Bursting Rate Variability

In this paper, a new electromyographic phenomenon, referred to as Bursting Rate Variability (BRV), is reported. Not only does it manifest itself visually as a train of short periods of accrued surface electromyographic (sEMG) activity in the traces, but it has a deeper underpinning because the sEMG bursts are synchronous with wavelet packets in the D8 subband of the Daubechies 3 (db3) wavelet decomposition of the raw signal referred to as “D8 doublets”—which are absent during muscle relaxation. Moreover, the db3 wavelet decomposition reconstructs the entire sEMG bursts with two contiguous relatively high detail coefficients at level 8, suggesting a high incidence of two consecutive neuronal discharges. Most importantly, the timing between successive bursts shows some variability, hence the BRV acronym. Contrary to Heart Rate Variability (HRV), where the R-wave is easily identified, here, time-localization of the burst requires a statistical waveform matching between the “D8 doublet” and the burst in the raw sEMG signal. Furthermore, statistical fitting of the empirical distribution of return times shows a striking difference between control and quadriplegic subjects. Finally, the BRV rate appears to be within 60–88 bursts per minute on average among 9 human subjects, suggesting a possible connection between BRV and HRV.

Modelling migration in birds: competition's role in maintaining individual variation

Animals exhibit extensive intraspecific variation in behaviour. Causes of such variation are less well understood. Here, we ask when competition leads to the maintenance of multiple behavioural strategies. We model variability using the timing of bird migration as an example. Birds often vary in when they return from non-breeding grounds to establish breeding territories. We assume that early-arriving birds (counting permanent residents as ‘earliest’) select the best territories. But arriving before the optimal (frequency-independent) breeding date incurs a fitness penalty. Using simulations, we find stable sets of return dates. When year-round residency is viable, the greatest between-individual variation occurs when a small proportion of permanent residents is favoured, and the rest of the population varies in their return times. However, when fitness losses due to year-round residency exceed the benefits of breeding in the worst territory, all individuals migrate, although their return dates often vary continuously. In that case, individual variation is inversely related to fitness risks and positively related to territory inequality. This result is applicable across many systems: when there is more to gain through competition, or when its risks are small, a diversity of individual strategies prevails. Additionally, stability can depend upon the distribution of resources.

Extrinsic and intrinsic factors influencing the emergence and return of Asian particolored bats Vespertilio sinensis

The circadian rhythm is an adaptive biological process, allows organisms to anticipate daily environmental changes and implement appropriate strategies. Circadian rhythms play a crucial role in the health and survival of organisms. However, little is known concerning how intrinsic and extrinsic factors affect animal daily rhythms in the field, especially in nocturnal animals. Here, we investigated the emergence and return times of Vesperilio sinensis, and also integrated environmental conditions (temperature, humidity and light intensity) and biotic factors (reproductive status and predation risk) to determine causes of variation in the activity rhythms of the bats. We found that variation in the first emergence time, the mid-emergence time, and the final return time were distinct. The results demonstrated that the emergence and return times of bats were affected by light intensity, reproductive status, and predation risk in a relatively complex pattern. Light intensity had the greatest contribution to activity rhythms. Moreover, we first investigated the effects of actual predators on the activity rhythms of bats; the results showed that the mid-emergence time of bats was earlier as predators were hunting, but the final return time was later when predators were present. This challenges the traditional view that high predation risk leads to later emergence and earlier return. Finally, our results also highlighted the importance of higher energy demands during the lactation period in bats to variation in activity rhythms. These results improve our understanding of the patterns and causes of variation in activity rhythms in bats and other nocturnal animals.

Reconstructing a minimal topological dynamical system from a set of return times

We investigate to what extent a minimal topological dynamical system is uniquely determined by a set of return times to some open set. We show that in many situations, this is indeed the case as long as the closure of this open set has no non-trivial translational symmetries. For instance, we show that under this assumption, two Kronecker systems with the same set of return times must be isomorphic. More generally, we show that if a minimal dynamical system has a set of return times that coincides with a set of return times to some open set in a Kronecker system with translationarily asymmetric closure, then that Kronecker system must be a factor. We also study similar problems involving nilsystems and polynomial return times. We state a number of questions on whether these results extend to other homogeneous spaces and transitive group actions, some of which are already interesting for finite groups.

