Computers Math

Corals in the Ocean are made up of coral polyps, a small soft creature with a stem and tentacles, they are responsible for nourishing the corals, and aid the coral’s survival by generating self-made currents through motion of their soft bodies.
Scientists from WMG at the University of Warwick, led by Eindhoven University of Technology in the Netherlands, developed a 1cm by 1cm wireless artificial aquatic polyp, which can remove contaminants from water. Apart from cleaning, this soft robot could be also used in medical diagnostic devices by aiding in picking up and transporting specific cells for analysis.
In the paper, ‘An artificial aquatic polyp that wirelessly attracts, grasps, and releases objects’ researchers demonstrate how their artificial aquatic polyp moves under the influence of a magnetic field, while the tentacles are triggered by light. A rotating magnetic field under the device drives a rotating motion of the artificial polyp’s stem. This motion results in the generation of an attractive flow which can guide suspended targets, such as oil droplets, towards the artificial polyp.
Once the targets are within reach, UV light can be used to activate the polyp’s tentacles, composed of photo-active liquid crystal polymers, which then bend towards the light enclosing the passing target in the polyp’s grasp. Target release is then possible through illumination with blue light.
Dr Harkamaljot Kandail, from WMG, University of Warwick was responsible for creating state of the art 3D simulations of the artificial aquatic polyps. The simulations are important to help understand and elucidate the stem and tentacles generate the flow fields that can attract the particles in the water.
The simulations were then used to optimise the shape of the tentacles so that the floating particles could be grabbed quickly and efficiently.
Dr Harkamaljot Kandail, from WMG, University of Warwick comments:
“Corals are such a valuable ecosystem in our oceans, I hope that the artificial aquatic polyps can be further developed to collect contaminant particles in real applications. The next stage for us to overcome before being able to do this is to successfully scale up the technology from laboratory to pilot scale. To do so we need to design an array of polyps which work harmoniously together where one polyp can capture the particle and pass it along for removal.”
Marina Pilz Da Cunha, from the Eindhoven University of Technology, Netherlands adds:
“The artificial aquatic polyp serves as a proof of concept to demonstrate the potential of actuator assemblies and serves as an inspiration for future devices. It exemplifies how motion of different stimuli-responsive polymers can be harnessed to perform wirelessly controlled tasks in an aquatic environment.”

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Whether you are playing Go in a park amid chirping birds, a gentle breeze and kids playing catch nearby or you are playing in a den with a ticking clock on a bookcase and a purring cat on the sofa, if the game situation is identical and clear, your next move likely would be, too, regardless of those different conditions. You’ll still play the same next move despite a wide range of internal feelings or even if a few neurons here and there are just being a little erratic. How does the brain overcome unpredictable and varying disturbances to produce reliable and stable computations? A new study by MIT neuroscientists provides a mathematical model showing how such stability inherently arises from several known biological mechanisms.
More fundamental than the willful exertion of cognitive control over attention, the model the team developed describes an inclination toward robust stability that is built in to neural circuits by virtue of the connections, or “synapses” that neurons make with each other. The equations they derived and published in PLOS Computational Biology show that networks of neurons involved in the same computation will repeatedly converge toward the same patterns of electrical activity, or “firing rates,” even if they are sometimes arbitrarily perturbed by the natural noisiness of individual neurons or arbitrary sensory stimuli the world can produce.
“How does the brain make sense of this highly dynamic, non-linear nature of neural activity?” said co-senior author Earl Miller, Picower Professor of Neuroscience in The Picower Institute for Learning and Memory and the Department of Brain and Cognitive Sciences (BCS) at MIT. “The brain is noisy, there are different starting conditions — how does the brain achieve a stable representation of information in the face of all these factors that can knock it around?”
To find out, Miller’s lab, which studies how neural networks represent information, joined forces with BCS colleague and mechanical engineering Professor Jean-Jacques Slotine, who leads the Nonlinear Systems Laboratory at MIT. Slotine brought the mathematical method of “contraction analysis,” a concept developed in control theory, to the problem along with tools his lab developed to apply the method. Contracting networks exhibit the property of trajectories that start from disparate points ultimately converging into one trajectory, like tributaries in a watershed. They do so even when the inputs vary with time. They are robust to noise and disturbance, and they allow for many other contracting networks to be combined together without a loss of overall stability — much like brain typically integrates information from many specialized regions.
“In a system like the brain where you have [hundreds of billions] of connections the questions of what will preserve stability and what kinds of constraints that imposes on the system’s architecture become very important,” Slotine said.
Math reflects natural mechanisms
Leo Kozachkov, a graduate student in both Miller’s and Slotine’s labs, led the study by applying contraction analysis to the problem of the stability of computations in the brain. What he found is that the variables and terms in the resulting equations that enforce stability directly mirror properties and processes of synapses: inhibitory circuit connections can get stronger, excitatory circuit connections can get weaker, both kinds of connections are typically tightly balanced relative to each other, and neurons make far fewer connections than they could (each neuron, on average, could make roughly 10 million more connections than it does).

