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In general, Indonesians are still fairly unfamiliar with online investment, including online investment platforms and current rapid technological developments. This is the capital for perpetrators of illegal investment fraud online to commit their crimes. Often the illegal investment crime ends up being a case of fraud, even the victim's funds are difficult to return. This research is intended to find out about the statutory policies in handling criminal cases of illegal investment fraud online, and steps in suppressing cases of illegal investment fraud so as to create legal protection for investors. The method used in this study is normative juridical by combining various literature related to illegal online investment in Indonesia. Research shows that the legal protection of investors in illegal online investments has met the formulation contained in Articles 1 and 2 of the ITE Law. However, not all provisions stipulated in the ITE Law are related to online investment fraud. Only one clause in article 28 paragraph (1) contains acts as stipulated in article 378 of the Criminal Code on fraud. Although the elements in Article 378 of the Criminal Code are fully fulfilled, there is an element of online fraud. Until now, electronic media has not been known in the Criminal Code and the Criminal Code

Previous studies on oscillator populations with two-simplex interaction have reported novel phenomena such as discontinuous desynchronization transitions and multistability of synchronized states. However, the noise effect is not well understood. Here, we study a higher-order network of noisy oscillators with generic interactions consisting of one-simplex and two types of two-simplex interactions. We observe that when a type of two-simplex interaction is dominant, synchrony is eroded and eventually disappears even for infinitesimally weak noise. Nevertheless, synchronized states may persist for extended periods, with the lifetime increasing approximately exponentially with the strength of the two-simplex interaction. When one-simplex or another type of two-simplex interaction is sufficiently strong, noise erosion is prevented, and synchronized states become persistent. A weakly nonlinear analysis reveals that as one-simplex coupling increases, the synchronized state appears supercritically or subscritically, depending on the interaction strength. Furthermore, assuming weak noise and using Kramers' rate theory, we derive a closed dynamical equation for the Kuramoto order parameter, from which the time scale of the erosion process is derived. Our study elucidates the synchronization and desynchronization of oscillator assemblies in higher-order networks and is expected to provide insights into such systems' design and control principles.

The coexistence of an abnormal rhythm and a normal steady state is often observed in nature (e.g., epilepsy). Such a system is modeled as a bistable oscillator that possesses both a limit cycle and a fixed point. Although bistable oscillators under several perturbations have been addressed in the literature, the mechanism of oscillation quenching, a transition from a limit cycle to a fixed point, has not been fully understood. In this study, we analyze quenching using the extended Stuart-Landau oscillator driven by periodic forces. Numerical simulations suggest that the entrainment to the periodic force induces the amplitude change of a limit cycle. By reducing the system with an averaging method, we investigate the bifurcation structures of the periodically driven oscillator. We find that oscillation quenching occurs by the homoclinic bifurcation when we use a periodic force combined with quadratic feedback. In conclusion, we develop a state-transition method in a bistable oscillator using periodic forces, which would have the potential for practical applications in controlling and annihilating abnormal oscillations. Moreover, we clarify the rich and diverse bifurcation structures behind periodically driven bistable oscillators, which we believe would contribute to further understanding the complex behaviors in non-autonomous systems., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

The neural oscillator model proposed by Matsuoka is a piecewise affine system that exhibits distinctive periodic solutions. Although such typical oscillation patterns have been widely studied, little is understood about the dynamics of convergence to certain fixed points and bifurcations between the periodic orbits and fixed points in this model. We performed fixed point analysis on a two-neuron version of the Matsuoka oscillator model, the result of which explains the mechanism of oscillation and the discontinuity-induced bifurcations such as subcritical/supercritical Hopf-like, homoclinic-like and grazing bifurcations. Furthermore, it provided theoretical predictions concerning a logarithmic oscillation-period scaling law and noise-induced oscillations observed around those bifurcations. These results are expected to underpin further investigations into oscillatory and transient neuronal activities concerning central pattern generators., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).)

Synchronization, which is caused by mutual coupling, and turnover, which is the replacement of old components with new ones, are observed in various open systems consisting of many components. Although these phenomena can co-occur, the interplay of coupling and turnover has been overlooked. Here, we analyze coupled phase oscillators with turnover and reveal that two distinct transitions occur, depending on both coupling and turnover: desynchronization and what we name stochastic oscillation quenching. Importantly, the latter requires both the turnover and coupling to be sufficiently intense.

