9,464 research outputs found
SPECS: a non-parametric method to identify tissue-specific molecular features for unbalanced sample groups
Background
To understand biology and differences among various tissues or cell types, one typically searches for molecular features that display characteristic abundance patterns. Several specificity metrics have been introduced to identify tissue-specific molecular features, but these either require an equal number of replicates per tissue or they can’t handle replicates at all.
Results
We describe a non-parametric specificity score that is compatible with unequal sample group sizes. To demonstrate its usefulness, the specificity score was calculated on all GTEx samples, detecting known and novel tissue-specific genes. A webtool was developed to browse these results for genes or tissues of interest. An example python implementation of SPECS is available at https://github.com/celineeveraert/SPECS. The precalculated SPECS results on the GTEx data are available through a user-friendly browser at specs.cmgg.be.
Conclusions
SPECS is a non-parametric method that identifies known and novel specific-expressed genes. In addition, SPECS could be adopted for other features and applications
On the molecules of numerical semigroups, Puiseux monoids, and Puiseux algebras
A molecule is a nonzero non-unit element of an integral domain (resp.,
commutative cancellative monoid) having a unique factorization into
irreducibles (resp., atoms). Here we study the molecules of Puiseux monoids as
well as the molecules of their corresponding semigroup algebras, which we call
Puiseux algebras. We begin by presenting, in the context of numerical
semigroups, some results on the possible cardinalities of the sets of molecules
and the sets of reducible molecules (i.e., molecules that are not
irreducibles/atoms). Then we study the molecules in the more general context of
Puiseux monoids. We construct infinitely many non-isomorphic atomic Puiseux
monoids all whose molecules are atoms. In addition, we characterize the
molecules of Puiseux monoids generated by rationals with prime denominators.
Finally, we turn to investigate the molecules of Puiseux algebras. We provide a
characterization of the molecules of the Puiseux algebras corresponding to
root-closed Puiseux monoids. Then we use such a characterization to find an
infinite class of Puiseux algebras with infinitely many non-associated
reducible molecules.Comment: 21 pages, 2 figure
A Decidable Class of Nested Iterated Schemata (extended version)
Many problems can be specified by patterns of propositional formulae
depending on a parameter, e.g. the specification of a circuit usually depends
on the number of bits of its input. We define a logic whose formulae, called
"iterated schemata", allow to express such patterns. Schemata extend
propositional logic with indexed propositions, e.g. P_i, P_i+1, P_1, and with
generalized connectives, e.g. /\i=1..n or i=1..n (called "iterations") where n
is an (unbound) integer variable called a "parameter". The expressive power of
iterated schemata is strictly greater than propositional logic: it is even out
of the scope of first-order logic. We define a proof procedure, called DPLL*,
that can prove that a schema is satisfiable for at least one value of its
parameter, in the spirit of the DPLL procedure. However the converse problem,
i.e. proving that a schema is unsatisfiable for every value of the parameter,
is undecidable so DPLL* does not terminate in general. Still, we prove that it
terminates for schemata of a syntactic subclass called "regularly nested". This
is the first non trivial class for which DPLL* is proved to terminate.
Furthermore the class of regularly nested schemata is the first decidable class
to allow nesting of iterations, i.e. to allow schemata of the form /\i=1..n
(/\j=1..n ...).Comment: 43 pages, extended version of "A Decidable Class of Nested Iterated
Schemata", submitted to IJCAR 200
Quantifying the Scope for Efficiency Defense in Merger Control: The Werden-Froeb-Index
In both US and EU merger control, merger-specific efficiencies are recognized as a possible defense for horizontal mergers that raise competition concerns. We introduce the Werden-Froeb-index (WFI) to assist in evaluating these efficiencies. The index measures the average reduction in marginal costs required to restore pre-merger equilibrium prices and quantities after the merger is consummated. It has low information requirements and can deal with any number of firms in price- or quantity-competition merging fully or partially, and a large class of demand and cost functions. We show how the WFI complements Phase I merger inquiries as a screening mechanism.
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