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Robert Boyer

Publications and source records attributed to Robert Boyer.

6 recordsLinked to original sources

Modeling revolutions in networked societies: learning from the Tunisian spring

Economic competition and deregulation have led to a polarization of societies between a small, increasingly powerful elite and a majority of socially excluded individuals, marginalized and unconnected to political representations. This is the breeding ground for protest movements, relayed by local ties and amplified by social networks. Based on the characteristics revealed by socio-economic research into the Arab revolutions of the 2010s, this article proposes a formalization inspired by the theory of complex systems. We discuss the conditions under which an initial localized event - for example, the suicide of a street vendor condemned to ruin in a small Tunisian town - can trigger an explosion of the number of opponents to the regime, typical of a revolutionary episode. We consider a network model of agents and oppressors where pair interactions are controlled by a fear parameter, or the inclination of the individuals to rebel despite of repression. The model exhibits a phase transition at a critical threshold above which the quiescent state becomes unstable. Furthermore, the ability of individuals to forge triadic relationships accelerates the process of joining a rising rebellion, making the transition more abrupt, in the form of a brutal discontinuity that can be described as revolutionary. The imposition of a counter-revolution by the hardening of repression can be explained by the hysteresis property displayed by the model: when mobilization has extended the initial network and made it partially permanent, repression by the authorities must be tightened to higher levels than before to regain control.

physics.soc-ph

Plane Partition Polynomial Asymptotics

The plane partition polynomial $Q_n(x)$ is the polynomial of degree $n$ whose coefficients count the number of plane partitions of $n$ indexed by their trace. Extending classical work of E.M. Wright, we develop the asymptotics of these polynomials inside the unit disk using the circle method.

math.NT

Periodic attractors of random truncator maps

This paper introduces the \textit{truncator} map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify its periodic orbits using properties of endomorphisms of the resulting algebraic structure. A stochastic model is constructed on these endomorphisms, which leads to the classification of the distribution of periodic orbits for random truncator maps. This framework is applied to investigate the periodic transitions of Bornholdt's spin market model.

math.PR

Properties of a renewal process approximation for a spin market model

In this short note we investigate the natur of the phase transitions in a spin market model as a function of the interaction strength between local and global effects. We find that the stochastic dynamics of this stylized market model exhibit a periodicity whose dependence on the coupling constant in the Ising-like Hamiltonian is robust to changes in the temperature and the size of the market.

math.PR

Statistical properties of the phase transitions in a spin model for market microstructure

Increased day-trading activity and the subsequent jump in intraday volatility and trading volume fluctuations has raised considerable interest in models for financial market microstructure. We investigate the random transitions between two phases of an agent-based spin market model on a random network. The objective of the agents is to balance their desire to belong to the global minority and simultaneously to the local majority. We show that transitions between the "ordered" and "disordered" phases follow a Poisson process with a rate that is a monotonically decreasing function of the network connectivity.

math.PR

On the Zero Attractor of the Euler Polynomials

We study the limiting behavior of the zeros of the Euler polynomials. When linearly scaled, they approach a definite curve in the complex plane related to the Szego curve which governs the behavior of the roots of the Taylor polynomials associated to the exponential function. Further, under a conformal transformation, the scaled zeros are uniformly distributed.

math.CO