10,363 research outputs found
Minimising biases in Full Configuration Interaction Quantum Monte Carlo
We show that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a
Markov Chain in its present form. We construct the Markov matrix of FCIQMC for
a two determinant system and hence compute the stationary distribution. These
solutions are used to quantify the dependence of the population dynamics on the
parameters defining the Markov chain. Despite the simplicity of a system with
only two determinants, it still reveals a population control bias inherent to
the FCIQMC algorithm. We investigate the effect of simulation parameters on the
population control bias for the neon atom and suggest simulation setups to in
general minimise the bias. We show a reweighting scheme to remove the bias
caused by population control commonly used in Diffusion Monte Carlo [J. Chem.
Phys. 99, 2865 (1993)] is effective and recommend its use as a post processing
step.Comment: Supplementary material available as 'Ancillary Files
Cattle Trade and the Risk of Importing Animal Diseases into the Netherlands
Projections of live cattle trade in the EU-25 assist to reduce the uncertainty on the risk of importing animal diseases in the Netherlands. The accession of 10 member states to the European Union has a potentially large impact on livestock trade in the EU as it liberalized in one stroke a trade that was administered by the Management Committee for Beef until May 1, 2004. The approach combines AG-Memod partial equilibrium with GTAP general equilibrium modelling in order to estimate the impact of quota liberalization. Quota removal will substantially alter the regional structure of livestock imports, as the share of new EU member states in the east triples to 25%. The risk outlook indicates a need for enhanced animal health services in the new member states.livestock, animal disease, trade, projections, quota, EU-enlargement, Risk and Uncertainty, F17, I18, Q17,
Exploring the parameter space of an endohedral atom in a cylindrical cavity
Endohedral fullerenes, or endofullerenes, are chemical systems of fullerene
cages encapsulating single atoms or small molecules. These species provide an
interesting challenge of Potential Energy Surface (PES) determination as
examples of non-covalently bonded, bound systems. While the majority of studies
focus on C as the encapsulating cage, introducing some anisotropy by
using a different fullerene, e.g., C can unveil a double well potential
along the unique axis. By approximating the potential as a pairwise
Lennard-Jones (LJ) summation over the fixed C cage atoms, the parameter space
of the Hamiltonian includes three tunable variables:
representing the mass of the trapped species, the LJ energy, and length scales
respectively. Fixing the mass and allowing the others to vary can imitate the
potentials of endohedral species trapped in more elongated fullerenes. We
choose to explore the LJ parameter space of an endohedral atom in C with
[20cm, 150cm], and [2.85\r{A} ,
3.05\r{A}].
As the barrier height and positions of these wells vary between [1cm,
264cm] and [0.35\r{A}, 0.85\r{A}] respectively, using a 3D direct
product basis of 1D harmonic oscillator (HO) wavefunctions centred at the
origin where there is a local maximum is unphysical. Instead we propose the use
of a non-orthogonal basis set, using 1D HO wavefunctions centred in each
minimum and compare this to other choices. The ground state energy of the
X@C is tracked across the LJ parameter space, along with its
corresponding nuclear translational wavefunctions. A classification of the
wavefunction characteristics, namely the prolateness and ``peanut-likeness''
based on its statistical moments is also proposed.Comment: 14 pages, 14 figure
Homology of free quantum groups
We compute the Hochschild homology of the free orthogonal quantum group
. We show that it satisfies Poincar\'e duality and should be considered
to be a 3-dimensional object. We then use recent results of R. Vergnioux to
derive results about the -homology of and estimates on the
free entropy dimension of its set of generators. In particular, we show that
the Betti-numbers of all vanish and that the free entropy
dimension is less than 1.Comment: 8 page
Observation and inverse problems in coupled cell networks
A coupled cell network is a model for many situations such as food webs in
ecosystems, cellular metabolism, economical networks... It consists in a
directed graph , each node (or cell) representing an agent of the network
and each directed arrow representing which agent acts on which one. It yields a
system of differential equations , where the component
of depends only on the cells for which the arrow
exists in . In this paper, we investigate the observation problems in
coupled cell networks: can one deduce the behaviour of the whole network
(oscillations, stabilisation etc.) by observing only one of the cells? We show
that the natural observation properties holds for almost all the interactions
Open-source development experiences in scientific software: the HANDE quantum Monte Carlo project
The HANDE quantum Monte Carlo project offers accessible stochastic algorithms
for general use for scientists in the field of quantum chemistry. HANDE is an
ambitious and general high-performance code developed by a
geographically-dispersed team with a variety of backgrounds in computational
science. In the course of preparing a public, open-source release, we have
taken this opportunity to step back and look at what we have done and what we
hope to do in the future. We pay particular attention to development processes,
the approach taken to train students joining the project, and how a flat
hierarchical structure aids communicationComment: 6 pages. Submission to WSSSPE
Catastrophic regime shifts in model ecological communities are true phase transitions
Ecosystems often undergo abrupt regime shifts in response to gradual external
changes. These shifts are theoretically understood as a regime switch between
alternative stable states of the ecosystem dynamical response to smooth changes
in external conditions. Usual models introduce nonlinearities in the
macroscopic dynamics of the ecosystem that lead to different stable attractors
among which the shift takes place. Here we propose an alternative explanation
of catastrophic regime shifts based on a recent model that pictures ecological
communities as systems in continuous fluctuation, according to certain
transition probabilities, between different micro-states in the phase space of
viable communities. We introduce a spontaneous extinction rate that accounts
for gradual changes in external conditions, and upon variations on this control
parameter the system undergoes a regime shift with similar features to those
previously reported. Under our microscopic viewpoint we recover the main
results obtained in previous theoretical and empirical work (anomalous
variance, hysteresis cycles, trophic cascades). The model predicts a gradual
loss of species in trophic levels from bottom to top near the transition. But
more importantly, the spectral analysis of the transition probability matrix
allows us to rigorously establish that we are observing the fingerprints, in a
finite size system, of a true phase transition driven by background
extinctions.Comment: 19 pages, 11 figures, revised versio
Superposition as memory: unlocking quantum automatic complexity
Imagine a lock with two states, "locked" and "unlocked", which may be
manipulated using two operations, called 0 and 1. Moreover, the only way to
(with certainty) unlock using four operations is to do them in the sequence
0011, i.e., where . In this scenario one might think that the
lock needs to be in certain further states after each operation, so that there
is some memory of what has been done so far. Here we show that this memory can
be entirely encoded in superpositions of the two basic states "locked" and
"unlocked", where, as dictated by quantum mechanics, the operations are given
by unitary matrices. Moreover, we show using the Jordan--Schur lemma that a
similar lock is not possible for .
We define the semi-classical quantum automatic complexity of a
word as the infimum in lexicographic order of those pairs of nonnegative
integers such that there is a subgroup of the projective unitary
group PU with and with such that, in terms of a
standard basis and with , we have
and for all with . We show that is
unbounded and not constant for strings of a given length. In particular, and
.Comment: Lecture Notes in Computer Science, UCNC (Unconventional Computation
and Natural Computation) 201
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