When is a Network a Network? Multi-Order Graphical Model Selection in Pathways and Temporal Networks

We introduce a framework for the modeling of sequential data capturing pathways of varying lengths observed in a network. Such data are important, e.g., when studying click streams in information networks, travel patterns in transportation systems, information cascades in social networks, biological pathways or time-stamped social interactions. While it is common to apply graph analytics and network analysis to such data, recent works have shown that temporal correlations can invalidate the results of such methods. This raises a fundamental question: when is a network abstraction of sequential data justified? Addressing this open question, we propose a framework which combines Markov chains of multiple, higher orders into a multi-layer graphical model that captures temporal correlations in pathways at multiple length scales simultaneously. We develop a model selection technique to infer the optimal number of layers of such a model and show that it outperforms previously used Markov order detection techniques. An application to eight real-world data sets on pathways and temporal networks shows that it allows to infer graphical models which capture both topological and temporal characteristics of such data. Our work highlights fallacies of network abstractions and provides a principled answer to the open question when they are justified. Generalizing network representations to multi-order graphical models, it opens perspectives for new data mining and knowledge discovery algorithms.Comment: 10 pages, 4 figures, 1 table, companion python package pathpy available on gitHu

Uniform asymptotics of the coefficients of unitary moment polynomials

Keating and Snaith showed that the $2k^{th}$ absolute moment of the characteristic polynomial of a random unitary matrix evaluated on the unit circle is given by a polynomial of degree $k^2$. In this article, uniform asymptotics for the coefficients of that polynomial are derived, and a maximal coefficient is located. Some of the asymptotics are given in explicit form. Numerical data to support these calculations are presented. Some apparent connections between random matrix theory and the Riemann zeta function are discussed.Comment: 31 pages, 1 figure, 2 tables. A few minor misprints fixe

Random matrices with external source and KP τ\tau functions

In this paper we prove that the partition function in the random matrix model with external source is a KP $\tau$ function.Comment: 12 pages, title change

Analytical probabilistic approach to the ground state of lattice quantum systems: exact results in terms of a cumulant expansion

We present a large deviation analysis of a recently proposed probabilistic approach to the study of the ground-state properties of lattice quantum systems. The ground-state energy, as well as the correlation functions in the ground state, are exactly determined as a series expansion in the cumulants of the multiplicities of the potential and hopping energies assumed by the system during its long-time evolution. Once these cumulants are known, even at a finite order, our approach provides the ground state analytically as a function of the Hamiltonian parameters. A scenario of possible applications of this analyticity property is discussed.Comment: 26 pages, 5 figure

A Note on the Pfaffian Integration Theorem

Two alternative, fairly compact proofs are presented of the Pfaffian integration theorem that is surfaced in the recent studies of spectral properties of Ginibre's Orthogonal Ensemble. The first proof is based on a concept of the Fredholm Pfaffian; the second proof is purely linear-algebraic.Comment: 8 pages; published versio

Predictors of Walking App Users With Comparison of Current Users, Previous Users, and Informed Nonusers in a Sample of Dutch Adults: Questionnaire Study

BACKGROUND: The last decade has seen a substantial increase in the use of mobile health apps and research into the effects of those apps on health and health behaviors. In parallel, research has aimed at identifying population subgroups that are more likely to use those health apps. Current evidence is limited by two issues. First, research has focused on broad health apps, and little is known about app usage for a specific health behavior. Second, research has focused on comparing current users and current nonusers, without considering subgroups of nonusers. OBJECTIVE: We aimed to provide profile distributions of current users, previous users, and informed nonusers, and to identify predictor variables relevant for profile classification. METHODS: Data were available from 1683 people who participated in a Dutch walking event in Amsterdam that was held in September 2017. They provided information on demographics, self-reported walking behavior, and walking app usage, as well as items from User Acceptance of Information Technology, in an online survey. Data were analyzed using discriminant function analysis and multinomial logistic regression analysis. RESULTS: Most participants were current walking app users (899/1683, 53.4%), while fewer participants were informed nonusers (663/1683, 39.4%) and very few were previous walking app users (121/1683, 7.2%). Current walking app users were more likely to report walking at least 5 days per week and for at least 30 minutes per bout (odds ratio [OR] 1.44, 95% CI 1.11-1.85; P=.005) and more likely to be overweight (OR 1.72, 95% CI 1.24-2.37; P=.001) or obese (OR 1.49, 95% CI 1.08-2.08; P=.005) as compared with informed nonusers. Further, current walking app users perceived their walking apps to be less boring, easy to use and retrieve information, and more helpful to achieve their goals. Effect sizes ranged from 0.10 (95% CI 0.08-0.30) to 1.58 (95% CI 1.47-1.70). CONCLUSIONS: The distributions for walking app usage appeared different from the distributions for more general health app usage. Further, the inclusion of two specific subgroups of nonusers (previous users and informed nonusers) provides important information for health practitioners and app developers to stimulate continued walking app usage, including making information in those apps easy to understand and making it easy to obtain information from the apps, as well as preventing apps from becoming boring and difficult to use for goal attainment

