Project acronym 1stProposal
Project An alternative development of analytic number theory and applications
Researcher (PI) ANDREW Granville
Host Institution (HI) UNIVERSITY COLLEGE LONDON
Call Details Advanced Grant (AdG), PE1, ERC-2014-ADG
Summary The traditional (Riemann) approach to analytic number theory uses the zeros of zeta functions. This requires the associated multiplicative function, say f(n), to have special enough properties that the associated Dirichlet series may be analytically continued. In this proposal we continue to develop an approach which requires less of the multiplicative function, linking the original question with the mean value of f. Such techniques have been around for a long time but have generally been regarded as “ad hoc”. In this project we aim to show that one can develop a coherent approach to the whole subject, not only reproving all of the old results, but also many new ones that appear inaccessible to traditional methods.
Our first goal is to complete a monograph yielding a reworking of all the classical theory using these new methods and then to push forward in new directions. The most important is to extend these techniques to GL(n) L-functions, which we hope will now be feasible having found the correct framework in which to proceed. Since we rarely know how to analytically continue such L-functions this could be of great benefit to the subject.
We are developing the large sieve so that it can be used for individual moduli, and will determine a strong form of that. Also a new method to give asymptotics for mean values, when they are not too small.
We wish to incorporate techniques of analytic number theory into our theory, for example recent advances on mean values of Dirichlet polynomials. Also the recent breakthroughs on the sieve suggest strong links that need further exploration.
Additive combinatorics yields important results in many areas. There are strong analogies between its results, and those for multiplicative functions, especially in large value spectrum theory, and its applications. We hope to develop these further.
Much of this is joint work with K Soundararajan of Stanford University.
Summary
The traditional (Riemann) approach to analytic number theory uses the zeros of zeta functions. This requires the associated multiplicative function, say f(n), to have special enough properties that the associated Dirichlet series may be analytically continued. In this proposal we continue to develop an approach which requires less of the multiplicative function, linking the original question with the mean value of f. Such techniques have been around for a long time but have generally been regarded as “ad hoc”. In this project we aim to show that one can develop a coherent approach to the whole subject, not only reproving all of the old results, but also many new ones that appear inaccessible to traditional methods.
Our first goal is to complete a monograph yielding a reworking of all the classical theory using these new methods and then to push forward in new directions. The most important is to extend these techniques to GL(n) L-functions, which we hope will now be feasible having found the correct framework in which to proceed. Since we rarely know how to analytically continue such L-functions this could be of great benefit to the subject.
We are developing the large sieve so that it can be used for individual moduli, and will determine a strong form of that. Also a new method to give asymptotics for mean values, when they are not too small.
We wish to incorporate techniques of analytic number theory into our theory, for example recent advances on mean values of Dirichlet polynomials. Also the recent breakthroughs on the sieve suggest strong links that need further exploration.
Additive combinatorics yields important results in many areas. There are strong analogies between its results, and those for multiplicative functions, especially in large value spectrum theory, and its applications. We hope to develop these further.
Much of this is joint work with K Soundararajan of Stanford University.
Max ERC Funding
2 011 742 €
Duration
Start date: 2015-08-01, End date: 2020-07-31
Project acronym ACMO
Project Systematic dissection of molecular machines and neural circuits coordinating C. elegans aggregation behaviour
Researcher (PI) Mario De Bono
Host Institution (HI) MEDICAL RESEARCH COUNCIL
Call Details Advanced Grant (AdG), LS5, ERC-2010-AdG_20100317
Summary Elucidating how neural circuits coordinate behaviour, and how molecules underpin the properties of individual neurons are major goals of neuroscience. Optogenetics and neural imaging combined with the powerful genetics and well-described nervous system of C. elegans offer special opportunities to address these questions. Previously, we identified a series of sensory neurons that modulate aggregation of C. elegans. These include neurons that respond to O2, CO2, noxious cues, satiety state, and pheromones. We propose to take our analysis to the next level by dissecting how, in mechanistic molecular terms, these distributed inputs modify the activity of populations of interneurons and motoneurons to coordinate group formation. Our strategy is to develop new, highly parallel approaches to replace the traditional piecemeal analysis.
