ERC FUNDED PROJECTS

We propose to elucidate the structural design principles of naturally occurring antibody complementarity-determining regions (CDRs) and to computationally design novel antibody functions. Antibodies represent the most versatile known system for molecular recognition. Research has yielded many insights into antibody design principles and promising biotechnological and pharmaceutical applications. Still, our understanding of how CDRs encode specific loop conformations lags far behind our understanding of structure-function relationships in non-immunological scaffolds. Thus, design of antibodies from first principles has not been demonstrated. We propose a computational-experimental strategy to address this challenge. We will: (a) characterize the design principles and sequence elements that rigidify antibody CDRs. Natural antibody loops will be subjected to computational modeling, crystallography, and a combined in vitro evolution and deep-sequencing approach to isolate sequence features that rigidify loop backbones; (b) develop a novel computational-design strategy, which uses the >1000 solved structures of antibodies deposited in structure databases to realistically model CDRs and design them to recognize proteins that have not been co-crystallized with antibodies. For example, we will design novel antibodies targeting insulin, for which clinically useful diagnostics are needed. By accessing much larger sequence/structure spaces than are available to natural immune-system repertoires and experimental methods, computational antibody design could produce higher-specificity and higher-affinity binders, even to challenging targets; and (c) develop new strategies to program conformational change in CDRs, generating, e.g., the first allosteric antibodies. These will allow targeting, in principle, of any molecule, potentially revolutionizing how antibodies are generated for research and medicine, providing new insights on the design principles of protein functional sites.

1 499 930 €

Start date: 2013-09-01, End date: 2018-08-31

In a typical learning problem one tries to approximate an unknown function by a function from a given class using random data, sampled according to an unknown measure. In this project we will be interested in parameters that govern the complexity of a learning problem. It turns out that this complexity is determined by the geometry of certain sets in high dimension that are connected to the given class (random coordinate projections of the class). Thus, one has to understand the structure of these sets as a function of the dimension - which is given by the cardinality of the random sample. The resulting analysis leads to many theoretical questions in Asymptotic Geometric Analysis, Probability (most notably, Empirical Processes Theory) and Combinatorics, which are of independent interest beyond the application to Learning Theory. Our main goal is to describe the role of various complexity parameters involved in a learning problem, to analyze the connections between them and to investigate the way they determine the geometry of the relevant high dimensional sets. Some of the questions we intend to tackle are well known open problems and making progress towards their solution will have a significant theoretical impact. Moreover, this project should lead to a more complete theory of learning and is likely to have some practical impact, for example, in the design of more efficient learning algorithms.

750 000 €

Start date: 2009-03-01, End date: 2014-02-28

Since their discovery, Quantum Hall Effects have unfolded intriguing avenues of research, exhibiting a multitude of unexpected exotic states: accurate quantized conductance states; particle-like and hole-conjugate fractional states; counter-propagating charge and neutral edge modes; and fractionally charged quasiparticles - abelian and (predicted) non-abelian. Since the sought-after anyonic statistics of fractional states is yet to be verified, I propose to launch a thorough search for it employing new means. I believe that our studies will serve the expanding field of the emerging family of topological materials. Our on-going attempts to observe quasiparticles (qp’s) interference, in order to uncover their exchange statistics (under ERC), taught us that spontaneous, non-topological, ‘neutral edge modes’ are the main culprit responsible for qp’s dephasing. In an effort to quench the neutral modes, we plan to develop a new class of micro-size interferometers, based on synthetically engineered fractional modes. Flowing away from the fixed physical edge, their local environment can be controlled, making it less hospitable for the neutral modes. Having at hand our synthetized helical-type fractional modes, it is highly tempting to employ them to form localize para-fermions, which will extend the family of exotic states. This can be done by proximitizing them to a superconductor, or gapping them via inter-mode coupling. The less familiar thermal conductance measurements, which we recently developed (under ERC), will be applied throughout our work to identify ‘topological orders’ of exotic states; namely, distinguishing between abelian and non-abelian fractional states. The proposal is based on an intensive and continuous MBE effort, aimed at developing extremely high purity, GaAs based, structures. Among them, structures that support our new synthetic modes that are amenable to manipulation, and others that host rare exotic states, such as v=5/2, 12/5, 19/8, and 35/16.

1 801 094 €

Start date: 2019-05-01, End date: 2024-04-30

Distributed systems underlie many modern technologies, a prime example being the Internet. The ever-increasing abundance of distributed systems necessitates their design and usage to be backed by strong theoretical foundations. A major challenge that distributed systems face is the lack of a central authority, which brings many aspects of uncertainty into the environment, in the form of unknown network topology or unpredictable dynamic behavior. A practical restriction of distributed systems, which is at the heart of this proposal, is the limited bandwidth available for communication between the network components. A central family of distributed tasks is that of local tasks, which are informally described as tasks which are possible to solve by sending information through only a relatively small number of hops. A cornerstone example is the need to break symmetry and provide a better utilization of resources, which can be obtained by the task of producing a valid coloring of the nodes given some small number of colors. Amazingly, there are still huge gaps between the known upper and lower bounds for the complexity of many local tasks. This holds even if one allows powerful assumptions of unlimited bandwidth. While some known algorithms indeed use small messages, the complexity gaps are even larger compared to the unlimited bandwidth case. This is not a mere coincidence, and in fact the existing theoretical infrastructure is provably incapable of giving stronger lower bounds for many local tasks under limited bandwidth. This proposal zooms in on this crucial blind spot in the current literature on the theory of distributed computing, namely, the study of local tasks under limited bandwidth. The goal of this research is to produce fast algorithms for fundamental distributed local tasks under restricted bandwidth, as well as understand their limitations by providing lower bounds.

1 486 480 €

Start date: 2018-06-01, End date: 2023-05-31

"I propose to lead an international observational effort to characterize the population of massive planets, brown dwarf and stellar secondaries orbiting their parent stars with short periods, up to 10-30 days. The effort will utilize the superb, accurate, continuous lightcurves of more than hundred thousand stars obtained recently by two space missions – CoRoT and Kepler. I propose to use these lightcurves to detect non-transiting low-mass companions with a new algorithm, BEER, which I developed recently together with Simchon Faigler. BEER searches for the beaming effect, which causes the stellar intensity to increase if the star is moving towards the observer. The combination of the beaming effect with other modulations induced by a low-mass companion produces periodic modulation with a specific signature, which is used to detect small non-transiting companions. The accuracy of the space mission lightcurves is enough to detect massive planets with short periods. The proposed project is equivalent to a radial-velocity survey of tens of thousands of stars, instead of the presently active surveys which observe only hundreds of stars. We will use an assortment of telescopes to perform radial velocity follow-up observations in order to confirm the existence of the detected companions, and to derive their masses and orbital eccentricities. We will discover many tens, if not hundreds, of new massive planets and brown dwarfs with short periods, and many thousands of new binaries. The findings will enable us to map the mass, period, and eccentricity distributions of planets and stellar companions, determine the upper mass of planets, understand the nature of the brown-dwarf desert, and put strong constrains on the theory of planet and binary formation and evolution."

1 737 600 €

Start date: 2012-01-01, End date: 2016-12-31

Despite that C–H functionalization represents a paradigm shift from the standard logic of organic synthesis, the selective activation of non-functionalized alkanes has puzzled chemists for centuries and is always referred to one of the remaining major challenges in chemical sciences. Alkanes are inert compounds representing the major constituents of natural gas and petroleum. Converting these cheap and widely available hydrocarbon feedstocks into added-value intermediates would tremendously affect the field of chemistry. For long saturated hydrocarbons, one must distinguish between non-equivalent but chemically very similar alkane substrate C−H bonds, and for functionalization at the terminus position, one must favor activation of the stronger, primary C−H bonds at the expense of weaker and numerous secondary C-H bonds. The goal of this work is to develop a general principle in organic synthesis for the preparation of a wide variety of more complex molecular architectures from saturated hydrocarbons. In our approach, the alkane will first be transformed into an alkene that will subsequently be engaged in a metal-catalyzed hydrometalation/migration sequence. The first step of the sequence, ideally represented by the removal of two hydrogen atoms, will be performed by the use of a mutated strain of Rhodococcus. The position and geometry of the formed double bond has no effect on the second step of the reaction as the metal-catalyzed hydrometalation/migration will isomerize the double bond along the carbon skeleton to selectively produce the primary organometallic species. Trapping the resulting organometallic derivatives with a large variety of electrophiles will provide the desired functionalized alkane. This work will lead to the invention of new, selective and efficient processes for the utilization of simple hydrocarbons and valorize the synthetic potential of raw hydrocarbon feedstock for the environmentally benign production of new compounds and new materials.

