The Experts below are selected from a list of 106932 Experts worldwide ranked by ideXlab platform
Idriss Mazari - One of the best experts on this subject based on the ideXlab platform.
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optimisation of the Total Population Size for logistic diffusive equations bang bang property and fragmentation rate
arXiv: Analysis of PDEs, 2021Co-Authors: Idriss Mazari, Grégoire Nadin, Yannick PrivatAbstract:In this article, we give an in-depth analysis of the problem of optimising the Total Population Size for a standard logistic-diffusive model. This optimisation problem stems from the study of spatial ecology and amounts to the following question: assuming a species evolves in a domain, what is the best way to spread resources in order to ensure a maximal Population Size at equilibrium? {In recent years, many authors contributed to this topic.} We settle here the proof of two fundamental properties of optimisers: the bang-bang one which had so far only been proved under several strong assumptions, and the other one is the fragmentation of maximisers. Here, we prove the bang-bang property in all generality using a new spectral method. The technique introduced to demonstrate the bang-bang character of optimizers can be adapted and generalized to many optimization problems with other classes of bilinear optimal control problems where the state equation is semilinear and elliptic. We comment on it in a conclusion section. Regarding the geometry of maximisers, we exhibit a blow-up rate for the $BV$-norm of maximisers as the diffusivity gets smaller: if $\Omega$ is an orthotope and if $m_\mu$ is an optimal control, then $\Vert m_\mu\Vert_{BV}\gtrsim \sqrt{\mu}$. The proof of this results relies on a very fine energy argument.
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optimisation of the Total Population Size with respect to the initial condition for semilinear parabolic equations two scale expansions and symmetrisations
arXiv: Analysis of PDEs, 2021Co-Authors: Idriss Mazari, Grégoire Nadin, Ana Isis Toledo MarreroAbstract:In this article, we propose in-depth analysis and characterisation of the optimisers of the following optimisation problem: how to choose the initial condition $u_0$ in order to maximise the spatial integral at a given time of the solution of the semilinear equation $u_t-\Delta u=f(u)$, under $L^\infty$ and $L^1$ constraints on $u_0$? Our contribution in the present paper is to give a characterisation of the behaviour of the optimiser $\overline{u}_0$ when it does not saturate the $L^\infty$ constraints, which is a key step in implementing efficient numerical algorithms. We give such a characterisation under mild regularity assumptions by proving that in that case $\overline{u}_0$ can only take values in the "zone of concavity" of $f$. This is done using two-scale asymptotic expansions. We then show how well-known isoperimetric inequalities yield a full characterisation of maximisers when $f$ is convex. Finally, we provide several numerical simulations in one and two dimensions that illustrate and exemplify the fact that such characterisations significantly improves the computational time. All our theoretical results are in the one-dimensional case and we offer several comments about possible generalisations to other contexts, or obstructions that may prohibit doing so.
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optimisation of the Total Population Size with respect to the initial condition for semilinear parabolic equations two scale expansions and symmetrisations
Nonlinearity, 2021Co-Authors: Idriss Mazari, Grégoire Nadin, Ana Isis Toledo MarreroAbstract:In this article, we propose in-depth analysis and characterisation of the optimisers of the following optimisation problem: how to choose the initial condition u0 in order to maximise the spatial integral at a given time of the solution of the semilinear equation ut −∆u = f (u), under L ∞ and L 1 constraints on u0? Our contribution in the present paper is to give a characterisation of the behaviour of the optimiser u0 when it does not saturate the L ∞ constraints, which is a key step in implementing efficient numerical algorithms. We give such a characterisation under mild regularity assumptions by proving that in that case u0 can only take values in the "zone of concavity" of f. This is done using two-scale asymptotic expansions. We then show how well-known isoperimetric inequalities yield a full characterisation of maximisers when f is convex. Finally, we provide several numerical simulations in one and two dimensions that illustrate and exemplify the fact that such characterisations significantly improves the computational time. All our theoretical results are in the one-dimensional case and we offer several comments about possible generalisations to other contexts, or obstructions that may prohibit doing so.
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a fragmentation phenomenon for a nonenergetic optimal control problem optimization of the Total Population Size in logistic diffusive models
Siam Journal on Applied Mathematics, 2021Co-Authors: Idriss Mazari, Domenec RuizbaletAbstract:Following several recent works devoted to the analysis of spatial heterogeneity in reaction-diffusion equations, we investigate the problem of optimizing the Total Population Size for logistic diff...
