On fractional derivatives and primitives of periodic functions

In this paper we prove that the fractional derivative or the fractional primitive of a $T$-periodic function cannot be a $\tilde{T}$-periodic function, for any period $\tilde{T}$, with the exception of the zero function.Comment: 12 page

Fixed Exchange Rates, Inflation and Macroeconomic Discipline

We use data from Guatemala and Honduras to investigate some implications of the Purchasing Power Parity theory over the long run. In particular, we address two questions. First, to what extent did the fixed exchange rate regime impose macroeconomic discipline on these countries. Second, what was the impact of terms of trade shocks and growth differentials on inflation rate differentials between those countries and the United States. We found that the fixed parities regime worked properly until the mid-1970s, providing some constraint on central bank behavior. However, the evidence suggests that the fixed exchange rate system was not sufficient to avoid inflation outbursts and balance of payments crises. Specifically, it was unable to accommodate large negative terms of trade shocks in the late 1970s and early 1980s.

Efficiency of Human Activity on Information Spreading on Twitter

Understanding the collective reaction to individual actions is key to effectively spread information in social media. In this work we define efficiency on Twitter, as the ratio between the emergent spreading process and the activity employed by the user. We characterize this property by means of a quantitative analysis of the structural and dynamical patterns emergent from human interactions, and show it to be universal across several Twitter conversations. We found that some influential users efficiently cause remarkable collective reactions by each message sent, while the majority of users must employ extremely larger efforts to reach similar effects. Next we propose a model that reproduces the retweet cascades occurring on Twitter to explain the emergent distribution of the user efficiency. The model shows that the dynamical patterns of the conversations are strongly conditioned by the topology of the underlying network. We conclude that the appearance of a small fraction of extremely efficient users results from the heterogeneity of the followers network and independently of the individual user behavior.Comment: 29 pages, 10 figure

Exploring accumulative query expansion for relevance feedback

For the participation of Dublin City University (DCU) in the Relevance Feedback (RF) track of INEX 2010, we investigated the relation between the length of relevant text passages and the number of RF terms. In our experiments, relevant passages are segmented into non-overlapping windows of xed length which are sorted by similarity with the query. In each retrieval iteration, we extend the current query with the most frequent terms extracted from these word windows. The number of feedback terms corresponds to a constant number, a number proportional to the length of relevant passages, and a number inversely proportional to the length of relevant passages, respectively. Retrieval experiments show a signicant increase in MAP for INEX 2008 training data and improved precisions at early recall levels for the 2010 topics as compared to the baseline Rocchio feedback