We propose to:
1) Harness next generation sequencing (NGS) to forward genetics, rapidly to identify a molecular ¿parts list¿ for aggregation. Much of the genetics has been done: we have identified almost 200 mutations that inhibit or enhance aggregation but otherwise show no overt phenotype. A pilot study of 50 of these mutations suggests they identify dozens of genes not previously implicated in aggregation. NGS will allow us to molecularly identify these genes in a few months, providing multiple entry points to study molecular and circuitry mechanisms for behaviour.
2) Develop new methods to image the activity of populations of neurons in immobilized and freely moving animals, using genetically encoded indicators such as the calcium sensor cameleon and the voltage indicator mermaid.
This will be the first time a complex behaviour has been dissected in this way. We expect to identify novel conserved molecular and circuitry mechanisms.
Summary
Elucidating how neural circuits coordinate behaviour, and how molecules underpin the properties of individual neurons are major goals of neuroscience. Optogenetics and neural imaging combined with the powerful genetics and well-described nervous system of C. elegans offer special opportunities to address these questions. Previously, we identified a series of sensory neurons that modulate aggregation of C. elegans. These include neurons that respond to O2, CO2, noxious cues, satiety state, and pheromones. We propose to take our analysis to the next level by dissecting how, in mechanistic molecular terms, these distributed inputs modify the activity of populations of interneurons and motoneurons to coordinate group formation. Our strategy is to develop new, highly parallel approaches to replace the traditional piecemeal analysis.
We propose to:
1) Harness next generation sequencing (NGS) to forward genetics, rapidly to identify a molecular ¿parts list¿ for aggregation. Much of the genetics has been done: we have identified almost 200 mutations that inhibit or enhance aggregation but otherwise show no overt phenotype. A pilot study of 50 of these mutations suggests they identify dozens of genes not previously implicated in aggregation. NGS will allow us to molecularly identify these genes in a few months, providing multiple entry points to study molecular and circuitry mechanisms for behaviour.
2) Develop new methods to image the activity of populations of neurons in immobilized and freely moving animals, using genetically encoded indicators such as the calcium sensor cameleon and the voltage indicator mermaid.
This will be the first time a complex behaviour has been dissected in this way. We expect to identify novel conserved molecular and circuitry mechanisms.
Max ERC Funding
2 439 996 €
Duration
Start date: 2011-04-01, End date: 2017-03-31
Project acronym AdOMiS
Project Adaptive Optical Microscopy Systems: Unifying theory, practice and applications
Researcher (PI) Martin BOOTH
Host Institution (HI) THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Call Details Advanced Grant (AdG), PE7, ERC-2015-AdG
Summary Recent technological advances in optical microscopy have vastly broadened the possibilities for applications in the biomedical sciences. Fluorescence microscopy is the central tool for investigation of molecular structures and dynamics that take place in the cellular and tissue environment. Coupled with progress in labeling methods, these microscopes permit observation of biological structures and processes with unprecedented sensitivity and resolution. This work has been enabled by the engineering development of diverse optical systems that provide different capabilities for the imaging toolkit. All such methods rely upon high fidelity optics to provide optimal resolution and efficiency, but they all suffer from aberrations caused by refractive index variations within the specimen. It is widely accepted that in many applications this fundamental problem prevents optimum operation and limits capability. Adaptive optics (AO) has been introduced to overcome these limitations by correcting aberrations and a range of demonstrations has shown clearly its potential. Indeed, it shows great promise to improve virtually all types of research or commercial microscopes, but significant challenges must still be met before AO can be widely implemented in routine imaging. Current advances are being made through development of bespoke AO solutions to individual imaging tasks. However, the diversity of microscopy methods means that individual solutions are often not translatable to other systems. This proposal is directed towards the creation of theoretical and practical frameworks that tie together AO concepts and provide a suite of scientific tools with broad application. This will be achieved through a systems approach that encompasses theoretical modelling, optical engineering and the requirements of biological applications. Additional outputs will include practical designs, operating protocols and software algorithms that will support next generation AO microscope systems.
