Archive for June 2010

Implicit Bias

25th June 2010, 07:26 am

At an AWIS–NSF meeting in DC, I am learning about implicit bias, that none of us see things objectively, as in the following amazing optical illusions:

The Tables

The Checkerboard (and video)

Squares

Spinning Woman

T-Rex

The following human figures on the left are exactly the same color and shade as those on the right:

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For information on similar gender biases, see the brochure by WISELI on “Reviewing Applicants.”

Note added 25 May 2011. AWIS has posted some webcasts. One study found that readers of CVs identical except for a man’s or a woman’s name at the top preferred to hire the man. The same study  found no such difference for tenure decisions.

Category: General interest  |  3 Comments

Variation Formulae for Perimeter and Volume Densities

22nd June 2010, 07:45 am

For Rn+1 with volume density f and perimeter density g, for a normal variation u of a surface with classical mean curvature H, the first variation of volume and perimeter are given by:

\delta ^1V=-\int uf,

\delta ^1P=-\int [(g/f)nH - (1/f)(\partial g/\partial n)] uf.

For a volume-preserving variation, the second variation of perimeter is given by:
\delta ^2P=\int g|\nabla u|^2-g|\sigma|^2u^2-f\frac{\partial (g/f)}{\partial n}u^2nH+u^2\frac{\partial ^2g}{\partial n^2}-\frac 1fu^2\frac{\partial f}{\partial n}\frac{\partial g}{\partial n},

where \sigma is the second fundamental form, so that \sigma^2 is the sum of the squares of the principal curvatures. Continue reading ‘Variation Formulae for Perimeter and Volume Densities’ »

Category: Math  |  1 Comment