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DynSys.bib
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@book{morters2010brownian,
author = {M\"{o}rters, P and Peres, Y and Schramm, O and Werner, W},
file = {:Users/dom/Dropbox/Private/Stochastic/brbook.pdf:pdf},
isbn = {9780521760188},
publisher = {Cambridge University Press},
series = {Cambridge series on statistical and probabilistic mathematics},
title = {{Brownian motion}},
url = {http://books.google.co.uk/books?id=e-TbA-dSrzYC},
year = {2010}
}
@article{VonHandel2007,
author = {von Handel, Ramon},
title = {{Stochastic Calculus, Filtering, and Stochastic Control (Lecture Notes)}},
year = {2007}
}
@article{Doucet2012,
author = {Doucet, A.},
title = {{Sequential Monte Carlo Methods for Bayesian Computation}},
year = {2012}
}
@book{protter2004stochastic,
title={Stochastic Integration and Differential Equations: Version 2.1},
author={Protter, P.E.},
isbn={9783540003137},
lccn={2003059169},
series={Applications of mathematics},
url={http://books.google.co.uk/books?id=mJkFuqwr5xgC},
year={2004},
publisher={Springer}
}
@book{rogers2000diffusions,
title={Diffusions, Markov Processes and Martingales: Volume 2, It{\^o} Calculus},
author={Rogers, L.C.G. and Williams, D.},
isbn={9780521775939},
lccn={00269117},
series={Cambridge Mathematical Library},
url={https://books.google.co.uk/books?id=bDQy-zoHWfcC},
year={2000},
publisher={Cambridge University Press}
}
@book{steele2001stochastic,
title={Stochastic Calculus and Financial Applications},
author={Steele, J.M.},
isbn={9781468493054},
series={Applications of Mathematics},
url={https://books.google.co.uk/books?id=fsgkBAAAQBAJ},
year={2001},
publisher={Springer New York}
}
@book{Srkk:2013:BFS:2534502,
author = {Särkkä, Simo},
title = {Bayesian Filtering and Smoothing},
year = {2013},
isbn = {1107619289, 9781107619289},
publisher = {Cambridge University Press},
address = {New York, NY, USA},
}
@article{RTS-1965,
abstract = {{This paper considers the problem of estimating the states of linear dynamic systems in the presence of additive Gaussian noise. Difference equations relating the estimates for the problems of filtering and smoothing are derived as well as a similar set of equations relating the covariance of the errors. The derivation is based on the method of maximum likelihood and depends primarily on the simple manipulation of the probability density functions. The solutions are in a form easily mechanized on a digital computer. A numerical example is included to show the advantage of smoothing in reducing the errors in estimation. In the Appendix the results for discrete systems are formally extended to continuous systems.}},
author = {Rauch, H. E. and Striebel, C. T. and Tung, F.},
citeulike-article-id = {2206895},
journal = {Journal of the American Institute of Aeronautics and Astronautics},
month = aug,
number = {8},
pages = {1445--1450},
posted-at = {2010-12-01 14:05:07},
priority = {2},
title = {{Maximum Likelihood Estimates of Linear Dynamic Systems}},
volume = {3},
year = {1965}
}
@misc{Cappe:IntroToSMC:Online,
author = {Cappé, Olivier},
title = {An Introduction to Sequential Monte Carlo for Filtering and Smoothing},
year = {2008},
url = {http://www-irma.u-strasbg.fr/~guillou/meeting/cappe.pdf}
}
@ARTICLE{RSPSA1927:115,
author = {{Kermack}, W.~O. and {McKendrick}, A.~G.},
title = "{A Contribution to the Mathematical Theory of Epidemics}",
journal = {Proceedings of the Royal Society of London Series A},
year = 1927,
month = aug,
volume = 115,
pages = {700-721},
doi = {10.1098/rspa.1927.0118},
adsurl = {http://adsabs.harvard.edu/abs/1927RSPSA.115..700K},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{bmj-influenza,
title = "{Influenza in a boarding school}",
journal = {British Medical Journal},
year = 1978,
month = mar,
pages = {587}
}
@article{doi:10.1021/j150111a004,
author = {Alfred J. Lotka},
title = {Contribution to the Theory of Periodic Reactions},
journal = {The Journal of Physical Chemistry},
volume = {14},
number = {3},
pages = {271-274},
year = {1909},
doi = {10.1021/j150111a004},
URL = {http://dx.doi.org/10.1021/j150111a004},
eprint = {http://dx.doi.org/10.1021/j150111a004}
}
@article{Volterra1926,
abstract = {Lotka–Volterra equations for predator-prey equations; first-order, non-linear, differential equations frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.},
author = {Volterra, Vito},
journal = {Memorie della R. Accademia dei Lincei},
number = {2},
pages = {31--113},
title = {{Variazioni e fluttuazioni del numero d'individui in specie animali conviventi}},
url = {http://www.liberliber.it/biblioteca/v/volterra/variazioni{\_}e{\_}fluttuazioni/pdf/volterra{\_}variazioni{\_}e{\_}fluttuazioni.pdf},
volume = {6},
year = {1926}
}
@article{Moral2015,
