45,930 research outputs found
Total Representations
Almost all representations considered in computable analysis are partial. We
provide arguments in favor of total representations (by elements of the Baire
space). Total representations make the well known analogy between numberings
and representations closer, unify some terminology, simplify some technical
details, suggest interesting open questions and new invariants of topological
spaces relevant to computable analysis.Comment: 30 page
Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension
A fundamental problem in the dimension theory of self-affine sets is the
construction of high-dimensional measures which yield sharp lower bounds for
the Hausdorff dimension of the set. A natural strategy for the construction of
such high-dimensional measures is to investigate measures of maximal Lyapunov
dimension; these measures can be alternatively interpreted as equilibrium
states of the singular value function introduced by Falconer. Whilst the
existence of these equilibrium states has been well-known for some years their
structure has remained elusive, particularly in dimensions higher than two. In
this article we give a complete description of the equilibrium states of the
singular value function in the three-dimensional case, showing in particular
that all such equilibrium states must be fully supported. In higher dimensions
we also give a new sufficient condition for the uniqueness of these equilibrium
states. As a corollary, giving a solution to a folklore open question in
dimension three, we prove that for a typical self-affine set in ,
removing one of the affine maps which defines the set results in a strict
reduction of the Hausdorff dimension
Measure equivalence rigidity of the mapping class group
We show that the mapping class group of a compact orientable surface with
higher complexity has the following extreme rigidity in the sense of measure
equivalence: if the mapping class group is measure equivalent to a discrete
group, then they are commensurable up to finite kernel. Moreover, we describe
all lattice embeddings of the mapping class group into a locally compact second
countable group. We also obtain similar results for finite direct products of
mapping class groups.Comment: 39 page
Linearly Typed Dyadic Group Sessions for Building Multiparty Sessions
Traditionally, each party in a (dyadic or multiparty) session implements
exactly one role specified in the type of the session. We refer to this kind of
session as an individual session (i-session). As a generalization of i-session,
a group session (g-session) is one in which each party may implement a group of
roles based on one channel. In particular, each of the two parties involved in
a dyadic g-session implements either a group of roles or its complement. In
this paper, we present a formalization of g-sessions in a multi-threaded
lambda-calculus (MTLC) equipped with a linear type system, establishing for the
MTLC both type preservation and global progress. As this formulated MTLC can be
readily embedded into ATS, a full-fledged language with a functional
programming core that supports both dependent types (of DML-style) and linear
types, we obtain a direct implementation of linearly typed g-sessions in ATS.
The primary contribution of the paper lies in both of the identification of
g-sessions as a fundamental building block for multiparty sessions and the
theoretical development in support of this identification.Comment: This paper can be seen as the pre-sequel to classical linear
multirole logic (CLML). arXiv admin note: substantial text overlap with
arXiv:1603.0372
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