Slow Fluctuations Research Articles

Sensory processing in humans and mice fluctuates between external and internal modes.

Perception is known to cycle through periods of enhanced and reduced sensitivity to external information. Here, we asked whether such slow fluctuations arise as a noise-related epiphenomenon of limited processing capacity or, alternatively, represent a structured mechanism of perceptual inference. Using 2 large-scale datasets, we found that humans and mice alternate between externally and internally oriented modes of sensory analysis. During external mode, perception aligns more closely with the external sensory information, whereas internal mode is characterized by enhanced biases toward perceptual history. Computational modeling indicated that dynamic changes in mode are enabled by 2 interlinked factors: (i) the integration of subsequent inputs over time and (ii) slow antiphase oscillations in the impact of external sensory information versus internal predictions that are provided by perceptual history. We propose that between-mode fluctuations generate unambiguous error signals that enable optimal inference in volatile environments.

Nonergodic Measurements of Qubit Frequency Noise.

Slow fluctuations of a qubit frequency are one of the major problems faced by quantum computers. To understand their origin it is necessary to go beyond the analysis of their spectra. We show that characteristic features of the fluctuations can be revealed using comparatively short sequences of periodically repeated Ramsey measurements, with the sequence duration smaller than needed for the noise to approach the ergodic limit. The outcomes distribution and its dependence on the sequence duration are sensitive to the nature of the noise. The time needed for quantum measurements to display quasiergodic behavior can strongly depend on the measurement parameters.

Heterogeneity of the attractor of the Lorenz ’96 model: Lyapunov analysis, unstable periodic orbits, and shadowing properties

It is well known that the predictability of weather and climate is strongly state-dependent. Special, easily recognisable, and extremely relevant atmospheric states like blockings are associated with anomalous instability. This reflects the general property that the attractors of chaotic systems can feature considerable heterogeneity in terms of dynamical properties, and specifically, of their instability. The attractor of a chaotic system is densely populated by unstable periodic orbits (UPOs) that can be used to approximate any forward trajectory through the so-called shadowing. Dynamical heterogeneity can lead to the presence of UPOs with different number of unstable dimensions. This phenomenon – unstable dimensions variability – is a serious breakdown of hyperbolicity and has considerable implications in terms of the structural stability of the system and of the possibility to model accurately its behaviour through numerical models. As a step in the direction of better understanding the properties of high-dimensional chaotic systems, here we provide an extensive numerical investigation of the variability of the dynamical properties across the attractor of the much studied Lorenz ’96 model. By combining the Lyapunov analysis of the tangent space with the study of the shadowing of the chaotic trajectory performed by a very large set of UPOs, we show that the observed variability in the number of unstable dimensions is associated with the presence of a substantial number of finite-time Lyapunov exponents that fluctuate about zero also when very long averaging times are considered. The transition between regions of the attractor with different degrees of instability is associated with a significant drop of the quality of the shadowing. By performing a coarse graining based on the shadowing UPOs, we are able to characterise the slow fluctuations of the system between regions featuring, on the average, anomalously high and anomalously low instability. In turn, such regions are associated, respectively, with states of anomalously high and low energy, thus providing a clear link between the microscopic and thermodynamical properties of the system.

Reward Modulates Visual Responses in the Superficial Superior Colliculus of Mice.

The processing of sensory input is constantly adapting to behavioral demands and internal states. The drive to obtain reward, e.g., searching for water when thirsty, is a strong behavioral demand and associating the reward with its source, a certain environment or action, is paramount for survival. Here, we show that water reward increases subsequent visual activity in the superficial layers of the superior colliculus (SC), which receive direct input from the retina and belong to the earliest stages of visual processing. We trained mice of either sex to perform a visual decision task and recorded the activity of neurons in the SC using two-photon calcium imaging and high-density electrophysiological recordings. Responses to visual stimuli in around 20% of visually responsive neurons in the superficial SC were affected by reward delivered in the previous trial. Reward mostly increased visual responses independent from modulations due to pupil size changes. The modulation of visual responses by reward could not be explained by movements like licking. It was specific to responses to the following visual stimulus, independent of slow fluctuations in neural activity and independent of how often the stimulus was previously rewarded. Electrophysiological recordings confirmed these results and revealed that reward affected the early phase of the visual response around 80 ms after stimulus onset. Modulation of visual responses by reward, but not pupil size, significantly improved the performance of a population decoder to detect visual stimuli, indicating the relevance of reward modulation for the visual performance of the animal.SIGNIFICANCE STATEMENT To learn which actions lead to food, water, or safety, it is necessary to integrate the receiving of reward with sensory stimuli related to the reward. Cortical stages of sensory processing have been shown to represent stimulus-reward associations. Here, we show, however, that reward influences neurons at a much earlier stage of sensory processing, the superior colliculus (SC), receiving direct input from the retina. Visual responses were increased shortly after the animal received the water reward, which led to an improved stimulus signal in the population of these visual neurons. Reward modulation of early visual responses may thus improve perception of visual environments predictive of reward.

