Aurelia Butler

There is a great need to generate various types of cells for use in new therapies to replace tissues that are lost due to disease or injuries, or for studies outside the human body to improve our understanding of how organs and tissues function in health and disease. Many of these efforts start with human induced pluripotent stem cells (iPSCs) that, in theory, have the capacity to differentiate into virtually any cell type in the right culture conditions. The 2012 Nobel Prize awarded to Shinya Yamanaka recognized his discovery of a strategy that can reprogram adult cells to become iPSCs by providing them with a defined set of gene-regulatory transcription factors (TFs). However, progressing from there to efficiently generating a wide range of cell types with tissue-specific differentiated functions for biomedical applications has remained a challenge.
While the expression of cell type-specific TFs in iPSCs is the most often used cellular conversion technology, the efficiencies of guiding iPSC through different “lineage stages” to the fully functional differentiated state of, for example, a specific heart, brain, or immune cell currently are low, mainly because the most effective TF combinations cannot be easily pinpointed. TFs that instruct cells to pass through a specific cell differentiation process bind to regulatory regions of genes to control their expression in the genome. However, multiple TFs must function in the context of larger gene regulatory networks (GRNs) to drive the progression of cells through their lineages until the final differentiated state is reached.
Now, a collaborative effort led by George Church, Ph.D. at Harvard’s Wyss Institute for Biologically Inspired Engineering and Harvard Medical School (HMS), and Antonio del Sol, Ph.D., who leads Computational Biology groups at CIC bioGUNE, a member of the Basque Research and Technology Alliance, in Spain, and at the Luxembourg Centre for Systems Biomedicine (LCSB, University of Luxembourg), has developed a computer-guided design tool called IRENE, which significantly helps increase the efficiency of cell conversions by predicting highly effective combinations of cell type-specific TFs. By combining IRENE with a genomic integration system that allows robust expression of selected TFs in iPSCs, the team demonstrated their approach to generate higher numbers of natural killer cells used in immune therapies, and melanocytes used in skin grafts, than other methods. In a scientific first, generated breast mammary epithelial cells, whose availability would be highly desirable for the repopulation of surgically removed mammary tissue. The study is published in Nature Communications.
“In our group, the study naturally built on the ‘TFome’ project, which assembled a comprehensive library containing 1,564 human TFs as a powerful resource for the identification of TF combinations with enhanced abilities to reprogram human iPSCs to different target cell types,” said Wyss Core Faculty member Church. “The efficacy of this computational algorithm will boost a number of our tissue engineering efforts at the Wyss Institute and HMS, and as an open resource can do the same for many researchers in this burgeoning field.” Church is the lead of the Wyss Institute’s Synthetic Biology platform, and Professor of Genetics at HMS and of Health Sciences and Technology at Harvard and MIT.
Tooling up
Several computational tools have been developed to predict combinations of TFs for specific cell conversions, but almost exclusively these are based on the analysis of gene expression patterns in many cell types. Missing in these approaches was a view of the epigenetic landscape, the organization of the genome itself around genes and on the scale of entire chromosome sections which goes far beyond the sequence of the naked genomic DNA.

