The inverse conjunction fallacy

If people believe that some property is true of all members of a class such as sofas, then they should also believe that the same property is true of all members of a conjunctively defined subset of that class such as uncomfortable handmade sofas. A series of experiments demonstrated a failure to observe this constraint, leading to what is termed the inverse conjunction fallacy. Not only did people often express a belief in the more general statement but not in the more specific, but also when they accepted both beliefs, they were inclined to give greater confidence to the more general. It is argued that this effect underlies a number of other demonstrations of fallacious reasoning, particularly in category-based induction. Alternative accounts of the phenomenon are evaluated, and it is concluded that the effect is best interpreted in terms of intensional reasoning [Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review, 90, 293–315.]

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

Exact ground states of a staggered supersymmetric model for lattice fermions

We study a supersymmetric model for strongly interacting lattice fermions in the presence of a staggering parameter. The staggering is introduced as a tunable parameter in the manifestly supersymmetric Hamiltonian. We obtain analytic expressions for the ground states in the limit of small and large staggering for the model on the class of doubly decorated lattices. On this type of lattice there are two ground states, each with a different density. In one limit we find these ground states to be a simple Wigner crystal and a valence bond solid (VBS) state. In the other limit we find two types of quantum liquids. As a special case, we investigate the quantum liquid state on the one dimensional chain in detail. It is characterized by a massless kink that separates two types of order.Comment: 21 pages, 6 figures, v2: largely rewritten version with more emphasis on physical interpretatio

Long time motion of NLS solitary waves in a confining potential

We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schroedinger equations with a confining, slowly varying external potential, $V(x)$. A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential $V(x)$ over a long time interval.Comment: 42 pages, 2 figure

Effects of surface forces and phonon dissipation in a three-terminal nano relay

We have performed a theoretical analysis of the operational characteristics of a carbon-nanotube-based three-terminal nanorelay. We show that short range and van der Waals forces have a significant impact on the characteristics of the relay and introduce design constraints. We also investigate the effects of dissipation due to phonon excitation in the drain contact, which changes the switching time scales of the system, decreasing the longest time scale by two orders of magnitude. We show that the nanorelay can be used as a memory element and investigate the dynamics and properties of such a device

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

The impact of Chinese import penetration on the South African manufacturing sector

This article uses a Chenery-type decomposition and econometric estimation to evaluate the impact of Chinese trade on production and employment in South African manufacturing from 1992 to 2010. The results suggest that increased import penetration from China caused South African manufacturing output to be 5 per cent lower in 2010 than it otherwise would have been. The estimated reduction of total employment in manufacturing as a result of trade with China is larger – in 2010 about 8 per cent – because the declines in output were concentrated on labour-intensive industries and because the increase in imports raised labour productivity within industries

Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves

We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u), where B is a small and bounded, slowly varying function and f is a nonlinearity. Many variable coefficient KdV-type equations can be rescaled into this equation. We study the long time behaviour of solutions with initial conditions close to a stable, B=0 solitary wave. We prove that for long time intervals, such solutions have the form of the solitary wave, whose centre and scale evolve according to a certain dynamical law involving the function B(t,x), plus an H^1-small fluctuation.Comment: 19 page

A theory of normed simulations

In existing simulation proof techniques, a single step in a lower-level specification may be simulated by an extended execution fragment in a higher-level one. As a result, it is cumbersome to mechanize these techniques using general purpose theorem provers. Moreover, it is undecidable whether a given relation is a simulation, even if tautology checking is decidable for the underlying specification logic. This paper introduces various types of normed simulations. In a normed simulation, each step in a lower-level specification can be simulated by at most one step in the higher-level one, for any related pair of states. In earlier work we demonstrated that normed simulations are quite useful as a vehicle for the formalization of refinement proofs via theorem provers. Here we show that normed simulations also have pleasant theoretical properties: (1) under some reasonable assumptions, it is decidable whether a given relation is a normed forward simulation, provided tautology checking is decidable for the underlying logic; (2) at the semantic level, normed forward and backward simulations together form a complete proof method for establishing behavior inclusion, provided that the higher-level specification has finite invisible nondeterminism.Comment: 31 pages, 10figure