2 499 375 €

Start date: 2018-11-01, End date: 2023-10-31

Cell motility is a fascinating dynamic process crucial for a wide variety of biological phenomena including defense against injury or infection, embryogenesis and cancer metastasis. A spatially extended, self-organized, mechanochemical machine consisting of numerous actin polymers, accessory proteins and molecular motors drives this process. This impressive assembly self-organizes over several orders of magnitude in both the temporal and spatial domains bridging from the fast dynamics of individual molecular-sized building blocks to the persistent motion of whole cells over minutes and hours. The molecular players involved in the process and the basic biochemical mechanisms are largely known. However, the principles governing the assembly of the motility apparatus, which involve an intricate interplay between biophysical processes and biochemical reactions, are still poorly understood. The proposed research is focused on investigating the biophysical aspects of the self-organization processes underlying cell motility and trying to adapt these processes to instill motility in artificial cells. Important biophysical characteristics of moving cells such as the intracellular fluid flow and membrane tension will be measured and their effect on the motility process will be examined, using fish epithelial keratocytes as a model system. The dynamics of the system will be further investigated by quantitatively analyzing the morphological and kinematic variation displayed by a population of cells and by an individual cell through time. Such measurements will feed into and direct the development of quantitative theoretical models. In parallel, I will work toward the development of a synthetic physical model system for cell motility by encapsulating the actin machinery in a cell-sized compartment. This synthetic system will allow cell motility to be studied in a simplified and controlled environment, detached from the complexity of the living cell.

900 000 €

Start date: 2008-08-01, End date: 2013-07-31

Digital signal processing (DSP) is a revolutionary paradigm shift enabling processing of physical data in the digital domain where design and implementation are considerably simplified. However, state-of-the-art analog-to-digital convertors (ADCs) preclude high-rate wideband sampling and processing with low cost and energy consumption, presenting a major bottleneck. This is mostly due to a traditional assumption that sampling must be performed at the Nyquist rate, that is, twice the signal bandwidth. Modern applications including communications, medical imaging, radar and more use signals with high bandwidth, resulting in prohibitively large Nyquist rates. Our ambitious goal is to introduce a paradigm shift in ADC design that will enable systems capable of low-rate, wideband sensing and low-rate DSP. While DSP has a rich history in exploiting structure to reduce dimensionality and perform efficient parameter extraction, current ADCs do not exploit such knowledge. We challenge current practice that separates the sampling stage from the processing stage and exploit structure in analog signals already in the ADC, to drastically reduce the sampling and processing rates. Our preliminary data shows that this allows substantial savings in sampling and processing rates --- we show rate reduction of 1/28 in ultrasound imaging, and 1/30 in radar detection. To achieve our overreaching goal we focus on three interconnected objectives -- developing the 1) theory 2) hardware and 3) applications of sub-Nyquist sampling. Our methodology ties together two areas on the frontier of signal processing: compressed sensing (CS), focused on finite length vectors, and analog sampling. Our research plan also inherently relies on advances in several other important areas within signal processing and combines multi-disciplinary research at the intersection of signal processing, information theory, optimization, estimation theory and hardware design.

2 400 000 €

Start date: 2015-08-01, End date: 2020-07-31

Modern cryptography has deeply rooted connections with computational complexity theory and other areas of computer science. This proposal suggests to explore several {\em new connections} between questions in cryptography and questions from other domains, including computational complexity, coding theory, and even the natural sciences. The project is expected to broaden the impact of ideas from cryptography on other domains, and on the other hand to benefit cryptography by applying tools from other domains towards better solutions for central problems in cryptography.

1 459 703 €

Start date: 2010-12-01, End date: 2015-11-30

Clouds and precipitation play a crucial role in the Earth's energy balance, global atmospheric circulation and the water cycle. Despite their importance, clouds still pose the largest uncertainty in climate research. I propose a new approach for studying anthropogenic effects on cloud fields and rain, tackling the challenge from both scientific ends: reductionism and systems approach. We will develop a novel research approach using observations and models interactively that will allow us to “peel apart” detailed physical processes. In parallel we will develop a systems view of cloud fields looking for Emergent Behavior rising out of the complexity, as the end result of all of the coupled processes. Better understanding of key processes on a detailed (reductionist) manner will enable us to formulate the important basic rules that control the field and to look for emergence of the overall effects. We will merge ideas and methods from four different disciplines: remote sensing and radiative transfer, cloud physics, pattern recognition and computer vision and ideas developed in systems approach. All of this will be done against the backdrop of natural variability of meteorological systems. The outcomes of this work will include fundamental new understanding of the coupled surface-aerosol-cloud-precipitation system. More importantly this work will emphasize the consequences of human actions on the environment, and how we change our climate and hydrological cycle as we input pollutants and transform the Earth’s surface. This work will open new horizons in cloud research by developing novel methods and employing the bulk knowledge of pattern recognition, complexity, networking and self organization to cloud and climate studies. We are proposing a long-term, open-ended program of study that will have scientific and societal relevance as long as human-caused influences continue, evolve and change.

1 428 169 €

Start date: 2012-09-01, End date: 2017-08-31

"Combinatorics, and its interplay with geometry, has fascinated our ancestors as shown by early stone carvings in the Neolithic period. Modern combinatorics is motivated by the ubiquity of its structures in both pure and applied mathematics. The work of Hochster and Stanley, who realized the relation of enumerative questions to commutative algebra and toric geometry made a vital contribution to the development of this subject. Their work was a central contribution to the classification of face numbers of simple polytopes, and the initial success lead to a wealth of research in which combinatorial problems were translated to algebra and geometry and then solved using deep results such as Saito's hard Lefschetz theorem. As a caveat, this also made branches of combinatorics reliant on algebra and geometry to provide new ideas. In this proposal, I want to reverse this approach and extend our understanding of geometry and algebra guided by combinatorial methods. In this spirit I propose new combinatorial approaches to the interplay of curvature and topology, to isoperimetry, geometric analysis, and intersection theory, to name a few. In addition, while these subjects are interesting by themselves, they are also designed to advance classical topics, for example, the diameter of polyhedra (as in the Hirsch conjecture), arrangement theory (and the study of arrangement complements), Hodge theory (as in Grothendieck's standard conjectures), and realization problems of discrete objects (as in Connes embedding problem for type II factors). This proposal is supported by the review of some already developed tools, such as relative Stanley--Reisner theory (which is equipped to deal with combinatorial isoperimetries), combinatorial Hodge theory (which extends the ``K\""ahler package'' to purely combinatorial settings), and discrete PDEs (which were used to construct counterexamples to old problems in discrete geometry)."

1 337 200 €

Start date: 2016-12-01, End date: 2021-11-30

The overarching objective of this interdisciplinary project is to elucidate mechanisms through which billions of individual clocks in the body communicate with each other and tick in harmony. The mammalian circadian timing system consists of a master clock in the brain and subsidiary oscillators in almost every cell of the body. Since these clocks anticipate environmental changes and function together to orchestrate daily physiology and behavior their temporal synchronization is critical. Our recent finding that oxygen serves as a resetting cue for circadian clocks points towards the unprecedented involvement of blood gases as time signals. We will apply cutting edge continuous physiological measurements in freely moving animals, alongside biochemical/molecular biology approaches and advanced cell culture setup to determine the molecular role of oxygen, carbon dioxide and pH in circadian clock communication and function. The intricate nature of the mammalian circadian system demands the presence of communication mechanisms between clocks throughout the body at multiple levels. While previous studies primarily addressed the role of the master clock in resetting peripheral clocks, our knowledge regarding the communication among clocks between and within peripheral organs is rudimentary. We will reconstruct the mammalian circadian system from the bottom up, sequentially restoring clocks in peripheral tissues of a non-rhythmic animal to (i) obtain a system-view of the peripheral circadian communication network; and (ii) study novel tissue-derived circadian communication mechanisms. This integrative proposal addresses fundamental aspects of circadian biology. It is expected to unravel the circadian communication network and shed light on how billions of clocks in the body function in unison. Its impact extends beyond circadian rhythms and bears great potential for research on communication between cells/tissues in various fields of biology.