A Highly Ordered Nitroxide Side Chain for Distance Mapping and Monitoring Slow Structural Fluctuations in Proteins.

The online version contains supplementary material available at 10.1007/s00723-023-01618-8.

Exploration of Vegetation Change Trend in the Greater Khingan Mountains Area of China Based on EEMD Method

Vegetation, especially forest ecosystems, plays an important role in the global energy flow and material cycle. The vegetation index (VI) is an important index reflecting the dynamic change in vegetation and directly reflects the response of ecosystem to global climate change. The Greater Khingan Mountains Forest region is located in the northeast of China. It is the largest primeval forest region in China, which is well preserved and less affected by human activities. It is of great significance to study the driving mechanism of forest vegetation change for future ecological prediction and management. In this study, GIMMS NDVI data were used to explore the characteristics of nonlinear temporal and spatial variation of NDVI in the Greater Khingan Mountains and its relationship with climatic factors. Firstly, the EEMD method was used to analyze the characteristics of vegetation change in the study area from 1982 to 2015. Secondly, the relationship between vegetation change and climate was discussed by using precipitation and temperature data. The results showed that the following: (1) from 1982 to 2015, the interannual change in vegetation in the Greater Khingan Mountains presented a trend of slow fluctuation and gradual decrease (SLOPE = −0.1645/10,000, p < 0.01). (2) The spatial distribution of vegetation change had obvious geographical differences, and in the central region, the overall distribution characteristics had an obvious browning trend, and in the northwest and southeast, the distribution characteristics had a green trend. (3) The correlation analysis results of vegetation change and climate factors showed that NDVI change was significantly positively correlated with temperature and precipitation; additionally, NDVI change was more correlated with temperature with a range of 0.8–1 than precipitation. (4) The results of vegetation attribution analysis in four typical areas of the study area showed that the following: the coniferous forest area has good cold tolerance and drought tolerance, the correlation between vegetation change and climate factors (temperature, precipitation) was not the strongest, which was 0.537 and 0.828, respectively. The ecological transition area and the broad-leaved forest area, which was located at the edge of the study area, have relatively fragile ecosystems, showed a strong correlation with precipitation, and the correlation coefficients reached 0.670 and 0.632, respectively. The surface water resources provide favorable conditions for the growth of vegetation, it showed a weak correlation with precipitation, and the correlation coefficient was 0.5349.

Statistical Properties of Alfvén Ion Cyclotron Waves and Kinetic Alfvén Waves in the Inner Heliosphere

Alfvén ion cyclotron waves (ACWs) and kinetic Alfvén waves (KAWs) are found to exist at <0.3 au observed by Parker Solar Probe in Alfvénic slow solar winds. To examine the statistical properties of the background parameters for ACWs and KAWs and related wave disturbances, both wave events observed by Parker Solar Probe are selected and analyzed. The results show that there are obvious differences in the background and disturbance parameters between ACWs and KAWs. ACW events have a relatively higher occurrence rate but with a total duration slightly shorter than KAW events. The median background magnetic field magnitude and the related background solar wind speed of KAW events are larger than those of ACWs. The distributions of the relative disturbances of the proton velocity, proton temperature, the proton number density, and β cover wider ranges for ACW events than for KAW events. The results may be important for the understanding of the nature and characteristics of Alfvénic slow solar wind fluctuations at ion scales near the Sun, and provide the information of the background field and plasma parameters and the wave disturbances of ACWs and KAWs for further relevant theoretical modeling or numerical simulations.

