(The talk will be given in English)

Speaker:     Prof. Michael Margaliot
                     EE, Tel Aviv University

Monday, November 25^th, 2019
15:00 - 16:00

Room 011, Kitot Bldg., Faculty of Engineering

A Generalization of Linear Positive Systems with Applications to Nonlinear Systems: Invariant Sets and the Poincare–Bendixon Property
Abstract

The dynamics of linear positive systems maps the positive orthant to itself. In other words, it maps a set of vectors with zero sign variations to itself. This raises the following question: what linear systems map the set of vectors with k sign variations to itself? We address this question using tools from the theory of cooperative dynamical systems and the theory of totally positive matrices. This yields a generalization of positive linear systems called kpositive linear systems, that reduces to positive systems for k = 1. We describe applications of this new type of systems to the analysis of nonlinear dynamical systems. In particular, we show that such systems admit certain explicit invariant sets, and for the case k = 2 establish the Poincare-Bendixon property for certain trajectories. 
This is joint work with Eyal Weiss.

Short Bio
Michael Margaliot received the BSc (cum laude) and MSc degrees in Elec. Eng. from the Technion—Israel Institute of Technology in 1992 and 1995, respectively, and the PhD degree (summa cum laude) from Tel Aviv University in 1999. He was a post-doctoral fellow in the Dept. of Theoretical Math. at the Weizmann Institute of Science. In 2000, he joined the Dept. of Elec. Eng.–Systems, Tel Aviv University, where he is currently a Professor. His research interests include the stability analysis of differential inclusions and switched systems, optimal control theory, computation with words, Boolean control networks, contraction theory, and systems biology. He served as an Associate Editor for IEEE Transactions on Automatic Control during 2015–2017.‏

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SCHOOL OF MECHANICAL ENGINEERING SEMINAR
Wednesday, December 4, 2019 at 14:00
Wolfson Building of Mechanical Engineering, Room 206

Active Matter: `active thermodynamics’ and the dynamics of biopolymer gels

Tomer Markovich
CTBP, Rice University and DAMTP, University of Cambridge

Active materials are composed of many components that can convert energy from its environment (usually in the form of chemical energy) into directed mechanical motion. Time reversal symmetry is thus locally broken, leading to a variety of novel phenomena such as motility induced phase separation, reversal of the Ostwald process and flocking. Examples of active matter are abundant and range from living matter such as bacteria, actomyosin networks and bird flocks to Janus particles, colloidal rollers and macroscale driven chiral rods. Nevertheless, in many cases experiments on active materials exhibit equilibrium like properties (e.g., sedimentation of bacteria). In the first part of the talk I will try to answer the important question: how do we know a system is `active’? And if it is, can we have generic observables as in equilibrium thermodynamics? Can we measure how far it is from equilibrium? In the second part of the talk I will focus on examples of activity in biopolymer gels, such as the cytoskeleton of living cells. I will show some of the effects of active motors with emphasis on chiral motors. The latter does not have a unique hydrodynamic description, which one can utilize to gain access to the microscopic details of the complex motors using macroscopic measurements. I will also discuss non-motor activity and demonstrate how it can result in contractility, e.g., in the process of cell division.

Bio
Dr. Tomer Markovich is Postdoctoral Research Associate in the Center for Theoretical and Biological Physics (CTBP) at Rice University working with Professor Fred MacKintosh. He obtained his PhD in Physics at Tel Aviv University under the supervision of Professor David Andelman in 2017. Prior to his current appointment, Tomer was a Blavtanik Postdoctoral Fellow in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge working with Professor Michael Cates.

Speaker: Assaf Ben-Yishai

Ph.D. student under the supervision of Prof. Ofer Shayevitz

Monday, November 4^th, 2019 at 15:00
Room 206, Wolfson Mechanical Eng. Bldg., Faculty of Engineering

Interaction in Gaussian and Binary Channels

Abstract

The celebrated channel coding theorem proved by Claude Shannon in 1948, shows that information can be reliably conveyed over a noisy channel as long as its rate does not exceed a fundamental limit called the channel capacity. The scenario considered in Shannon’s original paper (and in the majority of the works following it), is where one user sends a long predetermined message to another user over a noisy channel using a codebook, i.e., by encoding the message into a codeword – a long predetermined sequence of channel inputs. In this research, we study two basic two-party communication scenarios that are richer than the prototypical problem considered by Shannon.

