Classical molecular dynamics (MD) simulations based on atomic models play an increasingly important role in a wide range of applications in physics, biology, and chemistry. Nonetheless, generating genuine knowledge about biological systems using MD simulations remains challenging. Protein tyrosine kinases are important cellular signaling enzymes that regulate cell growth, proliferation, metabolism, differentiation, and migration. Due to the large conformational changes and long timescales involved in their function, these kinases present particularly challenging problems to modern computational and theoretical frameworks aimed at elucidating the dynamics of complex biomolecular systems. Markov state models have achieved limited success in tackling the broader conformational ensemble and biased methods are often employed to examine specific long timescale events. Recent advances in machine learning continue to push the limitations of current methodologies and provide notable improvements when integrated with the existing frameworks. A broad perspective is drawn from a critical review of recent studies.

In this paper, we examine a population model with carrying capacity, time delay, and sources of additive and multiplicative environmental noise. We find that time delay, noise sources and their correlation induce regime shifts and transitions between the population survival state and the extinction state. To explore the transition mechanism between these two states, we analyzed the shift time to extinction, or the delayed extinction time, of populations. The main finding is that the extinction transition time as a function of the noise intensity shows a maximum, indicating the existence of an appropriate noise intensity leading to a maximal delayed extinction. This nonmonotonic behavior, with a maximum, is a signature of the noise-enhanced stability phenomenon, observed in many physical and complex metastable systems. In particular, this maximum increases (or decreases) as the cross-correlation intensity or the delay time in the death process increases. Furthermore, the signal-to-noise ratio as a function of noise intensity shows a maximum, which is a signature of the stochastic resonance phenomenon in the population dynamics model investigated in the presence of time delay and environmental noise.

In this work, we elaborate on two recently discovered invariance principles, according to which transport coefficients are, to a large extent, independent of the microscopic definition of the densities and currents of the conserved quantities being transported (energy, momentum, mass, charge). The first such principle, , allows one to define a quantum adiabatic energy current from density-functional theory, from which the heat conductivity can be uniquely defined and computed using equilibrium ab initio molecular dynamics. When combined with a novel topological definition of , gauge invariance also sheds new light onto the mechanisms of charge transport in ionic conductors. The second principle, , allows one to extend the analysis to multi-component systems. These invariance principles can be combined with new spectral analysis methods for the current time series to be fed into the Green-Kubo formula to obtain accurate estimates of transport coefficients from relatively short molecular dynamics simulations.

Collective wisdom is the ability of a group to perform more effectively than any individual alone. Through an evolutionary game-theoretic model of collective prediction, we investigate the role that reinforcement learning stimulus may play the role in enhancing collective voting accuracy. And collective voting bias can be dismissed through self-reinforcing global cooperative learning. Numeric simulations suggest that the provided method can increase collective voting accuracy. We conclude that real-world systems might seek reward-based incentive mechanism as an alternative to surmount group decision error.

What determines the stability of networks inferred from dynamical behavior of a system? Internal and external shocks in a system can destabilize the topological properties of comovement networks. In real-world data, this creates a trade-off between identification of turbulent periods and the problem of high dimensionality. Longer time-series reduces the problem of high dimensionality, but suffers from mixing turbulent and non-turbulent periods. Shorter time-series can identify periods of turbulence more accurately, but introduces the problem of high dimensionality, so that the underlying linkages cannot be estimated precisely. In this paper, we exploit high-frequency multivariate financial data to analyze the origin of instability in the inferred networks during periods free from external disturbances. We show that the topological properties captured via centrality ordering is highly unstable even during such non-turbulent periods. Simulation results with multivariate Gaussian and fat-tailed stochastic process calibrated to financial data show that both sampling frequencies and the presence of outliers cause instability in the inferred network. We conclude that instability of network properties do not necessarily indicate systemic instability.