Diverse complex systems often undergo sudden changes in their states, such as epileptic seizures, climate changes, and social uprisings. Such behavior has been modeled by noise-induced escape of bistable elements, which is the escape from an attracting state driven by a fluctuation in the system's state. We consider a system of interacting bistable elements and investigate the effect of diffusive coupling among elements on the process of noise-induced escape. We focus on the influence of the coupling strength over the escape time, which is the time it takes for noise-induced escape to occur. We performed numerical simulations and observed that weak coupling reduced the mean escape time, whereas strong coupling impeded escape. We argue that, although diffusive coupling both facilitates and impedes escape, the facilitating effect is dominant when coupling is weak. For weak coupling cases, we develop an approximate theory that can predict the mean and variance of escape times. In contrast, strong coupling reduces the effective noise intensity to impede escape. Our results suggest that diffusive coupling among multistable elements contributes to regulating the rate of transitions among attracting states., (© 2024. The Author(s).)

Various oscillatory phenomena occur in the world. Because some are associated with abnormal states (e.g. epilepsy), it is important to establish ways to terminate oscillations by external stimuli. However, despite the prior development of techniques for stabilizing unstable oscillations, relatively few studies address the transition from oscillatory to resting state in nonlinear dynamics. This study mainly analyzes the oscillation-quenching of metronomes on a platform as an example of such transitions. To facilitate the analysis, we describe the impulsive force (escapement mechanism) of a metronome by a fifth-order polynomial. By performing both averaging approximation and numerical simulation, we obtain a phase diagram for synchronization and oscillation quenching. We find that quenching occurs when the feedback to the oscillator increases, which will help explore the general principle regarding the state transition from oscillatory to resting state. We also numerically investigate the bifurcation of out-of-phase synchronization and beat-like solution. Despite the simplicity, our model successfully reproduces essential phenomena in interacting mechanical clocks, such as the bistability of in-phase and anti-phase synchrony and oscillation quenching occurring for a large mass ratio between the oscillator and the platform. We believe that our simple model will contribute to future analyses of other dynamics of mechanical clocks., (© 2024. The Author(s).)

This study deals with an existing mathematical model of asymmetrically interacting agents. We analyze the following two previously unfocused features of the model: (i) synchronization of growth rates and (ii) initial value dependence of damped oscillation. By applying the techniques of variable transformation and timescale separation, we perform the stability analysis of a diverging solution. We find that (i) all growth rates synchronize to the same value that is as small as the smallest growth rate and (ii) oscillatory dynamics appear if the initial value of the slowest-growing agent is sufficiently small. Furthermore, our analytical method proposes a way to apply stability analysis to an exponentially diverging solution, which we believe is also a contribution of this study. Although the employed model is originally proposed as a model of infectious disease, we do not discuss its biological relevance but merely focus on the technical aspects., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed signals. A popular method of phase reconstruction is based on the Hilbert transform, which can only reconstruct the interpretable phase from a limited class of signals, e.g., narrow band signals. To address this issue, we propose an extended Hilbert transform method that accurately reconstructs the phase from various oscillatory signals. The proposed method is developed by analyzing the reconstruction error of the Hilbert transform method with the aid of Bedrosian's theorem. We validate the proposed method using synthetic data and show its systematically improved performance compared with the conventional Hilbert transform method with respect to accurately reconstructing the phase. Finally, we demonstrate that the proposed method is potentially useful for detecting the phase shift in an observed signal. The proposed method is expected to facilitate the study of synchronization phenomena from experimental data., (© 2023. The Author(s).)

Complex networks often possess communities defined based on network connectivity. When dynamics undergo in a network, one can also consider dynamical communities, i.e., a group of nodes displaying a similar dynamical process. We have investigated both analytically and numerically the development of a dynamical community structure, where the community is referred to as a group of nodes synchronized in frequency, in networks of phase oscillators. We first demonstrate that using a few example networks, the community structure changes when network connectivity or interaction strength is varied. In particular, we found that community switching, i.e., a portion of oscillators change the group to which they synchronize, occurs for a range of parameters. We then propose a three-oscillator model: a bidirectional, weighted chain of three Kuramoto phase oscillators, as a theoretical framework for understanding the community formation and its variation. Our analysis demonstrates that the model shows a variety of partially synchronized patterns: oscillators with similar natural frequencies tend to synchronize for weak coupling, while tightly connected oscillators tend to synchronize for strong coupling. We obtain approximate expressions for the critical coupling strengths by employing a perturbative approach in a weak coupling regime and a geometric approach in strong coupling regimes. Moreover, we elucidate the bifurcation types of transitions between different patterns. Our theory might be useful for understanding the development of partially synchronized patterns in a wider class of complex networks than community structured networks.

