We introduce a novel computational framework, Principal Variety Analysis (PVA), for primarily nonlinear data modeling. PVA accommodates algebraic sets as the target subspace through which limitations of other existing approaches is dealt with. PVA power is demonstrated in this paper for learning kinematics of objects, as an important application. PVA takes recorded coordinates of some pre-speci...

In this paper, the concept of toric difference varieties is defined and four equivalent descriptions for toric difference varieties are presented in terms of difference rational parametrization, difference coordinate rings, toric difference ideals, and group actions by difference tori. Connections between toric difference varieties and affine N[x]-semimodules are established by proving the corr...

*Extension Crop Specialist, Professor of Forage Genetics and Research Associate in Forages, respectively, Department of Plant & Soil Sciences, Montana State University, Bozeman, MT 59717 Alfalfa—the most productive and most widely adapted forage species—is indeed “Queen of the Forages.” A grower’s initial decision to produce alfalfa and subsequent choice of varieties have long-term consequences...

Let fa,b(z, z̄) = z a1+b1 1 z̄ b1 1 + · · ·+z an+bn n z̄ bn n be a polar weighted homogeneous polynomial with aj > 0, bj ≥ 0, j = 1, . . . , n and let fa(z) = z1 1 + · · ·+z an n be the associated weighted homogeneous polynomial. Consider the corresponding link variety Ka,b = f −1 a,b (0) ∩ S2n−1 and Ka = f−1 a (0) ∩ S2n−1. Ruas-Seade-Verjovsky [4] proved that the Milnor fibrations of fa,b and fa ...

Multi-view Geometry is reviewed from an Algebraic Geometry perspective and multi-focal tensors are constructed as equivariant projections of the Grassmannian. A connection to the principal minor assignment problem is made by considering several flatlander cameras. The ideal of the quadrifocal variety is computed up to degree 6 using the representations of GL(3) in the polynomial ring on the spa...

The authors examined the influence of age on variety seeking in 3 experiments. When given choices among jellybeans or music, age differences in variety seeking emerged. Younger adults selected similar levels of variety when choosing what to consume immediately and what to consume later. In contrast, older adults consistently chose less variety when making choices to be consumed at a later time ...

JCB • VOLUME 173 • NUMBER 6 • 2006 826 Disorder for variety D isordered regions in proteins are prime real estate for alternative splicing, say Pedro Romero, Keith Dunker (Indiana University-Purdue University, Indianapolis, IN), and colleagues fi nd that d. The innate disorder allows protein variation that in turn increases functional diversity. Both splicing and disorder are more common in mul...

It is argued that creativity might be amplified through the co-operative sharing of brain power (in contrast to Ashby’s amplification of intelligence by restricting attention to the problem). This argument is extended to the act of design (seen as the making of the new), where it is proposed that the nature of the computer is to encourage co-operative sharing because, by making perfect copies, ...

*Extension Crop Specialist, Professor of Forage Genetics and Research Associate in Forages, respectively, Department of Plant & Soil Sciences, Montana State University, Bozeman, MT 59717 Alfalfa—the most productive and most widely adapted forage species—is indeed “Queen of the Forages.” A grower’s initial decision to produce alfalfa and subsequent choice of varieties have long-term consequences...