Abstract. In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics p. Let g be such a series, then g has a fixed point at the origin and the corresponding lower ramification numbers of g are then, up to a constant, the degree of the first non-linear term of p-power iterates of g. The result is a complete characterization of power series g having ramification numbers of the form 2(1 + p + · · · + p n ). Furthermore, in proving said characterization we explicitly compute the first significant terms of g at its pth iterate.

In this paper we study the geometric location of periodic points of power series defined over fields of positive characteristic p. We find a lower bound for the norm of all nonzero periodic points in the open unit disk of 2-ramified power series. We prove that this bound is optimal for a large class of power series. Our main technical result is a computation of the first significant terms of p-power iterates of 2-ramified power series. As a by-product we obtain a self-contained proof of the characterization of 2-ramified power series.

In this paper we consider wildly ramified power series, i.e., power series defined over a field of positive characteristic, fixing the origin, where it is tangent to the identity. In this setting we introduce a new invariant under change of coordinates called the second residue fixed point index. As the name suggests this invariant is closely related to the residue fixed point index, and they coincide in the case that the power series have small multiplicity. Finally, we characterize power series with large multiplicity having the smallest possible multiplicity at the origin under iteration, in terms of this new invariant.

Most previous work related to tweet classification have focused on identifying a given tweet as a spam, or to classify a Twitter user account as a spammer or a bot. In most cases the tweet classification has taken place offline, on a pre-collected dataset of tweets. In this paper we present an on-the-fly approach to classify each newly downloaded tweet as autogenerated or not. We define an autogenerated tweet (AGT) as a tweet where all or parts of the natural language content is generated automatically by a bot or other type of program.Our on-the-fly approach makes use of two classifiers. The first classifies a tweet solely based on the twitter text and the tweet metadata that comes with every tweet. It is used for tweets posted by unknown users with no available tweet history. An unknown user also triggers a batch job to start downloading the missing user timeline information. The second classifier is used for tweets posted by a user where the user timeline is downloaded and available. Initially, it will be the first classifier that handles most of the tweets. This will gradually change and after an initialization phase where we download historic data for the most active users, we reach a state where the second classifier handles a vast majority of all the tweets.A simulation using our on-the-fly detection mechanism indicates that we can handle Twitter streams with up to 68,000 unique users each day. The bottleneck is the time required to download new user timelines. The AGT detection is very accurate. In a set of 5,000 tweets we correctly classified about 98% of all AGTs using a subject-wise cross-validation.

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