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“The changing epigenetic landscape in differentiating cells predicts areas in the genome undergoing physical changes that are critical for key TFs to gain access to their target genes. Analyzing these changes can inform more accurately about GRNs and their participating TFs that drive specific cell conversions,” said co-first author Evan Appleton, Ph.D. Appleton is a Postdoctoral Fellow in Church’s group who joined forces with Sascha Jung, Ph.D., from del Sol’s group in the new study. “Our collaborators in Spain had developed a computational approach that integrated those epigenetic changes with changes in gene expression to produce critical TF combinations as an output, which we were in an ideal position to test.”
The team used their computational “Integrative gene Regulatory Network model” (IRENE) approach to reconstruct the GRN controlling iPSCs, and then focused on three target cell types with clinical relevance to experimentally validate TF combinations prioritized by IRENE. To deliver TF combinations into iPSCs, they deployed a transposon-based genomic integration system that can integrate multiple copies of a gene encoding a TF into the genome, which allows all factors of a combination to be stably expressed. Transposons are DNA elements that can jump from one position of the genome to another, or in this case from an exogenously provided piece of DNA into the genome.
“Our research team composed of scientists from the LCSB and CIC bioGUNE has a long-standing expertise in developing computational methods to facilitate cell conversion. IRENE is an additional resource in our toolbox and one for which experimental validation has demonstrated it substantially increased efficiency in most tested cases,” corresponding author Del Sol, who is Professor at LCSB and CIC bioGUNE. “Our fundamental research should ultimately benefit patients, and we are thrilled that IRENE could enhance the production of cell sources readily usable in therapeutic applications, such as cell transplantation and gene therapies.”
Validating the computer-guided design tool in cells
The researchers chose human mammary epithelial cells (HMECs) as a first cell type. Thus far HMECs are obtained from one tissue environment, dissociated, and transplanted to one where breast tissue has been resected. HMECs generated from patients’ cells, via an intermediate iPSC stage, could provide a means for less invasive and more effective breast tissue regeneration. One of the combinations that was generated by IRENE enabled the team to convert 14% of iPSCs into differentiated HMECs in iPSC-specific culture media, showing that the provided TFs were sufficient to drive the conversion without help from additional factors.
The team then turned their attention to melanocytes, which can provide a source of cells in cellular grafts to replace damaged skin. This time they performed the cell conversion in melanocyte destination medium to show that the selected TFs work under culture conditions optimized for the desired cell type. Two out of four combinations were able to increase the efficiency of melanocyte conversion by 900% compared to iPSCs grown in destination medium without the TFs. Finally, the researchers compared combinations of TFs prioritized by IRENE to generate natural killer (NK) cells with a state-of-the-art differentiation method based on cell culture conditions alone. Immune NK cells have been found to improve the treatment of leukemia. The researchers’ approach outperformed the standard with five out of eight combinations increasing the differentiation of NK cells with critical markers by up to 250%.
“This novel computational approach could greatly facilitate a range of cell and tissue engineering efforts at the Wyss Institute and many other sites around the world. This advance should greatly expand our toolbox as we strive to develop new approaches in regenerative medicine to improve patients’ lives,” said Wyss Founding Director Donald Ingber, M.D., Ph.D., who is also the Judah Folkman Professor of Vascular Biology at HMS and Boston Children’s Hospital, and Professor of Bioengineering at the Harvard John A. Paulson School of Engineering and Applied Sciences. More

Light-emitting diodes (LEDs) have revolutionized the displays industry. LEDs use electric current to produce visible light without the excess heat found in traditional light bulbs, a glow called electroluminescence. This breakthrough led to the eye-popping, high-definition viewing experience we’ve come to expect from our screens. Now, a group of physicists and chemists have developed a new type of LED that utilizes spintronics without needing a magnetic field, magnetic materials or cryogenic temperatures; a “quantum leap” that could take displays to the next level.
“The companies that make LEDs or TV and computer displays don’t want to deal with magnetic fields and magnetic materials. It’s heavy and expensive to do it,” said Valy Vardeny, distinguished professor of physics and astronomy at the University of Utah. “Here, chiral molecules are self-assembled into standing arrays, like soldiers, that actively spin polarize the injected electrons, which subsequently lead to circularly polarized light emission. With no magnetic field, expensive ferromagnets and with no need for extremely low temperatures. Those are no-nos for the industry.”
Most opto-electronic devices, such as LEDs, only control charge and light and not the spin of the electrons. The electrons possess tiny magnetic fields that, like the Earth, have magnetic poles on opposite sides. Its spin may be viewed as the orientation of the poles and can be assigned binary information — an “up” spin is a “1,” a “down” is a “0.” In contrast, conventional electronics only transmit information through bursts of electrons along a conductive wire to convey messages in “1s” and “0s.” Spintronic devices, however, could utilize both methods, promising to process exponentially more information than traditional electronics.
One barrier to commercial spintronics is setting the electron spin. Presently, one needs to produce a magnetic field to orient the electron spin direction. Researchers from the University of Utah and the National Renewable Energy Laboratory (NREL) developed technology that acts as an active spin filter made of two layers of material called chiral two-dimension metal-halide perovskites. The first layer blocks electrons having spin in the wrong direction, a layer that the authors call a chiral-induced spin filter. Then when the remaining electrons pass through the second light-emitting perovskite layer, they cause the layer to produce photons that move in unison along a spiral path, rather than a conventional wave pattern, to produce circular polarized electroluminescence.
The study was published in the journal Science on March 12, 2021.
Left-handed, right-handed molecules
The scientists exploited a property called chirality that describes a particular type of geometry. Human hands are a classic example; the right and left hands are arranged as mirrors of one another, but they will never perfectly align, no matter the orientation. Some compounds, such as DNA, sugar and chiral metal-halide perovskites, have their atoms arranged in a chiral symmetry. A “left-handed” oriented chiral system may allow transport of electrons with “up” spins but block electrons with “down” spins, and vice versa.

