Law of the iterated logarithm for random graphs

A milestone in probability theory is the law of the iterated logarithm (LIL), proved by Khinchin and independently by Kolmogorov in the 1920s, which asserts that for iid random variables with mean 0 and variance 1 In this paper we prove that LIL holds for various functionals of random graphs and hypergraphs models. We first prove LIL for the number of copies of a fixed subgraph H. Two harder results concern the number of global objects: perfect matchings and Hamiltonian cycles. The main new ingredient in these results is a large deviation bound, which may be of independent interest. For random k‐uniform hypergraphs, we obtain the Central Limit Theorem and LIL for the number of Hamilton cycles.     

Ultrafast gas chromatography coupled to electronic nose to identify volatile biomarkers in exhaled breath from chronic obstructive pulmonary disease patients: A pilot study

An analytical method to identify volatile organic compounds (VOCs) in the exhaled breath from patients with a diagnosis of chronic obstructive pulmonary disease (COPD) using a ultrafast gas chromatography system equipped with an electronic nose detector (FGC eNose) has been developed. A prospective study was performed in 23 COPD patients and 33 healthy volunteers; exhalation breathing tests were performed with Tedlar bags. Each sample was analyzed by FCG eNose and the identification of VOCs was based on the Kovats index. Raw data were reduced by principal component analysis (PCA) and canonical discriminant analysis [canonical analysis of principal coordinates (CAP)]. The FCG eNose technology was able to identify 17 VOCs that distinguish COPD patients from healthy volunteers. At all stages of PCA and CAP the discrimination between groups was obvious. Chemical prints were correctly classified up to 82.2%, and were matched with 78.9% of the VOCs detected in the exhaled breath samples. Receiver operating characteristic curve analysis indicated the sensitivity and specificity to be 96% and 91%, respectively. This pilot study demonstrates that FGC eNose is a useful tool to identify VOCs as biomarkers in exhaled breath from COPD patients. Further studies should be performed to enhance the clinical relevance of this quick and ease methodology for COPD diagnosis.     

Benchmarking culture in Europe: A data envelopment analysis approach to identify city-specific strengths

Culture is an integral part of a city's quality of life, a driver of urban change, and a genuine economic sector. To support benchmarking of urban culture and facilitate peer learning amongst policymakers, the European Commission has recently created the ‘Cultural and Creative Cities Index’. While this index builds on a standardised method to aggregate 29 indicators for the 155 selected cities, it is explicitly acknowledged that a ‘gold standard’ for a ‘Cultural and Creative City’ does not exist. Instead, different approaches should be allowed for in capturing cities’ cultural and creative vitality. This is the point of departure for this paper, which employs a Benefit-of-the-Doubt (BoD) modelling approach to allow cities to combine such respect for performance diversity with peer learning and benchmarking. Expert-based weights are used to provide expert-consistent bounds for the shares of key dimensions in a city's final BoD index value. We identify three city clusters, amongst which there are large performance differences. Accordingly, we focus on the within-group identification of peer cities and target values, which we illustrate in more detail for Bilbao, Krak?w and Umeå, towards the formulation of fit-for-purpose policy measures that can support culture-led development.     

Coleman automorphisms of finite groups and their minimal normal subgroups

In this paper, we show that all Coleman automorphisms of a finite group with self-central minimal non-trivial characteristic subgroup are inner; therefore the normalizer property holds for these groups. Using our methods we show that the holomorph and wreath product of finite simple groups, among others, have no non-inner Coleman automorphisms. As a further application of our theorems, we provide partial answers to questions raised by M. Hertweck and W. Kimmerle. Furthermore, we characterize the Coleman automorphisms of extensions of a finite nilpotent group by a cyclic p-group. Finally, we note that class-preserving Coleman automorphisms of p-power order of some nilpotent-by-nilpotent groups are inner, extending a result by J. Hai and J. Ge, where p is a prime number.     

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.