Calcium signaling is pivotal to the circadian clockwork in the suprachiasmatic nucleus (SCN), particularly in rhythm entrainment to environmental light-dark cycles. Here, we show that a small G-protein Gem, an endogenous inhibitor of high-voltage-activated voltage-dependent calcium channels (VDCCs), is rapidly induced by light in SCN neurons via the calcium (Ca 2+ )-mediated CREB/CRE transcriptional pathway. Gem attenuates light-induced calcium signaling through its interaction with VDCCs. The phase-shift magnitude of locomotor activity rhythms by light, at night, increases in Gem-deficient (Gem -/- ) mice. Similarly, in SCN slices from Gem -/- mice, depolarizing stimuli induce larger phase shifts of clock gene transcription rhythms that are normalized by the application of an L-type VDCC blocker, nifedipine. Voltage-clamp recordings from SCN neurons reveal that Ca 2+ currents through L-type channels increase in Gem -/- mice. Our findings suggest that transcriptionally activated Gem feeds back to suppress excessive light-evoked L-type VDCC activation, adjusting the light-induced phase-shift magnitude to an appropriate level in mammals., Competing Interests: Declaration of interests None of the authors has any competing financial interests to declare., (Copyright © 2022 The Authors. Published by Elsevier Inc. All rights reserved.)

The hemagglutination inhibition (HAI) assay is one of the detection methods for influenza virus (IFV) under global influenza surveillance, which uses freshly prepared animal red blood cells (RBCs). Here, we demonstrate that a mixed glycan-modified polystyrene microparticle, which can be chemically prepared in advance, can replace animal RBCs in the HAI assay. A mixture of azide-conjugated glycans containing sialyl- and sulfated-lactose moieties was produced from Madin-Darby canine kidney (MDCK) cells, which are used for IFV isolation, and then immobilized on the surface of a polystyrene microparticle using click chemistry. Human HA and IFV were detected with high sensitivity when using the mixed glycan-immobilized particle.

We formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture, stating the existence of a perturbed trajectory shadowing every unperturbed trajectory on the system attractor for any small enough perturbation of arbitrary duration and a corresponding unique time isomorphism, which we identify as phase such that phase shifts between the unperturbed trajectory and its perturbed shadow are well defined. The phase sensitivity function is the solution of an adjoint linear equation and can be used to estimate the average change of phase velocity to small time dependent or independent perturbations. These changes in frequency are experimentally accessible, giving a convenient way to define and measure phase response curves for chaotic oscillators. The shadowing trajectory and the phase can be constructed explicitly in the tangent space of an unperturbed trajectory using co-variant Lyapunov vectors. It can also be used to identify the limits of the regime of linear response.

Measurements of interaction intensity are generally achieved by observing responses to perturbations. In biological and chemical systems, external stimuli tend to deteriorate their inherent nature, and thus, it is necessary to develop noninvasive inference methods. In this paper, we propose theoretical methods to infer coupling strength and noise intensity simultaneously in two well-synchronized noisy oscillators through observations of spontaneously fluctuating events such as neural spikes. A phase oscillator model is applied to derive formulae relating each of the parameters to spike time statistics. Using these formulae, each parameter is inferred from a specific set of statistics. We verify these methods using the FitzHugh-Nagumo model as well as the phase model. Our methods do not require external perturbations and thus can be applied to various experimental systems., Competing Interests: The authors declare no competing interest., (Copyright © 2022 the Author(s). Published by PNAS.)

Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao et al. [Nature (London) 530, 307 (2016)0028-083610.1038/nature16948] proposed a theoretical framework to reduce dynamical systems on networks, which are high dimensional in general, to one-dimensional dynamical systems. The accuracy of this one-dimensional reduction relies on three approximations in addition to the assumption that the network has a negligible degree correlation. In the present study, we analyze the accuracy of the one-dimensional reduction assuming networks without degree correlation. We do so mainly through examining the validity of the individual assumptions underlying the method. Across five dynamical system models, we find that the accuracy of the one-dimensional reduction hinges on the spread of the equilibrium value of the state variable across the nodes in most cases. Specifically, the one-dimensional reduction tends to be accurate when the dispersion of the node's state is small. We also find that the correlation between the node's state and the node's degree, which is common for various dynamical systems on networks, is unrelated to the accuracy of the one-dimensional reduction.

