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Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenbergan associate professor in the department of applied mathematics and computer science at the Technical University of Denmarkhad published online, when he discovered their findings had unwittingly given away a solution to a centuries-old graph problem.

Holm, an assistant professor of computer science at the University of Copenhagen, was relieved no one had caught the solution first. It was a real Eureka! moment, he says. It suddenly seemed obvious.

Holm and Rotenberg were trying to find a shortcut for determining whether a graph is planarthat is, if it could be drawn flat on a surface without any of its lines crossing each other (flat drawings of a graph are also called embeddings).

Putting it very bluntly, we formally quantified why something is a terrible drawing.

To mathematicians, a graph often looks different than what most of us are taught in school. A graph in this case is any number of points, called nodes, connected by pairwise relations, called edges. In other words, an edge is a curve that connects two nodes. Under this definition, a graph can represent anything from the complex wiring inside a computer chip to a road map of a city, in which the streets of Manhattan could be represented as edges, and their intersections represented as nodes. The study of such graphs is called graph theory.

Engineers need to find planarity in a graph when, for example, they are designing a computer chip without a crossed wire. But assessing for planarity amid the addition and removal of edges is difficult without drawing the graph yourself and trying not to cross any lines (See The Three Utilities Problem below, which was originally published in an issue of The Strand Magazine in 1913).

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Assessing for planarity becomes even more complicated in larger graphs with lots of nodes and edges, says Rotenberg. This is a real-world issue. Quantum computer chips, for instance, are highly advanced, and finding efficient ways to assess their planarity without wasting time and money is crucial to their development.

These three houses each need access to water, gas, and electricitybut for safety reasons the lines connecting the utilities and houses cannot cross. Grab a sheet of paper, draw out this scenario, and try to connect all three houses to all three utilities without any two lines crossing. Check the solution at the bottom of this page when you think you have the right answer.

In their original 2019 paper published on the preprint server arXivwhere research often first sees the light of day before peer reviewHolm and Rotenberg classified a type of embedding called a balanced or good embedding.

Holm explains that these good embeddings tend to balance the [time] costs of inserting edges so that no possible edge insertion costs too much compared to the rest. This is a concept borrowed for balanced decision trees in computer science, which are designed with evenly dispersed branches for minimized search time. Put another way, good embeddings are easier to add new edges to without violating planarity.

If you were to look at it, Holm says, a good embedding would be simple, unconvoluted. The standard example is the so-called Ladder Graph. A balanced embedding of this graph looks exactly like a ladder. But Holm says: In an unbalanced embedding, it is hardly recognizable.

It seems subjective to say the Ladder Graph is good and its alternatives are bad, but Holm and Rotenberg articulated in their paper why those statements were mathematically true. Putting it very bluntly, we formally quantified why something is a terrible drawing, says Rotenberg, referring to a bad embedding. What the pair didnt realize at the time was that their class of good embeddings played an essential role in speeding up the process of dynamic planarity testing.

When adding a new edge to a planar graph is required, there are two scenarios: There is a safe way to add the edge, possibly after modifying the drawing, or no drawing admitting the edge exists. But in some cases, the embedding of a graph itself might be disguising a way the edge could be inserted in planar fashion. To reveal those alternative paths, mathematicians flip an embedding to change its orientation while keeping it mathematically identical, because the relationship between the connected nodes and edges hasnt changed.

These flips might make it possible to add edges between two newly arranged nodes, edges that would have otherwise violated planarity. Holm and Rotenberg discovered the flips that lead to successful edge insertion and deletion tended to fall into their class of so-called good embeddings. Similarly, these good embeddings require fewer flips overall to successfully add new edges. A win-win.

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The pair have suggested numerous applications for their work, including chip design, surface meshes, and road networks, but Rotenberg has admitted: What attracts us to this problem is its puzzle-like nature. The two are cautious to predict more commercial applications because completing flips in real-world graph designs can be challenging.

However, they say that their approach to assessing dynamic graphs (i.e., graphs that change via insertions and deletions) could impact how mathematicians approach similar problems. Essentially, while their algorithm assesses planarity, it also tracks and calculates changes to the graphs, performing what is called a recourse analysis, says Rotenberg.

