Computers Math

In 2018, when Professor Laurie Santos introduced her course “Psychology and the Good Life,” a class on the science of happiness, it became the most popular in the history of Yale, attracting more than 1,200 undergraduate enrollees that first semester. An online course based on those teachings became a global phenomenon. By latest count, 3.38 million people have enrolled to take the free Coursera.org course, called “The Science of Well Being.”
But the popularity of the course posed an interesting question. Does taking the course and participating in homework assignments — which include nurturing social connections, compiling a gratitude list, and meditation — really help improve a sense of well-being?
The answer is yes, according to two new studies that measured the psychological impact on individuals who took Santos’s or a similar course. The findings suggest that free online courses that teach principles of positive psychology can enrich the lives of millions of people.
In the latest study, published April 14 in the journal PLOS ONE, researchers at Johns Hopkins University and Yale found that people who took the online “Science of Well Being” course reported a greater sense of well-being than those enrolled in another Yale Coursera course, “Introduction to Psychology.” Although learners in both classes said they experienced significant improvement in their well-being after taking the courses, those who took the “Science of Well-Being” course reported greater mental health benefits than those learning about the basics of psychology.
Unlike the psychology course, “The Science of Well Being” requires participants to do exercises known to improve psychological health, such as improving sleep patterns, developing exercise routines, and practicing meditation, the authors say. Before and after taking the course, participants answered questions designed to measure factors related to psychological health such as positive emotions, engagement, and strength of relationships.
“Knowledge is great but it isn’t enough. You also have to do the work,” said lead author David Yaden, research fellow in the Department of Psychiatry and Behavioral Sciences at Johns Hopkins.
A similar study in Health Psychology Open, conducted by researchers at Yale and the University of Bristol, surveyed people who took either a live or an online credit-bearing course based on Santos’s original class and found similar psychological benefits for enrollees.
Yaden stressed, however, that the classes are not a substitute for professional treatment for those who suffer from diagnosed mental illness. “These courses are not a panacea or replacement for psychotherapy or medication,” he said.
However, both Yaden and Santos, who co-authored the study, say the findings show that massive open online courses can provide at least modest value to millions of people at no cost.
“We wanted to know if we could scale these benefits and we can,” Santos said. “Even bringing a small mental health benefit to millions of people can have a huge value.”
Other authors of the PLOS ONE paper are Jennifer Claydon,, Meghan Bathgate, and Belinda Platt of the Yale Poorvu Center for Teaching and Learning.
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Materials provided by Yale University. Original written by Bill Hathaway. Note: Content may be edited for style and length. More

Research breakthrough in understanding how neural systems process and store information.
A team of scientists from the University of Exeter and the University of Auckland have made a breakthrough in the quest to better understand how neural systems are able to process and store information.
The researchers, including lead author Dr Kyle Wedgwood from the University of Exeter’s Living Systems Institute, have made a significant discovery in how a single cell can store electrical patterns, similar to memories.
They compared sophisticated mathematical modelling to lab-based experiments to determine how different parameters, such as how long it takes for neuronal signals to be processed and how sensitive a cell is to external signals, affect how neural systems encode information.
The research team found that a single neuron is able to select between different patterns, dependent on the properties of each individual stimulus.
The research offers a new step towards developing a greater understanding of how information is encoded and stored in the brain, which could open up fresh insights into the cause and treatment of conditions such as dementia.
The research is published in the Journal of the Royal Society Interface on Wednesday, April 14th 2021.
Dr Wedgwood, from the University of Exeter’s Living Systems Institute said: “This work highlights how mathematical analysis and wet-lab experiments can be closely integrated to shed new light on fundamental problems in neuroscience.
“That the theoretical predictions were so readily confirmed in experiments gives us great confidence in the mathematical approach as a tool for understanding how individual cells store patterns of activity. In the long run, we hope that this is the first step to a better understanding of memory formation in neural networks.”
According to Professor Krauskopf from the University of Auckland: “The research shows that a living neuron coupled to itself is able to sustain different patterns in response to a stimulus. This is an exciting first step towards understanding how groups of neurons are able to respond to external stimuli in a precise temporal manner.”
“Communication between neurons occurs over large distances. The communication delay associated with this plays an important role in shaping the overall response of a network. This insight is crucial to how neural systems encode memories, which is one of the most fundamental questions in neuroscience,” adds Professor Tsaneva form the University of Exeter’s Living Systems Institute.