Contact reduction is an effective strategy to mitigate the spreading of epidemic. However, the existing reaction-diffusion equations for infectious disease are unable to characterize this effect. Thus, we here propose an extended susceptible-infected-recovered model by incorporating contact rate into the standard SIR model, and concentrate on investigating its impact on epidemic transmission. We analytically derive the epidemic thresholds on homogeneous and heterogeneous networks, respectively. The effects of contact rate on spreading speed, scale and outbreak threshold are explored on ER and SF networks. Simulations results show that epidemic dissemination is significantly mitigated when contact rate is reduced. Importantly, epidemic spreads faster on heterogeneous networks while broader on homogeneous networks, and the outbreak thresholds of the former are smaller.

Digital contact tracing has been suggested as an effective strategy for controlling an epidemic without severely limiting personal mobility. Here, we use smartphone proximity data to explore how social structure affects contact tracing of COVID-19. We model the spread of COVID-19 and find that the effectiveness of contact tracing depends strongly on social network structure and heterogeneous social activity. Contact tracing is shown to be remarkably effective in a workplace environment and the effectiveness depends strongly on the minimum duration of contact required to initiate quarantine. In a realistic social network, we find that forward contact tracing with immediate isolation can reduce an epidemic by more than 70%. In perspective, our findings highlight the necessity of incorporating social heterogeneity into models of mitigation strategies.

A mapping of a macromolecule is a prescription to construct a simplified representation of the system in which only a subset of its constituent atoms is retained. As the specific choice of the mapping affects the analysis of all-atom simulations as well as the construction of coarse-grained models, the characterisation of the has recently attracted increasing attention. We here introduce a notion of scalar product and distance between reduced representations, which allows the study of the metric and topological properties of their space in a quantitative manner. Making use of a Wang-Landau enhanced sampling algorithm, we exhaustively explore such space, and examine the qualitative features of mappings in terms of their squared norm. A one-to-one correspondence with an interacting lattice gas on a finite volume leads to the emergence of discontinuous phase transitions in mapping space, which mark the boundaries between qualitatively different reduced representations of the same molecule.

The recently developed model of the epidemic spread of two virus strains in a closed population is generalized to the situation typical for the couple of strains delta and omicron, when there is a high probability of omicron infection soon enough after recovering from delta infection. This model can be considered as a kind of combination of SIR and SIS models for the case of competition of two strains of the same virus with different contagiousness in a population. The obtained equations and results can be directly implemented for practical calculations of the replacement of strains of the SARS-CoV-2 virus. A comparison between the estimated replacement time and the corresponding statistics shows reasonable agreement.

We illustrate the algorithmic advantages of the recently introduced single-boson exchange (SBE) formulation for the one-loop functional renormalization group (fRG), by applying it to the two-dimensional Hubbard model on a square lattice. We present a detailed analysis of the fermion-boson Yukawa couplings and of the corresponding physical susceptibilities by studying their evolution with temperature and interaction strength, both at half filling and finite doping. The comparison with the conventional fermionic fRG decomposition shows that the rest functions of the SBE algorithm, which describe correlation effects beyond the SBE processes, play a negligible role in the weak-coupling regime above the pseudo-critical temperature, in contrast to the rest functions of the conventional fRG. Remarkably, they remain finite also at the pseudo-critical transition, whereas the corresponding rest functions of the conventional fRG implementation diverge. As a result, the SBE formulation of the fRG flow allows for a substantial reduction of the numerical effort in the treatment of the two-particle vertex function, paving a promising route for future multiboson and multiloop extensions.

The last three years have been an extraordinary time with the COVID-19 pandemic killing millions, affecting and distressing billions of people worldwide. Authorities took various measures such as turning school and work to remote and prohibiting social relations via curfews. In order to mitigate the negative impact of the epidemics, researchers tried to estimate the future of the pandemic for different scenarios, using forecasting techniques and epidemics simulations on networks. Intending to better represent the real-life in an urban town in high resolution, we propose a novel multi-layer network model, where each layer corresponds to a different interaction that occurs daily, such as "household", "work" or "school". Our simulations indicate that locking down "friendship" layer has the highest impact on slowing down epidemics. Hence, our contributions are twofold, first we propose a parametric network generator model; second, we run SIR simulations on it and show the impact of layers.

