11,851 research outputs found
Axiomatizations of quasi-polynomial functions on bounded chains
Two emergent properties in aggregation theory are investigated, namely
horizontal maxitivity and comonotonic maxitivity (as well as their dual
counterparts) which are commonly defined by means of certain functional
equations. We completely describe the function classes axiomatized by each of
these properties, up to weak versions of monotonicity in the cases of
horizontal maxitivity and minitivity. While studying the classes axiomatized by
combinations of these properties, we introduce the concept of quasi-polynomial
function which appears as a natural extension of the well-established notion of
polynomial function. We give further axiomatizations for this class both in
terms of functional equations and natural relaxations of homogeneity and median
decomposability. As noteworthy particular cases, we investigate those
subclasses of quasi-term functions and quasi-weighted maximum and minimum
functions, and provide characterizations accordingly
Spectral analysis of Markov kernels and application to the convergence rate of discrete random walks
Let be a Markov chain on a measurable space \X with
transition kernel and let V:\X\r[1,+\infty). The Markov kernel is
here considered as a linear bounded operator on the weighted-supremum space
\cB_V associated with . Then the combination of quasi-compactness
arguments with precise analysis of eigen-elements of allows us to estimate
the geometric rate of convergence of to its
invariant probability measure in operator norm on \cB_V. A general procedure
to compute for discrete Markov random walks with identically
distributed bounded increments is specified
How the structure of precedence constraints may change the complexity class of scheduling problems
This survey aims at demonstrating that the structure of precedence
constraints plays a tremendous role on the complexity of scheduling problems.
Indeed many problems can be NP-hard when considering general precedence
constraints, while they become polynomially solvable for particular precedence
constraints. We also show that there still are many very exciting challenges in
this research area
Pseudo-polynomial functions over finite distributive lattices
In this paper we consider an aggregation model f: X1 x ... x Xn --> Y for
arbitrary sets X1, ..., Xn and a finite distributive lattice Y, factorizable as
f(x1, ..., xn) = p(u1(x1), ..., un(xn)), where p is an n-variable lattice
polynomial function over Y, and each uk is a map from Xk to Y. The resulting
functions are referred to as pseudo-polynomial functions. We present an
axiomatization for this class of pseudo-polynomial functions which differs from
the previous ones both in flavour and nature, and develop general tools which
are then used to obtain all possible such factorizations of a given
pseudo-polynomial function.Comment: 16 pages, 2 figure
Volume distortion in groups
Given a space in , a cycle in may be filled with a chain in two
ways: either by restricting the chain to or by allowing it to be anywhere
in . When the pair acts on , we define the -volume
distortion function of in to measure the large-scale difference between
the volumes of such fillings. We show that these functions are quasi-isometry
invariants, and thus independent of the choice of spaces, and provide several
bounds in terms of other group properties, such as Dehn functions. We also
compute the volume distortion in a number of examples, including characterizing
the -volume distortion of in , where is a
diagonalizable matrix. We use this to prove a conjecture of Gersten.Comment: 27 pages, 10 figure
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