Hamilton Institute Seminars (HD / large)

Speaker:

Prof. T. Laffey

Abstract:

Let σ = (λ_1,...,λ_n) be a list of complex numbers which we aim to realize constructively as the spectrum of a nonnegative matrix. Most constructions available in the literature rely on building matrices related to companion matrices from the polynomial f(x) = (x-λ_1)...(x-λ_n). Kim, Ormes and Roush (JAMS 2000) showed how certain formal power series related to f(x), which have all coefficients, other than the leading one, negative, can be used in finding constructions over the semiring of polynomials with nonnegative coefficients, while, in joint work, Šmigoc and this author (ELA 17 (2008) 333-342, LAMA 58 (2010), 1053-1059) have used polynomials having all their non-leading coefficients negative, to find realizations when σ has not more than two entries with positive real parts. Beginning with the observation that if λ_1,...,λ_n are all positive, then the Taylor expansion of the nth root of F(t) = (1-λ_1t)...(1-λ_nt) about t=0 has all its non-leading coefficients negative, we present a number of results on the negativity of the coefficients of power series and their applications to nonnegative matrices.

Speaker:

Prof. R. Loewy

Abstract:

Let K be a proper (i.e., closed, pointed, full and convex) cone in R^n. We consider A∈R^(n×n) which is K-primitive, that is, there exists a positive integer l such that A^l.x ∈ int K for every 0≠x∈K. The smallest such l is called the exponent of A, denoted by γ(A).

For a polyhedral cone K, the maximum value of γ(A), taken over all K-primitive matrices A, is denoted by γ(K). Our main result is that for any positive integers m,n, 3 ≤ n ≤ m, the maximum value of γ(K), as K runs through all n-dimensional polyhedral cones with m extreme rays, equals

( n - 1 )( m - 1 ) + ½( 1 + (-1)^{(n-1)m} ).

We will consider various uniqueness issues related to the main result as well as its connections to known results.

This talk is based on a joint work with Micha Perles and Bit-Shun Tam.

Speaker:

Prof. S. Friedland

Abstract:

In this talk we will discuss a number of generalizations of results on nonnegative matrices to nonnegative tensors as: irreducibility and weak irreducibility, Perron-Frobenius theorem, Collatz-Wielandt characterization, Kingman's inequality, Karlin-Ost and Friedland theorems, tropical spectral radius, diagonal scaling, Friedland-Karlin inequality, nonnegative multilinear forms.

Speaker:

Prof. G. Bianchi

Abstract:

In this talk we address the following question: What is the minimum theoretical delay performance achievable by an overlay peer-to-peer streaming system where the streamed content is subdivided into chunks? We first start to show that, when posed for chunk-based systems, and as a consequence of the store-and-forward way in which chunks are delivered across the network, this question has a fundamentally different answer with respect to the case of systems where the streamed content is distributed through one or more flows (sub-streams). We then proceed by defining a convenient performance metric, called "stream diffusion metric", which is directly related to the end-to-end minimum delay achievable in a P2P streaming network, but which allows us to circumvent the complexity emerging when directly dealing with delay. We further derive a performance bound for such metric, and we show how this bound relates to two fundamental parameters: the upload bandwidth available at each node, and the number of neighbors a node may deliver chunks to. Quite interestingly, in this bound, n-step Fibonacci sequences play a key role, and appear to set the laws that characterize the optimal operation of chunk-based systems. Finally, we constructively show by means of which topologies and system operation this bound is attainable.

Speaker:

Prof. J. Leonard

Abstract:

This talk will have two parts. In part one, we will review recent progress in mobile robotics, focusing on the problems of simultaneous mapping and localization (SLAM) and cooperative navigation of mobile sensor networks. The problem of SLAM is stated as follows: starting from an initial position, a mobile robot travels through a sequence of positions and obtains a set of sensor measurements at each position. The goal is for the mobile robot to process the sensor data to compute an estimate of its position while concurrently building a map of the environment. We will present SLAM results for several scenarios including land robot mapping of large-scale environments and undersea mapping using optical imaging sensors. We will also describe work on cooperative navigation for networks of autonomous underwater vehicles (AUVs) and autonomous sea-surface vehicles (ASVs).