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a fragmentation phenomenon for a non energetic optimal control problem optimisation of the Total Population Size in logistic diffusive models
arXiv: Optimization and Control, 2020Co-Authors: Idriss Mazari, Domenec RuizbaletAbstract:Following some recent works, we investigate the problem of optimising the Total Population Size for logistic diffusive models with respect to resources distributions. Using the spatially heterogeneous Fisher-KPP equation, we obtain a surprising fragmentation phenomenon: depending on the scale of diffusivity (i.e the dispersal rate), it is better to either concentrate or fragment resources. Our main result is that, the smaller the dispersal rate of the species in the domain, the more optimal resources distributions tend to oscillate. This is in sharp contrast with other criteria in Population dynamics, such as the classical problem of optimising the survival ability of a species, where concentrating resources is always favourable, regardless of the diffusivity. Our study is completed by numerous numerical simulations that confirm our results.
John Harwood - One of the best experts on this subject based on the ideXlab platform.
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modelling the Population Size and dynamics of the british grey seal
Aquatic Conservation-marine and Freshwater Ecosystems, 2019Co-Authors: Len Thomas, Debbie Jf Russell, C D Duck, Christopher Morris, Mike Lonergan, Fanny Empacher, Dave Thompson, John HarwoodAbstract:Grey seals (Halichoerus grypus) were the first mammals to be protected by an Act of Parliament in the UK and are currently protected under UK, Scottish, and EU conservation legislation. Reporting requirements under each of these statutes requires accurate and timely Population estimates. Monitoring is principally conducted by aerial surveys of the breeding colonies; these are used to produce estimates of annual pup production. Translating these data to estimates of adult Population Size requires information about demographic parameters such as fecundity and sex ratio. An age‐structured Population dynamics model is presented, which includes density dependence in pup survival, with separate carrying capacities in each of the four breeding regions considered (North Sea, Inner Hebrides, Outer Hebrides, and Orkney). This model is embedded within a Bayesian state–space modelling framework, allowing the Population model to be linked to available data and the use of informative prior distributions on demographic parameters. A computer‐intensive fitting algorithm is presented based on particle filtering methods. The model is fitted to region‐level pup production estimates from 1984 to 2010 and an independent estimate of adult Population Size, derived from aerial surveys of hauled‐out seals in 2008. The fitted model is used to estimate Total Population Size from 1984 to 2010. The Population in the North Sea region has increased at a near‐constant rate; growth in the other three regions began to slow in the mid‐1990s and these Populations appear to have reached carrying capacity. The Total Population Size of seals aged 1 year or older in 2010 was estimated to be 116 100 (95% CI 98 400–138 600), an increase of <1% on the previous year. The modelling and fitting methods are widely applicable to other wildlife Populations where diverse sources of information are available and inference is required for the underlying Population dynamics.
Len Thomas - One of the best experts on this subject based on the ideXlab platform.
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modelling the Population Size and dynamics of the british grey seal
Aquatic Conservation-marine and Freshwater Ecosystems, 2019Co-Authors: Len Thomas, Debbie Jf Russell, C D Duck, Christopher Morris, Mike Lonergan, Fanny Empacher, Dave Thompson, John HarwoodAbstract:Grey seals (Halichoerus grypus) were the first mammals to be protected by an Act of Parliament in the UK and are currently protected under UK, Scottish, and EU conservation legislation. Reporting requirements under each of these statutes requires accurate and timely Population estimates. Monitoring is principally conducted by aerial surveys of the breeding colonies; these are used to produce estimates of annual pup production. Translating these data to estimates of adult Population Size requires information about demographic parameters such as fecundity and sex ratio. An age‐structured Population dynamics model is presented, which includes density dependence in pup survival, with separate carrying capacities in each of the four breeding regions considered (North Sea, Inner Hebrides, Outer Hebrides, and Orkney). This model is embedded within a Bayesian state–space modelling framework, allowing the Population model to be linked to available data and the use of informative prior distributions on demographic parameters. A computer‐intensive fitting algorithm is presented based on particle filtering methods. The model is fitted to region‐level pup production estimates from 1984 to 2010 and an independent estimate of adult Population Size, derived from aerial surveys of hauled‐out seals in 2008. The fitted model is used to estimate Total Population Size from 1984 to 2010. The Population in the North Sea region has increased at a near‐constant rate; growth in the other three regions began to slow in the mid‐1990s and these Populations appear to have reached carrying capacity. The Total Population Size of seals aged 1 year or older in 2010 was estimated to be 116 100 (95% CI 98 400–138 600), an increase of <1% on the previous year. The modelling and fitting methods are widely applicable to other wildlife Populations where diverse sources of information are available and inference is required for the underlying Population dynamics.
