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Register a new userAnalyses of Aggregate Fluctuations of Firm Network Based on the Self-Organized Criticality Model
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Hiroyasu Inoue
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This study examine the difference in the size of avalanches among industries triggered by demand shocks, which can be rephrased by control of the economy or fiscal policy, and by using the production-inventory model and observed data. We obtain the following results. (1) The size of avalanches follows power law. (2) The mean sizes of avalanches for industries are diverse but their standard deviations highly overlap. (3) We compare the simulation with an input-output table and with the actual policies. They are compatible.
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Self-organized criticality (SOC) refers to the ability of complex systems to evolve towards a 2nd-order phase transition at which interactions between system components lead to scale-invariant events beneficial for system performance. For the last two decades, considerable experimental evidence accumulated that the mammalian cortex with its diversity in cell types and connections might exhibit SOC. Here we review experimental findings of isolated, layered cortex preparations to self-organize towards four dynamical motifs identified in the cortex in vivo: up-states, oscillations, neuronal avalanches, and coherence potentials. During up-states, the synchronization observed for nested theta/gamma-oscillations embeds scale-invariant neuronal avalanches that exhibit robust power law scaling in size with a slope of -3/2 and a critical branching parameter of 1. This dynamical coordination, tracked in the local field potential (nLFP) and pyramidal neuron activity using 2-photon imaging, emerges autonomously in superficial layers of organotypic cortex cultures and acute cortex slices, is homeostatically regulated, displays separation of time scales, and reveals unique size vs. quiet time dependencies. A threshold operation identifies coherence potentials; avalanches that in addition maintain the precise time course of propagated synchrony. Avalanches emerge under conditions of external driving. Control parameters are established by the balance of excitation and inhibition (E/I) and the neuromodulator dopamine. This rich dynamical repertoire is not observed in dissociated cortex cultures, which lack cortical layers and exhibit dynamics similar to a 1st-order phase transition. The precise interactions between up-states, nested oscillations, avalanches, and coherence potentials in superficial cortical layers provide compelling evidence for SOC in the brain.
We present an analysis of the credit market of Japan. The analysis is performed by investigating the bipartite network of banks and firms which is obtained by setting a link between a bank and a firm when a credit relationship is present in a given time window. In our investigation we focus on a community detection algorithm which is identifying communities composed by both banks and firms. We show that the clusters obtained by directly working on the bipartite network carry information about the networked nature of the Japanese credit market. Our analysis is performed for each calendar year during the time period from 1980 to 2011. Specifically, we obtain communities of banks and networks for each of the 32 investigated years, and we introduce a method to track the time evolution of these communities on a statistical basis. We then characterize communities by detecting the simultaneous over-expression of attributes of firms and banks. Specifically, we consider as attributes the economic sector and the geographical location of firms and the type of banks. In our 32 year long analysis we detect a persistence of the over-expression of attributes of clusters of banks and firms together with a slow dynamics of changes from some specific attributes to new ones. Our empirical observations show that the credit market in Japan is a networked market where the type of banks, geographical location of firms and banks and economic sector of the firm play a role in shaping the credit relationships between banks and firms.
The concept of percolation is combined with a self-consistent treatment of the interaction between the dynamics on a lattice and the external drive. Such a treatment can provide a mechanism by which the system evolves to criticality without fine tuning, thus offering a route to self-organized criticality (SOC) which in many cases is more natural than the weak random drive combined with boundary loss/dissipation as used in standard sand-pile formulations. We introduce a new metaphor, the e-pile model, and a formalism for electric conduction in random media to compute critical exponents for such a system. Variations of the model apply to a number of other physical problems, such as electric plasma discharges, dielectric relaxation, and the dynamics of the Earths magnetotail.
The well known Sandpile model of self-organized criticality generates avalanches of all length and time scales, without tuning any parameters. In the original models the external drive is randomly selected. Here we investigate a drive which depends on the present state of the system, namely the effect of favoring sites with a certain height in the deposition process. If sites with height three are favored, the system stays in a critical state. Our numerical results indicate the same universality class as the original model with random depositition, although the stationary state is approached very differently. In constrast, when favoring sites with height two, only avalanches which cover the entire system occur. Furthermore, we investigate the distributions of sites with a certain height, as well as the transient processes of the different variants of the external drive.
Stationarity of the constituents of the body and of its functionalities is a basic requirement for life, being equivalent to survival in first place. Assuming that the resting state activity of the brain serves essential functionalities, stationarity entails that the dynamics of the brain needs to be regulated on a time-averaged basis. The combination of recurrent and driving external inputs must therefore lead to a non-trivial stationary neural activity, a condition which is fulfilled for afferent signals of varying strengths only close to criticality. In this view, the benefits of working vicinity of a second-order phase transition, such as signal enhancements, are not the underlying evolutionary drivers, but side effects of the requirement to keep the brain functional in first place. It is hence more appropriate to use the term self-regulated in this context, instead of self-organized.
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