Abstract Musical sequences are correlated dynamical processes that may differ depending on musical styles. We aim to quantify the correlations through power spectral analysis of pitch sequences in a large corpus of musical compositions as well as improvised performances. Using a multitaper method we extend the power spectral estimates down to the smallest possible frequencies optimizing the tradeoff between bias and variance. The power spectral densities reveal a characteristic behavior; they typically follow inverse power laws (1/f β -noise), yet only down to a cutoff frequency, where they end in a plateau. Correspondingly the pitch autocorrelation function exhibits slow power law decays only up to a cutoff time, beyond which the correlations vanish. We determine cutoff times between 4 and 100 quarter note units for the compositions and improvisations of the corpus, serving as a measure for the degree of persistence and predictability in music. The histogram of exponents β for the power law regimes has a pronounced peak near β = 1 for classical compositions, but is much broader for jazz improvisations.

To which extent and how do jazz musicians synchronize their timing to create swing? Swing is a salient feature of jazz music, yet its main psychoacoustical and musical components have remained elusive—save the obvious long-short subdivision of quarter notes. In particular, the possible role of microtiming deviations for swing has been a subject of long-standing controversy. Adopting an operational definition of swing we present a study which ultimately demonstrates a positive effect of certain microtiming deviations on swing. We manipulate the timing of original piano recordings to carry out an experiment with professional and semi-professional jazz musicians measuring the swing of different timing conditions. Thereby we prove that slightly delayed downbeats and synchronized offbeats of a soloist with respect to a rhythm section enhance swing. Analyzing a set of 456 jazz improvisations we find that many jazz musicians do use minute downbeat delays. These results show that systematic microtiming deviations in the form of downbeat delays are a key component of swing in jazz.

The severity of infectious diseases and epidemics increases drastically, when pathogens start being transmitted between humans, as thereby they can dispose of human traffic networks for their spreading. This can transform an epidemic into a worldwide threatening pandemic, as the current COVID-19 crisis has shown. Traffic networks exist on multiple scales and the spreading of pathogens exhibits superdiffusive properties. This talk will emphasize and analyze the key role of human mobility for the modeling, forecast, and control of epidemic spreading. A major problem is posed by the limited availability of statistical data on human mobility. Various proxies are now utilized since we suggested dollar bills as proxies for human moblity. Recent work on endemic diseases in populations open to migration will be discussed.

This paper investigates the role of cantori for the quantum dynamics of a chaotic system with two degrees of freedom. They can act as barriers more drastically than in classical mechanics and inhibit the diffusive growth of mean square displacements. The asymptotic distribution decays exponentially in their vicinity. The penetration probability and depth of a KAM-torus are also determined.

Jazz music that swings has the fascinating power to elicit a pleasant sensation of flow in listeners and the desire to synchronize body movements with the music. Whether microtiming deviations (MTDs), i.e. small timing deviations below the bar or phrase level, enhance the swing feel is highly debated in the current literature. Studies on other groove related genres did not find evidence for a positive impact of MTDs. The present study addresses jazz music and swing in particular, as there is some evidence that microtiming patterns are genre-specific. We recorded twelve piano jazz standards played by a professional pianist and manipulated the natural MTDs of the recordings in systematic ways by quantizing, expanding and inverting them. MTDs were defined with respect to a grid determined by the average swing ratio. The original and manipulated versions were presented in an online survey and evaluated by 160 listeners with various musical skill levels and backgrounds. Across pieces the quantized versions (without MTDs) were rated slightly higher and versions with expanded MTDs were rated lower with regard to swing than the original recordings. Unexpectedly, inversion had no impact on swing ratings except for two pieces. Our results suggest that naturally fluctuating MTDs are not an essential factor for the swing feel.

The magneto-resistance of antidot lattices shows pronounced peaks, which became a hallmark of ballistic electron transport. While most studies agree that they reflect the interplay of regular and chaotic motion in the quasi-classical dynamics, the exact mechanism has been surprisingly controversial. Inspired by recent experiments on graphene antidot lattices showing that the effect survives strong impurity scattering, we give a new explanation of the peaks linked to a fundamental relation between collision times and accessible phase space volumes, accounting for their robustness. Due to the fundamental nature of the mechanism described it will be relevant in many mesoscopic transport phenomena.

