OpenLLM-France/wikimedia huggingface dataset:
# Cell biology/Synaptic Transmission

Here is the link to the ITunes U Lecture from Berkeley. Synaptic Transmission
I will post my notes soon. Please feel free to add details or make changes where necessary. Contact me via email if you need help. Thanks, April
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## Channel Receptor Types (Overview)

There are several types of known synaptic channel types.
* Ionotropic channels involved in (or inhibiting) an action potential or train of action potentials, are: M-currents (or M-channels), T-currents, L-currents, C-currents, AHP currents, N-currents, GIRK channels, GABA$_A$, GABA$_B$. These can exist presynaptically or postsynaptically.
* G-Protein Coupled Receptors (GPCRs) are metabotropic second messenger channels (usually postsynaptic). Ordinarily, a ligand will bind and the alpha subunit will have one effect, and the beta-gamma subunit may have another. The GPCR type is generally named after its alpha unit's effect and are referred to as Gs (or Gαs), Gq, Gi, and Go (the latter 2 are frequently lumped together as Gi/o. In many sensory organs, the GPCR is a 7-transmembrane protien unit comprised of alpha helices. There are certain exceptions.
* Noteworthy example: Interneurons may innervate the presynaptic sensory terminals (as in Aplysia), to use a GPCR to alter motor neuron output (short-term facilitation) via change in open channel probability. Subsequent stimulation of transcription further affects long-term facilitation.
Author's note: this is a broad overview of a few types of synaptic transmission with a few examples that do not divulge much detail. I included key words to encourage pages to be created as branches, explaining in more detail, each part of synaptic transmission.
# C Source Code/Loops

Loops allow a programmer to execute the same code repeatedly. These are often called "repetition" constructs. We will make heavy use of conditional statements in this section.
# Advanced Classical Mechanics/Solving Problems

* Read the problem
* Draw a diagram
* Identify the degrees of freedom
* Assign a coordinate to each degree of freedom
* Calculate $T$ and $V$ in terms of the coordinates
** Sometimes $T$ is difficult; use Cartesian coordinates or whatever system is convenient
** Convert to the coordinate system in (4)
* Look for cyclic coordinates
** Each one gives you a "first integral".
** A "first integral" is a first-order differential equation. It is usually easier to solve than Lagrange's equations which are second order.
* If only one coordinate remains, you can either
** Use Lagrange's equations, or
** Use the conservation of $H$ if $\partial L/\partial t=0$
* If more than one coordinate remains, it is often easier to use Lagrange's equations for each of them, because the Hamiltonian usually couples the degrees of freedom.
* You should have as many equations as degrees of freedom. Solve them!
* Apply the boundary conditions.
# Advanced Economics

The course objective is to provide students with a concise course on Economics. At the end of the course, the student should have an in-depth understanding of how people make decisions, how people interact, and how the economy as a whole works. This course will provide a framework for viewing and interpreting the economic world enabling the learner to think like an Economist.

## Lectures

* Lecture I: Foundations of Economics (incomplete; collaboration welcomed.)

## See Also

* Economics
* Wikipedia: Economics
# Advanced Classical Mechanics/Poisson Brackets
### Poisson Brackets

