48,476 research outputs found
Beyond topological persistence: Starting from networks
Persistent homology enables fast and computable comparison of topological
objects. However, it is naturally limited to the analysis of topological
spaces. We extend the theory of persistence, by guaranteeing robustness and
computability to significant data types as simple graphs and quivers. We focus
on categorical persistence functions that allow us to study in full generality
strong kinds of connectedness such as clique communities, -vertex and
-edge connectedness directly on simple graphs and monic coherent categories.Comment: arXiv admin note: text overlap with arXiv:1707.0967
The labour market in CGE models
This chapter reviews options of labour market modelling in a CGE framework. On the labour supply side, two principal modelling options are distinguished and discussed: aggregated, representative households and microsimulation based on individual household data. On the labour demand side, we focus on the substitution possibilities between different types of labour in production. With respect to labour market coordination, we discuss several wage-forming mechanisms and involuntary unemployment. --computable general equilibrium model,labour market,labour supply,labour demand,microsimulation,involuntary unemployment
Attracting and repelling Lagrangian coherent structures from a single computation
Hyperbolic Lagrangian Coherent Structures (LCSs) are locally most repelling
or most attracting material surfaces in a finite-time dynamical system. To
identify both types of hyperbolic LCSs at the same time instance, the standard
practice has been to compute repelling LCSs from future data and attracting
LCSs from past data. This approach tacitly assumes that coherent structures in
the flow are fundamentally recurrent, and hence gives inconsistent results for
temporally aperiodic systems. Here we resolve this inconsistency by showing how
both repelling and attracting LCSs are computable at the same time instance
from a single forward or a single backward run. These LCSs are obtained as
surfaces normal to the weakest and strongest eigenvectors of the Cauchy-Green
strain tensor.Comment: Under consideration for publication in Chaos/AI
Inductive-data-type Systems
In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the last
two authors presented a combined language made of a (strongly normalizing)
algebraic rewrite system and a typed lambda-calculus enriched by
pattern-matching definitions following a certain format, called the "General
Schema", which generalizes the usual recursor definitions for natural numbers
and similar "basic inductive types". This combined language was shown to be
strongly normalizing. The purpose of this paper is to reformulate and extend
the General Schema in order to make it easily extensible, to capture a more
general class of inductive types, called "strictly positive", and to ease the
strong normalization proof of the resulting system. This result provides a
computation model for the combination of an algebraic specification language
based on abstract data types and of a strongly typed functional language with
strictly positive inductive types.Comment: Theoretical Computer Science (2002
Banach Spaces as Data Types
We introduce the operators "modified limit" and "accumulation" on a Banach
space, and we use this to define what we mean by being internally computable
over the space. We prove that any externally computable function from a
computable metric space to a computable Banach space is internally computable.
We motivate the need for internal concepts of computability by observing that
the complexity of the set of finite sets of closed balls with a nonempty
intersection is not uniformly hyperarithmetical, and thus that approximating an
externally computable function is highly complex.Comment: 20 page
The computability path ordering
This paper aims at carrying out termination proofs for simply typed
higher-order calculi automatically by using ordering comparisons. To this end,
we introduce the computability path ordering (CPO), a recursive relation on
terms obtained by lifting a precedence on function symbols. A first version,
core CPO, is essentially obtained from the higher-order recursive path ordering
(HORPO) by eliminating type checks from some recursive calls and by
incorporating the treatment of bound variables as in the com-putability
closure. The well-foundedness proof shows that core CPO captures the essence of
computability arguments \'a la Tait and Girard, therefore explaining its name.
We further show that no further type check can be eliminated from its recursive
calls without loosing well-foundedness, but for one for which we found no
counterexample yet. Two extensions of core CPO are then introduced which allow
one to consider: the first, higher-order inductive types; the second, a
precedence in which some function symbols are smaller than application and
abstraction
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