Time-Discretization of Hamiltonian Dynamical Systems

Difference equations for Hamiltonian systems are derived from a discrete variational principle. The difference equations completely determine piecewise-linear, continuous trajectories which exactly conserve the Hamiltonian function at the midpoints of each linear segment. A generating function exists for transformations between the vertices of the trajectories. Existence and uniqueness results are present as well as simulation results for a simple pendulum and an inverse square law system

A Variable Time-Step Midpoint Scheme for Hamiltonian Systems

A smooth time-step selection formula for the midpoint method is derived which minimize deviations in the Hamiltonian function along piecewise-linear phase space trajectories of autonomous Hamiltonian systems. The time-step formula is implemented in a second order pre­dictor/corrector scheme and applied to Kepler\u27s problem. The formula significantly improves energy conservation as well as the accuracy of the configuration space trajectory. Peak errors in position and momentum coordinates are not significantly reduced, but the time behavior of the errors is markedly more regular

Intrinsic Contact Geometry of Protein Dynamics

We introduce a new measure for comparing protein structures that is especially applicable to analysis of molecular dynamics simulation results. The new measure generalizes the widely used root-mean-squared-deviation (RMSD) measure from three dimensional to n-dimensional Euclidean space, where n equals the number of atoms in the protein molecule. The new measure shows that despite significant fluctuations in the three dimensional geometry of the estrogen receptor protein, the protein\u27s intrinsic contact geometry is remarkably stable over nanosecond time scales. The new measure also identifies significant structural changes missed by RMSD for a residue that plays a key biological role in the estrogen receptor protein

A Data-driven Approach Towards Human-robot Collaborative Problem Solving in a Shared Space

We are developing a system for human-robot communication that enables people to communicate with robots in a natural way and is focused on solving problems in a shared space. Our strategy for developing this system is fundamentally data-driven: we use data from multiple input sources and train key components with various machine learning techniques. We developed a web application that is collecting data on how two humans communicate to accomplish a task, as well as a mobile laboratory that is instrumented to collect data on how two humans communicate to accomplish a task in a physically shared space. The data from these systems will be used to train and fine-tune the second stage of our system, in which the robot will be simulated through software. A physical robot will be used in the final stage of our project. We describe these instruments, a test-suite and performance metrics designed to evaluate and automate the data gathering process as well as evaluate an initial data set.Comment: 2017 AAAI Fall Symposium on Natural Communication for Human-Robot Collaboratio

Can an Engineering Competition Catalyze Curriculum Innovation?

This article describes the ongoing efforts of a multidisciplinary group of faculty at an undergraduate institution to form a team and compete in the IBM AI XPRIZE competition. We describe the advantages and disadvantages of faculty participation in major engineering competitions over more traditional professional activities at undergraduate engineering institutions. Our discussion is focused on the benefits to three major groups: undergraduate students, faculty, and academic institutions. We use examples from our one year of experience in the competition and from the literature to illustrate these benefits. Already observed benefits from the competition include increased student engagement, development and introduction of a new minor in cognitive science, the purchase of a state-of-the-art robot and a deep learning server, enhanced multidisciplinary collaboration among faculty, and heightened awareness among administrators of the growing importance of artificial intelligence (AI) technologies. Results of a student survey regarding their involvement in with the team are presented

Index Terms

protein structure alignment, structural bioinformatics, contact maps, spectral methods We present two algorithms that use spectral methods to align protein folds. One of the algorithms is suitable for database searches, the other for difficult alignments. We present computational results for 780 pairwise alignments used to classify 40 proteins as well as results for a separate set of 36 protein alignments used for comparison to four other alignment algorithms. We also provide a mathematically rigorous development of the intrinsic geometry underlying our spectral approach.