1 999 945 €

Start date: 2018-03-01, End date: 2023-02-28

The efficiency of cryptographic constructions is a fundamental question. Theoretically, it is important to understand how much computational resources are needed to guarantee strong notions of security. Practically, highly efficient schemes are always desirable for real-world applications. More generally, the possibility of cryptography with low complexity has wide applications for problems in computational complexity, combinatorial optimization, and computational learning theory. In this proposal we aim to understand what are the minimal computational resources needed to perform basic cryptographic tasks. In a nutshell, we suggest to focus on three main objectives. First, we would like to get better understanding of the cryptographic hardness of random local functions. Such functions can be computed by highly-efficient circuits and their cryptographic hardness provides a strong and clean formulation for the conjectured average-case hardness of constraint satisfaction problems - a fundamental subject which lies at the core of the theory of computer science. Our second objective is to harness our insights into the hardness of local functions to improve the efficiency of basic cryptographic building blocks such as pseudorandom functions. Finally, our third objective is to expand our theoretical understanding of garbled circuits, study their limitations, and improve their efficiency. The suggested project can bridge across different regions of computer science such as random combinatorial structures, cryptography, and circuit complexity. It is expected to impact central problems in cryptography, while enriching the general landscape of theoretical computer science.

1 265 750 €

Start date: 2015-05-01, End date: 2021-04-30

The creation of new molecular entities and subsequent exploitation of their properties is central to a broad spectrum of research disciplines from medicine to materials. Most –if not all- of the efforts of organic chemists were directed to the development of creative strategies to built carbon-carbon and carbon-heteroatom bonds in a predictable and efficient manner. But is the creation of new bonds the only approach that organic chemistry should follow? Could we design the synthesis of challenging molecular skeleton no more through the construction of carbon-carbon bonds but rather through selective cleavage of carbon-carbon bonds (C-C bond activation)? The goal of this work is to develop powerful synthetic approaches for the selective C-C bond activation and demonstrate that it has the potential to be a general principle in organic synthesis for the regio-, diastereo- and even enantiomerically enriched preparation of adducts despite that C-C single bonds belong among the least reactive functional groups in chemistry. The realization of this synthetic potential requires the ability to functionalize selectively one C-C bond in compounds containing many such bonds and an array of functional groups. This site selective C-C bond activation is one of the greatest challenges that must be met to be used widely in complex-molecular synthesis. To emphasize the practicality of C-C bond activation, we will prepare in a single-pot operation challenging molecular framework possessing various stereogenic centers from very simple starting materials through selective C-C bond activation. Ideally, alkenes will be in-situ transformed into alkanes that will subsequently undergo the C-C activation even in the presence of functional group. This work will lead to ground-breaking advances when non-strained cycloalkanes (cyclopentane, cyclohexane) will undergo this smooth C-C bond activation with friendly and non toxic organometallic species.

2 367 495 €

Start date: 2013-11-01, End date: 2018-10-31

Colloidal semiconductor nanocrystals have already found significant use in various arenas, including bioimaging, displays, lighting, photovoltaics and catalysis. Here we aim to harness the extremely broad synthetic toolbox of colloidal semiconductor quantum dots in order to utilize them as unique sources of quantum states of light, extending well beyond the present attempts to use them as single photon sources. By tailoring the shape, size, composition and the organic ligand layer of quantum dots, rods and platelets, we propose their use as sources exhibiting a deterministic number of emitted photons upon saturated excitation and as tunable sources of correlated and entangled photon pairs. The versatility afforded in their fabrication by colloidal synthesis, rather than by epitaxial growth, presents a potential pathway to overcome some of the significant limitations of present-day solid state sources of nonclassical light, including color tunability, fidelity and ease of assembly into devices. This program is a concerted effort both on colloidal synthesis of complex multicomponent semiconductor nanocrystals and on cutting edge photophysical studies at the single nanocrystal level. This should enable new types of emitters of nonclassical light, as well as provide a platform for the implementation of recently suggested schemes in quantum optics which have never been experimentally demonstrated. These include room temperature sources of exactly two (or more) photons, correlated photon pairs from quantum dot molecules and entanglement based on time reordering. Fulfilling the optical and material requirements from this type of system, including photostability, control of carrier-carrier interactions, and a large quantum yield, will inevitably reveal some of the fundamental properties of coupled carriers in strongly confined structures.

2 000 000 €

Start date: 2016-05-01, End date: 2021-04-30

Computational cameras go beyond 2D images and allow the extraction of more dimensions from the visual world such as depth, multiple viewpoints and multiple illumination conditions. They also allow us to overcome some of the traditional photography challenges such as defocus blur, motion blur, noise and resolution. The increasing variety of computational cameras is raising the need for a meaningful comparison across camera types. We would like to understand which cameras are better for specific tasks, which aspects of a camera make it better than others and what is the best performance we can hope to achieve. Our 2008 paper introduced a general framework to address the design and analysis of computational cameras. A camera is modeled as a linear projection in ray space. Decoding the camera data then deals with inverting the linear projection. Since the number of sensor measurements is usually much smaller than the number of rays, the inversion must be treated as a Bayesian inference problem accounting for prior knowledge on the world. Despite significant progress which has been made in the recent years, the space of computational cameras is still far from being understood. Computational camera analysis raises the following research challenges: 1) What is a good way to model prior knowledge on ray space? 2) Seeking efficient inference algorithms and robust ways to decode the world from the camera measurements. 3) Evaluating the expected reconstruction accuracy of a given camera. 4) Using the expected reconstruction performance for evaluating and comparing camera types. 5) What is the best camera? Can we derive upper bounds on the optimal performance? We propose research on all aspects of computational camera design and analysis. We propose new prior models which will significantly simplify the inference and evaluation tasks. We also propose new ways to bound and evaluate computational cameras with existing priors.

756 845 €

Start date: 2010-12-01, End date: 2015-11-30

"In recent years, the importance of superimposing the contribution of the measure to that of the metric, in determining the underlying space's (generalized Ricci) curvature, has been clarified in the works of Lott, Sturm, Villani and others, following the definition of Curvature-Dimension introduced by Bakry and Emery. We wish to systematically incorporate this important idea of considering the measure and metric in tandem, in the study of questions pertaining to isoperimetric and concentration properties of convex domains in high-dimensional Euclidean space, where a-priori there is only a trivial metric (Euclidean) and trivial measure (Lebesgue). The first step of enriching the class of uniform measures on convex domains to that of non-negatively curved (""log-concave"") measures in Euclidean space has been very successfully implemented in the last decades, leading to substantial progress in our understanding of volumetric properties of convex domains, mostly regarding concentration of linear functionals. However, the potential advantages of altering the Euclidean metric into a more general Riemannian one or exploiting related Riemannian structures have not been systematically explored. Our main paradigm is that in order to progress in non-linear questions pertaining to concentration in Euclidean space, it is imperative to cast and study these problems in the more general Riemannian context. As witnessed by our own work over the last years, we expect that broadening the scope and incorporating tools from the Riemannian world will lead to significant progress in our understanding of the qualitative and quantitative structure of isoperimetric minimizers in the purely Euclidean setting. Such progress would have dramatic impact on long-standing fundamental conjectures regarding concentration of measure on high-dimensional convex domains, as well as other closely related fields such as Probability Theory, Learning Theory, Random Matrix Theory and Algorithmic Geometry."

1 194 190 €

Start date: 2015-10-01, End date: 2020-09-30

Cosmic explosions, the violent deaths of stars, play a crucial role in many of the most interesting open questions in physics today. These events serve as “cosmic accelerators” for ultra-high-energy particles that are beyond reach for even to most powerful terrestrial accelerators, as well as distant sources for elusive neutrinos. Explosions leave behind compact neutron stars and black hole remnants, natural laboratories to study strong gravity. Acting as cosmic furnaces, these explosions driven the chemical evolution of the Universe Cosmic explosions trigger and inhibit star formation processes, and drive galactic evolution (“feedback”). Distances measured using supernova explosions as standard candles brought about the modern revolution in our view of the accelerating Universe, driven by enigmatic “dark energy”. Understanding the nature of cosmic explosions of all types is thus an extremely well-motivated endeavour. I have been studying cosmic explosions for over a decade, and since the earliest stages of my career, have followed an ambition to figure out the nature of cosmic explosions of all types, and to search for new types of explosions. Having already made several key discoveries, I now propose to undertake a comprehensive program to systematically tackle this problem.I review below the progress made in this field and the breakthrough results we have achieved so far, and propose to climb the next step in this scientific and technological ladder, combining new powerful surveys with comprehensive multi-wavelength and multi-disciplinary (observational and theoretical) analysis. My strategy is based on a combination of two main approaches: detailed studies of single objects which serve as keys to specific questions; and systematic studies of large samples, some that I have, for the first time, been able to assemble and analyze, and those expected from forthcoming efforts. Both approaches have already yielded tantalizing results.

