Hierarchy Of Time Scales Research Articles

VENICE: A multi-scale operator-splitting algorithm for multi-physics simulations

Context. We present VENICE, an operator-splitting algorithm to integrate a numerical model on a hierarchy of timescales. Aims. VENICE allows a wide variety of different physical processes operating on different scales to be coupled on individual and adaptive time-steps. It therewith mediates the development of complex multi-scale and multi-physics simulation environments with a wide variety of independent components. Methods. The coupling between various physical models and scales is dynamic, and realised through (Strang) operators splitting using adaptive time-steps. Results. We demonstrate the functionality and performance of this algorithm using astrophysical models of a stellar cluster, first coupling gravitational dynamics and stellar evolution, then coupling internal gravitational dynamics with dynamics within a galactic background potential, and finally combining these models while also introducing dwarf galaxy-like perturbers. These tests show numerical convergence for decreasing coupling timescales, demonstrate how VENICE can improve the performance of a simulation by shortening coupling timescales when appropriate, and provide a case study of how VENICE can be used to gradually build up and tune a complex multi-physics model. Although the examples provided here couple dedicated numerical models, VENICE can also be used to efficiently solve systems of stiff differential equations.

Unusual spin dynamics in the van der Waals antiferromagnet FeGa2S4

Spin dynamics in the van der Waals antiferromagnet FeGa2S4with triangular lattices are investigated using magnetometry, neutron scattering, and muon spin relaxation measurements. The characteristic spin relaxation time is thoroughly clarified over thirteen orders of magnitude. Although the temperature dependence of DC and AC susceptibilities recalls a conventional spin-glass transition, nonlinear susceptibilities showing no divergences at the anomalous temperature,T∗=16.87(7) K, deny that and instead hint at other mechanisms. Elastic neutron scattering together with previously measured muon results depict a slowly fluctuated (∼10-5 s) spin state aboveT∗. In juxtaposing the underlying simplest structure among frustrated magnets with an intricate hierarchy of time scales, FeGa2S4can be a playground for studying temporal spin correlations in the two-dimensional limit.

Bound-state confinement after trap-expansion dynamics in integrable systems

Abstract Integrable systems possess stable families of quasiparticles, which are composite objects (bound states) of elementary excitations. Motivated by recent quantum computer experiments, we investigate bound-state transport in the spin- 1 / 2 anisotropic Heisenberg chain (XXZ chain). Specifically, we consider the sudden vacuum expansion of a finite region A prepared in a non-equilibrium state. In the hydrodynamic regime, if interactions are strong enough, bound states remain confined in the initial region. Bound-state confinement persists until the density of unbound excitations remains finite in the bulk of A. Since region A is finite, at asymptotically long times bound states are ‘liberated’ after the ‘evaporation’ of the unbound excitations. Fingerprints of confinement are visible in the space-time profiles of local spin-projection operators. To be specific, here we focus on the expansion of the p-Néel states, which are obtained by repetition of a unit cell with p up spins followed by p down spins. Upon increasing p, the bound-state content is enhanced. In the limit p → ∞ one obtains the domain-wall initial state. We show that for p < 4, only bound states with n > p are confined at large chain anisotropy. For p ≳ 4 , bound states with n = p are also confined, consistent with the absence of transport in the limit p → ∞ . The scenario of bound-state confinement leads to a hierarchy of timescales at which bound states of different sizes are liberated, which is also reflected in the dynamics of the von Neumann entropy.

Atmosphere and ocean interactions

The nature and extent of the main interactions between the Earth’s atmosphere and the ocean are briefly reviewed, introducing the main properties of these two planetary systems, the hierarchy of timescales and spatial scales characterizing their processes, and the main mechanisms involved. To clarify these mechanisms, a few examples of exchanges of momentum, energy, and mass exchanges are briefly outlined. The paper aims at stimulating students to discover the fascinating interplay among two of the most relevant components of our planet, such as the atmosphere and the ocean, and suggests resources for further exploration.Graphical abstract

A hierarchy of processing complexity and timescales for natural sounds in human auditory cortex.