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“These are all things that neuroscientists have found, but they haven’t linked them to this stability property,” Kozachkov said. “In a sense, we’re synthesizing some disparate findings in the field to explain this common phenomenon.”
The new study, which also involved Miller lab postdoc Mikael Lundqvist, was hardly the first to grapple with stability in the brain, but the authors argue it has produced a more advanced model by accounting for the dynamics of synapses and by allowing for wide variations in starting conditions. It also offers mathematical proofs of stability, Kozachkov added.
Though focused on the factors that ensure stability, the authors noted, their model does not go so far as to doom the brain to inflexibility or determinism. The brain’s ability to change — to learn and remember — is just as fundamental to its function as its ability to consistently reason and formulate stable behaviors.
“We’re not asking how the brain changes,” Miller said. “We’re asking how the brain keeps from changing too much.”
Still, the team plans to keep iterating on the model, for instance by encompassing a richer accounting for how neurons produce individual spikes of electrical activity, not just rates of that activity.
They are also working to compare the model’s predictions with data from experiments in which animals repeatedly performed tasks in which they needed to perform the same neural computations, despite experiencing inevitable internal neural noise and at least small sensory input differences.
Finally, the team is considering how the models may inform understanding of different disease states of the brain. Aberrations in the delicate balance of excitatory and inhibitory neural activity in the brain is considered crucial in epilepsy, Kozachkov notes. A symptom of Parkinson’s disease, as well, entails a neurally-rooted loss of motor stability. Miller adds that some patients with autism spectrum disorders struggle to stably repeat actions (e.g. brushing teeth) when external conditions vary (e.g. brushing in a different room).
The National Institute of Mental Health, the Office of Naval Research, the National Science Foundation and the JPB Foundation supported the research More

New research at the University of Warwick has (pardon the pun) put a new spin on a mathematical analogy involving a jumping grasshopper and its ideal lawn shape. This work could help us understand the spin states of quantum-entangled particles.
The grasshopper problem was devised by physicists Olga Goulko (then at UMass Amherst), Adrian Kent and Damián Pitalúa-García (Cambridge). They asked for the ideal lawn shape that would maximize the chance that a grasshopper, starting from a random position on the lawn and jumping a fixed distance in a random direction, lands back on the lawn. Intuitively one might expect the answer to be a circular lawn, at least for small jumps. But Goulko and Kent actually proved otherwise: various shapes from a cogwheel pattern to some disconnected patches of lawn performed better for different jump sizes (link to the technical paper).
Beyond surprises about lawn shapes and grasshoppers, the research provided useful insight into Bell-type inequalities relating probabilities of the spin states of two separated quantum-entangled particles. The Bell inequality, proved by physicist John Stewart Bell in 1964 and later generalised in many ways, demonstrated that no combination of classical theories with Einstein’s special relativity is able to explain the predictions (and later actual experimental observations) of quantum theory.
The next step was to test the grasshopper problem on a sphere. The Bloch sphere is a geometrical representation of the state space of a single quantum bit. A great circle on the Bloch sphere defines linear polarization measurements, which are easily implemented and commonly used in Bell and other cryptographic tests. Because of the antipodal symmetry for the Bloch sphere, a lawn covers half the total surface area, and the natural hypothesis would be that the ideal lawn is hemispherical. Researchers in the Department of Computer Science at the University of Warwick, in collaboration with Goulko and Kent, investigated this problem and found that it too requires non-intuitive lawn patterns. The main result is that the hemisphere is never optimal, except in the special case when the grasshopper needs exactly an even number of jumps to go around the equator. This research shows that there are previously unknown types of Bell inequalities.
One of the paper’s authors — Dmitry Chistikov from the Centre for Discrete Mathematics and its Applications (DIMAP) and the Department of Computer Science, at the University of Warwick, commented:
“Geometry on the sphere is fascinating. The sine rule, for instance, looks nicer for the sphere than the plane, but this didn’t make our job easy.”
The other author from Warwick, Professor Mike Paterson FRS, said:
“Spherical geometry makes the analysis of the grasshopper problem more complicated. Dmitry, being from the younger generation, used a 1948 textbook and pen-and-paper calculations, whereas I resorted to my good old Mathematica methods.”
The paper, entitled ‘Globe-hopping’, is published in the Proceedings of the Royal Society A. It is interdisciplinary work involving mathematics and theoretical physics, with applications to quantum information theory.
The research team: Dmitry Chistikov and Mike Paterson (both from the University of Warwick), Olga Goulko (Boise State University, USA), and Adrian Kent (Cambridge), say that the next steps to give even more insight into quantum spin state probabilities are looking for the most grasshopper-friendly lawns on the sphere or even letting the grasshopper boldly go jumping in three or more dimensions.

