Spotlight on Prof. Aviv Gibali

Q&A with Prof. Aviv Gibali Head of the Department of Applied Mathematics

Prof. Aviv Gibali

One of HIT’s latest recruits, Prof. Aviv Gibali, uses the power of mathematics to optimize medical and industrial practices in new and original ways. We met up with Prof. Gibali to hear about his research interests.

How do you come up with new mathematical solutions for industrial needs?

What usually happens is that I meet interesting people from various fields and during our discussions, I realize that mathematics, specifically optimization, can be used to overcome hurdles they encounter. The world is constantly advancing and consequently, it is constantly in need of new mathematical solutions, alongside, naturally, solutions to “old” problems. This is especially true in the field of data science: we rely more and more on computers, but there is a limit to how much we can increase computers’ calculation abilities, and this is where mathematics comes in with its creativity and finds solutions to big problems. Mathematics was, and will forever remain, the absolute language of everything and the approach used to model and solve problems.

What is optimization exactly?

Optimization is a mathematical concept in which there is a goal function is minimized/maximized and constraints that need to be fulfilled. A goal could be shortening my travel time to HIT, maximizing my profit, limiting my expenses, or complying with a dietary requirement, like meeting the daily recommended amount of iron. Of course, there are also constraints. For example, in the case of shortening travel time, the constraints would be the mode of transportation (bus, train, taxi, etc.), the number of stops, toll roads, as well as other considerations. As a mathematician, my first goal is to model the problem; this means translating the practical problem into mathematical language. Then, optimization tools are used to solve the problem, followed by the simulation and evaluation of the solutions. The abovementioned steps are a general process that is applied to any field. Amazingly, oftentimes you’ll find that a mathematical model for one problem can also be used for another problem, one that doesn’t even seem related. For example, understanding the shape of a tumor within the body can be achieved using an algorithm similar to those already used in online stores for testing how a buyer’s foot fits a specific shoe.

Can you give me an example of how optimization is used for solving a problem in Industry?

As a member of the Mathematics for Industry Network [MI-NET], I was invited to a Hackathon where the company Engino presented a challenge to the participants. Its smart Lego-like pieces can be used to build a wide range of models, and the company wanted to learn of means to identify new models that can be constructed with a kit containing a specific array of pieces; it also wanted to be able to retroactively define the guidelines for building each of the many possible models. This five-day intensive Hackathon led to the publication of a manuscript that provided a solution to this problem in a prestigious journal in the field of operation research. The company has implemented our algorithmic solution on its website in the form of videos that show how the various models can be built.

Another example is research I conducted during my postdoc at The Fraunhofer Institute for Industrial Mathematics ITWM (https://www.itwm.fraunhofer.de/en.html), Germany. At the request of the gemstones industry, we successfully defined a mathematical tool that can be implemented in a machine so that it could polish and cut “beautiful” gemstones.

Another example that comes to mind is consultation work I did for a startup company that wanted to significantly reduce the cost of headphones while still providing top-notch noise filters. Today, such headphones cost around 300 USD and they wanted to bring the price down to 10–20 USD. Instead of investing in the digital components, they wanted to use mathematics to apply an adaptive filter for noise reduction. In physical terms, noise is a sound wave that merges with the sound wave that the listener wants to hear; the sum of the two waves is what reaches the ear. The goal was to be able to identify this sum and remove it. However, the noise's amplitude and frequency constantly change; thus, this problem requires an algorithm for a filter that can adapt to changing noise conditions. Once this problem is viewed through the lens of mathematics, one can indeed come up with a suitable solution.

As you can see, optimization and algorithms can be implemented across the spectrum of industries.

Can you use optimization to advance medicine?

Here are a few examples of current projects related to the field of medical image processing. One such project that I am looking into is a potential collaboration with Sheba Medical Center: they want to be able to reconstruct the original shape and location of an extracted tumor within the body, which will aid the pathologist’s work.

I am also working with physicians and medical physicist from Germany to develop a method that enables imaging a tumor and then treating a specific location of interest observed in the image directly afterward. This is a complicated project because some parts of the body, such as the lungs, are constantly moving. Thus, in order to provide an accurate treatment, the surgeon needs a way to determine the real future location of a specific point observed in the image. Practically speaking, this means that an image is taken and, immediately afterward, the precise tumor location is irradiated based on the output of an algorithm that uses the image as source input.

I have also developed an algorithm that can remove unwanted image disturbances resonating from metal implants in computerized tomography (CT) images.

How widespread is the use of optimization approaches in Israel?

Most of the Israeli industry is classical/traditional. Its many small companies have no idea that many of their problems can be solved with the help of mathematical tools; consequently, mathematicians can greatly contribute to the industry. The big challenge is to convince people from all sectors that as industrial problems become ever more sophisticated, relying on mathematical modeling and understanding is becoming a necessity.

It is this perspective that drives my efforts to nurture the next generation of leading Israeli mathematicians. I actively promote mathematical education on all levels, from elementary school to higher education. In particular, I give lectures in schools about the important role of mathematics in everyday life and how it can be found everywhere. I also try to engage high-school mathematics teachers by organizing workshops on the importance of mathematics in real life. In addition, I organize joint events between mathematicians and industry people to increase awareness of the applications of mathematics in the industry.

Prof. Aviv Gibali joined the Faculty of Sciences at Holon Institute of Technology as the head of the applied mathematics program in October 2023. He received his PhD in Mathematics from the Technion (Israel Institute of Technology), in 2012; he conducted his postdoctoral research at Fraunhofer ITWM, Germany, until 2014. In the years 2014-2023, Prof. Gibali was a faculty member at the Mathematics Department of Braude College of Engineering, Karmiel; he also served as the department’s head in 2020-2023. In addition to his academic background, Prof. Gibali has over 10 years of experience in the field of intensity-modulated radiation therapy (IMRT) and image reconstruction. He has published more than 90 research papers and has collaborated with many leading experts in the field of continuous optimization. Prof. Gibali is a sought-after lecturer who has won many awards for the quality of his teaching; he also donates much of his time to improving education and lecturing at schools and organizations outside academia.