Efficient behavior is supported by humans' ability to rapidly recognize acoustically distinct sounds as members of a common category. Within auditory cortex, there are critical unanswered questions regarding the organization and dynamics of sound categorization. Here, we performed intracerebral recordings in the context of epilepsy surgery as 20 patient-participants listened to natural sounds. We built encoding models to predict neural responses using features of these sounds extracted from different layers within a sound-categorization deep neural network (DNN). This approach yielded highly accurate models of neural responses throughout auditory cortex. The complexity of a cortical site's representation (measured by the depth of the DNN layer that produced the best model) was closely related to its anatomical location, with shallow, middle, and deep layers of the DNN associated with core (primary auditory cortex), lateral belt, and parabelt regions, respectively. Smoothly varying gradients of representational complexity also existed within these regions, with complexity increasing along a posteromedial-to-anterolateral direction in core and lateral belt, and along posterior-to-anterior and dorsal-to-ventral dimensions in parabelt. When we estimated the time window over which each recording site integrates information, we found shorter integration windows in core relative to lateral belt and parabelt. Lastly, we found a relationship between the length of the integration window and the complexity of information processing within core (but not lateral belt or parabelt). These findings suggest hierarchies of timescales and processing complexity, and their interrelationship, represent a functional organizational principle of the auditory stream that underlies our perception of complex, abstract auditory information.

An encompassed representation of timescale hierarchies in first-order reaction network

Complex networks are pervasive in various fields such as chemistry, biology, and sociology. In chemistry, first-order reaction networks are represented by a set of first-order differential equations, which can be constructed from the underlying energy landscape. However, as the number of nodes increases, it becomes more challenging to understand complex kinetics across different timescales. Hence, how to construct an interpretable, coarse-graining scheme that preserves the underlying timescales of overall reactions is of crucial importance. Here, we develop a scheme to capture the underlying hierarchical subsets of nodes, and a series of coarse-grained (reduced-dimensional) rate equations between the subsets as a function of time resolution from the original reaction network. Each of the coarse-grained representations guarantees to preserve the underlying slow characteristic timescales in the original network. The crux is the construction of a lumping scheme incorporating a similarity measure in deciphering the underlying timescale hierarchy, which does not rely on the assumption of equilibrium. As an illustrative example, we apply the scheme to four-state Markovian models and Claisen rearrangement of allyl vinyl ether (AVE), and demonstrate that the reduced-dimensional representation accurately reproduces not only the slowest but also the faster timescales of overall reactions although other reduction schemes based on equilibrium assumption well reproduce the slowest timescale but fail to reproduce the second-to-fourth slowest timescales with the same accuracy. Our scheme can be applied not only to the reaction networks but also to networks in other fields, which helps us encompass their hierarchical structures of the complex kinetics over timescales.

A multi-methodological approach to record dynamics and timescales of the plumbing system of Zaro (Ischia Island, Italy)

Determining the time spans of processes related to the assembly of eruptible magma at active volcanoes is fundamental to understand magma chamber dynamics and assess volcanic hazard. This information can be recorded in the chemical zoning of crystals. Nevertheless, this kind of study is still poorly employed for the active volcanoes of the Neapolitan area (Southern Italy), in particular, for Ischia island where the risk is extremely high and this information can provide the basis for probabilistic volcanic hazard assessment. For these reasons, we acquired chemical composition on clinopyroxene crystals erupted at Ischia during the Zaro eruption (6.6 ± 2.2 ka) and performed numerical simulations of the input of mafic magma into a trachytic reservoir, in order to investigate various aspects of pre-eruptive dynamics occurring at different timescales. This event emplaced a ~ 0.1 km3 lava complex, in which the main trachytic lava flows host abundant mafic to felsic enclaves. Previous petrological investigation suggested that mafic magma(s) mixed/mingled with a trachytic one, before the eruption. In this work, the clinopyroxene zoning patterns depict the growth of crystals in different magmatic environments, recording sequential changes occurred in the plumbing system before the eruption. The evolution of the plumbing system involved a hierarchy of timescales: a few hours for magma mingling caused by mafic recharge(s) and likely occurred multiple times over a decade during which a dominant magmatic environment was sustained before the eruption. Such timescales must be considered in volcanic hazard assessment at Ischia and similar active volcanoes in densely populated areas.

