1,720,997 research outputs found
Maximum entropy model for business cycle synchronization
Full text linkThe global economy is a complex dynamical system, whose cyclical fluctuations can mainly be characterized by simultaneous recessions or expansions of major economies. Thus, the researches on the synchronization phenomenon are key to understanding and controlling the dynamics of the global economy. Based on a pairwise maximum entropy model, we analyze the business cycle synchronization of the G7 economic system. We obtain a pairwise-interaction network, which exhibits certain clustering structure and accounts for 45% of the entire structure of the interactions within the G7 system. We also find that the pairwise interactions become increasingly inadequate in capturing the synchronization as the size of economic system grows. Thus, higher-order interactions must be taken into account when investigating behaviors of large economic systems
Asymmetric stochastic resetting: Modeling catastrophic events
Full text linkIn the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then the process recommences. Hitherto, the resetting mechanism has been introduced as a symmetric reset about the preferred location. However, in nature, there are several instances where a system can only reset from certain directions, e.g., catastrophic events. Motivated by this, we consider a continuous stochastic process on the positive real line. The process is interrupted at random times occurring at a constant rate, and then the former relocates to a value only if the current one exceeds a threshold; otherwise, it follows the trajectory defined by the underlying process without resetting. An approach to obtain the exact nonequilibrium steady state of such systems and the mean first passage time to reach the origin is presented. Furthermore, we obtain the explicit solutions for two different model systems. Some of the classical results found in symmetric resetting, such as the existence of an optimal resetting, are strongly modified. Finally, numerical simulations have been performed to verify the analytical findings, showing an excellent agreement
Recent developments and future perspectives in statistical mechanics of ecological systems
No full textStatistical mechanics provides insights into linking microscopic details with macroscopic behavior, and this approach has extended to ecology with powerful results. In this perspective we review recent progress in the statistical mechanics pertaining to ecosystems, focusing on research directions which have the potential to uncover new important features of ecological communities across scales. These include the understanding of Damuth's and Kleiber's scaling laws, which suggest deep connections between body size, metabolism and population dynamics. Also, recent developments in microbial ecology are shifting attention towards functional dynamics, emphasizing gene function instead of species identity, which contributes to maintaining community stability amid taxonomic diversity. Finally, we argue that the interaction of ecological and evolutionary scales can enrich our understanding of biodiversity, resilience, and adaptability, linking community dynamics with evolutionary processes in an integrated ecological framewor
Probing noise in gene expression and protein production
Full text linkWe derive exact solutions of simplified models for the temporal evolution of the protein concentration within a cell population arbitrarily far from the stationary state. We show that monitoring the dynamics can assist in modeling and understanding the nature of the noise in gene expression. We analyze the dispersion of the process, i.e., the ratio of the variance to the mean at arbitrary time, and introduce a measure, the fractional protein distribution, which can be used to probe the phase of transcription of DNA into mRNA
Spatial Patterns Emerging from a Stochastic Process Near Criticality
Full text linkThere is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community of individuals which undergoes local birth-death, immigration, and local jumps on a regular lattice. We study its properties when the system is close to its critical point. Even if this model violates detailed balance, within a physically relevant regime dominated by fluctuations, it is possible to calculate analytically the probability density function of the number of individuals living in a given volume, which captures the close-to-critical behavior of the community across spatial scales. We find that the resulting distribution satisfies an equation where spatial effects are encoded in appropriate functions of space, which we calculate explicitly. The validity of the analytical formulae is confirmed by simulations in the expected regimes. We finally discuss how this model in the critical-like regime is in agreement with several biodiversity patterns observed in tropical rain forests
Delay effects on the stability of large ecosystems
Full text linkThe common intuition among the ecologists of the midtwentieth century was that large ecosystems should bemore stable than those with a smaller number of species.This view was challenged by Robert May, who found a stability bound for randomly assembled ecosystems; they become unstable for a sufficiently large number of species. In the present work, we show that May's bound greatly changes when the past population densities of a species affect its own current density. This is a common feature in real systems, where the effects of species' interactions may appear after a time lag rather than instantaneously.The local stability of these models with self-interaction is described by bounds, which we characterize in the parameter space.We find a critical delay curve that separates the region of stability fromthat of instability, and correspondingly, we identify a critical frequency curve that provides the characteristic frequencies of a system at the instability threshold. Finally, we calculate analytically the distributions of eigenvalues that generalizeWigner's aswell asGirko's laws. Interestingly,we find that, for sufficiently large delays, the eigenvalues of a randomly coupled system are complex even when the interactions are symmetric
Inferring plant ecosystem organization from species occurrences.
