Correlations of record events as a test for heavy-tailed distributions

A record is an entry in a time series that is larger or smaller than all previous entries. If the time series consists of independent, identically distributed random variables with a superimposed linear trend, record events are positively (negatively) correlated when the tail of the distribution is heavier (lighter) than exponential. Here we use these correlations to detect heavy-tailed behavior in small sets of independent random variables. The method consists of converting random subsets of the data into time series with a tunable linear drift and computing the resulting record correlations.Comment: Revised version, to appear in Physical Review Letter

Lifelong learning in evolving graphs with limited labeled data and unseen class detection

Large-scale graph data in the real-world are often dynamic rather than static. The data are changing with new nodes, edges, and even classes appearing over time, such as in citation networks and research-and-development collaboration networks. Graph neural networks (GNNs) have emerged as the standard method for numerous tasks on graph-structured data. In this work, we employ a two-step procedure to explore how GNNs can be incrementally adapted to new unseen graph data. First, we analyze the verge between transductive and inductive learning on standard benchmark datasets. After inductive pretraining, we add unlabeled data to the graph and show that the models are stable. Then, we explore the case of continually adding more and more labeled data, while considering cases, where not all past instances are annotated with class labels. Furthermore, we introduce new classes while the graph evolves and explore methods that automatically detect instances from previously unseen classes. In order to deal with evolving graphs in a principled way, we propose a lifelong learning framework for graph data along with an evaluation protocol. In this framework, we evaluate representative GNN architectures. We observe that implicit knowledge within model parameters becomes more important when explicit knowledge, i.e., data from past tasks, is limited. We find that in open-world node classification, the data from surprisingly few past tasks are sufficient to reach the performance reached by remembering data from all past tasks. In the challenging task of unseen class detection, we find that using a weighted cross-entropy loss is important for stabilit

Spin-orbit hybrid entanglement of photons and quantum contextuality

We demonstrate electromagnetic quantum states of single photons and of correlated photon pairs exhibiting "hybrid" entanglement between spin and orbital angular momentum. These states are obtained from entangled photon pairs emitted by spontaneous parametric down conversion, by employing a $q$-plate for coupling the spin and orbital degrees of freedom of a photon. Entanglement and contextual quantum behavior (that is also non-local, in the case of photon pairs) is demonstrated by the reported violation of the Clauser-Horne-Shimony-Holt inequality. In addition a classical analog of the hybrid spin-orbit photonic entanglement is reported and discussed.Comment: 5 pages, 3 figure

Records and sequences of records from random variables with a linear trend

We consider records and sequences of records drawn from discrete time series of the form $X_{n}=Y_{n}+cn$, where the $Y_{n}$ are independent and identically distributed random variables and $c$ is a constant drift. For very small and very large drift velocities, we investigate the asymptotic behavior of the probability $p_n(c)$ of a record occurring in the $n$th step and the probability $P_N(c)$ that all $N$ entries are records, i.e. that $X_1 < X_2 < ... < X_N$. Our work is motivated by the analysis of temperature time series in climatology, and by the study of mutational pathways in evolutionary biology.Comment: 21 pages, 7 figure

Study on the Implications of Asynchronous GMO Approvals for EU Imports of Animal Feed Products

The aim of this study is to understand the implications of asynchronous approvals for genetically modified organisms (GMOs) that are imported to the European Union for use within animal feed products, specifically with regard to the EU livestock sector, as well as upon the upstream and downstream economic industries related to it. Asynchronous approval refers to the situation in which there is a delay in the moment when a genetically modified (GM) event – modifying a specific trait of a plant or animal – is allowed to be used in one country in comparison to another country. In the perspective of this study, the asynchronous GMO approvals concern the use of GM varieties of plants that are approved in the countries which supply them to the EU, in one form or another of feed material, before these are approved by the EU

Large-uncertainty intelligent states for angular momentum and angle

The equality in the uncertainty principle for linear momentum and position is obtained for states which also minimize the uncertainty product. However, in the uncertainty relation for angular momentum and angular position both sides of the inequality are state dependent and therefore the intelligent states, which satisfy the equality, do not necessarily give a minimum for the uncertainty product. In this paper, we highlight the difference between intelligent states and minimum uncertainty states by investigating a class of intelligent states which obey the equality in the angular uncertainty relation while having an arbitrarily large uncertainty product. To develop an understanding for the uncertainties of angle and angular momentum for the large-uncertainty intelligent states we compare exact solutions with analytical approximations in two limiting cases.Comment: 20 pages, 9 figures, submitted to J. Opt. B special issue in connection with ICSSUR 2005 conferenc

Derivative moments in turbulent shear flows

We propose a generalized perspective on the behavior of high-order derivative moments in turbulent shear flows by taking account of the roles of small-scale intermittency and mean shear, in addition to the Reynolds number. Two asymptotic regimes are discussed with respect to shear effects. By these means, some existing disagreements on the Reynolds number dependence of derivative moments can be explained. That odd-order moments of transverse velocity derivatives tend not vanish as expected from elementary scaling considerations does not necessarily imply that small-scale anisotropy persists at all Reynolds numbers.Comment: 11 pages, 7 Postscript figure