TY - CONF AB - Smart contracts are programs that are stored and executed on the Blockchain and can receive, manage and transfer money (cryptocurrency units). Two important problems regarding smart contracts are formal analysis and compiler optimization. Formal analysis is extremely important, because smart contracts hold funds worth billions of dollars and their code is immutable after deployment. Hence, an undetected bug can cause significant financial losses. Compiler optimization is also crucial, because every action of a smart contract has to be executed by every node in the Blockchain network. Therefore, optimizations in compiling smart contracts can lead to significant savings in computation, time and energy. Two classical approaches in program analysis and compiler optimization are intraprocedural and interprocedural analysis. In intraprocedural analysis, each function is analyzed separately, while interprocedural analysis considers the entire program. In both cases, the analyses are usually reduced to graph problems over the control flow graph (CFG) of the program. These graph problems are often computationally expensive. Hence, there has been ample research on exploiting structural properties of CFGs for efficient algorithms. One such well-studied property is the treewidth, which is a measure of tree-likeness of graphs. It is known that intraprocedural CFGs of structured programs have treewidth at most 6, whereas the interprocedural treewidth cannot be bounded. This result has been used as a basis for many efficient intraprocedural analyses. In this paper, we explore the idea of exploiting the treewidth of smart contracts for formal analysis and compiler optimization. First, similar to classical programs, we show that the intraprocedural treewidth of structured Solidity and Vyper smart contracts is at most 9. Second, for global analysis, we prove that the interprocedural treewidth of structured smart contracts is bounded by 10 and, in sharp contrast with classical programs, treewidth-based algorithms can be easily applied for interprocedural analysis. Finally, we supplement our theoretical results with experiments using a tool we implemented for computing treewidth of smart contracts and show that the treewidth is much lower in practice. We use 36,764 real-world Ethereum smart contracts as benchmarks and find that they have an average treewidth of at most 3.35 for the intraprocedural case and 3.65 for the interprocedural case. AU - Chatterjee, Krishnendu AU - Goharshady, Amir Kafshdar AU - Goharshady, Ehsan Kafshdar ID - 6490 SN - 9781450359337 T2 - Proceedings of the 34th ACM Symposium on Applied Computing TI - The treewidth of smart contracts VL - Part F147772 ER - TY - JOUR AB - Interprocedural analysis is at the heart of numerous applications in programming languages, such as alias analysis, constant propagation, and so on. Recursive state machines (RSMs) are standard models for interprocedural analysis. We consider a general framework with RSMs where the transitions are labeled from a semiring and path properties are algebraic with semiring operations. RSMs with algebraic path properties can model interprocedural dataflow analysis problems, the shortest path problem, the most probable path problem, and so on. The traditional algorithms for interprocedural analysis focus on path properties where the starting point is fixed as the entry point of a specific method. In this work, we consider possible multiple queries as required in many applications such as in alias analysis. The study of multiple queries allows us to bring in an important algorithmic distinction between the resource usage of the one-time preprocessing vs for each individual query. The second aspect we consider is that the control flow graphs for most programs have constant treewidth. Our main contributions are simple and implementable algorithms that support multiple queries for algebraic path properties for RSMs that have constant treewidth. Our theoretical results show that our algorithms have small additional one-time preprocessing but can answer subsequent queries significantly faster as compared to the current algorithmic solutions for interprocedural dataflow analysis. We have also implemented our algorithms and evaluated their performance for performing on-demand interprocedural dataflow analysis on various domains, such as for live variable analysis and reaching definitions, on a standard benchmark set. Our experimental results align with our theoretical statements and show that after a lightweight preprocessing, on-demand queries are answered much faster than the standard existing algorithmic approaches. AU - Chatterjee, Krishnendu AU - Goharshady, Amir Kafshdar AU - Goyal, Prateesh AU - Ibsen-Jensen, Rasmus AU - Pavlogiannis, Andreas ID - 7158 IS - 4 JF - ACM Transactions on Programming Languages and Systems SN - 0164-0925 