15,000 research outputs found
Quaternions, octonions and Bell-type inequalities
Multipartite Bell-type inequalities are derived for general systems. They
involve up to eight observables with arbitrary spectra on each site. These
inequalities are closely related to the algebras of quaternions and octonions.Comment: 4 pages, no figure
Relaxed Bell inequalities and Kochen-Specker theorems
The combination of various physically plausible properties, such as no
signaling, determinism, and experimental free will, is known to be incompatible
with quantum correlations. Hence, these properties must be individually or
jointly relaxed in any model of such correlations. The necessary degrees of
relaxation are quantified here, via natural distance and information-theoretic
measures. This allows quantitative comparisons between different models in
terms of the resources, such as the number of bits, of randomness,
communication, and/or correlation, that they require. For example, measurement
dependence is a relatively strong resource for modeling singlet state
correlations, with only 1/15 of one bit of correlation required between
measurement settings and the underlying variable. It is shown how various
'relaxed' Bell inequalities may be obtained, which precisely specify the
complementary degrees of relaxation required to model any given violation of a
standard Bell inequality. The robustness of a class of Kochen-Specker theorems,
to relaxation of measurement independence, is also investigated. It is shown
that a theorem of Mermin remains valid unless measurement independence is
relaxed by 1/3. The Conway-Kochen 'free will' theorem and a result of Hardy are
less robust, failing if measurement independence is relaxed by only 6.5% and
4.5%, respectively. An appendix shows the existence of an outcome independent
model is equivalent to the existence of a deterministic model.Comment: 19 pages (including 3 appendices); v3: minor clarifications, to
appear in PR
The Impacts of Climate Change on Chinese Agriculture - Phase II National Level Study final report
Quaternionic Root Systems and Subgroups of the
Cayley-Dickson doubling procedure is used to construct the root systems of
some celebrated Lie algebras in terms of the integer elements of the division
algebras of real numbers, complex numbers, quaternions and octonions. Starting
with the roots and weights of SU(2) expressed as the real numbers one can
construct the root systems of the Lie algebras of SO(4),SP(2)=
SO(5),SO(8),SO(9),F_{4} and E_{8} in terms of the discrete elements of the
division algebras. The roots themselves display the group structures besides
the octonionic roots of E_{8} which form a closed octonion algebra. The
automorphism group Aut(F_{4}) of the Dynkin diagram of F_{4} of order 2304, the
largest crystallographic group in 4-dimensional Euclidean space, is realized as
the direct product of two binary octahedral group of quaternions preserving the
quaternionic root system of F_{4}.The Weyl groups of many Lie algebras, such
as, G_{2},SO(7),SO(8),SO(9),SU(3)XSU(3) and SP(3)X SU(2) have been constructed
as the subgroups of Aut(F_{4}). We have also classified the other non-parabolic
subgroups of Aut(F_{4}) which are not Weyl groups. Two subgroups of orders192
with different conjugacy classes occur as maximal subgroups in the finite
subgroups of the Lie group of orders 12096 and 1344 and proves to be
useful in their constructions. The triality of SO(8) manifesting itself as the
cyclic symmetry of the quaternionic imaginary units e_{1},e_{2},e_{3} is used
to show that SO(7) and SO(9) can be embedded triply symmetric way in SO(8) and
F_{4} respectively
A stochastic template placement algorithm for gravitational wave data analysis
This paper presents an algorithm for constructing matched-filter template
banks in an arbitrary parameter space. The method places templates at random,
then removes those which are "too close" together. The properties and
optimality of stochastic template banks generated in this manner are
investigated for some simple models. The effectiveness of these template banks
for gravitational wave searches for binary inspiral waveforms is also examined.
The properties of a stochastic template bank are then compared to the
deterministically placed template banks that are currently used in
gravitational wave data analysis.Comment: 14 pages, 11 figure
Future cereal production in China: Modelling the interaction of climate change, water availability and socio-economic scenarios. The Impacts of Climate Change on Chinese Agriculture – Phase II Final Report
Improved Stack-Slide Searches for Gravitational-Wave Pulsars
We formulate and optimize a computational search strategy for detecting
gravitational waves from isolated, previously-unknown neutron stars (that is,
neutron stars with unknown sky positions, spin frequencies, and spin-down
parameters). It is well known that fully coherent searches over the relevant
parameter-space volumes are not computationally feasible, and so more
computationally efficient methods are called for. The first step in this
direction was taken by Brady & Creighton (2000), who proposed and optimized a
two-stage, stack-slide search algorithm. We generalize and otherwise improve
upon the Brady-Creighton scheme in several ways. Like Brady & Creighton, we
consider a stack-slide scheme, but here with an arbitrary number of
semi-coherent stages and with a coherent follow-up stage at the end. We find
that searches with three semi-coherent stages are significantly more efficient
than two-stage searches (requiring about 2-5 times less computational power for
the same sensitivity) and are only slightly less efficient than searches with
four or more stages. We calculate the signal-to-noise ratio required for
detection, as a function of computing power and neutron star spin-down-age,
using our optimized searches.Comment: 19 pages, 7 figures, RevTeX
Random lattice superstrings
We propose some new simplifying ingredients for Feynman diagrams that seem
necessary for random lattice formulations of superstrings. In particular, half
the fermionic variables appear only in particle loops (similarly to loop
momenta), reducing the supersymmetry of the constituents of the Type IIB
superstring to N=1, as expected from their interpretation in the 1/N expansion
as super Yang-Mills.Comment: Section 5 which describes contributions of the string measure adde
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