Academic Summer Highlights - What Are Yours?

Next Tuesday is the first day of classes of the new 2016-2017 academic year at the University of Massachusetts Amherst and students have started to arrive back to campus and the town.

It was a terrific summer and I thought it would be fun to share some of the highlights.

In late April, after teaching my last classes at the Isenberg School of Management, I flew to England to begin my Visiting Fellowship at All Souls College at Oxford University. The experience of being at Oxford for two and a half months (during the trinity term) was magical and many times I felt as though I was living in a novel. Below is a photo of the Visiting Fellows, who hailed from Israel, Australia, England, and the US, along with our Dean, Dr. Simon Hornblower.

While at Oxford, my new book, Competing on Supply Chain Quality: A Network Economics Perspective, was published, and when I returned to Amherst, I celebrated with my co-author, Dr. Dong "Michelle" Li.

I also had the pleasure of making a very short (4 day) trip back to the US in late May to see my daughter, Alexandra, graduate summa cum laude and with honors from college. I am especially happy that she was a STEM major and had an incredible educational experience at Lafayette College, which is also her father's alma mater, serving as President of the crew team, to start.

Back at Oxford my husband and daughter joined me for a while and we visited one of my former doctoral students, Dr. Stavros Siokos, who is a very successful financier in London.

While in England, it  was also very special to give invited seminars at Imperial College in London and at Lancaster University. Our operations research colleagues tend to be the best hosts!

While in Europe, I also had the pleasure of traveling to Poznan, Poland to speak at the EURO conference, which was fabulous and I got to see former students and many colleagues from around the world.

One "lowlight" as opposed to highlight of this summer was waking up in Oxford the day after the UK voted to leave the European Union - known as Brexit. Everyone was walking around Oxford as in a daze and we were so upset that we penned an OpEd, Why we are stronger together,  that appeared in the Daily Hampshire Gazette.

Coming back from Europe I was delighted to see that the STEM Gems book, authored by Stephanie Espy, on 44 women role models in STEM (and I am one of the women featured), had been published and my copies had arrived. My daughter and nieces are the happy recipients of some of the copies and I also gave one to the Isenberg Dean Dr. Mark A. Fuller and to deserving doctoral students for inspiration!

In late August, it was time to drive my daughter to grad school, where she will be working on her PhD.

Then it was time to celebrate with my academic daughters. My doctoral student, Deniz Besik, successfully passed her core exam in Management Science at the Isenberg School on April 5,

and Sara Saberi became my 19th PhD student to successfully defend her PhD, which she did on August 12. She is now an Assistant Professor at the Foisie School of Business at Worcester Polytechnic Institute (WPI).

And, of course, no academic summer would be complete without getting some research papers written and, hopefully, accepted for publication! Two highlights were having the paper, Physical Proof of the Occurrence of the Braess Paradox in Electrical Circuits,  Ladimer S. Nagurney and Anna Nagurney,  published in  EPL (Europhysics Letters) 115 (2016) 28004, and having the paper,  A Generalized Nash Equilibrium Network Model for Post-Disaster Humanitarian Relief, Anna Nagurney, Emilio Alvarez Flores, and Ceren Soylu, accepted for publication in Transportation Research E. UMass Amherst posted a nice article on our latest Braess Paradox paper.

Working with other members of our great Supernetwork Team this summer has also been a big pleasure!

This summer the Olympics also took place in Rio and I would be remiss not to mention that one of the highlights was watching Michael Hixon, who is a student at Indiana University, and who also grew up in our neighborhood in Amherst (his parents live up the street from us),  receive a silver medal in diving,  I watched the competitions that he was in via videostream and I was mesmerized and as nervous as when my daughter competed in figure skating.

And, as educators, this is always an exciting time of the year during which we anticipate what will the new academic year bring?!  I have been working on my course lectures and am looking forward to meeting new students and new colleagues.

As for this summer, it will be hard to have a better one, but who knows what kind of adventures await next year!

