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  • We will start with an expository overview of various approaches and equivalences to the Connes Embedding Problem and then focus on three of Slofstraâ s contributions.
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  • The results of blind prediction of the structures of monomeric and oligomeric proteins obtained in the recent CASP/CAPRI experiment by the KIAS-Gdansk/Czaplewski groups, by using the physics-based coarse-grained UNRES force field [1] and information from databases are presented. For both monomeric and oligomeric targets, the methodology of the KIAS-Gdansk/Czaplewski groups included extensive conformational search by means of the Multiplexed Replica Exchange Molecular Dynamics (MREMD) simulations [2] with the UNRES force field [3], with geometry restraints from server models [4,5]. For the monomeric targets, the restraints were derived from fragments with similar geometry that occured in the server models (the consensus fragments), while monomer geometries except for the terminal, flexible loop, and linker regions, were restrained in oligomer simulations. The server models were selected mainly based on DeepQA score [6] ranking; when the score was below 0.5, models from the servers which performed well in previous CASP exercises: Zhang, Quark, and BAKER-ROSETTASERVER were selected. For oligomeric targers, monomers were modeled first and, subsequently, initial oligomeric structures were modeled based with the aid of the packing proposed by the HHpred server [7]; for smaller targets the monomers were oriented randomly. The results of MREMD simulations were processed by using the Weighted Histogram Analysis Method (WHAM) [8] to obtain the probabilities of conformations and subsequently subjected to cluster analysis to obtain the 5 (CASP) or 10 (CAPRI) families of conformations, from which the conformations closest to the mean conformations were, in turn, selected as candidate predictions [1], which were subsequently converted to all-atom conformations submitted to CASP/CAPRI. The obtained models were ranked solely based on the computed probabilities of the families obtained by summing up the probabilities of the constituent conformations computed by WHAM based on the UNRES effective function [1]. <br> <br> Acknowledgments: This research was supported by grant UMO-2017/26/M/ST4/00044 from the National Science Centre of Poland (Narodowe Centrum Nauki). <br> <br> [1] A. Liwo et al., J. Mol. Model. 20 (2014): 2306. <br> [2] Y.M. Rhee et al., Biophys. J. 84 (2003): 775-786. <br> [3] C. Czaplewski et al., J. Chem. Theor. Comput. 5 (2009): 627-640. <br> [4] P. Krupa et al., J. Chem. Inf. Model. 55 (2015): 1271-1281. <br> [5] M. Mozolewska et al., J. Chem. Inf. Model. 56 (2016): 2263-2279. <br> [6] R. Cao et al., BMC Bioinformatics. 17 (2016): 495. <rb> [7] L. Zimmermann et al., J Mol Biol. 430 (2018): 2237-2243. <br> [8] S. Kumar et al., J. Comput. Chem., (2001) 8, 1011-1021.
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  • A short summary of the well-posed IBVP for the vacuum Einstein field equations in harmonic coordinates formulated in Comm. Math. Phys. 289, 1099-1129 (2009) will be provided.
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  • The interplay between coherent and dissipative processes that governs both bio-inspired as well as engineered quantum networks supports a rich tapestry of non-equilibrium phenomena. These hold promise for enabling quantum-enhanced light harvesting, molecular electronics, generation of thermopower, and nanoscale sensing. A theoretical challenge consists of developing well-founded and tractable models for exploring the dynamics of systems that are simultaneously strongly coupled to more than one environment, for instance through interactions with surrounding electromagnetic and vibrational modes â typical for many networks comprised of condensed matter nanostructures. In this talk, I will cover our recent work in this area, with a particular focus on master equation approaches.
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  • Biological evolution can be described as a population climbing a fitness landscape, and has inspired a variety of derivative-free optimization algorithms. Here we describe how phenotype evolution has sophisticated optimization properties. In particular, natural selection approximates second order gradient descent (Newton's method), and recombination is efficient in generating diversity. We use these insights to design a new type of derivative-free optimization algorithm for continuous problems.
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  • The sunflower conjecture is one of the famous open problems in combinatorics. In attempting to improve the current known bounds, we discovered connections to objects studies in TCS, such as randomness extractors and DNFs, as well as to new questions in pseudo-randomness. I will describe some of these connections and the many open problems that arise. Based on joint works with Ryan Alweiss, Xin Li, Noam Solomon and Jiapeng Zhang.
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  • Over the last ten years high-throughput sequencing has enabled increasingly quantitative measurements of the diversity of lymphocyte receptor repertoires. A striking finding of these sequencing efforts has been that the clone sizes of cells sharing the same receptor are heavy-tail distributed. Here, we present a simple neutral birth-death model for immune repertoire formation in which all cells compete for a global resource. Homeostatic control of proliferation leads to a founder effect, in which large clones emerge early when there is less competition. We show that this mechanism produces a transient but long-lived regime of power-law scaling of clone sizes. A reanalysis of a cohort study shows that indeed early founded T cell clones are over-represented among the most abundant clones. We use data about how the founder effect diminishes over time to constrain how much peripheral selection impacts immune repertoire dynamics. Overall, our work suggests that dynamical processes early in life have a strong and long-lasting influence on the structure of the immune repertoire.
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  • Tsirelson's problem asks a question about modeling locality in quantum mechanics; roughly speaking, whether the tensor product and commuting models for specifying bipartite correlations are equivalent. Ozawa showed that Tsirelson's problem is equivalent to Connes' Embedding Problem In the talk I will start from Tsirelson's problem and outline a possible approach to its resolution that goes through the theory of nonlocal games in quantum information and interactive proofs in complexity theory. The talk will be introductory and largely based on the work of others, including Navascues, Pironio and Acin, and Doherty, Liang, Toner, and Wehner. I will not assume any background in complexity theory.
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