TI - Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth VL - 41 ER - TY - JOUR AB - We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms. AU - Chatterjee, Krishnendu AU - Fu, Hongfei AU - Goharshady, Amir Kafshdar ID - 7014 IS - 4 JF - ACM Transactions on Programming Languages and Systems TI - Non-polynomial worst-case analysis of recursive programs VL - 41 ER - TY - JOUR AB - Based on a novel control scheme, where a steady modification of the streamwise velocity profile leads to complete relaminarization of initially fully turbulent pipe flow, we investigate the applicability and usefulness of custom-shaped honeycombs for such control. The custom-shaped honeycombs are used as stationary flow management devices which generate specific modifications of the streamwise velocity profile. Stereoscopic particle image velocimetry and pressure drop measurements are used to investigate and capture the development of the relaminarizing flow downstream these devices. We compare the performance of straight (constant length across the radius of the pipe) honeycombs with custom-shaped ones (variable length across the radius) and try to determine the optimal shape for maximal relaminarization at minimal pressure loss. The optimally modified streamwise velocity profile is found to be M-shaped, and the maximum attainable Reynolds number for total relaminarization is found to be of the order of 10,000. Consequently, the respective reduction in skin friction downstream of the device is almost by a factor of 5. The break-even point, where the additional pressure drop caused by the device is balanced by the savings due to relaminarization and a net gain is obtained, corresponds to a downstream stretch of distances as low as approximately 100 pipe diameters of laminar flow. AU - Kühnen, Jakob AU - Scarselli, Davide AU - Hof, Björn ID - 6486 IS - 11 JF - Journal of Fluids Engineering SN - 00982202 TI - Relaminarization of pipe flow by means of 3D-printed shaped honeycombs VL - 141 ER - TY - JOUR AB - Following the recent observation that turbulent pipe flow can be relaminarised bya relatively simple modification of the mean velocity profile, we here carry out aquantitative experimental investigation of this phenomenon. Our study confirms thata flat velocity profile leads to a collapse of turbulence and in order to achieve theblunted profile shape, we employ a moving pipe segment that is briefly and rapidlyshifted in the streamwise direction. The relaminarisation threshold and the minimumshift length and speeds are determined as a function of Reynolds number. Althoughturbulence is still active after the acceleration phase, the modulated profile possessesa severely decreased lift-up potential as measured by transient growth. As shown,this results in an exponential decay of fluctuations and the flow relaminarises. Whilethis method can be easily applied at low to moderate flow speeds, the minimumstreamwise length over which the acceleration needs to act increases linearly with theReynolds number. AU - Scarselli, Davide AU - Kühnen, Jakob AU - Hof, Björn ID - 6228 JF - Journal of Fluid Mechanics SN - 00221120 TI - Relaminarising pipe flow by wall movement VL - 867 ER - TY - JOUR AB - Polar auxin transport plays a pivotal role in plant growth and development. PIN auxin efflux carriers regulate directional auxin movement by establishing local auxin maxima, minima, and gradients that drive multiple developmental processes and responses to environmental signals. Auxin has been proposed to modulate its own transport by regulating subcellular PIN trafficking via processes such as clathrin-mediated PIN endocytosis and constitutive recycling. Here, we further investigated the mechanisms by which auxin affects PIN trafficking by screening auxin analogs and identified pinstatic acid (PISA) as a positive modulator of polar auxin transport in Arabidopsis thaliana. PISA had an auxin-like effect on hypocotyl elongation and adventitious root formation via positive regulation of auxin transport. PISA did not activate SCFTIR1/AFB signaling and yet induced PIN accumulation at the cell surface by inhibiting PIN internalization from the plasma membrane. This work demonstrates PISA to be a promising chemical tool to dissect the regulatory mechanisms behind subcellular PIN trafficking and auxin transport. AU - Oochi, A AU - Hajny, Jakub AU - Fukui, K AU - Nakao, Y AU - Gallei, Michelle C AU - Quareshy, M AU - Takahashi, K AU - Kinoshita, T AU - Harborough, SR AU - Kepinski, S AU - Kasahara, H AU - Napier, RM AU - Friml, Jiří AU - Hayashi, KI ID - 6260 IS - 2 JF - Plant Physiology SN - 0032-0889 TI - Pinstatic acid promotes auxin transport by inhibiting PIN internalization VL - 180 ER - TY - JOUR AB - Segregation of maternal determinants within the oocyte constitutes the first step in embryo patterning. In zebrafish oocytes, extensive ooplasmic