A Generalized Nash Equilibrium Model for Post-Disaster Humanitarian Relief - Case Study on Hurricane Katrina and Beyond

The devastating floods in Baton Rouge, Louisiana, 11 years after Hurricane Katrina,  which have resulted in the worst natural disaster in the US since Hurricane Sandy,  as well as the 6.2 magnitude earthquake that hit central Italy about 100 miles from Rome recently, demonstrate the impact that disasters have on societies. The response phase is essential to finding survivors and saving victims.

Every spring I teach my Humanitarian Logistics and Healthcare class at the Isenberg School of Management and it continues to be one of the most fascinating courses that I have ever taught. On this blog I have written posts about many of the truly special guest speakers that have come to share  their experiences in emergency management and disaster response with the students.

This past Spring, one of the students in the class, Emilio Alvarez Flores, who graduated with a degree in Operations and Information Management from UMass Amherst in May 2016, was also working on his honors dissertation, since he was a member of the Commonwealth Honors College. I had the pleasure of co-supervising his dissertation, along with Professor Ceren Soylu of the Economics Department at UMass Amherst. The title of his thesis was: Optimizing Non-Governmental Organizations’ Operations and Fundraising: A Game-Theoretical Supply Chain Approach. Emilio defended his thesis at the Undergraduate Research Conference. Emilio was honored for his thesis (one of about a dozen) with a Deans Honors Award from the Commonwealth Honors College.

Emilio had been hard at work for about one year modeling the integration of supply chain aspects as well as financial funds raised by nongovernmental organizations with a focus on integrating in a model both supply chain aspects and financial fund aspects. Together wtih Professor Soylu we spent hours discussing and working out various aspects and versions of the model. One of the unique (and challenging) aspects of disaster relief is that NGOs and governments are nonprofits and derive some utility from helping victims post-disasters. At the same time, the former compete with one another for financial funds and, depending upon their response to disasters and visibility, they may get more or less of the financial funds. Also, NGOs need to minimize their costs since waste is not something that donors and stakeholders look kindly on.  Victims, on the other hand, need water, food, and medical supplies, as well as protection from the elements as soon as possible and, hopefully, no later than 72 hours. 

There have been numerous instances of surpluses of one kind of relief item being delivered to victims post-disasters, whereas shortages arise of other supplies. Hurricane Katrina, which struck southern parts of the United States in August 2005, is a vivid case. It was the costliest natural disaster in US history. Making landfall in August of 2005, Katrina caused extensive damages to property and infrastructure, left 450,000 people homeless, and took 1,833 lives in Florida, Texas, Mississippi, Alabama, and Louisiana. 63% of all insurance claims were in Louisiana with overall damages assessed as being in the rang of  $105 -$150 billion. In Louisiana alone, over 1.3 million people were affected, with Katrina being responsible for 300,000 jobs lost, 200,000 people left homeless, and over 1,500 fatalities. The New York Times reported that the Red Cross mismatched supplies with the victim’s needs; thereby, leading to obsolete inventory. 

In developing a model that is computable and would be based on data it was clear that the model had to be a game theory one. However, most models in the disaster relief and humanitarian logistics arenas are optimization models. Moreover, we were interested in evaluating policies in order to minimize materiel convergence and to assist in the delivery of the needed amounts of relief supplies to the destinations.

 Although a Nash Equilibrium model could be developed and we have a lot of experience in formulating, analyzing, and solving Nash Equilibrium models in a spectrum of supply chain applications from the pharmaceutical industry to food supply chains, the behavior there would be that of profit-maximization, which is not appropriate in the case of NGOs in disaster relief. Moreover, we wanted to explore what the possible impacts might be if there was a coordinating body, such as a supra NGO or governmental authority that would provide data as to the relief item needs in terms of lower and upper bounds at different points of demand. With such complicating constraints, which would be shared by the NGOs, the model would have to be a Generalized Nash Equilibrium model, and as far as we are aware there are no such models in the humanitarian relief sphere.

