Membrane Fluctuations Destabilize Clathrin Protein Lattice Order

ABSTRACTRaman spectroscopy is used in a variety of ways to monitor different aspects of the lattice damage caused by ion implantation into graphite. Particular attention is given to the use of Raman spectroscopy to monitor the restoration of lattice order by the annealing process, which depends critically on the annealing temperature and on the extent of the original lattice damage. At low fluences the highly disordered region is localized in the implanted region and relatively low annealing temperatures are required, compared with the implantation at high fluences where the highly disordered region extends all the way to the surface. At high fluences, annealing temperatures comparable to those required for the graphitization of carbons are necessary to fully restore lattice order.

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Membrane fluctuations mediate lateral interaction between cadherin bonds

Nature Physics ◽

10.1038/nphys4138 ◽

2017 ◽

Vol 13 (9) ◽

pp. 906-913 ◽

Cited By ~ 34

Author(s):

Susanne F. Fenz ◽

Timo Bihr ◽

Daniel Schmidt ◽

Rudolf Merkel ◽

Udo Seifert ◽

...

Keyword(s):

Lateral Interaction ◽

Membrane Fluctuations

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RATIONAL POLYHEDRA AND PROJECTIVE LATTICE-ORDERED ABELIAN GROUPS WITH ORDER UNIT

Communications in Contemporary Mathematics ◽

10.1142/s0219199712500174 ◽

2012 ◽

Vol 14 (03) ◽

pp. 1250017 ◽

Cited By ~ 10

Author(s):

LEONARDO CABRER ◽

DANIELE MUNDICI

Keyword(s):

Abelian Group ◽

Algebraic Topology ◽

Lattice Structure ◽

Order Unit ◽

Finitely Generated ◽

Lattice Order ◽

Translation Invariant ◽

Projective Lattice ◽

Rational Polyhedra ◽

Finitely Presented

An ℓ-groupG is an abelian group equipped with a translation invariant lattice-order. Baker and Beynon proved that G is finitely generated projective if and only if it is finitely presented. A unital ℓ-group is an ℓ-group G with a distinguished order unit, i.e. an element 0 ≤ u ∈ G whose positive integer multiples eventually dominate every element of G. Unital ℓ-homomorphisms between unital ℓ-groups are group homomorphisms that also preserve the order unit and the lattice structure. A unital ℓ-group (G, u) is projective if whenever ψ : (A, a) → (B, b) is a surjective unital ℓ-homomorphism and ϕ : (G, u) → (B, b) is a unital ℓ-homomorphism, there is a unital ℓ-homomorphism θ : (G, u) → (A, a) such that ϕ = ψ ◦ θ. While every finitely generated projective unital ℓ-group is finitely presented, the converse does not hold in general. Classical algebraic topology (à la Whitehead) is combined in this paper with the Włodarczyk–Morelli solution of the weak Oda conjecture for toric varieties, to describe finitely generated projective unital ℓ-groups.

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Commutative L-algebras and measure theory

Forum Mathematicum ◽

10.1515/forum-2020-0317 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Wolfgang Rump

Keyword(s):

Measure Theory ◽

Measurable Space ◽

Universal Covering ◽

Continuous Functions ◽

Stone Space ◽

Integration Theory ◽

General Measure ◽

Lattice Order ◽

Finitely Additive Measures ◽

Additive Measures

Abstract Measure and integration theory for finitely additive measures, including vector-valued measures, is shown to be essentially covered by a class of commutative L-algebras, called measurable algebras. The domain and range of any measure is a commutative L-algebra. Each measurable algebra embeds into its structure group, an abelian group with a compatible lattice order, and each (general) measure extends uniquely to a monotone group homomorphism between the structure groups. On the other hand, any measurable algebra X is shown to be the range of an essentially unique measure on a measurable space, which plays the role of a universal covering. Accordingly, we exhibit a fundamental group of X, with stably closed subgroups corresponding to a special class of measures with X as target. All structure groups of measurable algebras arising in a classical context are archimedean. Therefore, they admit a natural embedding into a group of extended real-valued continuous functions on an extremally disconnected compact space, the Stone space of the measurable algebra. Extending Loomis’ integration theory for finitely additive measures, it is proved that, modulo null functions, each integrable function can be represented by a unique continuous function on the Stone space.

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