28,836 research outputs found
Forecasts of the Scottish economy [March 2013]
After two quarters of negative growth, the Scottish economy delivered a strong performance in the third quarter of 2012. The UK economy as a whole saw negative growth in the final quarter of 2012 - and it looks likely that Scottish growth over 2012 will be close to zero. Over the coming year, we see slowing earnings growth, the introduction of welfare changes and continued fiscal consolidation weakening the domestic economy, while there could be increasing volatility, including potentially critical political shocks, in important export markets. The net result is a lowering of our central growth forecasts for 2013 and 2014. It continues to be true that risks are aligned to the downside again. Growth in the United States – Scotland's single largest export market – appears strong, highlighting opportunities, albeit further concentrating Scottish reliance on this market
Solving Hard Computational Problems Efficiently: Asymptotic Parametric Complexity 3-Coloring Algorithm
Many practical problems in almost all scientific and technological
disciplines have been classified as computationally hard (NP-hard or even
NP-complete). In life sciences, combinatorial optimization problems frequently
arise in molecular biology, e.g., genome sequencing; global alignment of
multiple genomes; identifying siblings or discovery of dysregulated pathways.In
almost all of these problems, there is the need for proving a hypothesis about
certain property of an object that can be present only when it adopts some
particular admissible structure (an NP-certificate) or be absent (no admissible
structure), however, none of the standard approaches can discard the hypothesis
when no solution can be found, since none can provide a proof that there is no
admissible structure. This article presents an algorithm that introduces a
novel type of solution method to "efficiently" solve the graph 3-coloring
problem; an NP-complete problem. The proposed method provides certificates
(proofs) in both cases: present or absent, so it is possible to accept or
reject the hypothesis on the basis of a rigorous proof. It provides exact
solutions and is polynomial-time (i.e., efficient) however parametric. The only
requirement is sufficient computational power, which is controlled by the
parameter . Nevertheless, here it is proved that the
probability of requiring a value of to obtain a solution for a
random graph decreases exponentially: , making
tractable almost all problem instances. Thorough experimental analyses were
performed. The algorithm was tested on random graphs, planar graphs and
4-regular planar graphs. The obtained experimental results are in accordance
with the theoretical expected results.Comment: Working pape
Statistics of the polariton condensate
The influence of polariton-polariton scattering on the statistics of the
polariton condensate in a non-resonantly excited semiconductor quantum well
embedded in a CdTe semiconductor microcavity is discussed. Taking advantage of
the existence of a bottleneck in the polariton dispersion curve, the polariton
states are separated into two domains: reservoir polaritons inside the
bottleneck and active polaritons with wave vector q whose energy lies below the
bottleneck. In the framework of the master equation formalism, the
non-equilibrium stationary reduced density matrix is calculated and the
statistics of polaritons in the condensate at q=0 is determined. The anomalous
correlations between the polaritons in the condensate and those with wave
vectors q, -q leads to an enhancement of the noise in the condensate. As a
consequence, the second order correlation function of the condensate does not
show the full coherence that is characteristic of laser emission.Comment: 35 pages, 5 figure
Asymptotic cosmological solutions for string/brane gases with solitonic fluxes
We present new cosmological solutions for brane gases with solitonic fluxes
that can dynamically explain the existence of three large spatial dimensions.
This reasserts the importance of fluxes for understanding the full space of
solutions in a potential implementation of the Brandenberger-Vafa mechanism
with M2-branes. Additionally, we study a particular example in which the
cosmological dynamics supported by a string gas with a NS flux in the
ten-dimensional dilaton gravity framework is asymptotically equivalent to that
of a M2-brane gas with a certain wrapping configuration in eleven-dimensional
supergravity. We speculate that this connection between the ten- and
eleven-dimensional implementations of the Brandenberger-Vafa mechanism could be
a general feature.Comment: 9 pages, 2 figures, revtex
- …