Project acronym BRAINCODES
Project Brain networks controlling social decisions
Researcher (PI) Christian Carl RUFF
Host Institution (HI) UNIVERSITAT ZURICH
Call Details Consolidator Grant (CoG), SH4, ERC-2016-COG
Summary Successful social interactions require social decision making, the ability to guide our actions in line with the goals and expectations of the people around us. Disordered social decision making – e.g., associated with criminal activity or psychiatric illnesses – poses significant financial and personal challenges to society. However, the brain mechanisms that enable us to control our social behavior are far from being understood. Here I will take decisive steps towards a causal understanding of these mechanisms by elucidating the role of functional interactions in the brain networks responsible for steering strategic, prosocial, and norm-compliant behavior. I will employ a unique multi-method approach that integrates computational modeling of social decisions with new combinations of multimodal neuroimaging and brain stimulation methods. Using EEG-fMRI, I will first identify spatio-temporal patterns of functional interactions between brain areas that correlate with social decision processes as identified by computational modeling of behavior in different economic games. In combined brain stimulation-fMRI studies, I will then attempt to affect – and in fact enhance – these social decision-making processes by modulating the identified brain network patterns with novel, targeted brain stimulation protocols and measuring the resulting effects on behavior and brain activity. Finally, I will examine whether the identified brain network mechanisms are indeed related to disturbed social decisions in two psychiatric illnesses characterized by maladaptive social behavior (post-traumatic stress disorder and autism spectrum disorder). My proposed work plan will generate a causal understanding of the brain network mechanisms that allow humans to control their social decisions, thereby elucidating a biological basis for individual differences in social behavior and paving the way for new perspectives on how disordered social behavior may be identified and hopefully remedied.
Summary
Successful social interactions require social decision making, the ability to guide our actions in line with the goals and expectations of the people around us. Disordered social decision making – e.g., associated with criminal activity or psychiatric illnesses – poses significant financial and personal challenges to society. However, the brain mechanisms that enable us to control our social behavior are far from being understood. Here I will take decisive steps towards a causal understanding of these mechanisms by elucidating the role of functional interactions in the brain networks responsible for steering strategic, prosocial, and norm-compliant behavior. I will employ a unique multi-method approach that integrates computational modeling of social decisions with new combinations of multimodal neuroimaging and brain stimulation methods. Using EEG-fMRI, I will first identify spatio-temporal patterns of functional interactions between brain areas that correlate with social decision processes as identified by computational modeling of behavior in different economic games. In combined brain stimulation-fMRI studies, I will then attempt to affect – and in fact enhance – these social decision-making processes by modulating the identified brain network patterns with novel, targeted brain stimulation protocols and measuring the resulting effects on behavior and brain activity. Finally, I will examine whether the identified brain network mechanisms are indeed related to disturbed social decisions in two psychiatric illnesses characterized by maladaptive social behavior (post-traumatic stress disorder and autism spectrum disorder). My proposed work plan will generate a causal understanding of the brain network mechanisms that allow humans to control their social decisions, thereby elucidating a biological basis for individual differences in social behavior and paving the way for new perspectives on how disordered social behavior may be identified and hopefully remedied.
Max ERC Funding
1 999 991 €
Duration
Start date: 2017-09-01, End date: 2022-08-31
Project acronym BUNGEE
Project Directed crop breeding using jumping genes
Researcher (PI) Etienne BUCHER
Host Institution (HI) EIDGENOESSISCHES DEPARTEMENT FUER WIRTSCHAFT, BILDUNG UND FORSCHUNG
Call Details Consolidator Grant (CoG), LS9, ERC-2016-COG
Summary The rapidly changing climate puts commonly used crop plants under strong pressure. It is therefore essential to develop novel breeding technologies to rapidly enhance crops to better withstand newly emerging stresses.
