### 英国论文代写|BIRMINGHAM UNIVERSITY MSC DISSERTATION | Trophic analysis of complex systems

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## 英国论文代写|Birmingham University MSc Dissertation |Trophic analysis of complex systems

Complex systems – be they brains, genomes, financial markets, ecosystems or society, to name but a few – are often represented as networks. We have shown how the concepts of trophic level (originally borrowed from ecology) and trophic coherence play a fundamental role in the structure and behaviour of a great many complex systems $[1,2]$

In this project the student will further develop the methods of trophic analysis [3,4] and apply them to real-world datasets relating to a variety of complex systems. This work will likely involve both mathematical and numerical research.

## 英国论文代写|Trophic analysis of complex systems选题导师介绍

Sam’s research focuses on complex systems, and in particular on the relationship between structure and dynamics. Many of the questions his work addresses relate to ecology, neuroscience or society.

Sam has many research interests, most of which can be placed under the umbrella of ‘complex systems’. Some of the topics he is currently working on are:

• Trophic structure of directed networks: Together with colleagues in Granada, Sam recently studied a network property called ‘trophic coherence’, (Johnson et al, PNAS, 2014). This and subsequent work (with colleagues Miguel Ángel Muñoz, Virginia Dominguez, Janis Klaise and Nick Jones) has shown that trophic coherence is related to many aspects of complex systems, including the prevalence of cycles and feedback loops, ecological stability, motif distributions and spreading processes such as epidemics and neuronal avalanches. It has also opened several questions, such as: Does trophic coherence account for the existence of large, complex ecosystems? Can trophic structure be used to identify node function in systems like gene regulatory networks? is there a general theory relating feedback and stability in complex, dynamical systems.
• Human ecology: Work with Weisi Guo, Xueke Lu and Guillem Mosquera has show that the prevalence of violence around the world is related to the spatial distribution of cities according to a remarkably simple and robust law. We are currently looking into the causes of this effect though a combination of data analysis and agent based modelling and looking for ways in which our results can be applied.
• Brain development: The neural network underlying all mental activity comes into being in a curious way: at birth it has a great many synapses (connections between neurons), about half of which are ‘pruned’ throughout infancy. Recent work with Ana Paula Millán, Joaquin Torres and Joaquin Marro describes a mechanism which could explain this phenomenon with a simple neural network model. We are now studying this process with more realistic neural modelling, looking into its effects in other complex systems.

## 英国论文代写|Trophic analysis of complex systems选题参考文献

References:

[1] S. Johnson, V. Domínguez-Garcia, L. Donetti, and M.A. Muñoz, “Trophic coherence determines food-web stability”, PNAS 111, 17923 (2014).
[2] S. Johnson and N.S. Jones, “Looplessness in networks is linked to trophic coherence”, PNAS 114, 5618 (2017). [3] S. Johnson, “Digraphs are different: Why directionality matters in complex systems”, Journal of Physics: Complexity, 1,015003 (2020).
[4] R.S. MacKay, S. Johnson, B. Sansom, “How directed is a directed network?”, Royal Society Open Science 7: $201138(2020)$.

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## 金融数学代写

• 随机微积分 Stochastic calculus
• 随机分析 Stochastic analysis
• 随机控制理论 Stochastic control theory
• 微观经济学 Microeconomics
• 数量经济学 Quantitative Economics
• 宏观经济学 Macroeconomics
• 经济统计学 Economic Statistics
• 经济学理论 Economic Theory
• 计量经济学 Econometrics

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