Relevant elments, Magnetization and Dynamical Properties in Kauffman Networks: a Numerical Study

This is the first of two papers about the structure of Kauffman networks. In this paper we define the relevant elements of random networks of automata, following previous work by Flyvbjerg and Flyvbjerg and Kjaer, and we study numerically their probability distribution in the chaotic phase and on the critical line of the model. A simple approximate argument predicts that their number scales as sqrt(N) on the critical line, while it is linear with N in the chaotic phase and independent of system size in the frozen phase. This argument is confirmed by numerical results. The study of the relevant elements gives useful information about the properties of the attractors in critical networks, where the pictures coming from either approximate computation methods or from simulations are not very clear.Comment: 22 pages, Latex, 8 figures, submitted to Physica

Kinetics of Coalescence, Annihilation, and the q-State Potts Model in One Dimension

The kinetics of the q-state Potts model in the zero temperature limit in one dimension is analyzed exactly through a generalization of the method of empty intervals, previously used for the analysis of diffusion-limited coalescence, A+A->A. In this new approach, the q-state Potts model, coalescence, and annihilation (A+A->0) all satisfy the same diffusion equation, and differ only in the imposed initial condition.Comment: 4 pages, RevTeX, submitted to Phys. Lett.

"As Nobody I was Sovereign": reading Derrida reading Blanchot

In Session 7 (26 February 2003) of The Beast and the Sovereign, Volume II, Jacques Derrida engages again with Maurice Blanchot, two days after the latter’s cremation. This intervention also appears as a post-face to Derrida’s 2003 edition of Parages, his collection of essays devoted to the work of Blanchot. In this article, I examine Derrida’s affinity to the work of Blanchot, as the one whose work ‘stood watch over and around what matters to me, for a long time behind me and forever still before me’ [The Beast and the Sovereign, Volume II, p. 176]. In doing so I look at the manner in which Derrida engaged with Blanchot in his work and how in examining this engagement another reading of sovereignty emerges, one which is not tethered to liberal models of sovereign will but one which eludes biopolitical ordering and may be seen as a form of disappearance. Through a reading of Derrida’s readings of Blanchot’s The Madness of the Day I emphasize the link of this alternative sovereignty to both writing and literature in order to demonstrate how a more radical thinking of sovereignty can be discovered in Derrida’s thought

Multiple Shocks in a Driven Diffusive System with Two Species of Particles

A one-dimensional driven diffusive system with two types of particles and nearest neighbors interactions has been considered on a finite lattice with open boundaries. The particles can enter and leave the system from both ends of the lattice and there is also a probability for converting the particle type at the boundaries. We will show that on a special manifold in the parameters space multiple shocks evolve in the system for both species of particles which perform continuous time random walks on the lattice.Comment: 11 pages, 1 figure, accepted for publication in Physica

Hierarchic trees with branching number close to one: noiseless KPZ equation with additional linear term for imitation of 2-d and 3-d phase transitions.

An imitation of 2d field theory is formulated by means of a model on the hierarhic tree (with branching number close to one) with the same potential and the free correlators identical to 2d correlators ones. Such a model carries on some features of the original model for certain scale invariant theories. For the case of 2d conformal models it is possible to derive exact results. The renormalization group equation for the free energy is noiseless KPZ equation with additional linear term.Comment: latex, 5 page

Phase Transition in NK-Kauffman Networks and its Correction for Boolean Irreducibility

In a series of articles published in 1986 Derrida, and his colleagues studied two mean field treatments (the quenched and the annealed) for \textit{NK}-Kauffman Networks. Their main results lead to a phase transition curve $K_c \, 2 \, p_c \left( 1 - p_c \right) = 1$ ($0 < p_c < 1$) for the critical average connectivity $K_c$ in terms of the bias $p_c$ of extracting a "$1$" for the output of the automata. Values of $K$ bigger than $K_c$ correspond to the so-called chaotic phase; while $K < K_c$, to an ordered phase. In~[F. Zertuche, {\it On the robustness of NK-Kauffman networks against changes in their connections and Boolean functions}. J.~Math.~Phys. {\bf 50} (2009) 043513], a new classification for the Boolean functions, called {\it Boolean irreducibility} permitted the study of new phenomena of \textit{NK}-Kauffman Networks. In the present work we study, once again the mean field treatment for \textit{NK}-Kauffman Networks, correcting it for {\it Boolean irreducibility}. A shifted phase transition curve is found. In particular, for $p_c = 1 / 2$ the predicted value $K_c = 2$ by Derrida {\it et al.} changes to $K_c = 2.62140224613 \dots$ We support our results with numerical simulations.Comment: 23 pages, 7 Figures on request. Published in Physica D: Nonlinear Phenomena: Vol.275 (2014) 35-4

'Genealogical misfortunes': Achille Mbembe's (re-)writing of postcolonial Africa

In his latest work, Sortir de la grande nuit, the Cameroonian social theorist, Achille Mbembe nuances his description of the ontological status of the postcolonial African subject, which he had theorized extensively in his best-known text, On the Postcolony, and at the same time exploits the conceptual resources of a number of Jean-Luc Nancy’s lexical innovations. This recent text is also a reprise of an earlier autobiographical essay, and the gesture of this ‘reinscription’ is critical to our understanding of Mbembe’s status as a contemporary ‘postcolonial thinker’, and the way in which he positions himself within a certain intellectual genealogy of postcolonial theory. Within this trajectory, I argue that we can read fruitfully his relationship to three influential figures: Jacques Derrida, Jean-Luc Nancy and Ruben Um Nyobè

Large Deviation Function of the Partially Asymmetric Exclusion Process

The large deviation function obtained recently by Derrida and Lebowitz for the totally asymmetric exclusion process is generalized to the partially asymmetric case in the scaling limit. The asymmetry parameter rescales the scaling variable in a simple way. The finite-size corrections to the universal scaling function and the universal cumulant ratio are also obtained to the leading order.Comment: 10 pages, 2 eps figures, minor changes, submitted to PR

Persistence exponent in a superantiferromagnetic quenching

We measure the persistence exponent in a phase separating two-dimensional spin system with non-conserved dynamics quenched in a region with four coexisting stripe phases. The system is an Ising model with nearest neighbor, next-to-the-nearest neighbor and plaquette interactions. Due the particular nature of the ground states, the order parameter is defined in terms of blocks of spins. Our estimate of the persistence exponent, $\theta=0.42$, differs from those of the two-dimensional Ising and four state Potts models. Our procedure allows the study of persistence properties also at finite temperature $T$: our results are compatible with the hypothesis that $\theta$ does not depend on $T$ below the critical point.Comment: LaTeX file with postscript figure

Distribution of repetitions of ancestors in genealogical trees

We calculate the probability distribution of repetitions of ancestors in a genealogical tree for simple neutral models of a closed population with sexual reproduction and non-overlapping generations. Each ancestor at generation g in the past has a weight w which is (up to a normalization) the number of times this ancestor appears in the genealogical tree of an individual at present. The distribution P_g(w) of these weights reaches a stationary shape P_\infty(w) for large g, i.e. for a large number of generations back in the past. For small w, P_\infty(w) is a power law with a non-trivial exponent which can be computed exactly using a standard procedure of the renormalization group approach. Some extensions of the model are discussed and the effect of these variants on the shape of P_\infty(w) are analysed.Comment: 20 pages, 5 figures included, to appear in Physica