But if you have passion for a problem to be solved and, frankly, you are obsessed with the formulation and solution, you will figure out a way and you will get it done.

The result is the paper, A Generalized Nash Equilibrium Network Model for Post-Disaster Humanitarian Relief, Anna Nagurney, Emilio Alvarez Flores, and Ceren Soylu,  which has now been accepted for publication in Transportation Research Part E: Logistics and Transportation Review. The paper contains a case study on Hurricane Katrina and also demonstrates how much better the solutions are under a Generalized Nash Equilibrium framework than under simply a Nash Equilibrium one in which each NGO just has to satisfy its own constraints.  

As our case study in the paper reveals: It is immediately clear that there is a large contrast between the relief item product flow patterns under the Generalized Nash and Nash Equilibria. For example, the Nash Equilibrium flow pattern results in about $500 million less in donations. While this has strong implications about how collaboration between NGOs can be beneficial for their fundraising efforts, the differences in the general flow pattern highlights a much stronger point. Under the Nash Equilibrium, NGOs successfully maximize their utility. Overall, the Nash Equilibrium solution leads to an increase of utility of roughly 21% when compared to the relief item flow patterns under the Generalized Nash Equilibrium. But they do so at the expense of those in need. In the Nash Equilibrium, each NGO chooses to supply relief items such that costs can be minimized. On the surface, this might be a good thing, but recall that, given the nature of disasters, it is usually more expensive to provide aid to demand points with the greatest needs. With this in mind, one can expect oversupply to the demand points with lower demand levels, and undersupply to the most affected under a purely competitive scheme. This behavior can be seen explicitly in our results. For example, St. Charles Parish in Louisiana receives roughly 795% of its upper demand, while Orleans Parish only receives about 30.5% of its minimum requirements. That means that much of the 21% in ‘increased’ utility is in the form of waste. In contrast, the supply chain product relief item flows under the Generalized Nash Equilibrium guarantee that minimum requirements will be met and that there will be no waste; that is to say, as long as there is a coordinating authority that can enforce the upper and lower bound constraints, the humanitarian relief flow patterns under this bounded competition will be significantly better than under untethered competition.

This paper, we believe, has big policy implications and we expect that it will also generate further research. It was quite the journey doing this research but with inspired collaborators with great passion it was also thrilling and we are ecstatic that the paper has been accepted for publication and in one of my favorite journals!

In late June, I gave an invited seminar at Lancaster University in England: Disaster Relief Supply Chains: Network Models, Algorithm, and Case Studies, in which I highlighted some of our research in this area and the last part of the presentation presents highlights from our Generalized Nash Equilibrium Model for Post-Humanitarian Relief paper.

The full presentation can be downloaded here.

Exciting Times at the Isenberg School of Management at UMass Amherst

Today was a picture perfect day - sunny but with a nice breeze and, after working on a supply chain paper with collaborators and finishing up some lectures for my Logistics & Transportation class that I will be teaching this Fall at the Isenberg School of Management, I decided to walk to UMass Amherst. It is about a 2 mile walk via the route that I took which is through the woods and fields and through campus. I needed to submit some class materials for copying and, although classes don't begin until September 6, I like to be prepared (way) ahead of time. This goes with my background in operations research and efficiency and also in emergency preparedness and supply chain disruption management!

The Isenberg School of Management is in the midst of a major new construction project - the addition of a $66 million Business Innovation Hub. We have even received a nice invitation for the groundbreaking celebration, which will take place on September 16, 2016 and will be officiated by our UMass Amherst Chancellor, Dr. Kumble Subbaswamy, and the Isenberg Dean. Dr. Mark A. Fuller.

The construction project has actually already begun and it will be an interesting year since all of my courses are in classrooms alongside of the area where the construction crew has set up equipment and a staging area. Fences blocking the area are put up from the Isenberg School to the Fine Arts Center which is resulting in new pathways and journeys for students, faculty, staff, and visitors and guests to navigate.

