Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals.
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 elementary particle 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.
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 neurons 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 neuronal networks, 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.
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”.
Mathematics is the language of the universe: It is probable that every major scientific discovery has used mathematics in some form.
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.
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.
Circa 2021
Swiss researchers said Monday they had calculated the mathematical constant pi to a new world-record level of exactitude, hitting 62.8 trillion figures using a supercomputer.
“The calculation took 108 days and nine hours” using a supercomputer, the Graubuenden University of Applied Sciences said in a statement.
In 1,832, Charles Darwin witnessed hundreds of ballooning spiders landing on the HMS Beagle while some 60 miles offshore. Ballooning is a phenomenon that’s been known since at least the days of Aristotle—and immortalized in E.B. White’s children’s classic Charlotte’s Web—but scientists have only recently made progress in gaining a better understanding of its underlying physics.
Now, physicists have developed a new mathematical model incorporating all the various forces at play as well as the effects of multiple threads, according to a recent paper published in the journal Physical Review E. Authors M. Khalid Jawed (UCLA) and Charbel Habchi (Notre Dame University-Louaize) based their new model on a computer graphics algorithm used to model fur and hair in such blockbuster films as The Hobbit and Planet of the Apes. The work could one day contribute to the design of new types of ballooning sensors for explorations of the atmosphere.
There are competing hypotheses for how ballooning spiders are able to float off into the air. For instance, one proposal posits that, as the air warms with the rising sun, the silk threads the spiders emit to spin their “parachutes” catch the rising convection currents (the updraft) that are caused by thermal gradients. A second hypothesis holds that the threads have a static electric charge that interacts with the weak vertical electric field in the atmosphere.
Summary: Using algebraic topography, researchers have created an algorithm that requires only a few examples to generate a large number of unique cells.
Source: EPFL
EPFL’s Blue Brain Project has found a way to use only mathematics to automatically draw neurons in 3D, meaning we are getting closer to being able to build digital twins of brains.
