Riccati equation for simulation of leads in quantum transport

Bravi, Malko; Farchioni, Riccardo; Grosso, Giuseppe; Parravicini, Giuseppe Pastori

doi:10.1103/physrevb.90.155445

Cited by 8 publications

(7 citation statements)

References 29 publications

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“…backwards in time, starting from the final boundary conditionμ b|s (T ) = 0. This is consistent with the theory of conditional Markov processes, for which calculating conditional distributions requires information to propagate both forward and backward in time (see also [48]). Note that unlike the marginal auxiliary means, the conditional auxiliary means can be nonzero as long as the subnetwork auxiliary variables we condition on are also nonzero.…”

Section: Nonlinear Memorysupporting

confidence: 87%

Statistical physics approaches to subnetwork dynamics in biochemical systems

Bravi¹,

Sollich²

2017

Phys. Biol.

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We apply a Gaussian variational approximation to model reduction in large biochemical networks of unary and binary reactions. We focus on a small subset of variables (subnetwork) of interest, e.g. because they are accessible experimentally, embedded in a larger network (bulk). The key goal is to write dynamical equations reduced to the subnetwork but still retaining the effects of the bulk. As a result, the subnetwork-reduced dynamics contains a memory term and an extrinsic noise term with non-trivial temporal correlations. We first derive expressions for this memory and noise in the linearized (Gaussian) dynamics and then use a perturbative power expansion to obtain first order nonlinear corrections. For the case of vanishing intrinsic noise, our description is explicitly shown to be equivalent to projection methods up to quadratic terms, but it is applicable also in the presence of stochastic fluctuations in the original dynamics. An example from the epidermal growth factor receptor signalling pathway is provided to probe the increased prediction accuracy and computational efficiency of our method.

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Section: Nonlinear Memorysupporting

confidence: 87%

Statistical physics approaches to subnetwork dynamics in biochemical systems

Bravi¹,

Sollich²

2017

Phys. Biol.

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“…However, currently available databases [27, 49] do not contain sufficiently diverse epitopes to train models that would generalize to unseen epitopes [56]. A further complication is that multiple TCR specificity motifs may co-exist even for a single epitope [30, 57], which cannot be captured by linear models [58]. Progress will be made possible by a combination of high-throughput experiments assaying many TCR-epitope pairs [59], and machine learning based techniques such as soNNia.…”

Section: Discussionmentioning

confidence: 99%

Deep generative selection models of T and B cell receptor repertoires with soNNia

Isacchini

Walczak

Mora

et al. 2020

Preprint

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Subclasses of lymphocytes carry different functional roles to work together to produce an immune response and lasting immunity. Additionally to these functional roles, T and B-cell lymphocytes rely on the diversity of their receptor chains to recognize different pathogens. The lymphocyte subclasses emerge from common ancestors generated with the same diversity of receptors during selection processes. Here we leverage biophysical models of receptor generation with machine learning models of selection to identify specific sequence features characteristic of functional lymphocyte repertoires and subrepertoires. Specifically using only repertoire level sequence information, we classify CD4+ and CD8+ T-cells, find correlations between receptor chains arising during selection and identify T-cells subsets that are targets of pathogenic epitopes. We also show examples of when simple linear classifiers do as well as more complex machine learning methods.

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“…9 and 10, we can calculate the density of states (DOS) at the 1D surface (parallel to x, normal to z). First, the Green's function is found by solving Dyson's equation 35,36 g…”

Section: Generic Surface Spin Splittingmentioning

confidence: 99%

Illuminating "spin-polarized" Bloch wave-function projection from degenerate bands in decomposable centrosymmetric lattices

Appelbaum

2018

Phys. Rev. B

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The combination of space inversion and time reversal symmetries results in doubly-degenerate Bloch states with opposite spin. Many lattices with these symmetries can be constructed by combining a noncentrosymmetric potential (lacking this degeneracy) with its inverted copy. Using simple models, we unravel the evolution of local spin-splitting during this process of inversion symmetry restoration, in the presence of spin-orbit interaction and sublattice coupling. Importantly, through an analysis of quantum mechanical commutativity, we examine the difficulty of identifying states that are simultaneously spatially segregated and spin polarized. We also explain how surface-sensitive experimental probes (such as angle-resolved photoemission spectroscopy, or ARPES) of 'hidden spin polarization' in layered materials are susceptible to unrelated spin splitting intrinsically induced by broken inversion symmetry at the surface.

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Riccati equation for simulation of leads in quantum transport

Cited by 8 publications

References 29 publications

Statistical physics approaches to subnetwork dynamics in biochemical systems

Statistical physics approaches to subnetwork dynamics in biochemical systems

Deep generative selection models of T and B cell receptor repertoires with soNNia

Illuminating "spin-polarized" Bloch wave-function projection from degenerate bands in decomposable centrosymmetric lattices

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