Interestingly, a clear link between transposable elements (TEs), crop improvement and varietal diversification exists. Furthermore, in recent years the importance of (TEs) in evolution and adaptation to stresses has been recognized. However the use of TEs in crop breeding is currently very limited because it is not possible to control TE mobility. My research group has identified a novel highly conserved epigenetic silencing mechanism that represses the activity of TEs in Arabidopsis. We also found drugs capable of inhibiting this mechanism. Because these drugs target highly conserved enzymes we were able to show that our drug treatment is also effective in rice. We are therefore able to produce TE bursts in a controlled manner in virtually any plant. We can thus, for the first time, generate and study TE bursts in crop plants in real time. More importantly, we found that the accumulation of novel insertions of a heat-stress inducible TE produced plants that, at a high frequency, were more resistant to heat stress. This suggests that the stress that was initially applied to activate a specific TE in the parent, lead to an improved tolerance to that specific stress in the progeny of that plant in a very straight-forward manner.
In this project I propose to accelerate plant breeding by testing and implementing a revolutionary TE-directed crop improvement technology. For that I plan to 1. Mobilize TEs in crop plants using selected stresses 2. Using these mobilized stress-responsive TEs breed novel crop plants resistant to those selected stresses and 3. Study the genetic and epigenetic impact of TE mobilization on host genomes. This project will have a broad impact on crop improvement and on the basic understanding of the evolutionary importance of TEs.
Summary
The rapidly changing climate puts commonly used crop plants under strong pressure. It is therefore essential to develop novel breeding technologies to rapidly enhance crops to better withstand newly emerging stresses.
Interestingly, a clear link between transposable elements (TEs), crop improvement and varietal diversification exists. Furthermore, in recent years the importance of (TEs) in evolution and adaptation to stresses has been recognized. However the use of TEs in crop breeding is currently very limited because it is not possible to control TE mobility. My research group has identified a novel highly conserved epigenetic silencing mechanism that represses the activity of TEs in Arabidopsis. We also found drugs capable of inhibiting this mechanism. Because these drugs target highly conserved enzymes we were able to show that our drug treatment is also effective in rice. We are therefore able to produce TE bursts in a controlled manner in virtually any plant. We can thus, for the first time, generate and study TE bursts in crop plants in real time. More importantly, we found that the accumulation of novel insertions of a heat-stress inducible TE produced plants that, at a high frequency, were more resistant to heat stress. This suggests that the stress that was initially applied to activate a specific TE in the parent, lead to an improved tolerance to that specific stress in the progeny of that plant in a very straight-forward manner.
In this project I propose to accelerate plant breeding by testing and implementing a revolutionary TE-directed crop improvement technology. For that I plan to 1. Mobilize TEs in crop plants using selected stresses 2. Using these mobilized stress-responsive TEs breed novel crop plants resistant to those selected stresses and 3. Study the genetic and epigenetic impact of TE mobilization on host genomes. This project will have a broad impact on crop improvement and on the basic understanding of the evolutionary importance of TEs.
Max ERC Funding
1 965 625 €
Duration
Start date: 2017-06-01, End date: 2022-05-31
Project acronym CONSTAMIS
Project Connecting Statistical Mechanics and Conformal Field Theory: an Ising Model Perspective
Researcher (PI) CLEMENT HONGLER
Host Institution (HI) ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Call Details Starting Grant (StG), PE1, ERC-2016-STG
Summary The developments of Statistical Mechanics and Quantum Field Theory are among the major achievements of the 20th century's science. During the second half of the century, these two subjects started to converge. In two dimensions, this resulted in a most remarkable chapter of mathematical physics: Conformal Field Theory (CFT) reveals deep structures allowing for extremely precise investigations, making such theories powerful building blocks of many subjects of mathematics and physics. Unfortunately, this convergence has remained non-rigorous, leaving most of the spectacular field-theoretic applications to Statistical Mechanics conjectural.
About 15 years ago, several mathematical breakthroughs shed new light on this picture. The development of SLE curves and discrete complex analysis has enabled one to connect various statistical mechanics models with conformally symmetric processes. Recently, major progress was made on a key statistical mechanics model, the Ising model: the connection with SLE was established, and many formulae predicted by CFT were proven.
Important advances towards connecting Statistical Mechanics and CFT now appear possible. This is the goal of this proposal, which is organized in three objectives:
(I) Build a deep correspondence between the Ising model and CFT: reveal clear links between the objects and structures arising in the Ising and CFT frameworks.
(II) Gather the insights of (I) to study new connections to CFT, particularly for minimal models, current algebras and parafermions.
(III) Combine (I) and (II) to go beyond conformal symmetry: link the Ising model with massive integrable field theories.
