Blind navigation

Supervisor(s): Guy Gilboa

Abstract:

Abstract: We will explore algorithms to navigate in areas where GPS is blind (being indoors or due to GPS jamming). The method is based on signal-processing and learning algorithms for smart, super-accurate, Inertial Measurement Units (IMU’s).

Musical harmony and synchronization

Supervisor(s): Eyal Buks

Abstract:

The main goal of this project is to examine the hypothesis that the physical process of synchronization plays a role in audio processing by a human brain. Some mathematical properties of the Hopf model of self-excited oscillation (SEO) and the Arnold model of synchronization suggest a connection to well-known phenomena in musical harmony. To further explore these connections, we will develop in this project a neural network model that will allow studding the response to musical stimulation.

The Spectrum of High Dimensional Networks

Supervisor(s): Dr. Omer Bobrowski, Dr. Emil Saucan

Abstract:

The graph Laplacian and its spectrum have been proven to be powerful mathematical tools that reveal fundamental properties about the structure and functionality of networks. Spectral analysis has conduced a variety of applications in Computer Science and related fields, such as clustering algorithms, randomized approximation methods, error correcting codes, and studying computational complexity. The most significant and abundant applications are in Communication Networks and related problems. In particular, in the analysis of routing algorithms, for minimizing congestion and devising efficient parallel architectures.

One of the main limitations of the graph Laplacian is that it only uses information about pairwise interactions in networks (see Figure (a)). However, in modern networks one can often find connections of higher degrees, that cannot be encoded by a graph. Consider, for example, the case of a social network. Using a graph, we can represent the information that Alice and Bob are friends, Bob and Carol are friends, and Carol and Alice are friends. We cannot say, however, whether Alice, Bob, and Carol, all get together as a group.

Simplicial complexes are high-dimensional generalizations of graphs, that in addition to vertices and edges, may also contain triangles, tetrahedra, and higher dimensional simplexes. These objects provide a natural way to represent such high-degree interactions in network (see Figure (b)). Simplicial complexes have their own notion of Laplacian, and the goal of this project is to study its spectrum. The main question we are interested is: “What can we learn about the structure of such high-dimensional networks, by analyzing their Laplacians”? We will consider both simulated as well as real-world networks, and examine both the spectrum and its corresponding harmonics. Our goal is to look for insights about the network behavior, as well as study the potential of signal processing on such high-dimensional objects (in a similar spirit to signal processing on graphs).

Deep Reinforcement Learning for Blockchain Security

Supervisor(s): Dr. Aviv Tamar and Dr. Ittay Eyal

Abstract:

The central novelty of blockchain protocols is their utilization of incentives to achieve security. The challenge is to defend against rational actors who optimize their gains by deviating from the protocol. Failure to achieve that implies reduced security, and possibly collapse of the system. However, analysis is difficult. The recent success of deep Reinforcement Learning (RL) in related problems hints on its applicability to address this challenge.

The goal of this project is to utilize deep-RL tools for the analysis of existing protocols, and potentially for novel protocol design. The main idea is to train an RL agent as an actor that maximizes gain using the blockchain protocol. Using state-of-the-art deep RL algorithms will enable training strong agents, which exploit any vulnerability of the protocol. Measuring the protocol’s performance against such agents will indicate its security. If successful, the project would have a direct impact on both academic research and the industry.

Pre-requisites:
– Strong python programming

Nice to have:
– Game-theory/RL background
– Distributed systems/networks background

Phase change memory as a building block for neuromorphic computing hardware

Supervisor(s):Dr. Yalon Eilam 

Abstract:

Crossbar arrays of non-volatile memory devices represent one possible path for implementing massively-parallel and highly energy-efficient neuromorphic computing systems. Phase change memory (PCM) is a mature memory technology and a leading candidate as a building block for neuromorphic computing hardware. One of the key limitations to implement PCM in artificial neural networks hardware is the non-linear nature of its resistance changes during programming. The goal of this project is to vary the programming pulse width of PCM devices in order to access a linear regime of the resistance change that will enable analog-type PCM. The project will include performing electrical measurements of PCM devices in a probe-station using a pulse generator, scope, and parameter analyzer.

עילם

“Ramanujan Machine” – Auto-generator for mathematical conjectures

Supervisor(s):Prof. Ido Kaminar

Abstract:

Math is roughly divided to “theory provers” and “theory conjecturing”. Some of the greatest mathematician are known for their theory conjecturing more than their proofs (e.g., Fermat’s last theorem, Hilbert’s problems). We’re developing computer algorithms to create a “Ramanujan Machine” – an auto-generator of mathematical conjectures, similar to the role great mathematicians took in the past. This is a unique research for those who wish to help in pioneering a new field.
We have focused so far on analytic formulas of mathematical constants. We aim to find new formulas for constants to which no such previous representation is known (e.g. the Feigenbaum constants), which will enable “reverse-engineering” the field in which they arise (e.g. chaos and bifurcation theory).
We have recently found new analytic representations for a few important mathematical constants (pi, e, and Apery’s constant, related to the Riemann Zeta function), and are looking forward for creative and motivated students to pursue new directions in this research.

Making qubits from a free electron

Supervisor(s):Prof. Ido Kaminar

Abstract:

Recent preliminary discoveries in our group show that it is possible to implement a single qubit on a single free electron using electron-laser interactions. This work aims to explore the prospects of processing quantum information on free electrons, suggesting a new and promising implementation for a quantum computer, using the infrastructure of the Ultrafast Transmission Electron Microscope (UTEM).
Based on the students’ background and preference, the project can concentrate on the theory side, building the foundations for free electron quantum computing, or on the experimental side, working with the group’s UTEM to plan and conduct experiments showing quantum information processing with free electrons.

Novel Display Technology

Supervisor(s):Prof. Anat Levin

Abstract:

We will work on the development of cool cutting edge display technologies capable of displaying 3D data without glasses, reproducing highlights and reacting to illumination. We will use modern tools in computer vision, computer graphics and image processing.

Seeing the invisible

Supervisor(s):Prof. Anat Levin
Abstract:
We work on the reconstruction of the internal structure of thick objects that cannot be seen directly, using new time of flight imaging technologies, combined with new optimization algorithms