Turbulence hierarchy in foreign exchange markets.

We present a multiscale stochastic analysis of foreign exchange rates using the H-theory formalism, which provides a hierarchical intermittency model for the information cascade in the currency market. We examine the distributions of returns and volatilities for the three most traded currency pairs: euro-U.S. dollar, U.S. dollar-Japanese yen, and British pound-U.S. dollar. We find that these markets have a hierarchy of timescales, with larger markets exhibiting more hierarchy levels. We provide a theoretical framework for understanding why the number of levels in the information cascade increases with market size, in analogy with similar behavior for the energy cascade in turbulence as a function of Reynolds number. We briefly argue that using turbulence-like models for financial markets can also provide valuable insights for developing efficient algorithmic trading strategies.

Intracortical recordings reveal vision-to-action cortical gradients driving human exogenous attention

Exogenous attention, the process that makes external salient stimuli pop-out of a visual scene, is essential for survival. How attention-capturing events modulate human brain processing remains unclear. Here we show how the psychological construct of exogenous attention gradually emerges over large-scale gradients in the human cortex, by analyzing activity from 1,403 intracortical contacts implanted in 28 individuals, while they performed an exogenous attention task. The timing, location and task-relevance of attentional events defined a spatiotemporal gradient of three neural clusters, which mapped onto cortical gradients and presented a hierarchy of timescales. Visual attributes modulated neural activity at one end of the gradient, while at the other end it reflected the upcoming response timing, with attentional effects occurring at the intersection of visual and response signals. These findings challenge multi-step models of attention, and suggest that frontoparietal networks, which process sequential stimuli as separate events sharing the same location, drive exogenous attention phenomena such as inhibition of return.

Bayesian inference is facilitated by modular neural networks with different time scales.

Various animals, including humans, have been suggested to perform Bayesian inferences to handle noisy, time-varying external information. In performing Bayesian inference by the brain, the prior distribution must be acquired and represented by sampling noisy external inputs. However, the mechanism by which neural activities represent such distributions has not yet been elucidated. Our findings reveal that networks with modular structures, composed of fast and slow modules, are adept at representing this prior distribution, enabling more accurate Bayesian inferences. Specifically, the modular network that consists of a main module connected with input and output layers and a sub-module with slower neural activity connected only with the main module outperformed networks with uniform time scales. Prior information was represented specifically by the slow sub-module, which could integrate observed signals over an appropriate period and represent input means and variances. Accordingly, the neural network could effectively predict the time-varying inputs. Furthermore, by training the time scales of neurons starting from networks with uniform time scales and without modular structure, the above slow-fast modular network structure and the division of roles in which prior knowledge is selectively represented in the slow sub-modules spontaneously emerged. These results explain how the prior distribution for Bayesian inference is represented in the brain, provide insight into the relevance of modular structure with time scale hierarchy to information processing, and elucidate the significance of brain areas with slower time scales.