The aim is to build one of the first rigorous bridges between Statistical Mechanics and CFT. It will help to close the gap between physical derivations and mathematical theorems. By linking the deep structures of CFT to concrete models that are applicable in many subjects, it will be potentially useful to theoretical and applied scientists.
Summary
The developments of Statistical Mechanics and Quantum Field Theory are among the major achievements of the 20th century's science. During the second half of the century, these two subjects started to converge. In two dimensions, this resulted in a most remarkable chapter of mathematical physics: Conformal Field Theory (CFT) reveals deep structures allowing for extremely precise investigations, making such theories powerful building blocks of many subjects of mathematics and physics. Unfortunately, this convergence has remained non-rigorous, leaving most of the spectacular field-theoretic applications to Statistical Mechanics conjectural.
About 15 years ago, several mathematical breakthroughs shed new light on this picture. The development of SLE curves and discrete complex analysis has enabled one to connect various statistical mechanics models with conformally symmetric processes. Recently, major progress was made on a key statistical mechanics model, the Ising model: the connection with SLE was established, and many formulae predicted by CFT were proven.
Important advances towards connecting Statistical Mechanics and CFT now appear possible. This is the goal of this proposal, which is organized in three objectives:
(I) Build a deep correspondence between the Ising model and CFT: reveal clear links between the objects and structures arising in the Ising and CFT frameworks.
(II) Gather the insights of (I) to study new connections to CFT, particularly for minimal models, current algebras and parafermions.
(III) Combine (I) and (II) to go beyond conformal symmetry: link the Ising model with massive integrable field theories.
The aim is to build one of the first rigorous bridges between Statistical Mechanics and CFT. It will help to close the gap between physical derivations and mathematical theorems. By linking the deep structures of CFT to concrete models that are applicable in many subjects, it will be potentially useful to theoretical and applied scientists.
Max ERC Funding
998 005 €
Duration
Start date: 2017-03-01, End date: 2022-02-28
Project acronym DeNovoImmunoDesign
Project Computational Design of Novel Functional Proteins for Immunoengineering
Researcher (PI) BRUNO EMANUEL FERREIRA DE SOUSA CORREIA
Host Institution (HI) ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Call Details Starting Grant (StG), LS9, ERC-2016-STG
Summary Finely orchestrated protein activities are at the heart of the most fundamental cellular processes. The rational and structure-based design of novel functional proteins holds the promise to revolutionize many important aspects in biology, medicine and biotechnology. Computational protein design has led the way on rational protein engineering, however many of these designed proteins were solely focused on structural accuracy and completely impaired of function. DeNovoImmunoDesign proposes novel computational design strategies centered on the exploration of de novo protein topologies and the use of structural flexibility with the ultimate goal of designing functional proteins. The proposed methodologies aim to solve a prevalent problem in computational design that relates to the lack of optimal design templates for the optimization of function. By expanding beyond the known protein structural space, our approaches represent new paradigms on the design of de novo functional proteins. DeNovoImmunoDesign will leverage our new methodologies to design functional proteins with rational approaches for two crucial biomedical endeavors - vaccine design and cancer immunotherapy. Our strategy for vaccine design is to engineer structure-based epitope-focused immunogens to elicit potent neutralizing antibodies – a requirement for vaccine protection. The underlying basis of cancer immunotherapy is the inhibition of key protein-protein interactions - an arena where rational design is lagging. To meet this central need we will develop innovative approaches to design new protein binders for cancer immunotherapy applications. DeNovoImmunoDesign is a multidisciplinary proposal where computation is intertwined with experimentation (biochemistry, structural biology and immunology). Our unique competences and groundbreaking research have all the components to translate into transformative advances for both basic and applied biology through innovations in rational protein design.
