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Identification of the expressome by machine learning on omics data.
Accurate annotation of plant genomes remains complex due to the presence of many pseudogenes arising from whole-genome duplication-generated redundancy or the capture and movement of gene fragments by transposable elements. Machine learning on genome-wide epigenetic marks, informed by transcriptomic and proteomic training data, could be used to improve annotations through classification of all putative protein-coding genes as either constitutively silent or able to be expressed. Expressed genes were subclassified as able to express both mRNAs and proteins or only RNAs, and CG gene body methylation was associated only with the former subclass. More than 60,000 protein-coding genes have been annotated in the reference genome of maize inbred B73. About two-thirds of these genes are transcribed and are designated the filtered gene set (FGS). Classification of genes by our trained random forest algorithm was accurate and relied only on histone modifications or DNA methylation patterns within the gene body; promoter methylation was unimportant. Other inbred lines are known to transcribe significantly different sets of genes, indicating that the FGS is specific to B73. We accurately classified the sets of transcribed genes in additional inbred lines, arising from inbred-specific DNA methylation patterns. This approach highlights the potential of using chromatin information to improve annotations of functional genes
The Inflation Technique for Causal Inference with Latent Variables
The problem of causal inference is to determine if a given probability
distribution on observed variables is compatible with some causal structure.
The difficult case is when the causal structure includes latent variables. We
here introduce the for tackling this problem. An
inflation of a causal structure is a new causal structure that can contain
multiple copies of each of the original variables, but where the ancestry of
each copy mirrors that of the original. To every distribution of the observed
variables that is compatible with the original causal structure, we assign a
family of marginal distributions on certain subsets of the copies that are
compatible with the inflated causal structure. It follows that compatibility
constraints for the inflation can be translated into compatibility constraints
for the original causal structure. Even if the constraints at the level of
inflation are weak, such as observable statistical independences implied by
disjoint causal ancestry, the translated constraints can be strong. We apply
this method to derive new inequalities whose violation by a distribution
witnesses that distribution's incompatibility with the causal structure (of
which Bell inequalities and Pearl's instrumental inequality are prominent
examples). We describe an algorithm for deriving all such inequalities for the
original causal structure that follow from ancestral independences in the
inflation. For three observed binary variables with pairwise common causes, it
yields inequalities that are stronger in at least some aspects than those
obtainable by existing methods. We also describe an algorithm that derives a
weaker set of inequalities but is more efficient. Finally, we discuss which
inflations are such that the inequalities one obtains from them remain valid
even for quantum (and post-quantum) generalizations of the notion of a causal
model.Comment: Minor final corrections, updated to match the published version as
closely as possibl
On first-order expressibility of satisfiability in submodels
Let be regular cardinals, , let
be a sentence of the language in a given
signature, and let express the fact that holds
in a submodel, i.e., any model in the signature satisfies
if and only if some submodel of satisfies . It was shown in [1] that, whenever is in
in the signature having less than
functional symbols (and arbitrarily many predicate symbols), then
is equivalent to a monadic existential sentence in the
second-order language , and that for any
signature having at least one binary predicate symbol there exists in
such that is not equivalent
to any (first-order) sentence in . Nevertheless, in
certain cases are first-order expressible. In this note,
we provide several (syntactical and semantical) characterizations of the case
when is in and is
or a certain large cardinal
Invariants of the dihedral group in characteristic two
We consider finite dimensional representations of the dihedral group
over an algebraically closed field of characteristic two where is an odd
integer and study the degrees of generating and separating polynomials in the
corresponding ring of invariants. We give an upper bound for the degrees of the
polynomials in a minimal generating set that does not depend on when the
dimension of the representation is sufficiently large. We also show that
is the minimal number such that the invariants up to that degree always form a
separating set. As well, we give an explicit description of a separating set
when is prime.Comment: 7 page
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