Project acronym AQSER
Project Automorphic q-series and their application
Researcher (PI) Kathrin Bringmann
Host Institution (HI) UNIVERSITAET ZU KOELN
Call Details Starting Grant (StG), PE1, ERC-2013-StG
Summary This proposal aims to unravel mysteries at the frontier of number theory and other areas of mathematics and physics. The main focus will be to understand and exploit “modularity” of q-hypergeometric series. “Modular forms are functions on the complex plane that are inordinately symmetric.” (Mazur) The motivation comes from the wide-reaching applications of modularity in combinatorics, percolation, Lie theory, and physics (black holes).
The interplay between automorphic forms, q-series, and other areas of mathematics and physics is often two-sided. On the one hand, the other areas provide interesting examples of automorphic objects and predict their behavior. Sometimes these even motivate new classes of automorphic objects which have not been previously studied. On the other hand, knowing that certain generating functions are modular gives one access to deep theoretical tools to prove results in other areas. “Mathematics is a language, and we need that language to understand the physics of our universe.”(Ooguri) Understanding this interplay has attracted attention of researchers from a variety of areas. However, proofs of modularity of q-hypergeometric series currently fall far short of a comprehensive theory to describe the interplay between them and automorphic forms. A recent conjecture of W. Nahm relates the modularity of such series to K-theory. In this proposal I aim to fill this gap and provide a better understanding of this interplay by building a general structural framework enveloping these q-series. For this I will employ new kinds of automorphic objects and embed the functions of interest into bigger families
A successful outcome of the proposed research will open further horizons and also answer open questions, even those in other areas which were not addressed in this proposal; for example the new theory could be applied to better understand Donaldson invariants.
Summary
This proposal aims to unravel mysteries at the frontier of number theory and other areas of mathematics and physics. The main focus will be to understand and exploit “modularity” of q-hypergeometric series. “Modular forms are functions on the complex plane that are inordinately symmetric.” (Mazur) The motivation comes from the wide-reaching applications of modularity in combinatorics, percolation, Lie theory, and physics (black holes).
The interplay between automorphic forms, q-series, and other areas of mathematics and physics is often two-sided. On the one hand, the other areas provide interesting examples of automorphic objects and predict their behavior. Sometimes these even motivate new classes of automorphic objects which have not been previously studied. On the other hand, knowing that certain generating functions are modular gives one access to deep theoretical tools to prove results in other areas. “Mathematics is a language, and we need that language to understand the physics of our universe.”(Ooguri) Understanding this interplay has attracted attention of researchers from a variety of areas. However, proofs of modularity of q-hypergeometric series currently fall far short of a comprehensive theory to describe the interplay between them and automorphic forms. A recent conjecture of W. Nahm relates the modularity of such series to K-theory. In this proposal I aim to fill this gap and provide a better understanding of this interplay by building a general structural framework enveloping these q-series. For this I will employ new kinds of automorphic objects and embed the functions of interest into bigger families
A successful outcome of the proposed research will open further horizons and also answer open questions, even those in other areas which were not addressed in this proposal; for example the new theory could be applied to better understand Donaldson invariants.
