Singular Points of Reducible Sextic Curves

There are 106 individual types of singular points for reducible complex sextic curves.</jats:p

Singular Points of Real Quartic and Quintic Curves

There are thirteen types of singular points for irreducible real quartic curves and seventeen types of singular points for reducible real quartic curves. This classification is originally due to D. A. Gudkov. There are nine types of singular points for irreducible complex quartic curves and ten types of singular points for reducible complex quartic curves. There are 42 types of real singular points for irreducible real quintic curves and 49 types of real singular points for irreducible real quintic curves. The classification of real singular points for irreducible real quintic curves is originally due to Golubina and Tai. There are 28 types of singular points for irreducible complex quintic curves and 33 types of singular points for reducible complex quintic curves. We derive the complete classification with proof by using the computer algebra system Maple. We clarify that the classification is based on computing just enough of the Puiseux expansion to separate the branches. Thus, the proof consists of a sequence of large symbolic computations that cam be done nicely using Maple

Singular Points of Real Sextic Curves I

A complete classification of the individual types of singular points is given for irreducible real sextic curves. This classification is derived by using the computer algebra system Maple. There are 191 types of singular points for real irreducible sextic curves. We clarify that the classification is based on computing just enough of the Puiseux expansion to separate the branches. A significant portion of the proof consists of a sequence of large symbolic computations that can be done nicely using Maple

Singular Points of Reducible Sextic Curves

There are 106 individual types of singular points for reducible complex sextic curves.Comment: 11 page

Mirroring to Build Trust in Digital Assistants

We describe experiments towards building a conversational digital assistant that considers the preferred conversational style of the user. In particular, these experiments are designed to measure whether users prefer and trust an assistant whose conversational style matches their own. To this end we conducted a user study where subjects interacted with a digital assistant that responded in a way that either matched their conversational style, or did not. Using self-reported personality attributes and subjects' feedback on the interactions, we built models that can reliably predict a user's preferred conversational style.Comment: Preprin

Two loop stress-energy tensor for inflationary scalar electrodynamics

We calculate the expectation value of the coincident product of two field strength tensors at two loop order in scalar electrodynamics on de Sitter background. The result agrees with the stochastic formulation which we have developed in a companion paper [2] for the nonperturbative resummation of leading logarithms of the scale factor. When combined with a previous computation of scalar bilinears [1], our current result also gives the two loop stress-energy tensor for inflationary scalar electrodynamics. This shows a secular decrease in the vacuum energy which derives from the vacuum polarization induced by the inflationary production of charged scalars.Comment: 62 pages, 1 eps figur