5,615 research outputs found
On the Construction of Substitutes
Gross substitutability is a central concept in Economics and is connected to
important notions in Discrete Convex Analysis, Number Theory and the analysis
of Greedy algorithms in Computer Science. Many different characterizations are
known for this class, but providing a constructive description remains a major
open problem. The construction problem asks how to construct all gross
substitutes from a class of simpler functions using a set of operations. Since
gross substitutes are a natural generalization of matroids to real-valued
functions, matroid rank functions form a desirable such class of simpler
functions.
Shioura proved that a rich class of gross substitutes can be expressed as
sums of matroid rank functions, but it is open whether all gross substitutes
can be constructed this way. Our main result is a negative answer showing that
some gross substitutes cannot be expressed as positive linear combinations of
matroid rank functions. En route, we provide necessary and sufficient
conditions for the sum to preserve substitutability, uncover a new operation
preserving substitutability and fully describe all substitutes with at most 4
items
The State of Impact Investing in Latin America
This report lays out an assessment of the current landscape, some of the critical challenges ahead and the likely path forward over the next five 5 to 10 years on impact investing in Latin America
Approximate dual representation for Yang-Mills SU(2) gauge theory
An approximate dual representation for non-Abelian lattice gauge theories in
terms of a new set of dynamical variables, the plaquette occupation numbers
(PONs) that are natural numbers, is discussed. They are the expansion indices
of the local series of the expansion of the Boltzmann factors for every
plaquette of the Yang-Mills action. After studying the constraints due to gauge
symmetry, the SU(2) gauge theory is solved using Monte Carlo simulations. For a
PONs configuration the weight factor is given by Haar-measure integrals over
all links whose integrands are products of powers of plaquettes. Herein,
updates are limited to changes of the PON at a plaquette or all PONs on a
coordinate plane. The Markov chain transition probabilities are computed
employing truncated maximal trees and the Metropolis algorithm. The algorithm
performance is investigated with different types of updates for the plaquette
mean value over a large range of s. Using a lattice very good
agreement with a conventional heath bath algorithm is found for the strong and
weak coupling limits. Deviations from the latter being below 0.1% for . The mass of the lightest glueball is evaluated and
reproduces the results found in the literature
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