Summary
Recent technological advances in optical microscopy have vastly broadened the possibilities for applications in the biomedical sciences. Fluorescence microscopy is the central tool for investigation of molecular structures and dynamics that take place in the cellular and tissue environment. Coupled with progress in labeling methods, these microscopes permit observation of biological structures and processes with unprecedented sensitivity and resolution. This work has been enabled by the engineering development of diverse optical systems that provide different capabilities for the imaging toolkit. All such methods rely upon high fidelity optics to provide optimal resolution and efficiency, but they all suffer from aberrations caused by refractive index variations within the specimen. It is widely accepted that in many applications this fundamental problem prevents optimum operation and limits capability. Adaptive optics (AO) has been introduced to overcome these limitations by correcting aberrations and a range of demonstrations has shown clearly its potential. Indeed, it shows great promise to improve virtually all types of research or commercial microscopes, but significant challenges must still be met before AO can be widely implemented in routine imaging. Current advances are being made through development of bespoke AO solutions to individual imaging tasks. However, the diversity of microscopy methods means that individual solutions are often not translatable to other systems. This proposal is directed towards the creation of theoretical and practical frameworks that tie together AO concepts and provide a suite of scientific tools with broad application. This will be achieved through a systems approach that encompasses theoretical modelling, optical engineering and the requirements of biological applications. Additional outputs will include practical designs, operating protocols and software algorithms that will support next generation AO microscope systems.
Max ERC Funding
3 234 789 €
Duration
Start date: 2016-09-01, End date: 2021-08-31
Project acronym AMSTAT
Project Problems at the Applied Mathematics-Statistics Interface
Researcher (PI) Andrew Stuart
Host Institution (HI) THE UNIVERSITY OF WARWICK
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary Applied mathematics is concerned with developing models with predictive capability, and with probing those models to obtain qualitative and quantitative insight into the phenomena being modelled. Statistics is data-driven and is aimed at the development of methodologies to optimize the information derived from data. The increasing complexity of phenomena that scientists and engineers wish to model, together with our increased ability to gather, store and interrogate data, mean that the subjects of applied mathematics and statistics are increasingly required to work in conjunction. This research proposal is concerned with a research program at the interface between these two disciplines, aimed at problems in differential equations where profusion of data and the sophisticated model combine to produce the mathematical problem of obtaining information from a probability measure on function space. Applications are far-reaching and include the atmospheric sciences, geophysics, chemistry, econometrics and signal processing. The objectives of the research are: (i) to create the systematic foundations for a range of problems at the applied mathematics and statistics interface which share the common mathematical structure underpinning the range of applications described above; (ii) to exploit this common mathematical structure to design effecient algorithms to sample probability measures on function space; (iii) to apply these algorithms to attack a range of significant problems arising in molecular dynamics and in the atmospheric sciences.
Summary
Applied mathematics is concerned with developing models with predictive capability, and with probing those models to obtain qualitative and quantitative insight into the phenomena being modelled. Statistics is data-driven and is aimed at the development of methodologies to optimize the information derived from data. The increasing complexity of phenomena that scientists and engineers wish to model, together with our increased ability to gather, store and interrogate data, mean that the subjects of applied mathematics and statistics are increasingly required to work in conjunction. This research proposal is concerned with a research program at the interface between these two disciplines, aimed at problems in differential equations where profusion of data and the sophisticated model combine to produce the mathematical problem of obtaining information from a probability measure on function space. Applications are far-reaching and include the atmospheric sciences, geophysics, chemistry, econometrics and signal processing. The objectives of the research are: (i) to create the systematic foundations for a range of problems at the applied mathematics and statistics interface which share the common mathematical structure underpinning the range of applications described above; (ii) to exploit this common mathematical structure to design effecient algorithms to sample probability measures on function space; (iii) to apply these algorithms to attack a range of significant problems arising in molecular dynamics and in the atmospheric sciences.
