@article{319, abstract = {We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with boundary conditions. The calculus of modelled distributions established in Hairer (Invent Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4) is extended to this setting. We formulate and solve fixed point problems in these spaces with a class of kernels that is sufficiently large to cover in particular the Dirichlet and Neumann heat kernels. These results are then used to provide solution theories for the KPZ equation with Dirichlet and Neumann boundary conditions and for the 2D generalised parabolic Anderson model with Dirichlet boundary conditions. In the case of the KPZ equation with Neumann boundary conditions, we show that, depending on the class of mollifiers one considers, a “boundary renormalisation” takes place. In other words, there are situations in which a certain boundary condition is applied to an approximation to the KPZ equation, but the limiting process is the Hopf–Cole solution to the KPZ equation with a different boundary condition.}, author = {Gerencser, Mate and Hairer, Martin}, issn = {14322064}, journal = {Probability Theory and Related Fields}, number = {3-4}, pages = {697–758}, publisher = {Springer}, title = {{Singular SPDEs in domains with boundaries}}, doi = {10.1007/s00440-018-0841-1}, volume = {173}, year = {2019}, } @article{429, abstract = {We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.}, author = {Ajanki, Oskari H and Erdös, László and Krüger, Torben H}, issn = {14322064}, journal = {Probability Theory and Related Fields}, number = {1-2}, pages = {293–373}, publisher = {Springer}, title = {{Stability of the matrix Dyson equation and random matrices with correlations}}, doi = {10.1007/s00440-018-0835-z}, volume = {173}, year = {2019}, } @inproceedings{5947, abstract = {Graph algorithms applied in many applications, including social networks, communication networks, VLSI design, graphics, and several others, require dynamic modifications - addition and removal of vertices and/or edges - in the graph. This paper presents a novel concurrent non-blocking algorithm to implement a dynamic unbounded directed graph in a shared-memory machine. The addition and removal operations of vertices and edges are lock-free. For a finite sized graph, the lookup operations are wait-free. Most significant component of the presented algorithm is the reachability query in a concurrent graph. The reachability queries in our algorithm are obstruction-free and thus impose minimal additional synchronization cost over other operations. We prove that each of the data structure operations are linearizable. We extensively evaluate a sample C/C++ implementation of the algorithm through a number of micro-benchmarks. The experimental results show that the proposed algorithm scales well with the number of threads and on an average provides 5 to 7x performance improvement over a concurrent graph implementation using coarse-grained locking.}, author = {Chatterjee, Bapi and Peri, Sathya and Sa, Muktikanta and Singhal, Nandini}, booktitle = {ACM International Conference Proceeding Series}, isbn = {978-1-4503-6094-4 }, location = {Bangalore, India}, pages = {168--177}, publisher = {ACM}, title = {{A simple and practical concurrent non-blocking unbounded graph with linearizable reachability queries}}, doi = {10.1145/3288599.3288617}, year = {2019}, } @article{5857, abstract = {A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, except that every pair of edges that do not share a vertex are allowed to cross an odd number of times. It is also shown that the maximum number of edges of a quasi-thrackle on n vertices is [Formula presented](n−1), and that this bound is best possible for infinitely many values of n.}, author = {Fulek, Radoslav and Pach, János}, issn = {0166218X}, journal = {Discrete Applied Mathematics}, number = {4}, pages = {266--231}, publisher = {Elsevier}, title = {{Thrackles: An improved upper bound}}, doi = {10.1016/j.dam.2018.12.025}, volume = {259}, year = {2019}, } @article{5944, abstract = {Understanding the thermodynamics of the duplication process is a fundamental step towards a comprehensive physical theory of biological systems. However, the immense complexity of real cells obscures the fundamental tensions between energy gradients and entropic contributions that underlie duplication. The study of synthetic, feasible systems reproducing part of the key ingredients of living entities but overcoming major sources of biological complexity is of great relevance to deepen the comprehension of the fundamental thermodynamic processes underlying life and its prevalence. In this paper an abstract—yet realistic—synthetic system made of small synthetic protocell aggregates is studied in detail. A fundamental relation between free energy and entropic gradients is derived for a general, non-equilibrium scenario, setting the thermodynamic conditions for the occurrence and prevalence of duplication phenomena. This relation sets explicitly how the energy gradients invested in creating and maintaining structural—and eventually, functional—elements of the system must always compensate the entropic gradients, whose contributions come from changes in the translational, configurational, and macrostate entropies, as well as from dissipation due to irreversible transitions. Work/energy relations are also derived, defining lower bounds on the energy required for the duplication event to take place. A specific example including real ternary emulsions is provided in order to grasp the orders of magnitude involved in the problem. It is found that the minimal work invested over the system to trigger a duplication event is around ~ 10−13J , which results, in the case of duplication of all the vesicles contained in a liter of emulsion, in an amount of energy around ~ 1kJ . Without aiming to describe a truly biological process of duplication, this theoretical contribution seeks to explicitly define and identify the key actors that participate in it.