1,009 research outputs found
Three-dimensional simplicial gravity and combinatorics of group presentations
We demonstrate how some problems arising in simplicial quantum gravity can be
successfully addressed within the framework of combinatorial group theory. In
particular, we argue that the number of simplicial 3-manifolds having a fixed
homology type grows exponentially with the number of tetrahedra they are made
of. We propose a model of 3D gravity interacting with scalar fermions, some
restriction of which gives the 2-dimensional self-avoiding-loop-gas matrix
model. We propose a qualitative picture of the phase structure of 3D simplicial
gravity compatible with the numerical experiments and available analytical
results.Comment: 24 page
Feedback: Baby Boomer Manager Offends Millennial Trainee
Hana Tan, a recently employed college graduate was in the midst of her training program when her manager\u27s manager, a fellow named Eric, humiliated her, in her view, in front of her training group by criticizing her use of a ponytail. She wondered, Should I quit? Do I have to take this stuff to get ahead? Should I report him? We discuss the incident in the context of phenomenology, Snyder\u27s self monitoring, Goffman\u27s presentation of self, embeddedness and the role of frank feedback
ImpaCT2: the impact of information and communication technologies on pupil learning and attainment
The report explores the impact of networked technologies on patterns of use of ICT in English, Mathematics and Science at Key Stages 2, 3 and 4 and the relative gain for high ICT users versus low ICT users in each of these subjects. This publication reports primarily on the outcomes of
Strand 1, but draws on some material from the other
strands of the study. ImpaCT2 was a major longitudinal study (1999-2002) involving 60 schools in England, its aims were to: identify the impact of networked technologies on the school and out-of-school environment; determine whether or not this impact affected the educational attainment of pupils aged 8 - 16 years (at Key Stages 2, 3, and 4); and provide information that would assist in the formation of national, local and school policies on the deployment of ICT
Full abstraction for fair testing in CCS (expanded version)
In previous work with Pous, we defined a semantics for CCS which may both be
viewed as an innocent form of presheaf semantics and as a concurrent form of
game semantics. We define in this setting an analogue of fair testing
equivalence, which we prove fully abstract w.r.t. standard fair testing
equivalence. The proof relies on a new algebraic notion called playground,
which represents the `rule of the game'. From any playground, we derive two
languages equipped with labelled transition systems, as well as a strong,
functional bisimulation between them.Comment: 80 page
How to write a coequation
There is a large amount of literature on the topic of covarieties,
coequations and coequational specifications, dating back to the early
seventies. Nevertheless, coequations have not (yet) emerged as an everyday
practical specification formalism for computer scientists. In this review
paper, we argue that this is partly due to the multitude of syntaxes for
writing down coequations, which seems to have led to some confusion about what
coequations are and what they are for. By surveying the literature, we identify
four types of syntaxes: coequations-as-corelations, coequations-as-predicates,
coequations-as-equations, and coequations-as-modal-formulas. We present each of
these in a tutorial fashion, relate them to each other, and discuss their
respective uses
Parametricity for Nested Types and GADTs
This paper considers parametricity and its consequent free theorems for
nested data types. Rather than representing nested types via their Church
encodings in a higher-kinded or dependently typed extension of System F, we
adopt a functional programming perspective and design a Hindley-Milner-style
calculus with primitives for constructing nested types directly as fixpoints.
Our calculus can express all nested types appearing in the literature,
including truly nested types. At the level of terms, it supports primitive
pattern matching, map functions, and fold combinators for nested types. Our
main contribution is the construction of a parametric model for our calculus.
This is both delicate and challenging. In particular, to ensure the existence
of semantic fixpoints interpreting nested types, and thus to establish a
suitable Identity Extension Lemma for our calculus, our type system must
explicitly track functoriality of types, and cocontinuity conditions on the
functors interpreting them must be appropriately threaded throughout the model
construction. We also prove that our model satisfies an appropriate Abstraction
Theorem, as well as that it verifies all standard consequences of parametricity
in the presence of primitive nested types. We give several concrete examples
illustrating how our model can be used to derive useful free theorems,
including a short cut fusion transformation, for programs over nested types.
Finally, we consider generalizing our results to GADTs, and argue that no
extension of our parametric model for nested types can give a functorial
interpretation of GADTs in terms of left Kan extensions and still be
parametric
Foundations of Algebraic Theories and Higher Dimensional Categories
Universal algebra uniformly captures various algebraic structures, by
expressing them as equational theories or abstract clones. The ubiquity of
algebraic structures in mathematics and related fields has given rise to
several variants of universal algebra, such as symmetric operads, non-symmetric
operads, generalised operads, and monads. These variants of universal algebra
are called notions of algebraic theory. In the first part of this thesis, we
develop a unified framework for notions of algebraic theory which includes all
of the above examples. Our key observation is that each notion of algebraic
theory can be identified with a monoidal category, in such a way that theories
correspond to monoid objects therein. We introduce a categorical structure
called metamodel, which underlies the definition of models of theories. We also
consider morphisms between notions of algebraic theory, which are a monoidal
version of profunctors. Every strong monoidal functor gives rise to an adjoint
pair of such morphisms, and provides a uniform way to establish isomorphisms
between categories of models in different notions of algebraic theory. A
general structure-semantics adjointness result and a double categorical
universal property of categories of models are also shown.
In the second part of this thesis, we shift from the general study of
algebraic structures, and focus on a particular algebraic structure: higher
dimensional categories. Among several existing definitions of higher
dimensional categories, we choose to look at the one proposed by Batanin and
later refined by Leinster. We show that the notion of extensive category plays
a central role in Batanin and Leinster's definition. Using this, we generalise
their definition by allowing enrichment over any locally presentable extensive
category.Comment: 134 pages, PhD thesi
Transforming structures by set interpretations
We consider a new kind of interpretation over relational structures: finite
sets interpretations. Those interpretations are defined by weak monadic
second-order (WMSO) formulas with free set variables. They transform a given
structure into a structure with a domain consisting of finite sets of elements
of the orignal structure. The definition of these interpretations directly
implies that they send structures with a decidable WMSO theory to structures
with a decidable first-order theory. In this paper, we investigate the
expressive power of such interpretations applied to infinite deterministic
trees. The results can be used in the study of automatic and tree-automatic
structures.Comment: 36 page
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