Multiplex networks frame the heterogeneous nature of real systems, where the multiple roles of nodes, both functionally and structurally, are well represented. We identify these vital nodes in a multiplex network so that we can control a pandemic outbreak like COVID-19, eliminate damage from a network attack, maintain traffic, and so on. Vital node identification has attracted scientists in various fields for decades. In this paper, we propose a hybrid supra-cycle number and hybrid supra-cycle ratio based on the cycle structure, and present an extensive experimental analysis by comparing our indexes and several different indexes in four real multiplex networks on layer nodes and multiplex nodes. The experimental results show that these proposed indexes have good robustness, synchronization, and transmission dynamics. Finally, we provide an in-depth understanding of multiplex networks and cycle structure, and we sincerely hope more valuable academic achievements are proposed in the future.

Human societies are constantly coping with global risks. In the face of these risks, people typically have two options, that is, to respond together as a whole (collective solution) or to respond independently (individual solution). Based on these two solutions, individuals have a variety of behavioral strategies. On the other hand, various regulatory bodies supported by the population limit people's choices and punish individuals who do not contribute to collective solutions. So with different risks, how do the two solutions, the various individual strategies, and the constraints from regulators affect the group's response to risk? This paper proposes an extended public goods game model involving opportunists and the regulator to explore the effectiveness of collective and individual solutions against risks. The results show that requiring individuals to invest more in the collective solution reduces the group' s success in resisting risk. To improve the group's ability to resist risk, investment in individual solution should be at least no less than that in collective solution. The establishment fund and punishment intensity of the regulatory agency have no significant effect on the success of collective and individual solutions. This inspires us to contemplate the role and measures of various types of authorities in coping with global risks.

Price dynamics in stock market is modelled by a statistical physics systems: Ising model. A comparative analysis of the historical dynamics of stock returns between the US, UK, and French markets is given. Since the Ising model requires binary inputs, the effect of binarization is studied. Then, using the TAP approximation method, external fields and coupling strengths are calculated. The fluctuation cycles of coupling strengths have a remarkable corresponding relationship with the important period of the financial market. The highlight of this paper is to verify the phase transition can also occur in the stock market and it reveals the transformation of the market state. The numerical solution in this paper is consistent with the exact solution obtained by Lars Onsager. Our findings can help to discover the economic cycles and provide more possibilities for studying financial markets using physical models.

We provide an overview of the Adaptive Resolution Simulation method (AdResS) based on discussing its basic principles and presenting its current numerical and theoretical developments. Examples of applications to systems of interest to soft matter, chemical physics, and condensed matter illustrate the method's advantages and limitations in its practical use and thus settle the challenge for further future numerical and theoretical developments.

A dynamical approach to nonequilibrium molecular dynamics (D-NEMD), proposed in the 1970s by Ciccotti et al., is undergoing a renaissance and is having increasing impact in the study of biological macromolecules. This D-NEMD approach, combining MD simulations in stationary (in particular, equilibrium) and nonequilibrium conditions, allows for the determination of the time-dependent structural response of a system using the Kubo-Onsager relation. Besides providing a detailed picture of the system's dynamic structural response to an external perturbation, this approach also has the advantage that the statistical significance of the response can be assessed. The D-NEMD approach has been used recently to identify a general mechanism of inter-domain signal propagation in nicotinic acetylcholine receptors, and allosteric effects in -lactamase enzymes, for example. It complements equilibrium MD and is a very promising approach to identifying and analysing allosteric effects. Here, we review the D-NEMD approach and its application to biomolecular systems, including transporters, receptors, and enzymes.

