Mouse Activity across Time Scales: Fractal Scenarios

In this work we devise a classification of mouse activity patterns based on accelerometer data using Detrended Fluctuation Analysis. We use two characteristic mouse behavioural states as benchmarks in this study: waking in free activity and slow-wave sleep (SWS). In both situations we find roughly the same pattern: for short time intervals we observe high correlation in activity - a typical 1/f complex pattern - while for large time intervals there is anti-correlation. High correlation of short intervals ( to : waking state and to : SWS) is related to highly coordinated muscle activity. In the waking state we associate high correlation both to muscle activity and to mouse stereotyped movements (grooming, waking, etc.). On the other side, the observed anti-correlation over large time scales ( to : waking state and to : SWS) during SWS appears related to a feedback autonomic response. The transition from correlated regime at short scales to an anti-correlated regime at large scales during SWS is given by the respiratory cycle interval, while during the waking state this transition occurs at the time scale corresponding to the duration of the stereotyped mouse movements. Furthermore, we find that the waking state is characterized by longer time scales than SWS and by a softer transition from correlation to anti-correlation. Moreover, this soft transition in the waking state encompass a behavioural time scale window that gives rise to a multifractal pattern. We believe that the observed multifractality in mouse activity is formed by the integration of several stereotyped movements each one with a characteristic time correlation. Finally, we compare scaling properties of body acceleration fluctuation time series during sleep and wake periods for healthy mice. Interestingly, differences between sleep and wake in the scaling exponents are comparable to previous works regarding human heartbeat. Complementarily, the nature of these sleep-wake dynamics could lead to a better understanding of neuroautonomic regulation mechanisms.     

Scaling effects and spatio-temporal multilevel dynamics in epileptic seizures

Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the complete loss of body control. In this paper, we aim to contribute towards a better understanding of the dynamical systems phenomena that cause seizures. Based on data analysis and modelling, seizure dynamics can be identified to possess multiple spatial scales and on each spatial scale also multiple time scales. At each scale, we reach several novel insights. On the smallest spatial scale we consider single model neurons and investigate early-warning signs of spiking. This introduces the theory of critical transitions to excitable systems. For clusters of neurons (or neuronal regions) we use patient data and find oscillatory behavior and new scaling laws near the seizure onset. These scalings lead to substantiate the conjecture obtained from mean-field models that a Hopf bifurcation could be involved near seizure onset. On the largest spatial scale we introduce a measure based on phase-locking intervals and wavelets into seizure modelling. It is used to resolve synchronization between different regions in the brain and identifies time-shifted scaling laws at different wavelet scales. We also compare our wavelet-based multiscale approach with maximum linear cross-correlation and mean-phase coherence measures.     

How the Scientific Community Reacts to Newly Submitted Preprints: Article Downloads,Twitter Mentions,and Citations

We analyze the online response to the preprint publication of a cohort of 4,606 scientific articles submitted to the preprint database arXiv.org between October 2010 and May 2011. We study three forms of responses to these preprints: downloads on the arXiv.org site, mentions on the social media site Twitter, and early citations in the scholarly record. We perform two analyses. First, we analyze the delay and time span of article downloads and Twitter mentions following submission, to understand the temporal configuration of these reactions and whether one precedes or follows the other. Second, we run regression and correlation tests to investigate the relationship between Twitter mentions, arXiv downloads, and article citations. We find that Twitter mentions and arXiv downloads of scholarly articles follow two distinct temporal patterns of activity, with Twitter mentions having shorter delays and narrower time spans than arXiv downloads. We also find that the volume of Twitter mentions is statistically correlated with arXiv downloads and early citations just months after the publication of a preprint, with a possible bias that favors highly mentioned articles.     

