Covariant integral quantization with rotational SO(3) symmetry is established for quantum motion on this group manifold. It can also be applied to Gabor signal analysis on this group. The corresponding phase space takes the form of a discrete-continuous hypercylinder. The central tool for implementing this procedure is the Weyl–Gabor operator, a non-unitary operator that operates on the Hilbert space of square-integrable functions on SO(3). This operator serves as the counterpart to the unitary Weyl or displacement operator used in constructing standard Schrödinger–Glauber–Sudarshan coherent states. We unveil a diverse range of properties associated with the quantizations and their corresponding semi-classical phase-space portraits, which are derived from different weight functions on the considered discrete-continuous hypercylinder. Certain classes of these weight functions lead to families of coherent states. Moreover, our approach allows us to define a Wigner distribution, satisfying the standard marginality conditions, along with its related Wigner transform.You can read the full article here: https://www.mdpi.com/2073-8994/15/11/2044
Monday, November 13, 2023
Covariant Integral Quantization of the Semi-Discrete SO(3)-Hypercylinder
Thursday, August 10, 2023
Majorana stellar representation of twisted photons
Majorana stellar representation, which visualizes a quantum spin as points on the Bloch sphere, allows quantum mechanics to accommodate the concept of trajectory, the hallmark of classical physics. We extend this notion to the discrete cylinder, which is the phase space of the canonical pair angle and orbital angular momentum. We demonstrate that the geometrical properties of the ensuing constellations aptly encapsulate the quantumness of the state.You can read the full article here https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.L032006
Majorana stellar representation of twisted photons. Authors: Nicolas Fabre, Andrei B. Klimov, Romain Murenzi, Jean-Pierre Gazeau, and Luis L. Sánchez-Soto. Learn more in Physical Review Research: https://t.co/d0o2LZBGQd. #Quantum pic.twitter.com/jkWYDTp4ko
— APS Physics (@APSphysics) July 13, 2023
Monday, July 3, 2023
TWAS’s 40th Anniversary
The World Academy of Sciences for the advancement of science in developing countries (TWAS) is an organization that has been at the forefront of promoting scientific excellence in the developing world.
Founded in 1983, TWAS has been a driving force in supporting scientists from diverse backgrounds and fostering global collaborations. This year marks the 40th anniversary of TWAS, and its President, Quarraisha Abdool Karim, has launched the celebrations to honor this momentous occasion.
On 25 May 2023, as the Executive Director of TWAS, I had the pleasure to open the anniversary event – a public lecture by TWAS President. I was joined onstage Stefano Fantoni, president of the Trieste International Foundation for the Progress and Freedom of Sciences (FIT); and Minister Plenipotentiary Giuseppe Pastorelli, director for integrated promotion and innovation at the Directorate General for Country Promotion of the ministry of Foreign Affairs and International Cooperation of Italy, a key supporter of TWAS.
From bridging the scientific divide to promoting sustainable development goals and empowering young scientists, TWAS has demonstrated its unwavering commitment to promoting scientific excellence worldwide. As we celebrate this milestone, let us remember that together we can forge a brighter and more equitable future through the power of scientific knowledge.
On the TWAS website https://twas.org/article/twas-president-launches-celebrations-academys-40th-anniversary you can read an article about the event.
With TWAS President Abdool Karim |
Integral Quantization for the Discrete Cylinder
by 1,* and 2
Abstract: Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalized positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a covariant way. One of their advantages is their ability to circumvent problems due to the presence of singularities in the classical models. In this paper, we implement covariant integral quantizations for systems whose phase space is Z × S^1 , i.e., for systems moving on the circle. The symmetry group of this phase space is the discrete & compact version of the Weyl–Heisenberg group, namely the central extension of the abelian group Z × SO(2). In this regard, the phase space is viewed as the right coset of the group with its center. The non-trivial unitary irreducible representation of this group, as acting on L ^2 (S^1), is square integrable on the phase space. We show how to derive corresponding covariant integral quantizations from (weight) functions on the phase space and resulting resolution of the identity. As particular cases of the latter we recover quantizations with de Bièvre-del Olmo–Gonzales and Kowalski–Rembielevski–Papaloucas coherent states on the circle. Another straightforward outcome of our approach is the Mukunda Wigner transform. We also look at the specific cases of coherent states built from shifted gaussians, Von Mises, Poisson, and Fejér kernels. Applications to stellar representations are in progress.
