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[submodule "templates/ncssm"]
path = templates/ncssm
url = [email protected]:curvenote-templates/ncssm
8 changes: 7 additions & 1 deletion papers/agrawala/article.md
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Nuclear Magnetic Resonance (NMR) is a fundamental tool in chemistry for elucidating the molecular structure of unidentified substances. The evaluation of 13C NMR spectra can be challenging due to the numerous factors that affect the peaks and their locations (chemical shifts). Chemists can use NMR spectroscopy in synthesizing new molecules to confirm the identity of the molecule produced. Since the NMR spectrum for the molecule does not exist, the chemists cannot compare their spectra with preexisting spectra to verify their results. To address this, an algorithm that predicts the chemical shifts of the 13C NMR spectra for compounds based on their molecular structure emerges as a solution, generating artificial spectra for comparison with real ones. This paper delineates a method to formulate such an algorithm using machine learning techniques. Multiple graph neural networks and a classical neural network underwent training on an NMR database to predict the chemical shifts of the 13C NMR spectra for several molecules. The accuracy of each neural network was tested by analyzing the difference between the predictions and the actual chemical shift values in the database using Mean Absolute Error (MAE). Notably, the graph neural networks had a higher accuracy and precision than the classical neural network. Among them, the Graph Transformer Network emerges as the most proficient performer. Chemists can utilize the Graph Transformer Network model to validate the synthesis of new compounds within a margin of error of approximately 2.599 ppm.
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## Introduction
Nuclear magnetic resonance (NMR) spectroscopy is an effective technique to deduce the molecular structure of a chemical compound. The NMR machine produces a spectrum that can be used in the process of structure elucidation. To predict the molecular structure, the relevant spectral features of the graph, such as the peak locations (chemical shifts), splitting pattern of the peaks, and the integration of the peaks, must be extracted and analyzed {cite:p}`https://doi.org/10.1039/B2RP90018A`. Interpreting the meaning behind the spectral features of the graph can help determine the structure of the molecule as the spectral features are affected by electron deshielding from electronegative atoms, magnetic anisotropy from pi bonds, and hydrogen bonding {cite:p}`https://doi.org/10.1039/B2RP90018A`. However, the process of unraveling the spectral features of the NMR spectra based on the molecular structure of the sample can be complex as there are many factors that affect the peaks of the NMR spectra.
Machine learning algorithms can be used to predict the spectral features of the NMR spectra of an organic compound based on its chemical structure {cite:p}`https://doi.org/10.1021/acs.jcim.0c00195`. The algorithm would learn the relationship between atoms and bonds in a molecule, and how it affects the NMR spectra of that molecule. Simple neural network algorithms simplify molecules by encapsulating each atom’s features within a vector, albeit at the cost of losing significant information about interatomic interactions. However, a more effective approach to representing molecules for machine learning algorithms emerges with the utilization of graphs {cite:p}`https://doi.org/10.1021/acs.jcim.0c00195`. The graph is composed of nodes, which represent the atoms, that are connected by edges, which represent the bonds between atoms. A graph neural network is a machine learning algorithm that can be used to simulate a compound by mapping out the molecular structure of the compound on a graph. Furthermore, they can be used to predict the chemical shifts of 13C NMR spectra for carbon compounds more accurately than a classic neural network {cite:p}`https://doi.org/10.1021/acs.jcim.0c00195`. The graph neural network algorithm can help scientists while they are producing a new compound as they could use the algorithm to verify if they made the correct compound.
Machine learning algorithms can be used to predict the spectral features of the NMR spectra of an organic compound based on its chemical structure {cite:p}`https://doi.org/10.1021/acs.jcim.0c00195`. The algorithm would learn the relationship between atoms and bonds in a molecule, and how it affects the NMR spectra of that molecule. Simple neural network algorithms simplify molecules by encapsulating each atom’s features within a vector, albeit at the cost of losing significant information about interatomic interactions. However, a more effective approach to representing molecules for machine learning algorithms emerges with the utilization of graphs {cite:p}`https://doi.org/10.1021/acs.jcim.0c00195`. The graph is composed of nodes, which represent the atoms, that are connected by edges, which represent the bonds between atoms. A graph neural network is a machine learning algorithm that can be used to simulate a compound by mapping out the molecular structure of the compound on a graph. Furthermore, they can be used to predict the chemical shifts of 13C NMR

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spectra for carbon compounds more accurately than a classic neural network {cite:p}`https://doi.org/10.1021/acs.jcim.0c00195`. The graph neural network algorithm can help scientists while they are producing a new compound as they could use the algorithm to verify if they made the correct compound.
Previous studies have shown that graph neural networks are effective in predicting the chemical shifts of 13C NMR spectra {cite:p}`https://doi.org/10.1021/acs.jcim.0c00195`. In this study, I aim to further improve the accuracy of the graph neural networks by introducing novel architectural frameworks that incorporate comprehensive data from both nodes and edges within each graph. The algorithm is tested by comparing the actual chemical shift values of 13C NMR spectra with the predicted chemical shift values from the algorithm for various carbon compounds. The actual chemical shift values of the 13C NMR spectra is obtained from the _NMRShiftDb2_ database.

