From Steiner Formulas for Cones to Concentration of Intrinsic Volumes

The intrinsic volumes of a convex cone are geometric functionals that return basic structural information about the cone. Recent research has demonstrated that conic intrinsic volumes are valuable for understanding the behavior of random convex optimization problems. This paper develops a systematic technique for studying conic intrinsic volumes using methods from probability. At the heart of this approach is a general Steiner formula for cones. This result converts questions about the intrinsic volumes into questions about the projection of a Gaussian random vector onto the cone, which can then be resolved using tools from Gaussian analysis. The approach leads to new identities and bounds for the intrinsic volumes of a cone, including a near-optimal concentration inequality.Comment: This version corrects errors in Propositions 3.3 and 3.4 and in Lemma 8.3 that appear in the published versio

The achievable performance of convex demixing

Demixing is the problem of identifying multiple structured signals from a superimposed, undersampled, and noisy observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. When the constituent signals follow a generic incoherence model, this analysis leads to precise recovery guarantees. These results admit an attractive interpretation: each signal possesses an intrinsic degrees-of-freedom parameter, and demixing can succeed if and only if the dimension of the observation exceeds the total degrees of freedom present in the observation

Robust computation of linear models by convex relaxation

Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER, that can reliably fit a low-dimensional model to this type of data. This approach parameterizes linear subspaces using orthogonal projectors, and it uses a relaxation of the set of orthogonal projectors to reach the convex formulation. The paper provides an efficient algorithm for solving the REAPER problem, and it documents numerical experiments which confirm that REAPER can dependably find linear structure in synthetic and natural data. In addition, when the inliers lie near a low-dimensional subspace, there is a rigorous theory that describes when REAPER can approximate this subspace.Comment: Formerly titled "Robust computation of linear models, or How to find a needle in a haystack

Preliminary Survey of the Terrestrial Isopods (Isopoda), Millipedes (Diplopoda), Harvestmen (Opiliones), and Spiders (Araneae) of Toft Point Natural Area, Door County, Wisconsin

Toft Point Natural Area is a National Natural Landmark owned and managed by the University of Wisconsin – Green Bay and located on the Lake Michigan shore of Wisconsin’s Door Peninsula. With twelve biotic communities on 700 acres, Toft Point contains considerable biological diversity. We conducted a preliminary survey of the arachnids (spiders and harvestmen, excluding mites and pseudoscorpions), millipedes (diplopods), and terrestrial isopods (Isopoda: Oniscoidea). Sampling occurred on three dates in 2001 using leaf litter collection with Berlese extraction and a timed collection by hand that incorporated a variety of techniques. Specimens from a 1992 survey and assorted collecting events were also used to compile a species list. The list includes five isopods, four millipedes, six harvestmen, and 113 spiders, including 16 new state records (two millipedes and 14 spiders) and 90 new Door County records. Litter collection and sampling in wetland habitats were both especially productive

A Miniature Robot for Isolating and Tracking Neurons in Extracellular Cortical Recordings

This paper presents a miniature robot device and control algorithm that can autonomously position electrodes in cortical tissue for isolation and tracking of extracellular signals of individual neurons. Autonomous electrode positioning can significantly enhance the efficiency and quality of acute electrophysiolgical experiments aimed at basic understanding of the nervous system. Future miniaturized systems of this sort could also overcome some of the inherent difficulties in estabilishing long-lasting neural interfaces that are needed for practical realization of neural prostheses. The paper describes the robot's design and summarizes the overall structure of the control system that governs the electrode positioning process. We present a new sequential clustering algorithm that is key to improving our system's performance, and which may have other applications in robotics. Experimental results in macaque cortex demonstrate the validity of our approach

A Low Cost Remote Sensing System Using PC and Stereo Equipment

A system using a personal computer, speaker, and a microphone is used to detect objects, and make crude measurements using a carrier modulated by a pseudorandom noise (PN) code. This system can be constructed using a personal computer and audio equipment commonly found in the laboratory or at home, or more sophisticated equipment that can be purchased at reasonable cost. We demonstrate its value as an instructional tool for teaching concepts of remote sensing and digital signal processing.Comment: Accepted for publication in American Journal of Physic

Can Power from Space Compete?

Satellite solar power (SSP) has been suggested as an alternative to terrestrial energy resources for electricity generation. In this study, we consider the market for electricity from the present to 2020, roughly the year when many experts expect SSP to be technically achievable. We identify several key challenges for SSP in competing with conventional electricity generation in developed and developing countries, discuss the role of market and economic analysis as technical development of SSP continues during the coming years, and suggest future research directions to improve understanding of the potential economic viability of SSP.

Random Filters for Compressive Sampling and Reconstruction

We propose and study a new technique for efficiently acquiring and reconstructing signals based on convolution with a fixed FIR filter having random taps. The method is designed for sparse and compressible signals, i.e., ones that are well approximated by a short linear combination of vectors from an orthonormal basis. Signal reconstruction involves a non-linear Orthogonal Matching Pursuit algorithm that we implement efficiently by exploiting the nonadaptive, time-invariant structure of the measurement process. While simpler and more efficient than other random acquisition techniques like Compressed Sensing, random filtering is sufficiently generic to summarize many types of compressible signals and generalizes to streaming and continuous-time signals. Extensive numerical experiments demonstrate its efficacy for acquiring and reconstructing signals sparse in the time, frequency, and wavelet domains, as well as piecewise smooth signals and Poisson processes