Motivated from a wide range of applications, various methods to control synchronization in coupled oscillators have been proposed. Previous studies have demonstrated that global feedback typically induces three macroscopic behaviors: synchronization, desynchronization, and oscillation quenching. However, analyzing all of these transitions within a single theoretical framework is difficult, and thus the feedback effect is only partially understood in each framework. Herein, we analyze a model of globally coupled phase oscillators exposed to global feedback, which shows all of the typical macroscopic dynamical states. Analytical tractability of the model enables us to obtain detailed phase diagrams where transitions and bistabilities between different macroscopic states are identified. Additionally, we propose strategies to steer the oscillators into targeted states with minimal feedback strength. Our study provides a useful overview of the effect of global feedback and is expected to serve as a benchmark when more sophisticated feedback needs to be designed.

Purpose: The clinical application of gemcitabine (GEM) is limited by its pharmacokinetic properties. The aim of this study was to characterize the stability in circulating plasma, tumor targeting, and payload release of liposome-encapsulated GEM, FF-10832., Methods: Antitumor activity was assessed in xenograft mouse models of human pancreatic cancer. The pharmacokinetics of GEM and its active metabolite dFdCTP were also evaluated., Results: In mice with Capan-1 tumors, the dose-normalized areas under the curve (AUCs) after FF-10832 administration in plasma and tumor were 672 and 1047 times higher, respectively, than after using unencapsulated GEM. The tumor-to-bone marrow AUC ratio of dFdCTP was approximately eight times higher after FF-10832 administration than after GEM administration. These results indicated that liposomal encapsulation produced long-term stability in circulating plasma and tumor-selective targeting of GEM. In mice with Capan-1, SUIT-2, and BxPC-3 tumors, FF-10832 had better antitumor activity and tolerability than GEM. Internalization of FF-10832 in tumor-associated macrophages (TAMs) was revealed by flow cytometry and confocal laser scanning microscopy, and GEM was efficiently released from isolated macrophages of mice treated with FF-10832. These results suggest that TAMs are one of the potential reservoirs of GEM in tumors., Conclusion: This study found that FF-10832 had favorable pharmacokinetic properties. The liposomal formulation was more effective and tolerable than unencapsulated GEM in mouse xenograft tumor models. Hence, FF-10832 is a promising candidate for the treatment of pancreatic cancer.

Motile human-skin fibroblasts form macroscopic swirling patterns when grown to confluence on a culture dish. In this paper, we investigate the effect of coating the culture-dish surface with collagen on the resulting pattern, using human-skin fibroblast NB1RGB cells as the model system. The presence of the collagen coating is expected to enhance the adherence of the fibroblasts to the dish surface, and thereby also enhance the traction that the fibroblasts have as they move. We find that, contrary to our initial expectation, the coating does not significantly affect the motility of the fibroblasts. Their eventual number density at confluence is also unaffected. However, the coherence length of cell orientation in the swirling pattern is diminished. We also find that the fibroblasts cultured in collagen-coated dishes are rounder in shape and shorter in perimeter, compared with those cultured in uncoated polystyrene or glass culture dishes. We hypothesise that the rounder cell-shape which weakens the cell-cell nematic contact interaction is responsible for the change in coherence length. A simple mathematical model of the migrating fibroblasts is constructed, which demonstrates that constant motility with weaker nematic interaction strength does indeed lead to the shortening of the coherence length.