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“If you try to transport electrons through these compounds, then the electron spin becomes aligned with the chirality of the material,” Vardeny said. Other spin filters do exist, but they either require some kind of magnetic field, or they can only manipulate electrons in a small area. “The beauty of the perovskite material that we used is that it’s two-dimensional — you can prepare many planes of 1 cm2 area that contain one million of a billion (1015) standing molecules with the same chirality.”
Metal-halide perovskite semiconductors are mostly used for solar cells these days, as they are highly efficient at converting sunlight to electricity. Since a solar cell is one of the most demanding applications of any semiconductor, scientists are discovering other uses exist as well, including spin-LEDs.
“We are exploring the fundamental properties of metal-halide perovskites, which has allowed us to discover new applications beyond photovoltaics,” said Joseph Luther, a co-author of the new paper and NREL scientist. “Because metal-halide perovskites, and other related metal halide organic hybrids, are some of the most fascinating semiconductors, they exhibit a host of novel phenomena that can be utilized in transforming energy.”
Although metal-halide perovskites are the first to prove the chiral-hybrid devices are feasible, they are not the only candidates for spin-LEDs. The general formula for the active spin filter is one layer of an organic, chiral material, another layer of an inorganic metal halide, such as lead iodine, another organic layer, inorganic layer and so on.
“That’s beautiful. I’d love that someone will come out with another 2-D organic/inorganic layer material that may do a similar thing. At this stage, it’s very general. I’m sure that with time, someone will find a different two-dimensional chiral material that will be even more efficient,” Vardeny said.
The concept proves that using these two dimensional chiral-hybrid systems gain control over spin without magnets and has “broad implications for applications such as quantum-based optical computing, bioencoding and tomography,” according to Matthew Beard, a senior research fellow and director of Center for Hybrid Organic Inorganic Semiconductors for Energy.
Vardeny and Xin Pan from the Department of Physics & Astronomy at the University of Utah co-authored the study. The other co-authors from NREL are Beard, Young-Hoon Kim, Yaxin Zhai, Haipeng Lu, Chuanxiao Xiao, E. Ashley Gaulding, Steven Harvey and Joseph Berry. All are part of CHOISE collaboration, an Energy Frontier Research Center (EFRC) funded by the Office of Science within DOE.
Funding for the research came from CHOISE. More