The Temporal Spectrum of Adult Mosquito Population Fluctuations: Conceptual and Modeling Implications

An improved understanding of mosquito population dynamics under natural environmental forcing requires adequate field observations spanning the full range of temporal scales over which mosquito abundance fluctuates in natural conditions. Here we analyze a 9-year daily time series of uninterrupted observations of adult mosquito abundance for multiple mosquito species in North Carolina to identify characteristic scales of temporal variability, the processes generating them, and the representativeness of observations at different sampling resolutions. We focus in particular on Aedes vexans and Culiseta melanura and, using a combination of spectral analysis and modeling, we find significant population fluctuations with characteristic periodicity between 2 days and several years. Population dynamical modelling suggests that the observed fast fluctuations scales (2 days-weeks) are importantly affected by a varying mosquito activity in response to rapid changes in meteorological conditions, a process neglected in most representations of mosquito population dynamics. We further suggest that the range of time scales over which adult mosquito population variability takes place can be divided into three main parts. At small time scales (indicatively 2 days-1 month) observed population fluctuations are mainly driven by behavioral responses to rapid changes in weather conditions. At intermediate scales (1 to several month) environmentally-forced fluctuations in generation times, mortality rates, and density dependence determine the population characteristic response times. At longer scales (annual to multi-annual) mosquito populations follow seasonal and inter-annual environmental changes. We conclude that observations of adult mosquito populations should be based on a sub-weekly sampling frequency and that predictive models of mosquito abundance must include behavioral dynamics to separate the effects of a varying mosquito activity from actual changes in the abundance of the underlying population.     

Quantifying Stock Return Distributions in Financial Markets

Being able to quantify the probability of large price changes in stock markets is of crucial importance in understanding financial crises that affect the lives of people worldwide. Large changes in stock market prices can arise abruptly, within a matter of minutes, or develop across much longer time scales. Here, we analyze a dataset comprising the stocks forming the Dow Jones Industrial Average at a second by second resolution in the period from January 2008 to July 2010 in order to quantify the distribution of changes in market prices at a range of time scales. We find that the tails of the distributions of logarithmic price changes, or returns, exhibit power law decays for time scales ranging from 300 seconds to 3600 seconds. For larger time scales, we find that the distributions tails exhibit exponential decay. Our findings may inform the development of models of market behavior across varying time scales.     

How Structure Shapes Dynamics: Knowledge Development in Wikipedia - A Network Multilevel Modeling Approach

Using a longitudinal network analysis approach, we investigate the structural development of the knowledge base of Wikipedia in order to explain the appearance of new knowledge. The data consists of the articles in two adjacent knowledge domains: psychology and education. We analyze the development of networks of knowledge consisting of interlinked articles at seven snapshots from 2006 to 2012 with an interval of one year between them. Longitudinal data on the topological position of each article in the networks is used to model the appearance of new knowledge over time. Thus, the structural dimension of knowledge is related to its dynamics. Using multilevel modeling as well as eigenvector and betweenness measures, we explain the significance of pivotal articles that are either central within one of the knowledge domains or boundary-crossing between the two domains at a given point in time for the future development of new knowledge in the knowledge base.     

Dynamics of immobilized and native Escherichia coli dihydrofolate reductase by quasielastic neutron scattering

The internal dynamics of native and immobilized Escherichia coli dihydrofolate reductase (DHFR) have been examined using incoherent quasielastic neutron scattering. These results reveal no difference between the high frequency vibration mean-square displacement of the native and the immobilized E. coli DHFR. However, length-scale-dependent, picosecond dynamical changes are found. On longer length scales, the dynamics are comparable for both DHFR samples. On shorter length scales, the dynamics is dominated by local jump motions over potential barriers. The residence time for the protons to stay in a potential well is tau = 7.95 +/- 1.02 ps for the native DHFR and tau = 20.36 +/- 1.80 ps for the immobilized DHFR. The average height of the potential barrier to the local motions is increased in the immobilized DHFR, and may increase the activation energy for the activity reaction, decreasing the rate as observed experimentally. These results suggest that the local motions on the picosecond timescale may act as a lubricant for those associated with DHFR activity occurring on a slower millisecond timescale. Experiments indicate a significantly slower catalytic reaction rate for the immobilized E. coli DHFR. However, the immobilization of the DHFR is on the exterior of the enzyme and essentially distal to the active site, thus this phenomenon has broad implications for the action of drugs distal to the active site.     