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New research shows how to measure the super-short bursts of high-frequency light emitted from free electron lasers (FELs). By using the light-induced ionization itself to create a femtosecond optical shutter, the technique encodes the electric field of the FEL pulse in a visible light pulse so that it can be measured with a standard, slow, visible-light camera.
“This work has the potential to lead to a new online diagnostic for FELs, where the exact pulse shape of each light pulse can be determined. That information can help both the end-user and the accelerator scientists,” said Pamela Bowlan, Los Alamos National Laboratory’s lead researcher on the project. The paper was published April 12, 2021 in Optica. “This work also paves the way for measuring x-ray pulses or femtosecond time-resolved x-ray images.”
Free electron lasers, which are driven by kilometer-long linear accelerators, emit bursts of short-wavelength light lasting one quadrillionth of a second. As a result, they can act as strobe lights for viewing the fastest events in nature — atomic or molecular motion — and therefore promise to revolutionize our understanding of almost any kind of matter.
Measuring such a vanishingly rapid burst of ionizing radiation has previously proved challenging. But while electronics are too slow to measure these light pulses, optical effects can be essentially instantaneous. Squeezing all of the energy of a continuous laser into short pulses means that femtosecond laser pulses are extremely bright and have the ability to modify a material’s absorption or refraction, creating effectively instantaneous “optical shutters.”
This idea has been widely used for measuring visible-light femtosecond laser pulses. But the higher-frequency extreme ultraviolet light from FELs interacts with matter differently; this light is ionizing, meaning that it pulls electrons out of their atoms. The researchers showed that ionization itself can be used as a “femtosecond optical shutter” for measuring extreme ultraviolet laser pulses at 31 nanometers.
“Ionization typically changes the optical properties of a material for nanoseconds, which is 10,000 times slower than the FEL pulse duration,” Bowlan said. “But the duration of the rising edge of ionization, determined by how long it takes the electron to leave the atom, is significantly faster. This resulting change in the optical properties can act as the fast shutter needed to measure the FEL pulses.”
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Reconfigurable materials can do amazing things. Flat sheets transform into a face. An extruded cube transforms into dozens of different shapes. But there’s one thing a reconfigurable material has yet to be able to change: its underlying topology. A reconfigurable material with 100 cells will always have 100 cells, even if those cells are stretched or squashed.
Now, researchers from the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) have developed a method to change a cellular material’s fundamental topology at the microscale. The research is published in Nature.
“Creating cellular structures capable of dynamically changing their topology will open new opportunities in developing active materials with information encryption, selective particle trapping, as well as tunable mechanical, chemical and acoustic properties,” said Joanna Aizenberg, the Amy Smith Berylson Professor of Materials Science at SEAS and Professor of Chemistry & Chemical Biology and senior author of the paper.
The researchers harnessed the same physics that clumps our hair together when it gets wet — capillary force. Capillary force works well on soft, compliant material, like our hair, but struggles with stiff cellular structures that require the bending, stretching or folding of walls, especially around strong, connected nodes. Capillary force is also temporary, with materials tending to return to their original configuration after drying.
In order to develop a long-lasting yet reversible method to transform the topology of stiff cellular microstructures, the researchers developed a two-tiered dynamic strategy. They began with a stiff, polymeric cellular microstructure with a triangular lattice topology, and exposed it to droplets of a volatile solvent chosen to swell and soften the polymer at the molecular scale. This made the material temporarily more flexible and in this flexible state, the capillary forces imposed by the evaporating liquid drew the edges of the triangles together, changing their connections with one another and transforming them into hexagons. Then, as the solvent rapidly evaporated, the material dried and was trapped in its new configuration, regaining its stiffness. The whole process took a matter of seconds.
“When you think about applications, it’s really important not to lose a material’s mechanical properties after the transformation process,” said Shucong Li, a graduate student in the Aizenberg Lab and co-first author of the paper. “Here, we showed that we can start with a stiff material and end with a stiff material through the process of temporarily softening it at the reconfiguration stage.”
The new topology of the material is so durable it can withstand heat or be submerged in some liquids for days without disassembling. Its robustness actually posed a problem for the researchers who had hoped to make the transformation reversible. More

When people are asked to draw the flower of a sunflower plant, almost everyone draws a large circle encircled by yellow petals.
“Actually, that structure is the flower head, or the capitulum, which may be composed of hundreds of flowers, also known as florets. The surrounding ‘petals’ are florets different in structure and function to those closer to the centre,” says Professor of Horticulture Paula Elomaa from the Faculty of Agriculture and Forestry, University of Helsinki, Finland.
