Search

Textbook wisdom advocates for smooth function fits and implies that interpolation of noisy data should lead to poor generalization. A related heuristic is that fitting parameters should be fewer than measurements (Occam's Razor). Surprisingly, contemporary machine learning (ML) approaches, cf. deep nets (DNNs), generalize well despite interpolating noisy data. This may be understood via Statistically Consistent Interpolation (SCI), i.e. data interpolation techniques that generalize optimally for big data. In this article we elucidate SCI using the weighted interpolating nearest neighbors (wiNN) algorithm, which adds singular weight functions to kNN (k-nearest neighbors). This shows that data interpolation can be a valid ML strategy for big data. SCI clarifies the relation between two ways of modeling natural phenomena: the rationalist approach (strong priors) of theoretical physics with few parameters and the empiricist (weak priors) approach of modern ML with more parameters than data. SCI shows that the purely empirical approach can successfully predict. However data interpolation does not provide theoretical insights, and the training data requirements may be prohibitive. Complex animal brains are between these extremes, with many parameters, but modest training data, and with prior structure encoded in species-specific mesoscale circuitry. Thus, modern ML provides a distinct epistemological approach different both from physical theories and animal brains.

Whole brain neuroanatomy using tera-voxel light-microscopic data sets is of much current interest. A fundamental problem in this field is the mapping of individual brain data sets to a reference space. Previous work has not rigorously quantified the distortions in brain geometry from in-vivo to ex-vivo brains due to the tissue processing, which will be important when computing properties such as local cell and process densities at the voxel level in creating reference brain maps. Further, existing approaches focus on registering uni-modal volumetric data; however, given the increasing interest in the marmoset model for neuroscience research, it is necessary to cross-register multi-modal data sets including MRIs and multiple histological series that can help address individual variations in brain architecture. Here we present a computational approach for same-subject multimodal MRI guided reconstruction of a histological series, jointly with diffeomorphic mapping to a reference atlas. We quantify the scale change during the different stages of histological processing of the brains using the Jacobian determinant of the diffeomorphic transformations involved. There are two major steps in the histology process with associated scale distortions (a) brain perfusion (b) histological sectioning and reassembly. By mapping the final image stacks to the ex-vivo post fixation MRI, we show that tape-transfer histology can be reassembled accurately into 3D volumes with a local scale change of 2.0 $\pm$ 0.4% per axis dimension. In contrast, the perfusion step, as assessed by mapping the in-vivo MRIs to the ex-vivo post fixation MRIs, shows a larger local scale change of 6.9 $\pm$ 2.1% per axis dimension. This is the first systematic quantification of the local metric distortions associated with whole-brain histological processing, and we expect that the results will generalize to other species.

While modern imaging technologies such as fMRI have opened exciting new possibilities for studying the brain in vivo, histological sections remain the best way to study the anatomy of the brain at the level of single neurons. The histological atlas changed little since 1909 and localizing brain regions is a still a labor intensive process performed only by experienced neuro-anatomists. Existing digital atlases such as the Allen Brain atlas are limited to low resolution images which cannot identify the detailed structure of the neurons. We have developed a digital atlas methodology that combines information about the 3D organization of the brain and the detailed texture of neurons in different structures. Using the methodology we developed an atlas for the mouse brainstem and mid-brain, two regions for which there are currently no good atlases. Our atlas is "active" in that it can be used to automatically align a histological stack to the atlas, thus reducing the work of the neuroanatomist., Comment: 8 pages, 10 figures, appeared in proceeding of MICCAI 2017

The next grand challenges for society and science are in the brain sciences. A collection of 60+ scientists from around the world, together with 10+ observers from national, private, and foundations, spent two days together discussing the top challenges that we could solve as a global community in the next decade. We eventually settled on three challenges, spanning anatomy, physiology, and medicine. Addressing all three challenges requires novel computational infrastructure. The group proposed the advent of The International Brain Station (TIBS), to address these challenges, and launch brain sciences to the next level of understanding., Comment: 6 pages

