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[{"model": "core.projectfund", "pk": 26844, "fields": {"project": 4036, "organisation": 2, "amount": 0, "start_date": "2020-09-30", "end_date": "2024-09-29", "raw_data": 42627}}]
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[{"model": "core.projectperson", "pk": 54110, "fields": {"project": 4036, "person": 11103, "role": "SUPER_PER"}}]
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[{"model": "core.projectfund", "pk": 18951, "fields": {"project": 4036, "organisation": 2, "amount": 0, "start_date": "2020-09-30", "end_date": "2024-09-29", "raw_data": 18940}}]
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| April 11, 2022, 3:46 a.m. |
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[{"model": "core.projectorganisation", "pk": 72432, "fields": {"project": 4036, "organisation": 5503, "role": "STUDENT_PP_ORG"}}]
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[{"model": "core.projectorganisation", "pk": 72431, "fields": {"project": 4036, "organisation": 44, "role": "LEAD_ORG"}}]
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[{"model": "core.projectperson", "pk": 44530, "fields": {"project": 4036, "person": 5912, "role": "STUDENT_PER"}}]
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| April 11, 2022, 3:46 a.m. |
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[{"model": "core.projectperson", "pk": 44529, "fields": {"project": 4036, "person": 5913, "role": "SUPER_PER"}}]
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| April 11, 2022, 1:47 a.m. |
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{"title": ["", "An SPDE Approach to Self-Excitatory Neuronal Models"], "description": ["", "\nThis project falls within the EPSRC Statistics and Applied Probability research area. \n\nThis project aims to study a system of interacting diffusions on the negative real line of the McKean-Vlasov type with a resetting component and all are influenced by an independent common source of noise. When one of the diffusions of the system hits zero, its value is reset and all other diffusions in the system will receive a continuous impulse to their value over a predetermined timescale. This system is a generalisation of noisy integrate-and-fire models in neuroscience that model the membrane potential of a neuron in biological systems. An important feature of these models is that when the membrane potential reaches a certain threshold it is instantly reset to some predetermined value and all other neurons in the system receive an impulse that affects their voltage. The primary hypothesis of noisy integrate-and-fire models is that the action potential threshold and shape are invariant from spike to spike, and thus a precise description of the spike can be omitted and simply sketched by a spiking threshold. The diffusion model captures solely spike generation and places the biological aspects of the neuron into the noise. It has been observed that neurons react in a predictable and reproducible manner to temporally structured stimuli. The main sources of stochasticity in the model arises from the innate stochasticity in the biological mechanisms which cause voltage changes in neurons and the neurons may receive inputs from other neurons in the system which are not being observed. The latter may be thought of as the common source of noise in the model.\n\nThe main objective of this project is to show the existence and uniqueness of the mean-field limit to the system of diffusions described above. Moreover, as the interactions between diffusions occur over predefined time scales, this project will attempt to show that, as the time scales on which interactions occur approach zero, the models where the interaction between diffusions occur instantly are recovered. Aside from these aims, this project will also attempt to prove the convergence of an Euler-Maruyama type method for the numerical solution of the limiting system.\n\nA further novelty of this research project comes from there being a common noise source felt by all diffusions in the finite system which leads to showing well-posedness and solutions to an SPDE that describes the law of the representative particle in the limiting system with infinite diffusions. The SPDE approach which will be employed by this project leads to looking for solutions being elements of the càdlàg functions taking values in the space of tempered distributions endowed with the M1 topology. This approach differs from existing literature as generally solutions to large scale limits of systems interacting diffusions are looked for in the space of probability measures on the space of càdlàg functions endowed with the M1 topology.\n\n"], "extra_text": ["", "\n\n\n\n"], "status": ["", "Active"]}
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| April 11, 2022, 1:47 a.m. |
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{"external_links": [15424]}
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| April 11, 2022, 1:47 a.m. |
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[{"model": "core.project", "pk": 4036, "fields": {"owner": null, "is_locked": false, "coped_id": "0e47d3f5-efee-4c96-a925-e00c17180346", "title": "", "description": "", "extra_text": "", "status": "", "start": null, "end": null, "raw_data": 18922, "created": "2022-04-11T01:37:47.382Z", "modified": "2022-04-11T01:37:47.382Z", "external_links": []}}]
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