# gst: overlapping substitutions and tilings.

AA << generalize the notion of (geometric) substitution rule to obtain overlapping substitutions. For such a substitution, the substitution matrix may have non-integer entries. (They) also show that the expansion constant is an algebraic integer under mild conditions. In general, overlapping substitutions may yield a patch with contradictory overlaps of tiles, even if it is locally consistent. >>

AA << give a sufficient condition for an overlapping substitution to be consistent, that is, no such contradiction will emerge. (They) also give many one-dimensional examples of overlapping substitution. (AA) finish by mentioning a construction of overlapping substitutions from Delone multi-sets with inflation symmetry. >>️

Shigeki Akiyama, Yasushi Nagai, Shu-Qin Zhang. Overlapping substitutions and tilings. arXiv: 2407.18666v2 [math.CO]. Aug 30, 2024. 

https://arxiv.org/abs/2407.18666

Also

keyword 'tile', in FonT

https://flashontrack.blogspot.com/search?q=tile 

keyword 'overlap', 'overlapping', in FonT

https://flashontrack.blogspot.com/search?q=overlap 

https://flashontrack.blogspot.com/search?q=overlapping

Keywords: gst, tiles, overlap, overlapping

# life: Black Death way revisited, the hypothesis, by Parag.

<< Good afternoon to everyone online and in the room. (..) Since yesterday, Denmark, Estonia, Lithuania, Netherlands and Nigeria have all reported their first cases. All these cases have links to Italy. 24 cases have been exported from Italy to 14 countries, and 97 cases have been exported from Iran to 11 countries. >>  

Tedros Adhanom Ghebreyesus.

WHO Director-General's opening remarks at the media briefing on COVID-19. WHO. Feb 28, 2020.

https://www.who.int/dg/speeches/detail/who-director-general-s-opening-remarks-at-the-media-briefing-on-covid-19---28-february-2020

<< A striking overlap exists between the path of today's viral spread and the path of the Black Death in the 1300s. >>

<< It is, of course, far too soon to make such dire predictions about Covid-19. But a striking overlap exists between the path of today's viral spread and the path that emerged in the 1300s. >>

<< The 14th-century plague is said to have originated in northwestern China, with bacteria contracted from marmots. Hebei Province bore the brunt of China’s plague fatalities, with 5 million of its residents perishing in the 1330s. Making its way westward via Silk Road merchants and caravans, the plague took several years to reach Persia, where it killed the Khan overlord Abu Said as well as half the population. In 1347, it entered Europe via Italy’s port of Genoa. >>

<< Now compare that to what we’re seeing today with Covid-19. This time around, the source of illness may have been pangolins or bats instead of marmots. It started in Wuhan, which just happens to be Hebei's capital. The coronavirus reached Iran in a couple of weeks, and so far has infected hundreds of people, even the country’s deputy health minister. Next to Iran, the next worst outbreak is in Italy, with more than 300 cases and rising quickly- and likely spreading through Europe exactly as the plague did centuries ago. >>

<< It is, perhaps no coincidence that, in the past two decades, China has been the origin of SARS, the swine flu, and now the Covid-19 coronavirus. Nor should we be surprised that Iran and Italy have emerged, once more, as waypoints for pandemic spread. What do Iran and Italy have in common today? They are two major anchors of China’s Belt and Road Initiative- also known as the 21st century’s new Silk Roads. >>

Parag Khanna. IDEAS. Covid-19 Is Traveling Along the New Silk Road. Wired. Feb 28, 2020.

https://www.wired.com/story/covid-19-is-traveling-along-the-new-silk-road/

Also

keyword 'virus' by FonT

https://flashontrack.blogspot.com/search?q=virus

keyword 'virus' by Notes

https://inkpi.blogspot.com/search?q=virus

# brain: seeing "ghosted" images

<< the human eye and brain are together capable of seeing "ghosted" images >>

<< it is possible to create ghost images with a technique using light to make an image without reflecting it off the original object. The technique is called "ghosting," >>

