Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more catastrophic.Taking an asymmetric Lévy-noise-induced tri-stable model with desirable,sub-desirable,and undesirable states as a prototype class of real systems,a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out.We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability,which is named as the absorbed region.Then,a new concept of the parameter dependent basin of the unsafe regime(PDBUR)under the asymmetric Lévy noise is introduced.It is an efficient tool for approximately quantifying the ranges of the parameters,where the noise-induced CTs from the desirable state directly to the undesirable one may occur.More importantly,it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.

Slowing down critical transitions via Gaussian white noise and periodic force

Stochastic perturbations and periodic excitations are generally regarded as sources to induce critical transitions in complex systems. However, we find that they are also able to slow down an imminent critical transition. To illustrate this phenomenon, a periodically driven bistable eutrophication model with Gaussian white noise is introduced as a prototype class of real systems.The residence probability(RP) is presented to measure the possibility that the given system stays in the oligotrophic state versus Gaussian white noise and periodic force. Variations in the mean first passage time(MFPT) and the mean velocity(MV) of the first right-crossing process are also calculated respectively. We show that the frequency of the periodic force can increase the MFPT while reduce the MV under different control parameters. Nevertheless, the noise intensity or the amplitude may result in an increase of the RP only in the case of control parameters approaching the critical values. Furthermore, for an impending critical transition, an increase of the RP appears with the interaction between the amplitude and noise intensity or the combination of the noise intensity and frequency, while the interaction of the frequency and amplitude leads to an extension of the MFPT or a decrease of the MV. As a result, an increase of the RP and MFPT, and a decrease of the MVobtained from our results claim that it is possible to slow down an imminent critical transition via Gaussian white noise and periodic force.

Critical transition Reynolds number for plane channel flow

The determination of the critical transition Reynolds number is of practical importance for some engineering problems. However, it is not available with the current theoretical method, and has to rely on experiments. For supersonic/hypersonic boundary layer flows, the experimental method for determination is not feasible either. Therefore, in this paper, a numerical method for the determination of the critical transition Reynolds number for an incompressible plane channel flow is proposed. It is basically aimed to test the feasibility of the method. The proposed method is extended to determine the critical Reynolds number of the supersonic/hypersonic boundary layer flow in the subsequent papers.

Universal critical properties of the Eulerian bond-cubic model

We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of n. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O（n） branch for n 〈 2 and the results obtained by previous transfer matrix calculations. For n = 2, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical 0（2） loop model. These results confirm that the cubic anisotropy is marginal at n = 2 but irrelevant for n〈2.

Voltage-controlled Kosterlitz–Thouless transitions and various kinds of Kondo behaviors in a triple dot device

The transport property and phase transition for a parallel triple dot device are studied by adopting Wilson＇s numerical renormalization group technique, focusing on the effects of level spacings between neighboring dot sites. By keeping dot 2at the half-filled level and tuning the level differences, it is demonstrated that the system transits from local spin quadruplet to triplet and doublet sequently, and three kinds of Kondo peaks at the Fermi surface could be found, which are separated by two Kosterlitz–Thouless type quantum phase transitions and correspond to spin-3/2, spin-1, and spin-1/2 Kondo effect,respectively. To obtain a detailed understanding of these problems, the charge occupation, the spin–spin correlation, the transmission coefficient, and the temperature-dependent magnetic moment are shown, and necessary physical arguments are given.

Observation of lateral long range order in superconducting FeTe thin films

We find that the superconductivity in the thin films of the formerly believed non-superconducting parent compound FeTe is accompanied by an emergence of second order with a correlation length of 742 nm and 258 nm at 10 K and 300 K, respectively. The structural phase transition found in iron pnictide superconductors, in non-superconducting FeTe bulk samples, and in FeSe superconducting thin films is not observed in the superconducting FeTe thin films. The interplay between superconductivity and long range order may suggest the crucial role of competition between electronic localization and itinerancy which leads to strong quantum fluctuations in the FeTe system.

Critical Transition Reynolds Number for the Incompressible Flat-plate Boundary Layer as Searched by Numerical Simulation

The critical transition Reynolds number is the lowest value at which the turbulent flow can hold in real flows.The determination of the critical transition Reynolds number not only is a scientific problem,but also is important for some engineering problems.However,there is no available theoretical method to search the critical value.For the hypersonic boundary layer with significant importance for engineering problems,there is no available experimental method to search the critical value so far.Consequently,it is imperative to take numerical method to search it.In this paper,direct numerical simulations(DNS)method is employed to determine the critical transition Reynolds number for the incompressible flat-plate boundary layer.Firstly,under the assumption of parallel flow,the temporal mode DNS is performed to determine the critical value as Re_(xpcr)=43767,which is quite close to the numerical results of other people.Secondly,under the condition of nonparallel flow,the spatial mode DNS is performed to determine the critical transition Reynolds number as Re_(xcr)=3×10^(5),which is well consistent with the experimental results.In principle,the proposed method in this paper can be extended to the supersonic/hypersonic boundary layer,and that problem will be discussed in the subsequent papers.

