Lifeboat Foundation

The “rank” of a graph is the number of loops it has; for each rank of graphs, there exists a moduli space. The size of this space grows quickly — if you fix the lengths of the graph’s edges, there are three graphs of rank 2, 15 of rank 3,111 of rank 4, and 2,314,204,852 of rank 10. On the moduli space, these lengths can vary, introducing even more complexity.

The shape of the moduli space for graphs of a given rank is determined by relationships between the graphs. As you walk around the space, nearby graphs should be similar, and should morph smoothly into one another. But these relationships are complicated, leaving the moduli space with mathematically unsettling features, such as regions where three walls of the moduli space pass through one another.

Mathematicians can study the structure of a space or shape using objects called cohomology classes, which can help reveal how a space is put together. For instance, consider one of mathematicians’ favorite shapes, the doughnut. On the doughnut, cohomology classes are simply loops.

It acted with rudimentary intelligence, learning, evolving and communicating with itself to grow more powerful.

A new model by a team of researchers led by Penn State and inspired by Crichton’s novel describes how biological or technical systems form complex structures equipped with signal-processing capabilities that allow the systems to respond to stimulus and perform functional tasks without external guidance.

“Basically, these little nanobots become self-organized and self-aware,” said Igor Aronson, Huck Chair Professor of Biomedical Engineering, Chemistry, and Mathematics at Penn State, explaining the plot of Crichton’s book. The novel inspired Aronson to study the emergence of collective motion among interacting, self-propelled agents. The research was recently published in Nature Communications.

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The math behind Evo-devo~

Continue reading “The math behind engineering living things (TMEB #3)” »

Quantum computing has entered a bit of an awkward period. There have been clear demonstrations that we can successfully run quantum algorithms, but the qubit counts and error rates of existing hardware mean that we can’t solve any commercially useful problems at the moment. So, while many companies are interested in quantum computing and have developed software for existing hardware (and have paid for access to that hardware), the efforts have been focused on preparation. They want the expertise and capability needed to develop useful software once the computers are ready to run it.

For the moment, that leaves them waiting for hardware companies to produce sufficiently robust machines—machines that don’t currently have a clear delivery date. It could be years; it could be decades. Beyond learning how to develop quantum computing software, there’s nothing obvious to do with the hardware in the meantime.

But a company called QuEra may have found a way to do something that’s not as obvious. The technology it is developing could ultimately provide a route to quantum computing. But until then, it’s possible to solve a class of mathematical problems on the same hardware, and any improvements to that hardware will benefit both types of computation. And in a new paper, the company’s researchers have expanded the types of computations that can be run on their machine.

Antibiotic resistance is a global threat to public health and associated with the overuse of antibiotics. Although non-antibiotic drugs occupy 95% of the drug market, their impact on the emergence and spread of antibiotic resistance remains unclear. Here we demonstrate that antidepressants, one of the most frequently prescribed drugs, can induce antibiotic resistance and persistence. Such effects are associated with increased reactive oxygen species, enhanced stress signature responses, and stimulation of efflux pump expression. Mathematical modeling also supported a role for antidepressants in the occurrence of antibiotic-resistant mutants and persister cells. Considering the high consumption of antidepressants (16,850 kg annually in the United States alone), our findings highlight the need to re-evaluate the antibiotic-like side effects of antidepressants.

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Stephen Hawking was one of the greatest scientific and analytical minds of our time, says NASA’s Michelle Thaller. She posits that Hawking might be one of the parents of an entirely new school of physics because he was working on some incredible stuff—concerning quantum entaglement— right before he died. He was even humble enough to go back to his old work about black holes and rethink his hypotheses based on new information. Not many great minds would do that, she says, relaying just one of the reasons Stephen Hawking will be so deeply missed. You can follow Michelle Thaller on Twitter at @mlthaller.

Continue reading “What Stephen Hawking would have discovered if he lived longer | NASA’s Michelle Thaller | Big Think” »

A key algorithm that quietly empowers and simplifies our electronics is the Fourier transform, which turns the graph of a signal varying in time into a graph that describes it in terms of its frequencies.

Packaging signals that represent sounds or images in terms of their frequencies allows us to analyze and adjust sound and image files, Richard Stern, professor of electrical and computer engineering at Carnegie Mellon University, tells Popular Mechanics. This mathematical operation also makes it possible for us to store data efficiently.

The invention of color TV is a great example of this, Stern explains. In the 1950s, television was just black and white. Engineers at RCA developed color television, and used Fourier transforms to simplify the data transmission so that the industry could introduce color without tripling the demands on the channels by adding data for red, green, and blue light. Viewers with black-and-white TVs could continue to see the same images as they saw before, while viewers with color TVs could now see the images in color.

Summary: Researchers explain how deep neural networks are able to learn complex physics.

Source: Rice University.

One of the oldest tools in computational physics — a 200-year-old mathematical technique known as Fourier analysis — can reveal crucial information about how a form of artificial intelligence called a deep neural network learns to perform tasks involving complex physics like climate and turbulence modeling, according to a new study.

Microsoft announced new AI-powered classroom tools today. The company sees its new “Learning Accelerators” as helping students sharpen their speaking and math skills — while making teachers’ jobs a little easier — as children prepare for an even more technologically enhanced world.

Speaker Progress is a new AI classroom tool for teachers. Microsoft says it saves them time by “streamlining the process of creating, reviewing, and analyzing speaking and presentation assignments for students, groups, and classrooms.” It can provide tidy summaries of presentation-based skills while highlighting areas to improve. Additionally, it lets teachers review student recordings, identify their needs and track progress.

It will be a companion for Speaker Coach, an existing feature Microsoft launched in 2021 that provides one-on-one speaking guidance and feedback. For example, it uses AI to give real-time pointers on pacing, pitch and filler words. “Speaker Coach is one of those tools that kind of was a lightbulb tool for a lot of students that I’ve worked with,” said an unnamed teacher in a Microsoft launch video. “Being able to practice and get real-time feedback is where Speaker Coach really comes in and helps our students, and it even helps us as adults.”