Bob Yirka. Human eye capable of seeing 'ghosted' images. Sep 4, 2018

https://m.phys.org/news/2018-09-human-eye-capable-ghosted-images.html

<< Computational ghost imaging relies on the decomposition of an image into patterns that are summed together with weights that measure the overlap of each pattern with the scene being imaged. These tasks rely on a computer. Here [AA] demonstrate that the computational integration can be performed directly with the human eye. >>

Alessandro Boccolini, Alessandro Fedrizzi, Daniele Faccio. Ghost imaging with the human eye. arXiv:1808.05137 [q-bio.NC] Aug 13, 2018.

https://arxiv.org/abs/1808.05137

# s-brain-ai-data-tool: abstract versus concrete behaviors: a hierarchically ordered connectome

a model <<  to show how the physical brain could give rise to abstract thought >>

the <<  work demonstrates (..) the basic operational paradigm of cognition, but shows that all cognitive behaviors exist on a hierarchy, starting with the most tangible behaviors such as finger tapping or pain, then to consciousness and extending to the most abstract thoughts and activities such as naming. This hierarchy of abstraction is related to the connectome structure of the whole human brain >>

Another outcome of the research <<  will be a new geometric data-science tool, which is likely to find widespread use in other fields where massive data is difficult to view coherently due to data overlap >>

http://www.umass.edu/newsoffice/article/how-brain-architecture-leads-abstract

P. Taylor, J. N. Hobbs, et al. The global landscape of cognition: hierarchical aggregation as an organizational principle of human cortical networks and functions. Scientific Reports, 2015; 5: 18112 DOI: 10.1038/srep18112

http://www.nature.com/articles/srep18112

# brain: the hypothesis of the genetic link between present moment attention and subjective wellbeing.

<< Considerable evidence supports the role of present-moment attention, a central feature of mindfulness, in subjective wellbeing maintenance and enhancement. >>️

<< Consistent with the “generalist genes hypothesis” and prior evidence, (AA) hypothesized that presence and subjective wellbeing would show a substantial genetic correlation and smaller environmental correlation. >>️

<< This study provides the first evidence known to us showing that present-centered attention, a primary component of mindfulness, has both genetic and environmental overlap with subjective wellbeing. >>️

Kirk Warren Brown, Fazil Aliev, et al. A multivariate twin study of the genetic association between present moment attention and subjective wellbeing. Sci Rep 13, 17456 (2023). doi: 10.1038/ s41598-023-42810-x.

https://www.nature.com/articles/s41598-023-42810-x 

Also: brain, Zen, in https://www.inkgmr.net/kwrds.html 

Keywords: present moment attention, mindfulness, subjective wellbeing, generalist genes hypothesis. 

# gst: apropos of vibrating pivots, driving a damped coplanar double pendulum.

AA << present results of linear and nonlinear motions of a parametrically driven coplanar double pendulum with velocity-dependent damping. The equations of motion of a damped double pendulum of unequal masses with its pivot vibrated vertically are different from those obtained under gravity modulation. 

Linear stability analysis shows that tongue-shaped marginal stability curves divide the plane of driving parameters into multiple regions of subharmonic and harmonic instabilities. The instability zones for one normal mode overlap with those for the other. 

The double pendulum may oscillate or rotate about its pivot harmonically or subharmonically. The limit cycles corresponding to the normal mode oscillations of a double pendulum of equal masses are squeezed into a line in its configuration space. 

For unequal masses, two marginal curves for subharmonic instabilities merge to form a double-well shaped curve in the presence of damping, which is qualitatively new. The pendulum shows driving amplitude sensitive multi-period complex oscillations for driving parameters near the extrema of the merged instability zones and boundaries of the overlapping zones. 

For larger driving amplitude, the pendulum shows subharmonic, harmonic or chaotic rotations. >>

️

Rebeka Sarkar, Krishna Kumar, Sugata Pratik Khastgir. Parametrically driven damped coplanar double pendulum. arXiv:2208.03292v1 [physics.class-ph]. Aug 2, 2022. 

https://arxiv.org/abs/2208.03292

Also

keyword 'pendulum' in FonT

https://flashontrack.blogspot.com/search?q=pendulum

keyword 'pendolo' | 'pendola' in Notes

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=pendolo

https://inkpi.blogspot.com/search?q=pendola

Keywords: gst, pendulum, double pendulum, instability, chaos, chaotic rotations