streaming leads to the segregation of ooplasm from yolk granules along the animal-vegetal axis of the oocyte. Here, we show that this process does not rely on cortical actin reorganization, as previously thought, but instead on a cell-cycle-dependent bulk actin polymerization wave traveling from the animal to the vegetal pole of the oocyte. This wave functions in segregation by both pulling ooplasm animally and pushing yolk granules vegetally. Using biophysical experimentation and theory, we show that ooplasm pulling is mediated by bulk actin network flows exerting friction forces on the ooplasm, while yolk granule pushing is achieved by a mechanism closely resembling actin comet formation on yolk granules. Our study defines a novel role of cell-cycle-controlled bulk actin polymerization waves in oocyte polarization via ooplasmic segregation. AU - Shamipour, Shayan AU - Kardos, Roland AU - Xue, Shi-lei AU - Hof, Björn AU - Hannezo, Edouard B AU - Heisenberg, Carl-Philipp J ID - 6508 IS - 6 JF - Cell SN - 00928674 TI - Bulk actin dynamics drive phase segregation in zebrafish oocytes VL - 177 ER - TY - JOUR AU - Schwayer, Cornelia AU - Shamipour, Shayan AU - Pranjic-Ferscha, Kornelija AU - Schauer, Alexandra AU - Balda, M AU - Tada, M AU - Matter, K AU - Heisenberg, Carl-Philipp J ID - 7001 IS - 4 JF - Cell SN - 0092-8674 TI - Mechanosensation of tight junctions depends on ZO-1 phase separation and flow VL - 179 ER - TY - THES AB - While cells of mesenchymal or epithelial origin perform their effector functions in a purely anchorage dependent manner, cells derived from the hematopoietic lineage are not committed to operate only within a specific niche. Instead, these cells are able to function autonomously of the molecular composition in a broad range of tissue compartments. By this means, cells of the hematopoietic lineage retain the capacity to disseminate into connective tissue and recirculate between organs, building the foundation for essential processes such as tissue regeneration or immune surveillance. Cells of the immune system, specifically leukocytes, are extraordinarily good at performing this task. These cells are able to flexibly shift their mode of migration between an adhesion-mediated and an adhesion-independent manner, instantaneously accommodating for any changes in molecular composition of the external scaffold. The key component driving directed leukocyte migration is the chemokine receptor 7, which guides the cell along gradients of chemokine ligand. Therefore, the physical destination of migrating leukocytes is purely deterministic, i.e. given by global directional cues such as chemokine gradients. Nevertheless, these cells typically reside in three-dimensional scaffolds of inhomogeneous complexity, raising the question whether cells are able to locally discriminate between multiple optional migration routes. Current literature provides evidence that leukocytes, specifically dendritic cells, do indeed probe their surrounding by virtue of multiple explorative protrusions. However, it remains enigmatic how these cells decide which one is the more favorable route to follow and what are the key players involved in performing this task. Due to the heterogeneous environment of most tissues, and the vast adaptability of migrating leukocytes, at this time it is not clear to what extent leukocytes are able to optimize their migratory strategy by adapting their level of adhesiveness. And, given the fact that leukocyte migration is characterized by branched cell shapes in combination with high migration velocities, it is reasonable to assume that these cells require fine tuned shape maintenance mechanisms that tightly coordinate protrusion and adhesion dynamics in a spatiotemporal manner. Therefore, this study aimed to elucidate how rapidly migrating leukocytes opt for an ideal migratory path while maintaining a continuous cell shape and balancing adhesive forces to efficiently navigate through complex microenvironments. The results of this study unraveled a role for the microtubule cytoskeleton in promoting the decision making process during path finding and for the first time point towards a microtubule-mediated function in cell shape maintenance of highly ramified cells such as dendritic cells. Furthermore, we found that migrating low-adhesive leukocytes are able to instantaneously adapt to increased tensile load by engaging adhesion receptors. This response was only occurring tangential to the substrate while adhesive properties in the vertical direction were not increased. As leukocytes are primed for rapid migration velocities, these results demonstrate that leukocyte integrins are able to confer a high level of traction forces parallel to the cell membrane along the direction of migration without wasting energy in gluing the cell to the substrate. Thus, the data in the here presented thesis