20,088 research outputs found
The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
In this Letter we show that an arbitrarily good approximation to the
propagator e^{itH} for a 1D lattice of n quantum spins with hamiltonian H may
be obtained with polynomial computational resources in n and the error
\epsilon, and exponential resources in |t|. Our proof makes use of the finitely
correlated state/matrix product state formalism exploited by numerical
renormalisation group algorithms like the density matrix renormalisation group.
There are two immediate consequences of this result. The first is that the
Vidal's time-dependent density matrix renormalisation group will require only
polynomial resources to simulate 1D quantum spin systems for logarithmic |t|.
The second consequence is that continuous-time 1D quantum circuits with
logarithmic |t| can be simulated efficiently on a classical computer, despite
the fact that, after discretisation, such circuits are of polynomial depth.Comment: 4 pages, 2 figures. Simplified argumen
Entanglement, quantum phase transitions, and density matrix renormalization
We investigate the role of entanglement in quantum phase transitions, and
show that the success of the density matrix renormalization group (DMRG) in
understanding such phase transitions is due to the way it preserves
entanglement under renormalization. We provide a reinterpretation of the DMRG
in terms of the language and tools of quantum information science which allows
us to rederive the DMRG in a physically transparent way. Motivated by our
reinterpretation we suggest a modification of the DMRG which manifestly takes
account of the entanglement in a quantum system. This modified renormalization
scheme is shown,in certain special cases, to preserve more entanglement in a
quantum system than traditional numerical renormalization methods.Comment: 5 pages, 1 eps figure, revtex4; added reference and qualifying
remark
MEASUREMENT AND TESTING FOR NEUTRALITY OF FOREIGN PRICE AND CPI TRANSMISSION IN RUSSIA
This paper examines domestic and international food market integration in Russia before and after the financial crisis of 1998. Using monthly prices of bread, pork, and beef in 80 regions of Russia from 1994 to 1999, we measure the short-run response of regional prices to changes in foreign prices and domestic inflation. We find that both changes in foreign prices and domestic inflation have distinct impacts on the prices of these commodities in different Russian markets, indicating poor market integration in the short run. An analysis of the effect of the financial crisis shows that market integration for bread and beef deteriorated after the crisis. However, integration improved for pork in some parts of Russia, and the integration of Siberian pork markets with Chinese pork markets also improved after the crisis.International Relations/Trade,
How are topics born? Understanding the research dynamics preceding the emergence of new areas
The ability to promptly recognise new research trends is strategic for many stake- holders, including universities, institutional funding bodies, academic publishers and companies. While the literature describes several approaches which aim to identify the emergence of new research topics early in their lifecycle, these rely on the assumption that the topic in question is already associated with a number of publications and consistently referred to by a community of researchers. Hence, detecting the emergence of a new research area at an embryonic stage, i.e., before the topic has been consistently labelled by a community of researchers and associated with a number of publications, is still an open challenge. In this paper, we begin to address this challenge by performing a study of the dynamics preceding the creation of new topics. This study indicates that the emergence of a new topic is anticipated by a significant increase in the pace of collaboration between relevant research areas, which can be seen as the âparentsâ of the new topic. These initial findings (i) confirm our hypothesis that it is possible in principle to detect the emergence of a new topic at the embryonic stage, (ii) provide new empirical evidence supporting relevant theories in Philosophy of Science, and also (iii) suggest that new topics tend to emerge in an environment in which weakly interconnected research areas begin to cross-fertilise
Fingerprint Policy Optimisation for Robust Reinforcement Learning
Policy gradient methods ignore the potential value of adjusting environment
variables: unobservable state features that are randomly determined by the
environment in a physical setting, but are controllable in a simulator. This
can lead to slow learning, or convergence to suboptimal policies, if the
environment variable has a large impact on the transition dynamics. In this
paper, we present fingerprint policy optimisation (FPO), which finds a policy
that is optimal in expectation across the distribution of environment
variables. The central idea is to use Bayesian optimisation (BO) to actively
select the distribution of the environment variable that maximises the
improvement generated by each iteration of the policy gradient method. To make
this BO practical, we contribute two easy-to-compute low-dimensional
fingerprints of the current policy. Our experiments show that FPO can
efficiently learn policies that are robust to significant rare events, which
are unlikely to be observable under random sampling, but are key to learning
good policies.Comment: ICML 201
Probabilistic Numerics and Uncertainty in Computations
We deliver a call to arms for probabilistic numerical methods: algorithms for
numerical tasks, including linear algebra, integration, optimization and
solving differential equations, that return uncertainties in their
calculations. Such uncertainties, arising from the loss of precision induced by
numerical calculation with limited time or hardware, are important for much
contemporary science and industry. Within applications such as climate science
and astrophysics, the need to make decisions on the basis of computations with
large and complex data has led to a renewed focus on the management of
numerical uncertainty. We describe how several seminal classic numerical
methods can be interpreted naturally as probabilistic inference. We then show
that the probabilistic view suggests new algorithms that can flexibly be
adapted to suit application specifics, while delivering improved empirical
performance. We provide concrete illustrations of the benefits of probabilistic
numeric algorithms on real scientific problems from astrometry and astronomical
imaging, while highlighting open problems with these new algorithms. Finally,
we describe how probabilistic numerical methods provide a coherent framework
for identifying the uncertainty in calculations performed with a combination of
numerical algorithms (e.g. both numerical optimisers and differential equation
solvers), potentially allowing the diagnosis (and control) of error sources in
computations.Comment: Author Generated Postprint. 17 pages, 4 Figures, 1 Tabl
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