Individual cellular activities fluctuate but are constantly coordinated at the population level via cell-cell coupling. A notable example is the somite segmentation clock, in which the expression of clock genes (such as Hes7) oscillates in synchrony between the cells that comprise the presomitic mesoderm (PSM) 1,2 . This synchronization depends on the Notch signalling pathway; inhibiting this pathway desynchronizes oscillations, leading to somite fusion 3-7 . However, how Notch signalling regulates the synchronicity of HES7 oscillations is unknown. Here we establish a live-imaging system using a new fluorescent reporter (Achilles), which we fuse with HES7 to monitor synchronous oscillations in HES7 expression in the mouse PSM at a single-cell resolution. Wild-type cells can rapidly correct for phase fluctuations in HES7 oscillations, whereas the absence of the Notch modulator gene lunatic fringe (Lfng) leads to a loss of synchrony between PSM cells. Furthermore, HES7 oscillations are severely dampened in individual cells of Lfng-null PSM. However, when Lfng-null PSM cells were completely dissociated, the amplitude and periodicity of HES7 oscillations were almost normal, which suggests that LFNG is involved mostly in cell-cell coupling. Mixed cultures of control and Lfng-null PSM cells, and an optogenetic Notch signalling reporter assay, revealed that LFNG delays the signal-sending process of intercellular Notch signalling transmission. These results-together with mathematical modelling-raised the possibility that Lfng-null PSM cells shorten the coupling delay, thereby approaching a condition known as the oscillation or amplitude death of coupled oscillators 8 . Indeed, a small compound that lengthens the coupling delay partially rescues the amplitude and synchrony of HES7 oscillations in Lfng-null PSM cells. Our study reveals a delay control mechanism of the oscillatory networks involved in somite segmentation, and indicates that intercellular coupling with the correct delay is essential for synchronized oscillation.

We provide a theoretical framework for quantifying the expected level of synchronization in a network of noisy oscillators. Through linearization around the synchronized state, we derive the following quantities as functions of the eigenvalues and eigenfunctions of the network Laplacian using a standard technique for dealing with multivariate Ornstein-Uhlenbeck processes: the magnitude of the fluctuations around a synchronized state and the disturbance coefficients α i that represent how strongly node i disturbs the synchronization. With this approach, we can quantify the effect of individual nodes and links on synchronization. Our theory can thus be utilized to find the optimal network structure for accomplishing the best synchronization. Furthermore, when the noise levels of the oscillators are heterogeneous, we can also find optimal oscillator configurations, i.e., where to place oscillators in a given network depending on their noise levels. We apply our theory to several example networks to elucidate optimal network structures and oscillator configurations.

Quiescence is important for sustaining neural stem cells (NSCs) in the adult brain over the lifespan. Lysosomes are digestive organelles that degrade membrane receptors after they undergo endolysosomal membrane trafficking. Enlarged lysosomes are present in quiescent NSCs (qNSCs) in the subventricular zone of the mouse brain, but it remains largely unknown how lysosomal function is involved in the quiescence. Here we show that qNSCs exhibit higher lysosomal activity and degrade activated EGF receptor by endolysosomal degradation more rapidly than proliferating NSCs. Chemical inhibition of lysosomal degradation in qNSCs prevents degradation of signaling receptors resulting in exit from quiescence. Furthermore, conditional knockout of TFEB, a lysosomal master regulator, delays NSCs quiescence in vitro and increases NSC proliferation in the dentate gyrus of mice. Taken together, our results demonstrate that enhanced lysosomal degradation is an important regulator of qNSC maintenance.

Experiments and supporting theoretical analysis are presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation, where the coupling is repulsive in the electrode potential. While attractive coupling generates phase clusters and desynchronized states, repulsive coupling results in synchronized oscillations. The experiments are interpreted with a phenomenological model that captures the waveform of the oscillations (exponential increase) followed by a refractory period. The globally coupled autocatalytic integrate-and-fire model predicts the development of partially synchronized states that occur through attracting heteroclinic cycles between out-of-phase two-cluster states. Similar behavior can be expected in many other systems where the oscillations occur close to a saddle-loop bifurcation, e.g., with Morris-Lecar neurons.

Ordered polarity alignment of cell populations plays vital roles in biology, such as in hair follicle alignment and asymmetric cell division. Although cell polarity is uniformly oriented along a tissue axis in many tissues, its mechanism is not well understood. In this paper, we propose a theoretical framework to understand the generic dynamical properties of polarity alignment in interacting cellular units, where each cell is described by a reaction-diffusion system, and the cells further interact with one another through the contacting surfaces between them. Using a perturbation method under the assumption of weak coupling between cells, we derive a reduced model in which polarity of each cell is described by only one variable. Essential dynamical properties including the effects of cell shape, coupling heterogeneity, external signal and noise can be clarified analytically. In particular, we show that the anisotropicity of the system, such as oriented cell elongation and axial asymmetry in the coupling strength, can serve as a global cue that drives the uniform orientation of cell polarity along a certain axis. Our study bridges the gap between detailed and phenomenological models, and it is expected to facilitate the study of polarity dynamics in various nonequilibrium systems.