Tuesday, June 28, 2022
New Frontiers in Global Research Series: Education, Science, and Technology for a More Sustainable World Event Recording
New Frontiers in Global Research Series: Education, Science, and Technology for a More Sustainable World Event Recording
On April 28, Northwestern Buffett hosted New Frontiers in Global Research Series: Education, Science, and Technology for a More Sustainable World. Romain Murenzi (Director of The World Academy of Sciences and both the former Minister of Education and former Minister of Science & Technology for Rwanda), Jean-Louis Sarbib (former Vice President and Senior Vice President for Human Development at the World Bank), and V.S. Subrahmanian (Professor of Computer Science at Northwestern University and Faculty Fellow at Northwestern’s Buffett Institute for Global Affairs) came together for a conversation about building science and technology education and capacity in developing and post-conflict countries. This event, and this series, implores us to consider how we define, assess, and analyze the “global” in global research and urges us to reflect upon the real-world implications of academic scholarship. Watch a recording here:
https://buffett.northwestern.edu/news/2022/new-frontiers-in-global-research-series-education,-science,-and-technology-for-a-more-sustainable-world-event-recording.html
Building Scientific Capacity in Developing Nations
Building Scientific Capacity in Developing Nations with Romain Murenzi, PhD
Building scientific capacity is essential to strong institutions and supporting problem-solving and innovation, especially in the Global South. Romain Murenzi, PhD, Executive Director of The World Academy of Sciences (TWAS) joins Annelise Riles to talk about United Nations Sustainable Development Goal 16, peace, justice and strong institutions, and how TWAS is working to meet this goal.
In this episode, Murenzi shares his story as a Rwandan refugee, raised in Burundi, who went on to receive a PhD in physics and later returned to his country of origin as Minister of Education, Science, Technology and Scientific Research. He shares examples of building scientific capacity in developing nations, such as TWAS South-South PhD and postdoctoral research fellowship program. He also says implementing simple technology, such as a coffee washing station, can transform the economies of developing nations and give farmers a chance to prosper.
Background reading:
- Connect with Murenzi on LinkedIn
- Find out more about the TWAS South-South PhD and postdoctoral research fellowship program
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Read the transcript of this show below
Annelise Riles [00:00:03] Welcome to the Breaking Boundaries podcast. I'm Annelise Riles, executive director of Northwestern University's Roberta Buffett Institute for Global Affairs. The Northwestern Buffett Institute is dedicated to breaking through traditional silos of expertise in geography, culture and language to surface novel solutions to pressing global challenges. This spring, we have been focusing on the United Nations Sustainable Development Goal 16, which is peace, justice and strong institutions. Today's guest, Romain Murenzi, says building scientific capacity is essential to strong institutions and supporting problem solving innovation, especially in developing nations. Dr. Murenzi is executive director of the World Academy of Sciences, a multilateral organization administered by the United Nations Educational, Scientific and Cultural Organization and funded by the Italian government. And it supports scientists and scientific innovation in the Global South. Welcome Romain and thank you so much for being here today.
Romain Murenzi [00:01:12] Thank you. Thank you for this invitation.
Annelise Riles [00:01:14] Let's start a little bit with your personal journey as a scientist. You were born in Rwanda, raised as a refugee in Burundi, and started your career as a high school math teacher in the early 1980s in rural Burundi. Can you tell us a little bit what your life was like as a child and where the spark to study science and physics came from?
