166 research outputs found
The fundamental pro-groupoid of an affine 2-scheme
A natural question in the theory of Tannakian categories is: What if you
don't remember \Forget? Working over an arbitrary commutative ring , we
prove that an answer to this question is given by the functor represented by
the \'etale fundamental groupoid \pi_1(\spec(R)), i.e.\ the separable
absolute Galois group of when it is a field. This gives a new definition
for \'etale \pi_1(\spec(R)) in terms of the category of -modules rather
than the category of \'etale covers. More generally, we introduce a new notion
of "commutative 2-ring" that includes both Grothendieck topoi and symmetric
monoidal categories of modules, and define a notion of for the
corresponding "affine 2-schemes." These results help to simplify and clarify
some of the peculiarities of the \'etale fundamental group. For example,
\'etale fundamental groups are not "true" groups but only profinite groups, and
one cannot hope to recover more: the "Tannakian" functor represented by the
\'etale fundamental group of a scheme preserves finite products but not all
products.Comment: 46 pages + bibliography. Diagrams drawn in Tik
Long-term Test Arrangement for Externally Strengthened Reinforced Concrete Elements
Methods for external strengthening of concrete use elements of very high tensional strength glued on to its tensioned surface. These elements may be of metal, carbon fibers (CFRP), glass fibers or others, usually having very good mechanical properties. However, these high-strength elements are normally attached to concrete by epoxy resins. Epoxy resins have a low Young`s modulus and therefore a higher rate of creep may have an influence on the long-term behavior of such external strengthening. In order to verify this idea experimentally a special space-saving arrangement of tests is described in this paper. Panels act as loaded beams but simultaneously as a load for the other panels in a stand. The different load magnitude acting on a different layer of panels should make it possible to study the long-term influence of the degree of shear force on the glue creep. Certainly, the glue creep may be dependent on the type of epoxy resin; therefore several epoxy resin types are included in the tests
Interaction and observation: categorical semantics of reactive systems trough dialgebras
We use dialgebras, generalising both algebras and coalgebras, as a complement
of the standard coalgebraic framework, aimed at describing the semantics of an
interactive system by the means of reaction rules. In this model, interaction
is built-in, and semantic equivalence arises from it, instead of being
determined by a (possibly difficult) understanding of the side effects of a
component in isolation. Behavioural equivalence in dialgebras is determined by
how a given process interacts with the others, and the obtained observations.
We develop a technique to inter-define categories of dialgebras of different
functors, that in particular permits us to compare a standard coalgebraic
semantics and its dialgebraic counterpart. We exemplify the framework using the
CCS and the pi-calculus. Remarkably, the dialgebra giving semantics to the
pi-calculus does not require the use of presheaf categories
Sound and complete axiomatizations of coalgebraic language equivalence
Coalgebras provide a uniform framework to study dynamical systems, including
several types of automata. In this paper, we make use of the coalgebraic view
on systems to investigate, in a uniform way, under which conditions calculi
that are sound and complete with respect to behavioral equivalence can be
extended to a coarser coalgebraic language equivalence, which arises from a
generalised powerset construction that determinises coalgebras. We show that
soundness and completeness are established by proving that expressions modulo
axioms of a calculus form the rational fixpoint of the given type functor. Our
main result is that the rational fixpoint of the functor , where is a
monad describing the branching of the systems (e.g. non-determinism, weights,
probability etc.), has as a quotient the rational fixpoint of the
"determinised" type functor , a lifting of to the category of
-algebras. We apply our framework to the concrete example of weighted
automata, for which we present a new sound and complete calculus for weighted
language equivalence. As a special case, we obtain non-deterministic automata,
where we recover Rabinovich's sound and complete calculus for language
equivalence.Comment: Corrected version of published journal articl
Improvement of Hypertension after Parathyroidectomy of Patients Suffering from Primary Hyperparathyroidism
Background. Primary hyperparathyroidism (PHPT) is one of the most common endocrine conditions and is accompanied by hypertension and increased cardiovascular mortality. The purpose of this study was to evaluate the effect of parathyroidectomy on systolic and diastolic blood pressure (BP) in hypertensive patients with PHPT and whether hypertension occurs more frequently in PHPT than in control group. Methods. A total of 1020 patients with proved PHPT who underwent surgery were compared with with 1020 age, sex, BMI, and smoking status matched controls. We evaluated changes in serum calcium, parathyroid hormone (PTH), uric acid, and BP before and 6 months after surgery. Results. Parathyroidectomy corrected PHPT and resulted in a substantial fall in both mean systolic (150 ± 3.8 to 138 ± 3.6âmmHg) and mean diastolic pressures (97 ± 3 to 88 ± 2.8âmmHg) of the hypertensive subjects; P < .01. In these patients, PTH, calcium, and uric acid normalized. 726 patients from 1020 with PHPT (69.8%) were found to be hypertensive whilst only 489 (47.8%) from 1020 of our control group. Conclusion. Parathyroidectomy in hypertensive patients reduces systolic and diastolic BP. PHPT is accompanied by a variety of metabolic complications, which are a risk factor for hypertension, and parathyroidectomy can improve these metabolic complications
Brown representability for space-valued functors
In this paper we prove two theorems which resemble the classical
cohomological and homological Brown representability theorems. The main
difference is that our results classify small contravariant functors from
spaces to spaces up to weak equivalence of functors.
