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A 53-Year-Old Network Coloring Conjecture Is Disproved (quantamagazine.org)
In just three pages, a Russian mathematician has presented a better way to color certain types
A paper posted online last month has disproved a 53-year-old conjecture about the best way to assign colors to the nodes of a network. The paper shows, in a mere three pages, that there are better ways to color certain networks than many mathematicians had supposed possible. Network coloring problems, which were inspired by the question of how to color maps so that adjoining countries are different colors, have been a focus of study among mathematicians for nearly 200 years. The goal is to figure out how to color the nodes of some network (or graph, as mathematicians call them) so that no two connected nodes share the same color. Depending on the context, such a coloring can provide an effective way to seat guests at a wedding, schedule factory tasks for different time slots, or even solve a sudoku puzzle.
Graph coloring problems tend to be simple to state, but they are often enormously hard to solve. Even the question that launched the field -- Do four colors suffice to color any map? -- took more than a century to answer (the answer is yes, in case you were wondering). The problem tackled in the new paper seemed, until now, to be no exception to this rule. Unsolved for more than 50 years, it concerns tensor products -- graphs made by combining two different graphs (call them G and H) in a specific way. The tensor product of G and H is a new, larger graph in which each node represents a pair of nodes from the original graphs -- one from G and one from H -- and two nodes in the tensor product are connected if both their corresponding nodes in G and their corresponding nodes in H are connected. |
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| There are no conversations. |
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| cauz |
June 17, 2019, 1:57 p.m. |
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| Stefan Banach |
A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. |
| Anant Agarwal |
The online credential, the online certificate is very different from an on campus certificate. And we really believe that online learning and the EdX platform and the EdX portal, these are ways in which - you can think of them as a rising tide that's going to lift all boats whether for students worldwide or on our campuses. |
| Fergie |
I'm a big online everything. But for me, shopping online started with music, obviously, then it went onto books, meditation CDs, and I just recently bought these electronic cigarettes. My husband is trying to quit smoking, so I went online and I bought those BluCigs cigarettes in every flavor for him. |
| Homaro Cantu |
I was just taught very early that if I didn't solve problems, I was headed for a very dark path. Problems were everywhere. Now, even if there are no problems, I look for problems. I'm like, 'You know what? I don't like the way this spoon works. I want to design a new spoon.' |
| Guillermo Cabrera Infante |
If you look closely, there is no book more visual than Three Trapped Tigers, in that it is filled with blank pages, dark pages, it has stars made of words, the famous magical cube made of numbers, and there is even a page which is a mirror. |
| William Jackson |
I pitched my last children's show presentation in the mid 1980's. The era of locally produced children's shows was over and the networks were not and are not interested in children's television. |
| Howard Gardner |
Anything that is worth teaching can be presented in many different ways. These multiple ways can make use of our multiple intelligences. |
| John Abizaid |
I think what actually works best is local-level individual targeting of key leadership nodes. |
| Thomas R. Insel |
Unlike the heart or kidney, which have a small, defined set of cell types, we still do not have a taxonomy of neurons, and neuroscientists still argue whether specific types of neurons are unique to humans. But there is no disputing that neurons are only about 10 percent of the cells in the human brain. |
| Gene Hackman |
Once, I optioned a novel and tried to do a screenplay on it, which was great fun, but I was too respectful. I was only 100 pages into the novel and I had about 90 pages of movie script going. I realized I had a lot to learn. |
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This is worse than when you're coloring and then you realize all of your crayons are the same color.
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Citizen Science Task: Come up with a color to match the crayon name!
Procedure:
1. Open up a color picker, for example, https://colorpicker.me/ or https://color.adobe.com/.
2. For each item in the numbered list: read them crayon names in list below and picture the color it describes.
3. Find that color in from your mind on your color picker and aim for high precision.
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Quantum Network Joins Four People Together For Encrypted Messaging
The quantum internet is starting small, but growing. Researchers have created a network that lets four users communicate simultaneously through channels secured by the laws of quantum physics, and they say it could easily be scaled up. Soren Wengerowsky at the University of Vienna and his colleagues devised a network that uses quantum key distribution (QKD) to keep messages secure [the link is paywalled]. The general principle of QKD is that two photons are entangled, meaning their quantum properties are linked.
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When I was in middle school I thought it was weird that people had favorite colors and lucky numbers so I decided that I'd have a lucky color and a favorite number. My favorite number was 17.5 and my lucky color was orange.
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North Korea Gets Second Route To Internet Via Russia Link
Russia is providing North Korea another way to get on the internet, according to cybersecurity outfit FireEye. In an interview on Monday, FireEye's chief technology officer for the Asia-Pacific region, Bryce Boland, said that Russia telecommunications company TransTeleCom opened a new link for users in North Korea. Until now, state-owned China United Network Communications Ltd. was the country's sole connection. Bloomberg reports:
"Having an additional loop via Russia gives North Korea more options for how they can operate and reduces the possibility for the United States to put pressure just on a single country to turn off their i...
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And then the people on the social network start acting out a play and it isn't explained but then it just shows up there!
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Millions of Smartphones in 11 Countries Were Taken Offline Yesterday by an Expired Certificate
Ericsson has confirmed that a fault with its software was the source of yesterday's massive network outage, which took millions of smartphones offline across the UK and Japan and created issues in almost a dozen countries. From a report:
In a statement, Ericsson said that the root cause was an expired certificate, and that "the faulty software that has caused these issues is being decommissioned." The statement notes that network services were restored to most customers on Thursday, while UK operator O2 said that its 4G network was back up as of early Friday morning.
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oogle's Voice-Generating AI Is Now Indistinguishable From Humans
Anonymous Coward 6 hours ago 75
An anonymous reader quotes a report from Quartz: A research paper published by Google this month -- which has not been peer reviewed -- details a text-to-speech system called Tacotron 2, which claims near-human accuracy at imitating audio of a person speaking from text. The system is Google's second official generation of the technology, which consists of two deep neural networks. The first network translates the text into a spectrogram (pdf), a visual way to represent audio frequencies over time. That spectrogram is then fed into WaveNet, a system from Alphabet's AI research lab DeepMind, which reads the chart and generates the corresponding audio elements accordingly. The Google researchers ...
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It still seems weird to me that Cantor's continuum hypothesis can't be proved or disproved in ZFC.
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Weaponized Health Communication: Twitter Bots
and Russian Trolls Amplify the Vaccine Debate
Objectives.
To understand how Twitter bots and trolls (
“
bots
”
) promote online health
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