Number of loops of size h in growing scale-free networks

The hierarchical structure of scale-free networks has been investigated focusing on the scaling of the number $N_h(t)$ of loops of size h as a function of the system size. In particular we have found the analytic expression for the scaling of $N_h(t)$ in the Barab\'asi-Albert (BA) scale-free network. We have performed numerical simulations on the scaling law for $N_h(t)$ in the BA network and in other growing scale free networks, such as the bosonic network (BN) and the aging nodes (AN) network. We show that in the bosonic network and in the aging node network the phase transitions in the topology of the network are accompained by a change in the scaling of the number of loops with the system size.Comment: 4 pages, 3 figure

The role of clustering and gridlike ordering in epidemic spreading

The spreading of an epidemic is determined by the connectiviy patterns which underlie the population. While it has been noted that a virus spreads more easily on a network in which global distances are small, it remains a great challenge to find approaches that unravel the precise role of local interconnectedness. Such topological properties enter very naturally in the framework of our two-timestep description, also providing a novel approach to tract a probabilistic system. The method is elaborated for SIS-type epidemic processes, leading to a quantitative interpretation of the role of loops up to length 4 in the onset of an epidemic.Comment: Submitted to Phys. Rev. E; 15 pages, 11 figures, 5 table

Mechanical challenges to freshwater residency in sharks and rays

Major transitions between marine and freshwater habitats are relatively infrequent, primarily as a result of major physiological and ecological challenges. Few species of cartilaginous fish have evolved to occupy freshwater habitats. Current thought suggests that the metabolic physiology of sharks has remained a barrier to the diversification of this taxon in freshwater ecosystems. Here, we demonstrate that the physical properties of water provide an additional constraint for this species-rich group to occupy freshwater systems. Using hydromechanical modeling, we show that occurrence in fresh water results in a two- to three-fold increase in negative buoyancy for sharks and rays. This carries the energetic cost of lift production and results in increased buoyancy-dependent mechanical power requirements for swimming and increased optimal swim speeds. The primary source of buoyancy, the lipidrich liver, offers only limited compensation for increased negative buoyancy as a result of decreasing water density; maintaining the same submerged weight would involve increasing the liver volume by very large amounts: 3- to 4-fold in scenarios where liver density is also reduced to currently observed minimal levels and 8-fold without any changes in liver density. The first data on body density from two species of elasmobranch occurring in freshwater (the bull shark Carcharhinus leucas, Muller and Henle 1839, and the largetooth sawfish Pristis pristis, Linnaeus 1758) support this hypothesis, showing similar liver sizes as marine forms but lower liver densities, but the greatest negative buoyancies of any elasmobranch studied to date. Our data suggest that the mechanical challenges associated with buoyancy control may have hampered the invasion of freshwater habitats in elasmobranchs, highlighting an additional key factor that may govern the predisposition of marine organisms to successfully establish in freshwater habitats

Unravelling small world networks

New classes of random graphs have recently been shown to exhibit the small world phenomenon - they are clustered like regular lattices and yet have small average pathlengths like traditional random graphs. Small world behaviour has been observed in a number of real life networks, and hence these random graphs represent a useful modelling tool. In particular, Grindrod [Phys. Rev. E 66 (2002) 066702-1] has proposed a class of range dependent random graphs for modelling proteome networks in bioinformatics. A property of these graphs is that, when suitably ordered, most edges in the graph are short-range, in the sense that they connect near-neighbours, and relatively few are long-range. Grindrod also looked at an inverse problem - given a graph that is known to be an instance of a range dependent random graph, but with vertices in arbitrary order, can we reorder the vertices so that the short-range/long-range connectivity structure is apparent? When the graph is viewed in terms of its adjacency matrix, this becomes a problem in sparse matrix theory: find a symmetric row/column reordering that places most nonzeros close to the diagonal. Algorithms of this general nature have been proposed for other purposes, most notably for reordering to reduce fill-in and for clustering large data sets. Here, we investigate their use in the small world reordering problem. Our numerical results suggest that a spectral reordering algorithm is extremely promising, and we give some theoretical justification for this observation via the maximum likelihood principle

A Temporal Filter for Binaural Hearing Is Dynamically Adjusted by Sound Pressure Level

In natural environments our auditory system is exposed to multiple and diverse signals of fluctuating amplitudes. Therefore, to detect, localize, and single out individual sounds the auditory system has to process and filter spectral and temporal information from both ears. It is known that the overall sound pressure level affects sensory signal transduction and therefore the temporal response pattern of auditory neurons. We hypothesize that the mammalian binaural system utilizes a dynamic mechanism to adjust the temporal filters in neuronal circuits to different overall sound pressure levels. Previous studies proposed an inhibitory mechanism generated by the reciprocally coupled dorsal nuclei of the lateral lemniscus (DNLL) as a temporal neuronal-network filter that suppresses rapid binaural fluctuations. Here we investigated the consequence of different sound levels on this filter during binaural processing. Our in vivo and in vitro electrophysiology in Mongolian gerbils shows that the integration of ascending excitation and contralateral inhibition defines the temporal properties of this inhibitory filter. The time course of this filter depends on the synaptic drive, which is modulated by the overall sound pressure level and N-methyl-D-aspartate receptor (NMDAR) signaling. In psychophysical experiments we tested the temporal perception of humans and show that detection and localization of two subsequent tones changes with the sound pressure level consistent with our physiological results. Together our data support the hypothesis that mammals dynamically adjust their time window for sound detection and localization within the binaural system in a sound level dependent manner