1 499 302 €

Start date: 2012-09-01, End date: 2017-08-31

The importance of understanding the functions of the basic building blocks of life, such as proteins, cannot be overstated (as asserted by two recent Nobel prizes in Chemistry), as this understanding unravels the mechanisms that control all organisms. The critical step towards such an understanding is to reveal the structures of these building blocks. A leading method for resolving such structures is cryo-electron microscopy (cryo-EM), in which the structure of a molecule is recovered from its images taken by an electron microscope, by using sophisticated mathematical algorithms (to which my group has made several key mathematical and algorithmic contributions). Due to hardware breakthroughs in the past three years, cryo-EM has made a giant leap forward, introducing capabilities that until recently were unimaginable, opening an opportunity to revolutionize our biological understanding. As extracting information from cryo-EM experiments completely relies on mathematical algorithms, the method’s deep mathematical challenges that have emerged must be solved as soon as possible. Only then cryo-EM could realize its nearly inconceivable potential. These challenges, for which no adequate solutions exist (or none at all), focus on integrating information from huge sets of extremely noisy images reliability and efficiently. Based on the experience of my research group in developing algorithms for cryo-EM data processing, gained during the past eight years, we will address the three key open challenges of the field – a) deriving reliable and robust reconstruction algorithms from cryo-EM data, b) developing tools to process heterogeneous cryo-EM data sets, and c) devising validation and quality measures for structures determined from cryo-EM data. The fourth goal of the project, which ties all goals together and promotes the broad interdisciplinary impact of the project, is to merge all our algorithms into a software platform for state-of-the-art processing of cryo-EM data.

1 751 250 €

Start date: 2017-03-01, End date: 2022-02-28

We target a frontier in nanocrystal science of combining disparate materials into a single hybrid nanosystem. This offers an intriguing route to engineer nanomaterials with multiple functionalities in ways that are not accessible in bulk materials or in molecules. Such control of novel material combinations on a single nanoparticle or in a super-structure of assembled nanoparticles, presents alongside with the synthesis challenges, fundamental questions concerning the physical attributes of nanoscale systems. My goals are to create new highly controlled hybrid nanoparticle systems, focusing on combinations of semiconductors and metals, and to decipher the fundamental principles governing doping in nanoparticles and charge and energy transfer processes among components of the hybrid systems. The research addresses several key challenges: First, in synthesis, combining disparate material components into one hybrid nanoparticle system. Second, in self assembly, organizing a combination of semiconductor (SC) and metal nanoparticle building blocks into hybrid systems with controlled architecture. Third in fundamental physico-chemical questions pertaining to the unique attributes of the hybrid systems, constituting a key component of the research. A first aspect concerns doping of SC nanoparticles with metal atoms. A second aspect concerns light-induced charge transfer between the SC part and metal parts of the hybrid constructs. A third related aspect concerns energy transfer processes between the SC and metal components and the interplay between near-field enhancement and fluorescence quenching effects. Due to the new properties, significant impact on nanocrystal applications in solar energy harvesting, biological tagging, sensing, optics and electropotics is expected.

2 499 000 €

Start date: 2010-06-01, End date: 2015-05-31

Unsupervised visual inference can often be performed by exploiting the internal redundancy inside a single visual datum (an image or a video). The strong repetition of patches inside a single image/video provides a powerful data-specific prior for solving a variety of vision tasks in a “blind” manner: (i) Blind in the sense that sophisticated unsupervised inferences can be made with no prior examples or training; (ii) Blind in the sense that complex ill-posed Inverse-Problems can be solved, even when the forward degradation is unknown. While the above fully unsupervised approach achieved impressive results, it relies on internal data alone, hence cannot enjoy the “wisdom of the crowd” which Deep-Learning (DL) so wisely extracts from external collections of images, yielding state-of-the-art (SOTA) results. Nevertheless, DL requires huge amounts of training data, which restricts its applicability. Moreover, some internal image-specific information, which is clearly visible, remains unexploited by today's DL methods. One such example is shown in Fig.1. We propose to combine the power of these two complementary approaches – unsupervised Internal Data Recurrence, with Deep Learning, to obtain the best of both worlds. If successful, this will have several important outcomes including: • A wide range of low-level & high-level inferences (image & video). • A continuum between Internal & External training – a platform to explore theoretical and practical tradeoffs between amount of available training data and optimal Internal-vs-External training. • Enable totally unsupervised DL when no training data are available. • Enable supervised DL with modest amounts of training data. • New applications, disciplines and domains, which are enabled by the unified approach. • A platform for substantial progress in video analysis (which has been lagging behind so far due to the strong reliance on exhaustive supervised training data).

2 466 940 €

Start date: 2018-05-01, End date: 2023-04-30

Model theory deals with general classes of structures (called models). Specific examples of such classes are: the class of rings or the class of algebraically closed fields. It turns out that counting the so-called complete types over models in the class has an important role in the development of model theory in general and stability theory in particular. Stable classes are those with relatively few complete types (over structures from the class); understanding stable classes has been central in model theory and its applications. Recently, I have proved a new dichotomy among the unstable classes: Instead of counting all the complete types, they are counted up to conjugacy. Classes which have few types up to conjugacy are proved to be so-called ``dependent'' classes (which have also been called NIP classes). I have developed (under reasonable restrictions) a ``recounting theorem'', parallel to the basic theorems of stability theory. I have started to develop some of the basic properties of this new approach. The goal of the current project is to develop systematically the theory of dependent classes. The above mentioned results give strong indication that this new theory can be eventually as useful as the (by now the classical) stability theory. In particular, it covers many well known classes which stability theory cannot treat.

1 748 000 €

Start date: 2014-03-01, End date: 2019-02-28

Nowadays, extensive collection and storage of massive data sets have become a routine in multiple disciplines and in everyday life. These large amounts of intricate data often make data samples arithmetic and basic comparisons problematic, raising new challenges to traditional data analysis objectives such as filtering and prediction. Furthermore, the availability of such data constantly pushes the boundaries of data analysis to new emerging domains, ranging from neuronal and social network analysis to multimodal sensor fusion. The combination of evolved data and new domains drives a fundamental change in the field of data analysis. Indeed, many classical model-based techniques have become obsolete since their models do not embody the richness of the collected data. Today, one notable avenue of research is the development of nonlinear techniques that transition from data to creating representations, without deriving models in closed-form. The vast majority of such existing data-driven methods operate directly on the data, a hard task by itself when the data are large and elaborated. The goal of this research is to develop a fundamentally new methodology for high dimensional data analysis with diffusion operators, making use of recent transformative results in manifold and geometry learning. More concretely, shifting the focus from processing the data samples themselves and considering instead structured data through the lens of diffusion operators will introduce new powerful “handles” to data, capturing their complexity efficiently. We will study the basic theory behind this nonlinear analysis, develop new operators for this purpose, and devise efficient data-driven algorithms. In addition, we will explore how our approach can be leveraged for devising efficient solutions to a broad range of open real-world data analysis problems, involving intrinsic representations, sensor fusion, time-series analysis, network connectivity inference, and domain adaptation.

1 260 000 €

Start date: 2019-02-01, End date: 2024-01-31

This research investigates a new measure that arises in information theory called directed information. Recent advances, including our preliminary results, shows that directed information arises in communication as the maximum rate that can be transmitted reliably in channels with feedback. The directed information is multi-letter expression and therefore very hard to optimize or compute. Our plan is first of all to find an efficient methodology for optimizing the measure using the dynamic programming framework and convex optimization tools. As an important by-product of finding the fundamental limits is finding coding schemes that achieves the limits. Second, we plan to find new roles for directed information in communication, especially in networks with bi-directional communication and in data compression with causal conditions. Third, encouraged by a preliminary work on interpretation of directed information in economics and estimation theory, we plan to show that directed information has interpretation in additional fields such as statistical physics. We plan to show that there is duality relation between different fields with causal constraints. Due to the duality insights and breakthroughs in one problem will lead to new insights in other problems. Finally, we will apply directed information as a statistical inference of causal dependence. We will show how to estimate and use the directed information estimator to measure causal inference between two or more process. In particular, one of the questions we plan to answer is the influence of industrial activities (e.g., $\text{CO}_2$ volumes) on the global warming. Our main focus will be to develop a deeper understanding of the mathematical properties of directed information, a process that is instrumental to each problem. Due to their theoretical proximity and their interdisciplinary nature, progress in one problem will lead to new insights in other problems. A common set of mathematical tools developed in

1 224 600 €

Start date: 2013-08-01, End date: 2019-07-31

Discrete Mathematics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. Some of the main reasons for this growth are the broad applications of tools and techniques from extremal and probabilistic combinatorics in the rapid development of theoretical Computer Science, in the spectacular recent results in Additive Number Theory and in the study of basic questions in Information Theory. While in the past many of the basic combinatorial results were obtained mainly by ingenuity and detailed reasoning, the modern theory has grown out of this early stage, and often relies on deep, well developed tools, like the probabilistic method, algebraic, topological and geometric techniques. The work of the principal investigator, partly jointly with several collaborators and students, and partly in individual efforts, has played a significant role in the introduction of powerful algebraic, probabilistic, spectral and geometric techniques that influenced the development of modern combinatorics. In the present project he aims to try and further develop such tools, trying to tackle some basic open problems in Combinatorics, as well as significant questions in Additive Combinatorics, Information Theory, and theoretical Computer Science. Progress on the problems mentioned in this proposal, and the study of related ones, is expected to provide new insights on these problems and to lead to the development of novel fruitful techniques that are likely to be useful in Discrete Mathematics as well as in related areas.

