Bounded Representations of Interval and Proper Interval Graphs

Klavik et al. [arXiv:1207.6960] recently introduced a generalization of recognition called the bounded representation problem which we study for the classes of interval and proper interval graphs. The input gives a graph G and in addition for each vertex v two intervals L_v and R_v called bounds. We ask whether there exists a bounded representation in which each interval I_v has its left endpoint in L_v and its right endpoint in R_v. We show that the problem can be solved in linear time for interval graphs and in quadratic time for proper interval graphs. Robert's Theorem states that the classes of proper interval graphs and unit interval graphs are equal. Surprisingly the bounded representation problem is polynomially solvable for proper interval graphs and NP-complete for unit interval graphs [Klav\'{\i}k et al., arxiv:1207.6960]. So unless P = NP, the proper and unit interval representations behave very differently. The bounded representation problem belongs to a wider class of restricted representation problems. These problems are generalizations of the well-understood recognition problem, and they ask whether there exists a representation of G satisfying some additional constraints. The bounded representation problems generalize many of these problems

A Mathematical Framework for Agent Based Models of Complex Biological Networks

Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis.Comment: To appear in Bulletin of Mathematical Biolog

Modeling the high-energy emission in GRB 110721A and implications on the early multiwavelength and polarimetric observations

GRB 110721A was detected by the Gamma-ray Burst Monitor and the Large Area Telescope (LAT) onboard the Fermi satellite and the Gamma-ray Burst Polarimeter onboard the IKAROS solar mission. Previous analysis done of this burst showed: i) a linear polarization signal with position angle stable ($\phi_p= 160^\circ\pm11$) and high degree of $\Pi=84^{+16}_{-28}$, ii) an extreme peak energy of a record-breaking at 15$\pm$2 MeV, and iii) a subdominant prompt thermal component observed right after the onset of this burst. In this paper, the LAT data around the reported position of GRB 110721A are analysed with the most recent software and then, the LAT light curve above 100 MeV was obtained. The LAT light curve is modelled in terms of adiabatic early-afterglow external shocks when the outflow propagates into a stellar wind. Additionally, we discuss the possible origins and also study the implications of the early-afterglow external shocks on the extreme peak energy observed at 15$\pm$2 MeV, the polarization observations and the subdominant prompt thermal component.Comment: 9 pages and one figure. Accepted for publication in Ap

Evaluating the effective numbers of independent tests and significant p-value thresholds in commercial genotyping arrays and public imputation reference datasets

Current genome-wide association studies (GWAS) use commercial genotyping microarrays that can assay over a million single nucleotide polymorphisms (SNPs). The number of SNPs is further boosted by advanced statistical genotype-imputation algorithms and large SNP databases for reference human populations. The testing of a huge number of SNPs needs to be taken into account in the interpretation of statistical significance in such genome-wide studies, but this is complicated by the non-independence of SNPs because of linkage disequilibrium (LD). Several previous groups have proposed the use of the effective number of independent markers (Me) for the adjustment of multiple testing, but current methods of calculation for Me are limited in accuracy or computational speed. Here, we report a more robust and fast method to calculate Me. Applying this efficient method [implemented in a free software tool named Genetic type 1 error calculator (GEC)], we systematically examined the Me, and the corresponding p-value thresholds required to control the genome-wide type 1 error rate at 0.05, for 13 Illumina or Affymetrix genotyping arrays, as well as for HapMap Project and 1000 Genomes Project datasets which are widely used in genotype imputation as reference panels. Our results suggested the use of a p-value threshold of ~10−7 as the criterion for genome-wide significance for early commercial genotyping arrays, but slightly more stringent p-value thresholds ~5 × 10−8 for current or merged commercial genotyping arrays, ~10−8 for all common SNPs in the 1000 Genomes Project dataset and ~5 × 10−8 for the common SNPs only within genes

A framework for interpreting genome-wide association studies of psychiatric disorders

Genome-wide association studies (GWAS) have yielded a plethora of new findings in the past 3 years. By early 2009, GWAS on 47 samples of subjects with attention-deficit hyperactivity disorder, autism, bipolar disorder, major depressive disorder and schizophrenia will be completed. Taken together, these GWAS constitute the largest biological experiment ever conducted in psychiatry (59 000 independent cases and controls, 7700 family trios and >40 billion genotypes). We know that GWAS can work, and the question now is whether it will work for psychiatric disorders. In this review, we describe these studies, the Psychiatric GWAS Consortium for meta-analyses of these data, and provide a logical framework for interpretation of some of the conceivable outcomes

Multiscale models for movement in oriented environments and their application to hilltopping in butterflies