Measuring magnetic 1/f noise in superconducting microstructures and the fluctuation-dissipation theorem

The performance of superconducting devices like qubits, superconducting quantum interference devices (SQUIDs), and particle detectors is often limited by finite coherence times and noise. Various types of slow fluctuators in the Josephson junctions and the passive parts of these superconducting circuits can be the cause, and devices usually suffer from a combination of different noise sources, which are hard to disentangle and therefore hard to eliminate. One contribution is magnetic noise caused by fluctuating magnetic moments of magnetic impurities or dangling bonds in superconducting inductances, surface oxides, insulating oxide layers, and adsorbates. In an effort to further analyze such sources of noise, we have developed an experimental set-up to measure both the complex impedance of superconducting microstructures, and the overall noise picked up by these structures. This allows for important sanity checks by connecting both quantities via the fluctuation-dissipation theorem. Since these two measurements are sensitive to different types of noise, we are able to identify and quantify individual noise sources. Furthermore, our measurements are not limited by the quantum noise limit of front-end SQUIDs, allowing us to measure noise caused by just a few ppm of impurities in close-by materials. We present measurements of the insulating layers of our devices, and magnetically doped noble metal layers in the vicinity of the pickup coils at and .

Linear Mode Decomposition in Magnetohydrodynamics Revisited

Small-amplitude fluctuations in the magnetized solar wind are measured typically by a single spacecraft. In the magnetohydrodynamics (MHD) description, fluctuations are typically expressed in terms of the fundamental modes admitted by the system. An important question is how to resolve an observed set of fluctuations, typically plasma moments such as the density, velocity, pressure, and magnetic field fluctuations, into their constituent fundamental MHD modal components. Despite its importance in understanding the basic elements of waves and turbulence in the solar wind, this problem has not yet been fully resolved. Here, we introduce a new method that identifies between wave modes and advected structures such as magnetic islands or entropy modes and computes the phase information associated with the eligible MHD modes. The mode-decomposition method developed here identifies the admissible modes in an MHD plasma from a set of plasma and magnetic field fluctuations measured by a single spacecraft at a specific frequency and an inferred wavenumber k m . We present data from three typical intervals measured by the Wind and Solar Orbiter spacecraft at ∼1 au and show how the new method identifies both propagating (wave) and nonpropagating (structures) modes, including entropy and magnetic island modes. This allows us to identify and characterize the separate MHD modes in an observed plasma parcel and to derive wavenumber spectra of entropic density, fast and slow magnetosonic, Alfvénic, and magnetic island fluctuations for the first time. These results help identify the fundamental building blocks of turbulence in the magnetized solar wind.

Long-term trends of aerosol and cloud fraction over Eastern China based on ground-based observations

We looked into the long-term variability of aerosols and clouds over Eastern China (EC) using MICAPS ground-based data from 1995 to 2019 and MODIS aerosol optical depth (AOD) retrieval from 2003 to 2019. The ground-based observed visibility (VIS) was used to characterize aerosol concentrations. Our study indicate that VIS shows a significant shift over EC in recent decades, as evidenced by falling (P1: 1995–2006)-flat (P2: 2007–2013)-rising (P3: 2014–2019) periods. Correspondingly, a change was observed in cloud fraction (CF) from a strong increase to a slow fluctuation during the three periods over the Beijing-Tianjin-Hebei (BTH), but no significant variation over the Yangtze River Delta (YRD) region. In addition, the CF-VIS shows a negative correlation during both P1 and P3 periods while this relationship weakened during P3 (35% weaker in BTH and 44% weaker in YRD). However, it is important to note that this weakening may be influenced by a few factors, such as data processing methods, the location of aerosols relative to the cloud, relative humidity (RH), and large-scale circulation etc. Further studies, including numerical simulations and analysis, are required to determine how much change of cloudiness is attributed to aerosols.

