Archive for the ‘mathematics’ category: Page 56

May 1, 2022

The basics of decentralized finance

Posted by in categories: blockchains, computing, cryptocurrencies, finance, information science, mathematics

Decentralized finance is built on blockchain technology, an immutable system that organizes data into blocks that are chained together and stored in hundreds of thousands of nodes or computers belonging to other members of the network.

These nodes communicate with one another (peer-to-peer), exchanging information to ensure that they’re all up-to-date and validating transactions, usually through proof-of-work or proof-of-stake. The first term is used when a member of the network is required to solve an arbitrary mathematical puzzle to add a block to the blockchain, while proof-of-stake is when users set aside some cryptocurrency as collateral, giving them a chance to be selected at random as a validator.

To encourage people to help keep the system running, those who are selected to be validators are given cryptocurrency as a reward for verifying transactions. This process is popularly known as mining and has not only helped remove central entities like banks from the equation, but it also has allowed DeFi to open more opportunities. In traditional finance, are only offered to large organizations, for members of the network to make a profit. And by using network validators, DeFi has also been able to cut down the costs that intermediaries charge so that management fees don’t eat away a significant part of investors’ returns.

Apr 26, 2022

The Human Calculator

Posted by in categories: education, mathematics

Thomas Fuller, an African sold into slavery in 1,724 at age 14, was sometimes known as the “Virginia Calculator” for his extraordinary ability to solve complex mathematical problems in his head. He was asked how many seconds there were in a year, he briefly answered 31,536,000 seconds.

He was asked again how many seconds a man who is 70 years old, 17 days and 12 hours lived, he answered in a minute and a half 2,210,500,800. One of the men was doing the problems on paper and informed Fuller that he was wrong because the answer was much smaller. Fuller hastily responded, “Nah, you forgot about leap years. When leap years were added to the account, the sums matched up.”

Fuller was one of the first cases recorded in the literature of the wise man syndrome, when in 1,789, Benjamin Rush, the father of American psychiatry, described his incredible ability to calculate, without having an education and training in mathematics, his ability was used as proof that enslaved African Americans were equal to whites in intelligence, fueling some pro-abolitionist discussions.

Apr 21, 2022

Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations

Posted by in categories: information science, mathematics, robotics/AI

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near.

Apr 19, 2022

How Wavelets Allow Researchers to Transform — and Understand — Data

Posted by in category: mathematics

Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals.

Apr 19, 2022

Research team measures the mass of the top quark with unparalleled accuracy

Posted by in categories: mathematics, particle physics, quantum physics

The CMS collaboration at the Large Hadron Collider (LHC) has performed the most accurate ever measurement of the mass of the top quark—the heaviest known elementary particle. The latest CMS result estimates the value of the top-quark mass with an accuracy of about 0.22%. The substantial gain in accuracy comes from new analysis methods and improved procedures to consistently and simultaneously treat different uncertainties in the measurement.

The precise knowledge of the top-quark mass is of paramount importance to understand our world at the smallest scale. Knowing this heaviest as intimately as possible is crucial because it allows testing of the internal consistency of the mathematical description of all elementary particles, called the Standard Model.

For example, if the masses of the W boson and Higgs boson are known accurately, the top-quark mass can be predicted by the Standard Model. Likewise, using the top-quark and Higgs-boson masses, the W-boson mass can be predicted. Interestingly, despite much progress, the theoretical-physics definition of mass, which has to do with the effect of quantum-physics corrections, is still tough to pin down for the top quark.

Apr 19, 2022

Study shows simple, computationally-light model can simulate complex brain cell responses

Posted by in categories: biotech/medical, chemistry, computing, mathematics, neuroscience

The brain is inarguably the single most important organ in the human body. It controls how we move, react, think and feel, and enables us to have complex emotions and memories. The brain is composed of approximately 86 billion neurons that form a complex network. These neurons receive, process, and transfer information using chemical and electrical signals.

Learning how respond to different signals can further the understanding of cognition and development and improve the management of disorders of the brain. But experimentally studying neuronal networks is a complex and occasionally invasive procedure. Mathematical models provide a non-invasive means to accomplish the task of understanding , but most current models are either too computationally intensive, or they cannot adequately simulate the different types of complex neuronal responses. In a recent study, published in Nonlinear Theory and Its Applications, IEICE, a research team led by Prof. Tohru Ikeguchi of Tokyo University of Science, has analyzed some of the complex responses of neurons in a computationally simple neuron model, the Izhikevich neuron model.

“My laboratory is engaged in research on neuroscience and this study analyzes the basic mathematical properties of a neuron model. While we analyzed a single neuron model in this study, this model is often used in computational neuroscience, and not all of its properties have been clarified. Our study fills that gap,” explains Prof. Ikeguchi. The research team also comprised Mr. Yota Tsukamoto and Ph.D. student Ms. Honami Tsushima, also from Tokyo University of Science.

Apr 18, 2022

Fractal Pattern in a Quantum Material Confirmed for the First Time!

Posted by in categories: mathematics, quantum physics

Image by: Arkadiusz Jadczyk.

The word fractal has become increasingly popular, although the concept started more than two centuries ago in the 17th century with prominent and prolific mathematician and philosopher Gottfried Wilhelm Leibnitz is believed to have addressed for the first time the notion of recursive self-similarity, and it wasn’t until 1960 that the concept was formally stabilized both theoretically and practically, through the mathematical development and computerized visualizations by Benoit Mandelbrot, who settled on the name “fractal”.

Apr 17, 2022

The universe would not make sense without mathematics

Posted by in categories: mathematics, space

Mathematics is the language of the universe: It is probable that every major scientific discovery has used mathematics in some form.

Apr 8, 2022

Blue Brain builds neurons with mathematics

Posted by in categories: biotech/medical, chemistry, computing, information science, mathematics, neuroscience

Santiago Ramón y Cajal, a Spanish physician from the turn of the 19th century, is considered by most to be the father of modern neuroscience. He stared down a microscope day and night for years, fascinated by chemically stained neurons he found in slices of human brain tissue. By hand, he painstakingly drew virtually every new type of neuron he came across using nothing more than pen and paper. As the Charles Darwin for the brain, he mapped every detail of the forest of neurons that make up the brain, calling them the “butterflies of the brain”. Today, 200 years later, Blue Brain has found a way to dispense with the human eye, pen and paper, and use only mathematics to automatically draw neurons in 3D as digital twins. Math can now be used to capture all the “butterflies of the brain”, which allows us to use computers to build any and all the billons of neurons that make up the brain. And that means we are getting closer to being able to build digital twins of brains.

These billions of neurons form trillions of synapses – where neurons communicate with each other. Such complexity needs comprehensive neuron models and accurately reconstructed detailed brain networks in order to replicate the healthy and disease states of the brain. Efforts to build such models and networks have historically been hampered by the lack of experimental data available. But now, scientists at the EPFL Blue Brain Project using algebraic topology, a field of Math, have created an algorithm that requires only a few examples to generate large numbers of unique cells. Using this algorithm – the Topological Neuronal Synthesis (TNS), they can efficiently synthesize millions of unique neuronal morphologies.

Apr 7, 2022

Massive Black Holes Shown to Act Like Quantum Particles

Posted by in categories: cosmology, mathematics, particle physics, quantum physics

Physicists are using quantum math to understand what happens when black holes collide. In a surprise, they’ve shown that a single particle can describe a collision’s entire gravitational wave.

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