Andrey Kupavskii

Prediction of retweet cascade size over time

Retweet cascades play an essential role in information diffusion in Twitter. Popular tweets reflect the current trends in Twitter, while Twitter itself is one of the most important online media. Thus, understanding the reasons why a tweet becomes popular is of great interest for sociologists, marketers and social media researches. What is even more important is the possibility to make a prognosis of a tweets future popularity. Besides the scientific significance of such possibility, this sort of prediction has lots of practical applications such as breaking news detection, viral marketing etc. In this paper we try to forecast how many retweets a given tweet will gain during a fixed time period. We train an algorithm that predicts the number of retweets during time T since the initial moment. In addition to a standard set of features we utilize several new ones. One of the most important features is the flow of the cascade. Another one is PageRank on the retweet graph, which can be considered as the measure of influence of users.

Two notions of unit distance graphs

A complete (unit) distance graph in ℝo(1))dn log2 n, while the number of distance graphs in ℝd on n labelled vertices is 2(1−1/⌊d/2⌋+o>(1))n 2/2. This is used to study a Ramsey type question involving these graphs. Finally, we discuss the following problem: what is the minimum number of edges a graph must have so that it is not realizable as a complete distance graph in ℝd?

On random subgraphs of Kneser and Schrijver graphs

A Kneser graph

Regular bipartite graphs and intersecting families

KG_{n,k}

Families with no s pairwise disjoint sets

is a graph whose vertices are in one-to-one correspondence with

New bounds for the distance Ramsey number

k

New Lower Bounds for epsilon-Nets

-element subsets of

Erdős–Ko–Rado theorem for {0,±1}-vectors

[n],

Counting Intersecting and Pairs of Cross-Intersecting Families

with two vertices connected if and only if the corresponding sets do not intersect. A famous result due to Lovasz states that the chromatic number of a Kneser graph

A size-sensitive inequality for cross-intersecting families

KG_{n,k}