Wesley Hough will present a documentary that he worked on while at Hanover College "In the Footsteps of Newton". For more details on the documentary visit the following http://www.hanover.edu/about/news?n=4590
Abstract:
We present a Multivariate Decomposition Method (MDM) for approximating integrals of functions with countably many variables. We assume that the integrands have mixed first order partial derivatives bounded in a γ = {γ_u }u⊂N+ -weighted Lp norm. We also assume that the integrands can be evaluated only at points with finitely many (d) coordinates different than zero and that the cost of such a sampling is equal to $(d) for a given cost function $. We show that MDM can approximate the integrals with the worst case error bounded by ε at cost proportional to −1+|O(ln(1/ε)/ ln(ln(1/ε)))| ε even if the cost function is exponential in d, i.e., $(d) = e^{O(d)}. This is an almost optimal method since all algorithms for univariate functions (d = 1) from this space have the cost bounded from below by Ω(1/ε).
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Dr. Gabriel Veith of Oak Ridge National Laboratory will be presenting a seminar titled Na, it is not another Li-ion battery.
Faculty Host: Dr. Susan Odom
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Dr. Mark Crocker of the Center for Applied Energy Research will be giving a seminar titled Catalysis for the Conversion of Biomass to Fuels and Chemicals.
Faculty Host: Dr. Steven Yates
Title: A brief introduction to quadratic spaces
of a field k is defined to be the minimum n such that 
has a solution over 
. It turns out that if 
, then 
for some 
. The proof is a beautiful application of Pfister forms.TITLE: Connecting Two Problems with a Spectrahedron
ABSTRACT: Spectrahedra are natural generalizations of polyhedra that arise as parameterizations of slices of the cone of positive semidefinite matrices. To a graph G we can associate a spectrahedron known as an elliptope. We will use the elliptope to connect two well-studied problems via their underlying geometry. The first problem is the well-known max-cut problem from linear programming, the feasible region of which is the cut polytope of G. The second problem is the positive semidefinite matrix completion problem whose solution is characterized by extremal rays of the cone of concentration matrices for G. We will begin with a brief introduction to the geometry of positive semidefinite matrices and spectrahedra. Then we will define these two problems and their associated convex bodies. Finally, we will see that for some graphs the facets of the cut polytope correspond to extremal rays of the cone of concentration matrices, and that this correspondence is given by the elliptope and its dual. Moreover, we will see that the shape of the facet decides the rank of the corresponding extremal ray.
True Songs is a record of a series of performances by a group of Japanese artists during the years since the triple disasters of March 11, 2011. Taking inspiration from the classic work by Miyazawa Kenji Night on the Milky Way Train, the event combines song, oral narrative, and spoken word performance. The group has taken the show throughout Japan, from Fukushima to a railroad car in Kyoto. One of the artists, Suga Keijiro, will be in attendance.
