model

1981 ◽  
Vol 11 (3) ◽  
pp. 235-244 ◽  
Author(s):  
Morihiro Notohara
Keyword(s):  
Backward Equation ◽  
Allelic Model

Embedding non-linear filtering in autonomous underwater vehicle dynamics via the Kolmogorov backward equation

2021 ◽  
pp. 014233122110196
Author(s):  
Ravish H. Hirpara ◽  
Shambhu N. Sharma
Keyword(s):  
State Vector ◽  
Autonomous Underwater Vehicle ◽  
Underwater Vehicle ◽  
Linear Filtering ◽  
Homogeneous Markov Process ◽  
Non Linear ◽  
Backward Equation ◽  
Noise Correction ◽  
Ito Process ◽  
Correction Terms

This paper revisits the state vector of an autonomous underwater vehicle (AUV) dynamics coupled with the underwater Markovian stochasticity in the ‘non-linear filtering’ context. The underwater stochasticity is attributed to atmospheric turbulence, planetary interactions, sea surface conditions and astronomical phenomena. In this paper, we adopt the Itô process, a homogeneous Markov process, to describe the AUV state vector evolution equation. This paper accounts for the process noise as well as observation noise correction terms by considering the underwater filtering model. The non-linear filtering of the paper is achieved using the Kolmogorov backward equation and the evolution of the conditional characteristic function. The non-linear filtering equation is the cornerstone formalism of stochastic optimal control systems. Most notably, this paper introduces the non-linear filtering theory into an underwater vehicle stochastic system by constructing a lemma and a theorem for the underwater vehicle stochastic differential equation that were not available in the literature.

scholarly journals Association between rs12252 and influenza susceptibility and severity: an updated meta-analysis

2018 ◽  
Vol 147 ◽  
Author(s):  
T. Chen ◽  
M. Xiao ◽  
J. Yang ◽  
Y. K. Chen ◽  
T. Bai ◽  
...  
Keyword(s):  
Single Nucleotide Polymorphism ◽  
Odds Ratio ◽  
Meta Analysis ◽  
Strong Association ◽  
Dominant Model ◽  
Healthy Individuals ◽  
Nucleotide Polymorphism ◽  
Single Nucleotide ◽  
Model C ◽  
Allelic Model

AbstractIn several lately published studies, the association between single-nucleotide polymorphism (SNP, rs12252) of IFITM3 and the risk of influenza is inconsistent. To further understand the association between the SNP of IFITM3 and the risk of influenza, we searched related studies in five databases including PubMed published earlier than 9 November 2017. Ten sets of data from nine studies were included and data were analysed by Revman 5.0 and Stata 12.0 in our updated meta-analysis, which represented 1365 patients and 5425 no-influenza controls from four different ethnicities. Here strong association between rs12252 and influenza was found in all four genetic models. The significant differences in the allelic model (C vs. T: odds ratio (OR) = 1.35, 95% confidence interval (CI) (1.03–1.79), P = 0.03) and homozygote model (CC vs. TT: OR = 10.63, 95% CI (3.39–33.33), P < 0.00001) in the Caucasian subgroup were discovered, which is very novel and striking. Also novel discoveries were found in the allelic model (C vs. T: OR = 1.37, 95% CI (1.08–1.73), P = 0.009), dominant model (CC + CT vs. TT: OR = 1.48, 95% CI (1.08–2.02), P = 0.01) and homozygote model (CC vs. TT: OR = 2.84, 95% CI (1.36–5.92), P = 0.005) when we compared patients with mild influenza with healthy individuals. Our meta-analysis suggests that single-nucleotide T to C polymorphism of IFITM3 associated with increasingly risk of severe and mild influenza in both Asian and Caucasian populations.

Convergence to a diffusion of a multi-allelic model in population genetics

1978 ◽  
Vol 10 (03) ◽  
pp. 538-562 ◽  
Author(s):  
Ken-Iti Sato
Keyword(s):  
Population Genetics ◽  
Markov Chain ◽  
Random Sampling ◽  
Lattice Points ◽  
Degenerate Diffusion ◽  
One Step ◽  
Step Transition ◽  
Two Stages ◽  
Allelic Model ◽  
Limit Diffusion

We consider a Markov chain on thed-dimensional (d-allelî) non-negative lattice points with the sum of components beingN,for which one-step transition consists of two stages—independent reproduction and random sampling. Convergence to a degenerate diffusion process whenN→ ∞ is proved. We show how difference among alleles in means and variances of offspring numbers affects the limit diffusion, giving a rigorous multi-allelic version of a result of Gillespie.

scholarly journals Association between prodynorphin gene polymorphisms and opioid dependence susceptibility: a meta-analysis