Recruitment of a critically endangered sawfish into a riverine nursery depends on natural flow regimes

The freshwater sawfish (Pristis pristis) was recently listed as the most Evolutionarily Distinct and Globally Endangered (EDGE) animal. The Fitzroy River in the remote Kimberley region of north-western Australia represents a significant stronghold for the species, which uses the freshwater reaches of the river as a nursery. There is also mounting pressure to develop the water resources of the region for agriculture that may substantially affect life history dynamics of sawfish in this system. However, the relationship between hydrology and population dynamics of freshwater sawfish was unknown. We used standardized catch data collected over 17 years to determine how wet season volume influences recruitment of freshwater sawfish into their riverine nursery. Negligible recruitment occurred in years with few days of high flood levels (above 98th percentile of cease-to-flow stage height), and relatively high recruitment occurred in years with 14 or more days of high flood levels. This relationship is indicative of a distinct boom-or-bust cycle, whereby freshwater sawfish rely almost entirely on the few years with large wet season floods, and the brief periods of highest water levels within these years, to replenish juvenile populations in the Fitzroy River nursery. This has direct implications for sustainable water resource management for the Fitzroy River basin in order to preserve one of the last known intact nursery habitats for this globally threatened species

Neurofilament light chain as a potential biomarker for monitoring neurodegeneration in X-linked adrenoleukodystrophy

X-linked adrenoleukodystrophy (X-ALD), the most frequent monogenetic disorder of brain white matter, is highly variable, ranging from slowly progressive adrenomyeloneuropathy (AMN) to life-threatening inflammatory brain demyelination (CALD). In this study involving 94 X-ALD patients and 55 controls, we tested whether plasma/serum neurofilament light chain protein (NfL) constitutes an early distinguishing biomarker. In AMN, we found moderately elevated NfL with increased levels reflecting higher grading of myelopathy-related disability. Intriguingly, NfL was a significant predictor to discriminate non-converting AMN from cohorts later developing CALD. In CALD, markedly amplified NfL levels reflected brain lesion severity. In rare cases, atypically low NfL revealed a previously unrecognized smoldering CALD disease course with slowly progressive myelin destruction. Upon halt of brain demyelination by hematopoietic stem cell transplantation, NfL gradually normalized. Together, our study reveals that blood NfL reflects inflammatory activity and progression in CALD patients, thus constituting a potential surrogate biomarker that may facilitate clinical decisions and therapeutic development

3D visualization processes for recreating and studying organismal form

The study of biological form is a vital goal of evolutionary biology and functional morphology. We review an emerging set of methods that allow scientists to create and study accurate 3D models of living organisms and animate those models for biomechanical and fluid dynamic analyses. The methods for creating such models include 3D photogrammetry, laser and CT-scanning, and 3D software. New multi-camera devices can be used to create accurate 3D models of living animals in the wild and captivity. New websites and virtual reality/augmented reality devices now enable the visualization and sharing of these data. We provide examples of these approaches for animals ranging from large whales to lizards and show applications for several areas: Natural history collections; body condition/scaling, bioinspired robotics, computational fluids dynamics (CFD), machine learning, and education. We provide two data sets to demonstrate the efficacy of CFD and machine learning approaches and conclude with a prospectus

Statistical mechanics of complex networks

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.Comment: 54 pages, submitted to Reviews of Modern Physic

Identification of animal movement patterns using tri-axial magnetometry

BackgroundAccelerometers are powerful sensors in many bio-logging devices, and are increasingly allowing researchers to investigate the performance, behaviour, energy expenditure and even state, of free-living animals. Another sensor commonly used in animal-attached loggers is the magnetometer, which has been primarily used in dead-reckoning or inertial measurement tags, but little outside that. We examine the potential of magnetometers for helping elucidate the behaviour of animals in a manner analogous to, but very different from, accelerometers. The particular responses of magnetometers to movement means that there are instances when they can resolve behaviours that are not easily perceived using accelerometers.MethodsWe calibrated the tri-axial magnetometer to rotations in each axis of movement and constructed 3-dimensional plots to inspect these stylised movements. Using the tri-axial data of Daily Diary tags, attached to individuals of number of animal species as they perform different behaviours, we used these 3-d plots to develop a framework with which tri-axial magnetometry data can be examined and introduce metrics that should help quantify movement and behaviour.ResultsTri-axial magnetometry data reveal patterns in movement at various scales of rotation that are not always evident in acceleration data. Some of these patterns may be obscure until visualised in 3D space as tri-axial spherical plots (m-spheres). A tag-fitted animal that rotates in heading while adopting a constant body attitude produces a ring of data around the pole of the m-sphere that we define as its Normal Operational Plane (NOP). Data that do not lie on this ring are created by postural rotations of the animal as it pitches and/or rolls. Consequently, stereotyped behaviours appear as specific trajectories on the sphere (m-prints), reflecting conserved sequences of postural changes (and/or angular velocities), which result from the precise relationship between body attitude and heading. This novel approach shows promise for helping researchers to identify and quantify behaviours in terms of animal body posture, including heading.ConclusionMagnetometer-based techniques and metrics can enhance our capacity to identify and examine animal behaviour, either as a technique used alone, or one that is complementary to tri-axial accelerometry