arXiv subjects

Pascal Grange

Publications and source records attributed to Pascal Grange.

At least 37 records · Page 2Linked to original sources

arXiv2015

Cell-type-specific computational neuroanatomy, simulations from the sagittal and coronal Allen Brain Atlas

The Allen Atlas of the adult mouse brain is a brain-wide, genome-wide data set that has been made available online, triggering a renaissance in neuroanatomy. In particular, it has been used to define brain regions in a computational, data-driven way, and to estimate the region-specificity of cell types characterized independently by their transcriptional activity. However, these results were based on one series of co-registered (coronal) ISH image series per gene, whereas the online ABA contains several image series per genes, including sagittal ones. Since the sagittal series cover mostly the left hemisphere, we can simulate the variability of results by repeatedly drawing a random image series for each gene and restricting the computation to the left hemisphere. This gives rise to an estimate of error bars on the results of computational neuroanatomy.

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arXiv2014

Automated placement of stereotactic injections using a laser scan of the skull

Stereotactic targeting is a commonly used technique for performing injections in the brains of mice and other animals. The most common method for targeting stereoscopic injections uses the skull indentations bregma and lambda as reference points and is limited in its precision by factors such as skull curvature and individual variation, as well as an incomplete correspondence between skull landmarks and brain locations. In this software tool, a 3D laser scan of the mouse skull is taken in vitro and registered onto a reference skull using a point cloud matching algorithm, and the parameters of the transformation are used to position a glass pipette to place tracer injections. The software was capable of registering sample skulls with less than 100 micron error, and was able to target an injection in a mouse with error of roughly 500 microns. These results indicate that using skull scan registration has the potential to be widely applicable in automating stereotactic targeting of tracer injections.

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arXiv2014

Cell-type-specific neuroanatomy of brain-wide expression of autism-related genes

Two cliques of genes identified computationally for their high co-expression in the mouse brain according to the Allen Brain Atlas, and for their enrichment in genes related to autism spectrum disorder, have recently been shown to be highly co-expressed in the cerebellar cortex, compared to what could be expected by chance. Moreover, the expression of these cliques of genes is not homogeneous across the cerebellum, and it has been noted that their gene expression pattern seems to highlight the granular layer. However, this observation was only made by eye, and recent advances in computational neuroanatomy allow to rank cell types in the mouse brain (characterized by their transcriptome profiles) according to the similarity between their density profiles and the expression profiles of the cliques. We establish by Monte Carlo simulation that with probability at least 99 percent, the expression profiles of the two cliques are more similar to the density profile of granule cells than 99 percent of the expression of cliques containing the same number of genes (Purkinje cells also score above 99 percent in one of the cliques). Thresholding the expression profiles shows that the signal is more intense in the granular layer.

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arXiv2014

Cell-type-specific transcriptomes and the Allen Atlas (II): discussion of the linear model of brain-wide densities of cell types

The voxelized Allen Atlas of the adult mouse brain (at a resolution of 200 microns) has been used in [arXiv:1303.0013] to estimate the region-specificity of 64 cell types whose transcriptional profile in the mouse brain has been measured in microarray experiments. In particular, the model yields estimates for the brain-wide density of each of these cell types. We conduct numerical experiments to estimate the errors in the estimated density profiles. First of all, we check that a simulated thalamic profile based on 200 well-chosen genes can transfer signal from cerebellar Purkinje cells to the thalamus. This inspires us to sub-sample the atlas of genes by repeatedly drawing random sets of 200 genes and refitting the model. This results in a random distribution of density profiles, that can be compared to the predictions of the model. This results in a ranking of cell types by the overlap between the original and sub-sampled density profiles. Cell types with high rank include medium spiny neurons, several samples of cortical pyramidal neurons, hippocampal pyramidal neurons, granule cells and cholinergic neurons from the brain stem. In some cases with lower rank, the average sub-sample can have better contrast properties than the original model (this is the case for amygdalar neurons and dopaminergic neurons from the ventral midbrain). Finally, we add some noise to the cell-type-specific transcriptomes by mixing them using a scalar parameter weighing a random matrix. After refitting the model, we observe than a mixing parameter of $5\%$ leads to modifications of density profiles that span the same interval as the ones resulting from sub-sampling.

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arXiv2013

Cell-type-specific microarray data and the Allen atlas: quantitative analysis of brain-wide patterns of correlation and density

The Allen Atlas of the adult mouse brain is used to estimate the region-specificity of 64 cell types whose transcriptional profile in the mouse brain has been measured in microarray experiments. We systematically analyze the preliminary results presented in [arXiv:1111.6217], using the techniques implemented in the Brain Gene Expression Analysis toolbox. In particular, for each cell-type-specific sample in the study, we compute a brain-wide correlation profile to the Allen Atlas, and estimate a brain-wide density profile by solving a quadratic optimization problem at each voxel in the mouse brain. We characterize the neuroanatomical properties of the correlation and density profiles by ranking the regions of the left hemisphere delineated in the Allen Reference Atlas. We compare these rankings to prior biological knowledge of the brain region from which the cell-type-specific sample was extracted.

