We present two main theorems along the lines of Lyapunov’s second method that guarantee asymptotic state consensus in multi-agent systems of agents in R with switching interconnection topologies. The two theorems complement each other in the sense that the first one is formulated in terms of the states of the agents in the multi-agent system, whereas the second one is formulated in terms of the...

We propose a two-stage optimization approach for protein folding simulation in the FCC lattice, inspired from the phenomenon of hydrophobic collapse. Given a protein sequence, the first stage of the approach produces compact protein structures with the maximal number of contacts among hydrophobic monomers, using the CPSP tools for optimal structure prediction in the HP model. The second stage u...

Using techniques of Kimchi and Magidor, we generalize an earlier result and show that it is relatively consistent for the first n strongly compact cardinals to be somewhat supercompact yet not fully supercompact. The class of strongly compact cardinals is, without a doubt, one of the most peculiar in the entire theory of large cardinals. As is well known, the class of strongly compact cardinals...

Essential א0-categoricity; i.e., א0-categoricity in some full countable language, is shown to be a robust notion for strongly minimal compact complex manifolds. Characterisations of triviality and essential א0-categoricity are given in terms of complex-analytic automorphisms, in the simply connected case, and correspondences in general. As a consequence it is pointed out that an example of McMu...

We prove four theorems concerning the number of normal measures a non-(κ+ 2)-strong strongly compact cardinal κ can carry.

An algebra of bounded linear operators on a Hilbert space is called strongly compact whenever each of its bounded subsets is relatively compact in the strong operator topology. The concept is most commonly studied for two algebras associated with a single operator T : the algebra alg(T ) generated by the operator, and the operator’s commutant com(T ). This paper focuses on the strong compactnes...

We construct three models in which there are different relationships among the classes of strongly compact, strong, and non-strong tall cardinals. In the first two of these models, the strongly compact and strong cardinals coincide precisely, and every strongly compact/strong cardinal is a limit of non-strong tall cardinals. In the remaining model, the strongly compact cardinals are precisely c...

A surprising consequence of non-linear flavor evolution is the spontaneous breaking initial symmetries neutrino gas propagating in a dense astrophysical environment. We explore conversion physics by taking into account polar and azimuthal angular distributions neutrinos present very first example symmetry context fast mixing nonlinear regime. Intriguingly, we find that does not always develop p...

In this paper we provide the derivation of a super compact pairwise model with only 4 equations in the context of describing susceptible-infected-susceptible (SIS) epidemic dynamics on heterogenous networks. The super compact model is based on a new closure relation that involves not only the average degree but also the second and third moments of the degree distribution. Its derivation uses an...