provide new insights into the pivotal role of cytoskeletal dynamics and the mechanisms of force transduction during leukocyte migration. Thereby the here presented results help to further define fundamental principles underlying leukocyte migration and open up potential therapeutic avenues of clinical relevance. AU - Kopf, Aglaja ID - 6891 KW - cell biology KW - immunology KW - leukocyte KW - migration KW - microfluidics SN - 978-3-99078-002-2 TI - The implication of cytoskeletal dynamics on leukocyte migration ER - TY - JOUR AB - During metazoan development, immune surveillance and cancer dissemination, cells migrate in complex three-dimensional microenvironments1,2,3. These spaces are crowded by cells and extracellular matrix, generating mazes with differently sized gaps that are typically smaller than the diameter of the migrating cell4,5. Most mesenchymal and epithelial cells and some—but not all—cancer cells actively generate their migratory path using pericellular tissue proteolysis6. By contrast, amoeboid cells such as leukocytes use non-destructive strategies of locomotion7, raising the question how these extremely fast cells navigate through dense tissues. Here we reveal that leukocytes sample their immediate vicinity for large pore sizes, and are thereby able to choose the path of least resistance. This allows them to circumnavigate local obstacles while effectively following global directional cues such as chemotactic gradients. Pore-size discrimination is facilitated by frontward positioning of the nucleus, which enables the cells to use their bulkiest compartment as a mechanical gauge. Once the nucleus and the closely associated microtubule organizing centre pass the largest pore, cytoplasmic protrusions still lingering in smaller pores are retracted. These retractions are coordinated by dynamic microtubules; when microtubules are disrupted, migrating cells lose coherence and frequently fragment into migratory cytoplasmic pieces. As nuclear positioning in front of the microtubule organizing centre is a typical feature of amoeboid migration, our findings link the fundamental organization of cellular polarity to the strategy of locomotion. AU - Renkawitz, Jörg AU - Kopf, Aglaja AU - Stopp, Julian A AU - de Vries, Ingrid AU - Driscoll, Meghan K. AU - Merrin, Jack AU - Hauschild, Robert AU - Welf, Erik S. AU - Danuser, Gaudenz AU - Fiolka, Reto AU - Sixt, Michael K ID - 6328 JF - Nature TI - Nuclear positioning facilitates amoeboid migration along the path of least resistance VL - 568 ER - TY - JOUR AU - Kopf, Aglaja AU - Sixt, Michael K ID - 6877 IS - 1 JF - Cell SN - 0092-8674 TI - The neural crest pitches in to remove apoptotic debris VL - 179 ER - TY - JOUR AU - Contreras, Ximena AU - Hippenmeyer, Simon ID - 6830 IS - 5 JF - Neuron SN - 08966273 TI - Memo1 tiles the radial glial cell grid VL - 103 ER - TY - JOUR AB - Cortical microtubule arrays in elongating epidermal cells in both the root and stem of plants have the propensity of dynamic reorientations that are correlated with the activation or inhibition of growth. Factors regulating plant growth, among them the hormone auxin, have been recognized as regulators of microtubule array orientations. Some previous work in the field has aimed at elucidating the causal relationship between cell growth, the signaling of auxin or other growth-regulating factors, and microtubule array reorientations, with various conclusions. Here, we revisit this problem of causality with a comprehensive set of experiments in Arabidopsis thaliana, using the now available pharmacological and genetic tools. We use isolated, auxin-depleted hypocotyls, an experimental system allowing for full control of both growth and auxin signaling. We demonstrate that reorientation of microtubules is not directly triggered by an auxin signal during growth activation. Instead, reorientation is triggered by the activation of the growth process itself and is auxin-independent in its nature. We discuss these findings in the context of previous relevant work, including that on the mechanical regulation of microtubule array orientation. AU - Adamowski, Maciek AU - Li, Lanxin AU - Friml, Jiří ID - 6627 IS - 13 JF - International Journal of Molecular Sciences TI - Reorientation of cortical microtubule arrays in the hypocotyl of arabidopsis thaliana is induced by the cell growth process and independent of auxin signaling VL - 20 ER - TY - JOUR AB - We propose a novel generic shape optimization method for CAD models based on the eXtended Finite Element Method (XFEM). Our method works directly on the intersection between the model and a regular simulation grid, without the need to mesh or remesh, thus removing a bottleneck of classical shape optimization strategies. This is made possible by a novel hierarchical integration scheme that accurately integrates finite element quantities with sub-element