Palindromes in starlike trees

In this note, we obtain an upper bound on the maximum number of distinct non-empty palindromes in starlike trees. This bound implies, in particular, that there are at most 4 n distinct non-empty palindromes in a starlike tree with three branches each of length n. For such starlike trees labelled with a binary alphabet, we sharpen the upper bound to 4 n − 1 and conjecture that the actual maximum is 4 n − 2. It is intriguing that this simple conjecture seems difficult to prove, in contrast to the proof of the bound

Enhanced covers of regular & indeterminate strings using prefix tables

A \itbf{cover} of a string x=x[1..n] is a proper substring u of x such that x can be constructed from possibly overlapping instances of u. A recent paper \cite{FIKPPST13} relaxes this definition --- an \itbf{enhanced cover} u of x is a border of x (that is, a proper prefix that is also a suffix) that covers a {\it maximum} number of positions in x (not necessarily all) --- and proposes efficient algorithms for the computation of enhanced covers. These algorithms depend on the prior computation of the \itbf{border array} β[1..n], where β[i] is the length of the longest border of x[1..i], 1≤i≤n. In this paper, we first show how to compute enhanced covers using instead the \itbf{prefix table}: an array π[1..n] such that π[i] is the length of the longest substring of x beginning at position i that matches a prefix of x. Unlike the border array, the prefix table is robust: its properties hold also for \itbf{indeterminate strings} --- that is, strings defined on {\it subsets} of the alphabet Σ rather than individual elements of Σ. Thus, our algorithms, in addition to being faster in practice and more space-efficient than those of \cite{FIKPPST13}, allow us to easily extend the computation of enhanced covers to indeterminate strings. Both for regular and indeterminate strings, our algorithms execute in expected linear time. Along the way we establish an important theoretical result: that the expected maximum length of any border of any prefix of a regular string x is approximately 1.64 for binary alphabets, less for larger one

Interpersonal effects of parents and adolescents on each other’s health behaviours: a dyadic extension of the theory of planned behaviour

Objective: Interpersonal relationships are important predictors of health outcomes and interpersonal influences on behaviours may be key mechanisms underlying such effects. Most health behaviour theories focus on intrapersonal factors and may not adequately account for interpersonal influences. We evaluate a dyadic extension of the Theory of Planned Behaviour by examining whether parent and adolescent characteristics (attitudes, subjective norms, perceived behavioural control and intentions) are associated with not only their own but also each other’s intentions/behaviours. Design: Using the Actor-Partner Interdependence Model, we analyse responses from 1717 parent-adolescent dyads from the Family Life, Activity, Sun, Health, and Eating study. Main Outcome Measures: Adolescents/parents completed self-reports of their fruit and vegetable consumption, junk food and sugary drinks consumption, engagement in physical activity, and engagement in screen time sedentary behaviours. Results: Parent/adolescent characteristics are associated with each other’s health-relevant intentions/behaviours above the effects of individuals’ own characteristics on their own behaviours. Parent/adolescent characteristics covary with each other’s outcomes with similar strength, but parent characteristics more strongly relate to adolescent intentions, whereas adolescent characteristics more strongly relate to parent behaviours. Conclusions: Parents and adolescents may bidirectionally influence each other’s health intentions/behaviours. This highlights the importance of dyadic models of health behaviour and suggests intervention targets

Search for Global Dipole Enhancements in the HiRes-I Monocular Data above 10^{18.5} eV

Several proposed source models for Ultra-High Energy Cosmic Rays (UHECRs) consist of dipole distributions oriented towards major astrophysical landmarks such as the galactic center, M87, or Centaurus A. We use a comparison between real data and simulated data to show that the HiRes-I monocular data for energies above 10^{18.5} eV is, in fact, consistent with an isotropic source model. We then explore methods to quantify our sensitivity to dipole source models oriented towards the Galactic Center, M87, and Centaurus A.Comment: 17 pages, 31 figure

Observation of the Ankle and Evidence for a High-Energy Break in the Cosmic Ray Spectrum

We have measured the cosmic ray spectrum at energies above $10^{17}$ eV using the two air fluorescence detectors of the High Resolution Fly's Eye experiment operating in monocular mode. We describe the detector, PMT and atmospheric calibrations, and the analysis techniques for the two detectors. We fit the spectrum to models describing galactic and extragalactic sources. Our measured spectrum gives an observation of a feature known as the ``ankle'' near $3\times 10^{18}$ eV, and strong evidence for a suppression near $6\times 10^{19}$ eV.Comment: 14 pages, 9 figures. To appear in Physics Letters B. Accepted versio

Balancing direct and indirect sources of navigational information in a leaderless model of collective animal movement

Navigation is an important movement process that enables individuals and groups of animals to find targets in space at different spatio-temporal scales. Earlier studies have shown how being in a group can confer navigational advantages to individuals, either through following more experienced leaders or through the pooling of many inaccurate compasses, a process known as the ‘many wrongs principle’. However, the exact mechanisms for how information is transferred and used within the group in order to improve both individual- and group-level navigational performance are not fully understood. Here we explore the relative weighting that should be given to different sources of navigational information by an individual within a navigating group at each step of the movement process. Specifically, we consider a direct goal-oriented source of navigational information such as the individual׳s own imperfect knowledge of the target (a ‘noisy compass’) alongside two indirect sources of navigational information: the previous movement directions of neighbours in the group (social information) and, for the first time in this context, the previous movement direction of the individual (persistence). We assume that all individuals are equal in their abilities and that direct navigational information is prone to higher errors than indirect information. Using computer simulations, we show that in such situations giving a high weighting to either type of indirect navigational information can serve to significantly improve the navigation success of groups. Crucially, we also show that if the quality of social information is reduced, e.g. by an individual׳s limited cognitive abilities, the best navigational strategy for groups assigns a considerable weighting to persistence, a behaviour that is neither social, nor directly aimed at navigating

Occupational Communication as Boundary Mechanism

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69000/2/10.1177_073088847400100404.pd

Has the evolution of complexity in the amphibian papilla influenced anuran speciation rates?

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72375/1/j.1420-9101.2006.01079.x.pd

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

The domestic garden: its contribution to urban green infrastructure

Domestic gardens provide a significant component of urban green infrastructure but their relative contribution to eco-system service provision remains largely un-quantified. ‘Green infrastructure’ itself is often ill-defined, posing problems for planners to ascertain what types of green infrastructure provide greatest benefit and under what circumstances. Within this context the relative merits of gardens are unclear; however, at a time of greater urbanization where private gardens are increasingly seen as a ‘luxury’, it is important to define their role precisely. Hence, the nature of this review is to interpret existing information pertaining to gardens /gardening per se, identify where they may have a unique role to play and to highlight where further research is warranted. The review suggests that there are significant differences in both form and management of domestic gardens which radically influence the benefits. Nevertheless, gardens can play a strong role in improving the environmental impact of the domestic curtilage, e.g. by insulating houses against temperature extremes they can reduce domestic energy use. Gardens also improve localized air cooling, help mitigate flooding and provide a haven for wildlife. Less favourable aspects include contributions of gardens and gardening to greenhouse gas emissions, misuse of fertilizers and pesticides, and introduction of alien plant species. Due to the close proximity to the home and hence accessibility for many, possibly the greatest benefit of the domestic garden is on human health and well-being, but further work is required to define this clearly within the wider context of green infrastructure