In order to exploit the properties of quantum physics technologically, quantum objects and their interaction must be precisely controlled. In many cases, this is done using light. Researchers at the University of Innsbruck and the Institute of Quantum Optics and Quantum Information (IQOQI) of the Austrian Academy of Sciences have now developed a method to individually address quantum emitters using tailored light pulses. “Not only is it important to individually control and read the state of the emitters,” says Oriol Romero-Isart, “but also to do so while leaving the system as undisturbed as possible.” Together with Juan Jose Garcia-Ripoll (IQOQI visiting fellow) from the Instituto de Fisica Fundamental in Madrid, Romero-Isart’s research group has now investigated how specifically engineered pulses can be used to focus light on a single quantum emitter.
Self-compressing light pulse
“Our proposal is based on chirped light pulses,” explains Silvia Casulleras, first author of the research paper. “The frequency of these light pulses is time-dependent.” So, similar to the chirping of birds, the frequency of the signal changes over time. In structures with certain electromagnetic properties — such as waveguides — the frequencies propagate at different speeds. “If you set the initial conditions of the light pulse correctly, the pulse compresses itself at a certain distance,” explains Patrick Maurer from the Innsbruck team. “Another important part of our work was to show that the pulse enables the control of individual quantum emitters.” This approach can be used as a kind of remote control to address, for example, individual superconducting quantum bits in a waveguide or atoms near a photonic crystal.
Wide range of applications
In their work, now published in Physical Review Letters, the scientists show that this method works not only with light or electromagnetic pulses, but also with other waves such as lattice oscillations (phonons) or magnetic excitations (magnons). The research group led by the Innsbruck experimental physicist Gerhard Kirchmair, wants to implement the concept for superconducting qubits in the laboratory in close collaboration with the team of theorists.
The research was financially supported by the European Union.

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Researchers at UCL have solved a major piece of the puzzle that makes up the ancient Greek astronomical calculator known as the Antikythera Mechanism, a hand-powered mechanical device that was used to predict astronomical events.
Known to many as the world’s first analogue computer, the Antikythera Mechanism is the most complex piece of engineering to have survived from the ancient world. The 2,000-year-old device was used to predict the positions of the Sun, Moon and the planets as well as lunar and solar eclipses.
Published in Scientific Reports, the paper from the multidisciplinary UCL Antikythera Research Team reveals a new display of the ancient Greek order of the Universe (Cosmos), within a complex gearing system at the front of the Mechanism.
Lead author Professor Tony Freeth (UCL Mechanical Engineering) explained: “Ours is the first model that conforms to all the physical evidence and matches the descriptions in the scientific inscriptions engraved on the Mechanism itself.
“The Sun, Moon and planets are displayed in an impressive tour de force of ancient Greek brilliance.”
The Antikythera Mechanism has generated both fascination and intense controversy since its discovery in a Roman-era shipwreck in 1901 by Greek sponge divers near the small Mediterranean island of Antikythera.

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The astronomical calculator is a bronze device that consists of a complex combination of 30 surviving bronze gears used to predict astronomical events, including eclipses, phases of the moon, positions of the planets and even dates of the Olympics.
Whilst great progress has been made over the last century to understand how it worked, studies in 2005 using 3D X-rays and surface imaging enabled researchers to show how the Mechanism predicted eclipses and calculated the variable motion of the Moon.
However, until now, a full understanding of the gearing system at the front of the device has eluded the best efforts of researchers. Only about a third of the Mechanism has survived, and is split into 82 fragments — creating a daunting challenge for the UCL team.
The biggest surviving fragment, known as Fragment A, displays features of bearings, pillars and a block. Another, known as Fragment D, features an unexplained disk, 63-tooth gear and plate.
Previous research had used X-ray data from 2005 to reveal thousands of text characters hidden inside the fragments, unread for nearly 2,000 years. Inscriptions on the back cover include a description of the cosmos display, with the planets moving on rings and indicated by marker beads. It was this display that the team worked to reconstruct.

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Two critical numbers in the X-rays of the front cover, of 462 years and 442 years, accurately represent cycles of Venus and Saturn respectively. When observed from Earth, the planets’ cycles sometimes reverse their motions against the stars. Experts must track these variable cycles over long time-periods in order to predict their positions.
“The classic astronomy of the first millennium BC originated in Babylon, but nothing in this astronomy suggested how the ancient Greeks found the highly accurate 462-year cycle for Venus and 442-year cycle for Saturn,” explained PhD candidate and UCL Antikythera Research Team member Aris Dacanalis.
Using an ancient Greek mathematical method described by the philosopher Parmenides, the UCL team not only explained how the cycles for Venus and Saturn were derived but also managed to recover the cycles of all the other planets, where the evidence was missing.
PhD candidate and team member David Higgon explained: “After considerable struggle, we managed to match the evidence in Fragments A and D to a mechanism for Venus, which exactly models its 462-year planetary period relation, with the 63-tooth gear playing a crucial role.”
Professor Freeth added: “The team then created innovative mechanisms for all of the planets that would calculate the new advanced astronomical cycles and minimize the number of gears in the whole system, so that they would fit into the tight spaces available.”
“This is a key theoretical advance on how the Cosmos was constructed in the Mechanism,” added co-author, Dr Adam Wojcik (UCL Mechanical Engineering). “Now we must prove its feasibility by making it with ancient techniques. A particular challenge will be the system of nested tubes that carried the astronomical outputs.” More