But these are exciting times and the project will take 3 years and will add much needed space for our activities. The Boston Globe already had coverage of the project.

And, that is not all that is going on in terms of construction. Today I had the pleasure of checking out our Operations and Information Management Analytics Lab which is on the ground level of the Isenberg School and should be ready for the first day of classes - September 6. Susan Boyer gave me a nice tour and the construction crew was busy with the wiring today.

There will also be a specially made podium in the room and two big screens.  The chairs are nice and light and easy to clean. The analytics lab was made possible by many generous donors, including alums, parents, and faculty.

Then it was time to check out my office which physical plant this summer replaced the flooring of, had my windows cleaned, and cleaned my Oriental rug, so it is sparkling for the students' arrival.

This year there are many events to look forward to, including the publication of my 14th book, Dynamics of Disasters: Key Concepts, Models, Algorithms, and Findings, which I co-edited with Professors Ilias S. Kotsireas and Panos M. Pardalos.

Wishing everyone a GREAT start to the new academic year!

Supernetworks Lab at the Isenberg School of Management

It is hard to believe that 15 years ago I founded the Virtual Center for Supernetworks at the Isenberg School of Management at the University of Massachusetts Amherst and have served as its Director ever since.  My co-author and former doctoral student, Dr. June Dong, and I had written the Supernetworks book, grants were coming in from the National Science Foundation and the AT&T Foundation, and there was and continues to be great interest surrounding networks to this day.

A big component of the Supernetwork Center is the Supernetworks Laboratory for Computation and Visualization, or the Supernetworks Lab, for short.

I am excited to report that we now have a new home at the Isenberg School for the lab. It is now housed in Room G11 and was formerly in G28. The lab has workspace for students as well as guests and visitors, a conference table for meetings and discussions, storage areas, shelves for books and boards for posting as well as a blackboard for discussions. We also have teleconferencing capabilities which is critical with our National Science Foundation grants, which tend to be multi-university ones.

When I look at the dissertations that have come out of the lab, as well as the publications, and the books, since its inception, it is clear that a community of support, excitement, and collaboration on both research and teaching leads to discoveries plus to great enjoyment. Also, the Center has Center Associates from academia and industry, and students, both graduate and undergraduate ones, creating great synergies. I have supported several undergraduates under NSF Research Experiences for Undergraduates grants. Two former Undergraduate Center Associates went on to receive the Leaders for the 21st Century Awards from the University of Massachusetts Amherst, upon their graduation, a select honor only given to about a dozen students a year. Doctoral Student Center Associated have been recipients of the Isenberg School Outstanding Doctoral Student Researcher Award and the Outstanding Doctoral Student Teaching Award as well as INFORMS Judith B. Liebman Awards.  Two Doctoral Student Center Associates have been awarded national dissertation awards and one received two Isenberg Scholar Awards!

The lab and its Associates have been involved in numerous activities, from organizing conferences and workshops, to editing journal volumes, and serving as Associate Editors, to being frequently invited speakers at many prestigious forums in both academia and industry. The Supernetworks Lab page on the Virtual Center for Supernetworks contains more information.

Also, since Doctoral Student Center Associates are always very active in the UMass Amherst INFORMS Student Chapter and frequently serve as officers, speakers can come to the Lab for meetings and discussions. We also have awards received by the Student Chapter from its parent society INFORMS (Institute for Operations Research and the Management Sciences)  (other awards of the chapter grace our beautiful Isenberg School atrium) and a big poster designed by the students.

What I am especially proud of is the great Supernetwork Team, whose members continue to work and collaborate together, building a resilient network across the miles. We are always stronger together!

Celebrating My 19th PhD Student's Successful Defense at the Isenberg School of Management

It is always a very special day when a doctoral student successfully defends her dissertation.  It s extra special when it is your doctoral student and you chaired her dissertation committee.

