Positive Solutions of Nonlinear Elliptic Eigenvalue Problems

We shall study a class of mildly nonlinear elliptic eigenvalue problems which are suggested by several recently occurring problems concerning the steady state temperature distribution of a physical medium in which heat is being generated nonlinearly

Why Build Multi-Use Greenways? Implications for New Jersey and Beyond

In this presentation, Bruce Donald will explain comprehensive research that investing in bicycle/pedestrian infrastructure has numerous benefits including public health, reduced transportation costs, increased access to reliable transportation, tourism, improved local economy, reduced user mortality rates, and environmental benefits. Solutions include developing a comprehensive pedestrian and bicycle network, as well as improving access to these facilities by all of New Jersey’s residents and its visitors. Investing in bicycle infrastructure is at the forefront of twenty-first-century economic development

Positive Solutions of Nonlinear Elliptic Eigenvalue Problems

We shall study a class of mildly nonlinear elliptic eigenvalue problems which are suggested by several recently occurring problems concerning the steady state temperature distribution of a physical medium in which heat is being generated nonlinearly

The EIGHT Manual: A System for Geometric Modelling and Three-Dimensional Graphics on the Lisp Machine

We describe a simple geometric modelling system called Eight which supports interactive creation, editing, and display of three-dimensional polyhedral solids. Perspective views of a polyhedral environment may be generated, and hidden surfaces removed. Eight proved useful for creating world models, and as an underlying system for modelling object interaction in robotics research and applications. It is documented here in order to make the facility available to other members of the Artificial Intelligence Laboratory.MIT Artificial Intelligence Laborator

Probabilistic Disease Classification of Expression-Dependent Proteomic Data from Mass Spectrometry of Human Serum

We have developed an algorithm called Q5 for probabilistic classification of healthy vs. disease whole serum samples using mass spectrometry. The algorithm employs Principal Components Analysis (PCA) followed by Linear Discriminant Analysis (LDA) on whole spectrum Surface-Enhanced Laser Desorption/Ionization Time of Flight (SELDI-TOF) Mass Spectrometry (MS) data, and is demonstrated on four real datasets from complete, complex SELDI spectra of human blood serum. Q5 is a closed-form, exact solution to the problem of classification of complete mass spectra of a complex protein mixture. Q5 employs a novel probabilistic classification algorithm built upon a dimension-reduced linear discriminant analysis. Our solution is computationally efficient; it is non-iterative and computes the optimal linear discriminant using closed-form equations. The optimal discriminant is computed and verified for datasets of complete, complex SELDI spectra of human blood serum. Replicate experiments of different training/testing splits of each dataset are employed to verify robustness of the algorithm. The probabilistic classification method achieves excellent performance. We achieve sensitivity, specificity, and positive predictive values above 97% on three ovarian cancer datasets and one prostate cancer dataset. The Q5 method outperforms previous full-spectrum complex sample spectral classification techniques, and can provide clues as to the molecular identities of differentially-expressed proteins and peptides

Objectives and Progress on Ground Vibration Testing for the Ares Launch Vehicles

NASA has conducted dynamic tests on each of its major launch vehicles during the past 45 years. Each test has provided invaluable data to correlate and correct analytical models used to predict structural responses to differing dynamics for these vehicles. With both Saturn V and Space Shuttle, hardware changes were also required to the flight vehicles to ensure crew and vehicle safety. The Ares I IVGVT will undoubtedly provide similar valuable test data to support successful flights of the Constellation Program. The IVGVT will provide test determined natural frequencies, mode shapes and damping for the Ares I. This data will be used to support controls analysis by providing this test data to reduce uncertainty in the models. The value of this testing has been proven by past launch vehicle successes and failures. Performing dynamic testing on the Ares vehicles will provide confidence that the launch vehicles will be safe and successful in their missions. In addition, IVGVT will provide the following benefits for the Ares rockets: a) IVGVT data along with Ares development flights like Ares I-X, Ares I-Y, Ares I-X Prime, and Orion-1 or others will reduce the risk to the Orion-2 crew. IVGVT will permit anchoring the various analytical and operational models used in so many different aspects of Ares operations. b) IVGVT data will permit better understanding of the structural and GN&C margins of the spacecraft and may permit mass savings or expanded day-of-launch opportunities or fewer constraints to launch. c) Undoubtedly IVGVT will uncover some of the "unknown unknowns" so often seen in developing, launching, and flying new spacecraft vehicles and data from IVGVT may help prevent a loss of vehicle or crew. d) IVGVT also will be the first time Ares I flight-like hardware is transported, handled, rotated, mated, stacked, and integrated. e) Furthermore, handling and stacking the IVGVT launch vehicle stacks will be an opportunity to understand certain aspects of vehicle operability much better (for example, handling procedures, touch-labor time to accomplish tasks, access at interfaces, access to stage mating bolts, access to avionics boxes, access to the Interstage, GSE functionality, and many other important aspects of Ares I operability). All of these results will provide for better vehicle safety and better stewardship of national resources as NASA begins its next phase of human space exploration

High-Throughput Inference of Protein-Protein Interaction Sites from Unassigned NMR Data by Analyzing Arrangements Induced By Quadratic Forms on 3-Manifolds

We cast the problem of identifying protein-protein interfaces, using only unassigned NMR spectra, into a geometric clustering problem. Identifying protein-protein interfaces is critical to understanding inter- and intra-cellular communication, and NMR allows the study of protein interaction in solution. However it is often the case that NMR studies of a protein complex are very time-consuming, mainly due to the bottleneck in assigning the chemical shifts, even if the apo structures of the constituent proteins are known. We study whether it is possible, in a high-throughput manner, to identify the interface region of a protein complex using only unassigned chemical shift and residual dipolar coupling (RDC) data. We introduce a geometric optimization problem where we must cluster the cells in an arrangement on the boundary of a 3-manifold. The arrangement is induced by a spherical quadratic form, which in turn is parameterized by SO(3)xR^2. We show that this formalism derives directly from the physics of RDCs. We present an optimal algorithm for this problem that runs in O(n^3 log n) time for an n-residue protein. We then use this clustering algorithm as a subroutine in a practical algorithm for identifying the interface region of a protein complex from unassigned NMR data. We present the results of our algorithm on NMR data for 7 proteins from 5 protein complexes and show that our approach is useful for high-throughput applications in which we seek to rapidly identify the interface region of a protein complex