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Concept# Symmetry in biology

Résumé

Symmetry in biology refers to the symmetry observed in organisms, including plants, animals, fungi, and bacteria. External symmetry can be easily seen by just looking at an organism. For example, the face of a human being has a plane of symmetry down its centre, or a pine cone displays a clear symmetrical spiral pattern. Internal features can also show symmetry, for example the tubes in the human body (responsible for transporting gases, nutrients, and waste products) which are cylindrical and have several planes of symmetry.
Biological symmetry can be thought of as a balanced distribution of duplicate body parts or shapes within the body of an organism. Importantly, unlike in mathematics, symmetry in biology is always approximate. For example, plant leaves – while considered symmetrical – rarely match up exactly when folded in half. Symmetry is one class of patterns in nature whereby there is near-repetition of the pattern element, either by reflection or rotation.
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BIO-692: Symmetry and Conservation in the Cell

This course instructs students in the use of advanced computational models and simulations in cell biology. The importance of dimensionality, symmetry and conservation in models of self-assembly, membranes, and polymer/filament scaling laws reveals how cells exploit these principles in life.

ME-482: Biomechanics of the musculoskeletal system

The basis for a mechanical description of the musculoskeletal system are presented. This description is based on the concepts of solid mechanics, physiology and anatomy of the musculoskeletal system. Concrete examples of the development of implants are also covered.

BIO-372: Microbiology

This course will provide an introduction to fundamental concepts in microbiology. Special emphasis will be given to the surprising and often counter-intuitive physical world inhabited by microorganisms.

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La prédation est l'action de prendre, de capturer.
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Francesco Libbi, Nicola Marzari

Phonon-assisted luminescence is a key property of defect centers in semiconductors, and can be measured to perform the readout of the information stored in a quantum bit, or to detect temperature variations. The investigation of phonon-assisted luminescence usually employs phenomenological models, such as that of Huang and Rhys, with restrictive assumptions that can fail to be predictive. In this work, we predict luminescence and study exciton-phonon couplings within a rigorous many-body perturbation theory framework, an analysis that has never been performed for defect centers. In particular, we study the optical emission of the negatively charged boron vacancy in 2D hexagonal boron nitride, which currently stands out among defect centers in 2D materials thanks to its promise for applications in quantum information and quantum sensing. We show that phonons are responsible for the observed luminescence, which otherwise would be dark due to symmetry. We also show that the symmetry breaking induced by the static Jahn-Teller effect is not able to describe the presence of the experimentally observed peak at 1.5 eV.

Conformal Field Theories (CFTs) are crucial for our understanding of Quantum Field Theory (QFT). Because of their powerful symmetry properties, they play the role of signposts in the space of QFTs. Any method that gives us information about their structure, and lets us compute their observables, is therefore of great interest. In this thesis we explore the large quantum number sector of CFTs, by describing a semiclassical expansion approach. The idea is to describe the theory in terms of fluctuations around a classical background, which corresponds to a superfluid state of finite charge density. We detail the implementation of the method in the case of U (1)-invariant lagrangian CFTs defined in the epsilon-expansion. After introducing the method for generic correlators, we illustrate it by performing the computation of several observables.First, we compute the scaling dimension of the lowest operator having a given large charge n under the U (1) symmetry. We demonstrate how the semiclassical result in this case bridges the gap between the naive diagrammatic computation (which fails at too large n) and the general large-charge expansion of CFTs (which is only valid for n large enough).Second, we apply the method to the computation of 3- and 4-point functions involving the same operator. This lets us derive some of the OPE (Operator Product Expansion) coefficients.Finally, we consider the rest of the spectrum of charge-n operators, and propose a way to classify them by studying their free-theory equivalent. In the free theory, we construct the complete set of primary operators with number of derivatives bounded by the charge.We also find a mapping between the excited states of the superfluid and the vacuum states of standard quantization, which is valid when the spin of said states is bounded by the square root of the charge.

Two-dimensional systems with C2T (PT) symmetry exhibit the Euler class topology E is an element of Z in each two-band subspace realizing a fragile topology beyond the symmetry indicators. By systematically studying the energy levels of Euler insulating phases in the presence of an external magnetic field, we reveal the robust gaplessness of the Hofstadter butterfly spectrum in the flat-band limit, while for the dispersive bands the gapping of the Landau levels is controlled by a hidden symmetry. We also find that the Euler class E of a two-band subspace gives a lower bound for the Chern numbers of the magnetic subgaps. Our study provides new fundamental insights into the fragile topology of flat-band systems going beyond the special case of E = 1 as, e.g., in twisted bilayer graphene, thus opening the way to a very rich, still mainly unexplored, topological landscape with higher Euler classes.