Max ERC Funding
1 693 501 €
Duration
Start date: 2008-12-01, End date: 2014-11-30
Project acronym AXONSURVIVAL
Project Axon survival: the role of protein synthesis
Researcher (PI) Christine Elizabeth Holt
Host Institution (HI) THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
Call Details Advanced Grant (AdG), LS5, ERC-2012-ADG_20120314
Summary Neurons make long-distance connections with synaptic targets via axons. These axons survive throughout the lifetime of an organism, often many years in mammals, yet how axons are maintained is not fully understood. Recently, we provided in vivo evidence that local mRNA translation in mature axons is required for their maintenance. This new finding, along with in vitro work from other groups, indicates that promoting axonal protein synthesis is a key mechanism by which trophic factors act to prevent axon degeneration. Here we propose a program of research to investigate the importance of ribosomal proteins (RPs) in axon maintenance and degeneration. The rationale for this is fourfold. First, recent genome-wide studies of axonal transcriptomes have revealed that protein synthesis (including RP mRNAs) is the highest functional category in several neuronal types. Second, some RPs have evolved extra-ribosomal functions that include signalling, such as 67LR which acts both as a cell surface receptor for laminin and as a RP. Third, mutations in different RPs in vertebrates cause unexpectedly specific defects, such as the loss of optic axons. Fourth, preliminary results show that RP mRNAs are translated in optic axons in response to trophic factors. Collectively these findings lead us to propose that locally synthesized RPs play a role in axon maintenance through either ribosomal or extra-ribosomal function. To pursue this proposal, we will perform unbiased screens and functional assays using an array of experimental approaches and animal models. By gaining an understanding of how local RP synthesis contributes to axon survival, our studies have the potential to provide novel insights into how components conventionally associated with a housekeeping role (translation) are linked to axon degeneration. Our findings could provide new directions for developing therapeutic tools for neurodegenerative disorders and may have an impact on more diverse areas of biology and disease.
Summary
Neurons make long-distance connections with synaptic targets via axons. These axons survive throughout the lifetime of an organism, often many years in mammals, yet how axons are maintained is not fully understood. Recently, we provided in vivo evidence that local mRNA translation in mature axons is required for their maintenance. This new finding, along with in vitro work from other groups, indicates that promoting axonal protein synthesis is a key mechanism by which trophic factors act to prevent axon degeneration. Here we propose a program of research to investigate the importance of ribosomal proteins (RPs) in axon maintenance and degeneration. The rationale for this is fourfold. First, recent genome-wide studies of axonal transcriptomes have revealed that protein synthesis (including RP mRNAs) is the highest functional category in several neuronal types. Second, some RPs have evolved extra-ribosomal functions that include signalling, such as 67LR which acts both as a cell surface receptor for laminin and as a RP. Third, mutations in different RPs in vertebrates cause unexpectedly specific defects, such as the loss of optic axons. Fourth, preliminary results show that RP mRNAs are translated in optic axons in response to trophic factors. Collectively these findings lead us to propose that locally synthesized RPs play a role in axon maintenance through either ribosomal or extra-ribosomal function. To pursue this proposal, we will perform unbiased screens and functional assays using an array of experimental approaches and animal models. By gaining an understanding of how local RP synthesis contributes to axon survival, our studies have the potential to provide novel insights into how components conventionally associated with a housekeeping role (translation) are linked to axon degeneration. Our findings could provide new directions for developing therapeutic tools for neurodegenerative disorders and may have an impact on more diverse areas of biology and disease.
Max ERC Funding
2 426 573 €
Duration
Start date: 2013-03-01, End date: 2018-09-30
Project acronym BEAM-ME-UP
Project From Radio-Frequency to Giga-Bit
Optical- and Quantum-Wireless
Researcher (PI) Lajos Hanzo
Host Institution (HI) UNIVERSITY OF SOUTHAMPTON
Call Details Advanced Grant (AdG), PE7, ERC-2012-ADG_20120216
Summary The majority of the globe's population carries a mobile phone, but with the increasing proliferation of smart phones and tablet-computers the tele-traffic is predicted to grow 1000-fold over the next decade, especially, when aiming for creating the impression of ubiquitous and flawless 'tele-presence' based on crisp, three-dimensional (3D) video with its sense of joy and wonder. For tele-presence to become a reality requires a further quantum-leap from the popular 3G/4G smart phones and tablet-computers. This project will create the link-level enabling techniques of this transformational quantum leap to immersive Giga-bit 3D video communications, relying on Optical Wireless (OW) hotspots and their ad hoc networking.