In the field of robotics, metals offer advantages like strength, durability, and electrical conductivity. But, they are heavy and rigid — properties that are undesirable in soft and flexible systems for wearable computing and human-machine interfaces.
Hydrogels, on the other hand, are lightweight, stretchable, and biocompatible, making them excellent materials for contact lenses and tissue engineering scaffolding. They are, however, poor at conducting electricity, which is needed for digital circuits and bioelectronics applications.
Researchers in Carnegie Mellon University’s Soft Machines Lab have developed a unique silver-hydrogel composite that has high electrical conductivity and is capable of delivering direct current while maintaining soft compliance and deformability. The findings were published in Nature Electronics.
The team suspended micrometer-sized silver flakes in a polyacrylamide-alginate hydrogel matrix. After going through a partial dehydration process, the flakes formed percolating networks that were electrically conductive and robust to mechanical deformations. By manipulating this dehydration and hydration process, the flakes can be made to stick together or break apart, forming reversible electrical connections.
Previous attempts to combine metals and hydrogels revealed a trade-off between improved electrical conductivity and lowered compliance and deformability. Majidi and his team sought to tackle this challenge, building on their expertise in developing stretchable, conductive elastomers with liquid metal.
“With its high electrical conductivity and high compliance or ‘squishiness,’ this new composite can have many applications in bioelectronics and beyond,” explained Carmel Majidi, professor of mechanical engineering. “Examples include a sticker for the brain that has sensors for signal processing, a wearable energy generation device to power electronics, and stretchable displays.”
The silver-hydrogel composite can be printed by standard methods like stencil lithography, similar to screen printing. The researchers used this technique to develop skin-mounted electrodes for neuromuscular electrical stimulation. According to Majidi, the composite could cover a large area of the human body, “like a second layer of nervous tissue over your skin.”
Future applications could include treating muscular disorders and motor disabilities, such as assisting someone with tremors from Parkinson’s disease or difficulty grasping something with their fingers after a stroke.

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Materials provided by College of Engineering, Carnegie Mellon University. Original written by Lisa Kulick. Note: Content may be edited for style and length. More

A new study demonstrates that machine-learning strategies can be applied to routinely collected physiological data, such as heart rate and blood pressure, to provide clues about pain levels in people with sickle cell disease. Mark Panaggio of Johns Hopkins University Applied Physics Laboratory and colleagues present these findings in the open-access journal PLOS Computational Biology.
Pain is subjective, and monitoring pain can be intrusive and time-consuming. Pain medication can help, but accurate knowledge of a patient’s pain is necessary to balance relief against risk of addiction or other unwanted effects. Machine-learning strategies have shown promise in predicting pain from objective physiological measurements, such as muscle activity or facial expressions, but few studies have applied machine learning to routinely collected data.
Now, Panaggio and colleagues have developed and applied machine-learning models to data from people with sickle cell disease who were hospitalized due to debilitating pain. These statistical models classify whether a patient’s pain was low, moderate, or high at each point during their stay based on routinely collected measurements of their blood pressure, heart rate, temperature, respiratory rate, and oxygen levels.
The researchers found that these vital signs indeed gave clues into the patients’ reported pain levels. By taking physiological data into account, their models outperformed baseline models in estimating subjective pain levels, detecting changes in pain, and identifying atypical pain levels. Pain predictions were most accurate when they accounted for changes in patients’ vital signs over time.
“Studies like ours show the potential that data-driven models based on machine learning have to enhance our ability to monitor patients in less invasive ways and ultimately, be able to provide more timely and targeted treatments,” Panaggio says.
Looking ahead, the researchers hope to leverage more comprehensive data sources and real-time monitoring tools, such as fitness trackers, to build better models for inferring and forecasting pain.