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arXiv2013

Computational neuroanatomy and co-expression of genes in the adult mouse brain, analysis tools for the Allen Brain Atlas

We review quantitative methods and software developed to analyze genome-scale, brain-wide spatially-mapped gene-expression data. We expose new methods based on the underlying high-dimensional geometry of voxel space and gene space, and on simulations of the distribution of co-expression networks of a given size. We apply them to the Allen Atlas of the adult mouse brain, and to the co-expression network of a set of genes related to nicotine addiction retrieved from the NicSNP database. The computational methods are implemented in {\ttfamily{BrainGeneExpressionAnalysis}}, a Matlab toolbox available for download.

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arXiv2012

What does the Allen Gene Expression Atlas tell us about mouse brain evolution?

We use the Allen Gene Expression Atlas (AGEA) and the OMA ortholog dataset to investigate the evolution of mouse-brain neuroanatomy from the standpoint of the molecular evolution of brain-specific genes. For each such gene, using the phylogenetic tree for all fully sequenced species and the presence of orthologs of the gene in these species, we construct and assign a discrete measure of evolutionary age. The gene expression profile of all gene of similar age, relative to the average gene expression profile, distinguish regions of the brain that are over-represented in the corresponding evolutionary timescale. We argue that the conclusions one can draw on evolution of twelve major brain regions from such a molecular level analysis supplements existing knowledge of mouse brain evolution and introduces new quantitative tools, especially for comparative studies, when AGEA-like data sets for other species become available. Using the functional role of the genes representational of a certain evolutionary timescale and brain region we compare and contrast, wherever possible, our observations with existing knowledge in evolutionary neuroanatomy.

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arXiv2012

Computational neuroanatomy and gene expression: optimal sets of marker genes for brain regions

The three-dimensional data-driven Allen Gene Expression Atlas of the adult mouse brain consists of numerized in-situ hybridization data for thousands of genes, co-registered to the Allen Reference Atlas. We propose quantitative criteria to rank genes as markers of a brain region, based on the localization of the gene expression and on its functional fitting to the shape of the region. These criteria lead to natural generalizations to sets of genes. We find sets of genes weighted with coefficients of both signs with almost perfect localization in all major regions of the left hemisphere of the brain, except the pallidum. Generalization of the fitting criterion with positivity constraint provides a lesser improvement of the markers, but requires sparser sets of genes.

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arXiv2012

A cell-type based model explaining co-expression patterns of genes in the brain

Much of the genome is expressed in the vertebrate brain, with individual genes exhibiting different spatially-varying patterns of expression. These variations are not independent, with pairs of genes exhibiting complex patterns of co-expression, such that two genes may be similarly expressed in one region, but differentially expressed in other regions. These correlations have been previously studied quantitatively, particularly for the gene expression atlas of the mouse brain, but the biological meaning of the co-expression patterns remains obscure. We propose a simple model of the co-expression patterns in terms of spatial distributions of underlying cell types. We establish the plausibility of the model in terms of a test set of cell types for which both the gene expression profiles and the spatial distributions are known.

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arXiv2011

Statistical analysis of co-expression properties of sets of genes in the mouse brain

We propose a quantitative method to estimate the statistical properties of sets of genes for which expression data are available and co-registered to a reference atlas of the brain. It is based on graph-theoretic properties of co-expression coefficients between pairs of genes. We apply this method to mouse genes from the Allen Gene Expression Atlas. Co-expression patterns of a list of several hundreds of genes related to addiction are analyzed, using ISH data produced for the mouse brain at the Allen Institute. It appears that large subsets of this set of genes are much more highly co-expressed than expected by chance.

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arXiv2011

Marker Genes for Anatomical Regions in the Brain: Insights from the Allen Gene Expression Atlas

Quantitative criteria are proposed to identify genes (and sets of genes) whose expression marks a specific brain region (or a set of brain regions). Gene-expression energies, obtained for thousands of mouse genes by numerization of in-situ hybridization images in the Allen Gene Expression Atlas, are used to test these methods in the mouse brain. Individual genes are ranked using integrals of their expression energies across brain regions. The ranking is generalized to sets of genes and the problem of optimal markers of a classical region receives a linear-algebraic solution. Moreover, the goodness of the fitting of the expression profile of a gene to the profile of a brain region is closely related to the co-expression of genes. The geometric interpretation of this fact leads to a quantitative criterion to detect markers of pairs of brain regions. Local properties of the gene-expression profiles are also used to detect genes that separate a given grain region from its environment.

