101 research outputs found
Hamming distance kernelisation via topological quantum computation
We present a novel approach to computing Hamming distance and its kernelisation within Topological Quantum Computation. This approach is based on an encoding of two binary strings into a topological Hilbert space, whose inner product yields a natural Hamming distance kernel on the two strings. Kernelisation forges a link with the field of Machine Learning, particularly in relation to binary classifiers such as the Support Vector Machine (SVM). This makes our approach of potential interest to the quantum machine learning community
VLT/NACO astrometry of the HR8799 planetary system. L'-band observations of the three outer planets
HR8799 is so far the only directly imaged multiple exoplanet system. The
orbital configuration would, if better known, provide valuable insight into the
formation and dynamical evolution of wide-orbit planetary systems. We present
L'-band observations of the HR8799 system obtained with NACO at VLT, adding to
the astrometric monitoring of the planets HR8799b, c and d. We investigate how
well the two simple cases of (i) a circular orbit and (ii) a face-on orbit fit
the astrometric data for HR8799d over a total time baseline of ~2 years. The
results indicate that the orbit of HR8799d is inclined with respect to our line
of sight, and suggest that the orbit is slightly eccentric or non-coplanar with
the outer planets and debris disk.Comment: 5 pages, 4 figures, 1 table, accepted for publication in A\&A.
Updated version includes minor changes made in the proof
On insertion-deletion systems over relational words
We introduce a new notion of a relational word as a finite totally ordered
set of positions endowed with three binary relations that describe which
positions are labeled by equal data, by unequal data and those having an
undefined relation between their labels. We define the operations of insertion
and deletion on relational words generalizing corresponding operations on
strings. We prove that the transitive and reflexive closure of these operations
has a decidable membership problem for the case of short insertion-deletion
rules (of size two/three and three/two). At the same time, we show that in the
general case such systems can produce a coding of any recursively enumerable
language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure
The cold origin of the warm dust around epsilon Eridani
Context: The K2V star eps Eri hosts one known inner planet, an outer Kuiper
belt analog, and an inner disk of warm dust. Spitzer/IRS measurements indicate
that the warm dust is present at distances as close as a few AU from the star.
Its origin is puzzling, since an "asteroid belt" that could produce this dust
would be unstable because of the known inner planet. Aims: Here we test the
hypothesis that the observed warm dust is generated by collisions in the outer
belt and is transported inward by Poynting-Robertson (P-R) drag and strong
stellar winds. Methods: We simulated a steady-state distribution of dust
particles outside 10AU with a collisional code and in the inner region (r<10AU)
with single-particle numerical integrations. By assuming homogeneous spherical
dust grains composed of water ice and silicate, we calculated the thermal
emission of the dust and compared it with observations. We investigated two
different orbital configurations for the inner planet inferred from RV
measurements, one with a highly eccentric orbit of e=0.7 and another one with a
moderate one of e=0.25. We also produced a simulation without a planet.
Results: Our models can reproduce the shape and magnitude of the observed SED
from mid-IR to sub-mm wavelengths, as well as the Spitzer/MIPS radial
brightness profiles. The best-fit dust composition includes both ice and
silicates. The results are similar for the two possible planetary orbits and
without a planet. Conclusions: The observed warm dust in the system can indeed
stem from the outer belt and be transported inward by P-R and stellar wind
drag. The inner planet has little effect on the distribution of dust, so that
the planetary orbit could not be constrained. Reasonable agreement between the
model and observations can only be achieved by relaxing the assumption of
purely silicate dust and assuming a mixture of silicate and ice in comparable
amounts.Comment: 9 pages, 9 figures, abstract abridge
Quantum Holonomy in Three-dimensional General Covariant Field Theory and Link Invariant
We consider quantum holonomy of some three-dimensional general covariant
non-Abelian field theory in Landau gauge and confirm a previous result
partially proven. We show that quantum holonomy retains metric independence
after explicit gauge fixing and hence possesses the topological property of a
link invariant. We examine the generalized quantum holonomy defined on a
multi-component link and discuss its relation to a polynomial for the link.Comment: RevTex, 12 pages. The metric independence of path integral measure is
justified and the case of multi-component link is discussed in detail. To be
published in Physical Review
On the relation between the connection and the loop representation of quantum gravity
Using Penrose binor calculus for () tensor expressions, a
graphical method for the connection representation of Euclidean Quantum Gravity
(real connection) is constructed. It is explicitly shown that: {\it (i)} the
recently proposed scalar product in the loop-representation coincide with the
Ashtekar-Lewandoski cylindrical measure in the space of connections; {\it (ii)}
it is possible to establish a correspondence between the operators in the
connection representation and those in the loop representation. The
construction is based on embedded spin network, the Penrose graphical method of
calculus, and the existence of a generalized measure on the space of
connections modulo gauge transformations.Comment: 19 pages, ioplppt.sty and epsfig.st
The Architectural Design Rules of Solar Systems based on the New Perspective
On the basis of the Lunar Laser Ranging Data released by NASA on the Silver
Jubilee Celebration of Man Landing on Moon on 21st July 1969-1994, theoretical