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What do you do after solving the answer to life, the universe, and everything? If you’re mathematicians Drew Sutherland and Andy Booker, you go for the harder problem.
In 2019, Booker, at the University of Bristol, and Sutherland, principal research scientist at MIT, were the first to find the answer to 42. The number has pop culture significance as the fictional answer to “the ultimate question of life, the universe, and everything,” as Douglas Adams famously penned in his novel “The Hitchhiker’s Guide to the Galaxy.” The question that begets 42, at least in the novel, is frustratingly, hilariously unknown.
In mathematics, entirely by coincidence, there exists a polynomial equation for which the answer, 42, had similarly eluded mathematicians for decades. The equation x3+y3+z3=k is known as the sum of cubes problem. While seemingly straightforward, the equation becomes exponentially difficult to solve when framed as a “Diophantine equation” — a problem that stipulates that, for any value of k, the values for x, y, and z must each be whole numbers.
When the sum of cubes equation is framed in this way, for certain values of k, the integer solutions for x, y, and z can grow to enormous numbers. The number space that mathematicians must search across for these numbers is larger still, requiring intricate and massive computations.
Over the years, mathematicians had managed through various means to solve the equation, either finding a solution or determining that a solution must not exist, for every value of k between 1 and 100 — except for 42.
In September 2019, Booker and Sutherland, harnessing the combined power of half a million home computers around the world, for the first time found a solution to 42. The widely reported breakthrough spurred the team to tackle an even harder, and in some ways more universal problem: finding the next solution for 3.

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Booker and Sutherland have now published the solutions for 42 and 3, along with several other numbers greater than 100, this week in the Proceedings of the National Academy of Sciences.
Picking up the gauntlet
The first two solutions for the equation x3+y3+z3 = 3 might be obvious to any high school algebra student, where x, y, and z can be either 1, 1, and 1, or 4, 4, and -5. Finding a third solution, however, has stumped expert number theorists for decades, and in 1953 the puzzle prompted pioneering mathematician Louis Mordell to ask the question: Is it even possible to know whether other solutions for 3 exist?
“This was sort of like Mordell throwing down the gauntlet,” says Sutherland. “The interest in solving this question is not so much for the particular solution, but to better understand how hard these equations are to solve. It’s a benchmark against which we can measure ourselves.”
As decades went by with no new solutions for 3, many began to believe there were none to be found. But soon after finding the answer to 42, Booker and Sutherland’s method, in a surprisingly short time, turned up the next solution for 3:5699368212219623807203 + (−569936821113563493509)3 + (−472715493453327032)3 = 3
The discovery was a direct answer to Mordell’s question: Yes, it is possible to find the next solution to 3, and what’s more, here is that solution. And perhaps more universally, the solution, involving gigantic, 21-digit numbers that were not possible to sift out until now, suggests that there are more solutions out there, for 3, and other values of k.