Bursting Reverberation as a Multiscale Neuronal Network Process Driven by Synaptic Depression-Facilitation

Neuronal networks can generate complex patterns of activity that depend on membrane properties of individual neurons as well as on functional synapses. To decipher the impact of synaptic properties and connectivity on neuronal network behavior, we investigate the responses of neuronal ensembles from small (5–30 cells in a restricted sphere) and large (acute hippocampal slice) networks to single electrical stimulation: in both cases, a single stimulus generated a synchronous long-lasting bursting activity. While an initial spike triggered a reverberating network activity that lasted 2–5 seconds for small networks, we found here that it lasted only up to 300 milliseconds in slices. To explain this phenomena present at different scales, we generalize the depression-facilitation model and extracted the network time constants. The model predicts that the reverberation time has a bell shaped relation with the synaptic density, revealing that the bursting time cannot exceed a maximum value. Furthermore, before reaching its maximum, the reverberation time increases sub-linearly with the synaptic density of the network. We conclude that synaptic dynamics and connectivity shape the mean burst duration, a property present at various scales of the networks. Thus bursting reverberation is a property of sufficiently connected neural networks, and can be generated by collective depression and facilitation of underlying functional synapses.     

Spatial and temporal scales relevant for conservation of dead-wood associated species: current status and perspectives

Dead wood is a key substrate for forest biodiversity, hosting a rich and often threatened biodiversity of wood-living species. However, the relationship between the occurrence of dead wood and associated species is modified by several environmental factors. Here we review the present state of knowledge on how dead wood on different spatial and temporal scales affects saproxylic biodiversity. We searched for peer-reviewed studies on saproxylic species that compared dead wood distribution on at least two spatial or temporal scales. We scanned close to 300 articles, of which 34 fit our criteria. 20 studies were directed towards the current amount of dead wood at different scale levels and how this relates to the abundance or occurrence of saproxylic species, embracing scales from 10 m to 10 km. 14 studies compared time-lagged effects of dead wood, covering time-lags from 25 years to more than 200 years. The reviewed articles focused mainly on European forest and addressed invertebrates (mostly beetles), alone or in combination with fungi (27 articles), fungi (six articles), or lichens (one article). Although the significance of dead wood for forest biodiversity is firmly established, the reviewed studies show that we still have limited knowledge of the relationship between saproxylic biodiversity and spatial and temporal scales. Based on the reviewed studies, we conclude that there is large variation in response to spatial and temporal dead wood patterns between different taxa and sub-groups. Still, several of the reviewed papers indicate that time-lagged effects deserve more attention, especially on a landscape scale and for specialized or red-listed species. Further work is required before firm management recommendations can be suggested.     

Time-oriented hierarchical method for computation of principal components using subspace learning algorithm

Principal Component Analysis (PCA) and Principal Subspace Analysis (PSA) are classic techniques in statistical data analysis, feature extraction and data compression. Given a set of multivariate measurements, PCA and PSA provide a smaller set of "basis vectors" with less redundancy, and a subspace spanned by them, respectively. Artificial neurons and neural networks have been shown to perform PSA and PCA when gradient ascent (descent) learning rules are used, which is related to the constrained maximization (minimization) of statistical objective functions. Due to their low complexity, such algorithms and their implementation in neural networks are potentially useful in cases of tracking slow changes of correlations in the input data or in updating eigenvectors with new samples. In this paper we propose PCA learning algorithm that is fully homogeneous with respect to neurons. The algorithm is obtained by modification of one of the most famous PSA learning algorithms--Subspace Learning Algorithm (SLA). Modification of the algorithm is based on Time-Oriented Hierarchical Method (TOHM). The method uses two distinct time scales. On a faster time scale PSA algorithm is responsible for the "behavior" of all output neurons. On a slower scale, output neurons will compete for fulfillment of their "own interests". On this scale, basis vectors in the principal subspace are rotated toward the principal eigenvectors. At the end of the paper it will be briefly analyzed how (or why) time-oriented hierarchical method can be used for transformation of any of the existing neural network PSA method, into PCA method.     

