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Our molecular simulations reveal that wild-type influenza fusion peptides are able to stabilize a highly fusogenic pre-fusion structure, i.e. a peptide bundle formed by four or more trans-membrane arranged fusion peptides. We rationalize that the lipid rim around such bundle has a non-vanishing rim energy (line-tension), which is essential to (i) stabilize… (More)
Motivated by mirror symmetry, we consider a Lagrangian fibra-tion X → B and Lagrangian maps f : L ֒→ X → B, when L has dimension 2, exhibiting an unstable singularity, and study how their caustic changes, in a neighbourhood of the unstable singularity, when slightly perturbed. The integral curves of ∇f x , for x ∈ B, where f x (y) = f (y) − x · y, called "… (More)
Motivated by mirror symmetry, we consider the Lagrangian fibration R 4 → R 2 and Lagrangian maps f : L ֒→ R 4 → R 2 , exhibiting an unstable singularity, and study how the bifurcation locus of gradient lines, the integral curves of ∇f x , for x ∈ B, where f x (y) = f (y) − x · y, changes when f is slightly perturbed. We consider the cases when f is the germ… (More)
The formation of an hourglass-shaped passage (stalk) connecting two apposed membranes is an essential initial step in membrane fusion. The most probable transition path from two separate membranes to a stalk, i.e., the minimum free-energy path (MFEP), is constructed using a combination of particle simulations and string method. For the reversible transition… (More)
Given the Lagrangian fibration T 4 → T 2 and a Lagrangian submanifold, exhibiting an elliptic umbilic and supporting a flat line bundle, we study, in the context of mirror symmetry, the " quantum " corrections necessary to solve the monodromy of the holomorphic structure of the mirror bundle on the dual fibration.
Quantum corrections to the holomorphic structure of the mirror bundle along the caustic and the bifurcation locus Abstract. Given, in the Lagrangian torus fibration R 4 → R 2 , a Lagrangian submanifold L, endowed with a trivial flat connection, the corresponding mirror object is constructed on the dual fibration by means of a family of Morse homologies… (More)
Given any Morse function f on a Whitney stratified complex analytic variety of complex dimension n, we prove the existence of a stratified gradient-like vector field for f such that the unstable set of a critical point p on a stratum S of complex dimension s has real dimension m(p) + n − s as was conjectured by Goresky and MacPherson.