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 Blind Watchmaker Network: Scale-freeness and Evolution

It is suggested that the degree distribution for networks of the cell-metabolism for simple organisms reflects an ubiquitous randomness. This implies that natural selection has exerted no or very little pressure on the network degree distribution during evolution. The corresponding random network, here termed the blind watchmaker network has a power-law degree distribution with an exponent gamma >= 2. It is random with respect to a complete set of network states characterized by a description of which links are attached to a node as well as a time-ordering of these links. No a priory assumption of any growth mechanism or evolution process is made. It is found that the degree distribution of the blind watchmaker network agrees very precisely with that of the metabolic networks. This implies that the evolutionary pathway of the cell-metabolism, when projected onto a metabolic network representation, has remained statistically random with respect to a complete set of network states. This suggests that even a biological system, which due to natural selection has developed an enormous specificity like the cellular metabolism, nevertheless can, at the same time, display well defined characteristics emanating from the ubiquitous inherent random element of Darwinian evolution. The fact that also completely random networks may have scale-free node distributions gives a new perspective on the origin of scale-free networks in general.Comment: 5 pages, 3 figure

From “where” and “when” to “what” and “why”: archival tags for monitoring “complex” behaviours in fish.

Understanding the movements (“where” and “when”) and behaviour (“what” and, hopefully, “why”) of individuals and populations is key to answering fundamental questions in fish ecology. The use of archival tags in telemetry studies of marine fish have, by and large, involved recording “simple” measurements of variables such as pressure (giving depth), temperature and light over extended timescales. These have then been used to provide information about location and movement of individuals. However, our understanding of more complex behaviours (i.e. what fish are doing as different from spatial movements) has usually been inferred from movement data because it has not been possible to record directly specific behavioural events such as feeding or spawning. This is because the events are usually infrequent, irregular and often quite brief and so not amenable to a technology based on taking regular but infrequent records of continuously available variables. The recent implementation of new sensors (e.g. physical movement, tri-axial accelerometers), rapid (< 30 Hz) sampling capabilities, enhanced memory and more complex data capture protocols has lead to the development of archival tags that can be used to detect and record complex behaviours such as feeding and spawning. We describe recent developments with archival tags and their use to monitor feeding and spawning in fish together with the application of tri-axial accelerometry that can be used to quantify behaviour and metabolic rate. These can then be used to assess the cost of behaviours with a view to understanding how appropriate they are as responses to environmental variability. Keywords: telemetry, behaviour, data storage ta

Distinct Distribution Patterns of Potassium Channel Sub-Units in Somato-Dendritic Compartments of Neurons of the Medial Superior Olive

Coincidence detector neurons of the medial superior olive (MSO) are sensitive to interaural time differences in the range of a few tens of microseconds. The biophysical basis for this remarkable acuity is a short integration time constant of the membrane, which is achieved by large low voltage-activated potassium and hyperpolarization-activated inward cation conductances. Additional temporal precision is thought to be achieved through a sub-cellular distribution of low voltage-activated potassium channel expression biased to the soma. To evaluate the contribution of potassium channels, we investigated the presence and sub-cellular distribution profile of seven potassium channel sub-units in adult MSO neurons of gerbils. We find that low- and high voltage-activated potassium channels are present with distinct sub-cellular distributions. Overall, low voltage-activated potassium channels appear to be biased to the soma while high voltage-activated potassium channels are more evenly distributed and show a clear expression at distal dendrites. Additionally, low voltage-activated potassium channel sub-units co-localize with glycinergic inputs while HCN1 channels co-localize more with high voltage-activated potassium channels. Functionally, high voltage-activated potassium currents are already active at low voltages near the resting potential. We describe a possible role of high voltage-activated potassium channels in modulating EPSPs in a computational model and contributing to setting the integration time window of coincidental inputs. Our data shows that MSO neurons express a large set of different potassium channels with distinct functional relevance

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

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

Distinct Distribution Patterns of Potassium Channel Sub-Units in Somato-Dendritic Compartments of Neurons of the Medial Superior Olive

Coincidence detector neurons of the medial superior olive (MSO) are sensitive to interaural time differences in the range of a few tens of microseconds. The biophysical basis for this remarkable acuity is a short integration time constant of the membrane, which is achieved by large low voltage-activated potassium and hyperpolarization-activated inward cation conductances. Additional temporal precision is thought to be achieved through a sub-cellular distribution of low voltage-activated potassium channel expression biased to the soma. To evaluate the contribution of potassium channels, we investigated the presence and sub-cellular distribution profile of seven potassium channel sub-units in adult MSO neurons of gerbils. We find that low- and high voltage-activated potassium channels are present with distinct sub-cellular distributions. Overall, low voltage-activated potassium channels appear to be biased to the soma while high voltage-activated potassium channels are more evenly distributed and show a clear expression at distal dendrites. Additionally, low voltage-activated potassium channel sub-units co-localize with glycinergic inputs while HCN1 channels co-localize more with high voltage-activated potassium channels. Functionally, high voltage-activated potassium currents are already active at low voltages near the resting potential. We describe a possible role of high voltage-activated potassium channels in modulating EPSPs in a computational model and contributing to setting the integration time window of coincidental inputs. Our data shows that MSO neurons express a large set of different potassium channels with distinct functional relevance

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