Asymptotic bounds on minimum number of disks required to hide a disk

We consider the problem of blocking all rays emanating from a closed unit disk with a minimum number of closed unit disks in the two-dimensional space, where the minimum distance from a disk to any other disk is given. We study the asymptotic behavior of the minimum number of disks as the minimum mutual distance approaches infinity. Using a regular ordering of disks on concentric circular rings we derive an upper bound and prove that the minimum number of disks required for blocking is quadratic in the minimum distance between the disks

Evaluating the semantic web: a task-based approach

The increased availability of online knowledge has led to the design of several algorithms that solve a variety of tasks by harvesting the Semantic Web, i.e. by dynamically selecting and exploring a multitude of online ontologies. Our hypothesis is that the performance of such novel algorithms implicity provides an insight into the quality of the used ontologies and thus opens the way to a task-based evaluation of the Semantic Web. We have investigated this hypothesis by studying the lessons learnt about online ontologies when used to solve three tasks: ontology matching, folksonomy enrichment, and word sense disambiguation. Our analysis leads to a suit of conclusions about the status of the Semantic Web, which highlight a number of strengths and weaknesses of the semantic information available online and complement the findings of other analysis of the Semantic Web landscape

The Effects of Twitter Sentiment on Stock Price Returns

Social media are increasingly reflecting and influencing behavior of other complex systems. In this paper we investigate the relations between a well-know micro-blogging platform Twitter and financial markets. In particular, we consider, in a period of 15 months, the Twitter volume and sentiment about the 30 stock companies that form the Dow Jones Industrial Average (DJIA) index. We find a relatively low Pearson correlation and Granger causality between the corresponding time series over the entire time period. However, we find a significant dependence between the Twitter sentiment and abnormal returns during the peaks of Twitter volume. This is valid not only for the expected Twitter volume peaks (e.g., quarterly announcements), but also for peaks corresponding to less obvious events. We formalize the procedure by adapting the well-known "event study" from economics and finance to the analysis of Twitter data. The procedure allows to automatically identify events as Twitter volume peaks, to compute the prevailing sentiment (positive or negative) expressed in tweets at these peaks, and finally to apply the "event study" methodology to relate them to stock returns. We show that sentiment polarity of Twitter peaks implies the direction of cumulative abnormal returns. The amount of cumulative abnormal returns is relatively low (about 1-2%), but the dependence is statistically significant for several days after the events

Individual and collective salvation in late Visigothic Spain

Bishop Julian of Toledo is remembered primarily as a key actor in the processes of king-making and -unmaking that went on in the Visigothic kingdom of the 670s. In the early part of the decade Julian’s Historia Wambae Regis legitimated King Wamba’s hold on the throne in opposition to a rebellion. The text also provides us with the first reference to unction in the early medieval West, while Julian’s actions in putting the same king through penance when he appeared to be on the brink of death in 680 and then insisting that the king could not resume his royal duties when he recovered have long attracted the attention of scholars of penance and conspiracy theorists alike. As the Bishop of Toledo, capital of the Visigothic kingdom, Julian was the main ecclesiastic in Visigothic Spain, presiding over four councils of Toledo (from the twelfth in 681 to the fifteenth in 687). Perhaps as a result of his historical significance in a poorly documented era, Julian’s plentiful writings about the end of time have largely been ignored; after all, they seem not to deal with ‘historical’ events. This is a shame, since Julian’s Prognosticum futuri saeculi was the most widely disseminated work of late seventh-century Spain: hundreds of manuscripts survive and there are well over one hundred references to the work in medieval library catalogues. The great success of the Prognosticum can be attributed to the contents of the three books, which deal with the origins of human death, the fate of the soul after death and the fate of the body at the resurrection, and thus address a series of theoretical and practical issues connected to death and its aftermath. The text was so popular because it was very easy to use, briefly summarizing a wide range of patristic opinions on death, the second coming of Christ and its aftermath

Iterative node localization for intelligent street lighting

In intelligent street lighting systems where light posts communicate wirelessly, location awareness is necessary for the system to provide context-aware services. To solve the specific localization problem, we developed an iterative algorithm based on the relation between the received signal strength and the distance to assign the known locations to the nodes. Our experimental results show small error rates in the number of wrongly localized nodes, which indicates the algorithm is applicable in practice

Hiding in the crowd: asympstotic bounds on blocking sets

We consider the problem of blocking all rays emanating from a unit disk U by a minimum number N_d of unit disks in the two-dimensional space, where each disk has at least a distance d to any other disk. We study the asymptotic behavior of N_d, as d tends to infinity. Using a regular ordering of disks on concentric circular rings we derive upper and lower bounds and prove that $\frac{\pi^2}{16} \leq \frac{N_d}{d^2} \leq \frac{\pi^2}{2}$, as d goes to infinity