In more detail, we show that every small contravariant functor from spaces to
spaces which takes coproducts to products up to homotopy and takes homotopy
pushouts to homotopy pullbacks is naturally weekly equivalent to a
representable functor.
The second representability theorem states: every contravariant continuous
functor from the category of finite simplicial sets to simplicial sets taking
homotopy pushouts to homotopy pullbacks is equivalent to the restriction of a
representable functor. This theorem may be considered as a contravariant analog
of Goodwillie's classification of linear functors.Comment: 19 pages, final version, accepted by the Israel Journal of
Mathematic
Hierarchical Graph Transformation
If systems are specified by graph transformation, large graphs should be structured in order to be comprehensible. In this paper, we present an approach for the rule-based transformation of hierarchically structured (hyper)graphs. In these graphs, distinguished hyperedges contain graphs that can be hierarchical again. Our framework extends the well-known double-pushout approach from at to hierarchical graphs. In particular, we show how pushouts and pushout complements of hierarchical graphs and graph morphisms can be constructed recursively. Moreover, we make rules more expressive by introducing variables which allow to copy and to remove hierarchical subgraphs in a single rule application
Semiring and semimodule issues in MV-algebras
In this paper we propose a semiring-theoretic approach to MV-algebras based
on the connection between such algebras and idempotent semirings - such an
approach naturally imposing the introduction and study of a suitable
corresponding class of semimodules, called MV-semimodules.
We present several results addressed toward a semiring theory for
MV-algebras. In particular we show a representation of MV-algebras as a
subsemiring of the endomorphism semiring of a semilattice, the construction of
the Grothendieck group of a semiring and its functorial nature, and the effect
of Mundici categorical equivalence between MV-algebras and lattice-ordered
Abelian groups with a distinguished strong order unit upon the relationship
between MV-semimodules and semimodules over idempotent semifields.Comment: This version contains some corrections to some results at the end of
Section
A coalgebraic view of bar recursion and bar induction
We reformulate the bar recursion and induction principles in terms of recursive and wellfounded coalgebras. Bar induction was originally proposed by Brouwer as an axiom to recover certain classically valid theorems in a constructive setting. It is a form of induction on non- wellfounded trees satisfying certain properties. Bar recursion, introduced later by Spector, is the corresponding function defnition principle.
We give a generalization of these principles, by introducing the notion of barred coalgebra: a process with a branching behaviour given by a functor, such that all possible computations terminate.
Coalgebraic bar recursion is the statement that every barred coalgebra is recursive; a recursive coalgebra is one that allows defnition of functions by a coalgebra-to-algebra morphism. It is a framework to characterize valid forms of recursion for terminating functional programs. One application of the principle is the tabulation of continuous functions: Ghani, Hancock and Pattinson defned a type of wellfounded trees that represent continuous functions on streams. Bar recursion allows us to prove that every stably continuous function can be tabulated to such a tree where by stability we mean that the modulus of continuity is also continuous.
Coalgebraic bar induction states that every barred coalgebra is well-founded; a wellfounded coalgebra is one that admits proof by induction
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