单词 | aperiodic |
例句 | Both therapies showed increased aperiodic activity levels in patients' brains post-treatment. New studies of brain activity explain benefits of electroconvulsive therapy 2023-11-16T05:00:00Z For decades mathematicians have been hunting for tile shapes like these that can form only nonrepeating arrangements, called aperiodic tilings. Discovery of Elusive ‘Einstein’ Tile Raises More Questions Than It Answers 2023-07-31T04:00:00Z The first such “aperiodic tiling” was discovered in the 1960s and comprised 104 different shapes. News at a glance: Weather radar, solar energy beamed from space, and an ode to Europa 2023-06-07T04:00:00Z This tiling pursuit first began in the 1960s, when the mathematician Hao Wang conjectured that it would be impossible to find a set of shapes that could tile a plane only aperiodically. With a New, Improved ‘Einstein,’ Puzzlers Settle a Math Problem 2023-06-01T04:00:00Z This discovery raised another question that has dogged mathematicians ever since: What is the minimum number of tile shapes that together can create an aperiodic tessellation? Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern 2023-04-10T04:00:00Z One of the functions of aperiodic activity in the brain is helping control how neurons turn on and off. New studies of brain activity explain benefits of electroconvulsive therapy 2023-11-16T05:00:00Z But was it possible to form an aperiodic tiling with tiles of only one shape—the hypothetical einstein? Discovery of Elusive ‘Einstein’ Tile Raises More Questions Than It Answers 2023-07-31T04:00:00Z Then in March, David Smith, a hobbyist in England, and colleagues produced an aperiodic tiling using a single 13-sided shape they called a “hat.” News at a glance: Weather radar, solar energy beamed from space, and an ode to Europa 2023-06-07T04:00:00Z Originally, the team discovered that the hat was part of a morphing continuum — an uncountable infinity of shapes, obtained by increasing and decreasing the edges of the hat — that produce aperiodic tilings using reflections. With a New, Improved ‘Einstein,’ Puzzlers Settle a Math Problem 2023-06-01T04:00:00Z In the decades that followed, mathematicians found smaller and smaller sets of tiles that can create aperiodic mosaics. Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern 2023-04-10T04:00:00Z While these findings establish a link between aperiodic activity and ECT benefits, the researchers stress the need for further investigation to leverage these insights in clinical applications. New studies of brain activity explain benefits of electroconvulsive therapy 2023-11-16T05:00:00Z Mathematicians have proved that this hierarchical structure means the tiling can't be split into repeating sections and thus must be aperiodic. Discovery of Elusive ‘Einstein’ Tile Raises More Questions Than It Answers 2023-07-31T04:00:00Z An aperiodic tiling displays no such “translational symmetry,” and mathematicians have long sought a single shape that could tile the plane in such a fashion. Elusive ‘Einstein’ Solves a Longstanding Math Problem 2023-03-28T04:00:00Z Investigating further — with a combination of traditional mathematical reasoning and drawing, plus computational handiwork by Dr. Kaplan and Dr. Myers — the team proved that this tiling was indeed aperiodic. With a New, Improved ‘Einstein,’ Puzzlers Settle a Math Problem 2023-06-01T04:00:00Z The researchers needed to mathematically prove that the tiling was aperiodic. Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern 2023-04-10T04:00:00Z They are currently exploring the possibility of using aperiodic activity as a metric of treatment effectiveness in other depression treatments, such as medications. New studies of brain activity explain benefits of electroconvulsive therapy 2023-11-16T05:00:00Z Penrose showed that a class of polygons now called Penrose tiles can combine to form aperiodic patterns, which never repeat themselves. Can Science Survive the Death of the Universe? 2021-06-16T04:00:00Z In less poetic terms, an einstein is an “aperiodic monotile,” a shape that tiles a plane, or an infinite two-dimensional flat surface, but only in a nonrepeating pattern. Elusive ‘Einstein’ Solves a Longstanding Math Problem 2023-03-28T04:00:00Z They called the new aperiodic tiling “chiral” because it is composed exclusively of either left- or right-handed tiles. With a New, Improved ‘Einstein,’ Puzzlers Settle a Math Problem 2023-06-01T04:00:00Z And as the mathematicians took a closer look at the shape, they realized that they could play with the lengths of the sides and still create a seamless, aperiodic mosaic. Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern 2023-04-10T04:00:00Z In 1944, Erwin Schrödinger published What Is Life?, which built on work by biophysicist Max Delbrück to suggest that genes were “aperiodic crystals”. The forgotten scientists who paved the way to the double helix 2019-04-15T04:00:00Z Here Schrödinger made the auspicious proposal that the genetic material is an “aperiodic crystal”: a structure with a specific but not periodic arrangement of atoms, encoding information that somehow guides the development of the organism. The landmark lectures of physicist Erwin Schrödinger helped to change attitudes in biology 2018-09-02T04:00:00Z Dr. Kaplan detected and unlocked telltale behavior that opened up a traditional aperiodicity proof — the method mathematicians “pull out of the drawer anytime you have a candidate set of aperiodic tiles,” he said. Elusive ‘Einstein’ Solves a Longstanding Math Problem 2023-03-28T04:00:00Z “Now there is no quibbling about whether the aperiodic tile set has one or two tiles,” Dr. Berger said in an email. With a New, Improved ‘Einstein,’ Puzzlers Settle a Math Problem 2023-06-01T04:00:00Z In these special cases, called aperiodic tilings, there’s no pattern that you can copy and paste to keep the tiling going. Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern 2023-04-10T04:00:00Z It was Gardner who introduced the public to Conway's Game of Life, Penrose's aperiodic tilings of the plane, and Mandelbrot's fractals. The man who magically made maths fun 2014-10-20T04:00:00Z The puberty phenomena teach that sex crises of every sort are dependent fundamentally upon fluctuations, periodic or aperiodic, of the sex index, as we have defined it. The Glands Regulating Personality First, they used methods that experts have relied on for decades to show that certain kinds of tiles can create aperiodic mosaics. Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern 2023-04-10T04:00:00Z This tells us that the tessellation must be aperiodic. Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern 2023-04-10T04:00:00Z Until now, aperiodic tilings always required at least two tiles of different shapes. Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern 2023-04-10T04:00:00Z If the mathematicians could prove that both of the polyiamond tilings are aperiodic, then the original tiling must be aperiodic as well. Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern 2023-04-10T04:00:00Z |
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