But such data gathering isnt superfluous. Rotenberg argues their solution shows that recourse analysis could have algorithmic applications in addition to being interesting in its own right, because here, it led to their efficient planarity test.

Analyzing dynamic mathematical concepts is an open field, she says, but therein lies the potential. The breakthroughs might have already happenedtheyre just hidden in the process.

Solution to the Three Utilities Problem: Its actually impossible in two-dimensional space.

Editor's Note: This story first appears in the March/April 2021 issue of Popular Mechanics magazine.

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The Three Utilities Problem | Graph Theory Breakthrough - Popular Mechanics

He appended a Covid-19 in popular culture section to the end of the article, which was left mostly blank, save for a few lines about the certainty of impending works of art that would reference the pandemic. Fellow editors immediately disputed the section, citing a lack of substance. I said, Just hang on, this is going to fill in, Wyatt said. If you think about the plague of the Middle Ages and how much literature and culture references the plague again now, this is a category we can create in advance because we know its going to fill out. And thats what happened. Indeed, it grew so big that it became its own article.

In his essay on Wikipedias relationship to breaking news, Brian Keegan notes the prodigious detail of the September 11, 2001 terrorist attack article in the months following the event. There was even a list of the nearly 3,000 casualties by name, location, and civilian status. Editors started to argue that the fastidiousness was unbecoming of the traditional encyclopedia that Wikipedia was trying to emulate stylistically, and eventually portions of the entry disappeared.

That Wikipedia articles can spring into existence overnight, grow, and then contract again, reflects the peculiar vicissitudes of record-keeping in the digital age. Because the online encyclopedia is living and breathing, it is bound to the present. Gradually, as the community comes to understand [the pandemic] with a macro perspective, two, three, five, 10 years out, some of those subpages will be deleted, or theyll be merged, Stinson said. The Tourism in Zanzibar page, for instance, may one day forgo its Covid-19 reference, especially if theres a surviving, comprehensive article about the pandemics effects on global tourism.

Wikimedia archives all deleted pages, of course, which is why Stephen Harrison, writing in Slate, astutely observed that todays Wikipedia revisions [will] become a historical artifact for future scholars studying this period.

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Wikipedia's Sprawling, Awe-Inspiring Coverage of the Pandemic - The New Republic

In honor of Women's History Month, Art House Productions, along with Hudson County Community College & Seton Hall University, present Art+Feminism Lecture on Wednesday, March 24 at 12:30pm EST via Zoom. Click here to register for the lecture.

On April 7 from 10:00am-1:00pm EST, the Walsh Library and the Walsh Gallery will host Seton Hall's second Art+Feminism Wikipedia edit-a-thon. All are invited to register to become "Wikipedians" and edit or create a Wikipedia page for an artist. Click here to register for the event.

According to the Art+Feminism website, the non-profit organization "directly addresses the inequality of gender, feminism, and the arts on Wikipedia." This is accomplished through a coordinated campaign of online training materials and volunteer-organized "edit-a-thons" at a variety of cultural and intellectual institutions across the globe.

In the lecture on March 24, Brooke Duffy and Jeanne Brasile will provide an overview of the ways in which women and gender diverse artists have traditionally been and continue to be excluded from the art historical canon and global art markets. They will share background information about the Art+Feminism organization and objectives of their wiki-thons. The lecture culminates with a hands-on activity in which participants can engage with, critically read, and converse about artist Wikipedia pages.

To request closed captions or ASL interpreters, please email info@arthouseproductions.org at least 72 hours before the event.

The mission of the Hudson County Community College Department of Cultural Affairs is to provide supplementary programs to stimulate awareness of the arts and foster creativity. We strive to complement the efforts of HCCC with cultural events, community programs, and educational initiatives. Our goal is to transcend the understanding of visual and performing arts by closing the distance between the experience of art and everyday life in the community we serve.

In 2015, the College established a Cultural Affairs Task Force comprising involved members of the community, as well as HCCC Trustees, Foundation Board Directors, educators and scholars. The result is a full calendar of arts programs and events each semester, most of which are free of cost, and are held on the College's Journal Square and North Hudson campuses. Please CLICK HERE to view this season's offerings.