Dynamic evolution law analysis of overburden separation and water flowing fracture under mining based on distributed optical fiber and information entropy theory

The water inrush from overburden separation is large and destructive, which is very easy to cause serious casualties and property losses. Therefore, a three-dimensional model of 150 cm × 150 cm × 60 cm (length × height × width) is established in the laboratory. And the dynamic development process of overburden separations and water flowing fractures in the process of coal mining in real time are analyzed based on distributed optical fiber and information entropy theory. The distributed optical fiber strain curve can well reflect the process and characteristics of overburden deformation and collapse. The strain curve of optical fiber shows a single peak or step shape at different mining stages. The separation position corresponds to the peak of the optical fiber strain curve or above the step. The change of strain value of optical fiber reflects the development, expansion and closure process of separation. The development height of the water flowing fractured zone corresponds to the lower part of the step of the strain curve. Strain information entropy realizes quantitative analysis of overburden system state. Strain information entropy can be divided into small amplitude rapid fluctuation period, sharp rapid adjustment period and stable slow fluctuation period. Water flowing fractures and separations are mainly produced during the period of the sharp rapid adjustment period. The height of the water flowing fractured zone and the height of the new separation increase step by step with the advance of the working face. The water flowing fractured zone finally develops to 86 cm of the model height. The highest position of the separation appears at the 112 cm height of the model. A new variable named growth rate of strain information entropy is defined, which can reflect the severity of the change of the overburden system state. When the key stratum breaks, the growth rate of strain information entropy increases significantly, which show that the key stratum plays a key role in controlling the overburden deformation process. In addition, the optical fiber strain curve can also reflect important information such as the change of advance support pressure, the distribution state of gangue in goaf and the breaking characteristics of key strata.

Cholinergic-related pupil activity reflects level of emotionality during motor performance.

Pupil size covaries with the diffusion rate of the cholinergic and noradrenergic neurons throughout the brain, which are essential to arousal. Recent findings suggest that slow pupil fluctuations during locomotion are an index of sustained activity in cholinergic axons, whereas phasic dilations are related to the activity of noradrenergic axons. Here, we investigated movement induced arousal (i.e., by singing and swaying to music), hypothesising that actively engaging in musical behaviour will provoke stronger emotional engagementin participants and lead todifferent qualitative patternsof tonic and phasic pupil activity. A challenge in the analysis of pupil data is the turbulent behaviour of pupil diameter due to exogenous ocular activity commonly encountered during motor tasks and the high variability typically found between individuals. To address this, we developed an algorithm that adaptively estimates and removes pupil responses to ocular events, as well as a functional data methodology, derived from Pfaffs' generalised arousal, that provides a new statistical dimension on how pupil data can be interpreted according to putative neuromodulatory signalling. We found that actively engaging in singing enhanced slow cholinergic-related pupil dilations and having the opportunity to move your body while performing amplified the effect of singing on pupil activity. Phasic pupil oscillations during motor execution attenuated in time, which isoften interpreted as a measure of sense of agency over movement.

Timescale separation in the coordinated switching of bacterial flagellar motors

The output of the bacterial chemotaxis signaling pathway, the level of the intracellular regulator CheY-P, modulates the rotation direction of the flagellar motor, thereby regulating bacterial run-and-tumble behavior. The multiple flagellar motors on an E. coli cell are controlled by a common cytoplasmic pool of CheY-P. Fluctuation of the CheY-P level was thought to be able to coordinate the switching of multiple motors. Here, we measured the correlation of rotation directions between two motors on a cell, finding that it surprisingly exhibits two well separated timescales. We found that the slow timescale (∼6 s) can be explained by the slow fluctuation of the CheY-P level due to stochastic activity of the chemotactic adaptation enzymes, whereas the fast timescale (∼0.3 s) can be explained by the random pulse-like fluctuation of the CheY-P level, due probably to the activity of the chemoreceptor clusters. We extracted information on the properties of the fast CheY-P pulses based on the correlation measurements. The two well-separated timescales in the fluctuation of CheY-P level help to coordinate multiple motors on a cell and to enhance bacterial chemotactic performance.

The effects of speech masking on neural tracking of acoustic and semantic features of natural speech