1 061 300 €

Start date: 2008-12-01, End date: 2013-11-30

Optical microscopy, perhaps the most important tool in biomedical investigation and clinical diagnostics, is currently held back by the assumption that it is not possible to noninvasively image microscopic structures more than a fraction of a millimeter deep inside tissue. The governing paradigm is that high-resolution information carried by light is lost due to random scattering in complex samples such as tissue. While non-optical imaging techniques, employing non-ionizing radiation such as ultrasound, allow deeper investigations, they possess drastically inferior resolution and do not permit microscopic studies of cellular structures, crucial for accurate diagnosis of cancer and other diseases. I propose a new kind of microscope, one that can peer deep inside visually opaque samples, combining the sub-micron resolution of light with the penetration depth of ultrasound. My novel approach is based on our discovery that information on microscopic structures is contained in random scattered-light patterns. It breaks current limits by exploiting the randomness of scattered light rather than struggling to fight it. We will transform this concept into a breakthrough imaging platform by combining ultrasonic probing and modulation of light with advanced digital signal processing algorithms, extracting the hidden microscopic structure by two complementary approaches: 1) By exploiting the stochastic dynamics of scattered light using methods developed to surpass the diffraction limit in optical nanoscopy and for compressive sampling, harnessing nonlinear effects. 2) Through the analysis of intrinsic correlations in scattered light that persist deep inside scattering tissue. This proposal is formed by bringing together novel insights on the physics of light in complex media, advanced microscopy techniques, and ultrasound-mediated imaging. It is made possible by the new ability to digitally process vast amounts of scattering data, and has the potential to impact many fields.

1 500 000 €

Start date: 2016-04-01, End date: 2021-03-31

Understanding how the Milky Way arrived at its present state requires a large volume of precision measurements of our Galaxy’s current makeup, as well as an empirically based understanding of the main processes involved in the Galaxy’s evolution. Such data are now about to arrive in the flood of quality information from Gaia and SDSS-V. The demography of the stars and of the compact stellar remnants in our Galaxy, in terms of phase-space location, mass, age, metallicity, and multiplicity are data products that will come directly from these surveys. I propose to integrate this information into a comprehensive picture of the Milky Way’s present state. In parallel, I will build a Galactic chemical evolution model, with input parameters that are as empirically based as possible, that will reproduce and explain the observations. To get those input parameters, I will measure the rates of supernovae (SNe) in nearby galaxies (using data from past and ongoing surveys) and in high-redshift proto-clusters (by conducting a SN search with JWST), to bring into sharp focus the element yields of SNe and the distribution of delay times (the DTD) between star formation and SN explosion. These empirically determined SN metal-production parameters will be used to find the observationally based reconstruction of the Galaxy’s stellar formation history and chemical evolution that reproduces the observed present-day Milky Way stellar population. The population census of stellar multiplicity with Gaia+SDSS-V, and particularly of short-orbit compact-object binaries, will hark back to the rates and the element yields of the various types of SNe, revealing the connections between various progenitor systems, their explosions, and their rates. The plan, while ambitious, is feasible, thanks to the data from these truly game-changing observational projects. My team will perform all steps of the analysis and will combine the results to obtain the clearest picture of how our Galaxy came to be.

1 859 375 €

Start date: 2019-10-01, End date: 2024-09-30

The proposal is to look for, and investigate, new ergodic theoretic types of behavior for dynamical systems which act on non compact spaces. These could include transience and non-trivial ways of escape to infinity, critical phenomena similar to phase transitions, and new types of measure rigidity. There are potential applications to smooth ergodic theory (non-uniform hyperbolicity), algebraic ergodic theory (actions on homogeneous spaces), and probability theory (weakly dependent stochastic processes).

539 479 €

Start date: 2009-10-01, End date: 2014-09-30

Expander graphs are finite graphs which play a fundamental role in many areas of computer science such as: communication networks, algorithms and more. Several areas of deep mathematics have been used in order to give explicit constructions of such graphs e.g. Kazhdan property (T) from representation theory of semisimple Lie groups, Ramanujan conjecture from the theory of automorphic forms and more. In recent years, computer science has started to pay its debt to mathematics: expander graphs are playing an increasing role in several areas of pure mathematics. The goal of the current research plan is to deepen these connections in both directions with special emphasis of the more recent and surprising application of expanders to group theory, the geometry of 3-manifolds and number theory.

1 082 504 €

Start date: 2008-10-01, End date: 2014-09-30

Combinatorics is an extremely fast growing mathematical discipline. While it started as a collection of isolated problems that were tackled using ad-hoc arguments it has since grown into a mature discipline which both incorporated into it deep tools from other mathematical areas, and has also found applications in other mathematical areas such as Additive Number Theory, Theoretical Computer Science, Computational Biology and Information Theory. The PI will work on a variety of problems in Extremal Combinatorics which is one of the most active subareas within Combinatorics with spectacular recent developments. A typical problem in this area asks to minimize (or maximize) a certain parameter attached to a discrete structure given several other constrains. One of the most powerful tools used in attacking problems in this area uses the so called Structure vs Randomness phenomenon. This roughly means that any {\em deterministic} object can be partitioned into smaller quasi-random objects, that is, objects that have properties we expect to find in truly random ones. The PI has already made significant contributions in this area and our goal in this proposal is to obtain further results of this caliber by tackling some of the hardest open problems at the forefront of current research. Some of these problems are related to the celebrated Hypergraph and Arithmetic Regularity Lemmas, to Super-saturation problems in Additive Combinatorics and Graph Theory, to problems in Ramsey Theory, as well as to applications of Extremal Combinatorics to problems in Theoretical Computer Science. Another major goal of this proposal is to develop new approaches and techniques for tackling problems in Extremal Combinatorics. The support by means of a 5-year research grant will enable the PI to further establish himself as a leading researcher in Extremal Combinatorics and to build a vibrant research group in Extremal Combinatorics.

1 221 921 €

Start date: 2015-03-01, End date: 2021-02-28

Standard spacecraft designs comprise modules assembled in a single monolithic structure. When unexpected situations occur, the spacecraft are unable to adequately respond, and significant functional and financial losses are unavoidable. For instance, if the payload of a spacecraft fails, the whole system becomes unserviceable and substitution of the entire spacecraft is required. It would be much easier to replace the payload module only than launch a completely new satellite. This idea gives rise to an emerging concept in space engineering termed disaggregated spacecraft. Disaggregated space architectures (DSA) consist of several physically-separated modules, interacting through wireless communication links to form a single virtual platform. Each module has one or more pre-determined functions: Navigation, attitude control, power generation and payload operation. The free-flying modules, capable of resource sharing, do not have to operate in a tightly-controlled formation, but are rather required to remain in bounded relative position and attitude, termed cluster flying. DSA enables novel space system architectures, which are expected to be much more efficient, adaptable, robust and responsive. The main goal of the proposed research is to develop beyond the state-of-the-art technologies in order to enable operational flight of DSA, by (i) developing algorithms for semi-autonomous long-duration maintenance of a cluster and cluster network, capable of adding and removing spacecraft modules to/from the cluster and cluster network; (ii) finding methods so as to autonomously reconfigure the cluster to retain safety- and mission-critical functionality in the face of network degradation or component failures; (iii) designing semi-autonomous cluster scatter and re-gather maneuvesr to rapidly evade a debris-like threat; and (iv) validating the said algorithms and methods in the Distributed Space Systems Laboratory in which the PI serves as a Principal Investigator.