Genetic differentiation on multiple spatial scales in an ecotype-forming marine snail with limited dispersal: Littorina saxatilis

The population genetic structure of marine species lacking free-swimming larvae is expected to be strongly affected by random genetic drift among populations, resulting in genetic isolation by geographical distance. At the same time, ecological separation over microhabitats followed by direct selection on those parts of the genome that affect adaptation might also be strong. Here, we address the question of how the relative importance of stochastic vs. selective structuring forces varies at different geographical scales. We use microsatellite DNA and allozyme data from samples of the marine rocky shore snail Littorina saxatilis over distance scales ranging from metres to 1000 km, and we show that genetic drift is the most important structuring evolutionary force at distances > 1 km. On smaller geographical scales (< 1 km), divergent selection between contrasting habitats affects population genetic structure by impeding gene flow over microhabitat borders (microsatellite structure), or by directly favouring specific alleles of selected loci (allozyme structure). The results suggest that evolutionary drivers of population genetic structure cannot a priori be assumed to be equally important at different geographical scales. © 2008 The Linnean Society of London, Biological Journal of the Linnean Society , 2008, 94 , 31–40.     

Multiway analysis of epilepsy tensors

MOTIVATION: The success or failure of an epilepsy surgery depends greatly on the localization of epileptic focus (origin of a seizure). We address the problem of identification of a seizure origin through an analysis of ictal electroencephalogram (EEG), which is proven to be an effective standard in epileptic focus localization. SUMMARY: With a goal of developing an automated and robust way of visual analysis of large amounts of EEG data, we propose a novel approach based on multiway models to study epilepsy seizure structure. Our contributions are 3-fold. First, we construct an Epilepsy Tensor with three modes, i.e. time samples, scales and electrodes, through wavelet analysis of multi-channel ictal EEG. Second, we demonstrate that multiway analysis techniques, in particular parallel factor analysis (PARAFAC), provide promising results in modeling the complex structure of an epilepsy seizure, localizing a seizure origin and extracting artifacts. Third, we introduce an approach for removing artifacts using multilinear subspace analysis and discuss its merits and drawbacks. RESULTS: Ictal EEG analysis of 10 seizures from 7 patients are included in this study. Our results for 8 seizures match with clinical observations in terms of seizure origin and extracted artifacts. On the other hand, for 2 of the seizures, seizure localization is not achieved using an initial trial of PARAFAC modeling. In these cases, first, we apply an artifact removal method and subsequently apply the PARAFAC model on the epilepsy tensor from which potential artifacts have been removed. This method successfully identifies the seizure origin in both cases.     

Reduction of slow-fast asymptotically autonomous systems with applications to gradostat models

Two distinguishing features characterize the population dynamic models considered in the present work. On the one hand, we consider several interacting organization levels associated to different time scales. On the other hand, the environment tends to be constant in the long term. The mathematical representation of these properties leads to slow-fast asymptotically autonomous systems. These characteristics add some realism in the models. However, the analytical study of this class of systems is generally hard to perform.Here we present a reduction technique that can be included among the so-called approximate aggregation methods. The existence of different time scales, together with the long term features, are used to build up a simpler system, which can be described by means of a lower number of state variables. The asymptotic behavior of the simplified model helps to study the original one.The reduction procedure is formulated in a general way. Following, two illustrations of asymptotically autonomous models with two time scales, in a gradostat, are given: a consumer–resource model and a competition model. Finally, a wider range of applications is suggested.     

