Archive for the ‘mathematics’ category: Page 9

Aug 9, 2023

New technique measures structured light in a single shot

Posted by in categories: mathematics, quantum physics

Structured light waves with spiral phase fronts carry orbital angular momentum (OAM), attributed to the rotational motion of photons. Recently, scientists have been using light waves with OAM, and these special “helical” light beams have become very important in various advanced technologies like communication, imaging, and quantum information processing. In these technologies, it’s crucial to know the exact structure of these special light beams. However, this has proven to be quite tricky.

Interferometry—superimposing a with a known reference field to extract information from the interference—can retrieve OAM spectrum information using a camera. As the camera only records the intensity of the interference, the measurement technique encounters additional crosstalk known as “signal-signal beat interference” (SSBI), which complicates the retrieval process. It’s like hearing multiple overlapping sounds, making it difficult to distinguish the original notes.

In a recent breakthrough reported in Advanced Photonics, researchers from Sun Yat-sen University and École Polytechnique Fédérale de Lausanne (EPFL) used a powerful mathematical tool called the Kramers-Kronig (KK) relation, which helps with understanding and solving the problem. This tool enabled them to untangle the complex helical pattern from the camera’s intensity-only measurements for single-shot retrieval in simple on-axis interferometry. Exploring the duality between the time-frequency and azimuth-OAM domains, they apply the KK approach to investigate various OAM fields, including Talbot self-imaged petals and fractional OAM modes.

Aug 8, 2023

David Chalmers

Posted by in categories: computing, education, mathematics, neuroscience

David Chalmers is a philosopher at New York University and the Australian National University. He is Professor of Philosophy and co-director of the Center for Mind, Brain, and Consciousness at NYU, and also Professor of Philosophy at ANU.

Chalmers works in the philosophy of mind and in related areas of philosophy and cognitive science. He is especially interested in consciousness, but am also interested in all sorts of other issues in the philosophy of mind and language, metaphysics and epistemology, and the foundations of cognitive science.

From an early age, he excelled at mathematics, eventually completing his undergraduate education at the University of Adelaide with a Bachelor’s degree in Mathematics and Computer Science. He then briefly studied at Lincoln College at the University of Oxford as a Rhodes Scholar before receiving his PhD at Indiana University Bloomington under Douglas Hofstadter. He was a Postdoctoral Fellow in the Philosophy-Neuroscience-Psychology program directed by Andy Clark at Washington University in St. Louis from 1993 to 1995, and his first professorship was at UC Santa Cruz, from August 1995 to December 1998.

Aug 8, 2023

Mathematical theory predicts self-organized learning in real neurons

Posted by in categories: mathematics, robotics/AI

An international collaboration between researchers at the RIKEN Center for Brain Science (CBS) in Japan, the University of Tokyo, and University College London has demonstrated that self-organization of neurons as they learn follows a mathematical theory called the free energy principle.

The principle accurately predicted how real neural networks spontaneously reorganize to distinguish incoming information, as well as how altering neural excitability can disrupt the process. The findings thus have implications for building animal-like artificial intelligences and for understanding cases of impaired learning. The study was published August 7 in Nature Communications.

When we learn to tell the difference between voices, faces, or smells, networks of neurons in our brains automatically organize themselves so that they can distinguish between the different sources of incoming information. This process involves changing the strength of connections between neurons, and is the basis of all learning in the .

Aug 4, 2023

Scientists Uncover a Surprising Link Between Pure Mathematics and Genetics

Posted by in categories: bioengineering, biotech/medical, encryption, evolution, genetics, mathematics

An interdisciplinary team of mathematicians, engineers, physicists, and medical scientists has discovered a surprising connection between pure mathematics and genetics. This connection sheds light on the structure of neutral mutations and the evolution of organisms.

Number theory, the study of the properties of positive integers, is perhaps the purest form of mathematics. At first sight, it may seem far too abstract to apply to the natural world. In fact, the influential American number theorist Leonard Dickson wrote “Thank God that number theory is unsullied by any application.”