The Poisson bracket of any two functions, $f(p_{i},q_{i},t)$ and $g(p_{i},q_{i},t)$, is:
$\{f,g\}=\sum _{i=1}^{N}\left({\frac {\partial f}{\partial q_{i}}}{\frac {\partial g}{\partial p_{i}}}-{\frac {\partial f}{\partial p_{i}}}{\frac {\partial g}{\partial q_{i}}}\right).$
In two dimensions, the multivariable chain rule, is $\mathrm {d} f(x,y)={\frac {\partial f}{\partial x}}\mathrm {d} x+{\frac {\partial f}{\partial y}}\mathrm {d} y$. Using implied summation notation (for the index j), we apply this to Hamilton's equations:
$\mathrm {d} H={\frac {\partial H}{\partial p_{j}}}\mathrm {d} p_{j}+{\frac {\partial H}{\partial q_{j}}}\mathrm {d} q_{j}+{\frac {\partial H}{\partial t}}\mathrm {d} t$
${\begin{aligned}{\frac {\mathrm {d} }{\mathrm {d} t}}f(p,q,t)&={\frac {\partial f}{\partial q}}{\frac {\mathrm {d} q}{\mathrm {d} t}}+{\frac {\partial f}{\partial p}}{\frac {\mathrm {d} p}{\mathrm {d} t}}+{\frac {\partial f}{\partial t}}\\&={\frac {\partial f}{\partial q}}{\frac {\partial H}{\partial p}}-{\frac {\partial f}{\partial p}}{\frac {\partial H}{\partial q}}+{\frac {\partial f}{\partial t}}\\&=\{f,H\}+{\frac {\partial f}{\partial t}}\,.\end{aligned}}$
As an aside, we note a connection to Quantum Mechanics: Ehrenfest theorem involves the operators and expectation values of quantum mechanics. It states:
${\frac {d}{dt}}\langle A^{op}\rangle ={\frac {1}{i\hbar }}\langle [A^{op},H^{op}]\rangle +\left\langle {\frac {\partial A^{op}}{\partial t}}\right\rangle ~,$
where $A^{op}$ is any operator of quantum mechanics, $\langle A^{op}\rangle$ is its expectation value, and
$[A^{op},H^{op}]=A^{op}H^{op}-H^{op}A^{op}$
is the commutator of $A^{op}$ and $H^{op}$.
# Controversies in Science/What killed the dinosaurs/A Critique of Dinosaur Extinction/Climate Change Theories

(Review Paper) Cited in Controversies in Science/What killed the dinosaurs/A Critique of Dinosaur Extinction/Climate Change Theories

### Placental Mammals

Leigh Van Valen and Bob Sloan’s theory is that due to the earth moving and cotenants forming this caused mountains to form and seas dried up. This caused the climate to change. Due to fossil plant evidence in Montana it suggests that the temperature decreased ten centigrade points colder, this occurred in the late Cretaceous period. This would have been able to cause a massive temperature decrease in the mountains and could affect the world. This also would have caused a major migration current because the dinosaurs would of headed to warm climates; such as the tropics. This theory relates to the idea that this allowed placental mammals to grow and live in the mountains, then they escaped and caused the extinction of Dinosaurs.
# Controversies in Science/What killed the dinosaurs/A Critique of Extinction, survivorship and evolution of planktic foraminifera across the Cretaceous/Tertiary boundary at El Kef, Tunisia

(Review Paper) Cited in Controversies in Science/What killed the dinosaurs/A Critique of Extinction, survivorship and evolution of planktic foraminifera across the Cretaceous/Tertiary boundary at El Kef, Tunisia

### Impact is not the reason for mass extinction

There is evidence that the Chicxulub Crater impact dates back over 300 000 years before the dinosaurs died.

### Methods

Geoscientist, Keller, collected evidence from four major events that occurred in Mexico and Texas. She gathered evidence within the fallout of glass beads from the Chicxulub immpact and within a layer of sandstone from 150 000 years later. The sandstone came from a shore area and was said to have surfaced due to a tsunami. Keller came to the conclusion that the two other events she collected data from were most likely a large impact or a volcano, and a smaller impact. The span from all these events were up to 150 000 years in between one another and the last one was about 100 000 years after the mass extinction of dinosaurs. These are all important but Kellers latest findings are the biggest step in proving her theory. Findings found in El Penon, Mexico prove that there was no geological disturbance.

### Results

The results display that the Chicxulub impact happened 330,000 years before the end of the fossils of the dinosaurs and that this impact is not associated with the extinction of dinosaurs. From the data, Keller was also able to identify that the Chicxulub impact did not extinct a single species within dinosaurs.
# Controversies in Science/What killed the dinosaurs/A Critique of Extraterrestrial Cause for the Cretaceous-Tertiary Extinction

(Review Paper) Cited in Controversies in Science/What killed the dinosaurs/A Critique of Extraterrestrial Cause for the Cretaceous-Tertiary Extinction

### Points

The earth was impacted with a large asteroid that send 60 times the asteroids mass into the atmosphere in the form of dust. The dust spread over the earth for several years, causing Cretaceous-Tertiary extinction. The dust blocked the sun which discontinued life for plants since there was no photosynthesis occurring due to the blockage of the sun. This created a chain reaction resulting in the extinction of all food chains..