Summary
Finely orchestrated protein activities are at the heart of the most fundamental cellular processes. The rational and structure-based design of novel functional proteins holds the promise to revolutionize many important aspects in biology, medicine and biotechnology. Computational protein design has led the way on rational protein engineering, however many of these designed proteins were solely focused on structural accuracy and completely impaired of function. DeNovoImmunoDesign proposes novel computational design strategies centered on the exploration of de novo protein topologies and the use of structural flexibility with the ultimate goal of designing functional proteins. The proposed methodologies aim to solve a prevalent problem in computational design that relates to the lack of optimal design templates for the optimization of function. By expanding beyond the known protein structural space, our approaches represent new paradigms on the design of de novo functional proteins. DeNovoImmunoDesign will leverage our new methodologies to design functional proteins with rational approaches for two crucial biomedical endeavors - vaccine design and cancer immunotherapy. Our strategy for vaccine design is to engineer structure-based epitope-focused immunogens to elicit potent neutralizing antibodies – a requirement for vaccine protection. The underlying basis of cancer immunotherapy is the inhibition of key protein-protein interactions - an arena where rational design is lagging. To meet this central need we will develop innovative approaches to design new protein binders for cancer immunotherapy applications. DeNovoImmunoDesign is a multidisciplinary proposal where computation is intertwined with experimentation (biochemistry, structural biology and immunology). Our unique competences and groundbreaking research have all the components to translate into transformative advances for both basic and applied biology through innovations in rational protein design.
Max ERC Funding
1 695 489 €
Duration
Start date: 2017-03-01, End date: 2022-02-28
Project acronym HyLEF
Project Hydrodynamic Limits and Equilibrium Fluctuations: universality from stochastic systems
Researcher (PI) ANA PATRICIA CARVALHO GONÇALVES
Host Institution (HI) INSTITUTO SUPERIOR TECNICO
Call Details Starting Grant (StG), PE1, ERC-2016-STG
Summary A classical problem in the field of interacting particle systems (IPS) is to derive the macroscopic laws of the thermodynamical quantities of a physical system by considering an underlying microscopic dynamics which is composed of particles that move according to some prescribed stochastic, or deterministic, law. The macroscopic laws can be partial differential equations (PDE) or stochastic PDE (SPDE) depending on whether one is looking at the convergence to the mean or to the fluctuations around that mean. One of the purposes of this research project is to give a mathematically rigorous description of the derivation of SPDE from different IPS. We will focus on the derivation of the stochastic Burgers equation (SBE) and its integrated counterpart, namely, the KPZ equation, as well as their fractional versions. The KPZ equation is conjectured to be a universal SPDE describing the fluctuations of randomly growing interfaces of 1d stochastic dynamics close to a stationary state. With this study we want to characterize what is known as the KPZ universality class: the weak and strong conjectures. The latter states that there exists a universal process, namely the KPZ fixed point, which is a fixed point of the renormalization group operator of space-time scaling 1:2:3, for which the KPZ is also invariant. The former states that the fluctuations of a large class of 1d conservative microscopic dynamics are ruled by stationary solutions of the KPZ. Our goal is threefold: first, to derive the KPZ equation from general weakly asymmetric systems, showing its universality; second, to derive new SPDE, which are less studied in the literature, as the fractional KPZ from IPS which allow long jumps, the KPZ with boundary conditions from IPS in contact with reservoirs or with defects, and coupled KPZ from IPS with more than one conserved quantity. Finally, we will analyze the fluctuations of purely strong asymmetric systems, which are conjectured to be given by the KPZ fixed point.
Summary
A classical problem in the field of interacting particle systems (IPS) is to derive the macroscopic laws of the thermodynamical quantities of a physical system by considering an underlying microscopic dynamics which is composed of particles that move according to some prescribed stochastic, or deterministic, law. The macroscopic laws can be partial differential equations (PDE) or stochastic PDE (SPDE) depending on whether one is looking at the convergence to the mean or to the fluctuations around that mean. One of the purposes of this research project is to give a mathematically rigorous description of the derivation of SPDE from different IPS. We will focus on the derivation of the stochastic Burgers equation (SBE) and its integrated counterpart, namely, the KPZ equation, as well as their fractional versions. The KPZ equation is conjectured to be a universal SPDE describing the fluctuations of randomly growing interfaces of 1d stochastic dynamics close to a stationary state. With this study we want to characterize what is known as the KPZ universality class: the weak and strong conjectures. The latter states that there exists a universal process, namely the KPZ fixed point, which is a fixed point of the renormalization group operator of space-time scaling 1:2:3, for which the KPZ is also invariant. The former states that the fluctuations of a large class of 1d conservative microscopic dynamics are ruled by stationary solutions of the KPZ. Our goal is threefold: first, to derive the KPZ equation from general weakly asymmetric systems, showing its universality; second, to derive new SPDE, which are less studied in the literature, as the fractional KPZ from IPS which allow long jumps, the KPZ with boundary conditions from IPS in contact with reservoirs or with defects, and coupled KPZ from IPS with more than one conserved quantity. Finally, we will analyze the fluctuations of purely strong asymmetric systems, which are conjectured to be given by the KPZ fixed point.
