2,815 research outputs found
Some results on Lipschitz quasi-arithmetic means
We present in this paper some properties of k-Lipschitz quasi-arithmetic means. The Lipschitz aggregation operations are stable with respect to input inaccuracies, what is a very important property for applications. Moreover, we provide sufficient conditions to determine when a quasi–arithemetic mean holds the k-Lipschitz property and allow us to calculate the Lipschitz constant k.<br /
Limit theorems for iterated random topical operators
Let A(n) be a sequence of i.i.d. topical (i.e. isotone and additively
homogeneous) operators. Let be defined by and
. This can modelize a wide range of systems including,
task graphs, train networks, Job-Shop, timed digital circuits or parallel
processing systems. When A(n) has the memory loss property, we use the spectral
gap method to prove limit theorems for . Roughly speaking, we show
that behaves like a sum of i.i.d. real variables. Precisely, we show
that with suitable additional conditions, it satisfies a central limit theorem
with rate, a local limit theorem, a renewal theorem and a large deviations
principle, and we give an algebraic condition to ensure the positivity of the
variance in the CLT. When A(n) are defined by matrices in the \mp semi-ring, we
give more effective statements and show that the additional conditions and the
positivity of the variance in the CLT are generic
Aggregation functions: Means
The two-parts state-of-art overview of aggregation theory summarizes the essential information concerning aggregation issues. Overview of aggregation properties is given, including the basic classification of aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with open arity (extended means).
Asymptotic Dimension
The asymptotic dimension theory was founded by Gromov in the early 90s. In
this paper we give a survey of its recent history where we emphasize two of its
features: an analogy with the dimension theory of compact metric spaces and
applications to the theory of discrete groups.Comment: Added some remarks about coarse equivalence of finitely generated
groups
Knife-Edge Conditions in the Modeling of Long-Run Growth Regularities
Balanced (exponential) growth cannot be generalized to a concept which would not require knife-edge conditions to be imposed on dynamic models. Already the assumption that a solution to a dynamical system (i.e. time path of an economy) satisfies a given functional regularity (e.g. quasi-arithmetic, logistic, etc.) imposes at least one knife-edge assumption on the considered model. Furthermore, it is always possible to find divergent and qualitative changes in dynamic behavior of the model – strong enough to invalidate its long-run predictions – if a certain parameter is infinitesimally manipulated.knife-edge condition, balanced growth, regular growth, bifurcation, growth model, long-run dynamics
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