### Methods

An increase in iridium, that is thought to be of extraterrestrial origin, was found in the limestone of places such as New Zealand, Denmark, and Italy. It dates back to the time of Cretaceous-Tertiary extinction 65 million years ago.
The levels of iridium had an increase of 30 times higher for Italy, 160 times higher for Denmark and 20 times for New Zealand.These high levels play a large role in the extinction on many species.

### Results

There is a marked difference between Cretaceous/Tertiary clay and boundary clay. Because the majority of iridium on Earth is found naturally in the planet's core, iridium in the crust was likely deposited by an extraterrestrial source. The impact of the meteor that likely did this would have created a massive dust cloud, hindering photosynthesis and thus killing off the plants first. Since there was no plants for the herbivores they died off next and then the carnivores were the biggest and last organism to die off..
Iridium is a major component of a meteorite, and it is what was found settled from the global cloud of dust which was caused when the meteorite hit the earth. It was also discovered that this global cloud of dust blocked the sun causing the planet to decrease in temperature also known as The Nuclear Winter
Grains of quarts were found in the K-T boundary layer, and the microscopic traces show proof of shock from the meteorites.
# Controversies in Science/What killed the dinosaurs/A critique of A review of Extinction and radiation: how the fall of dinosaurs led to the rise of mammals

(Review Paper) Cited in Controversies in Science/What killed the dinosaurs/A critique of A review of Extinction and radiation: how the fall of dinosaurs led to the rise of mammals

### Author argues against the single-cause extraterrestrial impact hypothesis

E. J. Sargis from Yale University reviews the book Extinction and radiation: how the fall of dinosaurs led to the rise of mammals by Archibald, J. David and states that the author argues against the single-cause extraterrestrial impact of a meteorite theory, instead he suspects events such as impact, volcanoes, sea level and climate change. The author dedicates six chapters to the study of fossils from nonavion dinosaurs, Mesozoic mammals, and eutherian mammals, also of the study of origin mammals post extinction and the patterns of the K-T boundary.
# Controversies in Science/What killed the dinosaurs/A Critique of Environmental versus genetic sex determination: a possible factor in dinosaur extinction?

(Review Paper) Cited in Controversies in Science/What killed the dinosaurs/A Critique of Environmental versus genetic sex determination: a possible factor in dinosaur extinction?

### Points Made

Studies show in current extinction patterns, that the sex ratio changes for TDS (Temperature-Dependent sex determination) animals changes based on significant climate change. This could also be true for the extinction pattern of dinosaurs which may have resulted in the preponderance of males.
In laboratory experiments, scientists found that they could control what sex a reptile embryo would develop into based on what temperature the embryo was exposed to. The temperature-sensitive switch that determines male or female varies depending on species but all reptile embryos that use TSD, such as dinosaurs, have this critical incubation time
Scientists can control whether there will be and all male or all female hatching depending on the constant temperature.
65 mya years ago a meteorite may have hit the earth, but it is more likely that the constant volcanic eruptions 31-34 mys drastically changed the temperature of the earth. The falling temperature would have affected the incubation of TSD-dependent reptile eggs.
Even a minor increase or decrease in present day temperature has been shown to have endangered some turtle species.

### Methods

Through molecular relationships, it has been determined that TSD achieves its sex ratio through temperature s in two separate ranges, below intermediate and above intermediate. This proved, that dependent on the species, and seen in dinosaurs, that certain embryos would develop as the male or female sex (generally whichever was the more dominant in the species). Note that TSD is persistent in reptiles.

### Results

Based on phylogenetic evidence, as well as the latest molecular genetic data, it has been determined that dinosaurs are a TSD species. TSD species have been shown to be affected by significant climate change which may have caused the procreation of an abundance of male dinosaurs with few females to continue the species.
In addition, mathematical evidence proves that temperature sensitive species, including dinosaurs, would be negatively affected by climate shift. This is especially significant in species with a slow recovery rate, and the birth and death rates after extreme climatic and environmental changes.
# Controversies in Science/What killed the dinosaurs/A critique of From The Cover: Chicxulub impact predates the K-T boundary mass extinction

(Review Paper) Cited in Controversies in Science/What killed the dinosaurs/A critique of From The Cover: Chicxulub impact predates the K-T boundary mass extinction

### Dinosaurs STILL alive after Chicxulub

It has been previously determined that Dinosaurs were extinct due to the Chicxulub crater. This article supports findings of a deeper core that predates the Cretaceous-Tertiary (K-T) boundary by at least 300,000 years. The Chicxulub crater did not cause mass extinction as commonly believed.