}, author = {Corominas-Murtra, Bernat}, issn = {20751729}, journal = {Life}, number = {1}, publisher = {MDPI}, title = {{Thermodynamics of duplication thresholds in synthetic protocell systems}}, doi = {10.3390/life9010009}, volume = {9}, year = {2019}, } @article{6029, abstract = {Protein micropatterning has become an important tool for many biomedical applications as well as in academic research. Current techniques that allow to reduce the feature size of patterns below 1 μm are, however, often costly and require sophisticated equipment. We present here a straightforward and convenient method to generate highly condensed nanopatterns of proteins without the need for clean room facilities or expensive equipment. Our approach is based on nanocontact printing and allows for the fabrication of protein patterns with feature sizes of 80 nm and periodicities down to 140 nm. This was made possible by the use of the material X-poly(dimethylsiloxane) (X-PDMS) in a two-layer stamp layout for protein printing. In a proof of principle, different proteins at various scales were printed and the pattern quality was evaluated by atomic force microscopy (AFM) and super-resolution fluorescence microscopy.}, author = {Lindner, Marco and Tresztenyak, Aliz and Fülöp, Gergö and Jahr, Wiebke and Prinz, Adrian and Prinz, Iris and Danzl, Johann G and Schütz, Gerhard J. and Sevcsik, Eva}, issn = {22962646}, journal = {Frontiers in Chemistry}, publisher = {Frontiers Media S.A.}, title = {{A fast and simple contact printing approach to generate 2D protein nanopatterns}}, doi = {10.3389/fchem.2018.00655}, volume = {6}, year = {2019}, } @article{6028, abstract = {We give a construction allowing us to build local renormalized solutions to general quasilinear stochastic PDEs within the theory of regularity structures, thus greatly generalizing the recent results of [1, 5, 11]. Loosely speaking, our construction covers quasilinear variants of all classes of equations for which the general construction of [3, 4, 7] applies, including in particular one‐dimensional systems with KPZ‐type nonlinearities driven by space‐time white noise. In a less singular and more specific case, we furthermore show that the counterterms introduced by the renormalization procedure are given by local functionals of the solution. The main feature of our construction is that it allows exploitation of a number of existing results developed for the semilinear case, so that the number of additional arguments it requires is relatively small.}, author = {Gerencser, Mate and Hairer, Martin}, journal = {Communications on Pure and Applied Mathematics}, number = {9}, pages = {1983--2005}, publisher = {Wiley}, title = {{A solution theory for quasilinear singular SPDEs}}, doi = {10.1002/cpa.21816}, volume = {72}, year = {2019}, } @inproceedings{5948, abstract = {We study the termination problem for nondeterministic probabilistic programs. We consider the bounded termination problem that asks whether the supremum of the expected termination time over all schedulers is bounded. First, we show that ranking supermartingales (RSMs) are both sound and complete for proving bounded termination over nondeterministic probabilistic programs. For nondeterministic probabilistic programs a previous result claimed that RSMs are not complete for bounded termination, whereas our result corrects the previous flaw and establishes completeness with a rigorous proof. Second, we present the first sound approach to establish lower bounds on expected termination time through RSMs.}, author = {Fu, Hongfei and Chatterjee, Krishnendu}, booktitle = {International Conference on Verification, Model Checking, and Abstract Interpretation}, location = {Cascais, Portugal}, pages = {468--490}, publisher = {Springer Nature}, title = {{Termination of nondeterministic probabilistic programs}}, doi = {10.1007/978-3-030-11245-5_22}, volume = {11388}, year = {2019}, } @article{5945, abstract = {In developing organisms, spatially prescribed cell identities are thought to be determined by the expression levels of multiple genes. Quantitative tests of this idea, however, require a theoretical framework capable of exposing the rules and precision of cell specification over developmental time. We use the gap gene network in the early fly embryo as an example to show how expression levels of the four gap genes can be jointly decoded into an optimal specification of position with 1% accuracy. The decoder correctly predicts, with no free parameters, the dynamics of pair-rule expression patterns at different developmental time points and in various mutant backgrounds. Precise cellular identities are thus available at the earliest stages of development, contrasting the prevailing view of positional information being slowly refined across successive layers of the patterning network. Our results suggest that developmental enhancers closely approximate a mathematically optimal decoding strategy.}, author = {Petkova, Mariela D. and Tkacik, Gasper and Bialek, William and Wieschaus, Eric F. and Gregor, Thomas}, journal = {Cell}, number = {4}, pages = {844--855.e15}, publisher = {Cell Press}, title = {{Optimal decoding of cellular identities in a genetic network}}, doi = {10.1016/j.cell.2019.01.007}, volume = {176}, year = {2019}, } @article{5943, abstract = {The hairpin instability of a jet in a crossflow (JICF) for a low jet-to-crossflow velocity ratio is investigated experimentally for a velocity ratio range of R ∈ (0.14, 0.75) and crossflow Reynolds numbers ReD ∈ (260, 640). From spectral analysis we characterize the Strouhal number and amplitude of the hairpin instability as a function of R and ReD. We demonstrate that the dynamics of the hairpins is well described by the Landau model, and, hence, that the instability occurs through Hopf bifurcation, similarly to other hydrodynamical oscillators such as wake behind different bluff bodies. Using the Landau model, we determine the precise threshold values of hairpin shedding. We also study the spatial dependence of this hydrodynamical instability, which shows a global behaviour.}, author = {Klotz, Lukasz and Gumowski, Konrad and Wesfreid, José Eduardo}, journal = {Journal of Fluid Mechanics}, pages = {386--406}, publisher = {Cambridge University Press}, title = {{Experiments on a jet in a crossflow in the low-velocity-ratio regime}}, doi = {10.1017/jfm.2018.974}, volume = {863}, year = {2019}, }