Max ERC Funding
1 179 496 €
Duration
Start date: 2016-12-01, End date: 2021-11-30
Project acronym McHAP
Project Entrapment of Hypoxic Cancer by Macrophages Loaded with HAP
Researcher (PI) Magdalena KROL
Host Institution (HI) SZKOLA GLOWNA GOSPODARSTWA WIEJSKIEGO
Call Details Starting Grant (StG), LS9, ERC-2016-STG
Summary The proposed project seeks to open a new research front within the field of drug delivery to the solid tumours. Unsatisfactory response of tumours to chemotherapy is mainly related to impaired diffusion of the anticancer drug because of decreased drug uptake due to poor vasculature. Moreover, the drug is not able to penetrate the most hypoxic sites. Cells from these ‘untreated’ sites are responsible for relapse and metastasis. However, these avascular regions attract macrophages that migrate even to areas far away from blood vessels. Therefore, they might constitute a unique delivery system of drug containing particles to these parts of the tumour mass. A promising example of such particles that could be used are ferritins, whose caged architecture allows for efficient drug encapsulation and whose uptake from macrophage cells has been well demonstrated. My recent ground breaking finding was that macrophages are also able to specifically and actively transfer these taken up ferritins (loaded with the compound of choice) to cancer cells. Thus, these preliminary results indicate the possibility to use macrophages to deliver ferritin encapsulated compounds directly to the tumour cells even in its hypoxic areas. Then, the use of hypoxia-activated prodrugs (HAP) which are selectively activated only in hypoxic regions will be exploited in order to make cancer therapy safer. However, the molecular mechanism of ferritin uptake by macrophages, their storage, and transport to the cancer cells represent key issues to be investigated and pave the way to the experimental design of the present project.
In the present project, we will develop and characterize a completely new and modern approach to anticancer therapy and drug delivery. As such we expect to be able to precisely administer drugs to the tumour site (even to the hypoxic regions) where it is activated by tumour-specific conditions, avoiding side effects of anticancer therapy.
Summary
The proposed project seeks to open a new research front within the field of drug delivery to the solid tumours. Unsatisfactory response of tumours to chemotherapy is mainly related to impaired diffusion of the anticancer drug because of decreased drug uptake due to poor vasculature. Moreover, the drug is not able to penetrate the most hypoxic sites. Cells from these ‘untreated’ sites are responsible for relapse and metastasis. However, these avascular regions attract macrophages that migrate even to areas far away from blood vessels. Therefore, they might constitute a unique delivery system of drug containing particles to these parts of the tumour mass. A promising example of such particles that could be used are ferritins, whose caged architecture allows for efficient drug encapsulation and whose uptake from macrophage cells has been well demonstrated. My recent ground breaking finding was that macrophages are also able to specifically and actively transfer these taken up ferritins (loaded with the compound of choice) to cancer cells. Thus, these preliminary results indicate the possibility to use macrophages to deliver ferritin encapsulated compounds directly to the tumour cells even in its hypoxic areas. Then, the use of hypoxia-activated prodrugs (HAP) which are selectively activated only in hypoxic regions will be exploited in order to make cancer therapy safer. However, the molecular mechanism of ferritin uptake by macrophages, their storage, and transport to the cancer cells represent key issues to be investigated and pave the way to the experimental design of the present project.
In the present project, we will develop and characterize a completely new and modern approach to anticancer therapy and drug delivery. As such we expect to be able to precisely administer drugs to the tumour site (even to the hypoxic regions) where it is activated by tumour-specific conditions, avoiding side effects of anticancer therapy.