### Methods

The International Continental Scientific Drilling Program (ICDP) drilled a new sample core within the Chicxulub crater and examined the fossil and mineral composition. The composition included iridium, and iridium is rare in the present on earth. Therefore the iridium in the sample core had to of come from space.

### Results

The objective was to determine the age of the K-T boundary layer to prove or disprove where this was the major event that caused the extinction of dinosaurs. The results of the core show Late Maastrichtian sediments and below the K-T boundary. These findings indicate that either the sediments between the breccia and the K-T boundary were deposited as backwash and crater infill after the impact event, or (ii) the Chicxulub impact predates the K-T boundary and hence was not the cause of the end-Cretaceous mass extinction as commonly believed.
# Controversies in Science/What killed the dinosaurs/A Critique Of Eruptions, Climate Change and Mass Extinction

(Review Paper) Cited in Controversies in Science/What killed the dinosaurs/A Critique Of Eruptions, Climate Change and Mass Extinction

### The Cause of Dinosaur Extinction

Although there may have been a meteorite that started the extinction of dinosaurs, a meteorite was not solely the cause of dinosaur extinction. Climate change is the largest factor of killing off the dinosaurs. This was caused by volcanic eruption releasing sulfur dioxide into the atmosphere that changed the composition of the gases. Greenhouse gases control the weather on Earth and if there were no gases the Earth would be too cold to sustain life. Therefore; when the volcanoes erupted, the climate changed significantly. This was the cause of dinosaur extinction.

### Methods

By examining the chemical composition of rocks in sedimentary layers, scientists can discern that these discrepencies contribute to the theory that the extinction of the dinosaurs can be linked to a major climate change.

### Results

Through dating mechanisms scientists can tell that a new volcano could have formed during that era (volcanic provinces: The Himalayas). This can give scientists clues that suggests these volcanoes were a benefiting factor to the extinction of the dinosaurs.
# Controversies in Science/What killed the dinosaurs/A critique of Mass extinction of birds at the cretaceous-palogene (k-pg) boundary

(Review Paper) Cited in Controversies in Science/What killed the dinosaurs/A critique of Mass extinction of birds at the cretaceous-palogene (k-pg) boundary

### Points Made

   * The extinction event that they suggest took place around this time period involves the very least one asteroid impact and likely an increase in volcanic activity. This would create a large amount of dust and ash which would linger in the atmosphere reducing the amount of sunlight able to reach the surface of the earth.
   * Molecular studies cannot clearly identify which species of birds were present at the end of the Cretaceous period which is why these authors relied on fossil records to execute this study.
   * The authors focus on 17 species of birds which were shown to have existed in the Cretaceous and none of them made the transition into the Paleogene era. Therefore, the authors believe that there was an extinction event (K-PG) near the end of the Cretaceous.
   * An interesting point raised by the others was the large diversification of birds towards the end of the Cretaceous but a lack of the very small and vary large birds that are present today..

### Methods

The authors studies the fossils of birds found in three different locations.
   * Hell Creek Formation (Montana, North & South Dakota)
   * Lance Formation (Wyoming)
   * Frechman Formation (Saskatchewan)
These fossils were most likely deposited at these locations in the later part of the Cretaceous period, about 300,000 years before the Paleogene period.
Researchers examined the fossils of the birds found in the regions described above and focused their researched on the coracoid bone to prevent overlapping of birds into the same categories. They chose this bone because it is quite commonly preserved and also has very little variation within the same species. This allowed them to determine if any of the species that they have identified are also present after the K-PG extinction event.
Since this data is focused on the western part of North America they researchers cannot conclusively infer that the findings will hold true all over the world but, although centered in North America, this was likely a global event.

