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  • The Harish-Chandra/Itzykson-Zuber integral and its additive counterpart, the Brezin-Gross-Witten integral, play an important role in random matrix theory. I will present recent work which proves a longstanding conjecture on the large dimension asymptotic behavior of these special functions.
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  • The performance enhancements observed in various models of continuous quantum thermal machines have been linked to the buildup of coherences in a preferred basis. But, is this connection always an evidence of 'quantum-thermodynamic supremacy' By force of example, we show that this is not the case. In particular, we compare a power-driven three-level continuous quantum refrigerator with a four-level combined cycle, partly driven by power and partly by heat. We focus on the weak driving regime and find the four-level model to be superior since it can operate in parameter regimes in which the three-level model cannot, it may exhibit a larger cooling rate, and, simultaneously, a better coefficient of performance. Furthermore, we find that the improvement in the cooling rate matches the increase in the stationary quantum coherences exactly. Crucially, though, we also show that the thermodynamic variables for both models follow from a classical representation based on graph theory. This implies that we can build incoherent stochastic-thermodynamic models with the same steady-state operation or, equivalently, that both coherent refrigerators can be emulated classically. More generally, we prove this for any $N$-level weakly driven device with a 'cyclic' pattern of transitions. Therefore, even if coherence is present in a specific quantum thermal machine, it is often not essential to replicate the underlying energy conversion process.
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  • Machine learning models are usually trained by a large number of observations (big data) to make predictions through the evaluation of complex mathematical objects. However, in many applications in science, particularly in quantum dynamics, obtaining observables is expensive so information is limited. In the present work, we consider the limit of â small dataâ . Usually, â big dataâ are for machines and â small dataâ are for humans, i.e. humans can infer physical laws given a few isolated observations, while machines require a huge array of information for accurate predictions. Here, we explore the possibility of machine learning that could build physical models based on very restricted information. In this talk, I will show how to build such models using Bayesian machine learning and how to apply such models to inverse problems aiming to infer the Hamiltonians from the dynamical observables. I will illustrate the methods by two applications: (1) the inverse problem in quantum reaction dynamics aiming to construct accurate potential energy surfaces based on reaction dynamics observables; (2) the model selection problem aiming to derive the particular lattice model Hamiltonian that gives to rise to specific quantum transport properties for particles in a phonon field.
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  • Existing proofs that deduce BPP=P from circuit lower bounds convert randomized algorithms into deterministic algorithms with a large polynomial slowdown. We convert randomized algorithms into deterministic ones with little slowdown. Specifically, assuming exponential lower bounds against nondeterministic circuits, we convert any randomized algorithm that errs rarely into a deterministic algorithm with a similar running time (with pre-processing), and any general randomized algorithm into a deterministic algorithm whose runtime is slower by a nearly linear multiplicative factor. Our results follow from a new, nearly optimal, explicit pseudorandom generator fooling circuits of size s with seed length (1+alpha)log s for an arbitrarily small constant alpha>0, under the assumption that there exists a function f in E that requires nondeterministic circuits of size at least 2^{(1-alpha')n}, where alpha = O(alpha'). The construction uses, among other ideas, a new connection between pseudoentropy generators and locally list recoverable codes.
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  • Processes induced by natural light (e.g. photosynthesis, vision) display properties distinct from those often studied in the laboratory using pulsed laser irradiation. The natural processes display complexities associated with systems operating in steady state and coupled to both an irradiative bath as well as a thermal protein environment. $$ $$ We have examined assorted problems associated with such systems, such as the presence or absence of stationary coherences, tests for the range of validity of secular vs nonsecular treatments, the generation of coherences under naturally slow turn-on of the radiation, rates of radiationless process under solar radiation, etc. Several of these will be described in this talk, with the remainder left for discussion during the meeting.
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  • Intrinsically disordered proteins are notorious for their conformational flexibility and capacity for interaction with different targets by acquiring distinct conformations depending on the specifics of the binding site. They can also engage in specific interactions without loosing conformational freedom, forming fuzzy complexes. The particular conformations favored by these proteins can be tuned by posttranslational modifications, such as phosphorylation. A common experimental strategy to study the effect of phosphorylation is to perform mutations of the modified residues by aspartate (D) or glutamate (E), under the assumption that the main effect of phosphorylation is the inclusion of negative charge. Whether the mutation to D or E is equivalent to phosphorylation is case dependent. In this work we explore the conformational landscape of an intrinsically disordered region at the C-terminus of adenoviral protein E1B55kDa, which is regulated by phosphorylation at three residues at the C-terminus, with the aim of establishing whether mutation to D or E is equivalent to modification by phosphorylation. In the context of the complete virus, the triple mutant with Ds produces a more efficient virus compared to wild type, and mutation to alanine (A), which cannot be phosphorylated, is equivalent to not having the full protein. We chose the last 20 residues of E1B55kDa as our reference peptide, as multiple disorder predictors consider it to be disordered. This peptide has only one cationic residue (arginine 9), and the C-terminal half is enriched in negative residues. We submitted the wild type sequence to Pepfold3, and obtained 100 different structures for it. Taking these as a reference, we built versions with three phosphorylated residues (two serines and one threonine), three Ds, three Es and three As. We placed each peptide in a water box with 0.15M NaCl using Charmm-gui, and ran it in NAMD in the NPT ensemble at 298K and 1 atm with the Charmm36m forcefield for 50 ns, achieving a total simulated time of 5 µs for each peptide variant. The distribution of the radius of gyration shows the prevalence of extended structures, with a slightly expanded ensemble for the triple D and triple E variants, and a slightly compressed one for the phosphorylated version, compared to the wild type. This is reflected in almost saturated hydration for the peptide in all its residues, except for a small decrease in hydration number for arginine 9 in the phosphorylated version. A closer look at intrapeptide hydrogen bonds reveals that there are few interactions in general, but arginine 9 engages in many more interactions with the phosphorylated residues than with the other charges in the peptide; the interaction with phosphorylated threonine 19 is preferred above all. This interaction leads to the formation of a loop that prefers to adopt disordered conformations, so we propose that it engages in fuzzy complexes with other proteins. In general, phosphorylation leads to an increase in alpha helix formation in the peptide, while substitution for Ds and Es leads to a loss of this structure. We conclude that phosphorylation and the mutation to D and E are not equivalent. <br> <br> Acknowledgments: This research was supported by a CONACYT scholarship for MARM and supercomputing time at the Laboratorio Nacional de Supercómputo del Sureste (LNS), LANCAD in México City, and the Laboratorio de Dinámica de Proteínas at UAEM.
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  • In order to justify certain model equations proposed in the biophysics literature for charge transport on polymers like DNA and protein, we consider a general class of discrete nonlinear Schroedinger equations on lattices, and prove that in the continuum limit, the limiting dynamics are given by a nonlinear Schroedinger equation (NLS) with a fractional Laplacian. In particular, a range of fractional powers arise from long-range lattice interactions in this limit, whereas the usual NLS with the non-fractional Laplacian arises from short-range interactions. We also obtain equations of motion for the expected position and momentum, the fractional counterpart of the well-known Newtonian equations of motion for the standard Schroedinger equation, and use a numerical method to suggest that the nonlocal Laplacian introduces decoherence, but that effect can be mitigated by the nonlinearity. Joint work with Gigliola Staffilani, Enno Lenzmann, and Yanzhi Zhang. Time permitting, I will talk about recent work defining biophysical machines that out-perform Turing machines, in joint work with Onyema Osuagwu and Daniel Inafuku.
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  • The attached file is a supplements to the author’s master’s thesis at https://circle.library.ubc.ca/handle/2429/72979
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