The expression of segmentation clock genes is self-oscillatory due to a delayed negative-feedback mechanism. Hubaud et al. (2017), reporting in Cell, now reveal that segmentation clock genes also exhibit properties of an excitable system, with Yap signaling setting the threshold for adopting an oscillatory state and Notch signaling triggering oscillations., (Copyright © 2017 Elsevier Inc. All rights reserved.)

The circadian system has been regarded as a limit cycle oscillator constructed by the integrated interaction of clock genes and proteins. Here, we investigated a mammalian circadian oscillation geometrically before and after a perturbation. We detected the singular point and transition from a type 1 to type 0 phase response curve (PRC) and determined the embedding dimension to show how many variables are needed to describe the limit cycle oscillation and relaxation process after a perturbation. As a perturbation, forskolin (FK) was administered to Rat-1 cells expressing the Per2::luc gene. By broadly and finely changing the phase and strength of the perturbation, we detected the transition of the PRC from type 1 to type 0 and a possible singular transition point, the property of which agreed quite well with our numerical simulation of the noisy Goodwin model, a simple yet canonical model for the transcription-translation feedback loop of the core clock genes. Furthermore, we estimated the embedding dimension of the limit cycle before and after the perturbation. The trajectory of the limit cycle was embedded in two dimensions but with the perturbation of the state point moved out of the trajectory, the relaxation process was generally embedded in higher dimensions. The average number of embedding dimensions at each dose of FK increased as the FK dose increased but most of the relaxation process was generally embedded within four dimensions. These findings support the existence of a circadian limit cycle oscillator in mammalian cells and suggest that a small number of variables determine the relaxation process after a perturbation.

Fibroblasts are the cells within the dermis layer of skin which are responsible for generating connective tissue, where collagen is the main component. However, the effects of collagen on the motion behavior of human skin fibroblasts were not studied well. We therefore propose an image analysis method to quantify the effects of collagen on the motion characteristics of fibroblasts. Images are divided into disjoint blocks and three gradient based descriptors, namely histogram of oriented gradients (HOG), the modified HOG (modiHOG), and the gradient direction histogram (GDH) are then applied to each block. These features can extract the orientation and shape or orientation only information of the skin fibroblasts from images. An orientation similarity function and a quantitative index, called first minimum similarity distance, are defined to quantify the orientation behavior of fibroblasts. An experiment with two sets of fibroblasts images, obtained from cell culture with and without collagen coating, demonstrates that the skin fibroblasts produce smaller orientation patterns, when they are cultured in the presence of collagen proteins. A statistical t-test is then performed, which validates the significant differences in the orientation behavior of the skin fibroblasts in the two cases mentioned.

Cold temperatures lead to nullification of circadian rhythms in many organisms. Two typical scenarios explain the disappearance of rhythmicity: the first is oscillation death, which is the transition from self-sustained oscillation to damped oscillation that occurs at a critical temperature. The second scenario is oscillation arrest, in which oscillation terminates at a certain phase. In the field of nonlinear dynamics, these mechanisms are called the Hopf bifurcation and the saddle-node on an invariant circle bifurcation, respectively. Although these mechanisms lead to distinct dynamical properties near the critical temperature, it is unclear to which scenario the circadian clock belongs. Here we reduced the temperature to dampen the reconstituted circadian rhythm of phosphorylation of the recombinant cyanobacterial clock protein KaiC. The data led us to conclude that Hopf bifurcation occurred at ∼19 °C. Below this critical temperature, the self-sustained rhythms of KaiC phosphorylation transformed to damped oscillations, which are predicted by the Hopf bifurcation theory. Moreover, we detected resonant oscillations below the critical temperature when temperature was periodically varied, which was reproduced by numerical simulations. Our findings suggest that the transition to a damped oscillation through Hopf bifurcation contributes to maintaining the circadian rhythm of cyanobacteria through resonance at cold temperatures., Competing Interests: The authors declare no conflict of interest.

The endogenous circadian clock drives oscillations that are completely synchronized with the environmental day-night rhythms with a period of approximately 24 hours. Temporal misalignment between one's internal circadian clock and the external solar time often occurs in shift workers and long-distance travelers; such misalignments are accompanied by sleep disturbances and gastrointestinal distress. Repeated exposure to jet lag and rotating shift work increases the risk of lifestyle-related diseases, such as cardiovascular complaints and metabolic insufficiencies. However, the mechanism behind the disruption of one's internal clock is not well understood. In this paper, we therefore present a new theoretical concept called "jet lag separatrix" to understand circadian clock disruption and slow recovery from jet lag based on the mathematical model describing the hierarchical structure of the circadian clock. To demonstrate the utility of our theoretical study, we applied it to predict that re-entrainment via a two-step jet lag in which a four-hour shift of the light-dark cycle is given in the span of two successive days requires fewer days than when given as a single eight-hour shift. We experimentally verified the feasibility of our theory in C57BL/6 strain mice, with results indicating that this pre-exposure of jet lag is indeed beneficial.

