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Category: mathematics – Page 173

A collaboration of physicists and a mathematician has made a significant step toward unifying general relativity and quantum mechanics by explaining how spacetime emerges from quantum entanglement in a more fundamental theory. The paper announcing the discovery by Hirosi Ooguri, a Principal Investigator at the University of Tokyo’s Kavli IPMU, with Caltech mathematician Matilde Marcolli and graduate students Jennifer Lin and Bogdan Stoica, will be published in Physical Review Letters as an Editors’ Suggestion “for the potential interest in the results presented and on the success of the paper in communicating its message, in particular to readers from other fields.”

Physicists and mathematicians have long sought a Theory of Everything (ToE) that unifies and quantum mechanics. General relativity explains gravity and large-scale phenomena such as the dynamics of stars and galaxies in the universe, while quantum mechanics explains microscopic phenomena from the subatomic to molecular scales.

The holographic principle is widely regarded as an essential feature of a successful Theory of Everything. The holographic principle states that gravity in a three-dimensional volume can be described by quantum mechanics on a two-dimensional surface surrounding the volume. In particular, the three dimensions of the volume should emerge from the two dimensions of the surface. However, understanding the precise mechanics for the emergence of the volume from the surface has been elusive.

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Computers use switches to perform calculations. A complex film with “quantum wells”—regions that allow electron motion in only two dimensions—can be used to make efficient switches for high-speed computers. For the first time, this oxide film exhibited a phenomenon, called resonant tunneling, in which electrons move between quantum wells at a specific voltage. This behavior allowed an extremely large ratio (about 100,000:1) between two states, which can be used in an electronic device as an ON/OFF switch to perform mathematical calculations (Nature Communications, “Resonant tunneling in a quantum oxide superlattice”).

Quantum wells

Efficient control of electron motion can be used to reduce the power requirements of computers. “Quantum wells” (QW) are regions that allow electron motion in only two dimensions. The lines (bottom) in the schematic show the probability of finding electrons in the structure. The structure is a complex oxide (top) with columns (stacked blue dots corresponding to an added element) where the electrons are free to move in only two dimensions. This is a special type of quantum well called a two-dimensional electron gas (2DEG). (Image: Ho Nyung Lee, Oak Ridge National Laboratory)

To meet our exponentially growing need for computing power without a corresponding jump in energy use, scientists need more efficient electronic versions of switches to perform calculations. Efficient switches need materials that switch between well-defined ON/OFF states. The results of this study could lead to a new class of energy-efficient electronics because these materials can ensure the electronic switches are ON or OFF. These electronic switches could lower power consumption in electronics enabling, for example, the development of high-speed supercomputers and cell phones with longer battery life.

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Ever really wanted to know what folks truly are thinking about?

A new experiment advances the idea that brain scans can teach us something about how the human mind works.

By Nathan Collins

Mind reading stands as one of science fiction’s most enduring improbabilities, alongside light-speed space travel and laser guns. But unlike those latter two, mind reading actually has a whiff of reality: In a new demonstration, psychologists have shown they can figure out how far along someone’s brain is in the process of solving a sophisticated math problem—a result that, more than anything else, indicates the promise of new brain-scanning techniques for understanding the human mind.

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Her computer, Karin Strauss says, contains her “digital attic”—a place where she stores that published math paper she wrote in high school, and computer science schoolwork from college.

She’d like to preserve the stuff “as long as I live, at least,” says Strauss, 37. But computers must be replaced every few years, and each time she must copy the information over, “which is a little bit of a headache.”

It would be much better, she says, if she could store it in DNA—the stuff our genes are made of.

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The Defense Advanced Research Projects Agency has demonstrated a new mathematical framework that works to help researchers discover patterns in complex scientific and engineering systems. DARPA said Thursday researchers at Stanford University created algorithms designed to explore patterns in data in order to gain insights into network structure and function under the Simplifying Complexity in Scientific Discovery [ ].

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Nice.

Networks are mathematical representations to explore and understand diverse, complex systems—everything from military logistics and global finance to air traffic, social media, and the biological processes within our bodies. In each of those systems, a hierarchy of recurring, meaningful internal patterns—such as molecules and proteins interacting inside cells, and capacitors and resistors operating within integrated circuits—determines the functions or behaviors of those systems. The larger and more intricate a system is, however, the harder it is for current network modeling techniques to uncover these patterns and represent them in organized, easy-to-understand ways.

Researchers at Stanford University, funded by DARPA’s Simplifying Complexity in Scientific Discovery (SIMPLEX) program, have made progress in overcoming these challenges through a framework they have developed for identifying and clustering what mathematicians call “motifs”: essential but often obscure patterns within systems that are the building blocks of mathematical modeling and that facilitate the computational representation of complex systems.

A research paper describing the team’s achievement was published in Science (“Higher-order organization of complex networks”). At the heart of the team’s success was the creation of algorithms that can automatically explore and prioritize the hidden patterns in data that are fundamental to explaining network structure and function.

a mathematical framework that automatically identifies and prioritizes the patterns that are fundamental to explaining network structure and function

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