Anatomical substructures of the human brain have characteristic cell-types, connectivity and local circuitry, which are reflected in area-specific transcriptome signatures, but the principles governing area-specific transcription and their relation to brain development are still being studied. In adult rodents, areal transcriptome patterns agree with the embryonic origin of brain regions, but the processes and genes that preserve an embryonic signature in regional expression profiles were not quantified. Furthermore, it is not clear how embryonic-origin signatures of adult-brain expression interplay with changes in expression patterns during development. Here we first quantify which genes have regional expression-patterns related to the developmental origin of brain regions, using genome-wide mRNA expression from post-mortem adult human brains. We find that almost all human genes (92%) exhibit an expression pattern that agrees with developmental brain-region ontology, but that this agreement changes at multiple phases during development. Agreement is particularly strong in neuron-specific genes, but also in genes that are not spatially correlated with neuron-specific or glia-specific markers. Surprisingly, agreement is also stronger in early-evolved genes. We further find that pairs of similar genes having high agreement to developmental region ontology tend to be more strongly correlated or anti-correlated, and that the strength of spatial correlation changes more strongly in gene pairs with stronger embryonic signatures. These results suggest that transcription regulation of most genes in the adult human brain is spatially tuned in a way that changes through life, but in agreement with development-determined brain regions.

Gene expression controls how the brain develops and functions. Understanding control processes in the brain is particularly hard since they involve numerous types of neurons and glia, and very little is known about which genes are expressed in which cells and brain layers. Here we describe an approach to detect genes whose expression is primarily localized to a specific brain layer and apply it to the mouse cerebellum. We learn typical spatial patterns of expression from a few markers that are known to be localized to specific layers, and use these patterns to predict localization for new genes. We analyze images of in-situ hybridization (ISH) experiments, which we represent using histograms of local binary patterns (LBP) and train image classifiers and gene classifiers for four layers of the cerebellum: the Purkinje, granular, molecular and white matter layer. On held-out data, the layer classifiers achieve accuracy above 94% (AUC) by representing each image at multiple scales and by combining multiple image scores into a single gene-level decision. When applied to the full mouse genome, the classifiers predict specific layer localization for hundreds of new genes in the Purkinje and granular layers. Many genes localized to the Purkinje layer are likely to be expressed in astrocytes, and many others are involved in lipid metabolism, possibly due to the unusual size of Purkinje cells.

The dynamics of contact processes on networks is often determined by the spectral radius of the networks adjacency matrices. A decrease of the spectral radius can prevent the outbreak of an epidemic, or impact the synchronization among systems of coupled oscillators. The spectral radius is thus tightly linked to network dynamics and function. As such, finding the minimal change in network structure necessary to reach the intended spectral radius is important theoretically and practically. Given contemporary big data resources such as large scale communication or social networks, this problem should be solved with a low runtime complexity. We introduce a novel method for the minimal decrease in weights of edges required to reach a given spectral radius. The problem is formulated as a convex optimization problem, where a global optimum is guaranteed. The method can be easily adjusted to an efficient discrete removal of edges. We introduce a variant of the method which finds optimal decrease with a focus on weights of vertices. The proposed algorithm is exceptionally scalable, solving the problem for real networks of tens of millions of edges in a short time.Motivated by the interplay between the spectral radius and dynamics, strategies for affecting phase transitions were first proposed in percolation problems. An early solution was a ranking of vertices by their connectivity [18,19]. This ranking was improved by a centrality measure specifically designed for ranking edges or vertices via spectral radius reduction-the dynamical importance method [20]. Taking a perturbative approach, the dynamical importance method is defined as the first order approximation of the relative decrease in the radius when an edge or vertex is removed from the network. This work was further expanded to include structural perturbations of removing or adding a small subgraph and second order terms [21]. A different line of research is focused on a closely related problem, where minimization of the spectral radius is constrained by the number of edges allowed to be removed. Interestingly, the proposed algorithms for this problem [22,23], offer similar ranking to that of the dynamical importance algorithm [20].The aforementioned algorithms share a common strategy-they perform a full removal of edges, which results in discrete solutions. In the case of weighted networks, where it is possible to regulate the weights of edges continuously, this all-or-none discrete edge removal is a drastic measure which provides a suboptimal solution. This strategy of discrete removal has two major shortcomings.First, in many real world applications, continuous reduction of weights of edges is favorable. One such example is found in epidemiological models on weighted networks. The aforementioned criticality of the spectral radius and the infection rate also applies to these models [5,24]. Worldwide epidemic spread is mediated through transportation networks, e.g., the spread of Influenza, SARS or Ebola through the global flight network [25][26][27][28]. In the...

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