Today is a very steamy day in Massachusetts with temperatures in the mid 90s but we celebrated, nonetheless, and for good reasons. Sara Saberi, my 19th PhD student, successfully defended her dissertation at the Isenberg School of Management this morning. Her concentration was Management Science. And, this is not Sara's first PhD, but her second. Her first is in Industrial Engineering from a university in Malaysia!

Sara's defense was at 8:30AM and she surprised us with some treats.

Sara's dissertation is entitled:  Network Game Theory Models of Services and Quality Competition with Application to Future Internet Architectures and Supply Chains. Her presentation can be downloaded here.

Her research was funded, in part, by  a three-year, $909,794, National Science Foundation grant to address some of the difficulties with new protocols and services on the Internet. The project, "Network Innovation through Choice," was part of a $2.7 million collaborative project. The project also included the University of Kentucky, North Carolina State University, and the Renaissance Computing Institute of Asheville, North Carolina. Professor Tilman Wolf, Associate Dean in the College of Engineering at UMass Amherst, who is also a Professor in the Department of Electrical and Computer Engineering, was the PI on the grant and I was a Co-PI.  Professor Wolf was also on Sara's doctoral dissertation committee. We received a one year extension on this grant and, together with Professor Wolf, I now have an NSF EAGER grant.

Sara also received not one, but two, Isenberg Scholar Awards from the University of Massachusetts Amherst, each for $10,000.

Sara's dissertation committee consisted, of Professor Adams Steven of my department at the Isenberg School of Management, and Professors Tilman Wolf and Michael Zink of the College of Engineering at UMass Amherst.

Sara did a great job presenting today.

After the successful defense, we went out to lunch at Judie's restaurant in downtown Amherst.

Sara, I am very pleased to say, begins a tenure track Assistant Professorship at the Foisie School of Business at Worcester Polytechnic Institute (WPI) this month! It will be very nice to have her in Massachusetts and only about an hour away. WPI is a research university and with the great colleagues and students there, Sara should thrive.

Several of Sara's research publications can be found below.

Supply Chain Network Competition in Price and Quality with Multiple Manufacturers and Freight Service Providers, Anna Nagurney, Sara Saberi, Shivani Shukla, and Jonas Floden, Transportation Research E 77: (2015) pp 248-267.

A Game Theory Model for a Differentiated Service-Oriented Internet with Duration-Based Contracts, Anna Nagurney, Sara Saberi, Tilman Wolf, and Ladimer S. Nagurney, Proceedings of ICS 2015: Operations Research and Computing: Algorithms and Software for Analytics, Brian Borchers, J. Paul Brooks, and Laura McLay, Editors , INFORMS (2015) pp 15-29.

A Network Economic Game Theory Model of a Service-Oriented Internet with Price and Quality Competition in Both Content and Network Provision, Sara Saberi, Anna Nagurney, and Tilman Wolf, Service Science 6(4): December (2014) pp 229-250.

A Dynamic Network Economic Model of a Service-Oriented Internet with Price and Quality Competition, Anna Nagurney, Dong Li, Sara Saberi, and Tilman Wolf, in Network Models in Economics and Finance, V.A. Kalyagin, P.M. Pardalos, and T. M. Rassias, Editors, Springer International Publishing Switzerland (2014) pp 239-264.

A Network Economic Game Theory Model of a Service-Oriented Internet with Choices and Quality Competition, Anna Nagurney, Dong Li, Tilman Wolf, and Sara Saberi, Netnomics 14(1-2): (2013) pp 1-25. (This article was recognized by ACM Computing Reviews as a Notable Article in Computing in 2013.)

A full list of my PhD students, up to Sara,  can be found on the academic genealogy website:
 https://genealogy.math.ndsu.nodak.edu/id.php?id=14557

  Great to see the academic family tree growing.

