12 research outputs found
Ising model with memory: coarsening and persistence properties
We consider the coarsening properties of a kinetic Ising model with a memory
field. The probability of a spin-flip depends on the persistence time of the
spin in a state. The more a spin has been in a given state, the less the
spin-flip probability is. We numerically studied the growth and persistence
properties of such a system on a two dimensional square lattice. The memory
introduces energy barriers which freeze the system at zero temperature. At
finite temperature we can observe an apparent arrest of coarsening for low
temperature and long memory length. However, since the energy barriers
introduced by memory are due to local effects, there exists a timescale on
which coarsening takes place as for the Ising model. Moreover the two point
correlation functions of the Ising model with and without memory are the same,
indicating that they belong to the same universality class.Comment: 10 pages, 7 figures; some figures and some comments adde
Multiscaled Cross-Correlation Dynamics in Financial Time-Series
The cross correlation matrix between equities comprises multiple interactions
between traders with varying strategies and time horizons. In this paper, we
use the Maximum Overlap Discrete Wavelet Transform to calculate correlation
matrices over different timescales and then explore the eigenvalue spectrum
over sliding time windows. The dynamics of the eigenvalue spectrum at different
times and scales provides insight into the interactions between the numerous
constituents involved.
Eigenvalue dynamics are examined for both medium and high-frequency equity
returns, with the associated correlation structure shown to be dependent on
both time and scale. Additionally, the Epps effect is established using this
multivariate method and analyzed at longer scales than previously studied. A
partition of the eigenvalue time-series demonstrates, at very short scales, the
emergence of negative returns when the largest eigenvalue is greatest. Finally,
a portfolio optimization shows the importance of timescale information in the
context of risk management
Spatial correlations in vote statistics: a diffusive field model for decision-making
We study the statistics of turnout rates and results of the French elections
since 1992. We find that the distribution of turnout rates across towns is
surprisingly stable over time. The spatial correlation of the turnout rates, or
of the fraction of winning votes, is found to decay logarithmically with the
distance between towns. Based on these empirical observations and on the
analogy with a two-dimensional random diffusion equation, we propose that
individual decisions can be rationalised in terms of an underlying "cultural"
field, that locally biases the decision of the population of a given region, on
top of an idiosyncratic, town-dependent field, with short range correlations.
Using symmetry considerations and a set of plausible assumptions, we suggest
that this cultural field obeys a random diffusion equation.Comment: 18 pages, 5 figures; added sociophysics references
Crises and collective socio-economic phenomena: simple models and challenges
Financial and economic history is strewn with bubbles and crashes, booms and
busts, crises and upheavals of all sorts. Understanding the origin of these
events is arguably one of the most important problems in economic theory. In
this paper, we review recent efforts to include heterogeneities and
interactions in models of decision. We argue that the Random Field Ising model
(RFIM) indeed provides a unifying framework to account for many collective
socio-economic phenomena that lead to sudden ruptures and crises. We discuss
different models that can capture potentially destabilising self-referential
feedback loops, induced either by herding, i.e. reference to peers, or
trending, i.e. reference to the past, and account for some of the phenomenology
missing in the standard models. We discuss some empirically testable
predictions of these models, for example robust signatures of RFIM-like herding
effects, or the logarithmic decay of spatial correlations of voting patterns.
One of the most striking result, inspired by statistical physics methods, is
that Adam Smith's invisible hand can badly fail at solving simple coordination
problems. We also insist on the issue of time-scales, that can be extremely
long in some cases, and prevent socially optimal equilibria to be reached. As a
theoretical challenge, the study of so-called "detailed-balance" violating
decision rules is needed to decide whether conclusions based on current models
(that all assume detailed-balance) are indeed robust and generic.Comment: Review paper accepted for a special issue of J Stat Phys; several
minor improvements along reviewers' comment
Simplification and analysis of a model of social interaction in voting
A recently proposed model of social interaction in voting is investigated by simplifying it down
into a version that is more analytically tractable and which allows a mathematical analysis to be performed.
This analysis clarifies the interplay of the different elements present in the system – social influence,
heterogeneity and noise – and leads to a better understanding of its properties. The origin of a regime
of bistability is identified. The insight gained in this way gives further intuition into the behaviour of the
original model
Staged Models for Interdisciplinary Research
Modellers of complex biological or social systems are often faced with an invidious choice: to use simple models with few mechanisms that can be fully analysed, or to construct complicated models that include all the features which are thought relevant. The former ensures rigour, the latter relevance. We discuss a method that combines these two approaches, beginning with a complex model and then modelling the complicated model with simpler models. The resulting "chain" of models ensures some rigour and relevance. We illustrate this process on a complex model of voting intentions, constructing a reduced model which agrees well with the predictions of the full model. Experiments with variations of the simpler model yield additional insights which are hidden by the complexity of the full model. This approach facilitated collaboration between social scientists and physicists- The complex model was specified based on the social science literature, and the simpler model constrained to agree (in core aspects) with the complicated model
The Index cohesive effect on stock market correlations
We present empirical examination and reassessment of the functional role of the market Index, using datasets of stock returns for eight years, by analyzing and comparing the results for two very different markets: 1) the New York Stock Exchange (NYSE), representing a large, mature market, and 2) the Tel Aviv Stock Exchange (TASE), representing a small, young market. Our method includes special collective (holographic) analysis of stock-Index correlations, of nested stock correlations (including the Index as an additional ghost stock) and of bare stock correlations (after subtraction of the Index return from the stocks returns). Our findings verify and strongly substantiate the assumed functional role of the index in the financial system as a cohesive force between stocks, i.e., the correlations between stocks are largely due to the strong correlation between each stock and the Index (the adhesive effect), rather than inter-stock dependencies. The Index adhesive and cohesive effects on the market correlations in the two markets are presented and compared in a reduced 3-D principal component space of the correlation matrices (holographic presentation). The results provide new insights into the interplay between an index and its constituent stocks in TASE-like versus NYSE-like markets