1,646 research outputs found
Ontology: A Linked Data Hub for Mathematics
In this paper, we present an ontology of mathematical knowledge concepts that
covers a wide range of the fields of mathematics and introduces a balanced
representation between comprehensive and sensible models. We demonstrate the
applications of this representation in information extraction, semantic search,
and education. We argue that the ontology can be a core of future integration
of math-aware data sets in the Web of Data and, therefore, provide mappings
onto relevant datasets, such as DBpedia and ScienceWISE.Comment: 15 pages, 6 images, 1 table, Knowledge Engineering and the Semantic
Web - 5th International Conferenc
Approximate substitutions and the normal ordering problem
In this paper, we show that the infinite generalised Stirling matrices
associated with boson strings with one annihilation operator are projective
limits of approximate substitutions, the latter being characterised by a finite
set of algebraic equations
Popularity-Driven Networking
We investigate the growth of connectivity in a network. In our model,
starting with a set of disjoint nodes, links are added sequentially. Each link
connects two nodes, and the connection rate governing this random process is
proportional to the degrees of the two nodes. Interestingly, this network
exhibits two abrupt transitions, both occurring at finite times. The first is a
percolation transition in which a giant component, containing a finite fraction
of all nodes, is born. The second is a condensation transition in which the
entire system condenses into a single, fully connected, component. We derive
the size distribution of connected components as well as the degree
distribution, which is purely exponential throughout the evolution.
Furthermore, we present a criterion for the emergence of sudden condensation
for general homogeneous connection rates.Comment: 5 pages, 2 figure
Entropy calculation for a toy black hole
In this note we carry out the counting of states for a black hole in loop
quantum gravity, however assuming an equidistant area spectrum. We find that
this toy-model is exactly solvable, and we show that its behavior is very
similar to that of the correct model. Thus this toy-model can be used as a nice
and simplifying `laboratory' for questions about the full theory.Comment: 18 pages, 4 figures. v2: Corrected mistake in bibliography, added
appendix with further result
Completeness of the Bethe Ansatz solution of the open XXZ chain with nondiagonal boundary terms
A Bethe Ansatz solution of the open spin-1/2 XXZ quantum spin chain with
nondiagonal boundary terms has recently been proposed. Using a numerical
procedure developed by McCoy et al., we find significant evidence that this
solution can yield the complete set of eigenvalues for generic values of the
bulk and boundary parameters satisfying one linear relation. Moreover, our
results suggest that this solution is practical for investigating the ground
state of this model in the thermodynamic limit.Comment: 15 pages, LaTeX; amssymb, amsmath, no figures, 5 tables; v2 contains
an additional footnote and a "Note Added"; v3 contains an Addendu
Monomiality principle, Sheffer-type polynomials and the normal ordering problem
We solve the boson normal ordering problem for
with arbitrary functions and and integer , where and
are boson annihilation and creation operators, satisfying
. This consequently provides the solution for the exponential
generalizing the shift operator. In the
course of these considerations we define and explore the monomiality principle
and find its representations. We exploit the properties of Sheffer-type
polynomials which constitute the inherent structure of this problem. In the end
we give some examples illustrating the utility of the method and point out the
relation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics
"Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005),
Myczkowce, Poland. 13 pages, 31 reference
The maximally entangled symmetric state in terms of the geometric measure
The geometric measure of entanglement is investigated for permutation
symmetric pure states of multipartite qubit systems, in particular the question
of maximum entanglement. This is done with the help of the Majorana
representation, which maps an n qubit symmetric state to n points on the unit
sphere. It is shown how symmetries of the point distribution can be exploited
to simplify the calculation of entanglement and also help find the maximally
entangled symmetric state. Using a combination of analytical and numerical
results, the most entangled symmetric states for up to 12 qubits are explored
and discussed. The optimization problem on the sphere presented here is then
compared with two classical optimization problems on the S^2 sphere, namely
Toth's problem and Thomson's problem, and it is observed that, in general, they
are different problems.Comment: 18 pages, 15 figures, small corrections and additions to contents and
reference
Codes for the Quantum Erasure Channel
The quantum erasure channel (QEC) is considered. Codes for the QEC have to
correct for erasures, i. e., arbitrary errors at known positions. We show that
four qubits are necessary and sufficient to encode one qubit and correct one
erasure, in contrast to five qubits for unknown positions. Moreover, a family
of quantum codes for the QEC, the quantum BCH codes, that can be efficiently
decoded is introduced.Comment: 6 pages, RevTeX, no figures, submitted to Physical Review A, code
extended to encode 2 qubits, references adde
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