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Materials science researchers have demonstrated the first electrically injected laser made with germanium tin. Used as a semiconducting material for circuits on electronic devices, the diode laser could improve micro-processing speed and efficiency at much lower costs. More

In 1952, Alan Turing published a study which described mathematically how systems composed of many living organisms can form rich and diverse arrays of orderly patterns. He proposed that this ‘self-organisation’ arises from instabilities in un-patterned systems, which can form as different species jostle for space and resources. So far, however, researchers have struggled to reproduce Turing patterns in laboratory conditions, raising serious doubts about its applicability. In a new study published in EPJ B, researchers led by Malbor Asllani at the University of Limerick, Ireland, have revisited Turing’s theory to prove mathematically how instabilities can occur through simple reactions, and in widely varied environmental conditions.

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The team’s results could help biologists to better understand the origins of many ordered structures in nature, from spots and stripes on animal coats, to clusters of vegetation in arid environments. In Turing’s original model, he introduced two diffusing chemical species to different points on a closed ring of cells. As they diffused across adjacent cells, these species ‘competed’ with each other as they interacted; eventually organising to form patterns. This pattern formation depended on the fact that the symmetry during this process could be broken to different degrees, depending on the ratio between the diffusion speeds of each species; a mechanism now named the ‘Turing instability.’ However, a significant drawback of Turing’s mechanism was that it relied on the unrealistic assumption that many chemicals diffuse at different paces.
Through their calculations, Asllani’s team showed that in sufficiently large rings of cells, where diffusion asymmetry causes both species to travel in the same direction, the instabilities which generate ordered patterns will always arise — even when competing chemicals diffuse at the same rate. Once formed, the patterns will either remain stationary, or propagate steadily around the ring as waves. The team’s result addresses one of Turing’s key concerns about his own theory, and is an important step forward in our understanding of the innate drive for living systems to organise themselves.

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Journal Reference:
Malbor Asllani, Timoteo Carletti, Duccio Fanelli, Philip K. Maini. A universal route to pattern formation in multicellular systems. The European Physical Journal B, 2020; 93 (7) DOI: 10.1140/epjb/e2020-10206-3

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Springer. (2020, August 7). Updating Turing’s model of pattern formation. ScienceDaily. Retrieved August 7, 2020 from www.sciencedaily.com/releases/2020/08/200807111942.htm
Springer. “Updating Turing’s model of pattern formation.” ScienceDaily. www.sciencedaily.com/releases/2020/08/200807111942.htm (accessed August 7, 2020). More

Geologists have developed a machine learning technique that highlights the potential for further deposits of the critical metal tungsten in SW England.
Tungsten is an essential component of high-performance steels but global production is strongly influenced by China and western countries are keen to develop alternative sources.
The work, published in the leading journal Geoscience Frontiers, has been led by Dr Chris Yeomans, from the Camborne School of Mines, and involved geoscientists from the University of Nottingham, Geological Survey of Finland (GTK) and the British Geological Survey.
The research applies machine learning to multiple existing datasets to examine the geological factors that have resulted in known tungsten deposits in SW England.
These findings are then applied across the wider region to predict areas where tungsten mineralisation is more likely and might have previously been overlooked. The same methodology could be applied to help in the exploration for other metals around the world.
Dr Yeomans, a Postdoctoral Research Fellow at the Camborne School of Mines, based at the University of Exeter’s Penryn Campus in Cornwall said: “We’re really pleased with the methodology developed and the results of this study.