Cells communicate with each other to coordinate their gene activities at the population level through signaling pathways. It has been shown that many gene activities are oscillatory and that the frequency and phase of oscillatory gene expression encode various types of information. However, whether or how such oscillatory information is transmitted from cell to cell remains unknown. Here, we developed an integrated approach that combines optogenetic perturbations and single-cell bioluminescence imaging to visualize and reconstitute synchronized oscillatory gene expression in signal-sending and signal-receiving processes. We found that intracellular and intercellular periodic inputs of Notch signaling entrain intrinsic oscillations by frequency tuning and phase shifting at the single-cell level. In this way, the oscillation dynamics are transmitted through Notch signaling, thereby synchronizing the population of oscillators. Thus, this approach enabled us to control and monitor dynamic cell-to-cell transfer of oscillatory information to coordinate gene expression patterns at the population level., (© 2017 Isomura et al.; Published by Cold Spring Harbor Laboratory Press.)

Purpose: The aim of this study was to examine the fit accuracy of e.max crowns by investigating marginal and internal gaps., Materials and Methods: In experiment 1, 60 e.max computer-aided design/computer-assisted manufacture (CAD/CAM) crowns were manufactured. The crowns were fabricated using optical scanning of artificial teeth (Op group) or scanning of a plaster model following a silicone impression (M group). Cement space settings of 90, 120, and 150 μm were applied. Marginal and internal crown gaps were compared among six conditions (Op90, Op120, Op150, M90, M120, M150). In experiment 2, e.max CAD crowns from the Op group (CADop group) and the M group (CADm group) were compared with e.max Press crowns (Press group) by measuring marginal and internal gaps of the crowns using Scheffe multiple comparison test. The level of significance was set at .05., Results: In experiment 1, the marginal gap of the Op90 group was significantly higher than that of the Op120 and Op150 groups. The marginal gap of the M90 group was significantly higher than those of the M120 and M150 groups, and the internal gap of the M90 group was significantly lower than that of the M150 group. Although there was no statistically significant difference in marginal gap among the three groups, the internal gap of the CADm group was significantly higher than the Press group., Conclusion: Although the variation in cement space settings and fabrication techniques affected accuracy, e.max CAD crowns fabricated using optical scanning of melamine teeth achieved a clinically acceptable fit.

We derive a concise and general expression of the energy dissipation rate for coupled oscillators rotating on circular trajectories by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. In the framework of phase oscillator models, it is known that the even and odd parts of the coupling function express the effect on collective and relative dynamics, respectively. We reveal that the odd part always decreases the dissipation upon synchronization, while the even part yields a characteristic square-root change of the dissipation near the bifurcation point whose sign depends on the specific system parameters. We apply our theory to hydrodynamically coupled Stokes spheres rotating on circular trajectories that can be interpreted as a simple model of synchronization of coupled oscillators in a biophysical system. We show that the coupled Stokes spheres gain the ability to do more work on the surrounding fluid as the degree of phase synchronization increases.

Notch signaling regulates tissue morphogenesis through cell-cell interactions. The Notch effectors Hes1 and Hes7 are expressed in an oscillatory manner and regulate developmental processes such as neurogenesis and somitogenesis, respectively. Expression of the mRNA for the mouse Notch ligand Delta-like1 (Dll1) is also oscillatory. However, the dynamics of Dll1 protein expression are controversial, and their functional significance is unknown. Here, we developed a live-imaging system and found that Dll1 protein expression oscillated in neural progenitors and presomitic mesoderm cells. Notably, when Dll1 expression was accelerated or delayed by shortening or elongating the Dll1 gene, Dll1 oscillations became severely dampened or quenched at intermediate levels, as modeled mathematically. Under this condition, Hes1 and Hes7 oscillations were also dampened. In the presomitic mesoderm, steady Dll1 expression led to severe fusion of somites and their derivatives, such as vertebrae and ribs. In the developing brain, steady Dll1 expression inhibited proliferation of neural progenitors and accelerated neurogenesis, whereas optogenetic induction of Dll1 oscillation efficiently maintained neural progenitors. These results indicate that the appropriate timing of Dll1 expression is critical for the oscillatory networks and suggest the functional significance of oscillatory cell-cell interactions in tissue morphogenesis., (© 2016 Shimojo et al.; Published by Cold Spring Harbor Laboratory Press.)

