An overview of the self-organizing map algorithm, on which the papers in this issue are based, is presented in this article.

The Self-Organizing Map

Dependence of biodiesel fuel properties on the structure of fatty acid alkyl esters

IEEE Transactions on Pattern Analysis and Machine Intelligence

Production of liquid biofuels from renewable resources

Progress and recent trends in biodiesel fuels

Test quantities of ethyl and methyl esters of four renewable fuels were processed, characterized and
performance tested. Canola, rapeseed, soybean oils, and beef tallow were the feedstocks for the methyl and ethyl esters. A
complete set of fuel properties and a comparison of each fuel in engine performance tests are reported. The study
examines short term engine tests with both methyl and ethyl ester fuels compared to number 2 diesel fuel (D2). Three
engine performance tests were conducted including an engine mapping procedure, an injector coking screening test, and
an engine power study. 
The gross heat contents of the biodiesel fuels, on a mass basis, were 9 to 13% lower than D2. The viscosities of
biodiesel were twice that of diesel. The cloud and pour points of D2 were significantly lower than the biodiesel fuels. The
biodiesel fuels produced slightly lower power and torque and higher fuel consumption than D2. 
In general, the physical and chemical properties and the performance of ethyl esters were comparable to those of the
methyl esters. Ethyl and methyl esters have almost the same energy. The viscosity of the ethyl esters is slightly higher and
the cloud and pour points are slightly lower than those of methyl esters. Engine tests demonstrated that methyl esters
produced slightly higher power and torque than ethyl esters. Fuel consumption when using the methyl and ethyl esters is
nearly identical. Some desirable attributes of the ethyl esters over methyl esters were: significantly lower smoke opacity,
lower exhaust temperatures, and lower pour point. The ethyl esters tended to have more injector coking than the methyl
esters, and the ethyl esters had a higher glycerol content than the methyl esters

Processing, characterization, and performance of eight fuels from lipids.

The solution set $V$ of a polynomial system, i.e., the set of common zeroes of a set of multivariate polynomials with complex coefficients, may contain several components, e.g., points, curves, surfaces, etc. Each component has attached to it a number of quantities, one of which is its dimension. Given a numerical approximation to a point $\mathbf{p}$ on the set $V$, this article presents an efficient algorithm to compute the maximum dimension of the irreducible components of $V$ which pass through $\mathbf{p}$, i.e., a local dimension test. Such a test is a crucial element in the homotopy-based numerical irreducible decomposition algorithms of Sommese, Verschelde, and Wampler. This article presents computational evidence to illustrate that the use of this new algorithm greatly reduces the cost of so-called “junk-point filtering,” previously a significant bottleneck in the computation of a numerical irreducible decomposition. For moderate size examples, this results in well over an order of magnitude improvement in the computation of a numerical irreducible decomposition. As the computation of a numerical irreducible decomposition is a fundamental backbone operation, gains in efficiency in the irreducible decomposition algorithm carry over to the many computations which require this decomposition as an initial step. Another feature of a local dimension test is that one can now compute the irreducible components in a prescribed dimension without first computing the numerical irreducible decomposition of all higher dimensions. For example, one may compute the isolated solutions of a polynomial system without having to carry out the full numerical irreducible decomposition.

/pdf/a-numerical-local-dimension-test-for-points-on-the-solution-p0z9q48pxf.pdf

A Numerical Local Dimension Test for Points on the Solution Set of a System of Polynomial Equations

Let ℰ be a vector bundle on Pn. There is a strong relationship between ℰ and its intermediate cohomology modules. In the case where ℰ has low rank, we exploit this relationship to provide various splitting criteria for ℰ. In particular, we give a splitting criterion for ℰ in terms of the vanishing of certain intermediate cohomology modules. We also show that the Horrocks-Mumford bundle is the only non-split rank two bundle on P4 with a Buchsbaum second cohomology module.

/pdf/monads-on-projective-spaces-30nwurf7wd.pdf

Monads on projective spaces

A flag representation for finite collections of subspaces of mixed dimensions

Many computer vision algorithms employ subspace models to represent data. Many of these approaches benefit from the ability to create an average or prototype for a set of subspaces. The most popular method in these situations is the Karcher mean, also known as the Riemannian center of mass. The prevalence of the Karcher mean may lead some to assume that it provides the best average in all scenarios. However, other subspace averages that appear less frequently in the literature may be more appropriate for certain tasks. The extrinsic manifold mean, the L2-median, and the flag mean are alternative averages that can be substituted directly for the Karcher mean in many applications. This paper evaluates the characteristics and performance of these four averages on synthetic and real-world data. While the Karcher mean generalizes the Euclidean mean to the Grassman manifold, we show that the extrinsic manifold mean, the L2-median, and the flag mean behave more like medians and are therefore more robust to the presence of outliers among the subspaces being averaged. We also show that while the Karcher mean and L2-median are computed using iterative algorithms, the extrinsic manifold mean and flag mean can be found analytically and are thus orders of magnitude faster in practice. Finally, we show that the flag mean is a generalization of the extrinsic manifold mean that permits subspaces with different numbers of dimensions to be averaged. The result is a "cookbook" that maps algorithm constraints and data properties to the most appropriate subspace mean for a given application.

https://www.cv-foundation.org/openaccess/content_cvpr_2014/papers/Marrinan_Finding_the_Subspace_2014_CVPR_paper.pdf

Chris Peterson

Papers

Processing, characterization, and performance of eight fuels from lipids.

A Numerical Local Dimension Test for Points on the Solution Set of a System of Polynomial Equations

Monads on projective spaces

A flag representation for finite collections of subspaces of mixed dimensions

Finding the Subspace Mean or Median to Fit Your Need