precision. For optimization, we efficiently compute analytical shape derivatives of the entire framework, from model intersection to integration rule generation and XFEM simulation. Moreover, we describe a differentiable projection of shape parameters onto a constraint manifold spanned by user-specified shape preservation, consistency, and manufacturability constraints. We demonstrate the utility of our approach by optimizing mass distribution, strength-to-weight ratio, and inverse elastic shape design objectives directly on parameterized 3D CAD models. AU - Hafner, Christian AU - Schumacher, Christian AU - Knoop, Espen AU - Auzinger, Thomas AU - Bickel, Bernd AU - Bächer, Moritz ID - 7117 IS - 6 JF - ACM Transactions on Graphics SN - 0730-0301 TI - X-CAD: Optimizing CAD Models with Extended Finite Elements VL - 38 ER - TY - JOUR AB - Suspended particles can alter the properties of fluids and in particular also affect the transition fromlaminar to turbulent flow. An earlier study [Mataset al.,Phys. Rev. Lett.90, 014501 (2003)] reported howthe subcritical (i.e., hysteretic) transition to turbulent puffs is affected by the addition of particles. Here weshow that in addition to this known transition, with increasing concentration a supercritical (i.e.,continuous) transition to a globally fluctuating state is found. At the same time the Newtonian-typetransition to puffs is delayed to larger Reynolds numbers. At even higher concentration only the globallyfluctuating state is found. The dynamics of particle laden flows are hence determined by two competinginstabilities that give rise to three flow regimes: Newtonian-type turbulence at low, a particle inducedglobally fluctuating state at high, and a coexistence state at intermediate concentrations. AU - Agrawal, Nishchal AU - Choueiri, George H AU - Hof, Björn ID - 6189 IS - 11 JF - Physical Review Letters SN - 00319007 TI - Transition to turbulence in particle laden flows VL - 122 ER - TY - THES AB - Decades of studies have revealed the mechanisms of gene regulation in molecular detail. We make use of such well-described regulatory systems to explore how the molecular mechanisms of protein-protein and protein-DNA interactions shape the dynamics and evolution of gene regulation. i) We uncover how the biophysics of protein-DNA binding determines the potential of regulatory networks to evolve and adapt, which can be captured using a simple mathematical model. ii) The evolution of regulatory connections can lead to a significant amount of crosstalk between binding proteins. We explore the effect of crosstalk on gene expression from a target promoter, which seems to be modulated through binding competition at non-specific DNA sites. iii) We investigate how the very same biophysical characteristics as in i) can generate significant fitness costs for cells through global crosstalk, meaning non-specific DNA binding across the genomic background. iv) Binding competition between proteins at a target promoter is a prevailing regulatory feature due to the prevalence of co-regulation at bacterial promoters. However, the dynamics of these systems are not always straightforward to determine even if the molecular mechanisms of regulation are known. A detailed model of the biophysical interactions reveals that interference between the regulatory proteins can constitute a new, generic form of system memory that records the history of the input signals at the promoter. We demonstrate how the biophysics of protein-DNA binding can be harnessed to investigate the principles that shape and ultimately limit cellular gene regulation. These results provide a basis for studies of higher-level functionality, which arises from the underlying regulation. AU - Igler, Claudia ID - 6371 KW - gene regulation KW - biophysics KW - transcription factor binding KW - bacteria SN - 2663-337X TI - On the nature of gene regulatory design - The biophysics of transcription factor binding shapes gene regulation ER - TY - JOUR AB - In this paper, we evaluate clock signals generated in ring oscillators and self-timed rings and the way their jitter can be transformed into random numbers. We show that counting the periods of the jittery clock signal produces random numbers of significantly better quality than the methods in which the jittery signal is simply sampled (the case in almost all current methods). Moreover, we use the counter values to characterize and continuously monitor the source of randomness. However, instead of using the widely used statistical variance, we propose to use Allan variance to do so. There are two main advantages: Allan variance is insensitive to low frequency noises such as flicker noise that are known to be autocorrelated and significantly less circuitry is required for its computation than that used to compute commonly used variance. We also show that it is essential to use