Our OpEd on Why We Are Stronger Together - Brexit and the Upcoming US Presidential Election

I have been back from beautiful Oxford, England for exactly one month. The memories of the Visiting Fellowship at All Souls College at Oxford University will always be with me from the cameraderie of the Fellows, the wonderful staff and delicious meals, the gardens, my office, and historic Oxford (plus I got a lot of research on supply chains completed).

While in Oxford, we engaged in numerous discussions over meals and afternoon tea and being there during the Trinity term was truly a historic time. The referendum take place on June 23, 2016 and we awoke to the shocking news that Great Britain had voted to exit the European Union (known as Brexit), although Oxford overwhelmingly voted to Remain. Also, we were all anticipating the nominations of the US Presidential candidates. Indeed, many of the conversation would include US politics and Hillary Clinton  or the latest on Trump.

As a researcher and educator but also a blogger I believe that it is very important to share information, commentary,  and opinions with the public.

While still in Oxford and reeling from the vote and the impact that it would have on the British economy and even research funding (plus one of my former doctoral students from UMass Amherst and co-author is a financier in London so we had some great insights as to the possible ramifications of Brexit),  my husband and I sat down that weekend and we wrote the OpEd: Why We Are Stronger Together. We submitted it exclusively to the Daily Hampshire Gazette (DHG) and we received the response quickly on a Sunday with the Editor telling us that it would be published the very next day since he liked it so much.

The  page on which our OpEd appears can be viewed here.

The direct link to the article is here.

One can also read it here.

Our OpEd ends with the following: We are  all stronger together with the free flow of people, ideas, services, and goods.  This enhances the education of our students and the resilience of our communities.

My other commentaries, OpEds, and Letters to the Editors can be viewed on the following page on the Virtual Center for Supernetworks website at the Isenberg School of Management.

Milestones Towards Your PhD

Congratulations! You have received admission into a doctoral program and will be supported by a fellowship or perhaps you will be working as a Teaching Assistant (TA) or a Research Assistant (RA). For the latter you might be supported by a professor's research grant.

Many graduate students are now starting to move to their new homes which will be the universities at which they will be pursuing their PhDs. Some travel hundreds of miles and some cross oceans and continents in pursuit of their dreams.

Graduate school is quite different from being an undergraduate and now you are officially an adult. You have identified a subject which is your passion and that you want to do research in. This, in itself is an achievement.

You will soon be registering for courses, undergoing orientation, and maybe even meeting your advisor for the very first time in person. Some universities bring prospective doctoral students to campus for interviews, but not all do.

The first year of graduate school is always exciting, since, unless you stay on at your undergraduate alma mater (as I did and amassed 4 degrees from Brown University), everything will be quite new to you.  There will be a new campus to explore, new friends to make, and new exciting courses to take, with a greater focus than in your undergraduate studies.

Following your first year of graduate study there will, most likely, be Milestone 1 and that is the Core Exam. Today, for example, one of my doctoral students had the oral component of her core exam, which was based on a paper that she had written over the summer, which she defended in front of her committee. Some programs and schools have one or two day written exams only and in our Management Science doctoral program at the Isenberg School we used to have such a core exam.  A few years ago we changed the model and now a student writes a paper on a theme that is agreed upon by the committee chair and her committee and it should be on research that he/she was involved in already, which really helps since the sooner you get into research and have the momentum the better for you and your graduation. It also helps a lot on the job market to have some good papers already placed, if not published.

Below is a photo of my happy doctoral student with her committee members after a successful core exam today.

In the second year of your doctoral studies you will be taking more courses and this is, typically, the case even if you matriculated with a Master's. For example, in our program, the doctoral students very often come with a Master's in Industrial Engineering or several of my students have matriculated with Master's degrees in Civil Engineering with a focus on Transportation or Mathematics or even Statistics.