Neural timescales reflect behavioral demands in freely moving rhesus macaques

Previous work demonstrated a highly reproducible cortical hierarchy of neural timescales at rest, with sensory areas displaying fast, and higher-order association areas displaying slower timescales. The question arises how such stable hierarchies give rise to adaptive behavior that requires flexible adjustment of temporal coding and integration demands. Potentially, this lack of variability in the hierarchical organization of neural timescales could reflect the structure of the laboratory contexts. We posit that unconstrained paradigms are ideal to test whether the dynamics of neural timescales reflect behavioral demands. Here we measured timescales of local field potential activity while male rhesus macaques foraged in an open space. We found a hierarchy of neural timescales that differs from previous work. Importantly, although the magnitude of neural timescales expanded with task engagement, the brain areas’ relative position in the hierarchy was stable. Next, we demonstrated that the change in neural timescales is dynamic and contains functionally-relevant information, differentiating between similar events in terms of motor demands and associated reward. Finally, we demonstrated that brain areas are differentially affected by these behavioral demands. These results demonstrate that while the space of neural timescales is anatomically constrained, the observed hierarchical organization and magnitude is dependent on behavioral demands.

Fate of dissipative hierarchy of timescales in the presence of unitary dynamics

Fate of dissipative hierarchy of timescales in the presence of unitary dynamics

A data-driven approach for timescale decomposition of biochemical reaction networks.

Understanding the dynamics of biological systems in evolving environments is a challenge due to their scale and complexity. Here, we present a computational framework for the timescale decomposition of biochemical reaction networks to distill essential patterns from their intricate dynamics. This approach identifies timescale hierarchies, concentration pools, and coherent structures from time-series data, providing a system-level description of reaction networks at physiologically important timescales. We apply this technique to kinetic models of hypothetical and biological pathways, validating it by reproducing analytically characterized or previously known concentration pools of these pathways. Moreover, by analyzing the timescale hierarchy of the glycolytic pathway, we elucidate the connections between the stoichiometric and dissipative structures of reaction networks and the temporal organization of coherent structures. Specifically, we show that glycolysis is a cofactor-driven pathway, the slowest dynamics of which are described by a balance between high-energy phosphate bond and redox trafficking. Overall, this approach provides more biologically interpretable characterizations of network dynamics than large-scale kinetic models, thus facilitating model reduction and personalized medicine applications. IMPORTANCE Complex interactions within interconnected biochemical reaction networks enable cellular responses to a wide range of unpredictable environmental perturbations. Understanding how biological functions arise from these intricate interactions has been a long-standing problem in biology. Here, we introduce a computational approach to dissect complex biological systems' dynamics in evolving environments. This approach characterizes the timescale hierarchies of complex reaction networks, offering a system-level understanding at physiologically relevant timescales. Analyzing various hypothetical and biological pathways, we show how stoichiometric properties shape the way energy is dissipated throughout reaction networks. Notably, we establish that glycolysis operates as a cofactor-driven pathway, where the slowest dynamics are governed by a balance between high-energy phosphate bonds and redox trafficking. This approach enhances our understanding of network dynamics and facilitates the development of reduced-order kinetic models with biologically interpretable components.

Dendrites contribute to the gradient of intrinsic timescales encompassing cortical and subcortical brain networks.

Cytoarchitectonic studies have uncovered a correlation between higher levels of cortical hierarchy and reduced dendritic size. This hierarchical organization extends to the brain's timescales, revealing longer intrinsic timescales at higher hierarchical levels. However, estimating the contribution of single-neuron dendritic morphology to the hierarchy of timescales, which is typically characterized at a macroscopic level, remains challenging. Here we mapped the intrinsic timescales of six functional networks using functional magnetic resonance imaging (fMRI) data, and characterized the influence of neuronal dendritic size on intrinsic timescales of brain regions, utilizing a multicompartmental neuronal modeling approach based on digitally reconstructed neurons. The fMRI results revealed a hierarchy of intrinsic timescales encompassing both cortical and subcortical brain regions. The neuronal modeling indicated that neurons with larger dendritic structures exhibit shorter intrinsic timescales. Together these findings highlight the contribution of dendrites at the neuronal level to the hierarchy of intrinsic timescales at the whole-brain level. This study sheds light on the intricate relationship between neuronal structure, cytoarchitectonic maps, and the hierarchy of timescales in the brain.