abstract = {We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is simulating bridges between given initial and final values. The basic idea is to introduce a schedule of intermediate weighting and resampling times between observation times, which guide particles towards the final state. This can always be done for continuous-time models, and may be done for discrete-time models under sparse observation regimes; our main focus is on continuous-time diffusion processes. The methods are broadly applicable in that they support multivariate models with partial observation, do not require simulation of the backward transition (which is often unavailable), and, where possible, avoid pointwise evaluation of the forward transition. When simulating bridges, the last cannot be avoided entirely without concessions, and we suggest an approach (reminiscent of Approximate Bayesian Computation) as a workaround. Compared to the bootstrap particle filter, the new methods deliver substantially reduced mean squared error in normalising constant estimates, even after accounting for execution time. The methods are demonstrated for state estimation with two toy examples, and for parameter estimation (within a particle marginal Metropolis–Hastings sampler) with three applied examples in econometrics, epidemiology and marine biogeochemistry.},
author = {Moral, Pierre Del and Murray, Lawrence M},
file = {:Users/dom/Library/Application Support/Mendeley Desktop/Downloaded/Moral, Murray - 2015 - Sequential Monte Carlo with Highly Informative Observations.pdf:pdf},
title = {{Sequential Monte Carlo with Highly Informative Observations}},
year = {2015}
}
@book{williams1991probability,
author = {Williams, D},
isbn = {9780521406055},
publisher = {Cambridge University Press},
series = {Cambridge mathematical textbooks},
title = {{Probability with martingales}},
url = {http://books.google.co.uk/books?id=RnOJeRpk0SEC},
year = {1991}
}
@article{Dureau2013,
abstract = {Epidemics are often modeled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions, seasonal effects, etc.). These models assign diffusion processes to the time-varying parameters, and our inferential procedure is based on a suitably adjusted adaptive particle Markov chain Monte Carlo algorithm. The performance of the proposed computational methods is validated on simulated data and the adopted model is applied to the 2009 H1N1 pandemic in England. In addition to estimating the effective contact rate trajectories, the methodology is applied in real time to provide evidence in related public health decisions. Diffusion-driven susceptible exposed infected retired-type models with age structure are also introduced.},
author = {Dureau, Joseph and Kalogeropoulos, Konstantinos and Baguelin, Marc},
doi = {10.1093/biostatistics/kxs052},
file = {:Users/dom/Library/Application Support/Mendeley Desktop/Downloaded/Dureau, Kalogeropoulos, Baguelin - 2013 - Capturing the time-varying drivers of an epidemic using stochastic dynamical systems.pdf:pdf},
issn = {1468-4357},
journal = {Biostatistics (Oxford, England)},
keywords = {Adult,Algorithms,Bayes Theorem,Biostatistics,Child,England,England: epidemiology,Epidemics,Epidemics: statistics {\&} numerical data,Humans,Influenza A Virus, H1N1 Subtype,Influenza, Human,Influenza, Human: epidemiology,Markov Chains,Models, Biological,Models, Statistical,Monte Carlo Method,Nonlinear Dynamics,Pandemics,Pandemics: statistics {\&} numerical data,Stochastic Processes,Time Factors},
month = {jul},
number = {3},
pages = {541--55},
pmid = {23292757},
title = {{Capturing the time-varying drivers of an epidemic using stochastic dynamical systems.}},
url = {http://biostatistics.oxfordjournals.org/content/early/2013/01/04/biostatistics.kxs052.abstract},
volume = {14},
year = {2013}
}
@article{Andrieu2010,
abstract = {Summary. Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to build efficient high dimensional proposal distributions by using sequential Monte Carlo methods. This allows us not only to improve over standard Markov chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so. We demonstrate these algorithms on a non-linear state space model and a L{\'{e}}vy-driven stochastic volatility model.},
author = {Andrieu, Christophe and Doucet, Arnaud and Holenstein, Roman},
doi = {10.1111/j.1467-9868.2009.00736.x},
file = {:Users/dom/Dropbox/Private/Bayesian/andrieu{\_}doucet{\_}holenstein{\_}PMCMC.pdf:pdf},
isbn = {1467-9868},
issn = {13697412},
journal = {Journal of the Royal Statistical Society. Series B: Statistical Methodology},
keywords = {Bayesian inference,Markov chain Monte Carlo methods,Sequential Monte Carlo methods,State space models},
number = {3},
pages = {269--342},
title = {{Particle Markov chain Monte Carlo methods}},
volume = {72},
year = {2010}
}
@article{Murray,
abstract = {LibBi is a software package for state-space modelling and
Bayesian inference on modern computer hardware,
including multi-core central processing units
(CPUs), many-core graphics processing units (GPUs)
and distributed-memory clusters of such devices. The
software parses a domain-specific language for model
specification, then optimises, generates, compiles
and runs code for the given model, inference method