Romain Murenzi [00:01:34] Thank you very much. Thank you. And my family was exiled in Burundi in the early sixties. I did my primary school, secondary school and college in Burundi. So growing up as a as a refugee in Bujumbura, the capital city, there were two cultural centers there, the French Cultural Center and the American Culture Center. Centre Culture America, Centre Culture Frances. And we used to go there and had opportunity to get access to books. In the American one actually, there were many books of scientists, Thomas Edison and other scientists, Albert Einstein, you know, history of physics and science and space. That gave me actually a dream. To be a scientist. And also in the French one, I was able to have a chance to read The Life of Marie Curie, you know, how she traveled from Poland and went to France. And this kind of story, when I was really in what I would call middle school, interested me a lot. But it happened also that I was very lucky. I was good in math during throughout my high school. I was the best kids in math. That was all I did in the fact that I wanted really to do science. So basically I could say that sparked me to do science. And then later in life, when I finished my bachelor's degree, I wanted to learn to be a math teacher. After my my bachelor's degree in mathematics, rather than having a job at the university, I was sent in rural area to teach mathematics, you know, an all girl school. And a year later, I was brought back to the capital to teach the best two schools in the country. It's a long story, but I ended up actually being the best math teacher of the country during that that period. And during that period also, I tried to get a scholarship for a period because as a refugee, I could not get a PhD from the government. I could not even be having a teaching assistantship. So, basically, after three years of struggling, I was able to get a scholarship to go to the Catholic University of Louvain, in Louvain I had a chance for tremendous growth, not only scientifically, but as a human, as a person, because the environment was really good. They gave me an opportunity to travel actually with my work in mathematical physics, I was given an opportunity to very early on to go to King's College of London, Queen Mary College. I went to to Rome. I visited cities such as Marseilles, Bordeaux and Paris. I had a chance to benefit from the European mobility, and that really made me not only a mathematical physicist, but also at the same time also to know Europe. Also, I'm not European, but you feel that you are a European. Whatever I went, I was actually received very well. I didn't even remember that I was a I was African or black in some sense because I was embedded in this young European when we were discussing mathematics and physics. That was really very interesting. And then in 1990, I had a job in Paris at the University of Paris to be a teaching assistant, but also to do research. I spent six months in Paris and then I got a postdoc in Toulouse, the south of France. But you have a lot of science institutions. I got a job in this European center called .... European Center for Advanced Computation and Research in scientific computation. Actually, it was one of the best scientific computation in Europe, and I was the only African there. So during that period I learned not only to link mathematical physics and computation, this is what actually two years later, in 1992, give me an opportunity to be hired at a newly created center for NSF, the Center for Theoretical Studies of Physical Systems at Clark Atlanta University, which is an HBCU historically black college. From 1992 to 2001. And that is I had an opportunity for growth not only scientifically, but also, again, as a human being by the end of the decade. By. By 2001, actually, nine years later, I had become a U.S. citizen. I had become a chair of the physics department. But also I was a full professor of physics. At the time my second dream, which was to work for my country of origin, seemed to be very, very far. But I was very wrong. In 2001 in the spring, I received a call, somebody asking me, saying that the government of Rwanda was inquiring if I was interested in being a minister of education of the country.
Annelise Riles [00:06:07] What an incredible story. And just imagining you as a middle school student already able to read both French and English and I imagine speaking at least one or two other languages. What a remarkable talent you were even at that age. Tell us a little bit, why did you choose to return to Rwanda when you were invited? What was it that drew you away from this wonderful position as chair of a physics department in the United States.
