27,397 research outputs found
Functorial Data Migration
In this paper we present a simple database definition language: that of
categories and functors. A database schema is a small category and an instance
is a set-valued functor on it. We show that morphisms of schemas induce three
"data migration functors", which translate instances from one schema to the
other in canonical ways. These functors parameterize projections, unions, and
joins over all tables simultaneously and can be used in place of conjunctive
and disjunctive queries. We also show how to connect a database and a
functional programming language by introducing a functorial connection between
the schema and the category of types for that language. We begin the paper with
a multitude of examples to motivate the definitions, and near the end we
provide a dictionary whereby one can translate database concepts into
category-theoretic concepts and vice-versa.Comment: 30 page
Two Optimal Strategies for Active Learning of Causal Models from Interventional Data
From observational data alone, a causal DAG is only identifiable up to Markov
equivalence. Interventional data generally improves identifiability; however,
the gain of an intervention strongly depends on the intervention target, that
is, the intervened variables. We present active learning (that is, optimal
experimental design) strategies calculating optimal interventions for two
different learning goals. The first one is a greedy approach using
single-vertex interventions that maximizes the number of edges that can be
oriented after each intervention. The second one yields in polynomial time a
minimum set of targets of arbitrary size that guarantees full identifiability.
This second approach proves a conjecture of Eberhardt (2008) indicating the
number of unbounded intervention targets which is sufficient and in the worst
case necessary for full identifiability. In a simulation study, we compare our
two active learning approaches to random interventions and an existing
approach, and analyze the influence of estimation errors on the overall
performance of active learning
A combinatorial realization of Schur-Weyl duality via crystal graphs and dual equivalence graphs
For any polynomial representation of the special linear group, the nodes of
the corresponding crystal may be indexed by semi-standard Young tableaux. Under
certain conditions, the standard Young tableaux occur, and do so with weight 0.
Standard Young tableaux also parametrize the vertices of dual equivalence
graphs. Motivated by the underlying representation theory, in this paper, we
explainthis connection by giving a combinatorial manifestation of Schur-Weyl
duality. In particular, we put a dual equivalence graph structure on the
0-weight space of certain crystal graphs, producing edges combinatorially from
the crystal edges. The construction can be expressed in terms of the local
characterizations given by Stembridge for crystal graphs and the author for
dual equivalence graphs.Comment: 9 pages, 6 figures To appear in DMTCS as part of the FPSAC 2008
conference proceeding
On palimpsests in neural memory: an information theory viewpoint
The finite capacity of neural memory and the
reconsolidation phenomenon suggest it is important to be able
to update stored information as in a palimpsest, where new
information overwrites old information. Moreover, changing
information in memory is metabolically costly. In this paper, we
suggest that information-theoretic approaches may inform the
fundamental limits in constructing such a memory system. In
particular, we define malleable coding, that considers not only
representation length but also ease of representation update,
thereby encouraging some form of recycling to convert an old
codeword into a new one. Malleability cost is the difficulty of
synchronizing compressed versions, and malleable codes are of
particular interest when representing information and modifying
the representation are both expensive. We examine the tradeoff
between compression efficiency and malleability cost, under a
malleability metric defined with respect to a string edit distance.
This introduces a metric topology to the compressed domain. We
characterize the exact set of achievable rates and malleability as
the solution of a subgraph isomorphism problem. This is all done
within the optimization approach to biology framework.Accepted manuscrip
Leavitt path algebras: the first decade
The algebraic structures known as {\it Leavitt path algebras} were initially
developed in 2004 by Ara, Moreno and Pardo, and almost simultaneously (using a
different approach) by the author and Aranda Pino.
During the intervening decade, these algebras have attracted significant
interest and attention, not only from ring theorists, but from analysts working
in C-algebras, group theorists, and symbolic dynamicists as well. The goal
of this article is threefold: to introduce the notion of Leavitt path algebras
to the general mathematical community; to present some of the important results
in the subject; and to describe some of the field's currently unresolved
questions.Comment: 53 pages. To appear, Bulletin of Mathematical Sciences. (page
numbering in arXiv version will differ from page numbering in BMS published
version; numbering of Theorems, etc ... will be the same in both versions
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