Critical parameters near the ferromagnetic-paramagnetic phase transition in La_(0.67–x)Y_xBa_(0.23)Ca_(0.1)MnO_3 compounds(x=0.10 and x=0.15)

The critical properties of the mixed manganite La0.67–x Y x Ba0.23Ca0.1Mn O3 with x=0.10 and x=0.15 around the paramagnetic（PM）-ferromagnetic（FM） phase transition were investigated through various techniques. These involved modified Arrott plots, Kouvel-Fisher method and Widom scaling relation. Magnetic data, analyzed in the critical region, using the above methods, yielded the critical exponents for（x=0.10） La0.57Y0.10Ba0.23Ca0.1Mn O3（β=0.312±0.002 and γ=1.147±0.003 at T C=299.23±0.05 K）. Moreover, the estimated critical exponents of（x=0.15） La0.52Y0.15Ba0.23Ca0.1Mn O3 were β=0.286±0.004 and γ=0.943±0.002 at T C=289.53±0.06 K. The critical exponents＇ values were close to the theoretical values of 3D-Ising model and tricritical mean-field model. These results suggested that the present composition should be close to a tricritical point in the La0.67–x Y x Ba0.23Ca0.1Mn O3 phase diagram. Expressing the field dependence as ΔS M∝H n allowed us to establish a relationship between the exponent n and the critical exponents of the material and to propose a phenomenological universal curve for the field dependence of ΔS M.

Locating the QCD critical end point through peaked baryon number susceptibilities along the freeze-out line

We investigate the baryon number susceptibilities up to fourth order along different freeze-out lines in a holographic QCD model with a critical end point（CEP）, and we propose that the peaked baryon number susceptibilities along the freeze-out line can be used as a clean signature to locate the CEP in the QCD phase diagram.On the temperature and baryon chemical potential plane, the cumulant ratio of the baryon number susceptibilities（up to fourth order） forms a ridge along the phase boundary, and develops a sword-shaped ＂mountain＂ standing upright around the CEP in a narrow and oblate region. The measurement of baryon number susceptibilities from heavy-ion collision experiments is along the freeze-out line. If the freeze-out line crosses the foot of the CEP mountain, then one can observe the peaked baryon number susceptibilities along the freeze-out line, and the kurtosis of the baryon number distributions has the highest magnitude. The data from the first phase of the beam energy scan program at the Relativistic Heavy Ion Collider indicates that there should be a peak of the kurtosis of the baryon number distribution at a collision energy of around 5 Ge V, which suggests that the freeze-out line crosses the foot of the CEP mountain and the summit of the CEP should be located nearby, around a collision energy of 3–7 GeV.

scGET:Predicting Cell Fate Transition During Early Embryonic Development by Single-cell Graph Entropy

During early embryonic development,cell fate commitment represents a critical transition or“tipping point”of embryonic differentiation,at which there is a drastic and qualitative shift of the cell populations.In this study,we presented a computational approach,scGET,to explore the gene–gene associations based on single-cell RNA sequencing(scRNAseq)data for critical transition prediction.Specifically,by transforming the gene expression data to the local network entropy,the single-cell graph entropy(SGE)value quantitatively characterizes the stability and criticality of gene regulatory networks among cell populations and thus can be employed to detect the critical signal of cell fate or lineage commitment at the single-cell level.Being applied to five scRNA-seq datasets of embryonic differentiation,scGET accurately predicts all the impending cell fate transitions.After identifying the“dark genes”that are non-differentially expressed genes but sensitive to the SGE value,the underlying signaling mechanisms were revealed,suggesting that the synergy of dark genes and their downstream targets may play a key role in various cell development processes.The application in all five datasets demonstrates the effectiveness of scGET in analyzing scRNA-seq data from a network perspective and its potential to track the dynamics of cell differentiation.The source code of scGET is accessible at https://github.com/zhongjiayuna/scGET_Project.