After the second year there is another Milestone to hurdle over - that of the Comprehensive Exam.  In some schools the comprehensive exam may be more of a dissertation proposal but in our program now this exam, as the name implies, should demonstrate breadth and depth of knowledge of a student based on coursework over two years. Again, a committee is formed, with a chair, and the committee prepares the exam, which the student works on over several weeks. After submission of the completed written part to the committee, an oral exam is held (not to be confused with going to the dentist).

When I was a doctoral student at Brown University I only had one exam and it was a long oral one.

Ideally, in the third year (usually at the end of the third year) a student should form a dissertation committee.  Some programs at UMass only require three members, including the chair. Ours requires four members and one member should be an external member.  The student prepares the dissertation proposal, which is written,  shares it with the committee, and, once a defense date is scheduled, then defends it orally with a presentation and is subject to questions. This is Milestone 3.

After the research for the dissertation is completed and the doctoral student's advisor is happy with the result a defense date for the dissertation is scheduled. This should be a pleasant and happy time (although I have been to defenses in which the student did not pass but this I believe is as much the fault of the advisor as of the student). The dissertation defense is Milestone 4 and, once the students passes this huge step, and the grad school and other paperwork is finalized and processed, the happy student can take part in gradation ceremonies to receive the PhD! Now you can be addressed as "Doctor!"

Next Friday, my 19th PhD student, Sara Saberi, will be defending her PhD. It is actually her second PhD. Some like to go through the above process more than once although it is certainly not common.

This will be an exciting occasion for both Sara and for her advisor as well as for the committee members. Sara will be an Assistant Professor at the Foisie School of Business at Worcester Polytechnic Institute (WPI) in Massachusetts, which is  research university and an ideal place for her. She begins he new position later this month. I supported Sara for two years on a National Science Foundation (NSF) Future Internet Architecture (FIA) grant. Also, in our program doctoral students are required to teach and this helps them on the academic job market so, typically, a doctoral student would teach in their 4th year of our program.

Best of luck to all PhD students on their journeys!

Physical Proof of the Occurrence of the Braess Paradox in Electrical Circuits

This morning we heard the good news - our paper, "Physical Proof of the Occurrence of the Braess Paradox in Electrical Circuits," had been accepted for publication in the journal Europhysics Letters (EPL). 

This paper we had worked on for over a year and had submitted it to the journal shortly before I left for England to begin my Visiting Fellowship at All Souls College at Oxford University at the end of April.

When we received the 2 reviews on this paper in July with one reviewer saying that the paper should be published in its present form and that the results were important, my co-author, who is also my husband, Professor Ladimer S. Nagurney, and I were quite pleased and felt very positive. We revised the paper to satisfy the other reviewer, which was a minor revision.

The paper we believe is very cool since, for the first time, it has been shown the electrons behave in a user-optimized manner, as has been postulated for drivers in a congested urban transportation network. Moreover, the addition of a new link can make the voltage, which is like the user path cost, or travel time in a transportation network,  increase. These findings were not only dome mathematically but actually using built circuits. This allows for experiments to be conducted in a laboratory setting and is yet another application in which the Braess paradox occurs, which, in its original form, demonstrated that the addition of a new link, which results in a new path for travellers, can actually make everyone worse off in the transportation network in terms of travel time. Hence, it can take you longer to get to work (or back home) if there are more routes than fewer ones even of the demand does not increase.

I have researched the Braess paradox since my PhD at Brown University and have also blogged about it.

There is a page on the paradox on the Supernetwork Center site: https://supernet.isenberg.umass.edu/braess/braess-new.html, where you can also find the translation of the original Braess (1968) article from German to English that I did with Professor Braess and my former doctoral student at the Isenberg School, Tina Wakolbinger, who is now a Professor at the Vienna University of Economics and Business in Austria.

Also, this paper we presented at the recent EURO conference in Poznan, Poland, which was a fantastic conference. Our presentation can be downloaded and viewed here. 

Almost 50 years since the publication of the Braess paradox paper, this phenomenon continues to fascinate and now we have additional physical evidence.