A giant inflorescence is beneficial, as it is effective in attracting pollinators. When pollinators move around the inflorescence, they pollinate hundreds of individual florets over the course of their journey.
The order of the florets in a flower head is not random. Instead, they are patterned into regular spirals whose number follows the Fibonacci sequence familiar from mathematics. Fibonacci numbers are the sum of the two preceding numbers in the sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
In the flower head, the number of left- and right-winding spirals is always two consecutive Fibonacci numbers. Sunflower flower heads can have as many as 89 right-winding and 144-left winding spirals, while the gerbera, another much-studied plant from the Asteraceae plant family, has fewer spirals (34/55).
The geometric regularity of nature has fascinated both biologists and mathematicians for centuries. More

In physics, things exist in “phases,” such as solid, liquid, gas. When something crosses from one phase to another, we talk about a “phase transition” — think about water boiling into steam, turning from liquid to gas.
In our kitchens water boils at 100oC, and its density changes dramatically, making a discontinuous jump from liquid to gas. However, if we turn up the pressure, the boiling point of water also increases, until a pressure of 221 atmospheres where it boils at 374oC. Here, something strange happens: the liquid and gas merge into a single phase. Above this “critical point,” there is no longer a phase transition at all, and so by controlling its pressure water can be steered from liquid to gas without ever crossing one.
Is there a quantum version of a water-like phase transition? “The current directions in quantum magnetism and spintronics require highly spin-anisotropic interactions to produce the physics of topological phases and protected qubits, but these interactions also favor discontinuous quantum phase transitions,” says Professor Henrik Rønnow at EPFL’s School of Basic Sciences.
Previous studies have focused on smooth, continuous phase transitions in quantum magnetic materials. Now, in a joint experimental and theoretical project led by Rønnow and Professor Frédéric Mila, also at the School of Basic Sciences, physicists at EPFL and the Paul Scherrer Institute have studied a discontinuous phase transition to observe the first ever critical point in a quantum magnet, similar to that of water. The work is now published in Nature.
The scientists used a “quantum antiferromagnet,” known in the field as SCBO (from its chemical composition: SrCu2(BO3)2). Quantum antiferromagnets are especially useful for understanding how the quantum aspects of a material’s structure affect its overall properties — for example, how the spins of its electrons interact to give its magnetic properties. SCBO is also a “frustrated” magnet, meaning that its electron spins can’t stabilize in some orderly structure, and instead they adopt some uniquely quantum fluctuating states.
In a complex experiment, the researchers controlled both the pressure and the magnetic field applied to milligram pieces of SCBO. “This allowed us to look all around the discontinuous quantum phase transition and that way we found critical-point physics in a pure spin system,” says Rønnow.
The team performed high-precision measurements of the specific heat of SCBO, which shows its readiness to “suck up energy.” For example, water absorbs only small amounts of energy at -10oC, but at 0oC and 100oC it can take up huge amounts as every molecule is driven across the transitions from ice to liquid and liquid to gas. Just like water, the pressure-temperature relationship of SCBO forms a phase diagram showing a discontinuous transition line separating two quantum magnetic phases, with the line ending at a critical point.
“Now when a magnetic field is applied, the problem becomes richer than water,” says Frédéric Mila. “Neither magnetic phase is strongly affected by a small field, so the line becomes a wall of discontinuities in a three-dimensional phase diagram — but then one of the phases becomes unstable and the field helps push it towards a third phase.”
To explain this macroscopic quantum behavior, the researchers teamed up with several colleagues, particularly Professor Philippe Corboz at the University of Amsterdam, who have been developing powerful new computer-based techniques.
“Previously it was not possible to calculate the properties of ‘frustrated’ quantum magnets in a realistic two- or three-dimensional model,” says Mila. “So SCBO provides a well-timed example where the new numerical methods meet reality to provide a quantitative explanation of a phenomenon new to quantum magnetism.”
Henrik Rønnow concludes: “Looking forward, the next generation of functional quantum materials will be switched across discontinuous phase transitions, so a proper understanding of their thermal properties will certainly include the critical point, whose classical version has been known to science for two centuries.” More

The electronic properties of solid materials are highly dependent on crystal structures and their dimensionalities (i.e., whether the crystals have predominantly 2D or 3D structures). As Professor Takayoshi Katase of Tokyo Institute of Technology notes, this fact has an important corollary: “If the crystal structure dimensionality can be switched reversibly in the same material, a drastic property change may be controllable.” This insight led Prof. Katase and his research team at Tokyo Institute of Technology, in partnership with collaborators at Osaka University and National Institute for Materials Science, to embark on research into the possibility of switching the crystal structure dimensionality of a lead-tin-selenide alloy semiconductor. Their results appear in a paper published in a recent issue of the peer-reviewed journal Science Advances.