In the first part of the research, we study the additive white Gaussian noise (AWGN) channel with noisy feedback. The AWGN with clean feedback has been originally studied by Schalkwijk & Kailath in 1966. They presented a coding scheme (the SK-scheme) based on scalar arithmetic and achieving remarkable improvement in the delay vs. reliability tradeoff compared to communication without feedback. However, this scheme is known to fail in the presence of arbitrarily low noise in the feedback channel. We show that the susceptibility to feedback noise can be overcome by using modulo-arithmetic over the feedback, maintaining essentially the same low-complexity as the SK-scheme. Our new scheme provides a fast decay in the error probability at rates close to the Shannon capacity, provided that the signal-to-noise ratio of the feedback channel is sufficiently larger than that of the feedforward channel. The idea of applying modulo operations over the feedback is then leveraged to obtain two more contributions: improved error exponents for the AWGN with noisy feedback, and a new achievable rate region for the AWGN broadcast channel with an AWGN multiple-access feedback.

In the second part of the research, we study the problem of interactive communication over binary-input channels. In this setup, originally presented by Schulman in 1992 and motivated by distributed computing, two parties wish to simulate an interactive protocol over a pair of noisy channels. In contrast to Shannon’s setup, the information exchanged by the parties is not predetermined but rather generated on-the-fly during the course of communication. Our first contribution is a structured coding scheme based on extended-Hamming codes and randomized error detection, which is proved to reliably simulate any protocol at a coding rate of at least 0.302 the Shannon channel capacity, for any binary-input symmetric-output memoryless channel. We further show that the randomness required by the scheme can be harvested from the channel, giving rise to a fully deterministic coding scheme.

An exact characterization of the interactive capacity for general protocols remains notoriously elusive to date. It is commonly believed that the interactive capacity is strictly smaller than the Shannon capacity; this was recently shown to be the case in the infinitesimal noise regime by Kol & Raz. Nevertheless, rather surprisingly, we show that the full Shannon capacity can be achieved when simulating arbitrary two-state protocols, as well as broad classes of finite-state protocols with a bounded number of states.

Speaker: Carmi Shimon

M.Sc. student under the supervision of Prof. Miriam Furst-Yust

Wednesday, October 30, 2019 at 15:00

Room 011, Kitot Bldg., Faculty of Engineering

The Advantage of Beamformer Cochlear Noise Reduction Algorithm to the Hearing Impaired

Abstract

Hearing aid (HA) research still have the challenge of improving the ability of the   hearing impaired (HI) to understand speech in a noisy environment. Modern HAs use multiple-channel noise reduction algorithms to reduce the background noise. A decade ago we have developed a Cochlear Noise Reduction Algorithm (CNRA) that mimics the way the cochlea process acoustic signals. We have shown experimentally that the algorithm significantly helps HI people, but not normal hearing (NH) people. In the current study we introduce a new algorithm:  Beamformer Cochlear Noise Reduction Algorithm  (BCNRA) which includes a beamformer (the Frost algorithm) followed by CNRA.  BCNRA was evaluated theoretically and experimentally by using a database of 150 Hebrew sentences embedded in different noise types and SNRs. The theoretical evaluation included derivation of Segmental SNR (sSNR) of the input signals, followed by Frost and followed by BCNRA. The analysis yielded a significant improvement in  sSNR of BCNRA relative to Frost especially in those parts of the sentences that did not include speech. In the experimental evaluation subjects were asked to indicate the words they heard while listening to  noisy sentences. The subjects were a group of 10 young normal hearing (NH) people and 10 old HI people who regularly use HAs. In the average the NH yielded an improvement of about 30% in words identification following both Frost BCNRA. On the other hand, the HI yielded an improvement of 30% following Frost and 50% following BCNRA. The benefit of BCNRA to the HI is probably due to its ability to separate words in the noisy sentences.