ERC FUNDED PROJECTS

The proposed project aims to create a center of excellence that aims at understanding the approximability of NP-hard optimization problems. In particular, for central problems like vertex cover, coloring of graphs, and various constraint satisfaction problems we want to study upper and lower bounds on how well they can be approximated in polynomial time. Many existing strong results are based on what is known as the Unique Games Conjecture (UGC) and a significant part of the project will be devoted to studying this conjecture. We expect that a major step needed to be taken in this process is to further develop the understanding of Boolean functions on the Boolean hypercube. We anticipate that the tools needed for this will come in the form of harmonic analysis which in its turn will rely on the corresponding results in the analysis of functions over the domain of real numbers.

2 376 000 €

Start date: 2009-01-01, End date: 2014-12-31

Magnetic fields in stars, planets, accretion discs, and galaxies are believed to be the result of a dynamo process converting kinetic energy into magnetic energy. This work focuses on the solar dynamo, but dynamos in other astrophysical systems will also be addressed. In particular, direct high-resolution three-dimensional simulations are used to understand particular aspects of the solar dynamo and ultimately to simulate the solar dynamo as a whole. Phenomenological approaches will be avoided in favor of obtaining rigorous results. A major problem is catastrophic quenching, i.e. the decline of dynamo effects in inverse proportion to the magnetic Reynolds number, which is huge. Tremendous advances have been made in the last few years since the cause of catastrophic quenching in dynamos has been understood in terms of magnetic helicity evolution. The numerical tools are now in place to allow for magnetic helicity fluxes via coronal mass ejections, thus alleviating catastrophic quenching. This work employs simulations in spherical shells, augmented by Cartesian simulations in special cases. The roles of the near-surface shear layer, the tachocline, as well as pumping in the bulk of the convection zone are to be clarified. The Pencil Code will be used for most applications. The code is third order in time and sixth order in space and is used for solving the hydromagnetic equations. It is a public domain code developed by roughly 20 scientists world wide and maintained under an a central versioning system at Nordita. Automatic nightly tests of currently 30 applications ensure the integrity of the code. It is used for a wide range of applications and may include the effects of radiation, self-gravity, dust, chemistry, variable ionization, cosmic rays, in addition to those of magnetohydrodynamics. The code with its infrastructure offers a good opportunity for individuals within a broad group of people to develop new tools that may automatically be useful to others.

2 220 000 €

Start date: 2009-02-01, End date: 2014-01-31

In this project, we will develop and use technology that combines synthetic genomics and live-cell imaging. These methods make it possible to study the intracellular biophysics at single-molecule detail in thousands of genetically different bacterial strains in parallel. Our approach is based on in situ genotyping of a barcoded strain library after phenotyping has been performed by live-cell imaging. Within the scope of the proposed project, the new technology will be used to solve mechanistic and structural questions of the bacterial cell cycle. To this end, we will explore two parallel but complementary applications. In the first application, we will determine the dynamic 3D structure of the E. coli chromosome at 1kb resolution throughout the cell cycle. The structure determination can be seen as a live-cell version of chromatin conformation capture, where we will follow the 3D distances of 10 000 pairs of chromosomal loci over the cell cycle at high resolution. In the second application, we will make a complete CRISPRi knockdown strain library where we can follow the replication forks of the E. coli chromosome and septum formation over the cell cycle in individual cells. Using this strategy, we will resolve how individual gene products contribute to the cell-to-cell accuracy in replication initiation and cell division. In particular, this approach allows us to address the challenging question of size sensing at replication initiation. How the cell can decide that it is large enough to initiate replication is still an open question despite decades of investigations. The general principles for high-end imaging of pool-synthesized cell libraries have nearly unlimited applications throughout cell biology. The specific applications explored in this project will take the understanding of the bacterial cell cycle to a new level and answer general questions about the chromosomal organization and cell size sensing.

2 411 410 €

Start date: 2021-01-01, End date: 2025-12-31

Collective behaviour is a widespread phenomenon in nature and technology making it a very important subject to study in various contexts. The main goal we intend to achieve in our multidisciplinary research is the identification and documentation of new unifying principles describing the essential aspects of collective motion, being one of the most relevant and spectacular manifestations of collective behaviour. We shall carry out novel type of experiments, design models that are both simple and realistic enough to reproduce the observations and develop concepts for a better interpretation of the complexity of systems consisting of many organisms and such non-living objects as interacting robots. We plan to study systems ranging from cultures of migrating tissue cells through flocks of birds to collectively moving devices. The interrelation of these systems will be considered in order to deepen the understanding of the main patterns of group motion in both living and non-living systems by learning about the similar phenomena in the two domains of nature. Thus, we plan to understand the essential ingredients of flocking of birds by building collectively moving unmanned aerial vehicles while, in turn, high resolution spatiotemporal GPS data of pigeon flocks will be used to make helpful conclusions for the best designs for swarms of robots. In particular, we shall construct and build a set of vehicles that will be capable, for the first time, to exhibit flocking behaviour in the three-dimensional space. The methods we shall adopt will range from approaches used in statistical physics and network theory to various new techniques in cell biology and collective robotics. All this will be based on numerous prior results (both ours and others) published in leading interdisciplinary journals. The planned research will have the potential of leading to ground breaking results with significant implications in various fields of science and technology.

1 248 000 €

Start date: 2009-03-01, End date: 2015-02-28