Holocene centennial variability in sea surface temperature and linkage with solar irradiance.

The climate periodically fluctuates on various time scales, however, there remains a lack of consensus on the centennial-scale variabilities and associated driving force. A continuous high-resolution sea surface temperature (SST) record allows for the detection of centennial-scale fluctuations. This study presents a high-resolution SST record covering the last 10,000 years based on the analysis of the alkenone unsaturation index in marine sediment cores off the southwest coast of the Korean Peninsula. Alkenone SST's spectral and wavelet analysis revealed significant periodicities of 414, 190, 135, 102, and 89 years at a > 90% confidence level. These cycles exhibit extreme proximity to the solar activity cycles of 353, 206 (Suess/de Vries cycles), 130, and 104-87 years (Gleissberg cycles), suggesting that the multidecadal to centennial variations in SST are linked to solar forcing. To the best of our knowledge, this is the first high-resolution Holocene SST record that all solar activity cycles on centennial scale match, suggesting centennial-scale variability in the climate system and illustrating the role of solar activity on SST change in the mid-latitude region of the Northern Hemisphere.

Roles of insolation forcing and CO2 forcing on Late Pleistocene seasonal sea surface temperatures.

Late Pleistocene changes in insolation, greenhouse gas concentrations, and ice sheets have different spatially and seasonally modulated climatic fingerprints. By exploring the seasonality of paleoclimate proxy data, we gain deeper insight into the drivers of climate changes. Here, we investigate changes in alkenone-based annual mean and Globigerinoides ruber Mg/Ca-based summer sea surface temperatures in the East China Sea and their linkages to climate forcing over the past 400,000 years. During interglacial-glacial cycles, there are phase differences between annual mean and seasonal (summer and winter) temperatures, which relate to seasonal insolation changes. These phase differences are most evident during interglacials. During glacial terminations, temperature changes were strongly affected by CO2. Early temperature minima, ~20,000 years before glacial terminations, except the last glacial period, coincide with the largest temperature differences between summer and winter, and with the timing of the lowest atmospheric CO2 concentration. These findings imply the need to consider proxy seasonality and seasonal climate variability to estimate climate sensitivity.

Various synchronous states due to coupling strength inhomogeneity and coupling functions in systems of coupled identical oscillators.

We study the effects of coupling strength inhomogeneity and coupling functions on locking behaviors of coupled identical oscillators, some of which are relatively weakly coupled to others while some are relatively strongly coupled. Through the stability analysis and numerical simulations, we show that several categories of fully locked or partially locked states can emerge and obtain the conditions for these categories. In this system with coupling strength inhomogeneity, locked and drifting subpopulations are determined by the coupling strength distribution and the shape of the coupling functions. Even the strongly coupled oscillators can drift while weakly coupled oscillators can be locked. The simulation results with Gaussian and power-law distributions for coupling strengths are compared and discussed.

Structure Shapes Dynamics and Directionality in Diverse Brain Networks: Mathematical Principles and Empirical Confirmation in Three Species.

Identifying how spatially distributed information becomes integrated in the brain is essential to understanding higher cognitive functions. Previous computational and empirical studies suggest a significant influence of brain network structure on brain network function. However, there have been few analytical approaches to explain the role of network structure in shaping regional activities and directionality patterns. In this study, analytical methods are applied to a coupled oscillator model implemented in inhomogeneous networks. We first derive a mathematical principle that explains the emergence of directionality from the underlying brain network structure. We then apply the analytical methods to the anatomical brain networks of human, macaque, and mouse, successfully predicting simulation and empirical electroencephalographic data. The results demonstrate that the global directionality patterns in resting state brain networks can be predicted solely by their unique network structures. This study forms a foundation for a more comprehensive understanding of how neural information is directed and integrated in complex brain networks.

Noise-induced organized slow fluctuations in networks of neural areas with interarea feed-forward excitation and inhibition.

Slow coherent spontaneous fluctuations (<0.1 Hz) in functional magnetic resonance imaging blood-oxygen-level-dependent signals have been observed for a resting state of the human brain. In this paper, considering feed-forward inhibition in addition to excitation between brain areas, which we assume to be in up (active) or down (quiescent) states, we propose a model for the generation and organization of the slow fluctuations. Connectivity with feed-forward excitation and inhibition between the areas makes the system have multiple stable states and organized slow fluctuations manifest as noise-induced slow transitions between the states. With various connectivities, we observe slow fluctuations and various organizations, including anticorrelated clusters, through numerical simulations.

Multiscale ensemble clustering for finding modules in complex networks.

The identification of modules in complex networks is important for the understanding of systems. Here, we propose an ensemble clustering method incorporating node groupings in various sizes and the sequential removal of weak ties between nodes which are rarely grouped together. This method successfully detects modules in various networks, such as hierarchical random networks and the American college football network, with known modular structures. Some of the results are compared with those obtained by modularity optimization and K-means clustering.

Zigzag turning preference of freely crawling cells.

