We consider the problem of finding the isolated common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. Normal form algorithms provide an algebraic approach to solve this problem. We use new characterizations of normal forms and describe accurate and efficient constructions that allow us to compute the algebra structure of R/I, and he...

Gene expression is controlled by the concerted interactions between transcription factors and chromatin regulators. While recent studies have identified global chromatin state changes across cell-types, it remains unclear to what extent these changes are co-regulated during cell-differentiation. Here we present a comprehensive computational analysis by assembling a large dataset containing geno...

Renin, an aspartyl protease that catalyzes the rate-limiting step of the renin-angiotensin system, is first synthesized as an inactive precursor, prorenin. Prorenin is activated by the proteolytic removal of an amino terminal prosegment in the dense granules of the juxtaglomerular (JG) cells of the kidney by one or more proteases whose identity is uncertain but commonly referred to as the prore...

Understanding the relationship between the dynamics of neural processes and the anatomical substrate of the brain is a central question in neuroscience. On the one hand, modern neuroimaging technologies, such as diffusion tensor imaging, can be used to construct structural graphs representing the architecture of white matter streamlines linking cortical and subcortical structures. On the other ...