Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

ENERGY AND VOLUME OF VECTOR FIELDS ON SPHERICAL DOMAINS

We present a "boundary version" for theorems about minimality of volume and energy functionals on a spherical domain of an odd-dimensional Euclidean sphere.

Serial bone marrow transplantation reveals in vivo expression of the pCLPG retroviral vector

Abstract Background Gene therapy in the hematopoietic system remains promising, though certain aspects of vector design, such as transcriptional control elements, continue to be studied. Our group has developed a retroviral vector where transgene expression is controlled by p53 with the intention of harnessing the dynamic and inducible nature of this tumor suppressor and transcription factor. We present here a test of in vivo expression provided by the p53-responsive vector, pCLPG. For this, we used a model of serial transplantation of transduced bone marrow cells. Results We observed, by flow cytometry, that the eGFP transgene was expressed at higher levels when the pCLPG vector was used as compared to the parental pCL retrovirus, where expression is directed by the native MoMLV LTR. Expression from the pCLPG vector was longer lasting, but did decay along with each sequential transplant. The detection of eGFP-positive cells containing either vector was successful only in the bone marrow compartment and was not observed in peripheral blood, spleen or thymus. Conclusions These findings indicate that the p53-responsive pCLPG retrovirus did offer expression in vivo and at a level that surpassed the non-modified, parental pCL vector. Our results indicate that the pCLPG platform may provide some advantages when applied in the hematopoietic system.

Modeling gene expression regulatory networks with the sparse vector autoregressive model

Abstract Background To understand the molecular mechanisms underlying important biological processes, a detailed description of the gene products networks involved is required. In order to define and understand such molecular networks, some statistical methods are proposed in the literature to estimate gene regulatory networks from time-series microarray data. However, several problems still need to be overcome. Firstly, information flow need to be inferred, in addition to the correlation between genes. Secondly, we usually try to identify large networks from a large number of genes (parameters) originating from a smaller number of microarray experiments (samples). Due to this situation, which is rather frequent in Bioinformatics, it is difficult to perform statistical tests using methods that model large gene-gene networks. In addition, most of the models are based on dimension reduction using clustering techniques, therefore, the resulting network is not a gene-gene network but a module-module network. Here, we present the Sparse Vector Autoregressive model as a solution to these problems. Results We have applied the Sparse Vector Autoregressive model to estimate gene regulatory networks based on gene expression profiles obtained from time-series microarray experiments. Through extensive simulations, by applying the SVAR method to artificial regulatory networks, we show that SVAR can infer true positive edges even under conditions in which the number of samples is smaller than the number of genes. Moreover, it is possible to control for false positives, a significant advantage when compared to other methods described in the literature, which are based on ranks or score functions. By applying SVAR to actual HeLa cell cycle gene expression data, we were able to identify well known transcription factor targets. Conclusion The proposed SVAR method is able to model gene regulatory networks in frequent situations in which the number of samples is lower than the number of genes, making it possible to naturally infer partial Granger causalities without any a priori information. In addition, we present a statistical test to control the false discovery rate, which was not previously possible using other gene regulatory network models.