1 500 000 €

Start date: 2011-10-01, End date: 2016-09-30

The world of digital signal processing, in particular computer graphics, vision and image processing, use linear and non-linear, explicit and implicit filtering extensively to analyze, process and synthesize images. Given nowadays high-resolution sensors, these operations are often very time consuming and are limited to devices with high-CPU power. Traditional linear translation-invariant (LTI) transformations, executed using convolution, requires O(N^2) operations. This can be lowered to O(N \log N) via FFT over suitable domains. There are very few sets of filters to which optimal, linear-time, procedures are known. This situation is more complicated in the newly-emerging domain of non-linear spatially-varying filters. Exact application of such filter requires O(N^2) operations and acceleration methods involve higher space dimension introducing severe memory cost and truncation errors. In this research proposal we intend to derive fast, linear-time, procedures for different types of LTI filters by exploiting a deep connection between convolution, spatially-homogeneous elliptic equations and the multigrid method for solving such equations. Based on this circular connection we draw novel prospects for deriving new multiscale filtering procedures. A second part of this research proposal is devoted to deriving efficient explicit and implicit non-linear spatially-varying edge-aware filters. One front consists of the derivation of novel multi-level image decomposition that mimics the action of inhomogeneous diffusion operators. The idea here is, once again, to bridge the gap with numerical analysis and use ideas from multiscale matrix preconditioning for the design of new biorthogonal second-generation wavelets. Moreover, this proposal outlines a new multiscale preconditioning paradigm combining ideas from algebraic multigrid and combinatorial matrix preconditioning. This intermediate approach offers new ways for overcoming fundamental shortcomings in this domain.

1 320 200 €

Start date: 2013-08-01, End date: 2018-07-31

We will study phase transitions and chemical and biological reactions in liquid mixtures in electric field gradients. These new phase transitions are essential in statistical physics and thermodynamics. We will examine theoretically the complex and yet unexplored phase ordering dynamics in which droplets nucleate and move under the external nonuniform force. We will look in detail at the interfacial instabilities which develop when the field is increased. We will investigate how time-varying potentials produce electromagnetic waves and how their spatial decay in the bistable liquid leads to phase changes. These transitions open a new and general way to control the spatio-temporal behaviour of chemical reactions by directly manipulating the solvents' concentrations. When two or more reagents are preferentially soluble in one of the mixture's components, field-induced phase separation leads to acceleration of the reaction. When the reagents are soluble in different solvents, field-induced demixing will lead to the reaction taking place at a slow rate and at a two-dimensional surface. Additionally, the electric field allows us to turn the reaction on or off. The numerical study and simulations will be complemented by experiments. We will study theoretically and experimentally biochemical reactions. We will find how actin-related structures are affected by field gradients. Using an electric field as a tool we will control the rate of actin polymerisation. We will investigate if an external field can damage cancer cells by disrupting their actin-related activity. The above phenomena will be studied in a microfluidics environment. We will elucidate the separation hydrodynamics occurring when thermodynamically miscible liquids flow in a channel and how electric fields can reversibly create and destroy optical interfaces, as is relevant in optofluidics. Chemical and biological reactions will be examined in the context of lab-on-a-chip.

1 482 200 €

Start date: 2010-08-01, End date: 2015-07-31

A fundamental research challenge in modern cryptography is understanding the necessary hardness assumptions required to build different cryptographic primitives. Attempts to answer this question have gained tremendous success in the last 20-30 years. Most notably, it was shown that many highly complicated primitives can be based on the mere existence of one-way functions (i.e., easy to compute and hard to invert), while other primitives cannot be based on such functions. This research has yielded fundamental tools and concepts such as randomness extractors and computational notions of entropy. Yet many of the most fundamental questions remain unanswered. Our first goal is to answer the fundamental question of whether cryptography can be based on the assumption that P not equal NP. Our second and third goals are to build a more efficient symmetric-key cryptographic primitives from one-way functions, and to establish effective methods for security amplification of cryptographic primitives. Succeeding in the second and last goals is likely to have great bearing on the way that we construct the very basic cryptographic primitives. A positive answer for the first question will be considered a dramatic result in the cryptography and computational complexity communities. To address these goals, it is very useful to understand the relationship between different types and quantities of cryptographic hardness. Such understanding typically involves defining and manipulating different types of computational entropy, and comprehending the power of security reductions. We believe that this research will yield new concepts and techniques, with ramification beyond the realm of foundational cryptography.

1 239 838 €

Start date: 2015-03-01, End date: 2021-02-28

The discovery of the fractional quantum Hall effect created a revolution in solid state research by introducing a new state of matter resulting from strong electron interactions. The new state is characterized by excitations (quasi-particles) that carry fractional charge, which are expected to obey fractional statistics. While odd denominator fractional states are expected to have an abelian statistics, the newly discovered 5/2 even denominator fractional state is expected to have a non-abelian statistics. Moreover, a large number of emerging proposals predict that the latter state can be employed for topological quantum computing ( Station Q was founded by Microsoft Corp. in order to pursue this goal). This proposal aims at studying the abelian and non-abelian fractional charges, and in particular to observe their peculiar statistics. While charges are preferably determined by measuring quantum shot noise, their statistics must be determined via interference experiments, where one particle goes around another. The experiments are very demanding since the even denominator fractions turn to be very fragile and thus can be observed only in the purest possible two dimensional electron gas and at the lowest temperatures. While until very recently such high quality samples were available only by a single grower (in the USA), we have the capability now to grow extremely pure samples with profound even denominator states. As will be detailed in the proposal, we have all the necessary tools to study charge and statistics of these fascinating excitations, due to our experience in crystal growth, shot noise and interferometry measurements.

2 000 000 €

Start date: 2009-01-01, End date: 2013-12-31

FractFrict is a comprehensive study of the space-time dynamics that lead to the failure of both bulk materials and frictionally bound interfaces. In these systems, failure is precipitated by rapidly moving singular fields at the tips of propagating cracks or crack-like fronts that cause material damage at microscopic scales. These generate damage that is macroscopically reflected as characteristic large-scale, modes of material failure. Thus, the structure of the fields that microscopically drive failure is critically important for an overall understanding of how macroscopic failure occurs. The innovative real-time measurements proposed here will provide fundamental understanding of the form of the singular fields, their modes of regularization and their relation to the resultant macroscopic modes of failure. Encompassing different classes of bulk materials and material interfaces. We aim to: [1] To establish a fundamental understanding of the dynamics of the near-tip singular fields, their regularization modes and how they couple to the macroscopic dynamics in both frictional motion and fracture. [2] To determine the types of singular failure processes in different classes of materials and interfaces (e.g. the brittle to ductile transition in amorphous materials, the role of fast fracture processes in frictional motion). [3] To establish local (microscopic) laws of friction/failure and how they evolve into their macroscopic counterparts [4]. To identify the existence and origins of crack instabilities in bulk and interface failure The insights obtained in this research will enable us to manipulate and/or predict material failure modes. The results of this study will shed considerable new light on fundamental open questions in fields as diverse as material design, tribology and geophysics.

2 265 399 €

Start date: 2010-12-01, End date: 2016-11-30

Supercomputers are strategically crucial for facilitating advances in science and technology: in climate change research, accelerated genome sequencing towards cancer treatments, cutting edge physics, devising engineering innovative solutions, and many other compute intensive problems. However, the future of super-computing depends on our ability to cope with the ever increasing rate of faults (bit flips and component failure), resulting from the steadily increasing machine size and decreasing operating voltage. Indeed, hardware trends predict at least two faults per minute for next generation (exascale) supercomputers. The challenge of ascertaining fault tolerance for high-performance computing is not new, and has been the focus of extensive research for over two decades. However, most solutions are either (i) general purpose, requiring little to no algorithmic effort, but severely degrading performance (e.g., checkpoint-restart), or (ii) tailored to specific applications and very efficient, but requiring high expertise and significantly increasing programmers' workload. We seek the best of both worlds: high performance and general purpose fault resilience. Efficient general purpose solutions (e.g., via error correcting codes) have revolutionized memory and communication devices over two decades ago, enabling programmers to effectively disregard the very likely memory and communication errors. The time has come for a similar paradigm shift in the computing regimen. I argue that exciting recent advances in error correcting codes, and in short probabilistically checkable proofs, make this goal feasible. Success along these lines will eliminate the bottleneck of required fault-tolerance expertise, and open exascale computing to all algorithm designers and programmers, for the benefit of the scientific, engineering, and industrial communities.

