Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.
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Category: mathematics – Page 143
Scientists at the University of Würzburg have been able to boost current super-resolution microscopy by a novel tweak. They coated the glass cover slip as part of the sample carrier with tailor-made biocompatible nanosheets that create a mirror effect. This method shows that localizing single emitters in front of a metal-dielectric coating leads to higher precision, brightness and contrast in Single Molecule Localization Microscopy (SMLM). The study was published in the Nature journal Light: Science and Applications.
The sharpness of a light microscope is limited by physical conditions—structures that are closer together than 0.2 thousandths of a millimeter blur, and can no longer be distinguished from each other. The cause of this blurring is diffraction. Each point-shaped object is therefore not shown as a point, but as a blurry spot.
With mathematical methods, the resolution can still be drastically improved. One method would calculate its exact center from the brightness distribution of the blurry spot. However, it only works if two closely adjacent points of the object are initially not simultaneously but subsequently visible, and are merged later in the image processing. This temporal decoupling prevents superimposition of the blurry spot. For years, researchers in life sciences have been using this tricky method for super high-resolution light microscopy of cells.
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by Eloisa Marchesoni
Today, I will talk about the recent creation of really intelligent machines, able to solve difficult problems, to recreate the creativity and versatility of the human mind, machines not only able to excel in a single activity but to abstract general information and find solutions that are unthinkable for us. I will not talk about blockchain, but about another revolution (less economic and more mathematical), which is all about computing: quantum computers.
Quantum computing is not really new, as we have been talking about it for a couple of decades already, but we are just now witnessing the transition from theory to realization of such technology. Quantum computers were first theorized at the beginning of the 1980s, but only in the last few years, thanks to the commitment of companies like Google and IBM, a strong impulse has been pushing the development of these machines. The quantum computer is able to use quantum particles (imagine them to be like electrons or photons) to process information. The particles act as positive or negative (i., the 0 and the 1 that we are used to see in traditional computer science) alternatively or at the same time, thus generating quantum information bits called “qubits”, which can have value either 0 or 1 or a quantum superposition of 0 and 1.
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How atoms arrange themselves at the smallest scale was thought to follow a ‘drum-skin’ rule, but mathematicians have now found a simpler solution.
Atomic arrangements in different materials can provide a lot of information about the properties of materials, and what the potential is for altering what they can be used for.
However, where two materials touch – at their interface – complex interactions arise that make predicting the arrangement of atoms difficult.
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Deep learning has been making it possible for powerful machines to approximate and imitate abilities and techniques once thought to be uniquely human. Mathematicians have struggled to explain how they work so well and may now get some answers by looking outside mathematics and into the nature of the universe.
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Modeling the Microbiome
Posted in biological, health, mathematics, physics
What the study shows, the researchers said, is that the interactions between the bacterial populations are as significant to the host’s overall fitness as their presence — the microbiome’s influence cannot be solely attributed to the presence or absence of individual species. “In a sense,” said Jones, “the microbiome’s influence on the host is more than the sum of its parts.”
The gut microbiome — the world of microbes that inhabit the human intestinal tract — has captured the interest of scientists and clinicians for its critical role in health. However, parsing which of those microbes are responsible for effects on our wellbeing remains a mystery.
Taking us one step closer to solving this puzzle, UC Santa Barbara physicists Eric Jones and Jean Carlson have developed a mathematical approach to analyze and model interactions between gut bacteria in fruit flies. This method could lead to a more sophisticated understanding of the complex interactions between human gut microbes.
Their finding appear in the Proceedings of the National Academy of Sciences.
Scientists look around the universe and see amazing structure. There are objects and processes of fantastic complexity. Every action in our universe follows exact laws of nature that are perfectly expressed in a mathematical language. These laws of nature appear fine-tuned to bring about life, and in particular, intelligent life. What exactly are these laws of nature and how do we find them?
The universe is so structured and orderly that we compare it to the most complicated and exact contraptions of the age. In the 18th and 19th centuries, the universe was compared to a perfectly working clock or watch. Philosophers then discussed the Watchmaker. In the 20th and 21st centuries, the most complicated object is a computer. The universe is compared to a perfectly working supercomputer. Researchers ask how this computer got its programming.
How does one explain all this structure? Why do the laws seem so perfect for producing life and why are they expressed in such exact mathematical language? Is the universe really as structured as it seems?
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A French physicist has won an Ig Nobel Prize for using mathematical formulas to determine whether cats are liquid or solid.
The Ig Nobel prizes are awarded every year by Improbable Research, an organization devoted to science and humor. The goal is to highlight scientific studies that first make people laugh, then think.
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