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A Power Law of Order 1/4 for Critical Mean Field Swendsen-Wang Dynamics
Introduction Statement of the results Mixing time preliminaries Outline of the proof of Theorem 2.1 Random graph estimates Supercritical case Subcritical case Critical Case Fast mixing of the Swendsen-Wang process on trees Acknowledgements Bibliography
CEO’s Overbearing Love
Rumors had it that the Li Clan's CEO, Gao Fujun, had taken up two places. The one who was lacking was because he was too ugly, so he didn't dare to show it to others.Everyday, he would walk around holding the little girl's hand and watch movies. When necessary, he would stretch out his hand to break the peach blossoms behind the little woman's back, happy to not be together.Only then did people find out that Boss Li was not ugly at all. That little woman had picked up a treasure from the good fortune she had accumulated in her previous life.
CEO’s Overbearing Love
Rumors had it that the Li Clan's CEO, Gao Fujun, had taken up two places. The one who was lacking was because he was too ugly, so he didn't dare to show it to others.Everyday, he would walk around holding the little girl's hand and watch movies. When necessary, he would stretch out his hand to break the peach blossoms behind the little woman's back, happy to not be together.Only then did people find out that Boss Li was not ugly at all. That little woman had picked up a treasure from the good fortune she had accumulated in her previous life.
CEO’s Overbearing Love
Rumors had it that the Li Clan's CEO, Gao Fujun, had taken up two places. The one who was lacking was because he was too ugly, so he didn't dare to show it to others.Everyday, he would walk around holding the little girl's hand and watch movies. When necessary, he would stretch out his hand to break the peach blossoms behind the little woman's back, happy to not be together.Only then did people find out that Boss Li was not ugly at all. That little woman had picked up a treasure from the good fortune she had accumulated in her previous life.
CEO’s Overbearing Love
Rumors had it that the Li Clan's CEO, Gao Fujun, had taken up two places. The one who was lacking was because he was too ugly, so he didn't dare to show it to others.Everyday, he would walk around holding the little girl's hand and watch movies. When necessary, he would stretch out his hand to break the peach blossoms behind the little woman's back, happy to not be together.Only then did people find out that Boss Li was not ugly at all. That little woman had picked up a treasure from the good fortune she had accumulated in her previous life.
CEO’s Overbearing Love
Rumors had it that the Li Clan's CEO, Gao Fujun, had taken up two places. The one who was lacking was because he was too ugly, so he didn't dare to show it to others.Everyday, he would walk around holding the little girl's hand and watch movies. When necessary, he would stretch out his hand to break the peach blossoms behind the little woman's back, happy to not be together.Only then did people find out that Boss Li was not ugly at all. That little woman had picked up a treasure from the good fortune she had accumulated in her previous life.
CEO’s Overbearing Love
Rumors had it that the Li Clan's CEO, Gao Fujun, had taken up two places. The one who was lacking was because he was too ugly, so he didn't dare to show it to others.Everyday, he would walk around holding the little girl's hand and watch movies. When necessary, he would stretch out his hand to break the peach blossoms behind the little woman's back, happy to not be together.Only then did people find out that Boss Li was not ugly at all. That little woman had picked up a treasure from the good fortune she had accumulated in her previous life.
CEO’s Overbearing Love
Rumors had it that the Li Clan's CEO, Gao Fujun, had taken up two places. The one who was lacking was because he was too ugly, so he didn't dare to show it to others.Everyday, he would walk around holding the little girl's hand and watch movies. When necessary, he would stretch out his hand to break the peach blossoms behind the little woman's back, happy to not be together.Only then did people find out that Boss Li was not ugly at all. That little woman had picked up a treasure from the good fortune she had accumulated in her previous life.
Critical Population and Error Threshold on the Sharp Peak Landscape for a Moran Model
The goal of this work is to propose a finite population counterpart to Eigen's model, which incorporates stochastic effects. The author considers a Moran model describing the evolution of a population of size of chromosomes of length over an alphabet of cardinality . The mutation probability per locus is . He deals only with the sharp peak landscape: the replication rate is for the master sequence and for the other sequences. He studies the equilibrium distribution of the process in the regime where
Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture
In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form of the conjecture.