The diagenetic fate of collagen as revealed by analytical pyrolysis of fossil fish scales from deep time

The mechanism of protein degradation has remained a topic of debate (specifically concerning their preservation in deep time), which has recently been invigorated due to multiple published reports of preservation ranging from Miocene to the Triassic that potentially challenge the convention that protein preservation beyond the Cenozoic is extremely uncommon or is expected to be absent altogether, and thus have attracted skepticism. In this paper, we analyze fossil fish scales from the Cretaceous, Jurassic, and Triassic using comprehensive pyrolysis gas chromatography coupled with time-of-flight mass spectrometry and compare the pyrolytic products so obtained with a well-preserved fish scale from Late Pliocene, in an attempt to better understand the effects of diagenesis on protein degradation at the molecular level through deep time. We find that the Pliocene fish scale displays a large number of N-bearing pyrolytic products, including abundant substituted cyclic 2,5-diketopiperazines (2,5-DKPs) which are diagnostic products of peptide and amino acid pyrolysis. We identify N-bearing compounds in the Mesozoic fish scales—however, among the 2,5-DKPs that were identified in the Pliocene scale, only diketodipyrrole (or cyclo (Pyr-Pyr)) is present in the Mesozoic scales. We discuss the implications of N-bearing pyrolytic products with emphasis on 2,5-DKPs in geological samples and conclude that the discrepancy in abundance and variety of N-bearing products between Pliocene and Mesozoic scales indicates that the protein component in the latter has been extensively diagenetically altered, while a suite of DKPs such as in the former would imply stronger evidence to indicate preservation of protein. We conclude that analytical pyrolysis is an effective tool for detecting preservation of intact proteins, as well as for providing insights into their degradation mechanisms, and can potentially be utilized to assign proteinaceous origin to a fossil sample of unknown affinity.     

Out of the dark: 350 million years of conservatism and evolution in diel activity patterns in vertebrates

Many animals are active only during a particular time (e.g., day vs. night), a partitioning that may have important consequences for species coexistence. An open question is the extent to which this diel activity niche is evolutionarily conserved or labile. Here, we analyze diel activity data across a phylogeny of 1914 tetrapod species. We find strong phylogenetic signal, showing that closely related species tend to share similar activity patterns. Ancestral reconstructions show that nocturnality was the most likely ancestral diel activity pattern for tetrapods and many major clades within it (e.g., amphibians, mammals). Remarkably, nocturnal activity appears to have been maintained continuously in some lineages for ～350 million years. Thus, we show that traits involved in local‐scale resource partitioning can be conserved over strikingly deep evolutionary time scales. We also demonstrate a potentially important (but often overlooked) metric of niche conservatism. Finally, we show that diurnal lineages appear to have faster speciation and diversification rates than nocturnal lineages, which may explain why there are presently more diurnal tetrapod species even though diurnality appears to have evolved more recently. Overall, our results may have implications for studies of community ecology, species richness, and the evolution of diet and communication systems.     

Analysis,classification, and coding of multielectrode spike trains with hidden Markov models

It is shown that hidden Markov models (HMMs) are a powerful tool in the analysis of multielectrode data. This is demonstrated for a 30-electrode measurement of neuronal spike activity in the monkey's visual cortex during the application of different visual stimuli. HMMs with optimized parameters code the information contained in the spatiotemporal discharge patterns as a probabilistic function of a Markov process and thus provide abstract dynamical models of the pattern-generating process. We compare HMMs obtained from vector-quantized data with models in which parametrized output processes such as multivariate Poisson or binomial distributions are assumed. In the latter cases the visual stimuli are recognized at rates of more than 90% from the neuronal spike patterns. An analysis of the models obtained reveals important aspects of the coding of information in the brain. For example, we identify relevant time scales and characterize the degree and nature of the spatiotemporal variations on these scales.     

