113,988 research outputs found
Identikit 2: An Algorithm for Reconstructing Galactic Collisions
Using a combination of self-consistent and test-particle techniques,
Identikit 1 provided a way to vary the initial geometry of a galactic collision
and instantly visualize the outcome. Identikit 2 uses the same techniques to
define a mapping from the current morphology and kinematics of a tidal
encounter back to the initial conditions. By requiring that various regions
along a tidal feature all originate from a single disc with a unique
orientation, this mapping can be used to derive the initial collision geometry.
In addition, Identikit 2 offers a robust way to measure how well a particular
model reproduces the morphology and kinematics of a pair of interacting
galaxies. A set of eight self-consistent simulations is used to demonstrate the
algorithm's ability to search a ten-dimensional parameter space and find
near-optimal matches; all eight systems are successfully reconstructed.Comment: 14 pages, 8 figures. Accepted for publication in MNRAS. To get a copy
with high-resolution figures, use the web interface, or download the
Identikit software, visit
http://www.ifa.hawaii.edu/faculty/barnes/research/identikit
Max-sum diversity via convex programming
Diversity maximization is an important concept in information retrieval,
computational geometry and operations research. Usually, it is a variant of the
following problem: Given a ground set, constraints, and a function
that measures diversity of a subset, the task is to select a feasible subset
such that is maximized. The \emph{sum-dispersion} function , which is the sum of the pairwise distances in , is
in this context a prominent diversification measure. The corresponding
diversity maximization is the \emph{max-sum} or \emph{sum-sum diversification}.
Many recent results deal with the design of constant-factor approximation
algorithms of diversification problems involving sum-dispersion function under
a matroid constraint. In this paper, we present a PTAS for the max-sum
diversification problem under a matroid constraint for distances
of \emph{negative type}. Distances of negative type are, for
example, metric distances stemming from the and norm, as well
as the cosine or spherical, or Jaccard distance which are popular similarity
metrics in web and image search
Exchange of Geometric Information Between Applications
The Web Geometry Laboratory (WGL) is a collaborative and adaptive e-learning
Web platform integrating a well known dynamic geometry system. Thousands of
Geometric problems for Geometric Theorem Provers (TGTP) is a Web-based
repository of geometric problems to support the testing and evaluation of
geometric automated theorem proving systems.
The users of these systems should be able to profit from each other. The TGTP
corpus must be made available to the WGL user, allowing, in this way, the
exploration of TGTP problems and their proofs. On the other direction TGTP
could gain by the possibility of a wider users base submitting new problems.
Such information exchange between clients (e.g. WGL) and servers (e.g. TGTP)
raises many issues: geometric search - someone, working in a geometric problem,
must be able to ask for more information regarding that construction; levels of
geometric knowledge and interest - the problems in the servers must be
classified in such a way that, in response to a client query, only the problems
in the user's level and/or interest are returned; different aims of each tool -
e.g. WGL is about secondary school geometry, TGTP is about formal proofs in
semi-analytic and algebraic proof methods, not a perfect match indeed;
localisation issues, e.g. a Portuguese user obliged to make the query and
process the answer in English; technical issues-many technical issues need to
be addressed to make this exchange of geometric information possible and
useful.
Instead of a giant (difficult to maintain) tool, trying to cover all, the
interconnection of specialised tools seems much more promising. The challenges
to make that connection work are many and difficult, but, it is the authors
impression, not insurmountable.Comment: In Proceedings ThEdu'17, arXiv:1803.0072
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
Escaping the Trap of too Precise Topic Queries
At the very center of digital mathematics libraries lie controlled
vocabularies which qualify the {\it topic} of the documents. These topics are
used when submitting a document to a digital mathematics library and to perform
searches in a library. The latter are refined by the use of these topics as
they allow a precise classification of the mathematics area this document
addresses. However, there is a major risk that users employ too precise topics
to specify their queries: they may be employing a topic that is only "close-by"
but missing to match the right resource. We call this the {\it topic trap}.
Indeed, since 2009, this issue has appeared frequently on the i2geo.net
platform. Other mathematics portals experience the same phenomenon. An approach
to solve this issue is to introduce tolerance in the way queries are understood
by the user. In particular, the approach of including fuzzy matches but this
introduces noise which may prevent the user of understanding the function of
the search engine.
In this paper, we propose a way to escape the topic trap by employing the
navigation between related topics and the count of search results for each
topic. This supports the user in that search for close-by topics is a click
away from a previous search. This approach was realized with the i2geo search
engine and is described in detail where the relation of being {\it related} is
computed by employing textual analysis of the definitions of the concepts
fetched from the Wikipedia encyclopedia.Comment: 12 pages, Conference on Intelligent Computer Mathematics 2013 Bath,
U
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