Principles for managing marine ecosystems prone to tipping points

As climatic changes and human uses intensify,resource managers and other decision makers are taking actions to either avoid or respond to ecosystem tipping points,or dramatic shifts in structure and function that are often costly and hard to reverse.Evidence indicates that explicitly addressing tipping points leads to improved management outcomes.Drawing on theory and examples from marine systems,we distill a set of seven principles to guide effective management in ecosystems with tipping points,derived from the best available science.These principles are based on observations that tipping points(1)are possible everywhere,(2)are associated with intense and/or multifaceted human use,(3)may be preceded by changes in earlywarning indicators,(4)may redistribute benefits among stakeholders,(5)affect the relative costs of action and inaction,(6)suggest biologically informed management targets,and(7)often require an adaptive response to monitoring.We suggest that early action to preserve system resilience is likely more practical,affordable,and effective than late action to halt or reverse a tipping point.We articulate a conceptual approach to management focused on linking management targets to thresholds,tracking early-warning signals of ecosystem instability,and stepping up investment in monitoring and mitigation as the likelihood of dramatic ecosystem change increases.This approach can simplify and economize management by allowing decision makers to capitalize on the increasing value of precise information about threshold relationships when a system is closer to tipping or by ensuring that restoration effort is sufficient to tip a system into the desired regime.

Self-organization Mechanism during the Bedform Process

This paper investigates the functional and morphological self organization phenomena that occur during the bedform process in river systems. The fluvial process has architecturally functional self organization actions that serve to self adjust the river regime. The bedform (or sand waves) process is part of the functional self organization at the middle level of the geometrical scale. By increasing the resistance of the mobile bed and simultaneously decreasing the capacity carrying sediment, the bedform serves to self adjust the river system. The morphological self organization of the bedform process is the basis for the functional self organization. The concept of the water sand interaction region is suggested, and a nonlinear model is constructed to describe the complex interaction among water flow, bed load transport, and local bed deformation, i e , the sand waves. A numerical simulation was developed based upon this model. The primary results show that the model is able to repeat many important phenomena in the bedform process, especially the critical phase transition.

The single-sample network module biomarkers(sNMB)method reveals the pre-deterioration stage of disease progression

The progression of complex diseases generally involves a pre-deterioration stage that occurs during the transition from a healthy state to disease deterioration,at which a drastic and qualitative shift occurs.The development of an effective approach is urgently needed to identify such a pre-deterioration stage or critical state just before disease deterioration,which allows the timely implementation of appropriate measures to prevent a catastrophic transition.However,identifying the pre-deterioration stage is a challenging task in clinical medicine,especially when only a single sample is available for most patients,which is responsible for the failure of most statistical methods.In this study,a novel computational method,called single-sample network module biomarkers(sNMB),is presented to predict the pre-deterioration stage or critical point using only a single sample.Specifically,the proposed single-sample index effectively quantifies the disturbance caused by a single sample against a group of given reference samples.Our method successfully detected the early warning signal of the critical transitions when applied to both a numerical simulation and four real datasets,including acute lung injury,stomach adenocarcinoma,esophageal carcinoma,and rectum adenocarcinoma.In addition,it provides signaling biomarkers for further practical application,which helps to discover prognostic indicators and reveal the underlying molecular mechanisms of disease progression.

The Damage Spreading Method in Monte Carlo Simulations:A Brief Overview and Applications to Confined Magnetic Materials

The Damage Spreading(DS)method allows the investigation of the effect caused by tiny perturbations,in the initial conditions of physical systems,on their final stationary or equilibrium states.The damage(D(t))is determined during the dynamic evolution of a physical system and measures the time dependence of the difference between a reference(unperturbed)configuration and an initially perturbed one.In this paper we first give a brief overview of Monte Carlo simulation results obtained by applying the DS method.Different model systems under study often exhibit a transition between a state where the damage becomes healed(the frozen phase)and a regime where the damage spreads arriving at a finite(stationary)value(the damaged phase),when a control parameter is finely tuned.These kinds of transitions are actually true irreversible phase transitions themselves,and the issue of their universality class is also discussed.Subsequently,the attention is focused on the propagation of damage in magnetic systems placed in confined geometries.The influence of interfaces between magnetic domains of different orientation on the spreading of the perturbation is also discussed,showing that the presence of interfaces enhances the propagation of the damage.Furthermore,the critical transition between propagation and nonpropagation of the damage is discussed.In all cases,the determined critical exponents suggest that the DS transition does not belong to the universality class of Directed Percolation,unlike many other systems exhibiting irreversible phase transitions.This result reflects the dramatic influence of interfaces on the propagation of perturbations in magnetic systems.