Listening environments contain background sounds that mask speech and lead to communication challenges. Sensitivity to slow acoustic fluctuations in speech can help segregate speech from background noise. Semantic context can also facilitate speech perception in noise, for example, by enabling prediction of upcoming words. However, not much is known about how different degrees of background masking affect the neural processing of acoustic and semantic features during naturalistic speech listening. In the current electroencephalography (EEG) study, participants listened to engaging, spoken stories masked at different levels of multi-talker babble to investigate how neural activity in response to acoustic and semantic features changes with acoustic challenges, and how such effects relate to speech intelligibility. The pattern of neural response amplitudes associated with both acoustic and semantic speech features across masking levels was U-shaped, such that amplitudes were largest for moderate masking levels. This U-shape may be due to increased attentional focus when speech comprehension is challenging, but manageable. The latency of the neural responses increased linearly with increasing background masking, and neural latency change associated with acoustic processing most closely mirrored the changes in speech intelligibility. Finally, tracking responses related to semantic dissimilarity remained robust until severe speech masking (−3 dB SNR). The current study reveals that neural responses to acoustic features are highly sensitive to background masking and decreasing speech intelligibility, whereas neural responses to semantic features are relatively robust, suggesting that individuals track the meaning of the story well even in moderate background sound.

The cholinergic basal forebrain provides a parallel channel for state-dependent sensory signaling to auditory cortex.

Cholinergic basal forebrain (CBF) signaling exhibits multiple timescales of activity with classic slow signals related to brain and behavioral states and fast, phasic signals reflecting behavioral events, including movement, reinforcement and sensory-evoked responses. However, it remains unknown whether sensory cholinergic signals target the sensory cortex and how they relate to local functional topography. Here we used simultaneous two-channel, two-photon imaging of CBF axons and auditory cortical neurons to reveal that CBF axons send a robust, nonhabituating and stimulus-specific sensory signal to the auditory cortex. Individual axon segments exhibited heterogeneous but stable tuning to auditory stimuli allowing stimulus identity to be decoded from population activity. However, CBF axons displayed no tonotopy and their frequency tuning was uncoupled from that of nearby cortical neurons. Chemogenetic suppression revealed the auditory thalamus as a major source of auditory information to the CBF. Finally, slow fluctuations in cholinergic activity modulated the fast, sensory-evoked signals in the same axons, suggesting that a multiplexed combination of fast and slow signals is projected from the CBF to the auditory cortex. Taken together, our work demonstrates a noncanonical function of the CBF as a parallel channel for state-dependent sensory signaling to the sensory cortex that provides repeated representations of a broad range of sound stimuli at all points on the tonotopic map.

Sleep cycle-dependent vascular dynamics in male mice and the predicted effects on perivascular cerebrospinal fluid flow and solute transport

Perivascular spaces are important highways for fluid and solute transport in the brain enabling efficient waste clearance during sleep. However, the underlying mechanisms augmenting perivascular flow in sleep are unknown. Using two-photon imaging of naturally sleeping male mice we demonstrate sleep cycle-dependent vascular dynamics of pial arteries and penetrating arterioles: slow, large-amplitude oscillations in NREM sleep, a vasodilation in REM sleep, and a vasoconstriction upon awakening at the end of a sleep cycle and microarousals in NREM and intermediate sleep. These vascular dynamics are mirrored by changes in the size of the perivascular spaces of the penetrating arterioles: slow fluctuations in NREM sleep, reduction in REM sleep and an enlargement upon awakening after REM sleep and during microarousals in NREM and intermediate sleep. By biomechanical modeling we demonstrate that these sleep cycle-dependent perivascular dynamics likely enhance fluid flow and solute transport in perivascular spaces to levels comparable to cardiac pulsation-driven oscillations.

Conformational dynamics of glucagon receptor domains revealed by single-molecule fluorescence microscopy.

G protein-coupled receptors (GPCRs) are integral membrane proteins involved in many cellular signaling processes. Representing the largest family of proteins with approximately 800 members in humans, GPCRs are the target for more than 40% of current pharmaceutical drugs. The structural and dynamic information is vital to understanding the activation mechanism of these receptors. Despite the availability of high-resolution structures of GPCRs at different conformational states, the dynamics of those conformational states at the molecular level are missing. We used total internal reflection fluorescence (TIRF) imaging to investigate the conformational dynamics of the glucagon receptor (GCGR), a class B family GPCR involved in glucose homeostasis. We expressed and purified GCGR from mammalian cells and analyzed them at a single molecule level. We used single-molecule Förster resonance energy transfer (smFRET) to observe the conformational dynamics of the donor and acceptor fluorophore-labeled GCGR molecules. We observed ligand-dependent slow and reversible conformational fluctuation of N-terminal extra cellular domain (ECD) without ligand binding. The addition of a saturated concentration of peptide ligand (Glucagon) altered the dynamics towards the lower FRET states. These results provide new insight into the structural dynamics of glucagon receptor and receptor activation.

