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  • One of the features that distinguishes biological systems is the wide range of scales in time and space on which processes and interactions occur. This is a form of complexity, but it is one that can sometimes be turned into an advantage. I will describe models for a couple of systems where my collaborators and I have found that to be the case. The first (from long ago) is a system with ladybugs preying on aphids. The ladybugs (which are highly mobile but reproduce slowly) experience the environment as a system of patches, while the aphids (which are much less mobile but reproduce quickly) experience each patch as spatial continuum. The second (more recent) is a system aimed at describing the evolution of dispersal. Dispersal starts with the movement of individuals, which can be observed by tracks or tracking and described in terms of random walks. That then produces spatial patterns, which then influence ecological interactions within and among populations. Those in turn exert selective pressure on traits that determine the spatial patterns, and finally the selective pressure together with the occasional the appearance of mutants results in the evolution of dispersal traits. All of these processes can, in some cases, operate on different scales in time and space. It turns out that this when this occurs it can be exploited to produce relatively simple models in some situations. The older research I will discuss was conducted in collaboration with Steve Cantrell; the newer was with Steve Cantrell, Mark Lewis, and Yuan Lou
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  • The study of nonequilibrium heat transport in molecular junctions (MJs) has gathered much attention in recent years due to its crucial role in the field of molecular electronics. To gain insight into the factors determining the heat currents in MJs, reduced models of MJs have been studied using both approximate and exact quantum dynamical methods. One such model, known as the nonequilibrium spin-boson (NESB) model, consists of a two-level system in contact with two harmonic oscillator baths at different temperatures. Recently, we developed a mixed quantum-classical framework for studying heat transport in MJs, which could enable the simulation of heat transport in more realistic models of MJs with many degrees of freedom [1]. In this talk, I will give an overview of this framework and discuss the ability of a novel mixed quantum-classical dynamics method, known as Deterministic Evolution of Coordinates with Initial Decoupled Equations (DECIDE) [2], for calculating the steady-state heat current in the NESB model in a variety of parameter regimes [3]. $$ $$ [1] Liu, J., Hsieh, C-Y., Segal, D., Hanna, G., J. Chem. Phys, 149, 224104 (2018). $$ $$ [2] Liu, J., Hanna, G., J. Phys. Chem. Lett., 9, 3928 (2018). $$ $$ [3] Carpio-Martinez, P., Hanna, G., J. Chem. Phys, in press.
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  • Nanotubular molecular self-aggregates are characterized by a high degree of symmetry and they are fundamental systems for light-harvesting and energy transport. While coherent effects are thought to be at the basis of their high efficiency, the relationship between structure, coherence and functionality is still an open problem. We analyze natural nanotubes present in Green Sulfur Bacteria. We show that they have the ability to support macroscopic coherent states, i.e. delocalized excitonic states coherently spread over many molecules, even at room temperature. Specifically, assuming a canonical thermal state we find, in natural structures, a large thermal coherence length, of the order of 1000 molecules. By comparing natural structures with other mathematical models, we show that this macroscopic coherence cannot be explained either by the magnitude of the nearest-neighbour coupling between the molecules, which would induce a thermal coherence length of the order of 10 molecules, or by the presence of long-range interactions between the molecules. Indeed we prove that the existence of macroscopic coherent states is an emergent property of such structures due to the interplay between geometry and cooperativity (superradiance and super-transfer). In order to prove that, we give evidence that the lowest part of the spectrum of natural systems is determined by a cooperatively enhanced coupling (super-transfer) between the eigenstates of modular sub-units of the whole structure. Due to this enhanced coupling strength, the density of states is lowered close to the ground state, thus boosting the thermal coherence length. As a striking consequence of the lower density of states, an energy gap between the excitonic ground state and the first excited state emerges. Such energy gap increases with the length of the nanotube (instead of decreasing as one would expect), up to a critical system size which is close to the length of the natural complexes considered. $$ $$ VIDEO-ABSTRACT: https://vimeo.com/313618747 $$ $$ REFERENCES: $$ $$ 1) Macroscopic coherence as an emergent property in molecular nanotubes, M. Gull; A. Valzelli; F. Mattiotti; M. Angeli; F. Borgonovi and G. L. Celardo; New J. Phys. 21 013019 (2019). $$ $$ 2) On the existence of superradiant excitonic states in microtubules G. L. Celardo; M. Angeli; T. J. A. Craddock and P. Kurian New J. Phys. 21 023005 (2019).
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  • I will give a treatment of tensor norms of C*-algebras and operator systems with the goal of explaining the major ideas behind Kirchberg's famous tensor product reformulation of Connes' Embedding Problem.