### Results

The studies found that the body size of birds varied greatly prior to the end of the Cretaceous period, though they didn't appear to represent the largest volant birds - larger species were found in the Mesozoic era. Larger birds (>10kg) and smaller birds (<200g) do not appear to be present immediately after the cretaceous period. There have been no recovered fossils of these species from the Paleogene era, but this only accounts for fossils found in North America. The study focused on 17 specific species of birds that were shown to exist in the Cretaceous period but didn't exist in the Paleogene period. These results indicate that an event occurred (at least one asteroid, if not more) that would lead to a mass extinction of these species during the Cretaceous era.
# Controversies in Science/What killed the dinosaurs/A Critique of The Extinction of the Dinosaurs in North America

(Review Paper) Cited in Controversies in Science/What killed the dinosaurs/A Critique of The Extinction of the Dinosaurs in North America

### Points Made

Thermal stress from an intense infrared radiation pulse may have resulted in the global wildfires which would have incinerated anything that was not sheltered during the event. This pulse may have been caused by a meteor or asteroid, however whether or not it was the factor or just one of many factors we are currently unable to state. While marine regression would contribute to the extinction of life along coastal regions, this cannot be attributed to the extinction of the dinosaurs due to as these events would have taken place over a million or so years. The asteroid event would have resulted in this regression but would not have been significant enough to eliminate the dinosaurs. Another factor of the extinction of the dinosaurs would be the dust from the meteorite covering the sun. This led to extinction of the plants due to low access to sunlight to create photosynthesis, which led to a domino effect in the food chain starting with the smallest organisms of life and ending with the biggest.

### Methods

Researchers were able to chart the extinction rates by using date charting techniques to determine when each individual organism died

### Results

The authors concluded that while the actual cause of the extinction can not yet be known, in part due to an inconsistent and inconvenient geological and fossil record, the evidence for a quick (10,000yr) extinction due to extreme climate change exists. The main question being whether or not an asteroid caused or significantly contributed to said change. Migratory records seem to support the asteroid hypothesis if you assume the impact aerosolized the ground it struck, ejecting it into the atmosphere and emitting a giant infrared burst that would have caused global wildfires, but the kill mechanism remains unknown.
Three separate research groups utilizing three different methods have developed strati-graphic quantifiable data regarding the dinosaur extinction in western North America regarding the late Cretaceous period. These studies indicated that the decline in the variance of the dinosaur population demonstrates an instantaneous geological event.
# Controversies in Science/What killed the dinosaurs/A critique of Extended period of extinctions across the Cretaceous/Tertiary boundary in planktonic foraminifera of continental-shelf sections: Implications for impact and volcanism theories

(Review Paper) Cited in Controversies in Science/What killed the dinosaurs/A critique of Extended period of extinctions across the Cretaceous/Tertiary boundary in planktonic foraminifera of continental-shelf sections: Implications for impact and volcanism theories

### Points Made

The extent of the spectrum of species extinction in and around the K/T boundary extends well before and after the Chicxulub impact boundary. Also, there were distinct extinction swells in periods both before and after the Chicxulub impact. The author seems extremely reliable in scientific knowledge, however she does not reach a clear conclusion for the cause of the mass extinctions explaining that there were most likely multiple variables and contributing factors to the scope of the extinction event.

### Methods

The author examined plankton fossils both in Mexico and in Texas. These areas were chosen due to the close proximity of where the crater had landed. Also, Mexico and Texas had the most significant impact from the crater therefore, examining fossils from these areas would help determine exactly what happened.

### Results

In the Mexican samples, only 26% of the species extinctions correspond with the K/T boundary and iridium band. In the Texas samples, no extinctions or animal changes appear to be correlated with the K/T boundary and iridium band.
The extinction at the K-T boundary is not completely compatible with the volcano or meteorite theories. Other causes should be considered.
# Determinant/C/Compute/1+3i 5-i/3-2i 4+i/Exercise

Compute the determinant of the matrix
    ${\begin{pmatrix}1+3{\mathrm {i} }&5-{\mathrm {i} }\\3-2{\mathrm {i} }&4+{\mathrm {i} }\end{pmatrix}}.$
# Determinant/Elementary matrices/Exercise

Compute the determinant of the elementary matrices.