Slow Time Phenomena in Heterogeneous Materials: from Microscopic Fluctuations to Macroscopic Relaxation

Slow time relaxation of elastic moduli with typically logarithmic time dependence is observed in many media interesting for materials science. This phenomenon is related to internal structure and is, hence, important for the development of present-day materials. Here, we provide a general explanation showing a close link between slow time phenomena and fluctuations on the microscopic and mesoscopic scales. We look for the origin of slow time phenomena in random walk or diffusion processes on microscopic scales. Some bonds occurring in the metastable state make a transition through the energy barriers due to small fluctuations slightly perturbing the statistical equilibrium. If the number of the excited bonds is small compared to the total number of bonds in a heterogeneous material, the process of the transition as a whole can be considered as mesoscopic fluctuations. Averaging over all transient bonds or states is revealed in the observed macroscopic relaxation of elastic moduli, velocities, and others. The functional dependence on time in the relaxation process has been shown to be controlled by the profile of energy barriers. The results obtained point to their possible applications in materials science.

Unveiling the spatial-temporal variation of urban land use efficiency of Yangtze River Economic Belt in China under carbon emission constraints

Under the constraint of carbon emission, measuring and analyzing the spatial-temporal evolution characteristics of urban land use efficiency in the Yangtze River Economic Belt is the inherent requirement of its ecological protection and sustainable development. In this paper, we calculated the urban land use efficiency of 107 cities in the Yangtze River Economic Belt from 2006 to 2020 by using the SBM-Undesirable model with unexpected output, and analyzed its temporal evolution trend and spatial correlation relationship by using kernel density and spatial autocorrelation method. The results showed that: except in 2020, the urban land use efficiency was generally low due to the COVID-19 epidemic, and the urban land use efficiency in other years was mostly concentrated in the middle levels, and showed a trend of slow fluctuation and rise year by year. The difference of urban land use efficiency level between regions increased, and the dispersion degree in upstream, midstream and downstream increased with each passing year. Urban land use efficiency spatial imbalance was significant, and the urban land use efficiency level of large and medium-sized cities was generally lower than that of cities with low economic development level. The spatial correlation was weak, and the global spatial autocorrelation was basically insignificant, while the local spatial agglomeration areas were mainly distributed in the upstream and downstream regions, with a small distribution range and weak spatial interaction. The distribution areas of the standard deviation ellipse were gradually flattened, and the center of gravity as a whole shift significantly to the southwest. The research results are helpful to understand the development history and future trend of urban land use efficiency in various regions, and propose that cities should consider the impact of public crisis events in advance, reasonably control the scale of land expansion, and lead coordinated development and other reasonable suggestions when formulating land use policies.

MAXI J1820+070 X-ray spectral-timing reveals the nature of the accretion flow in black hole binaries

ABSTRACT Black hole X-ray binaries display significant stochastic variability on short time-scales (0.01–100 s), with a complex pattern of lags in correlated variability seen in different energy bands. This behaviour is generally interpreted in a model where slow fluctuations stirred up at large radii propagate down through the accretion flow, modulating faster fluctuations generated at smaller radii. Coupling this scenario with radially stratified emission opens the way to measure the propagation time-scale from data, allowing direct tests of the accretion flow structure. We previously developed a model based on this picture and showed that it could fit the Neutron star Interior Composition Explorer (NICER; 0.5–10 keV) data from the brightest recent black hole transient, MAXI J1820+070. However, here we show it fails when extrapolated to higher energy variability data from the Insight-Hard X-ray Modulation Telescope(HXMT). We extend our model so that the spectrum emitted at each radius changes shape in response to fluctuations (pivoting) rather than just changing normalization. This gives the strong suppression of fractional variability as a function of energy seen in the data. The derived propagation time-scale is slower than predicted by a magnetically arrested disc (MAD), despite this system showing a strong jet. Our new model jointly fits the spectrum and variability up to 50 keV, though still cannot match all the data above this. Nonetheless, the good fit from 3 to 40 keV means the quasi-periodic oscillation (QPO) can most easily be explained as an extrinsic modulation of the flow, such as produced in the Lense–Thirring precession, rather than arising in an additional spectral-timing component such as the jet.