10,845 research outputs found
Microeconomic Structure determines Macroeconomic Dynamics. Aoki defeats the Representative Agent
Masanao Aoki developed a new methodology for a basic problem of economics:
deducing rigorously the macroeconomic dynamics as emerging from the
interactions of many individual agents. This includes deduction of the fractal
/ intermittent fluctuations of macroeconomic quantities from the granularity of
the mezo-economic collective objects (large individual wealth, highly
productive geographical locations, emergent technologies, emergent economic
sectors) in which the micro-economic agents self-organize.
In particular, we present some theoretical predictions, which also met
extensive validation from empirical data in a wide range of systems: - The
fractal Levy exponent of the stock market index fluctuations equals the Pareto
exponent of the investors wealth distribution. The origin of the macroeconomic
dynamics is therefore found in the granularity induced by the wealth / capital
of the wealthiest investors. - Economic cycles consist of a Schumpeter
'creative destruction' pattern whereby the maxima are cusp-shaped while the
minima are smooth. In between the cusps, the cycle consists of the sum of 2
'crossing exponentials': one decaying and the other increasing.
This unification within the same theoretical framework of short term market
fluctuations and long term economic cycles offers the perspective of a genuine
conceptual synthesis between micro- and macroeconomics. Joining another giant
of contemporary science - Phil Anderson - Aoki emphasized the role of rare,
large fluctuations in the emergence of macroeconomic phenomena out of
microscopic interactions and in particular their non self-averaging, in the
language of statistical physics. In this light, we present a simple stochastic
multi-sector growth model.Comment: 42 pages, 6 figure
Statistics and geometry of cosmic voids
We introduce new statistical methods for the study of cosmic voids, focusing
on the statistics of largest size voids. We distinguish three different types
of distributions of voids, namely, Poisson-like, lognormal-like and Pareto-like
distributions. The last two distributions are connected with two types of
fractal geometry of the matter distribution. Scaling voids with Pareto
distribution appear in fractal distributions with box-counting dimension
smaller than three (its maximum value), whereas the lognormal void distribution
corresponds to multifractals with box-counting dimension equal to three.
Moreover, voids of the former type persist in the continuum limit, namely, as
the number density of observable objects grows, giving rise to lacunar
fractals, whereas voids of the latter type disappear in the continuum limit,
giving rise to non-lacunar (multi)fractals. We propose both lacunar and
non-lacunar multifractal models of the cosmic web structure of the Universe. A
non-lacunar multifractal model is supported by current galaxy surveys as well
as cosmological -body simulations. This model suggests, in particular, that
small dark matter halos and, arguably, faint galaxies are present in cosmic
voids.Comment: 39 pages, 8 EPS figures, supersedes arXiv:0802.038
Euler Number and Percolation Threshold on a Square Lattice with Diagonal Connection Probability and Revisiting the Island-Mainland Transition
We report some novel properties of a square lattice filled with white sites,
randomly occupied by black sites (with probability ). We consider
connections up to second nearest neighbours, according to the following rule.
Edge-sharing sites, i.e. nearest neighbours of similar type are always
considered to belong to the same cluster. A pair of black corner-sharing sites,
i.e. second nearest neighbours may form a 'cross-connection' with a pair of
white corner-sharing sites. In this case assigning connected status to both
pairs simultaneously, makes the system quasi-three dimensional, with
intertwined black and white clusters. The two-dimensional character of the
system is preserved by considering the black diagonal pair to be connected with
a probability , in which case the crossing white pair of sites are deemed
disjoint. If the black pair is disjoint, the white pair is considered
connected. In this scenario we investigate (i) the variation of the Euler
number versus graph for varying , (ii)
variation of the site percolation threshold with and (iii) size
distribution of the black clusters for varying , when . Here is
the number of black clusters and is the number of white clusters, at a
certain probability . We also discuss the earlier proposed 'Island-Mainland'
transition (Khatun, T., Dutta, T. & Tarafdar, S. Eur. Phys. J. B (2017) 90:
213) and show mathematically that the proposed transition is not, in fact, a
critical phase transition and does not survive finite size scaling. It is also
explained mathematically why clusters of size 1 are always the most numerous
Diffusion geometry unravels the emergence of functional clusters in collective phenomena
Collective phenomena emerge from the interaction of natural or artificial
units with a complex organization. The interplay between structural patterns
and dynamics might induce functional clusters that, in general, are different
from topological ones. In biological systems, like the human brain, the overall
functionality is often favored by the interplay between connectivity and
synchronization dynamics, with functional clusters that do not coincide with
anatomical modules in most cases. In social, socio-technical and engineering
systems, the quest for consensus favors the emergence of clusters.
Despite the unquestionable evidence for mesoscale organization of many
complex systems and the heterogeneity of their inter-connectivity, a way to
predict and identify the emergence of functional modules in collective
phenomena continues to elude us. Here, we propose an approach based on random
walk dynamics to define the diffusion distance between any pair of units in a
networked system. Such a metric allows to exploit the underlying diffusion
geometry to provide a unifying framework for the intimate relationship between
metastable synchronization, consensus and random search dynamics in complex
networks, pinpointing the functional mesoscale organization of synthetic and
biological systems.Comment: 9 pages, 7 figure
Dynamics of the two-dimensional directed Ising model: zero-temperature coarsening
We investigate the laws of coarsening of a two-dimensional system of Ising
spins evolving under single-spin-flip irreversible dynamics at low temperature
from a disordered initial condition. The irreversibility of the dynamics comes
from the directedness, or asymmetry, of the influence of the neighbours on the
flipping spin. We show that the main characteristics of phase ordering at low
temperature, such as self-similarity of the patterns formed by the growing
domains, and the related scaling laws obeyed by the observables of interest,
which hold for reversible dynamics, are still present when the dynamics is
directed and irreversible, but with different scaling behaviour. In particular
the growth of domains, instead of being diffusive as is the case when dynamics
is reversible, becomes ballistic. Likewise, the autocorrelation function and
the persistence probability (the probability that a given spin keeps its sign
up to time ) have still power-law decays but with different exponents.Comment: 29 pages, 36 figure
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