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  • To date, it is possible to design proteins with an improved function starting from known scaffolds. This design applies to the enhancement of enzymatic capabilities, inhibitors of protein-protein interactions, among others [1]. The next generation for the design of functional proteins will be guided by the approach known as template-free design. The goal of this approach is to design a sequence of amino acids that will have a predefined function. A more conservative approach seeks to find a chain of amino acids that will fold into a predefined backbone geometry. A central challenge to the latter approach is the side chain packing problem (SCPP) that aims to find a set of rotamers that minimizes a given scoring function, for a fixed backbone geometry associated to a candidate sequence. In this talk, we will define the computational model for the SCPP, analyze the results achieved by state-of-the-art packers, and determine a lower bound for the maximum achievable accuracy of a simple rotamer library [2]. We also show that a strong limitation to reduce the gap between state-of-the-art results and the maximum attainable accuracy is the scoring function. Furthermore, we show that the limitation in the scoring function is not related to an incorrect weighting of its components nor to the constrained geometry of the crystal [3]. <br> <b> [1]. P.S. Huang, S.E. Boyken, and D. Baker. ¨The coming of age of de novo protein design¨. Nature 537 (7620): 320 â 327, 2016. <br> [2]. J. Colbes, R.I. Corona, C. Lezcano, D. Rodriguez, C.A. Brizuela. â Protein aide-chain packing problem: is there still room for improvement.â Briefings in Bioinformatics, doi:10.1093/bib/bbw079, 2016. <br> [3]. J. Colbes, S. Aguila, C.A. Brizuela. â Scoring of side-chain packings: An analysis of weight factors and molecular dynamics structuresâ . Journal of Chemical Information and Modeling, 58 (2), 443-452, 2018.
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  • When investigating quantum or semiclassical phenomena in a general relativistic context one usually resorts to quantum field theory in curved spacetime. However, traditional quantization methods rely on foliating spacetime into spacelike hypersurfaces or on fixing asymptotic boundary conditions in time. This is a serious limitation if for the problem of interest no suitable Cauchy hypersurfaces exist and/or if boundary conditions are naturally given on timelike hypersurfaces, either at finite locations or asymptotically. I will outline methods of quantization adapted to such situations and the conceptual insights on which they are based. If time permits I will comment on how this may contribute to the search for a quantum theory of gravity.
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  • André Picard has written extensively on Canadian public health issues. His most recent books include A Matter of Life and Death: Public Health Issues in Canada, and The Path to Health Care Reform: Policies and Politics. He has been the recipient of the Canadian Nurses’ Association Award of Excellence for Health Care Reporting, the Nursing in the Media Award of the Registered Nurses Association of Ontario, the International Media Prize of Sigma Theta Tau (Nursing Honour Society) and the Science and Society Book Prize. Other honours include the Queen Elizabeth II Diamond Jubilee Medal, the Centennial Prize of the Pan-American Health Organization for top public health reporter in the Americas, and Canada’s top newspaper columnist at the 2009 National Newspaper Awards. Picard holds an honorary degree from UBC.
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  • We consider the problems of testing isomorphism of tensors, p-groups, cubic forms, algebras, and more, which arise from a variety of areas, including machine learning, group theory, and cryptography. Despite a perhaps seeming similarity with Graph Isomorphism, the current-best algorithms for these problems (when given by bases) are still exponential - for most of them, even q^{n^2} over GF(q). Similarly, while efficient practical software exists for Graph Isomorphism, for these problems even the best current software can only handle very small instances (e.g., 10 x 10 x 10 over GF(13)). This raises the question of finding new algorithmic techniques for these problems, and/or of proving hardness results. We show that all of these problems are equivalent under polynomial-time reductions, giving rise to a class of problems we call Tensor Isomorphism-complete (TI-complete). We further show that testing isomorphism of d-tensors for any fixed d (at least 3) is equivalent to testing isomorphism of 3-tensors. Using the same techniques, we show two first-of-their-kind results for Group Isomorphism (GpI): (a) a reduction from isomorphism of p-groups of exponent p and class c < p, to isomorphism of p-groups of exponent p and class 2, and (b) a search-to-decision reduction for the latter class of groups in time |G|^{O(log log|G|)}. We note that while p-groups of class 2 have long been believed to be the hardest cases of GpI, as far as we are aware this is the first reduction from any larger class to this class of groups. Finally, we discuss a way to apply combinatorial methods from Graph Isomorphism (namely, Weisfeiler-Leman) to Group and Tensor Isomorphism. Based on joint works with Vyacheslav V. Futorny and Vladimir V. Sergeichuk (Lin. Alg. Appl., 2019; arXiv:1810.09219), with Peter A. Brooksbank, Yinan Li, Youming Qiao, and James B. Wilson (arXiv:1905.02518), and with Youming Qiao (arXiv:190X.XXXXX).
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