The Seton Hall University Libraries advance distinction in the Seton Hall communitys teaching, learning, and research through its provision of user-focused services, programs, and robust collections. Seton Hall University Libraries support excellence in academic and individual work, enable inquiry, foster intellectual and ethical integrity and respect for diverse points of view through user-focused services and robust collections as the intellectual and cultural heart of the University. The University Libraries are central to the Universitys intellectual life where students and faculty needs are the top priority. We lead through the provision of innovative services, programs, and resources within the Seton Hall community and beyond. The Walsh Gallery and Archives and Special Collections are the repositories for records, art and artifacts in support of the University Libraries and Seton Hall Universitys missions, goals and visions. In the Catholic intellectual tradition, we encourage the exchange of divergent points of view as we are the intellectual, ethical, cultural, and historical heart of the University. http://www.shu.edu

Art House Productions has long awarded adventurous and diverse performing artists with a stage to expose audiences to their ambitious and challenging projects. Art House Productions is a 501(c)(3) nonprofit organization committed to the development and presentation of the performing and visual arts in Jersey City, NJ. Art House Productions presents theater, performing and visual arts festivals, arts events, visual art exhibitions, and adult and youth art classes. For more information about our programs, please visit our website at http://www.arthouseproductions.org. Follow us on social media @arthouseproductions @arthouseprods. To sign up for Art House's mailing list, please click here: http://eepurl.com/hd1FCj.

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Art + Feminism Lecture and Wikipedia Edit-a-Thon to Take Place in Honor of Women's History Month - Broadway World

Tech companies are no stranger to controversy and workplace issues. Over the years, its become clear that no company is immune from diversity issues. But its the job of those in the diversity, equity and inclusion departments to create and foster environments that are welcoming to all.

Last year, in the wake of the police killings of George Floyd, Breonna Taylor and others, many companies spoke out in support of Black lives and the Black Lives Matter movement. At TechCrunch Sessions: Justice, well examine what some companies said at the time and how those statements align with where they are today.

Well also dive in to the myth of the pipeline problem, as well as the idea of imposter syndrome and how companies can help to shift the onus from the person experiencing feelings of doubt to the systems and cultures that perpetuate biases, sexism and racism. Well also, of course, talk about each companys DEI efforts over the years, where progress has been made and where theres still room for improvement.

To have this conversation, weve called on three DEI leaders from Uber, Facebook and Netflix to share their experiences, struggles and wins leading the charge for genuine inclusivity in tech.

Heres a bit about the three of them:

Bo Young Lee, Uber Chief Diversity Officer

Image Credits: Photo by Kimberly White/Getty Images for TechCrunch / Getty Images

Lee became Ubers first-ever chief diversity officer in early 2018. Lee joined about one year after former U.S. Attorney General Eric Holder and his law firm recommended Uber have a chief diversity officer. Holder and his firm were tapped in the aftermath of former Uber engineer Susan Fowlers allegations of sexual harassment at the company.

At TC Sessions: Justice, Ill chat with Lee about where Uber is today, as well as how it is doing in its mission to double Black representation in leadership by 2025.

Sandra Altine, VP of Workforce Diversity and Inclusion

(Photo courtesy of Facebook)

Altine joined Facebook last April after previously serving as the managing director of global diversity and inclusion for investor service Moodys.

Last year, Facebook committed to having 50% of its workforce be members of underrepresented groups, which includes BIPOC, women, disabled people and veterans. Over the next five years, Facebook also said its committed to increasing its Black employee base by 30%; currently 3.8% of its U.S.-based employees are Black.

Wade Davis, VP of Inclusion Strategy for Product

Photo courtesy of Netflix

Davis, who joined Netflix in this role in September 2019, works directly with product leaders at the company to implement inclusive policies and practices into the workplaces. He also works alongside other VPs at Netflix to improve upon diversity and inclusion within the workforce. Prior to joining Netflix, Davis consulted for Google, P&G and others.

Netflix released its first-ever diversity report just this year. Netflix had previously disclosed its data but had yet to make a full report out of it. Netflix did not lay out any concrete goals, but said its generally wanting to increase representation by hiring more inclusively and building out its recruiting networks.