The Spillover Effects among Crude Oil Future Markets under High-Frequency Data Environment: Trivariate VAR-BEKK-GARCH Model Based on Wavelet Multiresolution Analysis

With the rapid development of financial globalization, the interconnection of international financial markets has deepened, and the relationship between domestic and international crude oil futures market price fluctuations has been increasingly strengthened. This paper utilizes 1-minute high-frequency price data of INE, WTI, and BRENT crude oil. By employing wavelet multiresolution analysis to address the ‘Calendar Effect’ present in intraday high-frequency data, and decomposing financial time series into different hierarchy of time scales. On this basis, the VAR-BEKK-GARCH model is established to study the spillover effect among the three crude oil future markets from the perspective of different trading cycles. The main conclusions of this paper are as follows: (1) The energy spectrum of wavelet multiresolution analysis shows that the price fluctuations of domestic and international crude oil futures are mainly reflected in the short-term trading cycles of 1-4 minutes; (2) The empirical results of the VAR-BEKK-GARCH model indicate that there are significant bidirectional mean and volatility spillover effects among INE, WTI, and BRENT crude oil in each trading cycle. Specifically, the mean spillover effect between INE and WTI markets shows that the short-term mean spillover effect of INE crude oil on WTI crude oil is larger, which is contrast to the medium- and long-term effect, and there is no significant pattern in the volatility spillover effect. The overall mean and volatility spillover effects of INE crude oil on BRENT crude oil are relatively larger. The overall mean and volatility spillover effects of WTI crude oil on BRENT crude oil are also relatively larger.

A new radiation reaction approximation for particle dynamics in the strong field regime

Context. Following particle trajectories in the intense electromagnetic field of a neutron star is prohibited by the large ratio between the cyclotron frequency ωB and the stellar rotation frequency Ω. No fully kinetic simulations on a macroscopic scale and with realistic field strengths have been performed so far due to the huge computational cost implied by this enormous scale of separation. Aims. In this paper, we derive new expressions for the particle velocity subject to strong radiation reaction that are intended to be more accurate than the current state-of-the-art expression in the radiation reaction limit regime, the so-called Aristotelian regime. Methods. We shortened the timescale hierarchy by solving the particle equation of motion in the radiation reaction regime, where the Lorentz force is always and immediately balanced by the radiative drag, and including a friction not necessarily opposite to the velocity vector, as derived in the Landau-Lifshitz approximation. Results. Starting from the reduced Landau-Lifshitz equation (i.e., neglecting the field time derivatives), we found expressions for the velocity depending only on the local electromagnetic field configuration and on a new parameter related to the field strength that controls the strength of the radiative damping. As an example, we imposed a constant Lorentz factor γ during the particle motion. We found that for ultra-relativistic velocities satisfying γ ≳ 10, the difference between strong radiation reaction and the radiation reaction limit becomes negligible. Conclusions. The new velocity expressions produce results similar in accuracy to the radiation reaction limit approximation. We therefore do not expect this new method to improve the accuracy of neutron star magnetosphere simulations. The radiation reaction limit is a simple but accurate, robust, and efficient way to follow ultra-relativistic particles in a strong electromagnetic field.

Enthalpy effect on the kinetics of concurrent nucleation and chemical aging of aqueous organic aerosols: The stage of thermal relaxation

The size and composition distribution of an ensemble of aqueous organic droplets, evolving via nucleation and concomitant chemical aging, may be affected by the latent heat of condensation and enthalpy of heterogeneous chemical reactions, so the temperature of the droplet may deviate from the air temperature and thus become an independent variable of its state (additional to its size and composition variables). Using the formalism of the classical nucleation theory, we derive a partial differential equation for the temporal evolution of the distribution of an ensemble of such droplets with respect to all their variables of state via Taylor series expansions of the corresponding multidimensional discrete equation of balance, describing the material and heat exchange between droplets and air. The resulting kinetic equation goes beyond the framework of the Fokker-Planck approximation with respect to the temperature variable. A hierarchy of time scales of nonisothermal nucleation and concomitant chemical aging of aqueous organic aerosols is established and an analytical description of their thermal relaxation stage is developed, allowing one to estimate the characteristic time of the establishment of the equilibrium distribution of aerosol particles with respect to their temperatures. Theoretical results are illustrated with numerical calculations for the concurrent nucleation and chemical aging of model aqueous hydrophilic-hydrophobic organic aerosols in air.