## Methods
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14 changes: 10 additions & 4 deletions papers/covington/article.md
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An optical image of the NGC 1952 taken by the Hubble Space Telescope in 2005. The central glow highlights the pulsar.
```

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## Age Determination of NGC 1952 and PSR B0531+21 Using Radio Observations

Supernova remnants (SNRs) have been astronomical phenomena of interest since ancient times due to their brilliance in the visible spectrum. SNR events are evidenced in the artifacts of early civilizations. Records are believed to have begun in 185 C.E. Common type II supernovae occur due to the discontinuation of fusion in massive stars’ iron or nickel cores. However, in type III1 supernovae, the atomic nuclei of oxygen-neon-magnesium cores capture electrons. Both processes drive stellar collapse because of imbalances between gravity and pressure. Protons and electrons meld, forming a small, dense star supported by neutron degeneracy (more massive stars continue to collapse into black holes). Finally, this process produces a shock wave that expands inward and outward–expelling an array of gas and dust in the interstellar medium. Pulsars (PSRs), a form of a neutron star, rotate at extremely high velocities. Although they conserve much of their angular momentum, their periods gradually decline. Pulsars are detectable in gamma, x-ray, ultraviolet, or radio wavelengths due to the emission of synchrotron radiation from their magnetic poles.

A PSR’s characteristic age can be deduced from its period and derivative. The characteristic age assumes significant reductions in the initial period and an absence of magnetic field decay. Its accuracy indicates the relevance of these characteristics. The actual age, meanwhile, uses a pulsar’s braking magnitude and reveals whether multiple sources affect its spin-down.

The Crab Nebula, a remnant of a supernova and a type III plerion located within the constellation Taurus, and its associated pulsar are the subjects of this research. Age determinations assist historians in connecting SNRs to Chinese records of “guest stars.” However, we focus on the Crab because of sufficient evidence from the year it was first observed, proving the accuracy of our results. Additionally, ages confirm pulsar associations: A pulsar may gradually drift from a remnant’s center [@condon_essential_2017]. We compare two methods in their effective determination of the Crab SNR’s age: The first utilizes the remnant’s expansion, and the second relies on the spin properties of its pulsar.
The Crab Nebula, a remnant of a supernova and a type III plerion located within the constellation Taurus, and its associated pulsar are the subjects of this research. Age determinations assist historians in connecting SNRs to Chinese records of “guest stars.” However, we focus on the Crab because of sufficient evidence from the year it was first observed, proving the accuracy of our results. Additionally, ages confirm pulsar associations: A pulsar may gradually drift from a remnant’s center [@condon_essential_2017]. We compare

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two methods in their effective determination of the Crab SNR’s age: The first utilizes the remnant’s expansion, and the second relies on the spin properties of its pulsar.

## Methods

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\tau_c = \frac{P}{2\dot{P}}
```

With Equation @Equation_3, we then estimated the true age, $\tau$. Unlike the characteristic age, the true age of a pulsar incorporates 𝑛, the magnetic braking index or the loss of rotational energy due to ionized material traveling along the pulsar's magnetic field lines, and $P_0$, the initial period upon the formation of the pulsar.
With Equation @Equation_3, we then estimated the true age, $\tau$. Unlike the characteristic age, the true age of a pulsar incorporates $n$, the magnetic braking index or the loss of rotational energy due to ionized material traveling along the pulsar's magnetic field lines, and $P_0$, the initial period upon the formation of the pulsar.

```{math}
:label: Equation_3
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P = kP^{2-n}
```

A differentiated and rearranged form of Equation @Equation_4, which describes the relationship between the period, the constant, 𝑘, and the braking index, allowed us to solve for $n$: $n=2-\frac{P \ddot{P}{P}} {\dot{P}{P^2}}$. The derivations of $\ddot{P}{P}$ and $P_0$ require complex models actively being explored. The process is further complicated by numerous glitches or random and disruptive spin-up events experienced by the Crab PSR. However, recent studies have given estimates for $P_0$ [@zhang_evolution_2022], as well as [@malov_second_2017] between glitches: values which we use here.
A differentiated and rearranged form of Equation @Equation_4, which describes the relationship between the period, the constant, $k$, and the braking index, allowed us to solve for $n$: $n=2-\frac{P \ddot{P}{P}} {\dot{P}{P^2}}$. The derivations of $\ddot{P}{P}$ and $P_0$ require complex models actively being explored. The process is further complicated by numerous glitches or random and disruptive spin-up events experienced by the Crab PSR. However, recent studies have given estimates for $P_0$ [@zhang_evolution_2022], as well as [@malov_second_2017] between glitches: values which we use here.

## Results
### SNR Rate of Expression
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#### Characteristic Age

We determined the characteristic age to be $4.0395 \cdot 10^{10}$ seconds or $1280.9$ years. For millisecond pulsars, the characteristic age can be many times greater than the actual age, which indicates that $P_0$ is similar to $P$. Although the approximation above is reasonable, the actual age demonstrates higher accuracy. Using Equation @Equation_4 and a period second derivative of $2.7 \cdot 10^{24}$, $n$ was found to be $2.52$. The braking index is slightly less than the expected value of 3 if the spin-down were due solely to magnetic dipole radiation; therefore, other factors contribute to the pulsar’s loss of rotational velocity [@kou_rotational_2015].
We determined the characteristic age to be $4.0395 \cdot 10^{10}$ seconds or $1280.9$ years. For millisecond pulsars, the characteristic age can be many times greater than the actual age, which indicates that $P_0$ is similar to $P$. Although the approximation above is reasonable, the actual age demonstrates higher accuracy. Using Equation @Equation_4 and a period second derivative of $-2.7 \cdot 10^{-24}$, $n$ was found to be $2.52$. The braking index is slightly less than the expected value of 3 if the spin-down were due solely to magnetic dipole radiation; therefore, other factors contribute to the pulsar’s loss of rotational velocity [@kou_rotational_2015].

#### True Age

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PSRs: Pulsars
SNR: Supernova remnant
PSR: Pulsar
RFI: radio frequency interference
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