TITLE: Asymptotic depth of invariant chains of edge ideals
ABSTRACT: We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and their proofs also reveal surprising combinatorial and topological properties of corresponding graphs and their independence complexes. In particular, we are able to determine the asymptotic behavior of all reduced homology groups of these independence complexes. This is joint work with T.Q. Hoa, D.T. Hoang, D.V. Le and T.T. Nguyen.
TITLE: Asymptotic depth of invariant chains of edge ideals
ABSTRACT: We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and their proofs also reveal surprising combinatorial and topological properties of corresponding graphs and their independence complexes. In particular, we are able to determine the asymptotic behavior of all reduced homology groups of these independence complexes. This is joint work with T.Q. Hoa, D.T. Hoang, D.V. Le and T.T. Nguyen.
Telegram is riding high, adding tens of million of users this year. Now the bill is coming due.Telegram is one of the few significant social-media challengers to Facebook Inc., FB -1.90% on a trajectory toward one billion users active each month by the end of 2022, up from roughly 550 million today.
Telegram and Signal Havens for Right-Wing Extremists
Since the violent storming of Capitol Hill and subsequent ban of former U.S. President Donald Trump from Facebook and Twitter, the removal of Parler from Amazon’s servers, and the de-platforming of incendiary right-wing content, messaging services Telegram and Signal have seen a deluge of new users. In January alone, Telegram reported 90 million new accounts. Its founder, Pavel Durov, described this as “the largest digital migration in human history.” Signal reportedly doubled its user base to 40 million people and became the most downloaded app in 70 countries. The two services rely on encryption to protect the privacy of user communication, which has made them popular with protesters seeking to conceal their identities against repressive governments in places like Belarus, Hong Kong, and Iran. But the same encryption technology has also made them a favored communication tool for criminals and terrorist groups, including al Qaeda and the Islamic State.
