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In this paper we discuss a relation between Learning Theory and Regularization of linear ill-posed inverse problems. It is well known that Tikhonov regularization can be profitably used in the context of supervised learning, where it usually goes under the name of regularized least-squares algorithm. Moreover the gradient descent algorithm was studied(More)
In the literature on regularization, many different parameter choice methods have been proposed in both deterministic and stochastic settings. However, based on the available information, it is not always easy to know how well a particular method will perform in a given situation and how it compares to other methods. This paper reviews most of the existing(More)
We introduce a new method to efficiently approximate the number of infections resulting from a given initially infected node in a network of susceptible individuals. Our approach is based on counting the number of possible infection walks of various lengths to each other node in the network. We analytically study the properties of our method, in particular(More)
This paper describes research on the design of a GPS based relative position and attitude sensing mission called Orion. The current Orion design consists of a eet of 6 micro-satellites launched simultaneously into low Earth orbit to demonstrate coordinated attitude control, relative navigation and control, and formation initialization techniques in space.(More)
We prove the following estimate for the spectrum of the normalized Laplace operator ∆ on a finite graph G, 1− (1− k[t]) t ≤ λ1 ≤ · · · ≤ λN−1 ≤ 1 + (1− k[t]) 1 t , ∀ integers t ≥ 1. Here k[t] is a lower bound for the Ollivier-Ricci curvature on the neighborhood graph G[t] (here we use the convention G[1] = G), which was introduced by Bauer-Jost. In(More)
Formation Flying is quickly revolutionizing the way the space community conducts autonomous science missions around the Earth and in space. This technological revolution will provide new, innovative ways for this community to gather scientific information, share this information between space vehicles and the ground, and expedite the Human exploration of(More)
Using projection mapping enables us to bring virtual worlds into shared physical spaces. In this paper, we present a novel, adaptable and real-time projection mapping system, which supports multiple projectors and high quality rendering of dynamic content on surfaces of complex geometrical shape. Our system allows for smooth blending across multiple(More)