Constructions for key distribution patterns

Key distribution patterns (KDPs) are finite incidence structures satisfying a certain property which makes them widely used in minimizing the key storage and ensuring the security of communication between users in a large network. We construct a new KDP using t-design and combine two ω-KDPs to give new (ω-1)-KDPs, which provide secure communication in a large network and minimize the amount of key storage.     

Arbitrage without borrowing or short selling?

We show that a trader, who starts with no initial wealth and is not allowed to borrow money or short sell assets, is theoretically able to attain positive wealth by continuous trading, provided that she has perfect foresight of future asset prices, given by a continuous semimartingale. Such an arbitrage strategy can be constructed as a process of finite variation that satisfies a seemingly innocuous self-financing condition, formulated using a pathwise Riemann–Stieltjes integral. Our result exemplifies the potential intricacies of formulating economically meaningful self-financing conditions in continuous time, when one leaves the conventional arbitrage-free framework.     

Calculating approximation guarantees for partial set cover of pairs

As a part of a heuristic for the fast detection of new word combinations in text streams, we consider the NP-hard Partial Set Cover of Pairs problem. There we wish to cover a maximum number of pairs of elements by a prescribed number of sets from a given set family. While the approximation ratio of the greedy algorithm for the classic Partial Set Cover problem is completely understood, the same question for covering of pairs is intrinsically more complicated, since the pairs insert some graph-theoretic structure. The best approximation guarantee for the first greedy step can be rephrased as a problem in extremal combinatorics: Assume that we may place a fixed number of subsets of fixed and equal size in a set, how many different pairs of elements can we cover? In this paper we introduce a method to calculate optimal approximation guarantees, and we demonstrate its use on the smallest set families.     

Evaluation of the evolution of relationships between topics over time

Topics that attract public attention can originate from current events or developments, might be influenced by situations in the past, and often continue to be of interest in the future. When respective information is made available textually, one possibility of detecting such topics of public importance consists in scrutinizing, e.g., appropriate press articles using—given the continual growth of information—text processing techniques enriched by computer routines which examine present-day textual material, check historical publications, find newly emerging topics, and are able to track topic trends over time. Information clustering based on content-(dis)similarity of the underlying textual material and graph-theoretical considerations to deal with the network of relationships between content-similar topics are described and combined in a new approach. Explanatory examples of topic detection and tracking in online news articles illustrate the usefulness of the approach in different situations.     

Atomic decompositions and Hardy’s inequality on weak Hardy-Morrey spaces

We introduce the weak Hardy-Morrey spaces in this paper. We also obtain the atomic decompositions of the weak Hardy-Morrey spaces. By using these decompositions, we establish the Hardy inequalities on the weak Hardy-Morrey spaces.     

A mod 2 index theorem for pin<Superscript>−</Superscript> manifolds

We establish a mod 2 index theorem for real vector bundles over 8k + 2 dimensional compact pin^? manifolds. The analytic index is the reduced η invariant of (twisted) Dirac operators and the topological index is defined through KO-theory. Our main result extends the mod 2 index theorem of Atiyah and Singer (1971) to non-orientable manifolds.     

Multi-recurrence and van der Waerden systems

We explore recurrence properties arising from dynamical approach to the van der Waerden theorem and similar combinatorial problems. We describe relations between these properties and study their consequences for dynamics. In particular, we present a measure-theoretical analog of a result of Glasner on multi-transitivity of topologically weakly mixing minimal maps. We also obtain a dynamical proof of the existence of a C-set with zero Banach density.     

Quasi-triangular Hopf algebras and invariant Jacobians

We show that two module homomorphisms for groups and Lie algebras established by Xi can be generalized to the setting of quasi-triangular Hopf algebras. These module homomorphisms played a key role in his proof of a conjecture of Yau (1998). They will also be useful in the problem of decomposition of tensor products of modules. Additionally, we give another generalization of result of Xi in terms of Chevalley-Eilenberg complex.     

Estimated conditional score function for missing mechanism model with nonignorable nonresponse

Missing data mechanism often depends on the values of the responses, which leads to nonignorable nonresponses. In such a situation, inference based on approaches that ignore the missing data mechanism could not be valid. A crucial step is to model the nature of missingness. We specify a parametric model for missingness mechanism, and then propose a conditional score function approach for estimation. This approach imputes the score function by taking the conditional expectation of the score function for the missing data given the available information. Inference procedure is then followed by replacing unknown terms with the related nonparametric estimators based on the observed data. The proposed score function does not suffer from the non-identifiability problem, and the proposed estimator is shown to be consistent and asymptotically normal. We also construct a confidence region for the parameter of interest using empirical likelihood method. Simulation studies demonstrate that the proposed inference procedure performs well in many settings. We apply the proposed method to a data set from research in a growth hormone and exercise intervention study.