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estimating north pacific right whale eubalaena japonica density using passive acoustic cue counting
Endangered Species Research, 2011Co-Authors: Tiago Reis Marques, Lisa M Munger, Len Thomas, Sean M WigginsAbstract:We present a method for estimating animal density from fixed passive acoustic detec- tors, and illustrate it by estimating the density of North Pacific right whales Eubalaena japonica in the areas surrounding 3 hydrophones deployed in the southeastern Bering Sea in 2001 to 2002 and 2005 to 2006. Input data were the distances to detected right whale calls, estimated using a normal mode sound propagation model, and call production rate, estimated from encounters by survey vessels with right whale groups. Given the scarcity of information about this highly endangered species, we also extrapolate our results to provide a tentative estimate of the Total Population Size in shelf waters of the eastern Bering Sea. This gives a point estimate of 25 animals (CV 29.1%; 95% confidence interval 13-47), which agrees well with what little is known for this species. We discuss the assumptions underlying the method. Obtaining more reliable values requires a larger sample of randomly located hydrophones, together with improved estimates of call rate.
Mike Lonergan - One of the best experts on this subject based on the ideXlab platform.
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modelling the Population Size and dynamics of the british grey seal
Aquatic Conservation-marine and Freshwater Ecosystems, 2019Co-Authors: Len Thomas, Debbie Jf Russell, C D Duck, Christopher Morris, Mike Lonergan, Fanny Empacher, Dave Thompson, John HarwoodAbstract:Grey seals (Halichoerus grypus) were the first mammals to be protected by an Act of Parliament in the UK and are currently protected under UK, Scottish, and EU conservation legislation. Reporting requirements under each of these statutes requires accurate and timely Population estimates. Monitoring is principally conducted by aerial surveys of the breeding colonies; these are used to produce estimates of annual pup production. Translating these data to estimates of adult Population Size requires information about demographic parameters such as fecundity and sex ratio. An age‐structured Population dynamics model is presented, which includes density dependence in pup survival, with separate carrying capacities in each of the four breeding regions considered (North Sea, Inner Hebrides, Outer Hebrides, and Orkney). This model is embedded within a Bayesian state–space modelling framework, allowing the Population model to be linked to available data and the use of informative prior distributions on demographic parameters. A computer‐intensive fitting algorithm is presented based on particle filtering methods. The model is fitted to region‐level pup production estimates from 1984 to 2010 and an independent estimate of adult Population Size, derived from aerial surveys of hauled‐out seals in 2008. The fitted model is used to estimate Total Population Size from 1984 to 2010. The Population in the North Sea region has increased at a near‐constant rate; growth in the other three regions began to slow in the mid‐1990s and these Populations appear to have reached carrying capacity. The Total Population Size of seals aged 1 year or older in 2010 was estimated to be 116 100 (95% CI 98 400–138 600), an increase of <1% on the previous year. The modelling and fitting methods are widely applicable to other wildlife Populations where diverse sources of information are available and inference is required for the underlying Population dynamics.
Xiaohong Zhang - One of the best experts on this subject based on the ideXlab platform.
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the threshold of a deterministic and a stochastic siqs epidemic model with varying Total Population Size
Applied Mathematical Modelling, 2021Co-Authors: Xiaobing Zhang, Xiaohong ZhangAbstract:Abstract In this paper, a stochastic and a deterministic SIS epidemic model with isolation and varying Total Population Size are proposed. For the deterministic model, we establish the threshold R0. When R0 is less than 1, the disease-free equilibrium is globally stable, which means the disease will die out. While R0 is greater than 1, the endemic equilibrium is globally stable, which implies that the disease will spread. Moreover, there is a critical isolation rate δ*, when the isolation rate is greater than it, the disease will be eliminated. For the stochastic model, we also present its threshold R0s. When R0s is less than 1, the disease will disappear with probability one. While R0s is greater than 1, the disease will persist. We find that stochastic perturbation of the transmission rate (or the valid contact coefficient) can help to reduce the spread of the disease. That is, compared with stochastic model, the deterministic epidemic model overestimates the spread capacity of disease. We further find that there exists a critical the stochastic perturbation intensity of the transmission rate σ*, when the stochastic perturbation intensity of the transmission rate is bigger than it, the disease will disappear. At last, we apply our theories to a realistic disease, pneumococcus amongst homosexuals, carry out numerical simulations and obtain the empirical probability density under different parameter values. The critical isolation rate δ* is presented. When the isolation rate δ is greater than δ*, the pneumococcus amongst will be eliminated.