As a result, the Beam-Me-Up project will contribute to job- and wealth-creation in numeorus ways, as exemplified by the often-quoted economic benefits of 3G/4G phones on businesses. From an environmental perspective, flawless tele-presence has the potential of eliminating millions of flights/trips and hence will considerably reduce CO2 emissions, whilst reducing the related business-costs as well as saving precious time for the work-force. However, the transfiguration of the voice-only phone into today's intelligent smart phone was facilitated by a 1000-fold transmission-rate increase, which would result in a proportionally increased power consumption, CO2 emissions and in a soaring energy-bill. Tele-presence based on crisp Avatar-style 3D video has even higher bitrates and energy consumption. These radically new high-rate 3D tele-presence services can no longer be accommodated in the severely congested Radio Frequency (RF) band.
Hence the project will create a suite of new OW system components, operating in the visible-light domain and will conceive low-power, low-complexity OW solutions to enable immersive Giga-bit 3D wireless video communications over heterogeneous networks.
Summary
The majority of the globe's population carries a mobile phone, but with the increasing proliferation of smart phones and tablet-computers the tele-traffic is predicted to grow 1000-fold over the next decade, especially, when aiming for creating the impression of ubiquitous and flawless 'tele-presence' based on crisp, three-dimensional (3D) video with its sense of joy and wonder. For tele-presence to become a reality requires a further quantum-leap from the popular 3G/4G smart phones and tablet-computers. This project will create the link-level enabling techniques of this transformational quantum leap to immersive Giga-bit 3D video communications, relying on Optical Wireless (OW) hotspots and their ad hoc networking.
As a result, the Beam-Me-Up project will contribute to job- and wealth-creation in numeorus ways, as exemplified by the often-quoted economic benefits of 3G/4G phones on businesses. From an environmental perspective, flawless tele-presence has the potential of eliminating millions of flights/trips and hence will considerably reduce CO2 emissions, whilst reducing the related business-costs as well as saving precious time for the work-force. However, the transfiguration of the voice-only phone into today's intelligent smart phone was facilitated by a 1000-fold transmission-rate increase, which would result in a proportionally increased power consumption, CO2 emissions and in a soaring energy-bill. Tele-presence based on crisp Avatar-style 3D video has even higher bitrates and energy consumption. These radically new high-rate 3D tele-presence services can no longer be accommodated in the severely congested Radio Frequency (RF) band.
Hence the project will create a suite of new OW system components, operating in the visible-light domain and will conceive low-power, low-complexity OW solutions to enable immersive Giga-bit 3D wireless video communications over heterogeneous networks.
Max ERC Funding
2 470 416 €
Duration
Start date: 2013-03-01, End date: 2018-02-28
Project acronym BrainEnergy
Project Control of cerebral blood flow by capillary pericytes in health and disease
Researcher (PI) David ATTWELL
Host Institution (HI) UNIVERSITY COLLEGE LONDON
Call Details Advanced Grant (AdG), LS5, ERC-2016-ADG
Summary Pericytes, located at intervals along capillaries, have recently been revealed as major controllers of brain blood flow. Normally, they dilate capillaries in response to neuronal activity, increasing local blood flow and energy supply. But in pathology they have a more sinister role. After artery block causes a stroke, the brain suffers from the so-called “no-reflow” phenomenon - a failure to fully reperfuse capillaries, even after the upstream occluded artery has been reperfused successfully. The resulting long-lasting decrease of energy supply damages neurons. I have shown that a major cause of no-reflow lies in pericytes: during ischaemia they constrict and then die in rigor. This reduces capillary diameter and blood flow, and probably degrades blood-brain barrier function. However, despite their crucial role in regulating blood flow physiologically and in pathology, little is known about the mechanisms by which pericytes function.