1 824 467 €

Start date: 2019-06-01, End date: 2024-05-31

The proposed research contains two main directions in group theory and geometry: Independence of Group Elements and Geometric Rigidity. The first consists of problems related to the existence of free subgroups, uniform and effective ways of producing such, and analogous questions for finite groups where the analog of independent elements are elements for which the Cayley graph has a large girth, or non-small expanding constant. This line of research began almost a century ago and contains many important works including works of Hausdorff, Banach and Tarski on paradoxical decompositions, works of Margulis, Sullivan and Drinfeld on the Banach-Ruziewicz problem, the classical Tits Alternative, Margulis-Soifer result on maximal subgroups, the recent works of Eskin-Mozes-Oh and Bourgain-Gamburd, etc. Among the famous questions is Milnor's problem on the exponential verses polynomial growth for f.p. groups, originally stated for f.g. groups but reformulated after Grigorchuk's counterexample. Related works of the PI includes a joint work with Breuillard on the topological Tits alternative, where several well known conjectures were solved, e.g. the foliated version of Milnor's problem conjectured by Carriere, and on the uniform Tits alternative which significantly improved Tits' and EMO theorems. A joint work with Glasner on primitive groups where in particular a conjecture of Higman and Neumann was solved. A paper on the deformation varieties where a conjecture of Margulis and Soifer and a conjecture of Goldman were proved. The second involves extensions of Margulis' and Mostow's rigidity theorems to actions of lattices in general topological groups on metric spaces, and extensions of Kazhdan's property (T) for group actions on Banach and metric spaces. This area is very active today. Related work of the PI includes his joint work with Karlsson and Margulis on generalized harmonic maps, and his joint work with Bader, Furman and Monod on actions on Banach spaces.

750 000 €

Start date: 2008-07-01, End date: 2013-12-31

"Live-cell imaging combined with kinetic analyses has provided new biological insights on the gene expression pathway. However, such studies in mammalian cells typically require use of exogenous over-expressed gene constructs, which often form large tandem gene arrays and usually lack the complete endogenous regulatory sequences. It is therefore imperative to design methodology for analyzing gene expression kinetics of single alleles of endogenous genes. While certain steps have been taken in this direction, there are many experimental obstacles standing in the way of a robust genome-wide system for the in vivo examination of endogenous gene expression within the natural nuclear environment. GENEXP sets out to provide such a system. It will start with methodology for robust tagging of a multitude of endogenous genes and their transcribed mRNAs in human cells using the ""CD tagging"" approach. Thereby, in vivo mRNA synthesis at the nuclear site of RNA birth will be explored in a unique manner. A high-resolution study of gene expression, in particular mRNA transcription and mRNA export, under endogenous cellular context and using a genome-wide live-cell approach will be performed. GENEXP will specifically focus on the: i) Transcriptional kinetics of endogenous genes in single cells and cell populations; ii) Kinetics of mRNA export on the single molecule level; iii) Examination of the protein composition of endogenous mRNPs; iv) High throughput scan for drugs that affect gene expression and mRNA export. Altogether, GENEXP will provide breakthrough capability in kinetically quantifying the gene expression pathway of a large variety of endogenous genes, and the ability to examine the generated molecules on the single-molecule level. This will be done within their normal genomic and biological environment, at the single-allele level."

1 498 510 €

Start date: 2010-12-01, End date: 2015-11-30

Sometimes in the sciences there are different yet complementary descriptions for the same object. This extends to the particle-wave duality of quantum mechanics; one mathematical analog of this duality is the Fourier transform. Questions that are difficult when formulated in one language of science may become simple when interpreted in another. The Langlands conjecture posits the existence of a correspondence between problems in arithmetic and in Representation Theory. The Langlands conjecture has only been proven for a limited number of cases, but even this has solved problems such as the famous Fermat conjecture. The aim of this project is to continue study of the "classical" aspects of the Langlands conjecture and to extend the conjecture to the quantum geometric Langlands correspondence, higher-dimensional fields, Kac-Moody groups (with D.Gaitsgory: quantum Langlands correspondence; D.Gaitsgory and E. Hrushevsi: groups over higher-dimensional fields; A. Braverman: Kac-Moody groups; R. Bezrukavnikov, S.Debacker, Y.Varshavsky: classical aspects of the correspondence; A. Berenstein: geometric crystals and crystal bases). The quantum case is much more symmetric than the classical case and can lead in the limit q->0 to new insights into the classical case. The quantum case is also related to the multiple Dirichlet series. New results in the quantum case would lead to progress in understanding important Number Theoretic questions. Extending the Langlands correspondence to groups over higher-dimensional fields could substantially enlarge its applicability. Studying Kac-Moody groups would provide tools for the new important class of L-functions. This progress could lead to a proof of the existence of the analytic continuation of classical L-functions. The geometric Langlands correspondence is closely related to T-symmetry in 4-dimensional gauge theory and the understanding of this relation is important for both Mathematics and Physics.

1 277 060 €

Start date: 2010-01-01, End date: 2014-12-31

We consider the dynamics of actions on homogeneous spaces of algebraic groups, We propose to tackle the central open problems in the area, including understanding actions of diagonal groups on homogeneous spaces without an entropy assumption, a related conjecture of Furstenberg about measures on R / Z invariant under multiplication by 2 and 3, and obtaining a quantitative understanding of equidistribution properties of unipotent flows and groups generated by unipotents. This has applications in arithmetic, Diophantine approximations, the spectral theory of homogeneous spaces, mathematical physics, and other fields. Connections to arithmetic combinatorics will be pursued.

1 229 714 €

Start date: 2011-01-01, End date: 2016-12-31

Long gamma ray bursts (long GRBs) and core-collapse supernovae (CCSNe) are two of the most spectacular explosions in the Universe. They are a focal point of research for many reasons. Nevertheless, despite considerable effort during the last several decades, there are still many fundamental open questions regarding their physics. Long GRBs and CCSNe are related. We know that they are both an outcome of a massive star collapse, where in some cases, such collapse produces simultaneously a GRB and a SN. However, we do not know how a single stellar collapse can produce these two apparently very different explosions. The GRB-SN connection raises many questions, but it also offers new opportunities to learn on the two types of explosions. The focus of the proposed research is on the connection between CCSNe and GRBs, and on the physics of shock breakout. As I explain in this proposal, shock breakouts play an important role in this connection and therefore, I will develop a comprehensive theory of relativistic and Newtonian shock breakout. In addition, I will study the propagation of relativistic jets inside stars, including the effects of jet propagation and GRB engine on the emerging SN. This will be done by a set of interrelated projects that carefully combine analytic calculations and numerical simulations. Together, these projects will be the first to model a GRB and a SN that are simultaneously produced in a single star. This in turn will be used to gain new insights into long GRBs and CCSNe in general. This research will also make a direct contribution to cosmic explosions research in general. Any observable cosmic explosion must go through a shock breakout and a considerable effort is invested these days in large field of view surveys in search for these breakouts. This program will provide a new theoretical base for the interpretation of the upcoming observations.

1 468 180 €

Start date: 2012-01-01, End date: 2017-12-31

The large-scale assembly of nanowires (NWs) with controlled orientation on surfaces remains one challenge toward their integration into practical devices. A recent paper in Science from the PI’s group reported the guided growth of millimeter-long horizontal NWs with controlled orientations on crystal surfaces. The growth directions and crystallographic orientation of GaN NWs are controlled by their epitaxial relationship with different planes of sapphire, as well as by a graphoepitaxial effect that guides their growth along surface steps and grooves. Despite their interaction with the surface, these horizontally grown NWs have surprisingly few defects, exhibiting optical and electronic properties superior to those of vertically grown NWs. We observed that whereas in a 2D film stress accumulates in two directions, in a NW stress accumulates along its axis, but can relax in the transversal direction, making the 1D system much more tolerant to mismatch than a 2D film. This new 1D nanoscale effect, along with the graphoepitaxial effect, subverts the paradigm not only in the young field of NWs, but also in the established field of epitaxy. This paves the way to highly controlled semiconductor structures with potential applications not available by other means. The aim of this project is to investigate the guided growth of NWs and unleash its vast possibilities toward the realization of self-integrating nanosystems. First, we will generalize the guided growth of NWs to a variety of semiconductors and substrates, and produce ordered arrays of NWs with coherently modulated composition and doping. Second, we will conduct fundamental studies to investigate the correlated structure, growth mechanism, optical and electronic properties of guided NWs. Third, we will exploit the guided growth of NWs for the production of various functional self-integrating systems, including nanocircuits, LEDs, lasers, photovoltaic cells, photodetectors, photonic and nonlinear optical devices.