Semi-autonomous competency assessment of powered mobility device users

This paper describes a stand-alone sensor package and algorithms for aiding the assessment by an occupational therapist whether a person has the capacity to safely and effectively operate a powered mobility device such as a walking aid or a wheelchair. The sensor package employed consists of a laser range finder, an RGB camera and an inertial measurement unit that can be attached to any mobility device with minimal modifications. Algorithms for capturing the data received by the sensor package and for generating the map of the environment as well as the trajectory of the mobility device have been developed. Such information presents occupational therapists with the capability to provide a quantitative assessment of whether patients are ready to be safely deployed with mobile aids for their daily activities. Preliminary evaluation of the sensor package and associated algorithms based on experiments, conducted at the premises of the Prince of Wales Hospital in Sydney, are presented. © 2011 IEEE

What is a crystal?

Almost 25 years have passed since Shechtman discovered quasicrystals, and 15 years since the Commission on Aperiodic Crystals of the International Union of Crystallography put forth a provisional definition of the term crystal to mean ``any solid having an essentially discrete diffraction diagram.'' Have we learned enough about crystallinity in the last 25 years, or do we need more time to explore additional physical systems? There is much confusion and contradiction in the literature in using the term crystal. Are we ready now to propose a permanent definition for crystal to be used by all? I argue that time has come to put a sense of order in all the confusion.Comment: Submitted to Zeitschrift fuer Kristallographi

Правове регулювання повторного шлюбу у римському та ранньовізантійському праві

В статті досліджується традиційна проблема інституту повторного шлюбу в контексті його еволюції на засадах античних та християнських цінностей.В статье исследуется традиционная проблема института повторного брака в контексте его эволюции на принципах античных и христианских ценностей.In the article the traditional problem of institute of the deuterogamy is probed in the context of its evolution on principles of ancient and christian values

The importance of satisfying children’s basic psychological needs in primary school physical education for PE-motivation, and its relations with fundamental motor and PE-related skills

Background: Motivation for physical education (PE) is considered an important factor for the development of children’s physical skills during PE. According to self-determination theory, satisfaction of the psychological needs of autonomy, relatedness, and competence is related to higher levels of autonomous motivation, and lower levels of controlled motivation. To get a better insight into these relations, the present study examines whether satisfaction of the psychological needs is predictive of fundamental motor skills (FMS) and PE-related skills, both directly, and indirectly (via motivation, i.e. ‘the motivational sequence’). As PE-related skills are more representative to the skills that are generally practiced during PE, the strongest relations are expected for these types of skills. Method: In this study, 2224 children (51.6% boys, mean age 11.8 ± 0.55) of 89 primary schools filled out questionnaires assessing the satisfaction of their basic psychological needs and their motivation for PE. Using a block design, FMS were assessed using standardized tests, and a diverse set of PE-related skills that are explicitly practiced during PE-lessons were tested using valid and reliable tests. Structural equation models were built in Mplus to examine the hypothesized relations. Results: Competence, peer-relatedness, and teacher-relatedness were predictive of autonomous motivation, whereas only peer-relatedness was predictive of controlled motivation. Different relations with psychological needs and motivation were found for FMS and PE-related skills. Autonomous and controlled motivation predicted PE-related skills, whereas only controlled motivation predicted FMS, in both cases via direct and indirect paths. In addition, direct relations were found between competence and both FMS and PE-related skills, and of peer-relatedness and teacher-relatedness with FMS specifically. Conclusions: Satisfaction of the psychological needs seems important for children’s PE-motivation and for their skill development, both directly and indirectly. These results underline the important role that PE-teachers play in constructing a need-satisfying environment. The motivational sequence seems to be more applicable to PE-related skills than to FMS, showing that is important to choose adequate outcome measures when examining PE-motivation