Information flow across the cortical timescale hierarchy during narrative construction

When listening to spoken narratives, we must integrate information over multiple, concurrent timescales, building up from words to sentences to paragraphs to a coherent narrative. Recent evidence suggests that the brain relies on a chain of hierarchically organized areas with increasing temporal receptive windows to process naturalistic narratives. We hypothesized that the structure of this cortical processing hierarchy should result in an observable sequence of response lags between networks comprising the hierarchy during narrative comprehension. This study uses functional MRI to estimate the response lags between functional networks during narrative comprehension. We use intersubject cross-correlation analysis to capture network connectivity driven by the shared stimulus. We found a fixed temporal sequence of response lags-on the scale of several seconds-starting in early auditory areas, followed by language areas, the attention network, and lastly the default mode network. This gradient is consistent across eight distinct stories but absent in data acquired during rest or using a scrambled story stimulus, supporting our hypothesis that narrative construction gives rise to internetwork lags. Finally, we build a simple computational model for the neural dynamics underlying the construction of nested narrative features. Our simulations illustrate how the gradual accumulation of information within the boundaries of nested linguistic events, accompanied by increased activity at each level of the processing hierarchy, can give rise to the observed lag gradient.

Neural event segmentation of continuous experience in human infants

How infants experience the world is fundamental to understanding their cognition and development. A key principle of adult experience is that, despite receiving continuous sensory input, we perceive this input as discrete events. Here we investigate such event segmentation in infants and how it differs from adults. Research on event cognition in infants often uses simplified tasks in which (adult) experimenters help solve the segmentation problem for infants by defining event boundaries or presenting discrete actions/vignettes. This presupposes which events are experienced by infants and leaves open questions about the principles governing infant segmentation. We take a different, data-driven approach by studying infant event segmentation of continuous input. We collected whole-brain functional MRI (fMRI) data from awake infants (and adults, for comparison) watching a cartoon and used a hidden Markov model to identify event states in the brain. We quantified the existence, timescale, and organization of multiple-event representations across brain regions. The adult brain exhibited a known hierarchical gradient of event timescales, from shorter events in early visual regions to longer events in later visual and associative regions. In contrast, the infant brain represented only longer events, even in early visual regions, with no timescale hierarchy. The boundaries defining these infant events only partially overlapped with boundaries defined from adult brain activity and behavioral judgments. These findings suggest that events are organized differently in infants, with longer timescales and more stable neural patterns, even in sensory regions. This may indicate greater temporal integration and reduced temporal precision during dynamic, naturalistic perception.

Forced and spontaneous symmetry breaking in cell polarization.

How does breaking the symmetry of an equation alter the symmetry of its solutions? Here, we systematically examine how reducing underlying symmetries from spherical to axisymmetric influences the dynamics of an archetypal model of cell polarization, a key process of biological spatial self-organization. Cell polarization is characterized by nonlinear and non-local dynamics, but we overcome the theory challenges these traits pose by introducing a broadly applicable numerical scheme allowing us to efficiently study continuum models in a wide range of geometries. Guided by numerical results, we discover a dynamical hierarchy of timescales that allows us to reduce relaxation to a purely geometric problem of area-preserving geodesic curvature flow. Through application of variational results, we analytically construct steady states on a number of biologically relevant shapes. In doing so, we reveal non-trivial solutions for symmetry breaking.