Max ERC Funding
1 240 500 €
Duration
Start date: 2014-01-01, End date: 2019-04-30
Project acronym AttentionCircuits
Project Modulation of neocortical microcircuits for attention
Researcher (PI) Johannes Jakob Letzkus
Host Institution (HI) MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Call Details Starting Grant (StG), LS5, ERC-2013-StG
Summary At every moment in time, the brain receives a vast amount of sensory information about the environment. This makes attention, the process by which we select currently relevant stimuli for processing and ignore irrelevant input, a fundamentally important brain function. Studies in primates have yielded a detailed description of how attention to a stimulus modifies the responses of neuronal ensembles in visual cortex, but how this modulation is produced mechanistically in the circuit is not well understood. Neuronal circuits comprise a large variety of neuron types, and to gain mechanistic insights, and to treat specific diseases of the nervous system, it is crucial to characterize the contribution of different identified cell types to information processing. Inhibition supplied by a small yet highly diverse set of interneurons controls all aspects of cortical function, and the central hypothesis of this proposal is that differential modulation of genetically-defined interneuron types is a key mechanism of attention in visual cortex. To identify the interneuron types underlying attentional modulation and to investigate how this, in turn, affects computations in the circuit we will use an innovative multidisciplinary approach combining genetic targeting in mice with cutting-edge in vivo 2-photon microscopy-based recordings and selective optogenetic manipulation of activity. Importantly, a key set of experiments will test whether the observed neuronal mechanisms are causally involved in attention at the level of behavior, the ultimate readout of the computations we are interested in. The expected results will provide a detailed, mechanistic dissection of the neuronal basis of attention. Beyond attention, selection of different functional states of the same hard-wired circuit by modulatory input is a fundamental, but poorly understood, phenomenon in the brain, and we predict that our insights will elucidate similar mechanisms in other brain areas and functional contexts.
Summary
At every moment in time, the brain receives a vast amount of sensory information about the environment. This makes attention, the process by which we select currently relevant stimuli for processing and ignore irrelevant input, a fundamentally important brain function. Studies in primates have yielded a detailed description of how attention to a stimulus modifies the responses of neuronal ensembles in visual cortex, but how this modulation is produced mechanistically in the circuit is not well understood. Neuronal circuits comprise a large variety of neuron types, and to gain mechanistic insights, and to treat specific diseases of the nervous system, it is crucial to characterize the contribution of different identified cell types to information processing. Inhibition supplied by a small yet highly diverse set of interneurons controls all aspects of cortical function, and the central hypothesis of this proposal is that differential modulation of genetically-defined interneuron types is a key mechanism of attention in visual cortex. To identify the interneuron types underlying attentional modulation and to investigate how this, in turn, affects computations in the circuit we will use an innovative multidisciplinary approach combining genetic targeting in mice with cutting-edge in vivo 2-photon microscopy-based recordings and selective optogenetic manipulation of activity. Importantly, a key set of experiments will test whether the observed neuronal mechanisms are causally involved in attention at the level of behavior, the ultimate readout of the computations we are interested in. The expected results will provide a detailed, mechanistic dissection of the neuronal basis of attention. Beyond attention, selection of different functional states of the same hard-wired circuit by modulatory input is a fundamental, but poorly understood, phenomenon in the brain, and we predict that our insights will elucidate similar mechanisms in other brain areas and functional contexts.
Max ERC Funding
1 466 505 €
Duration
Start date: 2014-02-01, End date: 2019-01-31
Project acronym EVOLMAPPING
Project An integrated assessment of recent evolutionary change
through genome wide mapping of regulatory changes and signatures of selection in natural sculpin (Cottus) hybrids
Researcher (PI) Arne W. Nolte
Host Institution (HI) CARL VON OSSIETZKY UNIVERSITAET OLDENBURG
Call Details Starting Grant (StG), LS8, ERC-2013-StG
Summary It is the unprecedented access to genome wide data that highlights the potential of current evolutionary studies and this proposal aims at exploiting this progress to analyze evolutionary processes in a well-established fish system of hybrid speciation. We study natural populations of freshwater fish referred to as sculpins (Cottus). In these we have identified species that have recently (<200 years) hybridized as a result of secondary contact through man-made canals between river systems. This gave rise to a new lineage with new adaptations that have allowed it to invade habitats that were not used by the parental species before. We are thus also dealing with evolutionary change that is associated with man-made ecological perturbations, the analysis of which is particularly timely. It is now possible to perform a near exhaustive search to identify genes and to study gene expression as a measure of evolutionary change in Cottus. A combination of genetic mapping experiments and screens for genotypic selection can reveal loci and functions as targets of selection in the adaptive evolution of invasive Cottus. This proposal specifically aims at identifying genomic traits such as copy number changes of coding sequences or changes in the gene regulatory architecture that have evolved as a direct consequence of hybridization and to explore their implication in adaptive evolution. The results will contribute to our understanding of the genetics of adaptation and the invasion of a new environment. With respect to hybrid zones and the evolution of new species, we will identify candidate genes and functions that can explain barriers to reproduction in the wild. Finally, we will be able to make significant progress with respect to the genetics associated with hybrid speciation.
