11,492 research outputs found

### 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

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