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 - TY - CONF AB - We resolve in the affirmative conjectures of A. Skopenkov and Repovš (1998), and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings. Our proof of this result is constructive and almost immediately implies an efficient algorithm for testing whether a given piecewise linear map of a graph in a surface is approximable by an embedding. More precisely, an instance of this problem consists of (i) a graph G whose vertices are partitioned into clusters and whose inter-cluster edges are partitioned into bundles, and (ii) a region R of a 2-dimensional compact surface M given as the union of a set of pairwise disjoint discs corresponding to the clusters and a set of pairwise disjoint "pipes" corresponding to the bundles, connecting certain pairs of these discs. We are to decide whether G can be embedded inside M so that the vertices in every cluster are drawn in the corresponding disc, the edges in every bundle pass only through its corresponding pipe, and every edge crosses the boundary of each disc at most once. AU - Fulek, Radoslav AU - Kynčl, Jan ID - 185 SN - 978-3-95977-066-8 TI - Hanani-Tutte for approximating maps of graphs VL - 99 ER - TY - CONF AB - Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex. AU - Edelsbrunner, Herbert AU - Virk, Ziga AU - Wagner, Hubert ID - 188 TI - Smallest enclosing spheres and Chernoff points in Bregman geometry VL - 99 ER - TY - JOUR AB - A cornerstone of statistical inference, the maximum entropy framework is being increasingly applied to construct descriptive and predictive models of biological systems, especially complex biological networks, from large experimental data sets. Both its broad applicability and the success it obtained in different contexts hinge upon its conceptual simplicity and mathematical soundness. Here we try to concisely review the basic elements of the maximum entropy principle, starting from the notion of ‘entropy’, and describe its usefulness for the analysis of biological systems. As examples, we focus specifically on the problem of reconstructing gene interaction networks from expression data and on recent work attempting to expand our system-level understanding of bacterial metabolism. Finally, we highlight some extensions and potential limitations of the maximum entropy approach, and point to more recent developments that are likely to play a key role in the upcoming challenges of extracting structures and information from increasingly rich, high-throughput biological data. AU - De Martino, Andrea AU - De Martino, Daniele ID - 306 IS - 4 JF - Heliyon TI - An introduction to the maximum entropy approach and its application to inference problems in biology VL - 4 ER - TY - BOOK AB - This book first explores the origins of this idea, grounded in theoretical work on temporal logic and automata. The editors and authors are among the world's leading researchers in this domain, and they contributed 32 chapters representing a thorough view of the development and application of the technique. Topics covered include binary decision diagrams, symbolic model checking, satisfiability modulo theories, partial-order reduction, abstraction, interpolation, concurrency, security protocols, games, probabilistic model checking, and process algebra, and chapters on the transfer of theory to industrial practice, property specification languages for hardware, and verification of real-time systems and hybrid systems. The book will be valuable for researchers and graduate students engaged with the development of formal methods and verification tools. AU - Clarke, Edmund M. AU - Henzinger, Thomas A AU - Veith, Helmut AU - Bloem, Roderick ID - 3300 SN - 978-3-319-10574-1 TI - Handbook of Model Checking ER - TY - CHAP AB - Developmental processes are inherently dynamic and understanding them requires quantitative measurements of gene and protein expression levels in space and time. While live imaging is a powerful approach for obtaining such data, it is still a challenge to apply it over long periods of time to large tissues, such as the embryonic spinal cord in mouse and chick. Nevertheless, dynamics of gene expression and signaling activity patterns in this organ can be studied by collecting tissue sections at different developmental stages. In combination with immunohistochemistry, this allows for measuring the levels of multiple developmental regulators in a quantitative manner with high spatiotemporal resolution. The mean protein expression levels over time, as well as embryo-to-embryo variability can be analyzed. A key aspect of the approach is the ability to compare protein levels across different samples. This requires a number of considerations in sample preparation, imaging and data analysis. Here we present a protocol for obtaining time course data of dorsoventral expression patterns from mouse and chick neural tube in the first 3 days of neural tube development. The described workflow starts from embryo dissection and ends with a processed dataset. Software scripts for data analysis are included. The protocol is adaptable and instructions that allow the user to modify different steps are provided. Thus, the procedure can be altered for analysis of time-lapse images and applied to systems other than the neural tube. AU - Zagórski, Marcin P AU - Kicheva, Anna ID - 37 SN - 1064-3745 T2 - Morphogen Gradients TI - Measuring dorsoventral pattern and morphogen signaling profiles in the growing neural tube VL - 1863 ER - TY - JOUR AB - The hanging-drop network (HDN) is a technology platform based on a completely open microfluidic network at the bottom of an inverted, surface-patterned substrate. The platform is predominantly used for the formation, culturing, and interaction of self-assembled spherical microtissues (spheroids) under precisely controlled flow conditions. Here, we describe design, fabrication, and operation of microfluidic hanging-drop networks. AU - Misun, Patrick AU - Birchler, Axel AU - Lang, Moritz AU - Hierlemann, Andreas AU - Frey, Olivier ID - 305 JF - Methods in Molecular Biology TI - Fabrication and operation of microfluidic hanging drop networks VL - 1771 ER - TY - CONF AB - Probabilistic programs extend classical imperative programs with real-valued random variables and random branching. The most basic liveness property for such programs is the termination property. The qualitative (aka almost-sure) termination problem asks whether a given program program terminates with probability 1. While ranking functions provide a sound and complete method for non-probabilistic programs, the extension of them to probabilistic programs is achieved via ranking supermartingales (RSMs). Although deep theoretical results have been established about RSMs, their application to probabilistic programs with nondeterminism has been limited only to programs of restricted control-flow structure. For non-probabilistic programs, lexicographic ranking functions provide a compositional and practical approach for termination analysis of real-world programs. In this work we introduce lexicographic RSMs and show that they present a sound method for almost-sure termination of probabilistic programs with nondeterminism. We show that lexicographic RSMs provide a tool for compositional reasoning about almost-sure termination, and for probabilistic programs with linear arithmetic they can be synthesized efficiently (in polynomial time). We also show that with additional restrictions even asymptotic bounds on expected termination time can be obtained through lexicographic RSMs. Finally, we present experimental results on benchmarks adapted from previous work to demonstrate the effectiveness of our approach. AU - Agrawal, Sheshansh AU - Chatterjee, Krishnendu AU - Novotny, Petr ID - 325 IS - POPL TI - Lexicographic ranking supermartingales: an efficient approach to termination of probabilistic programs VL - 2 ER - TY - CHAP AB - Adventitious roots (AR) are de novo formed roots that emerge from any part of the plant or from callus in tissue culture, except root tissue. The plant tissue origin and the method by which they are induced determine the physiological properties of emerged ARs. Hence, a standard method encompassing all types of AR does not exist. Here we describe a method for the induction and analysis of AR that emerge from the etiolated hypocotyl of dicot plants. The hypocotyl is formed during embryogenesis and shows a determined developmental pattern which usually does not involve AR formation. However, the hypocotyl shows propensity to form de novo roots under specific circumstances such as removal of the root system, high humidity or flooding, or during de-etiolation. The hypocotyl AR emerge from a pericycle-like cell layer surrounding the vascular tissue of the central cylinder, which is reminiscent to the developmental program of lateral roots. Here we propose an easy protocol for in vitro hypocotyl AR induction from etiolated Arabidopsis seedlings. AU - Trinh, Hoang AU - Verstraeten, Inge AU - Geelen, Danny ID - 408 SN - 1064-3745 T2 - Root Development TI - In vitro assay for induction of adventitious rooting on intact arabidopsis hypocotyls VL - 1761 ER -