A Complete Classification of Tractability in RCC-5

We investigate the computational properties of the spatial algebra RCC-5 which is a restricted version of the RCC framework for spatial reasoning. The satisfiability problem for RCC-5 is known to be NP-complete but not much is known about its approximately four billion subclasses. We provide a complete classification of satisfiability for all these subclasses into polynomial and NP-complete respectively. In the process, we identify all maximal tractable subalgebras which are four in total.Comment: See http://www.jair.org/ for an online appendix and other files accompanying this articl

Spin glass like transition in a highly concentrated Fe-C nanoparticle system

A highly concentrated (17 vol.%) Fe-C nano-particle system, with a narrow size distribution $d = 5.4\pm 0.4$ nm, has been investigated using magnetic ac susceptibility measurements covering a wide range of frequencies (17 mHz - 170 Hz). A dynamic scaling analysis gives evidence for a phase transition to a low temperature spin-glass-like phase. The critical exponents associated with the transition are $z\nu = 10.5 \pm 2$ and $\beta = 1.1 \pm 0.2$. The reason why the scaling analysis works for this sample, while it may not work for other samples exhibiting collective behavior as evidenced by aging phenomena, is that the single particle contribution to $\chi''$ is vanishingly small for $T>T_g$ and hence all slow dynamics is due to collective behavior. This criterion can only be fulfilled for a highly concentrated nano-particle sample with a narrow size distribution.Comment: 2 pages, 3 figures, Proceeding for ICM200

Effect of exchange interaction on superparamagnetic relaxation

We use Langer's approach to calculate the reaction rate of a system of two (classical) spins interacting via the exchange coupling $J$ in a magnetic field $H$, with uniaxial anisotropy of constant $K$. We find a particular value of the exchange coupling, that is $j\equiv J/K = j_c\equiv 1-h^2$, where $h\equiv H/2K$, which separates two regimes corresponding to a two-stage and one-stage switching. For $j\gg j_c$ the N\'eel-Brown result for the one-spin problem is recovered.Comment: 7 pages, 2 eps figures, fig.1 of better quality can be provided upon reques

Non-equilibrium dynamics in an interacting nanoparticle system

Non-equilibrium dynamics in an interacting Fe-C nanoparticle sample, exhibiting a low temperature spin glass like phase, has been studied by low frequency ac-susceptibility and magnetic relaxation experiments. The non-equilibrium behavior shows characteristic spin glass features, but some qualitative differences exist. The nature of these differences is discussed.Comment: 7 pages, 11 figure

Tropically convex constraint satisfaction

A semilinear relation S is max-closed if it is preserved by taking the componentwise maximum. The constraint satisfaction problem for max-closed semilinear constraints is at least as hard as determining the winner in Mean Payoff Games, a notorious problem of open computational complexity. Mean Payoff Games are known to be in the intersection of NP and co-NP, which is not known for max-closed semilinear constraints. Semilinear relations that are max-closed and additionally closed under translations have been called tropically convex in the literature. One of our main results is a new duality for open tropically convex relations, which puts the CSP for tropically convex semilinaer constraints in general into NP intersected co-NP. This extends the corresponding complexity result for scheduling under and-or precedence constraints, or equivalently the max-atoms problem. To this end, we present a characterization of max-closed semilinear relations in terms of syntactically restricted first-order logic, and another characterization in terms of a finite set of relations L that allow primitive positive definitions of all other relations in the class. We also present a subclass of max-closed constraints where the CSP is in P; this class generalizes the class of max-closed constraints over finite domains, and the feasibility problem for max-closed linear inequalities. Finally, we show that the class of max-closed semilinear constraints is maximal in the sense that as soon as a single relation that is not max-closed is added to L, the CSP becomes NP-hard.Comment: 29 pages, 2 figure