Mathematical Curiosities

Fiann on Instagram: “Here is a shot along the vertebral column of my smallest ichthyosaur called Bella. At the end you’ll see how her vertebrae compare to the biggest vert I’ve found from the same location. This huge bone is from an animal that would have been over 8 metres long, which is a bit bigger than poor little Bella! These fossils are both around 198 million years old. Bella was prepared by the ever talented @alexander_james_moore.

Here is a semester project in the 2012 Mechatronic control systems engineering module at San Jose State University. This is a Proportional-Integral-Derivative controlled (PID), 6 degree of freedom (6-DOF) Stewart platform, which basically means it has six axes on the top plate. This prototype uses 6 radio controlled servo motors instead of the traditional use of hydraulic jacks or electronic actuators. (this video has sound)

Proportional-Integral-Derivative:

A PID controller continuously calculates an error value as the difference between a measured process variable and a desired setpoint. The controller attempts to minimize the error over time by adjustment of a control variable, such as the position of a set of servo motors or actuators,  to a new value, given by a weighted sum:

where Kp ,Ki , and Kd, all non-negative, denote the coefficients for the proportional, integral, and derivative terms, respectively (sometimes denoted P, I, and D).

P accounts for present values of the error , and is determined by the direction and magnitude the correction needs to be applied (e.g. if the error is large and positive, the control variable will be large and negative),

I accounts for past values of the error (e.g. if the output is not sufficient to reduce the size of the error, the control variable will accumulate over time, causing the controller to apply a stronger action through P), and

D accounts for possible future values of the error, based on its current rate of change. This part determines when and at what rate it needs to reduce the magnitude of its action, e.g as the ball fast approaches the desired set point at the centre of the plate.

[source]

Agatized Cerithium (Eocene) - Assa, Morocco

How Brain Develops Before Birth is Tightly Controlled by RNA Modification

A chemical tag added to RNA during embryonic development regulates how the early brain grows, according to research from the Perelman School of Medicine at the University of Pennsylvania. The findings were published in Cell.

(Image caption: A human forebrain organoid labeled with Green Fluorescent Protein (green), neural stem cell marker SOX2 (red) and cell nuclei marker (blue). Credit: Xuyu Qian and Guo-li Ming, Perelman School of Medicine, University of Pennsylvania)

Neuroscience professors Guo-li Ming, MD, PhD, and Hongjun Song, PhD, study the basic principles of how to make a working brain. “When this development goes awry, problems happen and may cause psychiatric disorders in people,” Song said. Ming and Song use animal models and organoids, also called mini-brains, made from human stem cells to relate their findings to conditions found in people.

In the last few years, scientists have discovered chemical modifications to messenger RNA (mRNA) across the genome at certain sites and found that these changes are dynamic, meaning that a specific chemical group is added and taken off by enzymes in a regular, patterned way. The chemical group studied in the Cell paper, m6A, is the most prevalent modification to mRNA in human cells.

“We asked: Is this another layer of regulation of gene expression?,” Ming said.

The current thinking is that a tightly controlled molecular process guides the complicated development of the brain before birth—and that the process relies on a precise sequence of genes being turned on and off. However, even subtle mistakes in this process can become amplified later. Song likens this process to a train moving onto the wrong track and ending up miles and miles from its intended destination.

The classic view of this control is that DNA codes for RNA, guiding which proteins will be made by cells. However, mRNA can be modified along the way so that it can produce proteins with many variations. A new field called epitranscriptomics was born out of this knowledge.

The Cell paper is the first study of epitranscriptomics in the embryonic mammalian brain, and the key is m6A, a marker for molecules bound for disposal within the cell. Normally, m6A-tagged mRNAs are related to such processes as cell replication and neuron differentiation, and m6A-tagging promotes their decay after they are no longer needed.  

If m6A is not added on the correct time schedule to a garbage-bound molecule, the developmental train goes down the wrong tracks. Ming and Song surmise that this is because developing brain cells get stuck at an earlier stage because the m6A cues for taking out the cellular trash are misread or not read at all.

The researchers found that in a mouse model with depleted m6A, cell replication is prolonged, so that stem-cell differentiation, which normally reels out daughter cells in an orderly fashion, gets stuck. The knockout mouse develops less brain cells such as neurons and glia cells, and therefore has abnormal circuitry and a non-functioning brain.

“We used an organoid, a mini-brain, made from human induced pluripotent stem cells to relate the mouse knockout findings to humans,” Ming said. “m6A signaling also regulates neuron development in human forebrain organoids.”

Neuron development in the mini-brains that Ming has developed is similar to what happens in people, modeling fetal brain development up to the second trimester.

“We were surprised when we found that human stem cells had a greater number of m6A tags compared to mouse cells,” Ming said. “Comparing the m6A-mRNA landscapes between mouse and human embryonic brain development showed us that human-specific m6A-tagging might be related to brain-disorder risk genes.”

Many of the genes associated with genetic risk for certain conditions, such as schizophrenia and autism spectrum disorder, are only m6A-tagged in humans, not in mice, raising the possibility that dysregulation at this level of gene expression may contribute to certain human brain disorders.

In the near future, the team plans to look for m6A levels in brain tissue donated by people who had psychiatric disorders, as well as if m6A regulates development and regeneration of the nervous system after birth.

Ammonites on Matrix (Quenstedtoceras sp., Jurassic) - Volga River, Ulyanovsk, Russia

This extremely artistic assemblage of large and small ammonites from Russia demonstrate an intense iridescence and highlights due to the presence of metallic Pyrite. The cluster has been positioned on a new matrix, as the grainy rock in which these Quenstedtoceras cephalopods were collected is not hard nor stable enough to display them permanently. The added component is an attractive piece of what is known as septarian, a mud-like material that grows in nodules. In this instance, yellowish Calcite crystals and gray sediment have formed the rock on which these colorful ammonites reside. The cluster is quite representative of the Volga River material, and that combination results in a dramatic display specimen.

Overall Measurements: 6.30 x 5.51 x 5.71 inches (16.00 x 14.00 x 14.50 cm)

Kelston Boys’ High School perform a massive haka in honour of the new Maori carving on campus

ロックマン２ / Mega Man2