61 research outputs found
Phase transitions in social sciences: two-populations mean field theory
A new mean field statistical mechanics model of two interacting groups of
spins is introduced and the phase transition studied in terms of their relative
size. A jump of the average magnetization is found for large values of the
mutual interaction when the relative percentage of the two populations crosses
a critical threshold. It is shown how the critical percentage depends on
internal interactions and on the initial magnetizations. The model is
interpreted as a prototype of resident-immigrant cultural interaction and
conclusions from the social sciences perspectives are drawn
Theory of collective opinion shifts: from smooth trends to abrupt swings
We unveil collective effects induced by imitation and social pressure by
analyzing data from three different sources: birth rates, sales of cell phones
and the drop of applause in concert halls. We interpret our results within the
framework of the Random Field Ising Model, which is a threshold model for
collective decisions accounting both for agent heterogeneity and social
imitation. Changes of opinion can occur either abruptly or continuously,
depending on the importance of herding effects. The main prediction of the
model is a scaling relation between the height h of the speed of variation peak
and its width of the form h ~ w^{-kappa}, with kappa = 2/3 for well
connected populations. Our three sets of data are compatible with such a
prediction, with kappa ~ 0.62 for birth rates, kappa ~ 0.71 for cell phones and
kappa ~ 0.64 for clapping. In this last case, we in fact observe that some
clapping samples end discontinuously (w=0), as predicted by the model for
strong enough imitation.Comment: 11 pages, 8 figure
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
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
Entanglement between Demand and Supply in Markets with Bandwagon Goods
Whenever customers' choices (e.g. to buy or not a given good) depend on
others choices (cases coined 'positive externalities' or 'bandwagon effect' in
the economic literature), the demand may be multiply valued: for a same posted
price, there is either a small number of buyers, or a large one -- in which
case one says that the customers coordinate. This leads to a dilemma for the
seller: should he sell at a high price, targeting a small number of buyers, or
at low price targeting a large number of buyers? In this paper we show that the
interaction between demand and supply is even more complex than expected,
leading to what we call the curse of coordination: the pricing strategy for the
seller which aimed at maximizing his profit corresponds to posting a price
which, not only assumes that the customers will coordinate, but also lies very
near the critical price value at which such high demand no more exists. This is
obtained by the detailed mathematical analysis of a particular model formally
related to the Random Field Ising Model and to a model introduced in social
sciences by T C Schelling in the 70's.Comment: Updated version, accepted for publication, Journal of Statistical
Physics, online Dec 201
Modelling avalanches in martensites
Solids subject to continuous changes of temperature or mechanical load often
exhibit discontinuous avalanche-like responses. For instance, avalanche
dynamics have been observed during plastic deformation, fracture, domain
switching in ferroic materials or martensitic transformations. The statistical
analysis of avalanches reveals a very complex scenario with a distinctive lack
of characteristic scales. Much effort has been devoted in the last decades to
understand the origin and ubiquity of scale-free behaviour in solids and many
other systems. This chapter reviews some efforts to understand the
characteristics of avalanches in martensites through mathematical modelling.Comment: Chapter in the book "Avalanches in Functional Materials and
Geophysics", edited by E. K. H. Salje, A. Saxena, and A. Planes. The final
publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-45612-6_
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
A review of wearable motion tracking systems used in rehabilitation following hip and knee replacement
Clinical teams are under increasing pressure to facilitate early hospital discharge for total hip replacement and total knee replacement patients following surgery. A wide variety of wearable devices are being marketed to assist with rehabilitation following surgery. A review of wearable devices was undertaken to assess the evidence supporting their efficacy in assisting rehabilitation following total hip replacement and total knee replacement. A search was conducted using the electronic databases including Medline, CINAHL, Cochrane, PsycARTICLES, and PubMed of studies from January 2000 to October 2017. Five studies met the eligibility criteria, and all used an accelerometer and a gyroscope for their technology. A review of the studies found very little evidence to support the efficacy of the technology, although they show that the use of the technology is feasible. Future work should establish which wearable technology is most valuable to patients, which ones improve patient outcomes, and the most economical model for deploying the technolog
A review of elliptical and disc galaxy structure, and modern scaling laws
A century ago, in 1911 and 1913, Plummer and then Reynolds introduced their
models to describe the radial distribution of stars in `nebulae'. This article
reviews the progress since then, providing both an historical perspective and a
contemporary review of the stellar structure of bulges, discs and elliptical
galaxies. The quantification of galaxy nuclei, such as central mass deficits
and excess nuclear light, plus the structure of dark matter halos and cD galaxy
envelopes, are discussed. Issues pertaining to spiral galaxies including dust,
bulge-to-disc ratios, bulgeless galaxies, bars and the identification of
pseudobulges are also reviewed. An array of modern scaling relations involving
sizes, luminosities, surface brightnesses and stellar concentrations are
presented, many of which are shown to be curved. These 'redshift zero'
relations not only quantify the behavior and nature of galaxies in the Universe
today, but are the modern benchmark for evolutionary studies of galaxies,
whether based on observations, N-body-simulations or semi-analytical modelling.
For example, it is shown that some of the recently discovered compact
elliptical galaxies at 1.5 < z < 2.5 may be the bulges of modern disc galaxies.Comment: Condensed version (due to Contract) of an invited review article to
appear in "Planets, Stars and Stellar
Systems"(www.springer.com/astronomy/book/978-90-481-8818-5). 500+ references
incl. many somewhat forgotten, pioneer papers. Original submission to
Springer: 07-June-201
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