a differential principle of randomness extraction from the jitter based on the use of two identical oscillators to avoid autocorrelations originating from external and internal global jitter sources and that this fact is valid for both kinds of rings. Last but not least, we propose a method of statistical testing based on high order Markov model to show the reduced dependencies when the proposed randomness extraction is applied. AU - Allini, Elie Noumon AU - Skórski, Maciej AU - Petura, Oto AU - Bernard, Florent AU - Laban, Marek AU - Fischer, Viktor ID - 10286 IS - 3 JF - IACR Transactions on Cryptographic Hardware and Embedded Systems TI - Evaluation and monitoring of free running oscillators serving as source of randomness VL - 2018 ER - TY - CONF AB - Solving parity games, which are equivalent to modal μ-calculus model checking, is a central algorithmic problem in formal methods, with applications in reactive synthesis, program repair, verification of branching-time properties, etc. Besides the standard compu- tation model with the explicit representation of games, another important theoretical model of computation is that of set-based symbolic algorithms. Set-based symbolic algorithms use basic set operations and one-step predecessor operations on the implicit description of games, rather than the explicit representation. The significance of symbolic algorithms is that they provide scalable algorithms for large finite-state systems, as well as for infinite-state systems with finite quotient. Consider parity games on graphs with n vertices and parity conditions with d priorities. While there is a rich literature of explicit algorithms for parity games, the main results for set-based symbolic algorithms are as follows: (a) the basic algorithm that requires O(nd) symbolic operations and O(d) symbolic space; and (b) an improved algorithm that requires O(nd/3+1) symbolic operations and O(n) symbolic space. In this work, our contributions are as follows: (1) We present a black-box set-based symbolic algorithm based on the explicit progress measure algorithm. Two important consequences of our algorithm are as follows: (a) a set-based symbolic algorithm for parity games that requires quasi-polynomially many symbolic operations and O(n) symbolic space; and (b) any future improvement in progress measure based explicit algorithms immediately imply an efficiency improvement in our set-based symbolic algorithm for parity games. (2) We present a set-based symbolic algorithm that requires quasi-polynomially many symbolic operations and O(d · log n) symbolic space. Moreover, for the important special case of d ≤ log n, our algorithm requires only polynomially many symbolic operations and poly-logarithmic symbolic space. AU - Chatterjee, Krishnendu AU - Dvořák, Wolfgang AU - Henzinger, Monika H AU - Svozil, Alexander ID - 10883 SN - 2398-7340 T2 - 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning TI - Quasipolynomial set-based symbolic algorithms for parity games VL - 57 ER - TY - CONF AB - We report on a novel strategy to derive mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. The technique combines the method of counting and the coherent state approach to study the growth of the correlations among the particles and in the radiation field. As an instructional example, we derive the Schrödinger–Klein–Gordon system of equations from the Nelson model with ultraviolet cutoff and possibly massless scalar field. In particular, we prove the convergence of the reduced density matrices (of the nonrelativistic particles and the field bosons) associated with the exact time evolution to the projectors onto the solutions of the Schrödinger–Klein–Gordon equations in trace norm. Furthermore, we derive explicit bounds on the rate of convergence of the one-particle reduced density matrix of the nonrelativistic particles in Sobolev norm. AU - Leopold, Nikolai K AU - Pickl, Peter ID - 11 TI - Mean-field limits of particles in interaction with quantised radiation fields VL - 270 ER - TY - JOUR AB - Two generalizations of Itô formula to infinite-dimensional spaces are given. The first one, in Hilbert spaces, extends the classical one by taking advantage of cancellations when they occur in examples and it is applied to the case of a group generator. The second one, based on the previous one and a limit procedure, is an Itô formula in a special class of Banach spaces having a product structure with the noise in a Hilbert component; again the key point is the extension due to a cancellation. This extension to Banach spaces and in particular the specific cancellation are motivated by path-dependent Itô calculus. AU - Flandoli, Franco AU - Russo, Francesco AU - Zanco, Giovanni A ID - 1215 IS - 2 JF - Journal of Theoretical Probability TI - Infinite-dimensional calculus under weak spatial regularity of the processes VL - 31 ER -