(A) We study in this paper some connections between the Fra¨ıssé theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures. A prime concern of topological dynamics is the study of continuous actions of (Hausdorff) topological groups G on (Hausdorff) compact spaces X. These are usually referred to as (co...

We propose a feasible experimental scheme to realize a three-dimensional chiral topological insulator with cold fermionic atoms in an optical lattice, which is characterized by an integer topological invariant distinct from the conventional Z(2) topological insulators and has a remarkable macroscopic zero-energy flat band. To probe its property, we show that its characteristic surface states--t...

Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational transitions that are associated with changes in molecular topology. For folded linear biomolecules, arrangement of intramolecular contacts is identified as a k...

When a vortex beam with a spiral phase structure passes through dynamic angular double slits (ADS), the interference pattern changes alternatively between destructive and constructive at the angular bisector of the ADS. This change is due to their phase difference. Based on this property, we experimentally demonstrate a simple method to precisely and efficiently determine the topological charge...

Another reason, no less compelling, for starting with Compactness is didactic: It makes it easier to grasp topological aspects of the notion (and the origin of its name). We can go deep in a topological direction, by explaining Compactness purely in terms of notions such as ultrafilters, ultraproducts, Hausdorff spaces, the finite-intersection property, and others, but that would take us furthe...

A new methodology that combines the generalized topological indices (GTI) and the down hill simplex optimisation procedure has been developed to search for optimised quantitative structure–property relationship models. The structural interpretation of the optimal molecular descriptors is attained analytically by means of the GTIs decomposition in terms of geodesics (shortest paths) in the molec...

We introduce a new topological semantics for evidence, evidencebased belief, knowledge and learning. This setting generalizes (and in a sense improves on) the evidence models for belief due to van Benthem and Pacuit, as well as our own previous work on (a topological semantics for) Stalnaker’s doxasticepistemic axioms. We prove completeness, decidability and finite model property for the associ...

The entire family of carefully oxygen-adjusted RBaCo2O5.5 or R2Ba2Co4O11 (R1⁄4Y, Ho–La) doubleperovskite oxides is systematically investigated for the lattice parameters, A-site cation disorder, and characteristic physical properties, i.e. the metal–insulator transition, ferromagnetic transition and socalled metamagnetic transition. With increasing size of the R constituent, the lattice paramet...

The dynamics of pressurized water networks are naturally modeled by differential-algebraic equations (DAE). This article investigates fundamental structural properties of such a DAE model under weak regularity assumptions. The usual algebraic index-1 condition is shown to be necessary and sufficient with respect to several index concepts, as well as sufficient for solvability in a strong sense....

This paper clarifies the relation between synchronization and graph topology. Applying the Connection Graph Stability method developed by Belykh et al. [2004a] to the study of synchronization in networks of coupled oscillators, we show which graph properties matter for synchronization. In particular, while we explicitly link the stability of synchronization with the average path length for a wi...