Romain Murenzi [00:06:33] After the genocide against the Tutsi in 1984, basically many young people who actually dreamed about returning back to their country of birth, actually, there was a massive return of exiled Rwandans from all over the world, in particular from the the neighboring countries, Burundi, Democratic Republic of the Congo, Tanzania, Uganda, but also many actually Rwandans who left their safe positions in in Europe and in North America to return back to Rwanda. Even a friend of mine, Dr. Charles Mulligan, there was a professor at Howard University and decided just to return to return back. So from 1984, I continue to think how can I do to help? So in 1996, in February, actually in the spring, Mrs. Claire Richardson, the CEO of the DFA, DFA, the Delta Force, the Gorilla Fund International, and I visited Rwanda at the University of Rwanda to see how we can help. I was sponsored by the ... And also Clark Atlanta University. During that historic visit, actually, I visited, I observed two things in terms of infrastructure. The building were okay. However, the books in the computing facility were destroyed. In particular, all the computers were stolen. Secondly, most of the teachers were foreign. There were still teachers from neighboring countries because most teachers, Rwandan teachers or they were killed or the they were the killers. So, imagine some of the teachers killed their own colleagues, the things that's how mad the madness of the genocide was. And then, so I could see that, and when they returned back to the U.S., I send a note to my other the Rwandan community, what they saw. And since that time, I will go to Rwanda to teach a class in physics every summer. And I think that may have caught the attention of the government, because not many people were coming to do that. To bring some books, you know, like we do, like the Boy Scouts you know. Sometimes I tell people from Diaspora, you don't need to wait until you bring a big lab. Just go there and do something every year. So, I did that even when when I go to Rwanda, I will jump in Burundi and give a seminar. So then and again, that's where in 2001, when I received a call, actually, I didn't hesitate for two reasons, actually, when I received the call, I said probably this is the right time. And not only I have published enough. So I thought I was already a full professor, but most importantly because of that, among the exiles, the returnees, when my my sibling, there were seven siblings who are living in Burundi with with that their families have returned. And each time I went there, I could see them how they were struggling, you know. So I said this give me not only opportunity to work for your country, but also to be to be with my siblings for quite some time. So then I requested the university, Clark Atlanta University, to give me a leave of absence for two years. Actually, when I left, I thought I going to stay for two years, but I stayed for eight years.
Annelise Riles [00:09:41] That's incredible. I love that idea that we can just do a good action every day. We don't have to wait for the great bolt of lightning. Tell us a little bit now about the World Academy of Sciences and your work there.
Romain Murenzi [00:09:56] So as you know, the the World Academy of Sciences was created in 1983 by Abdulsalam. To understand the the World Academy of Science, you need to understand Abdulsalam. Abdelsalam was a physicist from Pakistan. He's a muslim, but come from from a small sect in that from that country, which brings also challenges of integration in his own culture. When he returned back home, actually, he was not be integrated. He was not integrated. And I think at some point, even his life was threatened. So as a young man, he decided to return back to the UK. It happened that he had a vision. So he decided, as in 1964, to start the International Center for Theoretical Physics ... He had the idea, and then he worked with other scientists here and there who helped him to do that. His idea was that I was not able to stay in my own country. If I could create a center where scientists from the developing country could come and spend some time and return back home would be a very good thing. So he decided to create the Academy with the idea of being a voice for science, for the developing world, and also advancing science in the developing world. The Academy is going to celebrate 40 years next year. So this is something that is actually very, very rare, very interesting. So this means that advancing science in the developing world there, it has two components. The first component, you have some kind of programs, but also you have also actions, programs of building science capacity in the south PhD program. We have what we call South-South Fellowship Program, China, India, Malaysia, South Africa, Brazil. And now Turkey is joining these countries that have made it the country of the south, that has made it to development. These countries are donating fellowships for PhD. Now we have more than 100,200 student doing PhD in the centers in the South. So we call it South-South Fellowship Program, but we have also what we call mobility. We want somebody who is in a lab in the South to come in the north and spend one, 2 to 3 months. When I say the North means develop developed countries.
Annelise Riles [00:11:59] Tell us what kind of engagement can we universities in the Global North have? How can we contribute to this really important effort that you're making?
Romain Murenzi [00:12:09] So there are two ways that could be contribute with a program called Expert, somebody from the North, we will go to Africa and spend one, 2 to 3 months in a particular university. He can teach. He can give support in terms of capacity building, institutional capacity building. But what is very important if if the person, for example, he links with a professor in Burundi, for example, or in Benin, that professor, they can work together and publish together. So once a person has left, actually, he leaves something there. And we have concrete examples, but also a mobility. Mobility means that you could invite somebody to spend one month at the university. A PhD sometimes is difficult because there is the brain drain. But if somebody can come and spend one month, 2 to 3 months, it would be good. For example, if your institution, the the Buffett Institute, for example, who like to sponsor some young scientist to come in and spend some time on the issue related to sustainable development and in their own area of, of expertise, chemistry, biology but you link with some of your programs that will be very good.