Secondary osteon and Haversian canal dimensions as behavioral indicators

Variation in the size of structures within mature cortical bone is relevant to our understanding of apparent differences between human samples, and it is relevant to the development of histologically based age-estimation methods. It was proposed that variation may reflect effects of physical activity, through biomechanical and/or metabolic mechanisms. If these factors are local, femoral osteon area (On.Ar) should be more histologically variable than On.Ar in ribs. Ribs should show a higher variation in Haversian canal area (H.Ar) if they are sites of more remodeling activity and hence of arrested refilling of secondary osteons at time of death. This study compares On.Ar and H.Ar of secondary osteons from femora (15) and ribs (29) from 44 Holocene (Later Stone Age) foragers from South Africa (M = 19, F = 25) to values from paired femora and ribs from historic samples (Spitalfields and St. Thomas, 20 pairs from each). Fixed-effects analysis of variance demonstrates rib On.Ar to be significantly smaller than femur, but with no sex or age effects. The femur-to-rib On.Ar ratio is lower for the Holocene foragers than for the two modern samples because of relatively large rib On.Ar. Femora and ribs from the same skeleton normally show femoral On.Ar larger than rib On.Ar (37/44 pairs). Mean femoral values of On.Ar are more diverse than rib On.Ar values, but within-sample coefficients of variation are similar. Values for H.Ar are highly variable and do not reflect anatomical site, age, sex, or population effects. The patterning of osteon size does not appear to be linked to physical activity or to different rates of metabolic activity within the skeleton, at least not in a straightforward way.     

The antibacterial activity of honey derived from Australian flora

Chronic wound infections and antibiotic resistance are driving interest in antimicrobial treatments that have generally been considered complementary, including antimicrobially active honey. Australia has unique native flora and produces honey with a wide range of different physicochemical properties. In this study we surveyed 477 honey samples, derived from native and exotic plants from various regions of Australia, for their antibacterial activity using an established screening protocol. A level of activity considered potentially therapeutically useful was found in 274 (57%) of the honey samples, with exceptional activity seen in samples derived from marri (Corymbia calophylla), jarrah (Eucalyptus marginata) and jellybush (Leptospermum polygalifolium). In most cases the antibacterial activity was attributable to hydrogen peroxide produced by the bee-derived enzyme glucose oxidase. Non-hydrogen peroxide activity was detected in 80 (16.8%) samples, and was most consistently seen in honey produced from Leptospermum spp. Testing over time found the hydrogen peroxide-dependent activity in honey decreased, in some cases by 100%, and this activity was more stable at 4 °C than at 25 °C. In contrast, the non-hydrogen peroxide activity of Leptospermum honey samples increased, and this was greatest in samples stored at 25 °C. The stability of non-peroxide activity from other honeys was more variable, suggesting this activity may have a different cause. We conclude that many Australian honeys have clinical potential, and that further studies into the composition and stability of their active constituents are warranted.     

Epidemiologically Optimal Static Networks from Temporal Network Data

One of network epidemiology''s central assumptions is that the contact structure over which infectious diseases propagate can be represented as a static network. However, contacts are highly dynamic, changing at many time scales. In this paper, we investigate conceptually simple methods to construct static graphs for network epidemiology from temporal contact data. We evaluate these methods on empirical and synthetic model data. For almost all our cases, the network representation that captures most relevant information is a so-called exponential-threshold network. In these, each contact contributes with a weight decreasing exponentially with time, and there is an edge between a pair of vertices if the weight between them exceeds a threshold. Networks of aggregated contacts over an optimally chosen time window perform almost as good as the exponential-threshold networks. On the other hand, networks of accumulated contacts over the entire sampling time, and networks of concurrent partnerships, perform worse. We discuss these observations in the context of the temporal and topological structure of the data sets.     

How far do songbirds disperse?

Dispersal distances determine the scales over which many population processes occur. Knowledge of these distances may therefore be crucial in determining the appropriate spatial scales for research and management. However, dispersal distances are difficult to measure, especially for vagile organisms like songbirds. For these species, the use of traditional mark–recapture and radio‐telemetry methods is problematic. We used positive one‐year time‐lagged correlations in abundance to estimate natal dispersal distances. Using the North American Breeding Bird Survey database, we examined one‐year time‐lagged correlations between pairs of North American songbird samples separated by 10–100 km. We submit that consistent positive one‐year time‐lagged correlations reflect the exchange of individuals through dispersal. We found positive one‐year time‐lagged correlations between pairs of samples from 25 different songbird species. The median distances of these correlations ranged from 15 to 95 km, depending on the species. These distances were positively correlated with body size and wing length. Dispersal appears to be the most parsimonious explanation for the time‐lagged correlations we observed in these species. The putative dispersal distances we measured are generally an order of magnitude longer than those reported in the literature.