10,827 research outputs found
Coverage, Continuity and Visual Cortical Architecture
The primary visual cortex of many mammals contains a continuous
representation of visual space, with a roughly repetitive aperiodic map of
orientation preferences superimposed. It was recently found that orientation
preference maps (OPMs) obey statistical laws which are apparently invariant
among species widely separated in eutherian evolution. Here, we examine whether
one of the most prominent models for the optimization of cortical maps, the
elastic net (EN) model, can reproduce this common design. The EN model
generates representations which optimally trade of stimulus space coverage and
map continuity. While this model has been used in numerous studies, no
analytical results about the precise layout of the predicted OPMs have been
obtained so far. We present a mathematical approach to analytically calculate
the cortical representations predicted by the EN model for the joint mapping of
stimulus position and orientation. We find that in all previously studied
regimes, predicted OPM layouts are perfectly periodic. An unbiased search
through the EN parameter space identifies a novel regime of aperiodic OPMs with
pinwheel densities lower than found in experiments. In an extreme limit,
aperiodic OPMs quantitatively resembling experimental observations emerge.
Stabilization of these layouts results from strong nonlocal interactions rather
than from a coverage-continuity-compromise. Our results demonstrate that
optimization models for stimulus representations dominated by nonlocal
suppressive interactions are in principle capable of correctly predicting the
common OPM design. They question that visual cortical feature representations
can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure
Dismantling the Mantel tests
The simple and partial Mantel tests are routinely used in many areas of
evolutionary biology to assess the significance of the association between two
or more matrices of distances relative to the same pairs of individuals or
demes. Partial Mantel tests rather than simple Mantel tests are widely used to
assess the relationship between two variables displaying some form of
structure.
We show that contrarily to a widely shared belief, partial Mantel tests are
not valid in this case, and their bias remains close to that of the simple
Mantel test.
We confirm that strong biases are expected under a sampling design and
spatial correlation parameter drawn from an actual study.
The Mantel tests should not be used in case auto-correlation is suspected in
both variables compared under the null hypothesis. We outline alternative
strategies. The R code used for our computer simulations is distributed as
supporting material
Efficient algorithms to discover alterations with complementary functional association in cancer
Recent large cancer studies have measured somatic alterations in an
unprecedented number of tumours. These large datasets allow the identification
of cancer-related sets of genetic alterations by identifying relevant
combinatorial patterns. Among such patterns, mutual exclusivity has been
employed by several recent methods that have shown its effectivenes in
characterizing gene sets associated to cancer. Mutual exclusivity arises
because of the complementarity, at the functional level, of alterations in
genes which are part of a group (e.g., a pathway) performing a given function.
The availability of quantitative target profiles, from genetic perturbations or
from clinical phenotypes, provides additional information that can be leveraged
to improve the identification of cancer related gene sets by discovering groups
with complementary functional associations with such targets.
In this work we study the problem of finding groups of mutually exclusive
alterations associated with a quantitative (functional) target. We propose a
combinatorial formulation for the problem, and prove that the associated
computation problem is computationally hard. We design two algorithms to solve
the problem and implement them in our tool UNCOVER. We provide analytic
evidence of the effectiveness of UNCOVER in finding high-quality solutions and
show experimentally that UNCOVER finds sets of alterations significantly
associated with functional targets in a variety of scenarios. In addition, our
algorithms are much faster than the state-of-the-art, allowing the analysis of
large datasets of thousands of target profiles from cancer cell lines. We show
that on one such dataset from project Achilles our methods identify several
significant gene sets with complementary functional associations with targets.Comment: Accepted at RECOMB 201
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