8,737 research outputs found
Fractional supersymmetric Quantum Mechanics as a set of replicas of ordinary supersymmetric Quantum Mechanics
A connection between fractional supersymmetric quantum mechanics and ordinary
supersymmetric quantum mechanics is established in this Letter.Comment: Paper accepted for publication in Physics Letters
Bowtie-free graphs and generic automorphisms
We show that the -categorical existentially closed universal
bowtie-free graph of Cherlin-Shelah-Shi admits generic automorphisms in the
sense of Truss. Moreover, we show that this graph is not finitely
homogenisable.Comment: 14 page
A Context-theoretic Framework for Compositionality in Distributional Semantics
Techniques in which words are represented as vectors have proved useful in
many applications in computational linguistics, however there is currently no
general semantic formalism for representing meaning in terms of vectors. We
present a framework for natural language semantics in which words, phrases and
sentences are all represented as vectors, based on a theoretical analysis which
assumes that meaning is determined by context.
In the theoretical analysis, we define a corpus model as a mathematical
abstraction of a text corpus. The meaning of a string of words is assumed to be
a vector representing the contexts in which it occurs in the corpus model.
Based on this assumption, we can show that the vector representations of words
can be considered as elements of an algebra over a field. We note that in
applications of vector spaces to representing meanings of words there is an
underlying lattice structure; we interpret the partial ordering of the lattice
as describing entailment between meanings. We also define the context-theoretic
probability of a string, and, based on this and the lattice structure, a degree
of entailment between strings.
We relate the framework to existing methods of composing vector-based
representations of meaning, and show that our approach generalises many of
these, including vector addition, component-wise multiplication, and the tensor
product.Comment: Submitted to Computational Linguistics on 20th January 2010 for
revie
Representations and Properties of Generalized Statistics
A generalization of statistics is proposed and developed. The
generalized quantum statistics is completely specified by a set of
Jacobson generators satisfying a set of triple algebraic relations.
Fock-Hilbert representations and Bargmann-Fock realizations are derived.Comment: 12 pages, to appear in IJMPA (2006
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