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  • I will present a multiscale generalisation of the Bakry--Emery criterion for a measure to satisfy a Log-Sobolev inequality. It relies on the control of an associated PDE well known in renormalisation theory: the Polchinski equation. It implies the usual Bakry--Emery criterion, but we show that it remains effective for measures which are far from log-concave. Indeed, we prove that the massive continuum Sine-Gordon model on $R^2$ with $\beta < 6\pi$ satisfies asymptotically optimal Log-Sobolev inequalities for Glauber and Kawasaki dynamics. These dynamics can be seen as singular SPDEs recently constructed via regularity structures, but our results are independent of this theory. This is joint work with T. Bodineau.
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  • The advent of a new modeling paradigm known as â differentiable programmingâ makes possible bespoke machine-learned models of biological phenomena that are partly learned from data and partly informed by human-derived biophysical knowledge. In this talk I will describe three instantiations of this new approach for (i) de novo protein structure prediction, (ii) elucidation of the combinatorial grammar underlying metazoan signaling networks, and (iii) design of new protein function. In all cases qualitative improvements in model accuracy or speed, or both, are achieved using differentiable programming, enabling new scientific insights into biological macromolecules and the networks they comprise.
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  • About a third of the proteome consists of intrinsically disordered proteins (IDPs) that fold, whether fully or partially, upon binding to their partners [1]. IDPs use their inherent flexibility to play key regulatory roles in many biological processes [2]. Such flexibility makes their structural analysis extremely challenging, being nuclear magnetic resonance (NMR) the most suitable high-resolution technique. However, conventional NMR structure determination methods, which seek to determine a single high-resolution structure [3], are inadequate for IDPs. There are several tools available for the structural analysis of IDPs using NMR data and primarily Chemical Shifts (CS) [4-6]. However, a persistent problem is how to effectively sample the extensive, but not random, conformational space of IDPs. We have implemented a novel relational database, termed Glutton, that links all existing CS data with corresponding protein 3D structures with the goal of enabling the conformational analysis of IDPs directly from their experimental CS. Gluttonâ s uniqueness is in its focus on dihedral angle distributions consistent with a given set of CS rather than with unique structures. Such dihedral distributions define how native-like is the ensemble and lead to the effective calculation of large ensembles of structures that efficiently sample the available conformational space. With Glutton, we examined Nuclear Coactivator Binding Domain (NCBD), an IDP with NMR structure obtained using osmolyte stabilizers that is partly disordered in native conditions [7]. As means of comparison, we produced a 60ï ­s long MD simulation of NCBD in explicit solvent starting from the NMR structure and using the CHARMM36m force field with modified TIP3P water which was suggested as a good combination to explore the conformational space of IDPs [8]. The structural ensembles obtained from Glutton are based only on geometric considerations and CS restraints, but they can be further refined using additional computational (force field) and/or experimental (distance restraints) information. <p> <p> Acknowledgments: This work was supported by grants: the startup fund at the University of New Mexico, the W.M. Keck Foundation, the National Science Foundation [NSF-MCB-161759 and NSF-CREST-1547848] and the European Research Council [ERC-2012-AdG-323059]. <p> <p> [1] H.J. Dyson, P.E. Wright, Chem. Rev., 104, 3607â 3622, 2004 <p> [2] M.M. Babu, Biochem. Soc. Trans., 44, 1185â 1200, 2016 <p> [3] A.M., Gronenborn, G.M. Clore, Anal. Chem., 62, 2â 15, 1990 <p> [4] V. Ozenne, F. Bauer, L. Salmon, J. Huang, M.R. Jensen, S. Segard, P. Bernadó, C. Charavay, M. Blackledge, Bioinformatics, 28, 1463â 1470, 2012 <p> [5] M. Krzeminski, J.A. Marsh, C. Neale, W. Choy, J.D. Forman-Kay, Bioinformatics, 29, 398â 399, 2013 <p> [6] D.H. Brookes, T. Head-Gordon, J. Am. Chem. Soc., 138, 4530â 4538, 2016 <p> [7] A. Naganathan, M. Orozco, J. Am. Chem. Soc., 133, 12154â 12161, 2011 <p> [8] J. Huang, S. Rauscher, G. Nawrocki, T. Ran, M. Feig, B. L de Groot, H. Grubmüller, A.D. MacKerell Jr, Nat Methods, 14, 71â 73, 2017
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  • (Joint work with Y. Guo, E. Grenier and M. Suzuki) We consider the 2 fluid Euler-Poisson equation in 3d space and show that, when the mass of electron tends to 0, the solutions can be well approximated by the strong limit which solves the (1 fluid) Euler-Poisson equation for ions and an initial layer which disperses the excess electron density and velocity in short time. This is a singular limit, somewhat akin to the low-Mach number problem studied by Klainerman-Majda, Ukai and Metivier-Schochet, but in this case, the dispersive layer comes from a quasilinear equation involving coefficients depending on space and time (in fact depending on the strong limit), and the analysis relies on a local energy decay.