And yet, again and again, number theory finds unexpected applications in science and engineering, from leaf angles that (almost) universally follow the Fibonacci sequence, to modern encryption techniques based on factoring prime numbers. Now, researchers have demonstrated an unexpected link between number theory and evolutionary genetics.

Aug 2, 2023

How random chance changed the man who invented modern probability

Posted by in categories: genetics, mathematics, neuroscience

If two statisticians were to lose each other in an infinite forest, the first thing they would do is get drunk. That way, they would walk more or less randomly, which would give them the best chance of finding each other. However, the statisticians should stay sober if they want to pick mushrooms. Stumbling around drunk and without purpose would reduce the area of exploration, and make it more likely that the seekers would return to the same spot, where the mushrooms are already gone.

Such considerations belong to the statistical theory of “random walk” or “drunkard’s walk,” in which the future depends only on the present and not the past. Today, random walk is used to model share prices, molecular diffusion, neural activity, and population dynamics, among other processes. It is also thought to describe how “genetic drift” can result in a particular gene—say, for blue eye color—becoming prevalent in a population. Ironically, this theory, which ignores the past, has a rather rich history of its own. It is one of the many intellectual innovations dreamed up by Andrei Kolmogorov, a mathematician of startling breadth and ability who revolutionized the role of the unlikely in mathematics, while carefully negotiating the shifting probabilities of political and academic life in Soviet Russia.

Aug 1, 2023

The Universe May Be a Hologram, Meaning Our Entire Reality Could Be an Illusion

Posted by in categories: cosmology, holograms, mathematics


This holographic concept could explain a mystery about black holes, but the math may not represent reality.

Jul 29, 2023

The Anthropic Principle — How Your Existence Could Lead to a Multiverse

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

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Jul 27, 2023

July 1816: Fresnel’s Evidence for the Wave Theory of Light

Posted by in categories: education, engineering, mathematics, particle physics

Until the early 20th century, the question of whether light is a particle or a wave had divided scientists for centuries. Isaac Newton held the former stance and advocated for his “corpuscular” theory. But by the early 19th century, the wave theory was making a comeback, thanks in part to the work of a French civil engineer named Augustin-Jean Fresnel.

Born in 1,788 to an architect, the young Fresnel had a strict religious upbringing, since his parents were Jansenists — a radical sect of the Catholic Church that embraced predestination. Initially he was home-schooled, and did not show early academic promise; he could barely read by the time he was eight. Part of this may have been due to all the political upheaval in France at the time. Fresnel was just one year old when revolutionaries stormed the Bastille in 1,789, and five when the Reign of Terror began.

Eventually the family settled in a small village north of Caen, and when Fresnel was 12, he was enrolled in a formal school. That is where he discovered science and mathematics. He excelled at both, so much so that he decided to study engineering, first at the École Polytechnique in Paris, and then at the École Nacionale des Ponts et Chaussées.

Jul 26, 2023

DeepMind’s New AI made a Breakthrough in Computer Science!

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

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Jul 26, 2023

An 800-year-old mathematical trick could help with lunar navigation

Posted by in categories: mathematics, satellites

Kamilla Cziráki, a geophysics student at the Faculty of Science of Eötvös Loránd University (ELTE), has taken a new approach to researching the navigation systems that can be used on the surface of the moon to plan future journeys.

Working with Professor Gábor Timár, head of the Department of Geophysics and Space Sciences, Cziráki calculated the parameters used in the Earth’s GPS system for the moon using the method of mathematician Fibonacci, who lived 800 years ago. Their findings have been published in the journal Acta Geodaetica et Geophysica.

Now, as humanity prepares to return to the moon after half a century, the focus is on possible methods of lunar navigation. It seems likely that the modern successors to the lunar vehicles of the Apollo missions will now be assisted by some form of satellite navigation, similar to the GPS system on Earth. In the case of Earth, these systems do not take into account the actual shape of our planet, the geoid, not even the surface defined by sea level, but a rotating ellipsoid that best fits the geoid.

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