Summary
It is the unprecedented access to genome wide data that highlights the potential of current evolutionary studies and this proposal aims at exploiting this progress to analyze evolutionary processes in a well-established fish system of hybrid speciation. We study natural populations of freshwater fish referred to as sculpins (Cottus). In these we have identified species that have recently (<200 years) hybridized as a result of secondary contact through man-made canals between river systems. This gave rise to a new lineage with new adaptations that have allowed it to invade habitats that were not used by the parental species before. We are thus also dealing with evolutionary change that is associated with man-made ecological perturbations, the analysis of which is particularly timely. It is now possible to perform a near exhaustive search to identify genes and to study gene expression as a measure of evolutionary change in Cottus. A combination of genetic mapping experiments and screens for genotypic selection can reveal loci and functions as targets of selection in the adaptive evolution of invasive Cottus. This proposal specifically aims at identifying genomic traits such as copy number changes of coding sequences or changes in the gene regulatory architecture that have evolved as a direct consequence of hybridization and to explore their implication in adaptive evolution. The results will contribute to our understanding of the genetics of adaptation and the invasion of a new environment. With respect to hybrid zones and the evolution of new species, we will identify candidate genes and functions that can explain barriers to reproduction in the wild. Finally, we will be able to make significant progress with respect to the genetics associated with hybrid speciation.
Max ERC Funding
1 377 162 €
Duration
Start date: 2014-02-01, End date: 2019-01-31
Project acronym FUNCSPECGEN
Project What is the engine of biodiversity? Comparative and Functional Speciation Genetics in the Post-genomic Era
Researcher (PI) Jochen Brock Wacain Wolf
Host Institution (HI) LUDWIG-MAXIMILIANS-UNIVERSITAET MUENCHEN
Call Details Starting Grant (StG), LS8, ERC-2013-StG
Summary More than 150 years after the seminal works of Charles Darwin on speciation, we are beginning to unravel the genetic underpinnings of the splitting process (Ellegren H [..] JBW Wolf, Nature, in press). The genomic revolution is progressing at full speed, and for the first time in history we are equipped with the necessary tools to investigate the genomic architecture of speciation at base-pair resolution in any organisms of our choice. When integrated to the mature theoretical framework of the evolutionary sciences, this wealth of genome-scale data will produce fundamental insights into the processes governing adaptation and speciation.
Here, I identify a novel evolutionary model system - crows and ravens of the genus Corvus - and demonstrate its potential for speciation genetic and functional genomic research. Central to this system is the phylogenetically independent recurrence of a pied colour-pattern in several species that stands in contrasts to the predominant all-black plumage in the clade. Building on the idea that colour polymorphism can promote speciation through sexual selection, I choose a number of black and pied species pairs that can be positioned along a time line representing different stages of the speciation process. This comparative framework is unrivalled in its setup and is uniquely suited to study the genetics of speciation across different stages of species divergence. It also provides a promising entry point to the fascinating theme of parallel evolution.
This research program is among the first to harness the possibilities of the post-genomic era in a wild organism. Using a combination of population- and phylo-genomic approaches, single sperm sequencing, experimental work in a breeding population, systems biology approaches and in situ mRNA quantification at cellular resolution, this interdisciplinary program covers novel ground in the nascent field of functional avian genomics and pushes the boundaries of speciation genetic research.
Summary
More than 150 years after the seminal works of Charles Darwin on speciation, we are beginning to unravel the genetic underpinnings of the splitting process (Ellegren H [..] JBW Wolf, Nature, in press). The genomic revolution is progressing at full speed, and for the first time in history we are equipped with the necessary tools to investigate the genomic architecture of speciation at base-pair resolution in any organisms of our choice. When integrated to the mature theoretical framework of the evolutionary sciences, this wealth of genome-scale data will produce fundamental insights into the processes governing adaptation and speciation.