Annelise Riles [00:13:15] Let me just ask you finally a question that I ask all of my guests, which is, as you think about the future, what keeps you up at night? What are you most worried about? But also, what are you most hopeful for.
Romain Murenzi [00:13:30] For these days of the COVID 19 my worry is there is another pandemic. Africa and many poor countries have already basically lost two years of learning. If that happened again, they may it may slide and lose more years of learning, and that may have really, really impact on achieving the sustainable development goals. So that part of me worries these days, and this is why I think that time investment in broadband is very important. During my time as a Minister of Education in Science in the world, I was trying to promote computers in schools. But people say you don't need a computer, you need to build the classroom. So people thought that classroom was more important, but you realize actually even to have the book is not easy in those countries, but if you have a computer, you can store all the books that you want. My son, he went to school every day online. Like if he was in the classroom, he didn't miss a class. And so other kids in in Europe and in mostly in North America and other developed places. But when I think about the other ones, countries as Benin, Cameroon and other places, this kid didn't have that. And that can be very dramatic if that happened again. Yeah, but my my second thing is, is also because now people think that science is very important. Actually, over the years, we have understood the importance that science actually is important. If you want to reduce poverty, you need to grow your economy and you cannot grow your economy if you don't invest in science and technology. So that is something that is very, very important. So I will finish with with one example. In the early 2000, before 2000, the coffee of Rwanda was fetching at the market, probably $0.5 per kilo. And there was this U.S. aid program, a project with Michigan State University and Texas A&M University and the University of Rwanda for washing coffee, a station. A coffee washing station is an appropriate technology. It is a very well known technology. However, for the farmers of East Africa, in Central Africa, Rwanda, Burundi, Uganda this technology was not known or they didn't have access to it. So giving them access to that technology created a whole new way of seeing things and doing things in innovation. So having washing the coffee, drying it properly, sorting the beans, the coffee went from $0.5 to $5 per kilo, sometimes $10 per kilo. Even the coffee of Rwanda going into the shelves of Costco and and Starbucks. This means that from a farmer who has 1000 kilo going from $500 to $5000 even to more than that, you cherish completely the life of people. So this means that with tremendous economic growth during that period, just based on that small example, because the technology is applied. So there is there are a lot of technologies that exist already in the US. You need to create new technologies because you have almost used all these technologies. But in the Global South, in the least developed countries, these technologies have not been used. If they can be harnessed and be used, that can change the life of people. So in that that's really that's my hope to continue to do that. Yeah.
Annelise Riles [00:16:52] Well, what a fantastic story. Roman Murenzi, you are a remarkable example of the change that science can bring to the world. And we're so grateful for you being here today. Thank you so much.
Romain Murenzi [00:17:05] Thank you. Thank you, Annelise.
Annelise Riles [00:17:09] For more information on this episode and on the Northwestern Buffett Institute for Global Affairs, visit us at Buffett.northwestern.edu
Sunday, February 13, 2022
Looking into Africa's Future: The Fourth Industrial Revolution and the Role of ICT Education Authors Romain Murenzi, Max Paoli, Sena Galazzi, Sean Treacy
Abstract:
CT in education has been considered a luxury in developing countries, where, particularly in least developed countries, emphasis was placed more on building schools and classrooms. In 2020, the view of ICT and its role changed radically. Firstly, the COVID-19 pandemic highlighted ICT as a central tool. Secondly, the rise of the Fourth Industrial Revolution and awareness of its enormous potential placed ICT in a new light. Together, these triggers of change can be embraced in order to integrate key learning modules and lessons to form appropriate skills into curricula in developing countries. Frontier fields in science and technology must be promoted and supported especially in the education sector in Africa and the developing world in general.