Solving the potential field local minimum problem using internal agent states

We propose a new, extended artificial potential field method, which uses dynamic internal agent states. The internal states are modelled as a dynamical system of coupled first order differential equations that manipulate the potential field in which the agent is situated. The internal state dynamics are forced by the interaction of the agent with the external environment. Local equilibria in the potential field are then manipulated by the internal states and transformed from stable equilibria to unstable equilibria, allowiong escape from local minima in the potential field. This new methodology successfully solves reactive path planning problems, such as a complex maze with multiple local minima, which cannot be solved using conventional static potential fields

The density of stationary points in a high-dimensional random energy landscape and the onset of glassy behaviour

We calculate the density of stationary points and minima of a $N\gg 1$ dimensional Gaussian energy landscape. We use it to show that the point of zero-temperature replica symmetry breaking in the equilibrium statistical mechanics of a particle placed in such a landscape in a spherical box of size $L=R\sqrt{N}$ corresponds to the onset of exponential in $N$ growth of the cumulative number of stationary points, but not necessarily the minima. For finite temperatures we construct a simple variational upper bound on the true free energy of the $R=\infty$ version of the problem and show that this approximation is able to recover the position of the whole de-Almeida-Thouless line.Comment: a revised and shortened version with a few typos corrected and references added. To appear in JETP Letter

Anisotropy-based mechanism for zigzag striped patterns in magnetic thin films

In this work we studied a two dimensional ferromagnetic system using Monte Carlo simulations. Our model includes exchange and dipolar interactions, a cubic anisotropy term, and uniaxial out-of-plane and in-plane ones. According to the set of parameters chosen, the model including uniaxial out-of-plane anisotropy has a ground-state which consists of a canted state with stripes of opposite out-of-plane magnetization. When the cubic anisotropy is introduced zigzag patterns appear in the stripes at fields close to the remanence. An analysis of the anisotropy terms of the model shows that this configuration is related to specific values of the ratio between the cubic and the effective uniaxial anisotropy. The mechanism behind this effect is related to particular features of the anisotropy's energy landscape, since a global minima transition as a function of the applied field is required in the anisotropy terms. This new mechanism for zigzags formation could be present in monocrystal ferromagnetic thin films in a given range of thicknesses.Comment: 910 pages, 10 figure

Potential field based navigation for planetary rovers using internal states

The work in this paper aims to introduce analysis and applications for the internal state model which is a new model for a swarm of rovers interacting via pair-wise attractive and repulsive potentials. The internal state model updates the state of the art in overcoming the local minima problem through solving the problem with comparatively lower computation cost than other methods. The simulations results show that using the internal state model, a swarm of planetary rovers, rather than moving in a static potential field, are able to manipulate the potential according to their estimation of whether they are moving towards or away from the goal, which allows them to escape from and maneuver around a local minimum in the potential field to reach a goal. An application of a swarm of rovers to solve the problem for different shaped obstacles is introduced to show the efficiency of the model. The model proves stable convergence to a goal and provides similarities with the behaviour of real groups of animals

Statistical Mechanics of Community Detection

Starting from a general \textit{ansatz}, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the \textit{at hoc} introduced quality function from \cite{ReichardtPRL} and the modularity $Q$ as defined by Newman and Girvan \cite{Girvan03} as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further we show, how hierarchies and overlap in the community structure can be detected. Computationally effective local update rules for optimization procedures to find the ground state are given. We show how the \textit{ansatz} may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure

Modeling Ultraviolet Wind Line Variability in Massive Hot Stars

We model the detailed time-evolution of Discrete Absorption Components (DACs) observed in P Cygni profiles of the Si IV lam1400 resonance doublet lines of the fast-rotating supergiant HD 64760 (B0.5 Ib). We adopt the common assumption that the DACs are caused by Co-rotating Interaction Regions (CIRs) in the stellar wind. We perform 3D radiative transfer calculations with hydrodynamic models of the stellar wind that incorporate these large-scale density- and velocity-structures. We develop the 3D transfer code Wind3D to investigate the physical properties of CIRs with detailed fits to the DAC shape and morphology. The CIRs are caused by irregularities on the stellar surface that change the radiative force in the stellar wind. In our hydrodynamic model we approximate these irregularities by circular symmetric spots on the stellar surface. We use the Zeus3D code to model the stellar wind and the CIRs, limited to the equatorial plane. We constrain the properties of large-scale wind structures with detailed fits to DACs observed in HD 64760. A model with two spots of unequal brightness and size on opposite sides of the equator, with opening angles of 20 +/- 5 degr and 30 +/- 5 degr diameter, and that are 20 +/- 5 % and 8 +/- 5 % brighter than the stellar surface, respectively, provides the best fit to the observed DACs. The recurrence time of the DACs compared to the estimated rotational period corresponds to spot velocities that are 5 times slower than the rotational velocity. The mass-loss rate of the structured wind model for HD 64760 does not exceed the rate of the spherically symmetric smooth wind model by more than 1 %. The fact that DACs are observed in a large number of hot stars constrains the clumping that can be present in their winds, as substantial amounts of clumping would tend to destroy the CIRs.Comment: 58 pages, 16 figures, 1 animation. Accepted for publication in The Astrophysical Journal, Main Journal. More information and animations are available at http://alobel.freeshell.org/hotstars.htm

Wall following to escape local minima for swarms of agents using internal states and emergent behaviour

Natural examples of emergent behaviour, in groups due to interactions among the group's individuals, are numerous. Our aim, in this paper, is to use complex emergent behaviour among agents that interact via pair-wise attractive and repulsive potentials, to solve the local minima problem in the artificial potential based navigation method. We present a modified potential field based path planning algorithm, which uses agent internal states and swarm emergent behaviour to enhance group performance. The algorithm is used successfully to solve a reactive path-planning problem that cannot be solved using conventional static potential fields due to local minima formation. Simulation results demonstrate the ability of a swarm of agents to perform problem solving using the dynamic internal states of the agents along with emergent behaviour of the entire group