Here, I identify a novel evolutionary model system - crows and ravens of the genus Corvus - and demonstrate its potential for speciation genetic and functional genomic research. Central to this system is the phylogenetically independent recurrence of a pied colour-pattern in several species that stands in contrasts to the predominant all-black plumage in the clade. Building on the idea that colour polymorphism can promote speciation through sexual selection, I choose a number of black and pied species pairs that can be positioned along a time line representing different stages of the speciation process. This comparative framework is unrivalled in its setup and is uniquely suited to study the genetics of speciation across different stages of species divergence. It also provides a promising entry point to the fascinating theme of parallel evolution.
This research program is among the first to harness the possibilities of the post-genomic era in a wild organism. Using a combination of population- and phylo-genomic approaches, single sperm sequencing, experimental work in a breeding population, systems biology approaches and in situ mRNA quantification at cellular resolution, this interdisciplinary program covers novel ground in the nascent field of functional avian genomics and pushes the boundaries of speciation genetic research.
Max ERC Funding
1 494 300 €
Duration
Start date: 2014-04-01, End date: 2019-03-31
Project acronym OptoMotorPath
Project Optogenetic dissection of motor cortex dynamics and pathways
Researcher (PI) Ilka Diester
Host Institution (HI) ALBERT-LUDWIGS-UNIVERSITAET FREIBURG
Call Details Starting Grant (StG), LS5, ERC-2013-StG
Summary Within a densely interconnected network, selective communication can be achieved only if neuronal inputs and outputs are functionally segmented and if only one segment is selected for a given time and neural population. We focus here on this process in the primary motor cortex (M1) which projects to a variety of brain structures involved in motor generation and suppression as well as somatosensory perception. We propose to investigate what kind of information is sent to two of M1’s main target brain areas – the striatum and the somatosensory cortex by separate or partially overlapping neural subpopulations. To dissect the two pathways we will apply new optogenetic projection and stimulation strategies and combine them with controlled behavior and electrophysiological recordings conducted with advanced optoelectronic probes. The goal is to neurophysiologically characterize the two populations in a specially designed Go/NoGo task with sensorimotor component and understand their functional relevance for motor behavior. For causally defining the optimal stimulation frequencies for a specific task period, we will make use of real-time feedback by measuring ongoing oscillatory patterns and enhance or phase shift the synchronized activity in motor cortex and its targets. In particular, we will focus on beta and gamma band oscillations. While beta band activity has been mainly associated with the suppression of movements and with postural maintenance as well as sensorimotor integration and planning, elevated gamma band activity has been reported often during movement initiation and attention. We hypothesize that the best suited resonance frequencies differ between the two communication paths to S1 and striatum and that they might change across trial phases. Apart from the impact on basic science, finding out about the details of sensorimotor integration and the role of synchronization may lead to a better understanding of motor disorders, e.g. Parkinson’s disease.
Summary
Within a densely interconnected network, selective communication can be achieved only if neuronal inputs and outputs are functionally segmented and if only one segment is selected for a given time and neural population. We focus here on this process in the primary motor cortex (M1) which projects to a variety of brain structures involved in motor generation and suppression as well as somatosensory perception. We propose to investigate what kind of information is sent to two of M1’s main target brain areas – the striatum and the somatosensory cortex by separate or partially overlapping neural subpopulations. To dissect the two pathways we will apply new optogenetic projection and stimulation strategies and combine them with controlled behavior and electrophysiological recordings conducted with advanced optoelectronic probes. The goal is to neurophysiologically characterize the two populations in a specially designed Go/NoGo task with sensorimotor component and understand their functional relevance for motor behavior. For causally defining the optimal stimulation frequencies for a specific task period, we will make use of real-time feedback by measuring ongoing oscillatory patterns and enhance or phase shift the synchronized activity in motor cortex and its targets. In particular, we will focus on beta and gamma band oscillations. While beta band activity has been mainly associated with the suppression of movements and with postural maintenance as well as sensorimotor integration and planning, elevated gamma band activity has been reported often during movement initiation and attention. We hypothesize that the best suited resonance frequencies differ between the two communication paths to S1 and striatum and that they might change across trial phases. Apart from the impact on basic science, finding out about the details of sensorimotor integration and the role of synchronization may lead to a better understanding of motor disorders, e.g. Parkinson’s disease.