formulation of Earth-Moon tidal interaction was carried out and Planetary
Satellite Dynamics was established. It was found that this mathematical
analysis could as well be applied to Star and Planets system and since every
star could potentially contain an extra-solar system, hence we have a large
ensemble of exoplanets to test our new perspective on the birth and evolution
of solar systems. Till date 403 exoplanets have been discovered in 390
extra-solar systems. I have taken 12 single planet systems, 4 Brown Dwarf -
Star systems and 2 Brown Dwarf pairs. Following architectural design rules are
corroborated through this study of exoplanets. All planets are born at inner
Clarke Orbit what we refer to as inner geo-synchronous orbit in case of
Earth-Moon System. By any perturbative force such as cosmic particles or
radiation pressure, the planet gets tipped long of aG1 or short of aG1. Here
aG1 is inner Clarke Orbit. The exoplanet can either be launched on death spiral
as CLOSE HOT JUPITERS or can be launched on an expanding spiral path as the
planets in our Solar System are. It was also found that if the exo-planet are
significant fraction of the host star then those exo-planets rapidly migrate
from aG1 to aG2 and have very short Time Constant of Evolution as Brown Dwarfs
have. This vindicates our basic premise that planets are always born at inner
Clarke Orbit. This study vindicates the design rules which had been postulated
at 35th COSPAR Scientific Assembly in 2004 at Paris, France, under the title
,New Perspective on the Birth & Evolution of Solar Systems.Comment: This paper has been reported to Earth,Moon and Planets Journal as
MOON-S-09-0007
Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice
The statistical properties of random lattice knots, the topology of which is
determined by the algebraic topological Jones-Kauffman invariants was studied
by analytical and numerical methods. The Kauffman polynomial invariant of a
random knot diagram was represented by a partition function of the Potts model
with a random configuration of ferro- and antiferromagnetic bonds, which
allowed the probability distribution of the random dense knots on a flat square
lattice over topological classes to be studied. A topological class is
characterized by the highest power of the Kauffman polynomial invariant and
interpreted as the free energy of a q-component Potts spin system for
q->infinity. It is shown that the highest power of the Kauffman invariant is
correlated with the minimum energy of the corresponding Potts spin system. The
probability of the lattice knot distribution over topological classes was
studied by the method of transfer matrices, depending on the type of local
junctions and the size of the flat knot diagram. The obtained results are
compared to the probability distribution of the minimum energy of a Potts
system with random ferro- and antiferromagnetic bonds.Comment: 37 pages, latex-revtex (new version: misprints removed, references
added
The scattering of small bodies in planetary systems: constraints on the possible orbits of cometary material
The scattering of small bodies by planets is an important dynamical process
in planetary systems. We present an analytical model to describe this process
using the simplifying assumption that each particle's dynamics is dominated by
a single planet at a time. As such the scattering process can be considered as
a series of three body problems during each of which the Tisserand parameter
with respect to the relevant planet is conserved. This constrains the orbital
parameter space into which a particle can be scattered. Such arguments have
previously been applied to the process by which comets are scattered to the
inner Solar System from the Kuiper belt. Our analysis generalises this for an
arbitrary planetary system. For particles scattered from an outer belt directly
along a chain of planets, based on the initial value of the Tisserand
parameter, we find that it is possible to (i) determine which planets can eject
the particles from the system, (ii) define a minimum stellar distance to which
particles can be scattered, and (iii) constrain range of particle inclinations
(and hence the disc height) at different distances. Applying this to the Solar
System, we determine that the planets are close to optimally separated for
scattering particles between them. Concerning warm dust found around stars that
also have Kuiper belt analogues, we show that, if there is to be a dynamical
link between the outer and inner regions, then certain architectures for the
intervening planetary system are incapable of producing the observations.
Furthermore we show that for certain planetary systems, comets can be scattered
from an outer belt, or with fewer constraints, from an Oort cloud analogue,
onto star-grazing orbits, in support of a planetary origin to the metal
pollution and dustiness of some nearby white dwarfs
Barrier and internal wave contributions to the quantum probability density and flux in light heavy-ion elastic scattering
We investigate the properties of the optical model wave function for light
heavy-ion systems where absorption is incomplete, such as Ca
and O around 30 MeV incident energy. Strong focusing effects
are predicted to occur well inside the nucleus, where the probability density
can reach values much higher than that of the incident wave. This focusing is
shown to be correlated with the presence at back angles of a strong enhancement
in the elastic cross section, the so-called ALAS (anomalous large angle
scattering) phenomenon; this is substantiated by calculations of the quantum
probability flux and of classical trajectories. To clarify this mechanism, we
decompose the scattering wave function and the associated probability flux into
their barrier and internal wave contributions within a fully quantal
calculation. Finally, a calculation of the divergence of the quantum flux shows
that when absorption is incomplete, the focal region gives a sizeable
contribution to nonelastic processes.Comment: 16 pages, 15 figures. RevTeX file. To appear in Phys. Rev. C. The
figures are only available via anonynous FTP on
ftp://umhsp02.umh.ac.be/pub/ftp_pnt/figscat
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