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“There had been some serious doubt in the mathematical and computational communities, because [Mordell’s question] is very hard to test,” Sutherland says. “The numbers get so big so fast. You’re never going to find more than the first few solutions. But what I can say is, having found this one solution, I’m convinced there are infinitely many more out there.”
A solution’s twist
To find the solutions for both 42 and 3, the team started with an existing algorithm, or a twisting of the sum of cubes equation into a form they believed would be more manageable to solve:
k − z3 = x3 + y3 = (x + y)(x2 − xy + y2)
This approach was first proposed by mathematician Roger Heath-Brown, who conjectured that there should be infinitely many solutions for every suitable k. The team further modified the algorithm by representing x+y as a single parameter, d. They then reduced the equation by dividing both sides by d and keeping only the remainder — an operation in mathematics termed “modulo d” — leaving a simplified representation of the problem.
“You can now think of k as a cube root of z, modulo d,” Sutherland explains. “So imagine working in a system of arithmetic where you only care about the remainder modulo d, and we’re trying to compute a cube root of k.”
With this sleeker version of the equation, the researchers would only need to look for values of d and z that would guarantee finding the ultimate solutions to x, y, and z, for k=3. But still, the space of numbers that they would have to search through would be infinitely large.
So, the researchers optimized the algorithm by using mathematical “sieving” techniques to dramatically cut down the space of possible solutions for d.
“This involves some fairly advanced number theory, using the structure of what we know about number fields to avoid looking in places we don’t need to look,” Sutherland says.
A global task
The team also developed ways to efficiently split the algorithm’s search into hundreds of thousands of parallel processing streams. If the algorithm were run on just one computer, it would have taken hundreds of years to find a solution to k=3. By dividing the job into millions of smaller tasks, each independently run on a separate computer, the team could further speed up their search.
In September 2019, the researchers put their plan in play through Charity Engine, a project that can be downloaded as a free app by any personal computer, and which is designed to harness any spare home computing power to collectively solve hard mathematical problems. At the time, Charity Engine’s grid comprised over 400,000 computers around the world, and Booker and Sutherland were able to run their algorithm on the network as a test of Charity Engine’s new software platform.
“For each computer in the network, they are told, ‘your job is to look for d’s whose prime factor falls within this range, subject to some other conditions,'” Sutherland says. “And we had to figure out how to divide the job up into roughly 4 million tasks that would each take about three hours for a computer to complete.”
Very quickly, the global grid returned the very first solution to k=42, and just two weeks later, the researchers confirmed they had found the third solution for k=3 — a milestone that they marked, in part, by printing the equation on t-shirts.
The fact that a third solution to k=3 exists suggests that Heath-Brown’s original conjecture was right and that there are infinitely more solutions beyond this newest one. Heath-Brown also predicts the space between solutions will grow exponentially, along with their searches. For instance, rather than the third solution’s 21-digit values, the fourth solution for x, y, and z will likely involve numbers with a mind-boggling 28 digits.
“The amount of work you have to do for each new solution grows by a factor of more than 10 million, so the next solution for 3 will need 10 million times 400,000 computers to find, and there’s no guarantee that’s even enough,” Sutherland says. “I don’t know if we’ll ever know the fourth solution. But I do believe it’s out there.” More

How do you turn “dumb” headphones into smart ones? Rutgers engineers have invented a cheap and easy way by transforming headphones into sensors that can be plugged into smartphones, identify their users, monitor their heart rates and perform other services.
Their invention, called HeadFi, is based on a small plug-in headphone adapter that turns a regular headphone into a sensing device. Unlike smart headphones, regular headphones lack sensors. HeadFi would allow users to avoid having to buy a new pair of smart headphones with embedded sensors to enjoy sensing features.
“HeadFi could turn hundreds of millions of existing, regular headphones worldwide into intelligent ones with a simple upgrade,” said Xiaoran Fan, a HeadFi primary inventor. He is a recent Rutgers doctoral graduate who completed the research during his final year at the university and now works at Samsung Artificial Intelligence Center.
A peer-reviewed Rutgers-led paper on the invention, which results in “earable intelligence,” will be formally published in October at MobiCom 2021, the top international conference on mobile computing and mobile and wireless networking.
Headphones are among the most popular wearable devices worldwide and they continue to become more intelligent as new functions appear, such as touch-based gesture control, the paper notes. Such functions usually rely on auxiliary sensors, such as accelerometers, gyroscopes and microphones that are available on many smart headphones.
HeadFi turns the two drivers already inside all headphones into a versatile sensor, and it works by connecting headphones to a pairing device, such as a smartphone. It does not require adding auxiliary sensors and avoids changes to headphone hardware or the need to customize headphones, both of which may increase their weight and bulk. By plugging into HeadFi, a converted headphone can perform sensing tasks and play music at the same time.
The engineers conducted experiments with 53 volunteers using 54 pairs of headphones with estimated prices ranging from $2.99 to $15,000. HeadFi can achieve 97.2 percent to 99.5 percent accuracy on user identification, 96.8 percent to 99.2 percent on heart rate monitoring and 97.7 percent to 99.3 percent on gesture recognition.

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