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., Comment: 8 pages

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., Comment: 178 pages, 207 figures, 7 tables; v2: typos corrected; v3: more typos corrected, missing pseudo-code in section 3.5 written, image attachment changed in Figure 6, misuse of notation $r^{signal}$ corrected, conclusions unchanged

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., Comment: V1: 88 pages, 37 figures, 43 tables; V2: 137 pages, new section discussing different fitting panels

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., Comment: 25 pages, 8 figures, accepted in Quantitative Biology (2012) 0002

The Allen Brain Atlas project (ABA) generated a genome-scale collection of gene-expression profiles using in-situ hybridization. These profiles were co-registered to the three-dimensional Allen Reference Atlas (ARA) of the adult mouse brain. A set of more than 4,000 such volumetric data are available for the full brain, at a resolution of 200 microns. These data are presented in a voxel-by-gene matrix. The ARA comes with several systems of annotation, hierarchical (40 cortical regions, 209 sub-cortical regions in the whole brain), or non-hierarchical (12 regions in the left hemisphere, with refinement into 94 regions, and cortical layers). The high-dimensional nature of this dataset and the possible connection between anatomy and gene expression pose challenges to data analysis. We developed the Brain Gene Expression Analysis Toolbox, whose functionalities include: determination of marker genes for brain regions, statistical analysis of brain-wide co-expression patterns, and the computation of brain-wide correlation maps with cell-type specific microarray data., Comment: 59 pages; v2: bug fixed on page 5, preface added; v3: more bugs fixed, cell-type-specific data released (chapter 5); v4: references added, chapter 2 expanded; v5: download link fixed, more typos corrected; v6: download link fixed

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., Comment: 14 pages

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., Comment: 41 pages; v2: typos corrected

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., Comment: 26 pages, LaTeX

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., Comment: 13 pages, LaTeX

In this era of complete genomes, our knowledge of neuroanatomical circuitry remains surprisingly sparse. Such knowledge is however critical both for basic and clinical research into brain function. Here we advocate for a concerted effort to fill this gap, through systematic, experimental mapping of neural circuits at a mesoscopic scale of resolution suitable for comprehensive, brain-wide coverage, using injections of tracers or viral vectors. We detail the scientific and medical rationale and briefly review existing knowledge and experimental techniques. We define a set of desiderata, including brain-wide coverage; validated and extensible experimental techniques suitable for standardization and automation; centralized, open access data repository; compatibility with existing resources, and tractability with current informatics technology. We discuss a hypothetical but tractable plan for mouse, additional efforts for the macaque, and technique development for human. We estimate that the mouse connectivity project could be completed within five years with a comparatively modest budget., Comment: 41 pages

In comparative and developmental neuroanatomy one encounters questions regarding the deformation of neural tissue under stress. The motivation of this note is an observation (Barbas {\it et al}) that at cortical folds or gyri, the layers of neural tissue show relative thickening or thinning of upper or deep layers. In general, the material properties of a slab of neural tissue are not known, and even if known, would probably lead to a difficult problem in elasticity theory. Here a simple argument is presented to show that bending an elastic slab should produce a relative thickening of the layers on the inside of the bend. The argument is based on the incompressibility of the material and should therefore be fairly robust., Comment: 6 pages, 2 figures

We present a method for the real time prediction of punctate events in neural activity, based on the time-frequency spectrum of the signal, applicable both to continuous processes like local field potentials (LFP) as well as to spike trains. We test it on recordings of LFP and spiking activity acquired previously from the lateral intraparietal area (LIP) of macaque monkeys performing a memory-saccade task. In contrast to earlier work, where trials with known start times were classified, our method detects and classifies trials directly from the data. It provides a means to quantitatively compare and contrast the content of LFP signals and spike trains: we find that the detector performance based on the LFP matches the performance based on spike rates. The method should find application in the development of neural prosthetics based on the LFP signal. Our approach uses a new feature vector, which we call the 2D cepstrum., Comment: 30 pages, 6 figures; This version submitted to the IEEE Transactions in Biomedical Engineering