By using blood vessel imaging, patch-clamping, two-photon imaging, optogenetics, immunohistochemistry, mathematical modelling, and live human tissue obtained from neurosurgery, this programme of research will:
(i) define the signalling mechanisms controlling capillary constriction and dilation in health and disease;
(ii) identify the relative contributions of neurons, astrocytes and microglia to regulating pericyte tone;
(iii) develop approaches to preventing brain pericyte constriction and death during ischaemia;
(iv) define how pericyte constriction of capillaries and pericyte death contribute to Alzheimer’s disease;
(v) extend these results from rodent brain to human brain pericytes as a prelude to developing therapies.
The diseases to which pericytes contribute include stroke, spinal cord injury, diabetes and Alzheimer’s disease. These all have an enormous economic impact, as well as causing great suffering for patients and their carers. This work will provide novel therapeutic approaches for treating these diseases.
Summary
Pericytes, located at intervals along capillaries, have recently been revealed as major controllers of brain blood flow. Normally, they dilate capillaries in response to neuronal activity, increasing local blood flow and energy supply. But in pathology they have a more sinister role. After artery block causes a stroke, the brain suffers from the so-called “no-reflow” phenomenon - a failure to fully reperfuse capillaries, even after the upstream occluded artery has been reperfused successfully. The resulting long-lasting decrease of energy supply damages neurons. I have shown that a major cause of no-reflow lies in pericytes: during ischaemia they constrict and then die in rigor. This reduces capillary diameter and blood flow, and probably degrades blood-brain barrier function. However, despite their crucial role in regulating blood flow physiologically and in pathology, little is known about the mechanisms by which pericytes function.
By using blood vessel imaging, patch-clamping, two-photon imaging, optogenetics, immunohistochemistry, mathematical modelling, and live human tissue obtained from neurosurgery, this programme of research will:
(i) define the signalling mechanisms controlling capillary constriction and dilation in health and disease;
(ii) identify the relative contributions of neurons, astrocytes and microglia to regulating pericyte tone;
(iii) develop approaches to preventing brain pericyte constriction and death during ischaemia;
(iv) define how pericyte constriction of capillaries and pericyte death contribute to Alzheimer’s disease;
(v) extend these results from rodent brain to human brain pericytes as a prelude to developing therapies.
The diseases to which pericytes contribute include stroke, spinal cord injury, diabetes and Alzheimer’s disease. These all have an enormous economic impact, as well as causing great suffering for patients and their carers. This work will provide novel therapeutic approaches for treating these diseases.
Max ERC Funding
2 499 954 €
Duration
Start date: 2017-09-01, End date: 2022-08-31
Project acronym BRAINPOWER
Project Brain energy supply and the consequences of its failure
Researcher (PI) David Ian Attwell
Host Institution (HI) UNIVERSITY COLLEGE LONDON
Call Details Advanced Grant (AdG), LS5, ERC-2009-AdG
Summary Energy, supplied in the form of oxygen and glucose in the blood, is essential for the brain s cognitive power. Failure of the energy supply to the nervous system underlies the mental and physical disability occurring in a wide range of economically important neurological disorders, such as stroke, spinal cord injury and cerebral palsy. Using a combination of two-photon imaging, electrophysiological, molecular and transgenic approaches, I will investigate the control of brain energy supply at the vascular level, and at the level of individual neurons and glial cells, and study the deleterious consequences for the neurons, glia and vasculature of a failure of brain energy supply. The work will focus on the following fundamental issues: A. Vascular control of the brain energy supply (1) How important is control of energy supply at the capillary level, by pericytes? (2) Which synapses control blood flow (and thus generate functional imaging signals) in the cortex? B. Neuronal and glial control of brain energy supply (3) How is grey matter neuronal activity powered? (4) How is the white matter supplied with energy? C. The pathological consequences of a loss of brain energy supply (5) How does a fall of energy supply cause neurotoxic glutamate release? (6) How similar are events in the grey and white matter in energy deprivation conditions? (7) How does a transient loss of energy supply affect blood flow regulation? (8) How does brain energy use change after a period without energy supply? Together this work will significantly advance our understanding of how the energy supply to neurons and glia is regulated in normal conditions, and how the loss of the energy supply causes disorders which consume more than 5% of the costs of European health services (5% of ~1000 billion euro/year).