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“SW England is already the focus of UK mineral exploration for tungsten but we wanted to demonstrate that new machine learning approaches may provide additional insights and highlight areas that might otherwise be overlooked.”
SW England hosts the fourth biggest tungsten deposit in the world (Hemerdon, near Plympton), that resulted in the UK being the sixth biggest global tungsten producer in 2017; the mine is currently being re-developed by Tungsten West Limited.
The Redmoor tin-tungsten project, being developed by Cornwall Resources Limited, has also been identified as being a potentially globally significant mineral deposit.
The new study suggests that there may be a wider potential for tungsten deposits and has attracted praise from those currently involved in the development of tungsten resources in SW England.
James McFarlane, from Tungsten West, said: “Tungsten has only been of economic interest in the last 100 years or so, during which exploration efforts for this critical metal have generally been short-lived.
“As such is very encouraging to see work that aims to holistically combine the available data to develop a tungsten prospectivity model in an area that has world-class potential.”
Brett Grist, from Cornwall Resources added: “Our own work has shown that applying modern techniques can reveal world-class deposits in this historic and globally-significant mining district.
“Dr Yeomans’ assertion, that the likelihood of new discoveries of tungsten mineralisation may be enhanced by a high-resolution gravity survey, is something in which we see great potential.
“Indeed, such a programme could stimulate the new discovery of economically significant deposits of a suite of critical metals, here in the southwest of the UK, for years to come.”

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Engineers at the UCLA Samueli School of Engineering and their colleagues at Stanford School of Medicine have demonstrated that drug levels inside the body can be tracked in real time using a custom smartwatch that analyzes the chemicals found in sweat. This wearable technology could be incorporated into a more personalized approach to medicine — where an ideal drug and dosages can be tailored to an individual.
A study detailing the research was published in Proceedings of the National Academy of Sciences.
In general, medications are prescribed with a ‘one-size-fits-all’ approach — drugs are designed and prescribed based on statistical averages of their effectiveness. There are guidelines for factors such as patients’ weight and age. But in addition to these basic differentiators, our body chemistry constantly changes — depending on what we eat and how much we’ve exercised. And on top of these dynamic factors, every individual’s genetic makeup is unique and hence responses to medications can vary. This affects how fast drugs are absorbed, take effect and get eliminated from an individual.
According to the researchers, current efforts to personalize the drug dosage rely heavily on repeated blood draws at the hospital. The samples are then sent out to be analyzed in central labs. These solutions are inconvenient, time-consuming, invasive and expensive. That is why they are only performed on a small subset of patients and on rare occasions.
“We wanted to create a wearable technology that can track the profile of medication inside the body continuously and non-invasively,” said study leader Sam Emaminejad, an assistant professor of electrical and computer engineering at UCLA. “This way, we can tailor the optimal dosage and timing of the intake for each individual. And using this personalization approach, we can improve the efficacy of the therapeutic treatments.”
Because of their small molecular sizes, many different kinds of drugs end up in sweat, where their concentrations closely reflect the drugs’ circulating levels. That’s why the researchers created a smartwatch, equipped with a sensor that analyzes the sampled tiny droplets of sweat.
The team’s experiment tracked the effect of acetaminophen, a common over-the-counter pain medication, on individuals over the period of a few hours. First, the researchers stimulated sweat glands on the wrist by applying a small electric current, the same technique that Emaminejad’s research group demonstrated in previous wearable technologies.
This allowed the researchers to detect changes in body chemistry, without needing subjects to work up a sweat by exercising. As different drugs each have their own unique electrochemical signature, the sensor can be designed to look for the level of a particular medication at any given time.
“This technology is a game-changer and a significant step forward for realizing personalized medicine,” said study co-author Ronald W. Davis, a professor of biochemistry and genetics at Stanford Medical School. “Emerging pharmacogenomic solutions, which allow us to select drugs based on the genetic makeup of individuals, have already shown to be useful in improving the efficacy of treatments. So, in combination with our wearable solution, which helps us to optimize the drug dosages for each individual, we can now truly personalize our approaches to pharmacotherapy.”
What makes this study significant is the ability to accurately detect a drug’s unique electrochemical signal, against the backdrop of signals from many other molecules that may be circulating in the body and in higher concentrations than the drug, said the study’s lead author Shuyu Lin, a UCLA doctoral student and member of Emaminejad’s Interconnected and Integrated Bioelectronics Lab (I²BL). Emaminejad added that the technology could be adapted to monitor medication adherence and drug abuse.
“This could be particularly important for individuals with mental health issues, where doctors prescribe them prolonged pharmacotherapy treatments,” he said. ” The patients could benefit from such easy-to-use, noninvasive monitoring tools, while doctors could see how the medication is doing in the patient.” More

A new study found that 77% of low- to moderate-income American households fall below the asset poverty threshold, meaning that if their income were cut off they would not have the financial assets to maintain at least poverty-level status for three months. More