In the second part of the talk, we will provide an overview of MIT's entry in the 2007 DARPA Urban Challenge. The goal of this effort was to produce a car that can drive autonomously in traffic. Our team developed a novel strategy for using a large number of many inexpensive sensors, mounted on the vehicle periphery, and calibrated with a new cross-modal calibration technique. Lidar, camera, and radar data streams are processed using an innovative, locally smooth state representation that provides robust perception for real-time autonomous control. A resilient planning and control architecture has been developed for driving in traffic, comprised of an innovative combination of well-proven algorithms for mission planning, situational planning, situational interpretation, and trajectory control. The performance of our system in the NQE and race events will be reviewed, and ideas for future research will be discussed.

For more information, see http://grandchallenge.mit.edu

Joint work with Seth Teller, Michael Bosse, Paul Newman, Ryan Eustice, Matthew Walter, Hanumant Singh, Henrik Schmidt, Mike Benjamin, Alexander Bahr, Joseph Curcio, Andrew Patrikalakis, Matt Antone, David Barrett, Mitch Berger, Ryan Buckley, Stefan Campbell, Alexander Epstein, Gaston Fiore, Luke Fletcher, Emilio Frazzoli, Robert Galejs, Jonathan How, Albert Huang, Karl Iagnemma, Troy Jones, Sertac Karaman, Olivier Koch, Siddhartha Krishnamurthy, Yoshi Kuwata, Keoni Maheloni, David Moore, Katy Moyer, Edwin Olson, Andrew Patrikalakis, Steve Peters, Stephen Proulx, Nicholas Roy, Daniela Rus, Chris Sanders, Seth Teller, Justin Teo, Robert Truax, Matthew Walter, and Jonathan Williams.

Speaker:

Dr. T. Röfer

Abstract:

Building the software for a competitive robot soccer team is a challenging task. The robots have to perceive their environment, estimate where they and the other relevant object are located on the field, decide what to do, and execute those decisions. All this has to happen in real-time, on-board the robots, with limited computing power, and not only for a single robot, but for the whole team. The lecture will give a survey of these tasks, using the methods used by the team B-Human in the RoboCup Standard Platform League as an example.

Speaker:

C. Walz

Abstract:

A first introduction to R.

Speaker:

Dr. V. Lazzarini

Abstract:

Non-linear distortion methods form a set of elegant and computationally economic methods of synthesis and processing for musical applications. Among these, we find the famous Frequency Modulation synthesis, as developed by Chowning and made popular by Yamaha. In addition, various other techniques, including Discrete Summation Formulae, Waveshaping and Phase distortion, can be cast in the same group (and often be given alternative interpretations) of non-linear distortion methods. Research in the area has been very limited since the mid nineties, until a recent series of developments spurred new interest in these ideas. In this talk, I will first introduce briefly the principles of non-linear distortion, providing an overview of the area. I will then follow this with a tour of recent work, which will include adaptive methods, virtual analogue models and analysis-synthesis applications.

Speaker:

Dr. J. Petravic

Abstract:

In HIV dynamics models, it is commonly assumed that HIV-infected cells all have the same viral production and death rates. We explored the dynamics of viral production and death in vitro to determine the validity of this assumption. We infected human cells with HIV-1 constructs that expressed enhanced green fluorescent protein (EGFP) and determined the amount of viral proteins produced by infected cells. Analysis of the flow cytometry data showed that the productively infected cells exhibited a broad, approximately log-normal distribution of viral protein content (spanning several orders of magnitude) that changed its shape and mean fluorescence intensity over time, and that population death rate apparently did not correlate with its mean EGFP content.

We assumed that the observed EGFP fluorescence level represented the balance of protein production and degradation. In our model of the infected cell population, EGFP fluorescence distribution at any time depended on probability distributions of four independent parameters: time to the start of protein production, protein production and degradation rates, and the lifespan of infected cells. After exploration of possible combinations of parameter distributions, we found that a distribution of protein production rates that is negatively correlated to the times to start of production of viral can explain the observed time course of the distribution of EGFP intensity.

Speaker:

Dr. Y. Setty

Abstract:

In recent years, we have used software engineering tools to develop reactive models to simulate and analyze the development of organs. The modeled systems embody highly complex and dynamic processes, by which a set of precursor stem cells proliferate, differentiate and move, to form a functioning tissue. Three organs from diverse evolutionary organisms have been thus modeled: the mouse pancreas, the C. elegans gonad, and partial rodent brain development. Analysis and execution of the models provided dynamic representation of the development, anticipated known experimental results and proposed novel testable predictions. In my talk, I will l discuss challenges, goals and achievement in this direction in science.