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arXiv2011

Algorithmic choice of coordinates for injections into the brain: encoding a neuroanatomical atlas on a grid

Given an atlas of the brain and a number of injections to be performed in order to map out the connections between parts of the brain, we propose an algorithm to compute the coordinates of the injections. The algorithm is designed to sample the brain in the most homogeneous way compatible with the separation of brain regions. It can be applied to other species for which a neuroanatomical atlas is available. The computation is tested on the annotation at a resolution of 25 microns corresponding to the Allen Reference Atlas, which is hierarchical and consists of 209 regions. The resulting injection coordinates are being used for the injection protocol of the Mouse Brain Architecture project. Due to its large size and layered structure, the cerebral cortex is treated in a separate algorithm, which is more adapted to its geometry.

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arXiv2007

Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds

Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror \hat{M}, it is argued that the product M x \hat{M} is doubly fibered by supersymmetric three-tori, with both sets of fibers transverse to M and \hat{M}. The mirror map is then realized by T-dualizing the fibers. Mirror-symmetric properties of the fluxes, both geometric and non-geometric, are shown to agree with previous conjectures based on the requirement of mirror symmetry for Killing prepotentials. The fibers are conjectured to be destabilized by fluxes on generic SU(3)xSU(3) backgrounds, though they may survive at type-jumping points. T-dualizing the surviving fibers ensures the exchange of pure spinors under mirror symmetry.

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arXiv2006

T-duality with H-flux: non-commutativity, T-folds and G x G structure

Various approaches to T-duality with NSNS three-form flux are reconciled. Non-commutative torus fibrations are shown to be the open-string version of T-folds. The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds. The non-commutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy. This bivector is shown to exist in SU(3) x SU(3) structure compactifications, which have been proposed as mirrors to NSNS-flux backgrounds. The two SU(3)-invariant spinors are generically not parallel, thereby giving rise to a non-trivial Poisson bivector. Furthermore we show that for non-geometric T-duals, the Poisson bivector may not be decomposable into the tensor product of vectors.

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arXiv2005

Tachyon condensation and D-branes in generalized geometries

In generalized complex geometry, D-branes can be seen as maximally isotropic spaces and are thus in one-to-one correspondence with pure spinors. When considered on the sum of the tangent and cotangent bundles to the ambient space, all the branes are of the same dimension and the transverse scalars enter on par with the gauge fields; the split between the longitudinal and transverse directions is done in accordance with the type of the pure spinor corresponding to the given D-brane. We elaborate on the relation of this picture to the T-duality transformations and stability of D-branes. A discussion of tachyon condensation in the context of the generalized complex geometry is given, linking the description of D-branes as generalized complex submanifolds to their K-theoretic classification.

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arXiv2005

D-branes, actions effectives et symétrie miroir

This thesis is devoted to derivative corrections to the effective action of D-branes, and to mirror symmetry with D-branes. Series of derivative corrections first predicted by non-commutative gauge theory are completed by couplings between the metric and the gauge field. The result is interpreted as a deformation of the non-commutative gauge theory, whose structure survives. The derivation is applied to the tachyon field, whose potential is shown to be deformed by the very same corrections. Moreover, a prescription is given for the coupling of p-adic strings to a magnetic field, thus allowing to study p-adic solitons using non-commutative field-theory techniques. The link with topological D-branes is provided by the non-commutative description of D-branes in the B-model. The fibre bundles supported by the D-branes are still holomorphic in this description. Establishing this property involves the realization of D-branes as boundary conditions, within the framework of generalized complex geometry. This geometric framework is then used to describe mirror symmetry with D-branes on a Calabi--Yau manifold admitting a $T^3$-fibration. Two pure spinors, involved in the stability equations for topological D-branes, and modified by gauge fields, are exchanged, thus unifying Lagrangian and non-Lagrangian D-branes of the A-model as mirrors of stable D-branes of the B-model.

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arXiv2004

Deformation of p-adic String Amplitudes in a Magnetic Field

A new term in the p-adic world-sheet action is proposed, which couples a constant B-field to the boundary of the world-sheet at disk level. The induced deformation of tachyon scattering amplitudes by star-products is derived. This is in agreement with the deformation of effective action postulated in recent investigations of noncommutative solitons in p-adic string theory.

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arXiv2004

Modified pure spinors and mirror symmetry

It has been argued recently that mirror symmetry exchanges two pure spinors characterizing a generic manifold with SU(3)-structure. We show how pure spinors are modified in the presence of topological D-branes, so that they are still exchanged by mirror symmetry. This exchange emerges from the fact that the modified pure spinors come out as moment maps for the symmetries of A and B-models. The modification by the gauge field is argued to ensure the inclusion into the mirror exchange of the A-model non-Lagrangian branes endowed with a non-flat connection. Treating the connection as a distribution on an ambient six-manifold, assumed to be T^3-fibered, the proposed mirror formula is established by fiberwise T-duality.

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