Hilltopping butterflies direct their movement in response to topography, facilitating mating encounters via accumulation at summits. In this paper, we take hilltopping as a case study to explore the impact of complex orienteering cues on population dynamics. The modelling employs a standard multiscale framework, in which an individual's movement path is described as a stochastic 'velocity-jump' process and scaling applied to generate a macroscopic model capable of simulating large populations in landscapes. In this manner, the terms and parameters of the macroscopic model directly relate to statistical inputs of the individual-level model (mean speeds, turning rates and turning distributions). Applied to hilltopping in butterflies, we demonstrate how hilltopping acts to aggregate populations at summits, optimising mating for low-density species. However, for abundant populations, hilltopping is not only less effective but also possibly disadvantageous, with hilltopping males recording a lower mating rate than their non-hilltopping competitors. © 2013 Springer Science+Business Media Dordrecht

Education for Environmental Citizenship and Responsible Environmental Behaviour

The notion of Environmental Citizenship embodies behaviour – an actively involved citizen who exercises his/her environmental rights and obligations in the private and public spheres. Education for Environmental Citizenship implies behavioural change; its goal is to facilitate an individual’s intellectual growth (cognitive domain) and emotional capacity (affective domain) that may lead to a critical and actively engaged individual. Human behaviour is overwhelmingly sophisticated, and what shapes pro-environmental behaviour is complex and context specific. Furthermore, empirical research indicates a discrepancy between possessing environmental knowledge and environmentally supportive attitudes and behaving pro-environmentally. The point of departure of this chapter is that the social and psychological study of behaviour has much to inform the study of environmental behaviour and, deriving from this, to inform regarding the type of education towards behaviour/action in the goal of sustainable socioecological transformation. The chapter focuses on internal (psychosocial) factors. It presents selected models regarding factors influencing behavioural decisions that are acknowledged as influential theoretical frameworks for investigating pro-environmental behaviour, as well as various theories that inform these models. These are categorised into knowledge-based models; attitude-, value- and norm-oriented models; skills, self-efficacy and situational factors; and new approaches to environmental behaviour models. The chapter concludes with suggestions for Education for Environmental Citizenship deriving from the various models

Large publishing consortia produce higher citation impact research but co-author contributions are hard to evaluate

This paper introduces a simple agglomerative clustering method to identify large publishing consortia with at least 20 authors and 80% shared authorship between articles. Based on Scopus journal articles 1996-2018, under these criteria, nearly all (88%) of the large consortia published research with citation impact above the world average, with the exceptions being mainly the newer consortia for which average citation counts are unreliable. On average, consortium research had almost double (1.95) the world average citation impact on the log scale used (Mean Normalised Log Citation Score). At least partial alphabetical author ordering was the norm in most consortia. The 250 largest consortia were for nuclear physics and astronomy around expensive equipment, and for predominantly health-related issues in genomics, medicine, public health, microbiology and neuropsychology. For the health-related issues, except for the first and last few authors, authorship seem to primary indicate contributions to the shared project infrastructure necessary to gather the raw data. It is impossible for research evaluators to identify the contributions of individual authors in the huge alphabetical consortia of physics and astronomy, and problematic for the middle and end authors of health-related consortia. For small scale evaluations, authorship contribution statements could be used, when available

On-chip generation of high-dimensional entangled quantum states and their coherent control

Optical quantum states based on entangled photons are essential for solving questions in fundamental physics and are at the heart of quantum information science1. Specifically, the realization of high-dimensional states (D-level quantum systems, that is, qudits, with D > 2) and their control are necessary for fundamental investigations of quantum mechanics2, for increasing the sensitivity of quantum imaging schemes3, for improving the robustness and key rate of quantum communication protocols4, for enabling a richer variety of quantum simulations5, and for achieving more efficient and error-tolerant quantum computation6. Integrated photonics has recently become a leading platform for the compact, cost-efficient, and stable generation and processing of non-classical optical states7. However, so far, integrated entangled quantum sources have been limited to qubits (D = 2)8, 9, 10, 11. Here we demonstrate on-chip generation of entangled qudit states, where the photons are created in a coherent superposition of multiple high-purity frequency modes. In particular, we confirm the realization of a quantum system with at least one hundred dimensions, formed by two entangled qudits with D = 10. Furthermore, using state-of-the-art, yet off-the-shelf telecommunications components, we introduce a coherent manipulation platform with which to control frequency-entangled states, capable of performing deterministic high-dimensional gate operations. We validate this platform by measuring Bell inequality violations and performing quantum state tomography. Our work enables the generation and processing of high-dimensional quantum states in a single spatial mode