Summary
Energy, supplied in the form of oxygen and glucose in the blood, is essential for the brain s cognitive power. Failure of the energy supply to the nervous system underlies the mental and physical disability occurring in a wide range of economically important neurological disorders, such as stroke, spinal cord injury and cerebral palsy. Using a combination of two-photon imaging, electrophysiological, molecular and transgenic approaches, I will investigate the control of brain energy supply at the vascular level, and at the level of individual neurons and glial cells, and study the deleterious consequences for the neurons, glia and vasculature of a failure of brain energy supply. The work will focus on the following fundamental issues: A. Vascular control of the brain energy supply (1) How important is control of energy supply at the capillary level, by pericytes? (2) Which synapses control blood flow (and thus generate functional imaging signals) in the cortex? B. Neuronal and glial control of brain energy supply (3) How is grey matter neuronal activity powered? (4) How is the white matter supplied with energy? C. The pathological consequences of a loss of brain energy supply (5) How does a fall of energy supply cause neurotoxic glutamate release? (6) How similar are events in the grey and white matter in energy deprivation conditions? (7) How does a transient loss of energy supply affect blood flow regulation? (8) How does brain energy use change after a period without energy supply? Together this work will significantly advance our understanding of how the energy supply to neurons and glia is regulated in normal conditions, and how the loss of the energy supply causes disorders which consume more than 5% of the costs of European health services (5% of ~1000 billion euro/year).
Max ERC Funding
2 499 947 €
Duration
Start date: 2010-04-01, End date: 2016-03-31
Project acronym C-SENSE
Project Exploiting low dimensional models in sensing, computation and signal processing
Researcher (PI) Michael DAVIES
Host Institution (HI) THE UNIVERSITY OF EDINBURGH
Call Details Advanced Grant (AdG), PE7, ERC-2015-AdG
Summary The aim of this project is to develop the next generation of compressive and computational sensing and processing techniques.
The ability to identify and exploit good signal representations is pivotal in many signal and data processing tasks. During the last decade sparse representations have provided stunning performance gains for applications such as: imaging coding, computer vision, super-resolution microscopy and most recently in MRI, achieving many-fold acceleration through compressed sensing (CS).
However in most real world sensing it is generally not possible to fully adopt the random sampling strategies advocated by CS. Systems are often nonlinear, measurements have limited dynamic range, noise is rarely Gaussian and reconstruction is not always the final goal. Furthermore, iterative reconstruction techniques are often not adopted in commercial imaging systems as they typically incur at least an order of magnitude more computation than traditional techniques. Thus there is a real need for a new framework for generalized computationally accelerated sensing and processing techniques.
The research proposed here will build on the PIs recent work in this area and will develop and analyse a much richer class of hierarchical low dimensional signal models, accommodating everything from physical laws to data-driven models such as deep neural networks. It will provide quantitative guidance for system design and address sensing tasks beyond reconstruction including detection, classification and statistical estimation. It will also exploit low dimensional structure to reduce computational cost as well as estimation accuracy, challenging the notion that exploiting prior information must come at a computational cost.
This research will result in a new generation of data-driven, physics-aware and task-orientated sensing systems in application domains such as advanced radar, CT and MR imaging and emerging sensing modalities such as multispectral time-of-flight cameras.
Summary
The aim of this project is to develop the next generation of compressive and computational sensing and processing techniques.
The ability to identify and exploit good signal representations is pivotal in many signal and data processing tasks. During the last decade sparse representations have provided stunning performance gains for applications such as: imaging coding, computer vision, super-resolution microscopy and most recently in MRI, achieving many-fold acceleration through compressed sensing (CS).
