17,259 research outputs found
Some Bi-Hamiltonian Equations in
Hamiltonian formulation of N=3 systems is considered in general. The Jacobi
equation is solved in three classes. Compatible Poisson structures in these
classes are determined and explicitly given. The corresponding bi-Hamiltonian
systems are constructed and some explicit examples are given.Comment: 25 page
Ensembles of wrappers for automated feature selection in fish age classification
In feature selection, the most important features must be chosen so as to decrease the number thereof while retaining their discriminatory information. Within this context, a novel feature selection method based on an ensemble of wrappers is proposed and applied for automatically select features in fish age classification. The effectiveness of this procedure using an Atlantic cod database has been tested for different powerful statistical learning classifiers. The subsets based on few features selected, e.g. otolith weight and fish weight, are particularly noticeable given current biological findings and practices in fishery research and the classification results obtained with them outperforms those of previous studies in which a manual feature selection was performed.Peer ReviewedPostprint (author's final draft
A note on selecting maximals in finite spaces
Given a choice problem, the maximization rule may select many alternatives. In such
cases, it is common practice to interpret that the final choice will end up being made by
some random procedure, assigning to any maximal alternative the same probability of
being chosen. However, there may be reasons based on the same original preferences
for which it is suitable to select certain maximal alternatives over others. This paper
introduces two choice criteria induced by the original preferences such that maximizing
with respect to each of them may give a finer selection of alternatives than maximizing
with respect to the original preferences. Those criteria are built by means of several
preference relations induced by the original preferences, namely, two (weak) dominance
relations, two indirect preference relations and the dominance relations defined with the
help of those indirect preferences. It is remarkable that as the original preferences
approach being complete and transitive, those criteria become both simpler and closer to
such preferences. In particular, they coincide with the original preferences when these
are complete and transitive, in which case they provide the same solution as those
preference
A non-proposition-wise variant of majority voting for aggregating judgments
Majority voting is commonly used in aggregating judgments. The literature to date on judgment
aggregation (JA) has focused primarily on proposition-wise majority voting (PMV). Given a set of issues
on which a group is trying to make collective judgments, PMV aggregates individual judgments issue by
issue, and satisfies a salient property of JA rules—independence. This paper introduces a variant of
majority voting called holistic majority voting (HMV). This new variant also meets the condition of
independence. However, instead of aggregating judgments issue by issue, it aggregates individual
judgments en bloc. A salient and straightforward feature of HMV is that it guarantees the logical
consistency of the propositions expressing collective judgments, provided that the individual points of
view are consistent. This feature contrasts with the known inability of PMV to guarantee the consistency
of the collective outcome. Analogously, while PMV may present a set of judgments that have been
rejected by everyone in the group as collectively accepted, the collective judgments returned by HMV
have been accepted by a majority of individuals in the group and, therefore, rejected by a minority of
them at most. In addition, HMV satisfies a large set of appealing properties, as PMV also does. However,
HMV may not return any complete proposition expressing the judgments of the group on all the issues at
stake, even in cases where PMV does. Moreover, demanding completeness from HMV leads to
impossibility results similar to the known impossibilities on PMV and on proposition-wise JA rules in
genera
Complete intersections in simplicial toric varieties
Given a set of nonzero
vectors defining a simplicial toric ideal , where is an arbitrary field, we provide an algorithm for
checking whether is a complete intersection. This algorithm
does not require the explicit computation of a minimal set of generators of
. The algorithm is based on the application of some new results
concerning toric ideals to the simplicial case. For homogenous simplicial toric
ideals, we provide a simpler version of this algorithm. Moreover, when is
an algebraically closed field, we list all ideal-theoretic complete
intersection simplicial projective toric varieties that are either smooth or
have one singular point.Comment: 28 pages, 2 tables. To appear in Journal of Symbolic Computatio
Syzygies of differentials of forms
Given a standard graded polynomial ring over a field
of characteristic zero and a graded -subalgebra ,
one relates the module of K\"ahler -differentials of to
the transposed Jacobian module of the
forms by means of a {\em Leibniz map} \Omega_{A/k}\rar
\mathcal{D} whose kernel is the torsion of . Letting \fp
denote the -submodule generated by the (image of the) syzygy module of
and \fz the syzygy module of , there is a natural
inclusion \fp\subset \fz coming from the chain rule for composite
derivatives. The main goal is to give means to test when this inclusion is an
equality -- in which case one says that the forms are {\em
polarizable}. One surveys some classes of subalgebras that are generated by
polarizable forms. The problem has some curious connections with constructs of
commutative algebra, such as the Jacobian ideal, the conormal module and its
torsion, homological dimension in and syzygies, complete intersections and
Koszul algebras. Some of these connections trigger questions which have
interest in their own.Comment: 20 pages. Minor changes after referee's report and updated
bibliograph
A pooling approach to judgment aggregation
The literature has focused on a particular way of aggregating judgments: Given a set of yes or no
questions or issues, the individuals’ judgments are then aggregated separately, issue by issue.
Applied in this way, the majority method does not guarantee the logical consistency of the set of
judgments obtained. This fact has been the focus of critiques of the majority method and similar
procedures. This paper focuses on another way of aggregating judgments. The main difference is
that aggregation is made en bloc on all the issues at stake. The main consequence is that the
majority method applied in this way does always guarantee the logical consistency of the
collective judgments. Since it satisfies a large set of attractive properties, it should provide the
basis for more positive assessment if applied using the proposed pooling approach than if used
separately. The paper extends the analysis to the pooling supermajority and plurality rules, with
similar result
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