On the large order behaviour of the Potts model

Following the work by Houghton, Reeve and Wallace about an alternative formulation of the $n \to 0$ limit of the $(n+1)$ state Potts model in field theory for the large order behaviour of the perturbative expansion, we generalise their technique to all $n$ by establishing an equivalence in perturbation theory order by order with another bosonic field theory. Restricting ourselves to a cubic interaction, we obtain an explicit expression (in terms of~$n$) for the large order behaviour of the partition function.Comment: 16 pages, require TeXdra

Replica Fourier Transforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices

The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4-replica matrices $M^{\alpha \beta ; \gamma \delta}$, is shown to be dramatically simplified through the introduction of properly chosen operations on those objects. These are the Replica Fourier Transforms on ultrametric trees. Those transformations are defined and used in the present work.Comment: Latex file, 14 page

Stability of the Mezard-Parisi solution for random manifolds

The eigenvalues of the Hessian associated with random manifolds are constructed for the general case of $R$ steps of replica symmetry breaking. For the Parisi limit $R\to\infty$ (continuum replica symmetry breaking) which is relevant for the manifold dimension $D<2$, they are shown to be non negative.Comment: LaTeX, 15 page

Death of a Bail Bondsman: The Implementation and Successes of Nonmonetary, Risk-Based Bail Systems

The Eighth Amendment to the United States Constitution provides that bail, when afforded to a criminal defendant, not be excessive. However, there is no provision as to what form bail must take or how it is to be determined. Starting in the twilight of the nineteenth century, monetary conditions of bail became increasingly prevalent throughout the United States. Yet, in recent years, there has been a movement to eliminate the requirement that defendants pay their way to pretrial freedom. States have taken measures to move away from cash bail, ranging from significantly limiting its use to outright prohibitions against monetary conditions on bail. The impetus behind such reform measures is that monetary conditions on bail discriminate against lower income defendants by disparately leading to pretrial detention of individuals who cannot afford to pay the required sum. This Comment analyzes the relative success of the risk-based, nonmonetary bail systems that several states have implemented. This Comment begins by analyzing the history of the right to bail in the United States, starting with how such a right was understood at the time of the founding. Next, the evolution of the application of bail and the considerations behind pretrial release or detention determinations, are discussed. This Comment then proceeds to analyze how risk-based, nonmonetary bail systems have been codified and applied. Last, this Comment evaluates the impact that these schemes have had on the states of implementation and potential alterations that would allow for better administration of such legislation

Image restoration using the Q-Ising spin glass

We investigate static and dynamic properties of gray-scale image restoration (GSIR) by making use of the Q-Ising spin glass model, whose ladder symmetry allows to take in account the distance between two spins. We thus give an explicit expression of the Hamming distance between the original and restored images as a function of the hyper-parameters in the mean field limit. Finally, numerical simulations for real-world pictures are carried out to prove the efficiency of our model.Comment: 27pages, 13figures, revte