2,604 research outputs found
The economic analysis of multinationals and foreign direct investment: a review.
This article provides an up-to-date, comprehensive synthesis and evaluation of the existing literatura on multinational firms and foreign direct investment. Unlike most previous reviews it combines severalinsights showing their inconsistencies and complementarities. Through a chronological description it presents the main strands since the earliest perfect competition studies from the 1960s till some new recent contributions such as the knowledge-capital model, heterogeneous firms models, and internalisation issues. The paper also offers a new perspective, by reviewing the available computable general equilibrium models that include multinationals and foreign direct investment.Multinational enterprises, Foreign direct investment, Computable general equilibrium models.
Fine-grained entanglement loss along renormalization group flows
We explore entanglement loss along renormalization group trajectories as a
basic quantum information property underlying their irreversibility. This
analysis is carried out for the quantum Ising chain as a transverse magnetic
field is changed. We consider the ground-state entanglement between a large
block of spins and the rest of the chain. Entanglement loss is seen to follow
from a rigid reordering, satisfying the majorization relation, of the
eigenvalues of the reduced density matrix for the spin block. More generally,
our results indicate that it may be possible to prove the irreversibility along
RG trajectories from the properties of the vacuum only, without need to study
the whole hamiltonian.Comment: 5 pages, 3 figures; minor change
Optimal control of multiscale systems using reduced-order models
We study optimal control of diffusions with slow and fast variables and
address a question raised by practitioners: is it possible to first eliminate
the fast variables before solving the optimal control problem and then use the
optimal control computed from the reduced-order model to control the original,
high-dimensional system? The strategy "first reduce, then optimize"--rather
than "first optimize, then reduce"--is motivated by the fact that solving
optimal control problems for high-dimensional multiscale systems is numerically
challenging and often computationally prohibitive. We state sufficient and
necessary conditions, under which the "first reduce, then control" strategy can
be employed and discuss when it should be avoided. We further give numerical
examples that illustrate the "first reduce, then optmize" approach and discuss
possible pitfalls
Universality in the entanglement structure of ferromagnets
Systems of exchange-coupled spins are commonly used to model ferromagnets.
The quantum correlations in such magnets are studied using tools from quantum
information theory. Isotropic ferromagnets are shown to possess a universal
low-temperature density matrix which precludes entanglement between spins, and
the mechanism of entanglement cancellation is investigated, revealing a core of
states resistant to pairwise entanglement cancellation. Numerical studies of
one-, two-, and three-dimensional lattices as well as irregular geometries
showed no entanglement in ferromagnets at any temperature or magnetic field
strength.Comment: 4 pages, 2 figure
Configuration-Space Location of the Entanglement between Two Subsystems
In this paper we address the question: where in configuration space is the
entanglement between two particles located? We present a thought-experiment,
equally applicable to discrete or continuous-variable systems, in which one or
both parties makes a preliminary measurement of the state with only enough
resolution to determine whether or not the particle resides in a chosen region,
before attempting to make use of the entanglement. We argue that this provides
an operational answer to the question of how much entanglement was originally
located within the chosen region. We illustrate the approach in a spin system,
and also in a pair of coupled harmonic oscillators. Our approach is
particularly simple to implement for pure states, since in this case the
sub-ensemble in which the system is definitely located in the restricted region
after the measurement is also pure, and hence its entanglement can be simply
characterised by the entropy of the reduced density operators. For our spin
example we present results showing how the entanglement varies as a function of
the parameters of the initial state; for the continuous case, we find also how
it depends on the location and size of the chosen regions. Hence we show that
the distribution of entanglement is very different from the distribution of the
classical correlations.Comment: RevTex, 12 pages, 9 figures (28 files). Modifications in response to
journal referee
Three-Dimensional Quantification of Cellular Traction Forces and Mechanosensing of Thin Substrata by Fourier Traction Force Microscopy
We introduce a novel three-dimensional (3D) traction force microscopy (TFM)
method motivated by the recent discovery that cells adhering on plane surfaces
exert both in-plane and out-of-plane traction stresses. We measure the 3D
deformation of the substratum on a thin layer near its surface, and input this
information into an exact analytical solution of the elastic equilibrium
equation. These operations are performed in the Fourier domain with high
computational efficiency, allowing to obtain the 3D traction stresses from raw
microscopy images virtually in real time. We also characterize the error of
previous two-dimensional (2D) TFM methods that neglect the out-of-plane
component of the traction stresses. This analysis reveals that, under certain
combinations of experimental parameters (\ie cell size, substratums' thickness
and Poisson's ratio), the accuracy of 2D TFM methods is minimally affected by
neglecting the out-of-plane component of the traction stresses. Finally, we
consider the cell's mechanosensing of substratum thickness by 3D traction
stresses, finding that, when cells adhere on thin substrata, their out-of-plane
traction stresses can reach four times deeper into the substratum than their
in-plane traction stresses. It is also found that the substratum stiffness
sensed by applying out-of-plane traction stresses may be up to 10 times larger
than the stiffness sensed by applying in-plane traction stresses
Scaling of Entanglement Entropy in the Random Singlet Phase
We present numerical evidences for the logarithmic scaling of the
entanglement entropy in critical random spin chains. Very large scale exact
diagonalizations performed at the critical XX point up to L=2000 spins 1/2 lead
to a perfect agreement with recent real-space renormalization-group predictions
of Refael and Moore [Phys. Rev. Lett. {\bf 93}, 260602 (2004)] for the
logarithmic scaling of the entanglement entropy in the Random Singlet Phase
with an effective central charge . Moreover we
provide the first visual proof of the existence the Random Singlet Phase thanks
to the quantum entanglement concept.Comment: 4 pages, 3 figure
On two possible definitions of the free energy for collective variables
The aim of this mini-review article is to clarify the relation between two distinct formulations of the thermodynamic free energy for collective variables which can be found in the molecular dynamics literature. In doing so, we discuss the different ensemble concepts underlying the two definitions and reveal their relation to strong confinement (restraints) and molecular constraints. The latter analysis is based on a variant of Federer’s coarea formula which can be regarded as a generalization of Fubini’s theorem for iterated integrals to curvilinear coordinates and which implies the famous “blue moon” ensemble identity for computing conditional expectations using constrained simulations. For illustration we will present a few paradigmatic examples
Free energy computation by controlled Langevin processes
We propose a nonequilibrium sampling method for computing free energy profiles along a given reaction coordinate. The method consists of two parts: a controlled Langevin sampler that generates nonequilibrium bridge paths conditioned by the reaction coordinate, and Jarzynski’s formula for reweighting the paths. Our derivation of the equations of motion of the sampler is based on stochastic perturbation of a controlled dissipative Hamiltonian system, for which we prove Jarzynski’s identity as a special case of the Feynman-Kac formula. We illustrate our method by means of a suitable numerical example and briefly discuss issues of optimally choosing the control protocol for the reaction coordinate
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