Max ERC Funding
1 498 890 €
Duration
Start date: 2014-11-01, End date: 2019-10-31
Project acronym OscillInterference
Project Therapeutic Mechanisms and Long Term Effects of Directed Transcranial Alternating Current Stimulation in Epileptic Seizures
Researcher (PI) Antal Berényi
Host Institution (HI) Szegedi Tudomanyegyetem - Hungarian-Netherlands School of Educational Management
Call Details Starting Grant (StG), LS5, ERC-2013-StG
Summary A significant proportion of patients with epilepsy are refractive to pharmaceutical treatments. Recurrent, untreated epileptic seizures are associated with risk of adverse neurological, cognitive, and psychological outcomes. Despite years of study, there are still significant barriers to the management of these disorders. In my proposal I advance the hypothesis that time-targeted perturbation of neural network oscillations by transcranial electric stimulation (TES) decreases the duration of seizures. I hypothesize further that spatially focused TES and chronically applied TES intervention can also permanently reduce seizure occurrence. Our specific aims are designed to perform in vivo studies in rodent models of two seizure types (absence seizures and complex partial seizures) to evaluate the effectiveness of TES in abrogating pathologic network activity, and to use high resolution recording techniques and optogenetical methods to assess the neural mechanisms involved. Our results may help to establish general principles of the diverse epilepsy pathophysiology and introduce novel therapeutic approaches. We will establish a focal TES stimulation protocol to selectively interfere with brain regions previously identified as key structures in the pathomechanism of epilepsy. The deliverables of these experiments will make a significant advancement in the understanding of the pathomechanisms of these disorders, and will offer a new alternative treatment option as a complimentary therapeutic approach to the state of the art pharmaceutical products. The methods used in this project are unique and advanced as the first attempt to perform 512 channel extracellular recordings in the behaving animal to investigate the evolution of epileptic seizures at the neuronal network and cellular levels and by achieving spatially selective TES. The combination of these methods are deployed for both understanding the mechanisms of seizure evolution, and termination of seizures.
Summary
A significant proportion of patients with epilepsy are refractive to pharmaceutical treatments. Recurrent, untreated epileptic seizures are associated with risk of adverse neurological, cognitive, and psychological outcomes. Despite years of study, there are still significant barriers to the management of these disorders. In my proposal I advance the hypothesis that time-targeted perturbation of neural network oscillations by transcranial electric stimulation (TES) decreases the duration of seizures. I hypothesize further that spatially focused TES and chronically applied TES intervention can also permanently reduce seizure occurrence. Our specific aims are designed to perform in vivo studies in rodent models of two seizure types (absence seizures and complex partial seizures) to evaluate the effectiveness of TES in abrogating pathologic network activity, and to use high resolution recording techniques and optogenetical methods to assess the neural mechanisms involved. Our results may help to establish general principles of the diverse epilepsy pathophysiology and introduce novel therapeutic approaches. We will establish a focal TES stimulation protocol to selectively interfere with brain regions previously identified as key structures in the pathomechanism of epilepsy. The deliverables of these experiments will make a significant advancement in the understanding of the pathomechanisms of these disorders, and will offer a new alternative treatment option as a complimentary therapeutic approach to the state of the art pharmaceutical products. The methods used in this project are unique and advanced as the first attempt to perform 512 channel extracellular recordings in the behaving animal to investigate the evolution of epileptic seizures at the neuronal network and cellular levels and by achieving spatially selective TES. The combination of these methods are deployed for both understanding the mechanisms of seizure evolution, and termination of seizures.
Max ERC Funding
1 419 000 €
Duration
Start date: 2013-11-01, End date: 2018-10-31
