396 research outputs found
Multi-step Richardson-Romberg Extrapolation: Remarks on Variance Control and complexity
We propose a multi-step Richardson-Romberg extrapolation method for the
computation of expectations of a diffusion
when the weak time discretization error induced by the Euler scheme admits an
expansion at an order . The complexity of the estimator grows as
(instead of ) and its variance is asymptotically controlled by considering
some consistent Brownian increments in the underlying Euler schemes. Some Monte
carlo simulations carried with path-dependent options (lookback, barriers)
which support the conjecture that their weak time discretization error also
admits an expansion (in a different scale). Then an appropriate
Richardson-Romberg extrapolation seems to outperform the Euler scheme with
Brownian bridge.Comment: 28 pages, \`a para\^itre dans Monte Carlo Methods and Applications
Journa
Finite one dimensional impenetrable Bose systems: Occupation numbers
Bosons in the form of ultra cold alkali atoms can be confined to a one
dimensional (1d) domain by the use of harmonic traps. This motivates the study
of the ground state occupations of effective single particle states
, in the theoretical 1d impenetrable Bose gas. Both the system on a
circle and the harmonically trapped system are considered. The and
are the eigenvalues and eigenfunctions respectively of the one body
density matrix. We present a detailed numerical and analytic study of this
problem. Our main results are the explicit scaled forms of the density
matrices, from which it is deduced that for fixed the occupations
are asymptotically proportional to in both the circular
and harmonically trapped cases.Comment: 22 pages, 8 figures (.eps), uses REVTeX
Entanglement Percolation with Bipartite Mixed States
We develop a concept of entanglement percolation for long-distance singlet
generation in quantum networks with neighboring nodes connected by partially
entangled bipartite mixed states. We give a necessary and sufficient condition
on the class of mixed network states for the generation of singlets. States
beyond this class are insufficient for entanglement percolation. We find that
neighboring nodes are required to be connected by multiple partially entangled
states and devise a rich variety of distillation protocols for the conversion
of these states into singlets. These distillation protocols are suitable for a
variety of network geometries and have a sufficiently high success probability
even for significantly impure states. In addition to this, we discuss possible
further improvements achievable by using quantum strategies including
generalized forms of entanglement swapping.Comment: 6+ pages, 5 figures; Published versio
Structural and temporal patterns of the first global trading market
Little is known about the structural patterns and dynamics of the first global trading market (FGTM), which emerged during the sixteenth century as a result of the Iberian expansion, let alone how it compares to today's global financial markets. Here we build a representative network of the FGTM using information contained in 8725 (handwritten) Bills of Exchange from that time-which were (human) interpreted and digitalized into an online database. We show that the resulting temporal network exhibits a hierarchical, highly clustered and disassortative structure, with a power-law dependence on the connectivity that remains remarkably robust throughout the entire period investigated. Temporal analysis shows that, despite major turnovers in the number and nature of the links-suggesting fast adaptation in response to the geopolitical and financial turmoil experienced at the time-the overall characteristics of the FGTM remain robust and virtually unchanged. The methodology developed here demonstrates the possibility of building and analysing complex trading and finance networks originating from pre-statistical eras, enabling us to highlight the striking similarities between the structural patterns of financial networks separated by centuries in time.This research was supported by FCT-Portugal through grant nos FCT-TECH/0002/2007 (A.S.R. and A.P.), SFRH/BD/77389/2011 (F.L.P.), SFRH/BPD/76278/2011 (A.S.R.), PTDC/MAT-STA/3358/2014 (F.L.P., F.C.S. and J.M.P.), PTDC/EEI-SII/5081/2014 (F.L.P., F.C.S. and J.M.P.), UID/BIA/04050/2013 (J.M.P.) and UID/CEC/50021/2013 (F.C.S.), and by the European Science Foundation through grant no. DynCoopNet-06-TECT-FP-004 (A.S.R. and A.P.)
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