Musical rhythms performed by humans typically show temporal fluctuations. While they have been characterized in simple rhythmic tasks, it is an open question what is the nature of temporal fluctuations, when several musicians perform music jointly in all its natural complexity. To study such fluctuations in over 100 original jazz and rock/pop recordings played with and without metronome we developed a semi-automated workflow allowing the extraction of cymbal beat onsets with millisecond precision. Analyzing the inter-beat interval (IBI) time series revealed evidence for two long-range correlated processes characterized by power laws in the IBI power spectral densities. One process dominates on short timescales ($t < 8$ beats) and reflects microtiming variability in the generation of single beats. The other dominates on longer timescales and reflects slow tempo variations. Whereas the latter did not show differences between musical genres (jazz vs. rock/pop), the process on short timescales showed higher variability for jazz recordings, indicating that jazz makes stronger use of microtiming fluctuations within a measure than rock/pop. Our results elucidate principles of rhythmic performance and can inspire algorithms for artificial music generation. By studying microtiming fluctuations in original music recordings, we bridge the gap between minimalistic tapping paradigms and expressive rhythmic performances.

Characteristics of ballistic motion are observable in transport experiments when the associated time scale is shorter than the impurity scattering time. We point out a general mechanism that circumvents this rule by linking different time scales through phase space volume conservation, a fundamental property of Hamiltonian systems. This finding was inspired by recent experiments on graphene antidot lattices, which show ballistic transport effects despite strong impurity scattering. We therefore exemplify this general mechanism for electronic transport in antidot superlattices and explain magnetoresistance experiments in graphene samples.

Perception, cognition and behavior rely on flexible communication between microcircuits in distinct cortical regions. The mechanisms underlying rapid information rerouting between such microcircuits are still unknown. It has been proposed that changing patterns of coherence between local gamma rhythms support flexible information rerouting. The stochastic and transient nature of gamma oscillations in vivo, however, is hard to reconcile with such a function. Here we show that models of cortical circuits near the onset of oscillatory synchrony selectively route input signals despite the short duration of gamma bursts and the irregularity of neuronal firing. In canonical multiarea circuits, we find that gamma bursts spontaneously arise with matched timing and frequency and that they organize information flow by large-scale routing states. Specific self-organized routing states can be induced by minor modulations of background activity.

We investigate the effects of dichotomous noise added to a classical harmonic oscillator in the form of stochastic time-dependent gain and loss states, whose durations are sampled from two distinct exponential waiting time distributions. Despite the stochasticity, stability criteria can be formulated when averaging over many realizations in the asymptotic time limit and serve to determine the boundary line in parameter space that separates regions of growing amplitudes from those of decaying ones. Furthermore, the concept of   symmetry remains applicable for such a stochastic oscillator and we use it to distinguish between an underdamped symmetric phase and an overdamped asymmetric phase. In the former case, the limit of stability is marked by the same average duration for the gain and loss states, while in the the latter case, a higher duration of the loss state is necessary to keep the system stable. The overdamped phase has an ordered structure imposing a position-velocity ratio locking and is viewed as a phase transition from the underdamped phase, which instead displays a broad and more disordered, but nevertheless,   symmetric structure. We also address the short time limit and the dynamics of the moments of the position and the velocity with the aim of revealing the extremely rich dynamics offered by this apparently quite simple mechanical system. The notions established so far may be extended and applied in the stabilization of light propagation in metamaterials and optical fibres with randomly distributed regions of asymmetric active and passive media.

Tuning curves are the functions that relate the responses of sensory neurons to various values within one continuous stimulus dimension (such as the orientation of a bar in the visual domain or the frequency of a tone in the auditory domain). They are commonly determined by fitting a model e.g. a Gaussian or other bell-shaped curves to the measured responses to a small subset of discrete stimuli in the relevant dimension. However, as neuronal responses are irregular and experimental measurements noisy, it is often difficult to determine reliably the appropriate model from the data. We illustrate this general problem by fitting diverse models to representative recordings from area MT in rhesus monkey visual cortex during multiple attentional tasks involving complex composite stimuli. We find that all models can be well-fitted, that the best model generally varies between neurons and that statistical comparisons between neuronal responses across different experimental conditions are affected quantitatively and qualitatively by specific model choices. As a robust alternative to an often arbitrary model selection, we introduce a model-free approach, in which features of interest are extracted directly from the measured response data without the need of fitting any model. In our attentional datasets, we demonstrate that data-driven methods provide descriptions of tuning curve features such as preferred stimulus direction or attentional gain modulations which are in agreement with fit-based approaches when a good fit exists. Furthermore, these methods naturally extend to the frequent cases of uncertain model selection. We show that model-free approaches can identify attentional modulation patterns, such as general alterations of the irregular shape of tuning curves, which cannot be captured by fitting stereotyped conventional models. Finally, by comparing datasets across different conditions, we demonstrate effects of attention that are cell- and even stimulus-specific. Based on these proofs-of-concept, we conclude that our data-driven methods can reliably extract relevant tuning information from neuronal recordings, including cells whose seemingly haphazard response curves defy conventional fitting approaches.