and hardware platform. In presenting the software,
this work serves as an introduction to state-space
models and the specialised methods developed for
Bayesian inference with them. The focus is on
sequential Monte Carlo (SMC) methods such as the
particle filter for state estimation, and the
particle Markov chain Monte Carlo (PMCMC) and SMC 2
methods for parameter estimation. All are
well-suited to current computer hardware. Two
examples are given and developed throughout, one a
linear three-element windkessel model of the human
arterial system, the other a nonlinear Lorenz '96
model. These are specified in the prescribed
modelling language, and LibBi demonstrated by
performing inference with them. Empirical results
are presented, including a performance comparison of
the software with different hardware
configurations.},
author = {Murray, Lawrence M},
file = {:Users/dom/Library/Application Support/Mendeley
Desktop/Downloaded/Murray - Unknown - Bayesian
State-Space Modelling on High-Performance Hardware
Using LibBi.pdf:pdf},
title = {{Bayesian State-Space Modelling on High-Performance Hardware
Using LibBi}}
}
@book{Robinson2003,
abstract = {This book treats the theory of global attractors, a recent
development in the theory of partial differential
equations, in a way that also includes much of the
traditional elements of the subject. As such it
gives a quick but directed introduction to some
fundamental concepts, and by the end proceeds to
current research problems. Since the subject is
relatively new, this is the first book to attempt to
treat these various topics in a unified and didactic
way. It is intended to be suitable for first year
graduate students.},
author = {Robinson, Jc and Pierre, C},
booktitle = {Applied Mechanics Reviews},
doi = {10.1115/1.1579456},
isbn = {0521635640},
issn = {00036900},
number = {4},
pages = {B54},
title = {{Infinite-Dimensional Dynamical Systems: An Introduction to
Dissipative Parabolic PDEs and the Theory of Global
Attractors. Cambridge Texts in Applied Mathematics}},
url = {http://link.aip.org/link/AMREAD/v56/i4/pB54/s1{\&}Agg=doi},
volume = {56},
year = {2003}
}
@book{Temam1997,
abstract = {In this book the author presents the dynamical systems in
infinite dimension, especially those generated by
dissipative partial differential equations. This
book attempts a systematic study of infinite
dimensional dynamical systems generated by
dissipative evolution partial differential equations
arising in mechanics and physics and in other areas
of sciences and technology. This second edition has
been updated and extended.},
author = {Temam, Roger},
booktitle = {Appllied Mathematical Sciences},
doi = {10.1007/978-1-4684-0313-8},
isbn = {978-0-387-94866-9},
issn = {9780387948669},
title = {{Infinite-dimensional dynamical systems in mechanics and
physics}},
volume = {68},
year = {1997}
}
@book{Chueshov1999,
abstract = {U n i v e r s i t y l e c t u r e s i n c o n t e m p o r
a r y m a t h e m a t i c s Dissipative issipative
Systems ystems of Infinite-Dimensional
Infinite-Dimensional Introduction ntroduction Theory
Theory to the This book provides an exhau -stive
introduction to the scope of main ideas and methods
of the theory of infinite-dimensional dis -sipative
dynamical systems which has been rapidly developing
in re -cent years. In the examples sys tems
generated by nonlinear partial differential
equations arising in the different problems of
modern mechanics of continua are considered. The
main goal of the book is to help the reader to
master the basic strategies used in the study of
infinite-dimensional dissipative systems and to
qualify him/her for an independent scien -tific
research in the given branch. Experts in nonlinear
dynamics will find many fundamental facts in the
convenient and practical form in this book.},
author = {Chueshov, Constantin I and Khorolska, Maryna B},
booktitle = {from the Russian edition («ACTA»},
file = {:Users/dom/Library/Application Support/Mendeley
Desktop/Downloaded/Chueshov, Khorolska Author,
Chueshov I D Chueshov - 1999 - Introduction to the
Theory of Infinite-Dimensional Dissipative
Systems.pdf:pdf},
title = {{Introduction to the Theory of Infinite-Dimensional Dissipative Systems}},
year = {1999}
}
@Misc{stan1,
title = {Stan: A C++ Library for Probability and Sampling, Version
2.10.0},
author = {{Stan Development Team}},
year = {2015},
url = {http://mc-stan.org/},
}
@Manual{stan2,
title = {Stan Modeling Language User's Guide and Reference Manual,
Version 2.10.0},
author = {{Stan Development Team}},
year = {2015},
url = {http://mc-stan.org/},
}
@Article{stan3,
title = {The No-U-Turn Sampler: Adaptively Setting Path Lengths in
Hamiltonian Monte Carlo},
author = {Matthew D. Hoffman and Andrew Gelman},
year = {2014},
journal = {Journal of Machine Learning Research},
}
@Article{stan4,
title = {Stan: A Probabilistic Programming Language},
author = {Bob Carpenter},
year = {2015},
journal = {Journal of Statistical Software},
}
@Inbook{Torbett2009,
author="Torbett, Bruce E.
