On Cavity Approximations for Graphical Models

We reformulate the Cavity Approximation (CA), a class of algorithms recently introduced for improving the Bethe approximation estimates of marginals in graphical models. In our new formulation, which allows for the treatment of multivalued variables, a further generalization to factor graphs with arbitrary order of interaction factors is explicitly carried out, and a message passing algorithm that implements the first order correction to the Bethe approximation is described. Furthermore we investigate an implementation of the CA for pairwise interactions. In all cases considered we could confirm that CA[k] with increasing $k$ provides a sequence of approximations of markedly increasing precision. Furthermore in some cases we could also confirm the general expectation that the approximation of order $k$, whose computational complexity is $O(N^{k+1})$ has an error that scales as $1/N^{k+1}$ with the size of the system. We discuss the relation between this approach and some recent developments in the field.Comment: Extension to factor graphs and comments on related work adde

Replica symmetry breaking in the `small world' spin glass

We apply the cavity method to a spin glass model on a `small world' lattice, a random bond graph super-imposed upon a 1-dimensional ferromagnetic ring. We show the correspondence with a replicated transfer matrix approach, up to the level of one step replica symmetry breaking (1RSB). Using the scheme developed by M\'ezard & Parisi for the Bethe lattice, we evaluate observables for a model with fixed connectivity and $\pm J$ long range bonds. Our results agree with numerical simulations significantly better than the replica symmetric (RS) theory.Comment: 21 pages, 3 figure

Survey propagation at finite temperature: application to a Sourlas code as a toy model

In this paper we investigate a finite temperature generalization of survey propagation, by applying it to the problem of finite temperature decoding of a biased finite connectivity Sourlas code for temperatures lower than the Nishimori temperature. We observe that the result is a shift of the location of the dynamical critical channel noise to larger values than the corresponding dynamical transition for belief propagation, as suggested recently by Migliorini and Saad for LDPC codes. We show how the finite temperature 1-RSB SP gives accurate results in the regime where competing approaches fail to converge or fail to recover the retrieval state

Microscopic and flow cytometric semen assessment of Dutch AI-bucks : effect of semen processing procedures and their correlation to fertility

This study was done to determine the effects of processing techniques on the quality of semen from Dutch AI-bucks with the view on improving pregnancy rates after artificial insemination (AI) with liquid or frozen–thawed semen. Motility of spermatozoa was estimated under a microscope whereas the percentage live spermatozoa and the percentage live spermatozoa with intact acrosomes were determined by means of flow cytometry. Aspects of semen processing that were investigated are storage temperature of liquid semen (i), the effect of glycerol on liquid-stored semen (ii), removal of seminal plasma (iii) and type of extender (iv). The correlation between semen quality and fertility rates in inseminated does was also investigated. The percentage motile spermatozoa in semen stored in liquid form for 72 h progressively declined over time, irrespective of whether storage occurred at 4 or 18 °C. The percentage motile spermatozoa in semen stored at 18 °C was similar to that in semen stored at 4 °C if stored for 24 h but lower if stored for 48 h. Goats differ in the sensitivity of their spermatozoa to the deleterious effects of glycerol. Neither the removal of seminal plasma nor the type of extender had any effect on semen quality before freezing but semen frozen in a Tris–citric acid-glucose (TCG) buffer with egg yolk without removal of the seminal plasma had better quality after thawing than semen frozen in another diluent or after removal of seminal plasma. Remarkably no significant correlation between fertility and membrane integrity of spermatozoa could be found. Thus, although integrity assays for spermatozoa are useful to asses resistance to semen handling, the validity of these assays for predicting fertility is questioned.The authors acknowledge the contributions of the Dutch Goat AI Co-operation (GKN) by granting us access to their breeding bucks and thereby facilitating this research. This study was performed as part of the EU-supported projects: CRAFT FA-S2-9207 to strengthen the European goat industry by developing a new reproduction strategy, including the distribution of kidding during the year and AITECH for dissemination of Animal Insemination Technology for goats in Europe (Contract No. QLK5-CT-2002-30252)

Effects of non-invasive vagus nerve stimulation on cognitive and autonomic correlates of perseverative cognition

Stress and Psychopatholog

Optimal control as a graphical model inference problem

We reformulate a class of non-linear stochastic optimal control problems introduced by Todorov (2007) as a Kullback-Leibler (KL) minimization problem. As a result, the optimal control computation reduces to an inference computation and approximate inference methods can be applied to efficiently compute approximate optimal controls. We show how this KL control theory contains the path integral control method as a special case. We provide an example of a block stacking task and a multi-agent cooperative game where we demonstrate how approximate inference can be successfully applied to instances that are too complex for exact computation. We discuss the relation of the KL control approach to other inference approaches to control.Comment: 26 pages, 12 Figures; Machine Learning Journal (2012

The future of sovereignty in multilevel governance Europe: a constructivist reading

Multilevel governance presents a depiction of contemporary structures in EU Europe as consisting of overlapping authorities and competing competencies. By focusing on emerging non-anarchical structures in the international system, hence moving beyond the conventional hierarchy/anarchy dichotomy to distinguish domestic and international arenas, this seems a radical transformation of the familiar Westphalian system and to undermine state sovereignty. Paradoxically, however, the principle of sovereignty proves to be resilient despite its alleged empirical decline. This article argues that social constructivism can explain the paradox, by considering sovereign statehood as a process-dependent institutional fact, and by showing that multilevel governance can feed into this process