The coordinated motion of a cell is fundamental to many important biological processes such as development, wound healing, and phagocytosis. For eukaryotic cells, such as amoebae or animal cells, the cell motility is based on crawling and involves a complex set of internal biochemical events. A recent study reported very interesting crawling behavior of single cell amoeba: in the absence of an external cue, free amoebae move randomly with a noisy, yet, discernible sequence of 'run-and-turns' analogous to the 'run-and-tumbles' of swimming bacteria. Interestingly, amoeboid trajectories favor zigzag turns. In other words, the cells bias their crawling by making a turn in the opposite direction to a previous turn. This property enhances the long range directional persistence of the moving trajectories. This study proposes that such a zigzag crawling behavior can be a general property of any crawling cells by demonstrating that 1) microglia, which are the immune cells of the brain, and 2) a simple rule-based model cell, which incorporates the actual biochemistry and mechanics behind cell crawling, both exhibit similar type of crawling behavior. Almost all legged animals walk by alternating their feet. Similarly, all crawling cells appear to move forward by alternating the direction of their movement, even though the regularity and degree of zigzag preference vary from one type to the other.

Phase-response curves of coupled oscillators.

Many real oscillators are coupled to other oscillators, and the coupling can affect the response of the oscillators to stimuli. We investigate phase-response curves (PRCs) of coupled oscillators. The PRCs for two weakly coupled phase-locked oscillators are analytically obtained in terms of the PRC for uncoupled oscillators and the coupling function of the system. Through simulation and analytic methods, the PRCs for globally coupled oscillators are also discussed.

Delays and weakly coupled neuronal oscillators.

We use weakly coupled oscillator theory to study the effects of delays on coupled systems of neuronal oscillators. We explore, first, simple pairs with constant delays and then examine the role of distributed delays as would occur in systems with dendritic branches or in networks where there is a distance-dependent conductance delay. In the latter, we use mean field theory to show the emergence of travelling waves and the loss of synchronization. Next, we consider phase models with stronger coupling and delays in the state variables. We show that they have a richer dynamics but one that is still similar to the weakly coupled case.

Bistability between synchrony and incoherence in limit-cycle oscillators with coupling strength inhomogeneity.

The effect of coupling strength inhomogeneity on the synchronization of identical oscillators is investigated. Through simulations and analysis of phase-reduced models, it is shown that the mean value of coupling function and the degree of inhomogeneity in the total of coupling strength to the each oscillator cooperate to stabilize incoherent states. Under some circumstances, there can be bistability between coherent and incoherent states. Various cases of coupled Morris-Lecar oscillators are studied as examples of our results.

Partially locked states in coupled oscillators due to inhomogeneous coupling.

We investigate coupled identical phase oscillators with scale-free distribution of coupling strength. It is shown that partially locked states can occur due to the inhomogeneity in coupling and some properties of the coupling function. Various quantities of the partially locked states are computed through a self-consistency argument and the values show good agreement with simulation results.

Effects of axonal time delay on synchronization and wave formation in sparsely coupled neuronal oscillators.

We investigate the effects of axonal time delay when the neuronal oscillators are coupled by sparse and random connections. Using phase-reduced models with general coupling functions, we show that a small fraction of connections with time delay can destabilize synchronous states and induce near-regular wave states. An order parameter is introduced to characterize those states. We analyze the systems using mean-field-type approximation.

Emergence of chaotic itinerancy in simple ecological systems.

Chaotic itinerancy is a universal dynamical concept that describes itinerant motion among many different ordered states through chaotic transition in dynamical systems. Unlike the expectation of the prevalence of chaotic itinerancy in high-dimensional systems, we identify chaotic itinerant behavior from a relatively simple ecological system, which consists only of two coupled consumer-resource pairs. The system exhibits chaotic bursting activity, in which the explosion and the shrinkage of the population alternate indefinitely, while the explosion of one pair co-occurs with the shrinkage of the other pair. We analyze successfully the bursting activity in the framework of chaotic itinerancy, and find that large duration times of bursts tend to cluster in time, allowing the effective burst prognosis. We also investigate the control schemes on the bursting activity, and demonstrate that invoking the competitive rise of the consumer in one pair can even elongate the burst of the other pair rather than shorten it.

Wave formation by time delays in randomly coupled oscillators.

We study the dynamics of randomly coupled oscillators when interactions between oscillators are time delayed due to the finite and constant speed of coupling signals. Numerical simulations show that the time delays, proportional to the Euclidean distances between interacting oscillators, can induce near regular waves in addition to near in-phase synchronous oscillations even though oscillators are randomly coupled. We discuss the stability conditions for the wave states and the in-phase synchronous states.

Pattern formation in a two-dimensional array of oscillators with phase-shifted coupling.

We investigate the dynamics of a two-dimensional array of oscillators with phase-shifted coupling. Each oscillator is allowed to interact with its neighbors within a finite radius. The system exhibits various patterns including squarelike pinwheels, (anti)spirals with phase-randomized cores, and antiferro patterns embedded in (anti)spirals. We consider the symmetry properties of the system to explain the observed behaviors, and estimate the wavelengths of the patterns by linear analysis. Finally, we point out the implications of our work for biological neural networks.

Time-delayed spatial patterns in a two-dimensional array of coupled oscillators.

We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control parameter in this study. It is found that distance-dependent time delays induce various patterns including traveling rolls, squarelike and rhombuslike patterns, spirals, and targets. We analyzed the stability boundaries of the emerging patterns and briefly pointed out the possible empirical implications of such time-delayed patterns.