However in most real world sensing it is generally not possible to fully adopt the random sampling strategies advocated by CS. Systems are often nonlinear, measurements have limited dynamic range, noise is rarely Gaussian and reconstruction is not always the final goal. Furthermore, iterative reconstruction techniques are often not adopted in commercial imaging systems as they typically incur at least an order of magnitude more computation than traditional techniques. Thus there is a real need for a new framework for generalized computationally accelerated sensing and processing techniques.
The research proposed here will build on the PIs recent work in this area and will develop and analyse a much richer class of hierarchical low dimensional signal models, accommodating everything from physical laws to data-driven models such as deep neural networks. It will provide quantitative guidance for system design and address sensing tasks beyond reconstruction including detection, classification and statistical estimation. It will also exploit low dimensional structure to reduce computational cost as well as estimation accuracy, challenging the notion that exploiting prior information must come at a computational cost.
This research will result in a new generation of data-driven, physics-aware and task-orientated sensing systems in application domains such as advanced radar, CT and MR imaging and emerging sensing modalities such as multispectral time-of-flight cameras.
Max ERC Funding
2 212 048 €
Duration
Start date: 2016-09-01, End date: 2021-08-31
Project acronym COIMBRA
Project Combinatorial methods in noncommutative ring theory
Researcher (PI) Agata Smoktunowicz
Host Institution (HI) THE UNIVERSITY OF EDINBURGH
Call Details Advanced Grant (AdG), PE1, ERC-2012-ADG_20120216
Summary As noted by T Y Lam in his book, A first course in noncommutative rings, noncommutative ring theory is a fertile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential operators), noncommutative algebraic geometry (graded domains), arithmetic (orders, Brauer groups), universal algebra (co-homology of rings, projective modules) and quantum physics (quantum matrices). As such, noncommutative ring theory is an area which has the potential to produce developments in many areas and in an efficient manner. The main aim of the project is to develop methods which could be applicable not only in ring theory but also in other areas, and then apply them to solve several important open questions in mathematics. The Principal Investigator, along with two PhD students and two post doctorates, propose to: study basic open questions on infinite dimensional associative noncommutative algebras; pool their expertise so as to tackle problems from a number of related areas of mathematics using noncommutative ring theory, and develop new approaches to existing problems that will benefit future researchers. A part of our methodology would be to first improve (in some cases) Bergman's Diamond Lemma, and then apply it to several open problems. The Diamond Lemma gives bases for the algebras defined by given sets of relations. In general, it is very difficult to determine if the algebra given by a concrete set of relations is non-trivial or infinite dimensional. Our approach is to introduce smaller rings, which we will call platinum rings. The next step would then be to apply the Diamond Lemma to the platinum ring instead of the original rings. Such results would have many applications in group theory, noncommutative projective geometry, nonassociative algebras and no doubt other areas as well.
Summary
As noted by T Y Lam in his book, A first course in noncommutative rings, noncommutative ring theory is a fertile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential operators), noncommutative algebraic geometry (graded domains), arithmetic (orders, Brauer groups), universal algebra (co-homology of rings, projective modules) and quantum physics (quantum matrices). As such, noncommutative ring theory is an area which has the potential to produce developments in many areas and in an efficient manner. The main aim of the project is to develop methods which could be applicable not only in ring theory but also in other areas, and then apply them to solve several important open questions in mathematics. The Principal Investigator, along with two PhD students and two post doctorates, propose to: study basic open questions on infinite dimensional associative noncommutative algebras; pool their expertise so as to tackle problems from a number of related areas of mathematics using noncommutative ring theory, and develop new approaches to existing problems that will benefit future researchers. A part of our methodology would be to first improve (in some cases) Bergman's Diamond Lemma, and then apply it to several open problems. The Diamond Lemma gives bases for the algebras defined by given sets of relations. In general, it is very difficult to determine if the algebra given by a concrete set of relations is non-trivial or infinite dimensional. Our approach is to introduce smaller rings, which we will call platinum rings. The next step would then be to apply the Diamond Lemma to the platinum ring instead of the original rings. Such results would have many applications in group theory, noncommutative projective geometry, nonassociative algebras and no doubt other areas as well.
Max ERC Funding
1 406 551 €
Duration
Start date: 2013-06-01, End date: 2018-05-31