No abstract

No abstract

A long-standing paradigm in B cell immunology is that effective somatic hypermutation and affinity maturation require cycling between the dark zone and light zone of the germinal center. The cyclic re-entry hypothesis was first proposed based on considerations of the efficiency of affinity maturation using an ordinary differential equations model for B cell population dynamics. More recently, two-photon microscopy studies of B cell motility within lymph nodes in situ have revealed the complex migration patterns of B lymphocytes both in the preactivation follicle and post-activation germinal center. There is strong evidence that chemokines secreted by stromal cells and the regulation of cognate G-protein coupled receptors by these chemokines are necessary for the observed spatial cell distributions. For example, the distribution of B cells within the light and dark zones of the germinal center appears to be determined by the reciprocal interaction between the level of the CXCR4 and CXCR5 receptors and the spatial distribution of their respective chemokines CXCL12 and CXCL13. Computer simulations of individual-based models have been used to study the complex biophysical and mechanistic processes at the individual cell level, but such simulations can be challenging to parameterize and analyze. In contrast, ordinary differential equations are more tractable, but traditional compartment model formalizations ignore the spatial chemokine distribution that drives B cell redistribution. Motivated by the desire to understand the motility patterns observed in an individual-based simulation of B cell migration in the lymph node, we propose and analyze the dynamics of an ordinary differential equation model incorporating explicit chemokine spatial distributions. While there is experimental evidence that B cell migration patterns in the germinal center are driven by extrinsically regulated differentiation programs, the model shows, perhaps surprisingly, that feedback from receptor down-regulation induced by external chemokine fields can give rise to spontaneous interzonal and intrazonal oscillations in the absence of any extrinsic regulation. While the extent to which such simple feedback mechanisms contributes to B cell migration patterns in the germinal center is unknown, the model provides an alternative hypothesis for how complex B cell migration patterns might arise from very simple mechanisms.Electronic Supplementary MaterialThe online version of this article (doi:10.1007/s11538-012-9799-9) contains supplementary material, which is available to authorized users.

We consider the problem of recognizing objects in collections of art works, in view of automatically labeling, searching and organizing databases of art works. To avoid manually labelling objects, we introduce a framework for transferring a convolutional neural network (CNN), trained on available large collections of labelled natural images, to the context of drawings. We retrain both the top and the bottom layer of the network, responsible for the high-level classification output and the low-level features detection respectively, by transforming natural images into drawings. We apply this procedure to the drawings in the Jan Brueghel Wiki, and show the transferred CNN learns a discriminative metric on drawings and achieves good recognition accuracy. We also discuss why standard descriptorbased methods is problematic in the context of drawings.

Geometric Wavelets is a new multi-scale data representation technique which is useful for a variety of applications such as data compression, interpretation and anomaly detection. We have developed an interactive visualization with multiple linked views to help users quickly explore data sets and understand this novel construction. Currently the interface is being used by applied mathematicians to view results and gain new insights, speeding methods development. GEOMETRIC WAVELETSData sets such as images, documents or gene expression data may be modeled as point clouds in high-dimensional Euclidean space. In the case of images, each pixel can be thought of as one coordinate in a vector with a length equal to the number D of pixels in the image, and the intensity of each pixel corresponds to the coordinate magnitude in that pixel's direction. Real data points often have structure which has dimension d much smaller than the ambient space dimension D, for example under the well-studied case when they lie near a low-dimensional manifold M . Discovering and characterizing this lower-dimensional structure can dramatically affect the performance in tasks such as data compression, interpretation, outlier detection, classification clustering.If M is just a linear subspace, Principal Component Analysis (PCA) can discover a dictionary of d vectors which describe the data well at low computational cost. However, when M is nonlinear it is usually necessary to use random dictionaries or black box optimization, which are much more costly and in general do not yield interpretable features of the data. Geometric Wavelets [2] are multi-scale dictionary elements which are constructed directly from the data, adapt to arbitrary nonlinear manifolds, and have guarantees on the computational cost, the number of elements in the dictionary and the sparsity of the representation (as a function of an approximation error parameter). In particular they provide feature sets that may be particularly useful for data exploration, and tasks such as anomaly detection and classification.The mathematical details of the construction can be found in [1]. It proceeds in several steps: first, relationships between data points are computed with respect to a given similarity function. At the coarsest scale all data points are considered one group and global PCA is performed, yielding a d-dimensional plane fit to the data with axes in the directions of maximum variance, which we think of as a parallel of "scaling functions" in wavelet analysis. The projection of the data points onto this plane is the coarsest-scale approximation of the data. Next, the graph is split into two groups (e.g. by using METIS [3]). On each of these finer scale groups, PCA is again performed and the projection of the data points onto these two new planes will more accurately approximate M . To form a compact representation for the data at this finer scale, as in a wavelet decomposition, we only encode the differences between the original coarse projections of the data and the point...