3,901 research outputs found
Judgement aggregation functions and ultraproducts
The relationship between propositional model theory and social decision making via premise-based procedures is explored. A one-to-one correspondence between ultrafilters on the population set and weakly universal, unanimity-respecting, systematic judgment aggregation functions is established. The proof constructs an ultraproduct of profiles, viewed as propositional structures, with respect to the ultrafilter of decisive coalitions. This representation theorem can be used to prove other properties of such judgment aggregation functions, in particular sovereignty and monotonicity, as well as an impossibility theorem for judgment aggregation in finite populations. As a corollary, Lauwers and Van~Liedekerke's (1995) representation theorem for preference aggregation functions is derived.Judgment aggregation function; ultraproduct; ultrafilter
Effective One-Dimensional Models from Matrix Product States
In this paper we present a method for deriving effective one-dimensional
models based on the matrix product state formalism. It exploits translational
invariance to work directly in the thermodynamic limit. We show, how a
representation of the creation operator of single quasi-particles in both real
and momentum space can be extracted from the dispersion calculation. The method
is tested for the analytically solvable Ising model in a transverse magnetic
field. Properties of the matrix product representation of the creation operator
are discussed and validated by calculating the one-particle contribution to the
spectral weight. Results are also given for the ground state energy and the
dispersion.Comment: 17 pages, 8 figure
Topological singularities and the general classification of Floquet-Bloch systems
Recent works have demonstrated that the Floquet-Bloch bands of
periodically-driven systems feature a richer topological structure than their
non-driven counterparts. The additional structure in the driven case arises
from the periodicity of quasienergy, the energy-like quantity that defines the
spectrum of a periodically-driven system. Here we develop a new paradigm for
the topological classification of Floquet-Bloch bands, based on the
time-dependent spectrum of the driven system's evolution operator throughout
one driving period. Specifically, we show that this spectrum may host
topologically-protected degeneracies at intermediate times, which control the
topology of the Floquet bands of the full driving cycle. This approach provides
a natural framework for incorporating the role of symmetries, enabling a
unified and complete classification of Floquet-Bloch bands and yielding new
insight into the topological features that distinguish driven and non-driven
systems.Comment: 19 pages, 6 figure
Approximation algorithms for rectangle stabbing and interval stabbing problems.
Inthe weighted rectangle stabbing problem we are given a grid in R2 consisting of columns and rows each having a positive integral weight, and a set of closed axis-parallel rectangles each having a positive integral demand. The rectangles are placed arbitrarily in the grid with the only assumption that each rectangle is intersected by at least one column and at least one row. The objective is to find a minimum-weight (multi)set of columns and rows of the grid so that for each rectangle the total multiplicity of selected columns and rows stabbing it is at least its demand. A special case of this problem arises when each rectangle is intersected by exactly one row. We describe two algorithms, called STAB and ROUND, that are shown to be constant-factor approximation algorithms for different variants of this stabbing problem.Research; Approximation; Algorithms; Problems; Demand;
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