Max ERC Funding
1 413 750 €
Duration
Start date: 2017-01-01, End date: 2021-12-31
Project acronym PERVOL
Project Perception of Plant Volatiles
Researcher (PI) Matthias Erb
Host Institution (HI) UNIVERSITAET BERN
Call Details Starting Grant (StG), LS9, ERC-2016-STG
Summary The capacity to produce and perceive organic chemicals is essential for most cellular organisms. Plant leaves that are attacked by insect herbivores for instance start releasing distinct blends of herbivore-induced plant volatiles, which in turn can be perceived by non-attacked tissues. These tissues then respond more rapidly and more strongly to herbivore attack. One major question that constrains the current understanding of plant volatile communication is how plants perceive herbivore induced volatiles. Can plants smell danger by detecting certain volatiles with specific receptors? Or are other mechanisms at play? Answering these questions would push the boundaries of plant signaling research, as it would allow for the creation of perception impaired mutants to perform detailed analyses of the biological functions and potential agricultural benefits of plant volatile perception.
My recent work identified indole as a key herbivore induced volatile priming signal in maize. As indole is produced by many different plant species and has been well studied as a bacterial volatile, it is an ideal candidate to study the mechanisms and biological functions of plant volatile perception. The key objectives of PERVOL are 1) to develop a new high-throughput plant volatile sampling system for genetic screens of indole perception, 2) to use the system to identify molecular mechanisms of indole perception and 3) to create indole perception mutants to uncover novel biological functions of volatile priming. If successful, PERVOL will set technological standards by providing the community with an innovative and powerful volatile sampling system. Furthermore, it will push the field of plant volatile research by elucidating mechanisms of herbivore induced volatile perception, generating new genetic resources for functional investigations of plant volatile signaling and testing new potential biological functions of the perception of herbivore induced volatiles.
Summary
The capacity to produce and perceive organic chemicals is essential for most cellular organisms. Plant leaves that are attacked by insect herbivores for instance start releasing distinct blends of herbivore-induced plant volatiles, which in turn can be perceived by non-attacked tissues. These tissues then respond more rapidly and more strongly to herbivore attack. One major question that constrains the current understanding of plant volatile communication is how plants perceive herbivore induced volatiles. Can plants smell danger by detecting certain volatiles with specific receptors? Or are other mechanisms at play? Answering these questions would push the boundaries of plant signaling research, as it would allow for the creation of perception impaired mutants to perform detailed analyses of the biological functions and potential agricultural benefits of plant volatile perception.
My recent work identified indole as a key herbivore induced volatile priming signal in maize. As indole is produced by many different plant species and has been well studied as a bacterial volatile, it is an ideal candidate to study the mechanisms and biological functions of plant volatile perception. The key objectives of PERVOL are 1) to develop a new high-throughput plant volatile sampling system for genetic screens of indole perception, 2) to use the system to identify molecular mechanisms of indole perception and 3) to create indole perception mutants to uncover novel biological functions of volatile priming. If successful, PERVOL will set technological standards by providing the community with an innovative and powerful volatile sampling system. Furthermore, it will push the field of plant volatile research by elucidating mechanisms of herbivore induced volatile perception, generating new genetic resources for functional investigations of plant volatile signaling and testing new potential biological functions of the perception of herbivore induced volatiles.
Max ERC Funding
1 989 938 €
Duration
Start date: 2017-03-01, End date: 2022-02-28
Project acronym RandMat
Project Spectral Statistics of Structured Random Matrices
Researcher (PI) Antti Kenneth Viktor KNOWLES
Host Institution (HI) UNIVERSITE DE GENEVE
Call Details Starting Grant (StG), PE1, ERC-2016-STG
Summary The purpose of this proposal is a better mathematical understanding of certain classes of large random matrices. Up to very recently, random matrix theory has been mainly focused on mean-field models with independent entries. In this proposal I instead consider random matrices that incorporate some nontrivial structure. I focus on two types of structured random matrices that arise naturally in important applications and lead to a rich mathematical behaviour: (1) random graphs with fixed degrees, such as random regular graphs, and (2) random band matrices, which constitute a good model of disordered quantum Hamiltonians.
The goals are strongly motivated by the applications to spectral graph theory and quantum chaos for (1) and to the physics of conductance in disordered media for (2). Specifically, I will work in the following directions. First, derive precise bounds on the locations of the extremal eigenvalues and the spectral gap, ultimately obtaining their limiting distributions. Second, characterize the spectral statistics in the bulk of the spectrum, using both eigenvalue correlation functions on small scales and linear eigenvalue statistics on intermediate mesoscopic scales. Third, prove the delocalization of eigenvectors and derive the distribution of their components. These results will address several of the most important questions about the structured random matrices (1) and (2), such as expansion properties of random graphs, hallmarks of quantum chaos in random regular graphs, crossovers in the eigenvalue statistics of disordered conductors, and quantum diffusion.