2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Chang-wang Wang ◽  
Min Ma ◽  
Wei-guang Lu ◽  
Ru-qin Luo
Keyword(s):  
Gene Polymorphisms ◽  
Opioid Dependence ◽  
Meta Analysis ◽  
Asian Population ◽  
Case Control Studies ◽  
Exclusion Criteria ◽  
Future Studies ◽  
Larger Sample ◽  
Allelic Model ◽  
Summary Odds Ratio

Abstract Background Prodynorphin (PDYN) gene polymorphisms have been linked with opioid dependence (OD) with conflicting outcomes, the aim of this study is to synthesize the existing evidence of the association between PDYN polymorphisms and OD susceptibility. Methods Four databases including PubMed, EMBASE, Web of Science, and Wanfang were retrieved for relevant studies before August, 2018. All identified studies were evaluated using predetermined inclusion and exclusion criteria. Summary odds ratio (OR) and 95% confidence interval (95%CI) were calculated to appraise the association. Statistical analysis was performed using RevMan 5.3 software. Results A total of seven case-control studies with 3129 cases and 3289 controls were recruited in the meta-analysis. For rs910080, rs1997794, rs1022563, and rs2235749 polymorphisms of PDYN gene, there were six, four, five, and four studies eventually included, respectively. The findings indicated that rs910080 polymorphism was significantly correlated with OD among Asian population under allelic model (A vs. G, OR = 1.30, 95% CI 1.04–1.62, P = 0.02, FDR = 0.05) and dominant model (AA+AG vs. GG, OR = 1.25, 95% CI 1.04–1.51, P = 0.02, FDR = 0.05). However, rs1022563, rs1997794 and rs2235749 polymorphisms did not appear to associate with OD susceptibility. Conclusions There existed a significant association between rs1022563 polymorphism and OD among Asian population. As the included studies were not adequate to guarantee a robust and convincing conclusion, future studies with larger sample size among more ethnicities are recommended.

scholarly journals The infinitesimal generator of the stochastic Burgers equation

2020 ◽  
Vol 178 (3-4) ◽  
pp. 1067-1124
Author(s):  
Massimiliano Gubinelli ◽  
Nicolas Perkowski
Keyword(s):  
Burgers Equation ◽  
Martingale Problem ◽  
Uniqueness Result ◽  
Stochastic Pdes ◽  
Martingale Approach ◽  
Infinite Dimensional ◽  
Cylinder Test ◽  
Stochastic Burgers Equation ◽  
Trivial Intersection ◽  
Backward Equation

Abstract We develop a martingale approach for a class of singular stochastic PDEs of Burgers type (including fractional and multi-component Burgers equations) by constructing a domain for their infinitesimal generators. It was known that the domain must have trivial intersection with the usual cylinder test functions, and to overcome this difficulty we import some ideas from paracontrolled distributions to an infinite dimensional setting in order to construct a domain of controlled functions. Using the new domain, we are able to prove existence and uniqueness for the Kolmogorov backward equation and the martingale problem. We also extend the uniqueness result for “energy solutions” of the stochastic Burgers equation of Gubinelli and Perkowski (J Am Math Soc 31(2):427–471, 2018) to a wider class of equations. As applications of our approach we prove that the stochastic Burgers equation on the torus is exponentially $$L^2$$ L 2 -ergodic, and that the stochastic Burgers equation on the real line is ergodic.

Moments of the first-passage time of a Wiener process with drift between two elastic barriers

1995 ◽  
Vol 32 (4) ◽  
pp. 1007-1013 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Wiener Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Special Cases ◽  
Backward Equation ◽  
The One ◽  
First Passage Problem ◽  
Reflecting Barriers

The first-passage problem for the one-dimensional Wiener process with drift in the presence of elastic boundaries is considered. We use the Kolmogorov backward equation with corresponding boundary conditions to derive explicit closed-form expressions for the expected value and the variance of the first-passage time. Special cases with pure absorbing and/or reflecting barriers arise for a certain choice of a parameter constellation.

A stochastic theory of particle transport

1977 ◽  
Vol 358 (1692) ◽  
pp. 105-120 ◽  
Keyword(s):  
Particle Physics ◽  
Neutron Transport ◽  
Stochastic Theory ◽  
Single Chain ◽  
Amorphous Medium ◽  
History Of ◽  
Backward Equation ◽  
Mean And Variance ◽  
The Green Function ◽  
Regeneration Point

A probability balance equation is formulated for the number of particles present in a cascade resulting from multiple births at each collision. Janossy’s regeneration point method is used and it leads to an integro differential equation for the generating function from which statistical information can readily be extracted. The technique is applied to the interpretation of radiation damage cascades in a homogeneous, amorphous medium in which two particles are ‘born’ per collision. The history of a single chain is followed and equations for the mean and variance are obtained as well as for individual probabilities. It is further shown how the backward and forward forms of the Boltzmann equation are related via the Green function of the system. Additional study shows that the variance also obeys a forward type of equation although its solution is not obtained as conveniently as that of the corresponding backward equation. Several analogies are made with other branches of particle physics; in particular, cosmic rays and neutron transport.

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