26/03/2020
The Human Resources Strategy for Researchers

PhD contract in the field of Mathematics financed by the University Clermont Auvergne

This job offer has expired


  • ORGANISATION/COMPANY
    Université Clermont Auvergne
  • RESEARCH FIELD
    Mathematics
  • RESEARCHER PROFILE
    First Stage Researcher (R1)
  • APPLICATION DEADLINE
    21/05/2020 23:00 - Europe/Brussels
  • LOCATION
    France › AUBIERE
  • TYPE OF CONTRACT
    Other
  • JOB STATUS
    Other
  • HOURS PER WEEK
    35 H
  • OFFER STARTING DATE
    01/10/2020
  • REFERENCE NUMBER
    UCA/SF/0012
  • IS THE JOB RELATED TO STAFF POSITION WITHIN A RESEARCH INFRASTRUCTURE?
    Yes

Title of the thesis: Interacting populations : random v.s. deterministic models

Supervisor : Laurent Serlet

Laboratory : : Laboratoire de Mathématiques Blaise Pascal

University : Clermont Auvergne University

Email and Phone : laurent.serlet@uca.fr, 04 73 40 70 93

Possible co-supervisor :

Laboratory :

University :

Summary :

Modeling interacting populations is a subject that has already been widely studied. Such interaction can

be competition for food or, on the contrary, beneficial for both populations as for instance in the case of

male/female populations. Consequentely, according to the case considered and the model chosen, many different

behaviors can be observed. These models can be deterministic such as systems of differential equations (see

[Mu]) or random (Markov processes).

Figure 1 below is the representation of the joint evolution of males and females with initial unbalance.

The red discontinued line is the solution of the deterministic model whereas the blue trajectory is an instance of

the corresponding random model. In that case, the random trajectory is simply a noised version (more or less

according to the region) of the deterministic solution. But other phenomena can occur, as in Figure 2 where the

deterministic model predicts unbounded growth but the random model shows extinction.

The proposed work consists in selecting a few appropriate models and examining the relations between

random trajectories and deterministic solutions. Typically one expects that, under certain hypothesis,

convergence results hold when the numbers are big ; this is the « fluid » limit described in [DN] and the error term

is expected to be a diffusion. But one will also take interest in when and why the random model behaves

differently from the deterministic one.

Finally, it would be interesting to confront these models to real data, if such data can be found.

Prerequisites : differential equations ; Markov processes : chains, jump processes, diffusions, martingales (as

for instance in [Ku]) ; ability to perform simulations with Python.

First references :

 [DN] Darling R.W.R., Norris J.R. Differential equation approximations for Markov chains.

Probab. Surveys (5) p. 37-79 (2008).

 [Ku] Kurtz T.G. Lectures on stochastic analysis.

Download at : http://www.math.wisc.edu/~kurtz/735/main735.pdf

 [Mu] Murray J.D. Mathematical Biology. Springer.

 

More informations via the link :

https://sf.ed.uca.fr/financement-doctoral/contrat-doctoral-allocations-ministerielles/sujets-de-these-ed-sf-2020-proposes-au-concours/

 

 

To apply, please download the application file via the link :

https://sf.ed.uca.fr/financement-doctoral/contrat-doctoral-allocations-m...

 
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Benefits

 

 
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Eligibility criteria

 
 
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Selection process

Interested students must send two copies of their application to the secretariat of the doctoral school before 22 May 2020, the deadline.

Audition at the doctoral school of the selected candidates:

- 4 June morning: LAMP jury

- 11th June morning: LMV jury

- 11 June afternoon: Chemistry jury

- 12 June: Physics jury

19 June: ED SF council for allocations Doctoral allocations

 
 
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Additional comments

 
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Offer Requirements

  • REQUIRED EDUCATION LEVEL
    Mathematics: Master Degree or equivalent

Skills/Qualifications

 
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Specific Requirements

Speak French or very good level of English

 
 
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Map Information

Job Work Location Personal Assistance locations
Work location(s)
1 position(s) available at
Blaise Pascal Laboratory of Mathematics (LMBP)
France
Région Auvergne Rhône-Alpes
AUBIERE
63178
Campus Universitaire des Cézeaux TSA 60026 - CS 60026 3, Place Vasarely

Open, Transparent, Merit based Recruitment procedures of Researchers (OTM-R)

Know more about it at Université Clermont Auvergne

Know more about OTM-R

EURAXESS offer ID: 508385

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