To achieve these goals I will combine tools introduced in my previous work, such as local resampling of graphs and subdiagram resummation techniques, and in addition develop novel, robust techniques to address the more challenging goals. I expect the output of this proposal to contribute significantly to the understanding of structured random matrices.
Summary
The purpose of this proposal is a better mathematical understanding of certain classes of large random matrices. Up to very recently, random matrix theory has been mainly focused on mean-field models with independent entries. In this proposal I instead consider random matrices that incorporate some nontrivial structure. I focus on two types of structured random matrices that arise naturally in important applications and lead to a rich mathematical behaviour: (1) random graphs with fixed degrees, such as random regular graphs, and (2) random band matrices, which constitute a good model of disordered quantum Hamiltonians.
The goals are strongly motivated by the applications to spectral graph theory and quantum chaos for (1) and to the physics of conductance in disordered media for (2). Specifically, I will work in the following directions. First, derive precise bounds on the locations of the extremal eigenvalues and the spectral gap, ultimately obtaining their limiting distributions. Second, characterize the spectral statistics in the bulk of the spectrum, using both eigenvalue correlation functions on small scales and linear eigenvalue statistics on intermediate mesoscopic scales. Third, prove the delocalization of eigenvectors and derive the distribution of their components. These results will address several of the most important questions about the structured random matrices (1) and (2), such as expansion properties of random graphs, hallmarks of quantum chaos in random regular graphs, crossovers in the eigenvalue statistics of disordered conductors, and quantum diffusion.
To achieve these goals I will combine tools introduced in my previous work, such as local resampling of graphs and subdiagram resummation techniques, and in addition develop novel, robust techniques to address the more challenging goals. I expect the output of this proposal to contribute significantly to the understanding of structured random matrices.
Max ERC Funding
1 257 442 €
Duration
Start date: 2017-01-01, End date: 2021-12-31
Project acronym RSPDE
Project Regularity and Stability in Partial Differential Equations
Researcher (PI) Alessio FIGALLI
Host Institution (HI) EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Call Details Consolidator Grant (CoG), PE1, ERC-2016-COG
Summary "This project focuses on several problems in Partial Differential Equations (PDEs) and the Calculus of Variations. These include:
- Optimal transport and Monge-Ampère equations.
In the last 30 years, the optimal transport problem has been found to be useful to several areas
of mathematics. In particular, this problem is related to Monge-Ampère type equations, and understanding the regularity properties of solutions to such equations is an important question with applications to several other fields.
- Stability in functional and geometric inequalities.
Whether a minimizer of some inequality is ""stable'' in some suitable sense
is an important issue in order to understand and/or predict the evolution in time of a physical phenomenon.
For instance, quantitative stability results allow one to quantify the rate of convergence of a physical system to some steady state, and they can also be used to understand how much the system changes under the influence of exterior factors.
- Di Perna-Lions theory and PDEs.
The study of transport equations with rough coefficients is a very active research area. In particular, recent developments have been used to obtain new results on the semiclassical limit for the Schr\""odinger equation and on the Lagrangian structure of transport equations with singular vector-fields (for instance, the Vlasov-Poisson equation).
These problems, although apparently different, are actually deeply interconnected.
The PI aims to use his expertise in partial differential equations and geometric measure theory to introduce ideas and techniques that will lead to new groundbreaking results.
"
Summary
"This project focuses on several problems in Partial Differential Equations (PDEs) and the Calculus of Variations. These include:
- Optimal transport and Monge-Ampère equations.
In the last 30 years, the optimal transport problem has been found to be useful to several areas
of mathematics. In particular, this problem is related to Monge-Ampère type equations, and understanding the regularity properties of solutions to such equations is an important question with applications to several other fields.
- Stability in functional and geometric inequalities.
Whether a minimizer of some inequality is ""stable'' in some suitable sense
is an important issue in order to understand and/or predict the evolution in time of a physical phenomenon.
For instance, quantitative stability results allow one to quantify the rate of convergence of a physical system to some steady state, and they can also be used to understand how much the system changes under the influence of exterior factors.