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  • Force-free electrodynamics (FFE) describes a particular regime of magnetically dominated relativistic plasmas, which arise on several astrophysical scenarios of interest such as pulsars or active galactic nuclei. In those regimes, the electromagnetic field obeys a modified nonlinear version of Maxwell equations, while the plasma only accommodates to locally cancel out the Lorentz force. The aim of the present talk is to discuss the initial/boundary value formulation of FFE at some given astrophysical settings. We start by showing that, when restricted to the correct constraint submanifold, the system is symmetric hyperbolic: we introduce here a particular hyperbolization for the FFE equations [1], following a covariant approach due to R. Geroch [2]. Then, we analyze the characteristic structure of the resulting evolution system and use this information to construct appropriate boundary conditions [3,4]. In particular, we focus on the treatment to mimic the perfectly conducting surface of a neutron star, where incoming and outgoing physical modes needs to be combined on a very precise way. We shall illustrate this procedure with the simpler vacuum (linear) electrodynamics. Also, we discuss the methods employed to deal with the constraints of the theory at the boundaries. And finally, we show some results from our 3D numerical simulations based on this approach [4,5,6]. [1] F. Carrasco, O. Reula. PRD (93), 2016. DOI: 10.1103/PhysRevD.93.085013 [2] R. Geroch. â Partial differential equations of physicsâ . In General Relativity, pp. 19-60. Routledge, 1996. [3] F. Carrasco, O. Reula. PRD (96), 2017. DOI: 10.1103/PhysRevD.96.063006 [4] F. Carrasco, C. Palenzuela, O. Reula. PRD (98), 2018. DOI: 10.1103/PhysRevD.98.023010 [5] F. Carrasco, D. Viganò. C. Palenzuela, J. Pons. MNRAS Letters (484), 2019. DOI: 10.1093/mnrasl/slz016 [6] R. Cayuso, F. Carrasco, B. Sbarato, O. Reula. (arXiv:1905.00178), 2019.
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  • The rigorous detection and quantification of non-Markovianity in open quantum systems has recently gained a lot of attention. Despite generating many insights on the mathematical side, the proposed quantifiers of non-Markovianity are very hard to compute in practice and the relation to more traditional quantities of physical interest is not clear. In the first part of my talk I will present a very simple, yet rigorous way to witness non-Markovianty, which is based on linear response theory. In the second part of my talk I will discuss when (and when not) temporal negativities of the entropy production rate imply non-Markovianity. This creates an important link between the mathematical concept of non-Markovianity and a physical observable, which quantifies the overall irreversibility of the open system dynamics.
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  • Ecological species can spread their extinction risk in an uncertain environment by adopting a bet-hedging strategy, i.e, by diversifying individual phenotypes. I will present a theory of bet-hedging for populations colonizing an unknown environment that fluctuates either in space or time. We find that diversification is more favorable for range expansion than in the well-mixed case, supporting the view that range expansions promote diversification. For slow rates of variation, spatial fluctuations open more opportunities for bet-hedging than temporal variations. Opportunities for bet-hedging reduce in the limit of frequent environmental variations. These conclusions are robust against demographic stochasticity induced by finite population sizes. Ref. P. Villa-Martin, M.A. Muñoz, S. Pigolotti, Plos Comp. Biol. 15(4): e1006529 (2019).
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