and Friedman, Jeffrey S.",
editor="Elliott, Steven G.
and Foote, Mary Ann
and Molineux, Graham",
title="Erythropoiesis: an overview",
bookTitle="Erythropoietins, Erythropoietic Factors, and Erythropoiesis: Molecular, Cellular, Preclinical, and Clinical Biology",
year="2009",
publisher="Birkh{\"a}user Basel",
address="Basel",
pages="3--18",
isbn="978-3-7643-8698-6",
doi="10.1007/978-3-7643-8698-6_1",
url="http://dx.doi.org/10.1007/978-3-7643-8698-6_1"
}
@Article{Thibodeaux2011,
author="Thibodeaux, Jeremy J.
and Schlittenhardt, Timothy P.",
title="Optimal Treatment Strategies for Malaria Infection",
journal="Bulletin of Mathematical Biology",
year="2011",
volume="73",
number="11",
pages="2791--2808",
abstract="We develop a numerical method for estimating optimal parameters in a mathematical model of the within-host dynamics of malaria infection. The model consists of a quasilinear system of partial differential equations. Convergence theory for the computed parameters is provided. Following this analysis, we present several numerical simulations that suggest that periodic treatments that are in synchronization with the periodic bursting rate of infected erythrocytes are the most productive strategies.",
issn="1522-9602",
doi="10.1007/s11538-011-9650-8",
url="http://dx.doi.org/10.1007/s11538-011-9650-8"
}
@article{BELAIR1995317,
title = "Age-structured and two-delay models for erythropoiesis",
journal = "Mathematical Biosciences",
volume = "128",
number = "1",
pages = "317 - 346",
year = "1995",
note = "",
issn = "0025-5564",
doi = "http://dx.doi.org/10.1016/0025-5564(94)00078-E",
url = "http://www.sciencedirect.com/science/article/pii/002555649400078E",
author = "Jacques Belair and Michael C. Mackey and Joseph M. Mahaffy",
abstract = "An age-structured model is developed for erythropoiesis and is reduced to a system of threshold-type differential delay equations using the method of characteristics. Under certain assumptions, this model can be reduced to a system of delay differential equations with two delays. The parameters in the system are estimated from experimental data, and the model is simulated for a normal human subject following a loss of blood. The characteristic equation of the two-delay equation is analyzed and shown to exhibit Hopf bifurcations when the destruction rate of erythrocytes is increased. A numerical study for a rabbit with autoimmune hemolytic anemia is performed and compared with experimental data."