2 063 872 €

Start date: 2014-02-01, End date: 2019-01-31

Boolean function analysis is a topic of research at the heart of theoretical computer science. It studies functions on n input bits (for example, functions computed by Boolean circuits) from a spectral perspective, by treating them as real-valued functions on the group Z_2^n, and using techniques from Fourier and functional analysis. Boolean function analysis has been applied to a wide variety of areas within theoretical computer science, including hardness of approximation, learning theory, coding theory, and quantum complexity theory. Despite its immense usefulness, Boolean function analysis has limited scope, since it is only appropriate for studying functions on {0,1}^n (a domain known as the Boolean hypercube). Discrete harmonic analysis is the study of functions on domains possessing richer algebraic structure such as the symmetric group (the group of all permutations), using techniques from representation theory and Sperner theory. The considerable success of Boolean function analysis suggests that discrete harmonic analysis could likewise play a central role in theoretical computer science. The goal of this proposal is to systematically develop discrete harmonic analysis on a broad variety of domains, with an eye toward applications in several areas of theoretical computer science. We will generalize classical results of Boolean function analysis beyond the Boolean hypercube, to domains such as finite groups, association schemes (a generalization of finite groups), the quantum analog of the Boolean hypercube, and high-dimensional expanders (high-dimensional analogs of expander graphs). Potential applications include a quantum PCP theorem and two outstanding open questions in hardness of approximation: the Unique Games Conjecture and the Sliding Scale Conjecture. Beyond these concrete applications, we expect that the fundamental results we prove will have many other applications that are hard to predict in advance.

1 473 750 €

Start date: 2019-03-01, End date: 2024-02-29

We present a large variety of novel lines of research in Homogeneous Dynamics with emphasis on the dynamics of the diagonal group. Both new and classical applications are suggested, most notably to • Number Theory • Geometry of Numbers • Diophantine approximation. Emphasis is given to applications in • Diophantine properties of algebraic numbers. The proposal is built of 4 sections. (1) In the first section we discuss questions pertaining to topological and distributional aspects of periodic orbits of the diagonal group in the space of lattices in Euclidean space. These objects encode deep information regarding Diophantine properties of algebraic numbers. We demonstrate how these questions are closely related to, and may help solve, some of the central open problems in the geometry of numbers and Diophantine approximation. (2) In the second section we discuss Minkowski's conjecture regarding integral values of products of linear forms. For over a century this central conjecture is resisting a general solution and a novel and promising strategy for its resolution is presented. (3) In the third section, a novel conjecture regarding limiting distribution of infinite-volume-orbits is presented, in analogy with existing results regarding finite-volume-orbits. Then, a variety of applications and special cases are discussed, some of which give new results regarding classical concepts such as continued fraction expansion of rational numbers. (4) In the last section we suggest a novel strategy to attack one of the most notorious open problems in Diophantine approximation, namely: Do cubic numbers have unbounded continued fraction expansion? This novel strategy leads us to embark on a systematic study of an area in homogeneous dynamics which has not been studied yet. Namely, the dynamics in the space of discrete subgroups of rank k in R^n (identified up to scaling).

1 432 730 €

Start date: 2018-10-01, End date: 2023-09-30

"Expander graphs have been playing a fundamental role in many areas of computer science. During the last 15 years they have also found important and unexpected applications in pure mathematics. The goal of the current research is to develop systematically high-dimensional (HD) theory of expanders, i.e., simplicial complexes and hypergraphs which resemble in dimension d, the role of expander graphs for d = 1. There are several motivations for developing such a theory, some from pure mathematics and some from computer science. For example, Ramanujan complexes (the HD versions of the ""optimal"" expanders, the Ramanujan graphs) have already been useful for extremal hypergraph theory. One of the main goals of this research is to use them to solve other problems, such as Gromov's problem: are there bounded degree simplicial complexes with the topological overlapping property (""topological expanders""). Other directions of HD expanders have applications in property testing, a very important subject in theoretical computer science. Moreover they can be a tool for the construction of locally testable codes, an important question of theoretical and practical importance in the theory of error correcting codes. In addition, the study of these simplicial complexes suggests new quantum error correcting codes (QECC). It is hoped that it will lead to such codes which are also low density parity check (LDPC). The huge success and impact of the theory of expander graphs suggests that the high dimensional theory will also bring additional unexpected applications beside those which can be foreseen as of now."

1 592 500 €

Start date: 2016-08-01, End date: 2021-07-31

Machine learning has rapidly evolved in the last decade, significantly improving accuracy on tasks such as image classification. Much of this success can be attributed to the re-emergence of neural nets. However, learning algorithms are still far from achieving the capabilities of human cognition. In particular, humans can rapidly organize an input stream (e.g., textual or visual) into a set of entities, and understand the complex relations between those. In this project I aim to create a general methodology for semantic interpretation of input streams. Such problems fall under the structured-prediction framework, to which I have made numerous contributions. The proposal identifies and addresses three key components required for a comprehensive and empirically effective approach to the problem. First, we consider the holistic nature of semantic interpretations, where a top-down process chooses a coherent interpretation among the vast number of options. We argue that deep-learning architectures are ideally suited for modeling such coherence scores, and propose to develop the corresponding theory and algorithms. Second, we address the complexity of the semantic representation, where a stream is mapped into a variable number of entities, each having multiple attributes and relations to other entities. We characterize the properties a model should satisfy in order to produce such interpretations, and propose novel models that achieve this. Third, we develop a theory for understanding when such models can be learned efficiently, and how well they can generalize. To achieve this, we address key questions of non-convex optimization, inductive bias and generalization. We expect these contributions to have a dramatic impact on AI systems, from machine reading of text to image analysis. More broadly, they will help bridge the gap between machine learning as an engineering field, and the study of human cognition.

1 932 500 €

Start date: 2019-02-01, End date: 2024-01-31

Understanding the low-temperature behavior of quantum correlated materials has long been one of the central challenges in condensed matter physics. Such materials exhibit a number of interesting phenomena, such as anomalous transport behavior, complex phase diagrams, and high-temperature superconductivity. However, their understanding has been hindered by the lack of suitable theoretical tools to handle such strongly interacting quantum ``liquids.'' Recent years have witnessed a wave of renewed interest in this long-standing, deep problem, both from condensed matter, high energy, and quantum information physicists. The goal of this research program is to exploit the recent progress on these problems to open new ways of understanding strongly-coupled unconventional quantum fluids. We will perform large-scale, sign problem-free QMC simulations of metals close to quantum critical points, focusing on new regimes beyond the traditional paradigms. New ways to diagnose transport from QMC data will be developed. Exotic phase transitions between an ordinary and a topologically-ordered, fractionalized metal will be studied. In addition, insights will be gained from analytical studies of strongly coupled lattice models, starting from the tractable limit of a large number of degrees of freedom per unit cell. The thermodynamic and transport properties of these models will be studied. These solvable examples will be used to provide a new window into the properties of strongly coupled quantum matter. We will seek ``organizing principles'' to describe such matter, such as emergent local quantum critical behavior and a hydrodynamic description of electron flow. Connections will be made with the ideas of universal bounds on transport and on the rate of spread of quantum information, as well as with insights from other techniques. While our study will mostly focus on generic, universal features of quantum fluids, implications for specific materials will also be studied.

1 515 400 €

Start date: 2019-01-01, End date: 2023-12-31

In recent years, as first established in some 6 papers in Science and Nature from the PI s group, a new paradigm has emerged. This reveals the remarkable and unsuspected - role of hydration layers in modulating frictional forces between sliding surfaces or molecular layers in aqueous media, termed hydration lubrication, in which the lubricating mode is completely different from the classic one of oils or surfactants. In this project we address the substantial challenges that have now arisen: what are the underlying mechanisms controlling this effect? what are the potential breakthroughs that it may lead to? We will answer these questions through several interrelated objectives designed to address both fundamental aspects, as well as limits of applicability. We will use surface force balance (SFB) experiments, for which we will develop new methodologies, to characterize normal and frictional forces between atomically smooth surfaces where the nature of the surfaces (hydrophilic, hydrophobic, metallic, polymeric), as well as their electric potential, may be independently varied. We will examine mono- and multivalent ions to establish the role of relaxation rates and hydration energies in controlling the hydration lubrication, will probe hydration interactions at both hydrophobic/hydrophilic surfaces and will monitor slip of hydrated ions past surfaces. We will also characterize the hydration lubrication properties of a wide range of novel surface systems, including surfactants, liposomes, polymer brushes and, importantly, liposomes, using also synchrotron X-ray reflectometry for structural information. Attainment of these objectives should lead to conceptual breakthroughs both in our understanding of this new paradigm, and for its practical implications.

2 304 180 €

Start date: 2010-05-01, End date: 2015-04-30