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Category: mathematics – Page 114

Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a particular state. In this contribution, we propound the mathematical structure of the theory, separating the essentials from auxiliary formal tools. We provide a definition of a generalized IIT which has IIT 3.0 of Tononi et al., as well as the Quantum IIT introduced by Zanardi et al. as special cases. This provides an axiomatic definition of the theory which may serve as the starting point for future formal investigations and as an introduction suitable for researchers with a formal background.

Integrated Information Theory (IIT), developed by Giulio Tononi and collaborators [5, 45–47], has emerged as one of the leading scientific theories of consciousness. At the heart of the latest version of the theory [19, 25 26, 31 40] is an algorithm which, based on the level of integration of the internal functional relationships of a physical system in a given state, aims to determine both the quality and quantity (‘Φ value’) of its conscious experience.

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The Bernese theoretical astrophysicist Kevin Heng has achieved a rare feat: On paper, he has derived novel solutions to an old mathematical problem needed to calculate light reflections from planets and moons. Now, data can be interpreted in a simple way to understand planetary atmospheres, for example. The new formulae will likely be incorporated into future textbooks.

For millennia, humanity has observed the changing phases of the Moon. The rise and fall of sunlight reflected off the Moon, as it presents its different faces to us, is known as a “phase curve.” Measuring phase curves of the Moon and Solar System planets is an ancient branch of astronomy that goes back at least a century. The shapes of these phase curves encode information on the surfaces and atmospheres of these celestial bodies. In modern times, astronomers have measured the phase curves of exoplanets using space telescopes such as Hubble, Spitzer, TESS

Launched on April 18 2018, aboard a SpaceX Falcon 9 rocket, NASA’s Transiting Exoplanet Survey Satellite (TESS) is a mission to search nearby stars for undiscovered worlds with a gold of discovering thousands of exoplanets around nearby bright stars.

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Researchers from Skoltech, KTH Royal Institute of Technology, and Uppsala University have predicted the existence of antichiral ferromagnetism, a nontrivial property of some magnetic crystals that opens the door to a variety of new magnetic phenomena. The paper was published in the journal Physical Review B.

Chirality, or handedness, is an extremely important fundamental property of objects in many fields of physics, mathematics, chemistry and biology; a chiral object cannot be superimposed on its in any way. The simplest chiral objects are human hands, hence the term itself. The opposite of chiral is achiral: a circle or a square are simple achiral objects.

Chirality can be applied to much more complex entities; for instance, competing internal interactions in a can lead to the appearance of periodic magnetic textures in the structure that differ from their mirror images—this is called chiral ferromagnetic ordering. Chiral crystals are widely considered promising candidates for and processing device realization as information can be encoded via their nontrivial magnetic textures.

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A team of Swiss researchers from Graubuenden University of Applied Sciences has broken the record for calculating the mathematical constant pi. It is now known to an incredible level of exactitude, hitting 62.8 trillion figures thanks to the work of a supercomputer.

Pi represents the ratio between the radius of a circle and its circumference. You may recognize the first 10 digits, π=3.141592653, though there is an infinite number of digits that follow that decimal point.

To write all of the digits for the new record out on A4 paper, you would need almost 35 billion sheets, equivalent to about 52 percent of the mass of the Empire State Building. Putting those pieces of paper head to toe they would extend for over 10 million kilometers (6.5 million miles).

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Summary: Study reveals how the brain analyzes different types of speech which may be linked to how we comprehend sentences and calculate mathematical equations.

Source: SfN

Separate math and language networks segregate naturally when listeners pay attention to one type over the other, according to research recently published in Journal of Neuroscience.

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Determining if particular extreme hot or cold spells were caused by climate change could be made easier by a new mathematical method.

The , developed by physicists at the University of Reading and Uppsala University in Sweden, looks at the characteristics, or “fingerprints,” of a specific extreme weather event of interest, like a , in order to ascertain whether it can be attributed to natural variability of the climate or is a unique product of global warming.

The method also allows predictions to be made about how likely extreme climate events will be in the future.

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According to findings published in Learning and Individual Differences, a secure bond between father and child is particularly important for children’s development of coping skills related to mathematics. The longitudinal study found that the father-child bond predicted children’s math anxiety one year later, while the mother-child bond did not.

The term “math anxiety” is used to describe fear and apprehension surrounding math and can occur in children and adults alike. Math anxiety can arise in response to any situation that requires mathematics — from solving a math problem at school to calculating the tip at a restaurant.

Previous studies have uncovered parental factors that play a role in the development of math anxiety among children — for example, parents’ use of math at home with their children. There is also evidence that that the quality of the parent-child relationship influences math anxiety among children, but until now, no study had teased apart the specific roles of the mother-child versus father-child bond.

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Houston-based ThirdAI, a company building tools to speed up deep learning technology without the need for specialized hardware like graphics processing units, brought in $6 million in seed funding.

Neotribe Ventures, Cervin Ventures and Firebolt Ventures co-led the investment, which will be used to hire additional employees and invest in computing resources, Anshumali Shrivastava, Third AI co-founder and CEO, told TechCrunch.

Shrivastava, who has a mathematics background, was always interested in artificial intelligence and machine learning, especially rethinking how AI could be developed in a more efficient manner. It was when he was at Rice University that he looked into how to make that work for deep learning. He started ThirdAI in April with some Rice graduate students.

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