# 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

# 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

# brain: waiting for 'magic strings', psilocybin is a 'relatively safe' drug.

<< Psilocybin-containing mushrooms are used for recreational, spiritual, self-development and therapeutic purposes. However, physiologically relatively nontoxic, adverse reactions are occasionally reported. >>

The << study investigated the 12-month prevalence and nature of magic mushroom-related adverse reactions resulting in emergency medical treatment seeking in a global sample of (9.233) people reporting magic mushroom use. >>️

️

️ << The results confirm psilocybin mushrooms are a relatively safe drug, with serious incidents rare and short lasting. Providing harm-reduction information likely plays a key role in preventing adverse effects. More research is needed to examine the detailed circumstances and predictors of adverse reactions including rarer physiological reactions. >>️

Emma I Kopra, Jason A Ferris, et al. Adverse experiences resulting in emergency medical treatment seeking following the use of magic mushrooms. Journal of Psychopharmacology. 1-9. doi: 10.1177/ 02698811221084063. 

Apr 7, 2022.

https://journals.sagepub.com/doi/full/10.1177/02698811221084063

<< Psilocybin is currently being investigated in clinical trials for mental health conditions across the world, including in our department, (..) It is important to draw a distinction between the use of psilocybin in clinical or research settings and recreational magic mushroom use, with partly overlapping yet distinct safety considerations and risk profiles. >> Emma Kopra. 

Beth Ellwood. Large survey suggests psilocybin is a “relatively safe” drug, with serious reactions being rare and short-lived. May 4, 2022. 

https://www.psypost.org/2022/05/large-survey-suggests-psilocybin-is-a-relatively-safe-drug-with-serious-reactions-being-rare-and-short-lived-63075

Also

keyword 'magic string' in FonT

https://flashontrack.blogspot.com/search?q=magic+string

keyword 'psychedelic' in FonT

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

Keywords: brain, drugs, magic string, magic mushrooms, psilocybin, psychedelic

# geo: apropos of oscillations, a 'true polar wander' (TPW); Earth tip on its side 84 Ma ago.

<< It has been debated for the past few decades whether the outer, solid shell of the Earth can wobble about, or even tip over relative to the spin axis. Such a shift of Earth is called "true polar wander," (TPW) but the evidence for this process has been contentious. New research (..) provides some of the most convincing evidence to date that such planetary tipping has indeed occurred in Earth's past. >>️

<< The Earth is a stratified ball, with a solid metal inner core, a liquid metal outer core, and a solid mantle and overriding crust at the surface which we live on. All of this is spinning like a top, once per day. Because the Earth's outer core is liquid, the solid mantle and crust are able to slide around on top of it.  >>

️

Did the Earth tip on its side 84 million years ago? Tokyo Institute of Technology. Oct 18, 2021. 

https://phys.org/news/2021-10-earth-side-million-years.html

<< a new high-resolution palaeomagnetic record from two overlapping stratigraphic sections in Italy (..) provides evidence for a ~12° TPW oscillation from 86 to 78 Ma. This observation represents the most recent large-scale TPW documented and challenges the notion that the spin axis has been largely stable over the past 100 million years. >>️

Mitchell, R.N., Thissen, C.J.,  et al. A Late Cretaceous true polar wander oscillation. Nat Commun 12, 3629. doi: 10.1038/ s41467-021-23803-8. June 15, 2021. 

https://www.nature.com/articles/s41467-021-23803-8

keywords: gst, geo, geodynamics, geophysics, palaeomagnetism, oscillations, wobble, true polar wander, tpw

# brain: your brain needs to process quickly whether the sound is coming from, say, a bear or a chipmunk ...

<< When you are out in the woods and hear a cracking sound, your brain needs to process quickly whether the sound is coming from, say, a bear or a chipmunk >>

AA << has a new interpretation for an old observation, debunking an established theory in the process >>

Beth Miller. Bear or chipmunk? WashU Engineer finds how brain encodes sounds. Nov 7, 2017.

https://engineering.wustl.edu/news/Pages/Bear-or-chipmunk-WashU-Engineer-finds-how-brain-encodes-sounds.aspx

https://www.sciencedaily.com/releases/2017/11/171108151851.htm

AA found that << Dense and sparse coding may (..) work together dynamically in order to represent complex, temporally overlapping sensory content >>

Wensheng Sun, Dennis L. Barbour. Rate, not selectivity, determines neuronal population coding accuracy in auditory cortex. PLoS Biol 15(11): e2002459. doi:10.1371/journal.pbio.2002459 Nov 1, 2017.

http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.2002459