A fascinating phenomenon is the self-organization of coupled systems to a whole. This phenomenon is studied for a particular class of coupled oscillatory systems exhibiting so-called simultaneously diagonalizable matrices. For three exemplary systems, namely, an electric circuit, a coupled system of oscillatory neurons, and a system of coupled oscillatory gene regulatory pathways, eigenvectors and amplitude equations are derived. It is shown that for all three systems, only the unstable eigenvectors and their amplitudes matter for the dynamics of the systems on their respective limit cycle attractors. A general class of coupled second-order dynamical oscillators is presented in which stable limit cycles emerging via Hopf bifurcations are solely specified by appropriately defined unstable eigenvectors and their amplitudes. While the eigenvectors determine the orientation of limit cycles in state spaces, the amplitudes determine the evolution of states along those limit cycles. In doing so, it is shown that the unstable eigenvectors define reduced amplitude spaces in which the relevant long-term dynamics of the systems under consideration takes place. Several generalizations are discussed. First, if stable and unstable system parts exhibit a slow-fast dynamics, the fast variables may be eliminated and approximative descriptions of the emerging limit cycle dynamics in reduced amplitude spaces may be again obtained. Second, the principle of reduced amplitude spaces holds not only for coupled second-order oscillators, but can be applied to coupled third-order and higher order oscillators. Third, the possibility to apply the approach to multifrequency limit cycle attractors and other types of attractors is discussed.

Collective variable-based enhanced sampling methods have been widely used to study thermodynamic properties of complex systems. Efficiency and accuracy of these enhanced sampling methods are affected by two factors: constructing appropriate collective variables for enhanced sampling and generating accurate free energy surfaces. Recently, many machine learning techniques have been developed to improve the quality of collective variables and the accuracy of free energy surfaces. Although machine learning has achieved great successes in improving enhanced sampling methods, there are still many challenges and open questions. In this perspective, we shall review recent developments on integrating machine learning techniques and collective variable-based enhanced sampling approaches. We also discuss challenges and future research directions including generating kinetic information, exploring high-dimensional free energy surfaces, and efficiently sampling all-atom configurations.

The limitations of the classical Black-Scholes model are examined by comparing calculated and actual historical prices of European call options on stocks from several sectors of the S &P 500. Persistent differences between the two prices point to an expanded model proposed by Segal and Segal (PNAS 95:4072-4075, 1988) in which information not simultaneously observable or actionable with public information can be represented by an additional pseudo-Wiener process. A real linear combination of the original and added processes leads to a commutation relation analogous to that between a boson field and its canonical momentum in quantum field theory. The resulting pricing formula for a European call option replaces the classical volatility with the norm of a complex quantity, whose imaginary part is shown to compensate for the disparity between prices obtained from the classical Black-Scholes model and actual prices of the test call options. This provides market evidence for the influence of a non-classical process on the price of a security based on non-commuting operators.

The parquet approach to vertex corrections is unbiased but computationally demanding. Most applications are therefore restricted to small cluster sizes or rely on various simplifying approximations. We have recently shown that the bosonization of the parquet diagrams provides interpretative and algorithmic advantages over the original purely fermionic formulation. Here, we present first results of the numerical implementation of this method by applying it to the half-filled Hubbard model on the square lattice at weak coupling. The improved algorithmic performance allows us to evaluate the parquet approximation for a lattice, retaining the full momentum and frequency structure of the various vertex functions. We discuss their symmetries and consider parametrizations of their momentum dependence using the truncated-unity approximation.

Effects of ballistic transport on the temperature profiles and thermal resistance in nanowires are studied. Computer simulations of nanowires between a heat source and a heat sink have shown that in the middle of such wires the temperature gradient is reduced compared to Fourier's law with steep gradients close to the heat source and sink. In this work, results from molecular dynamics and phonon Monte Carlo simulations of the heat transport in nanowires are compared to a radiator model which predicts a reduced gradient with discrete jumps at the wire ends. The comparison shows that for wires longer than the typical mean free path of phonons the radiator model is able to account for ballistic transport effects. The steep gradients at the wire ends are then continuous manifestations of the discrete jumps in the model.