Geometrical smeariness – a new phenomenon of Fréchet means

Fréchet Means for Distributions of Persistence Diagrams

Given a distribution ρ on persistence diagrams and observations X1, ...Xn iid ∼ ρ we introduce an algorithm in this paper that estimates a Fréchet mean from the set of diagrams X1, ...Xn. If the underlying measure ρ is a combination of Dirac masses ρ = 1 m ∑m i=1 δZi then we prove the algorithm converges to a local minimum and a law of large numbers result for a Fréchet mean computed by the alg...

Fréchet Means of Curves for Signal

Probabilistic Fréchet Means and Statistics on Vineyards

In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [21], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (Dp,Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a f...

Quantum Computation by Geometrical Means

A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we present an explicit construction of a universal set of gates, represented by holonomies acting on degenerate states. 1. Prologue Abelian [Sha] and non-abelian [...

Scientific-academic narcissism a new phenomenon in academic settings

Narcissism is a type of personality disorder in which a person considers himself great and important and exaggeratedly feels capable and worthy. One of the places in which this disorder can occur is at the university level. The symptoms of this type of disorder can be seen in some faculty members and it seems that these people also have some kind of scientific-academic narcissism disorder. In t...