Gaps of saddle connection directions for some branched covers of tori

We compute the gap distribution of directions of saddle connections for two classes of translation surfaces. One class will be the translation surfaces arising from gluing two identical tori along a slit. These yield the first explicit computations of gap distributions for non-lattice translation surfaces. We show that this distribution has support at zero and quadratic tail decay. We also construct examples of translation surfaces in any genus $d>1$ that have the same gap distribution as the gap distribution of two identical tori glued along a slit. The second class we consider are twice-marked tori and saddle connections between distinct marked points with a specific orientation. These results can be interpreted as the gap distribution of slopes of affine lattices. We obtain our results by translating the question of gap distributions to a dynamical question of return times to a transversal under the horocycle flow on an appropriate moduli space.

Similar stretch reflexes and behavioral patterns are expressed by the dominant and non-dominant arms during postural control

Limb dominance is evident in many daily activities leading to the prominent idea that each hemisphere of the brain specializes in controlling different aspects of movement. Past studies suggest the dominant arm is primarily controlled via an internal model of limb dynamics that enables the nervous system to produce efficient movements. In contrast, the non-dominant arm may be primarily controlled via impedance mechanisms that rely on the strong modulation of sensory feedback from individual joints to control limb posture. We tested whether such differences are evident in behavioral responses and stretch reflexes following sudden displacement of the arm during posture control. Experiment 1 applied specific combinations of elbow-shoulder torque perturbations (the same for all participants). Peak joint displacements, return times, endpoint accuracy, and the directional tuning and amplitude of stretch reflexes in nearly all muscles were not statistically different between the two arms. Experiment 2 induced specific combinations of joint motion (the same for all participants). Again, peak joint displacements, return times, endpoint accuracy, and the directional tuning and amplitude of stretch reflexes in nearly all muscles did not differ statistically when countering the imposed loads with each arm. Moderate to strong correlations were found between stretch reflexes and behavioral responses to the perturbations with the two arms across both experiments. Collectively, the results do not support the idea that the dominant arm specializes in exploiting internal models and the non-dominant arm in impedance control by increasing reflex gains to counter sudden loads imposed on the arms during posture control.

Multiple Submerged Tidal Notches: A Witness of Sequences of Coseismic Subsidence in the Aegean Sea, Greece

In some islands of the Aegean, there is evidence of the occurrence of repeated rapid subsidences during the Late Holocene. In this paper, the shape of tidal notches that may be well-preserved underwater is recalled in order to reconstruct sequences of coseismic subsidences and other relative sea-level changes, which occurred during, at least, the last few millennia. A reanalysis of the published measurements of submerged tidal notches in several islands reveals that subsidence trends in many areas of the Aegean are not continuous with gradual movement but, also, are the result of repeated coseismic vertical subsidences of some decimetres at each time. The estimated average return times are of the order of approximately some centuries to one millennium. Although the results cannot be used for short-term predictions of earthquakes, they may provide useful indications on the long-term tectonic trends that are active in the Aegean region.

Multidimensional Multiplicative Combinatorial Properties of Dynamical Syndetic Sets

In this paper, it is shown that for a minimal system (X, G), if H is a normal subgroup of G with finite index n, then X can be decomposed into n components of closed sets such that each component is minimal under H-action. Meanwhile, we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms, the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension, extending a previous result by Glasscock, Koutsogiannis and Richter.

Potential Well in Poincaré Recurrence

From a physical/dynamical system perspective, the potential well represents the proportional mass of points that escape the neighbourhood of a given point. In the last 20 years, several works have shown the importance of this quantity to obtain precise approximations for several recurrence time distributions in mixing stochastic processes and dynamical systems. Besides providing a review of the different scaling factors used in the literature in recurrence times, the present work contributes two new results: (1) For ϕ-mixing and ψ-mixing processes, we give a new exponential approximation for hitting and return times using the potential well as the scaling parameter. The error terms are explicit and sharp. (2) We analyse the uniform positivity of the potential well. Our results apply to processes on countable alphabets and do not assume a complete grammar.