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Unveiling the weaving fractal network of connecting neurons -- ScienceDaily
Nature's fractals benefit from how they grow at multiple scales, said Taylor, who has long turned to fractals as bioinspiration. While trees have the most-recognized form of fractal branching, this work, he said, highlights how neurons are different from trees.
"Whereas the fractal character of trees originates predominantly from the distribution of branch sizes, the neurons also use the way their branches weave through space to generate their fractal character," Taylor said.
Scientists find evidence of mathematical structures in classic books | Books | The Guardian
The academics write in their paper that: “Studying characteristics of the sentence-length variability in a large corpus of world famous literary texts shows that an appealing and aesthetic optimum … involves self-similar, cascade-like alternations of various lengths of sentences.”
“An overwhelming majority of the studied texts simply obey such fractal attributes but especially spectacular in this respect are hypertext-like, ‘stream-of-consciousness’ novels. In addition, they appear to develop structures characteristic of irreducibly interwoven sets of fractals called multifractals.”
Sound localization: Where did that noise come from? -- ScienceDaily
"We humans find it difficult to assess, either visually or acoustically, how far away an object is from us," Wiegrebe says. "Our visual system makes use, among other things, of the phenomenon of parallax. When we move, the apparent position of an object that is closer to us moves more within our visual field than an object located further away. This relative motion provides information about the relative distance of the two objects. Localization of sounds is particularly challenging when the nature of the sound source is not clearly defined. It is not that difficult for us to estimate our distance from a speeding ambulance when we hear its siren. But when the sound is unknown, we cannot tell whether we are hearing a faint sound close by or a louder sound further away.
'Multi-dimensional universe' in brain networks: Using mathematics in a novel way in neuroscience, scientists demonstrate that the brain operates on many dimensions, not just the 3 dimensions that we are accustomed to -- ScienceDaily
Using algebraic topology in a way that it has never been used before in neuroscience, a team from the Blue Brain Project has uncovered a universe of multi-dimensional geometrical structures and spaces within the networks of the brain.
The research, published today in Frontiers in Computational Neuroscience, shows that these structures arise when a group of neurons forms a clique: each neuron connects to every other neuron in the group in a very specific way that generates a precise geometric object. The more neurons there are in a clique, the higher the dimension of the geometric object.
"We found a world that we had never imagined," says neuroscientist Henry Markram, director of Blue Brain Project and professor at the EPFL in Lausanne, Switzerland, "there are tens of millions of these objects even in a small speck of the brain, up through seven dimensions. In some networks, we even found structures with up to eleven dimensions."
Markram suggests this may explain why it has been so hard to understand the brain. "The mathematics usually applied to study networks cannot detect the high-dimensional structures and spaces that we now see clearly."
Fractal edges shown to be key to imagery seen in Rorschach inkblots -- ScienceDaily
"As you increase the D value, which makes for more visual complexity, the number of visual perceptions fall off," he said. "People see a lot more patterns in the simple ones." Inkblots with D values of 1.1 generate the highest numbers of perceived images, the team found.
The team then put their findings to a human test, generating computerized fractal patterns with varying D values. When seen for 10 seconds by psychology undergraduate psychology students at the University of New South Wales in Australia, the same trend between D values and imagery surfaced.
Fractal patterns are also found in the artwork of Jackson Pollock, whose abstract expressionist paintings captured Taylor's lifelong interest in childhood. Pollock's paintings from 1943 to 1952, Taylor has found, are composed of fractals with D values that increased from 1.1 to 1.7. That change was deliberate, Taylor said, as Pollock sought ways to reduce imagery figures seen in his earlier work.
Fractal edges shown to be key to imagery seen in Rorschach inkblots -- ScienceDaily
"These optical illusions seen in inkblots and sometimes in art are important for understanding the human visual system," said Taylor, who is director of the UO Materials Science Institute. "You learn important things from when our eyes get fooled. Fractal patterns in the inkblots are confusing the visual system. Why do you detect a bat or a butterfly when they were never there?"
How Complex Networks Explode with Growth
Public relations professionals often ask how D’Souza’s work might help their products go viral. She typically responds by pointing out that her models actually suppress viral behavior, at least in the short term. “Do you want to eke out all the gains as quickly as you can, or do you want to suppress [growth] so when it does happen, more people learn about it right away?” she said. The same holds true for political campaigns, according to Ziff. Following this model, they would spend much of their time early in the campaign on grassroots local efforts, building up localized clusters of connections and suppressing the emergence of long-range connections until the campaign was ready to go national with a big media splash.