Spontaneous bursting activity in cultured neuronal networks is initiated by leader neurons, which constitute a small subset of first-to-fire neurons forming a sub-network that recruits follower neurons into the burst. While the existence and stability of leader neurons is well established, the influence of stimulation on the leader-follower dynamics is not sufficiently understood. By combining multi-electrode array recordings with whole field optical stimulation of cultured Channelrhodopsin-2 transduced hippocampal neurons, we show that fade-in photo-stimulation induces a significant shortening of intra-burst firing rate peak delay of follower electrodes after offset of the stimulation compared to unperturbed spontaneous activity. Our study shows that optogenetic stimulation can be used to change the dynamical fine structure of self-organized network bursts.

Fluctuations in the profile of the ocean floor can lead to large variations in tsunami wave height. A theory linking this behaviour to the branched flow characteristics of electron waves through semiconductors may provide a framework for prediction. Tsunamis exhibit surprisingly strong height fluctuations. An in-depth understanding of the mechanisms that lead to these variations in wave height is a prerequisite for reliable tsunami forecasting. It is known, for example, that the presence of large underwater islands1 or the shape of the tsunami source2 can affect the wave heights. Here we show that the consecutive effect of even tiny fluctuations in the profile of the ocean floor (the bathymetry) can cause unexpectedly strong fluctuations in the wave height of tsunamis, with maxima several times higher than the average wave height. A novel approach combining stochastic caustic theory and shallow water wave dynamics allows us to determine the typical propagation distance at which the strongly focused waves appear. We demonstrate that owing to this mechanism the small errors present in bathymetry measurements can lead to drastic variations in predicted tsunami heights. Our results show that a precise knowledge of the ocean’s bathymetry is absolutely indispensable for reliable tsunami forecasts.

Spatial heterogeneity of a host population of mobile agents has been shown to be a crucial determinant of many aspects of disease dynamics, ranging from the proliferation of diseases to their persistence and to vaccination strategies. In addition, the importance of regional and structural differences grows in our modern world. Little is known, though, about the consequences when traits of a disease vary regionally. In this paper, we study the effect of a spatially varying per capita infection rate on the behaviour of livestock diseases. We show that the prevalence of an infectious livestock disease in a community of animals can paradoxically decrease owing to transport connections to other communities in which the risk of infection is higher. We study the consequences for the design of livestock transportation restriction measures and establish exact criteria to discriminate those connections that increase the level of infection in the community from those that decrease it.

Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the statistics of the highest waves is important for their analysis and forecast, it remains poorly understood, in particular, in the regime where the waves are highest. We suggest a new approach that greatly simplifies the mathematical analysis and calculate the scaling and the distribution of the highest waves valid for a wide range of parameters.

The magnitude and variability of Earth's biodiversity have puzzled scientists ever since paleontologic fossil databases became available. We identify and study a model of interdependent species where both endogenous and exogenous impacts determine the nonstationary extinction dynamics. The framework provides an explanation for the qualitative difference of marine and continental biodiversity growth. In particular, the stagnation of marine biodiversity may result from a global transition from an imbalanced to a balanced state of the species dependency network. The predictions of our framework are in agreement with paleontologic databases.

In self-organized critical (SOC) systems avalanche size distributions follow power-laws. Power-laws have also been observed for neural activity, and so it has been proposed that SOC underlies brain organization as well. Surprisingly, for spiking activity in vivo, evidence for SOC is still lacking. Therefore, we analyzed highly parallel spike recordings from awake rats and monkeys, anesthetized cats, and also local field potentials from humans. We compared these to spiking activity from two established critical models: the Bak-Tang-Wiesenfeld model, and a stochastic branching model. We found fundamental differences between the neural and the model activity. These differences could be overcome for both models through a combination of three modifications: (1) subsampling, (2) increasing the input to the model (this way eliminating the separation of time scales, which is fundamental to SOC and its avalanche definition), and (3) making the model slightly sub-critical. The match between the neural activity and the modified models held not only for the classical avalanche size distributions and estimated branching parameters, but also for two novel measures (mean avalanche size, and frequency of single spikes), and for the dependence of all these measures on the temporal bin size. Our results suggest that neural activity in vivo shows a mélange of avalanches, and not temporally separated ones, and that their global activity propagation can be approximated by the principle that one spike on average triggers a little less than one spike in the next step. This implies that neural activity does not reflect a SOC state but a slightly sub-critical regime without a separation of time scales. Potential advantages of this regime may be faster information processing, and a safety margin from super-criticality, which has been linked to epilepsy.