Excitable media can develop spiral chaos, in which the number of spirals changes chaotically with time. Depending on parameter values in dynamical equations, spiral chaos may permanently persist or spontaneously arrive at a steady state after a transient time, referred to as the lifetime. Previous numerical studies have demonstrated that the lifetime of transient spiral chaos increases exponentially with system size to a good approximation. In this study, using the fact that the number of spirals obeys a Gaussian distribution, we provide a general expression for the system size dependence of the lifetime for large system sizes, which is indeed exponential. We confirm that the expression is in good agreement with numerically obtained lifetimes for both excitable and oscillatory media with parameter sets near the onset of transient chaos. The expression we develop for the lifetime is expected to be useful for predicting lifetimes in large systems.

Occurrence of bi- and trirhythmicities (coexistence of two or three stable limit cycles, respectively, with distinctly different periods) has been studied experimentally by applying delayed feedback control to the copper-phosphoric acid electrochemical system oscillating close to a Hopf bifurcation point under potentiostatic condition. The oscillating electrode potential is delayed by τ and the difference between the present and delayed values is fed back to the circuit potential with a feedback gain K. The experiments were performed by determining the period of current oscillations T as a function of (both increasing and decreasing) τ at several fixed values of K. With small delay times, the period exhibits a sinusoidal type dependence on τ. However, with relatively large delays (typically τ ≫ T) for each feedback gain K, there exists a critical delay τcrit above which birhythmicity emerges. The experiments show that for weak feedback, Kτcrit is approximately constant. At very large delays, the dynamics becomes even more complex, and trirhythmicity could be observed. Results of numerical simulations based on a general kinetic model for metal electrodissolution were consistent with the experimental observations. The experimental and numerical results are also interpreted by using a phase model; the model parameters can be obtained from experimental data measured at small delay times. Analytical solutions to the phase model quantitatively predict the parameter regions for the appearance of birhythmicity in the experiments, and explain the almost constant value of Kτcrit for weak feedback.

Purpose: The purpose of this study was to evaluate prospectively the clinical effectiveness of immediate loading of implants with complete-arch fixed prostheses in edentulous maxillae after the implants were placed with flapless guided surgery., Materials and Methods: Patients with edentulous maxillae who visited a single dental clinic during the recruitment period (April 2011 to May 2012) were selected by consecutive sampling and predetermined selection criteria. Four to six implants were placed in each patient with flapless guided surgery. The outcome measures were insertion torque, surgical time, postoperative pain (100-mm visual analog scale), marginal bone level change, implant survival, and oral health-related quality of life. Patients were followed for up to 1 year., Results: Fifty patients received 290 implants. All implants were immediately loaded 2 hours after placement with prefabricated fixed provisional prostheses. Two patients dropped out of the study. Hence, analyses were conducted for 278 implants in 48 patients (26 men, 22 women; mean age 56.0 ± 8.3 years; age range, 34 to 74 years). The average insertion torque was 57.7 ± 16.6 Ncm, the average surgical time was 22.9 ± 4.7 minutes, and the average score for postoperative pain was 14.7 ± 9.3. One year after immediate loading, the implant survival rate was 98.6%. Four implants showed mobility early after implant placement and were lost. Mean marginal bone level changes were -0.32 ± 0.43 mm. Scores on the Oral Health Impact Profile-54 (Japanese version) improved significantly after prosthetic treatment., Conclusion: The results of this study indicate that this treatment method for edentulous maxillae is predictable, with a high implant survival rate and a clinically reasonable improvement in oral health-related quality of life.

We report on a synchronization-breaking instability observed in a noisy oscillator unidirectionally coupled to a pacemaker. Using a phase oscillator model, we find that, as the coupling strength is increased, the noisy oscillator lags behind the pacemaker more frequently and the phase slip rate increases, which may not be observed in averaged phase models such as the Kuramoto model. Investigation of the corresponding Fokker-Planck equation enables us to obtain the reentrant transition line between the synchronized state and the phase slip state. We verify our theory using the Brusselator model, suggesting that this reentrant transition can be found in a wide range of limit cycle oscillators.