- Di Perna-Lions theory and PDEs.
The study of transport equations with rough coefficients is a very active research area. In particular, recent developments have been used to obtain new results on the semiclassical limit for the Schr\""odinger equation and on the Lagrangian structure of transport equations with singular vector-fields (for instance, the Vlasov-Poisson equation).
These problems, although apparently different, are actually deeply interconnected.
The PI aims to use his expertise in partial differential equations and geometric measure theory to introduce ideas and techniques that will lead to new groundbreaking results.
"
Max ERC Funding
1 742 428 €
Duration
Start date: 2017-02-01, End date: 2022-01-31
Project acronym SynPlex
Project Tailored chemical complexity through evolution-inspired synthetic biology
Researcher (PI) Joern PIEL
Host Institution (HI) EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Call Details Advanced Grant (AdG), LS9, ERC-2016-ADG
Summary Creating true molecular complexity in a modular, combinatorial fashion is one of the great visions in applied enzymology and chemistry. Nature achieves this feat by using modular biosynthetic enzymes. These microbial proteins generate many of the most important natural products of therapeutic value, including antiinfective, anticancer, and immunosuppressive agents. To construct such compounds, each enzyme module incorporates and often modifies one building block in an assembly line-like process. Among the known modular enzymes, the recently discovered trans-acyltransferase polyketide synthases (trans-AT PKSs) exhibit an unparalleled biosynthetic diversity and tendency to form extensively mosaic-like hybrid enzymes during evolution. As a consequence, many bioactive polyketides generated by these enzymes exhibit combinatorial-like hybrid structures. This phenomenon provides unprecedented opportunities to understand the evolution of metabolic complexity and to apply these principles to metabolic engineering through parts-based synthetic biology. SynPlex will use a novel hypothesis-driven, multi-faceted strategy to interrogate and utilize the distinct combinatorial properties and metabolic richness of trans-AT PKSs. This multidisciplinary project aims to (i) unravel principles of how mosaic PKSs and their metabolites are formed in Nature, (ii) characterize non-canonical PKS components, (iii) create a toolbox of PKS parts for synthetic biology based on these evolutionary and biochemical principles, and (iv) harness the combinatorial potential of trans-AT systems to access complex natural as well as non-natural products. This innovative concept that merges evolutionary biology, enzymology, synthetic biology, and chemistry will result in a broad understanding of these most complex of all known proteins. It has the potential to provide generic, robust synthetic biology platforms to engineer complex polyketides with a wide range of features in a predictable way.
Summary
Creating true molecular complexity in a modular, combinatorial fashion is one of the great visions in applied enzymology and chemistry. Nature achieves this feat by using modular biosynthetic enzymes. These microbial proteins generate many of the most important natural products of therapeutic value, including antiinfective, anticancer, and immunosuppressive agents. To construct such compounds, each enzyme module incorporates and often modifies one building block in an assembly line-like process. Among the known modular enzymes, the recently discovered trans-acyltransferase polyketide synthases (trans-AT PKSs) exhibit an unparalleled biosynthetic diversity and tendency to form extensively mosaic-like hybrid enzymes during evolution. As a consequence, many bioactive polyketides generated by these enzymes exhibit combinatorial-like hybrid structures. This phenomenon provides unprecedented opportunities to understand the evolution of metabolic complexity and to apply these principles to metabolic engineering through parts-based synthetic biology. SynPlex will use a novel hypothesis-driven, multi-faceted strategy to interrogate and utilize the distinct combinatorial properties and metabolic richness of trans-AT PKSs. This multidisciplinary project aims to (i) unravel principles of how mosaic PKSs and their metabolites are formed in Nature, (ii) characterize non-canonical PKS components, (iii) create a toolbox of PKS parts for synthetic biology based on these evolutionary and biochemical principles, and (iv) harness the combinatorial potential of trans-AT systems to access complex natural as well as non-natural products. This innovative concept that merges evolutionary biology, enzymology, synthetic biology, and chemistry will result in a broad understanding of these most complex of all known proteins. It has the potential to provide generic, robust synthetic biology platforms to engineer complex polyketides with a wide range of features in a predictable way.
Max ERC Funding
2 495 755 €
Duration
Start date: 2017-08-01, End date: 2022-07-31