The lead-tin-selenide alloy, (Pb1-xSnx)Se is an appropriate focus for such research because the lead ions (Pb2+) and tin ions (Sn2+) favor distinct crystal dimensionalities. Specifically, pure lead selenide (PbSe) has a 3D crystal structure, whereas pure tin selenide (SnSe) has a 2D crystal structure. SnSe has bandgap of 1.1 eV, similar to the conventional semiconductor Si. Meanwhile, PbSe has narrow bandgap of 0.3 eV and shows 1 order of magnitude higher carrier mobility than SnSe. In particular, the 3D (Pb1-xSnx)Se has gathered much attention as a topological insulator. That is, the substitution for Pb with Sn in the 3D PbSe reduces the band gap and finally produces a gap-less Dirac-like state. Therefore, if these crystal structure dimensionality can be switched by external stresses such as temperature, it would lead to a giant functional phase transition, such as large electronic conductivity change and topological state transition, enhanced by the distinct electronic structure changes.
The alloying PbSe and SnSe would manipulate the drastic transition in structure, and such (Pb1-xSnx)Se alloy should induce strong frustration around phase boundaries. However, there is no direct phase boundary between the 3D PbSe and the 2D SnSe phases under thermal equilibrium. Through their experiments, Prof. Katase and his research team successfully developed a method for growing the nonequilibrium lead-tin-selenide alloy crystals with equal amounts of Pb2+ and Sn2+ ions (i.e., (Pb0.5Sn0.5)Se) that underwent direct structural phase transitions between 2D and 3D forms based on temperature. At lower temperatures, the 2D crystal structure predominated, whereas at higher temperatures, the 3D structure predominated. The low-temperature 2D crystal structure was more resistant to electrical current than the high-temperature 3D crystal was, and as the alloy was heated, its resistivity levels took a sharp dive around the temperatures at which the dimensionality phase transition occurred. The present strategy facilitates different structure dimensionality switching and further functional property switching in semiconductors using artificial phase boundary.
In sum, the research team developed a form of the semiconductor alloy (Pb1-xSnx)Se that undergoes temperature-dependent crystal dimensionality phase transitions, and these transitions have major implications for the alloy’s electronic properties. When asked about the importance of his team’s work, Prof. Katase notes that this form of the (Pb1-xSnx)Se alloy can “serve as a platform for fundamental scientific studies as well as the development of novel function in semiconductor technologies.” This specialized alloy may, therefore, lead to exciting new semiconductor technologies with myriad benefits for humanity.
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Physicists from Swansea University are part of an international research collaboration which has identified a new technique for testing the quality of quantum correlations.
Quantum computers run their algorithms on large quantum systems of many parts, called qubits, by creating quantum correlations across all of them. It is important to verify that the actual computation procedures lead to quantum correlations of desired quality.
However, carrying out these checks is resource-intensive as the number of tests required grows exponentially with the number of qubits involved.
Researchers from the College of Science, working with colleagues from Spain and Germany, have now proposed a new technique that helps to overcome this problem by significantly reducing the number of measurements while increasing the resilience against noise.
Their method offers a solution to the problem of certifying correlations in large systems and is explained in a new paper which has just been published in PRX Quantum, a journal from American Physical Society.
Research fellow Dr Farid Shahandeh, the lead scientist of this research, said: “To achieve this we combine two processes. Firstly, consider a juicer — it extracts the essence of the fruit by squeezing it into a small space. Similarly, in many cases quantum correlations in large systems can also be concentrated in smaller parts of the system. The ‘squeezing’ is done by measurements on the rest of the system called the localization process.
“Suppose the juicer directly converts the fruit into juice boxes without any labels. We don’t know what is inside — it could be apple juice, orange juice, or just water. One way to tell would be to open the box and taste it. The quantum comparison of this is to measure a suitable quantity that tells us whether quantum correlations exist within a system or not.
“This process is called witnessing and we call the combination of the two approaches conditional witnessing.”
In their research the physicists prove their method is efficient and generically tolerates higher levels of noise in experiments. They have also compared their approach with previous techniques in a class of quantum processors that use ions to demonstrate its efficiency.
Dr Shahandeh, the recipient of a Royal Commission for the Exhibition of 1851 research fellowship, added: “This is of crucial importance in current technology where the addition of each qubit unavoidably amplifies the complexity of quantum states and experimental imperfections.”
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