}
@article{sawyer1987binding,
title={Binding and receptor-mediated endocytosis of erythropoietin in Friend virus-infected erythroid cells.},
author={Sawyer, Stephen T and Krantz, SB and Goldwasser, E},
journal={Journal of Biological Chemistry},
volume={262},
number={12},
pages={5554--5562},
year={1987},
publisher={ASBMB}
}
@article{Ackleh200621,
title = "A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate ",
journal = "Mathematical Biosciences ",
volume = "204",
number = "1",
pages = "21 - 48",
year = "2006",
note = "",
issn = "0025-5564",
doi = "http://dx.doi.org/10.1016/j.mbs.2006.08.004",
url = "http://www.sciencedirect.com/science/article/pii/S002555640600126X",
author = "Azmy S. Ackleh and Keng Deng and Kazufumi Ito and Jeremy Thibodeaux",
keywords = "Erythropoiesis",
keywords = "Structured model",
keywords = "Finite difference approximation",
keywords = "Existence-uniqueness",
keywords = "Behavior of solutions ",
abstract = "We develop a quasilinear structured model that describes the regulation of erythropoiesis, the process in which red blood cells are developed. In our model, the maturation velocity of precursor cells is assumed to be a function of the erythropoietin hormone, and the decay rate of this hormone is assumed to be a function of the number of precursor cells, unlike other models which assume these parameters to be constants. Existence-uniqueness results are established and convergence of a finite difference approximation to the unique solution of the model is obtained. The finite difference scheme is then used to investigate the effects of these nonlinear parameters on the model dynamics. Our results show that a velocity of precursor cells maturation rate which is an increasing function of the hormone level and a decay rate of the hormone which is an increasing function of the number of precursor cells have a stabilizing effect on the dynamics of the model. While assuming that one parameter is a function and letting the other be a constant stabilizes the oscillations in the mature cells level, the effect is more significant when both parameters are taken to be functions. A study of robustness with respect to the forms of these functions and parameter sensitivity is also carried out. "
}
@article{Banks2003,
abstract = {Benzene (C 6 H 6) is a highly flammable, colorless liquid. Ubiquitous exposures result from its presence in gasoline vapors, cigarette smoke, and industrial processes. Benzene increases the incidence of leukemia in humans when they are exposed to high doses for extended periods; however, leukemia risks in humans subjected to low exposures are uncertain. The exposure-dose-response relationship of benzene in humans is expected to be nonlinear because benzene undergoes a series of metabolic transformations, detoxifying and activating, resulting in multiple metabolites that exert toxic effects on the bone marrow. Since benzene is a known human leukemogen, the toxicity of benzene in the bone marrow is of most importance. And because blood cells are produced in the bone marrow, we investigated the effects of benzene on hematopoiesis (blood cell production and development). An age-structured model was used to examine the process of erythropoiesis, the development of red blood cells. The existence and uniqueness of the solution of the system of coupled partial and ordinary differential equations was proven. In addition, an optimal control problem was formulated for the control of erythropoiesis. Numerical simulations were performed to compare the performance of the optimal feedback law and another feedback function that is based on the Hill function.},
author = {Banks, H T and Cole, Cammey E and Schlosser, Paul M and Tran, Hien T},
file = {:Users/dom/Library/Application Support/Mendeley Desktop/Downloaded/Banks et al. - 2003 - Modeling and Optimal Regulation of Erythropoiesis Subject to Benzene Intoxication.pdf:pdf},
title = {{Modeling and Optimal Regulation of Erythropoiesis Subject to Benzene Intoxication}},
url = {https://www.ncsu.edu/crsc/reports/ftp/pdf/crsc-tr03-49.pdf},
year = {2003}
}
@article{Ackleh2013,
author = {Ackleh, Azmy S. and Thibodeaux, Jeremy J.},
doi = {10.1002/num.21778},
file = {:Users/dom/Downloads/AT2{\_}revision.pdf:pdf},
issn = {0749159X},
journal = {Numerical Methods for Partial Differential Equations},
number = {November},
pages = {n/a--n/a},
title = {{A second-order finite difference approximation for a mathematical model of erythropoiesis}},
url = {http://doi.wiley.com/10.1002/num.21778},
year = {2013}
}
@article{gurtin1974non,
title={Non-linear age-dependent population dynamics},
author={Gurtin, Morton E and MacCamy, Richard C},
journal={Archive for Rational Mechanics and Analysis},
volume={54},
number={3},
pages={281--300},
year={1974},
publisher={Springer}
}
@article{hall2013pharmacokinetic,
title={Pharmacokinetic modelling of the anti-malarial drug artesunate and its active metabolite dihydroartemisinin},
author={Hall, Adam J and Chappell, Michael J and Aston, John AD and Ward, Stephen A},
journal={Computer methods and programs in biomedicine},
volume={112},
number={1},
pages={1--15},
year={2013},
publisher={Elsevier}
}
@Article{Jones_2000,
author = {Jones, Simon Peyton and Eber, Jean-Marc and Seward,
Julian},
title = {Composing contracts},
year = 2000,
doi = {10.1145/351240.351267},
url = {http://dx.doi.org/10.1145/351240.351267},
isbn = 1581132026,
journal = {Proceedings of the fifth ACM SIGPLAN international
conference on Functional programming - ICFP ’00},
publisher = {ACM Press}
}