Cortical free association dynamics: distinct phases of a latching network

A Potts associative memory network has been proposed as a simplified model of macroscopic cortical dynamics, in which each Potts unit stands for a patch of cortex, which can be activated in one of S local attractor states. The internal neuronal dynamics of the patch is not described by the model, rather it is subsumed into an effective description in terms of graded Potts units, with adaptation effects both specific to each attractor state and generic to the patch. If each unit, or patch, receives effective (tensor) connections from C other units, the network has been shown to be able to store a large number p of global patterns, or network attractors, each with a fraction a of the units active, where the critical load p_c scales roughly like p_c ~ (C S^2)/(a ln(1/a)) (if the patterns are randomly correlated). Interestingly, after retrieving an externally cued attractor, the network can continue jumping, or latching, from attractor to attractor, driven by adaptation effects. The occurrence and duration of latching dynamics is found through simulations to depend critically on the strength of local attractor states, expressed in the Potts model by a parameter w. Here we describe with simulations and then analytically the boundaries between distinct phases of no latching, of transient and sustained latching, deriving a phase diagram in the plane w-T, where T parametrizes thermal noise effects. Implications for real cortical dynamics are briefly reviewed in the conclusions

Global convergence of quorum-sensing networks

In many natural synchronization phenomena, communication between individual elements occurs not directly, but rather through the environment. One of these instances is bacterial quorum sensing, where bacteria release signaling molecules in the environment which in turn are sensed and used for population coordination. Extending this motivation to a general non- linear dynamical system context, this paper analyzes synchronization phenomena in networks where communication and coupling between nodes are mediated by shared dynamical quan- tities, typically provided by the nodes' environment. Our model includes the case when the dynamics of the shared variables themselves cannot be neglected or indeed play a central part. Applications to examples from systems biology illustrate the approach.Comment: Version 2: minor editions, added section on noise. Number of pages: 36

Symmetries, Stability, and Control in Nonlinear Systems and Networks

This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence analysis tools based on nonlinear contraction theory and virtual dynamical systems. This synergy between structural properties (symmetries) and convergence properties (contraction) is illustrated in the contexts of network motifs arising e.g. in genetic networks, of invariance to environmental symmetries, and of imposing different patterns of synchrony in a network.Comment: 16 pages, second versio

Matching the (DR4)-R-6 interaction at two-loops

The coefficient of the $D^6 {\cal R}^4$ interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be proportional to the integral of the Zhang-Kawazumi (ZK) invariant over the moduli space of genus-two Riemann surfaces. We demonstrate that the ZK invariant is an eigenfunction with eigenvalue 5 of the Laplace-Beltrami operator in the interior of moduli space. Exploiting this result, we evaluate the integral of the ZK invariant explicitly, finding agreement with the value of the two-loop $D^6 {\cal R}^4$ interaction predicted on the basis of S-duality and supersymmetry. A review of the current understanding of the $D^{2p} {\cal R}^4$ interactions in type II superstring theory compactified on a torus $T^d$ with $p \leq 3$ and $d \leq 4$ is included.Comment: 40 pages, various typos and coefficients corrected in version

Comparison of dns of compressible and incompressible turbulent droplet-laden heated channel flow with phase transition

In this paper a turbulent channel flow with dispersed droplets is examined. The dispersed phase is allowed to have phase transition, which leads to heat and mass transfer between the phases, and correspondingly modulates turbulent flow properties. As a point of reference we examine the flow of water droplets in air, containing also the vapor of water. The key element of this study concerns the treatment of the carrier phase as either a compressible or an incompressible fluid. We compare simulation results obtained with a pseudo-spectral discretization for the incompressible flow to those obtained with a finite volume approach for the compressible flow. The compressible formulation is not tailored for low Mach flow and we need to resort to a Mach number that is artificially high for simulation feasibility. We discuss differences in fluid flow, heat- and mass transfer and dispersed droplet properties. The main conclusion is that both formulations give a good general correspondence. Flow properties such as velocity fields agree very closely, while heat transfer as characterized by the Nusselt number differs by around 25%. Droplet sizes are shown to be slightly larger, particularly in the center of the channel, in case the compressible formulation is chosen. A low-Mach compressible formulation is required for a fully quantitative comparison

Security policy refinement using data integration: a position paper.

In spite of the wide adoption of policy-based approaches for security management, and many existing treatments of policy verification and analysis, relatively little attention has been paid to policy refinement: the problem of deriving lower-level, runnable policies from higher-level policies, policy goals, and specifications. In this paper we present our initial ideas on this task, using and adapting concepts from data integration. We take a view of policies as governing the performance of an action on a target by a subject, possibly with certain conditions. Transformation rules are applied to these components of a policy in a structured way, in order to translate the policy into more refined terms; the transformation rules we use are similar to those of global-as-view database schema mappings, or to extensions thereof. We illustrate our ideas with an example. Copyright 2009 ACM