386 research outputs found
Remarks on a five-dimensional Kaluza-Klein theory of the massive Dirac monopole
The Gross-Perry-Sorkin spacetime, formed by the Euclidean Taub-NUT space with
the time trivially added, is the appropriate background of the Dirac magnetic
monopole without an explicit mass term. One remarks that there exists a very
simple five-dimensional metric of spacetimes carrying massive magnetic
monopoles that is an exact solution of the vacuum Einstein equations. Moreover,
the same isometry properties as the original Euclidean Taub-NUT space are
preserved. This leads to an Abelian Kaluza-Klein theory whose metric appears as
a combinations between the Gross-Perry-Sorkin and Schwarzschild ones. The
asymptotic motion of the scalar charged test particles is discussed, now by
accounting for the mixing between the gravitational and magnetic effects.Comment: 7 page
Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context
Mathematical formulae represent complex semantic information in a concise
form. Especially in Science, Technology, Engineering, and Mathematics,
mathematical formulae are crucial to communicate information, e.g., in
scientific papers, and to perform computations using computer algebra systems.
Enabling computers to access the information encoded in mathematical formulae
requires machine-readable formats that can represent both the presentation and
content, i.e., the semantics, of formulae. Exchanging such information between
systems additionally requires conversion methods for mathematical
representation formats. We analyze how the semantic enrichment of formulae
improves the format conversion process and show that considering the textual
context of formulae reduces the error rate of such conversions. Our main
contributions are: (1) providing an openly available benchmark dataset for the
mathematical format conversion task consisting of a newly created test
collection, an extensive, manually curated gold standard and task-specific
evaluation metrics; (2) performing a quantitative evaluation of
state-of-the-art tools for mathematical format conversions; (3) presenting a
new approach that considers the textual context of formulae to reduce the error
rate for mathematical format conversions. Our benchmark dataset facilitates
future research on mathematical format conversions as well as research on many
problems in mathematical information retrieval. Because we annotated and linked
all components of formulae, e.g., identifiers, operators and other entities, to
Wikidata entries, the gold standard can, for instance, be used to train methods
for formula concept discovery and recognition. Such methods can then be applied
to improve mathematical information retrieval systems, e.g., for semantic
formula search, recommendation of mathematical content, or detection of
mathematical plagiarism.Comment: 10 pages, 4 figure
Generating random density matrices
We study various methods to generate ensembles of random density matrices of
a fixed size N, obtained by partial trace of pure states on composite systems.
Structured ensembles of random pure states, invariant with respect to local
unitary transformations are introduced. To analyze statistical properties of
quantum entanglement in bi-partite systems we analyze the distribution of
Schmidt coefficients of random pure states. Such a distribution is derived in
the case of a superposition of k random maximally entangled states. For another
ensemble, obtained by performing selective measurements in a maximally
entangled basis on a multi--partite system, we show that this distribution is
given by the Fuss-Catalan law and find the average entanglement entropy. A more
general class of structured ensembles proposed, containing also the case of
Bures, forms an extension of the standard ensemble of structureless random pure
states, described asymptotically, as N \to \infty, by the Marchenko-Pastur
distribution.Comment: 13 pages in latex with 8 figures include
Observables of the Euclidean Supergravity
The set of constraints under which the eigenvalues of the Dirac operator can
play the role of the dynamical variables for Euclidean supergravity is derived.
These constraints arise when the gauge invariance of the eigenvalues of the
Dirac operator is imposed. They impose conditions which restrict the
eigenspinors of the Dirac operator.Comment: Revised version, some misprints in the ecuations (11), (13) and (17)
corrected. The errors in the published version will appear cortected in a
future erratu
Hierarchy of Dirac, Pauli and Klein-Gordon conserved operators in Taub-NUT background
The algebra of conserved observables of the SO(4,1) gauge-invariant theory of
the Dirac fermions in the external field of the Kaluza-Klein monopole is
investigated. It is shown that the Dirac conserved operators have physical
parts associated with Pauli operators that are also conserved in the sense of
the Klein-Gordon theory. In this way one gets simpler methods of analyzing the
properties of the conserved Dirac operators and their main algebraic structures
including the representations of dynamical algebras governing the Dirac quantum
modes.Comment: 16 pages, latex, no figure
Programmable models of growth and mutation of cancer-cell populations
In this paper we propose a systematic approach to construct mathematical
models describing populations of cancer-cells at different stages of disease
development. The methodology we propose is based on stochastic Concurrent
Constraint Programming, a flexible stochastic modelling language. The
methodology is tested on (and partially motivated by) the study of prostate
cancer. In particular, we prove how our method is suitable to systematically
reconstruct different mathematical models of prostate cancer growth - together
with interactions with different kinds of hormone therapy - at different levels
of refinement.Comment: In Proceedings CompMod 2011, arXiv:1109.104
Evolutionary Events in a Mathematical Sciences Research Collaboration Network
This study examines long-term trends and shifting behavior in the
collaboration network of mathematics literature, using a subset of data from
Mathematical Reviews spanning 1985-2009. Rather than modeling the network
cumulatively, this study traces the evolution of the "here and now" using
fixed-duration sliding windows. The analysis uses a suite of common network
diagnostics, including the distributions of degrees, distances, and clustering,
to track network structure. Several random models that call these diagnostics
as parameters help tease them apart as factors from the values of others. Some
behaviors are consistent over the entire interval, but most diagnostics
indicate that the network's structural evolution is dominated by occasional
dramatic shifts in otherwise steady trends. These behaviors are not distributed
evenly across the network; stark differences in evolution can be observed
between two major subnetworks, loosely thought of as "pure" and "applied",
which approximately partition the aggregate. The paper characterizes two major
events along the mathematics network trajectory and discusses possible
explanatory factors.Comment: 30 pages, 14 figures, 1 table; supporting information: 5 pages, 5
figures; published in Scientometric
Random graph states, maximal flow and Fuss-Catalan distributions
For any graph consisting of vertices and edges we construct an
ensemble of random pure quantum states which describe a system composed of
subsystems. Each edge of the graph represents a bi-partite, maximally entangled
state. Each vertex represents a random unitary matrix generated according to
the Haar measure, which describes the coupling between subsystems. Dividing all
subsystems into two parts, one may study entanglement with respect to this
partition. A general technique to derive an expression for the average
entanglement entropy of random pure states associated to a given graph is
presented. Our technique relies on Weingarten calculus and flow problems. We
analyze statistical properties of spectra of such random density matrices and
show for which cases they are described by the free Poissonian
(Marchenko-Pastur) distribution. We derive a discrete family of generalized,
Fuss-Catalan distributions and explicitly construct graphs which lead to
ensembles of random states characterized by these novel distributions of
eigenvalues.Comment: 37 pages, 24 figure
Search for spontaneous muon emission from lead nuclei
We describe a possible search for muonic radioactivity from lead nuclei using
the base elements ("bricks" composed by lead and nuclear emulsion sheets) of
the long-baseline OPERA neutrino experiment. We present the results of a Monte
Carlo simulation concerning the expected event topologies and estimates of the
background events. Using few bricks, we could reach a good sensitivity level.Comment: 12 pages, 4 figure
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