Be sure to snag your tickets to TC Sessions: Justice here for just $5 here.

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Hear from Uber, Facebook and Netflix about diversity, equity and inclusion at TC Sessions: Justice - TechCrunch

Kyra Tan

Two weeks ago, President Rose announced a series of speakers who will each discuss an aspect of American democracy in light of the January 6 Capitol insurrection. While the series is laudable, Bowdoin has invited two figures who offer right-of-center opinions or votes that most Bowdoin students should consider problematic. In particular, the College has invited senator Susan Collins (R-Maine), but no corresponding Democratic-leaning politician (senator Angus King (I-Maine), again?) to discuss these recent events. In addition, the series next speaker, Suzanne Nossel, is a staunch opponent of what is often called cancel culture and has misconstrued the intentions and actions of its proponents, who are simply holding individuals responsible for their words, opinions and actions. The College has brought in some fantastic speakers this year, particularly Senator King, Eric Holder and DeRay McKesson 07, but I am disappointed by the invitation of these specific individuals for this series.

Collins, who said we need to get to know people who arent just like us and called for hearing opposing ideas at a 2016 talk at Bowdoin, has herself been avoiding voters who disagree with her, as she has not held a town hall in over 20 years. Collins, despite being the Republican senator who broke with Trump most often, has received significant criticism for her votes on federal justices and the Trump tax cuts and exhibits a level of hypocrisy that exemplifies the poor state of our political system, the subject of her talk.

Collins called the FBI investigation on the sexual assault allegations against Brett Kavanaugh very thorough, despite the failure to interview key witnesses and indications that the White House prevented a further investigation of perjury by Kavanaugh. She refused to support impeachment after President Trump asked for a Ukranian investigation of the Bidens and opposes the use of reconciliation for a new stimulus package despite voting for the Bush tax cuts, passed through reconciliation, after the Bush administration fired the Senate parliamentarian for his rulings on reconciliation. Still, as long as the often-evasive Collins is willing to take questions from students, this talk is a fantastic opportunity to hold her accountable for her past votes and statements, even if that is not Bowdoins intended purpose.

Nossel, meanwhile, is a Federalist Society (best known as a breeding ground for conservative justices) contributor who has criticized what she labels as cancel culture in op-eds and her recent book, Dare to Speak: Defining Free Speech for All. Nossel claims that cancel culture causes individuals to fear anything they say can and will be used against them by the places they depend on for education, employment and political representation. Nossel admits there are times when content is too vitriolic, bigoted, deceitful or misleading to be shared online, but seems to misunderstand, or willfully ignore, the part of cancel culture in which individuals face consequences for actions or speech that may be discriminatory or downright hurtful to certain groups of people.

The idea that individuals should not face consequences for their speech or opinions is laughably absurd. Newspapers, like the Bowdoin Orient itself, have the right to hire and fire journalists and columnists as they see fit and to publish other submissions in the same manner. In her 2020 resignation letter to the New York Times, former op-ed staff editor Bari Weiss described constant bullying by colleagues who pushed for her removal, but has since appeared on The View, published an op-ed on fighting back against woke culture in the New York Post, one of the most-read papers in the country, and operates a Substack titled common sense. Weiss, for all her talk about this New McCarthyism, is doing just fine.

There is also the question of community association in addition to perceived restrictions on speech. Workplaces and campus communities, as two examples, are ultimately collectives of individuals who make their own decisions about who they want to engage with. Interviewers consider the cultural fit of job applicants, so surely employers should care about the impact of a persons beliefs on their colleagues and customers. These groups are not some oppressive power about to crush vocal dissidents, but communities that care about the wellbeing of their members. Individuals who refuse to respect and validate their peers and colleagues, and who refuse to learn from those experiences, are capable of creating much more damage than any benefits from diversity of thought. Nobody should be cancelled for anything less extreme, but to suggest that we must engage with hostile and malicious people is just as constraining as any perceived censorship. I look forward to Collins and Nossels talks, but they are part of the problem, not the solution.

Michael Borecki is a member of the Class of 2021.

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OP ED: Collins, Nossel part of problem, not solution The Bowdoin Orient - The Bowdoin Orient