No full textIn this paper, we present an approach capable of extracting insights on ecosystem organization from merely occurrence (presence/absence) data. We extrapolate to the collective behavior by encapsulating some simplifying assumptions within a given set of constraints, and then examine their ecological implications. We show that by using the mean occurrence and co-occurrence of species as constraints, one is able to capture detailed statistics of a plant community distributed across a vast semiarid area of the United States. The approach allows us to quantify the species' effective couplings: Their frequencies exhibit a peak at zero and the minimal pairwise model is able to capture about 80% of the ecosystem structure. Our analysis reveals a relatively stronger impact of the species network on uncommon species and underscores the importance of species pairs experiencing positive couplings. Additionally, we study the associations among species and, interestingly, find that the frequencies of groups of different species, which the approach is able to capture, exhibit a power-law-like distribution
Finite-Time and Fixed-Time Consensus of Multiagent Networks with Pinning Control and Noise Perturbation
Full text linkIn this paper we investigate the finite-time and fixed-time consensus problems of multiagent networks with pinning control and noise perturbation. In order to reach the finite-time and fixed-time consensus, several pinning protocols are proposed. Compared with the consensus protocols without pinning control, the proposed finite-time and fixed-time protocols need to control only a small fraction of agents, which is practical and has advantages from the physical viewpoint of energy consumption. More specifically, the deterministic and stochastic protocols include the graph -Laplacian, a nonlinear generalization of the standard graph Laplacian. We show that, unlike the protocols with the standard (linear) graph Laplacian, those with the graph -Laplacian solve the finite-time as well as the fixed-time consensus problems. By using the finite-time and fixed-time stability theory and the algebra graph theory, sufficient conditions are established to ensure the finite-time and fixed-time consensus. Finally, numerical simulations are presented to illustrate the correctness of the theoretical results
Redundancy-selection trade-off in phenotype-structured populations
Full text linkRealistic fitness landscapes generally display a redundancy-fitness trade-off: highly fit trait configurations are inevitably rare, while less fit trait configurations are expected to be more redundant. The resulting sub-optimal patterns in the fitness distribution are typically described by means of effective formulations, where redundancy provided by the presence of neutral contributions is modelled implicitly, e.g. with a bias of the mutation process. However, the extent to which effective formulations are compatible with explicitly redundant landscapes is yet to be understood, as well as the consequences of a potential miss-match. Here we investigate the effects of such trade-off on the evolution of phenotype-structured populations, characterised by continuous quantitative traits. We consider a typical replication-mutation dynamics, and we model redundancy by means of two dimensional landscapes displaying both selective and neutral traits. We show that asymmetries of the landscapes will generate neutral contributions to the marginalised fitness-level description, that cannot be described by effective formulations, nor disentangled by the full trait distribution. Rather, they appear as effective sources, whose magnitude depends on the geometry of the landscape. Our results highlight new important aspects on the nature of sub-optimality. We discuss practical implications for rapidly mutant populations such as pathogens and cancer cells, where the qualitative knowledge of their trait and fitness distributions can drive disease management and intervention policies
Exact solution of dynamical mean-field theory for a linear system with annealed disorder
No full textWe investigate a disordered multi-dimensional linear system in which the interaction parameters are colored noises, varying stochastically in time with defined temporal correlations. We refer to this type of disorder as ‘annealed’, in contrast to quenched disorder in which couplings are fixed over time. Using generating functional methods, we extend dynamical mean-field theory to accommodate annealed disorder and employ it to find the exact solution of the linear model in the limit of a large number of degrees of freedom. Our analysis yields analytical results for the non-stationary autocorrelation, the stationary variance, the power spectral density, and the phase diagram of the model. Some unexpected features emerge upon changing the correlation time of the interactions. The stationary variance of the system and the critical variance of the disorder are generally found to be non-monotonic functions of the correlation time of the interactions. We also find that a re-entrant phase transition can take place when this correlation time is varied
- …
