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colbyford / README.md
Last active July 18, 2024 16:38
Expected value of |XY|^p for bivariate normal distribution where 0<p<2

Expected value of $|XY|^p$ for a bivariate normal distribution, where $(0 &lt; p &lt; 2)$

Disclaimer: This was generated using AI with Mathestral on Ollama and then edited by an underqualfied human.

Denote the bivariate normal random variables as $(X)$ and $(Y)$ with the following properties:

  • Mean vector: $\mu = (\mu_X, \mu_Y)$

  • Covariance matrix: $\Sigma = \binom{\sigma_X^2 , \rho \sigma_X \sigma_Y}{\rho \sigma_X \sigma_Y , \sigma_Y^2}$

@colbyford
colbyford / scipapers-chatgpt_articles.csv
Created March 22, 2023 15:27
Title URL
Predictions of the SARS-CoV-2 Omicron Variant (B.1.1.529) Spike Protein Receptor-Binding Domain Structure and Neutralizing Antibody Interactions https://www.frontiersin.org/articles/10.3389/fviro.2022.830202
An infectious SARS-CoV-2 B.1.1.529 Omicron virus escapes neutralization by therapeutic monoclonal antibodies https://www.nature.com/articles/s41591-021-01678-y
Imprinted SARS-CoV-2 humoral immunity induces convergent Omicron RBD evolution https://www.nature.com/articles/s41586-022-05644-7
Substantial Neutralization Escape by SARS-CoV-2 Omicron Variants BQ.1.1 and XBB.1 https://www.nejm.org/doi/10.1056/NEJMc2214314
ACE2 binding and antibody evasion in enhanced transmissibility of XBB.1.5 https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(23)00010-5/fulltext
@colbyford
colbyford / shiny_app_in_docker.Dockerfile
Created October 25, 2022 18:40
Example Dockerfile for running a Shiny app in a container
# FROM rocker/shiny-verse:latest
FROM rocker/shiny-verse:4.0.0
## Install any Linux system dependencies
RUN apt-get update && apt-get install -y \
sudo \
libcurl4-gnutls-dev \
libcairo2-dev \
libxt-dev \
libssl-dev
@colbyford
colbyford / azure-databricks-with-vnet-and-nsg.json
Last active July 13, 2022 14:13
ARM Template for deploying Azure Databricks with a VNet and Network Security Group
{
"$schema": "https://schema.management.azure.com/schemas/2015-01-01/deploymentTemplate.json#",
"contentVersion": "1.0.0.0",
"parameters": {
"location": {
"type": "String",
"defaultValue" : "eastus"
},
"workspaceName": {
"type": "String",
@colbyford
colbyford / BA.2.75_BA.5_CC12.1_HADDOCK.md
Created July 6, 2022 15:18
Comparison of CC12.1 antibody binding affinity of SARS-CoV-2 Omicron subvariants BA.2.75 and BA.5.
Antibody Antibody PDB Variant Variant ID RBD PDB HADDOCK score Van der Waals energy Electrostatic energy Desolvation energy Restraints violation energy Buried Surface Area
CC12.1 6XC2 Alpha B.1.1.7 6XC2 -198.6 -106.9 -342.6 -37.5 143.2 2778.5
CC12.1 6XC2 Beta B.1.351 7VX1 -171.9 -93.9 -298.1 -33.1 147.3 2698.8
CC12.1 6XC2 Delta B.1.617.2 7V7O -178.8 -100.2 -290.8 -33 125.3 2682.3
CC12.1 6XC2 Omicron B.1.1.529 7T9J -118.5 -76.4 -169.6 -20.8 125.8 2121.4
CC12.1 6XC2 Omicron (Subvariant) BA.2.75 AlphaFold2 -118.8 -72.3 -265.7 -8.9 155.7 2265.6
CC12.1 6XC2 Omicron (Subvariant) BA.5 AlphaFold2 -121.4 -78 -198.3 -18.6 147.3 2326.3
@colbyford
colbyford / pembrolizumab_vs_pemfauxlizumab_pd-1_binding.md
Created June 8, 2022 00:22
Pembrolizumab vs. Pemfauxlizumab PD-1 Binding from HADDOCK
PD-1 Binding Pembrolizumab Pemfauxlizumab
HADDOCK score -138.0 +/- 0.8 -60.6 +/- 4.2
Van der Waals energy -84.8 +/- 3.8 -33.0 +/- 1.6
Electrostatic energy -232.2 +/- 25.9 -292.2 +/- 32.7
Desolvation energy -7.8 +/- 1.6 18.5 +/- 2.8
Restraints violation energy 9.5 +/- 4.9 123.5 +/- 28.9
Buried Surface Area 2204.2 +/- 53.3 1678.7 +/- 60.2
@colbyford
colbyford / pembrolizumab_pemfauxlizumab_fabs.fasta
Last active June 8, 2022 00:35
Comparison of Pembrolizumab and AlphaFold2-hallucinated "Pemfauxlizumab" Fab Sequences
>Pembrolizumab Light Chain
EIVLTQSPATLSLSPGERATLSCRASKGVSTSGYSYLHWYQQKPGQAPRLLIYLASYLESGVPARFSGSGSGTDFTLTISSLEPEDFAVYYCQHSRDLPLTFGGGTKVEIKRTVAAPSVFIFPPSDEQLKSGTASVVCLLNNFYPREAKVQWKVDNALQSGNSQESVTEQDSKDSTYSLSSTLTLSKADYEKHKVYACEVTHQGLSSPVTKSFNRGEC
>Pemfauxlizumab Light Chain
PPTVTITPKHIHFDPGETFTVWATFSKPVYTDDGPKVKVYYRHPGGPYELLYKNATEKEPGWPDNIKTQYTGDRAWVTYDNMPECPHFYIYVRADVGGPPVWGKAVHLHCKCEPVPAEFYVIAAWLLWMLFWDVQIIAYVDGGCCEDHKVRVRLWGKDIKEPIKHYHPHCNPETNCHTHYYVLTLPAREFWKYRWVKFEYISPDGGKTQTAALWF
>Pembrolizumab Heavy Chain
QVQLVQSGVEVKKPGASVKVSCKASGYTFTNYYMYWVRQAPGQGLEWMGGINPSNGGTNFNEKFKNRVTLTTDSSTTTAYMELKSLQFDDTAVYYCARRDYRFDMGFDYWGQGTTVTVSSASTKGPSVFPLAPCSRSTSESTAALGCLVKDYFPEPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTKTYTCNVDHKPSNTKVDKRV
>Pemfauxlizumab Heavy Chain
EYKASCSRPIFCPIGETATITCTISGRDPRDENIMFYYRKPWGEMKYIGTVDTDDGKTTYDEEWKENVIATWDDDNNSATLTIKNLTRDMMMWFHVCVMDKKDGKGIDYCFSSARLFVFDKPFAAITAKKKDKAEIEVIACYPFHCHVSVGDGDDKDKLTQHYWKYTEDGYMICRVTKEKKVTAYCHRAGAKATIEE
@colbyford
colbyford / CC12.3_B.1.1.529_HADDOCK_results_table.csv
Created November 28, 2021 15:30
SARS-CoV-2 B.1.1.529 HADDOCK docking results with the CC12.3 antibody
Metric 6XC7 RBD w/ CC12.3 Predicted B.1.1.529 RBD w/ CC12.3 % Difference
Van der Waals energy -86.1 -93.1 8%
Electrostatic energy -248.1 -194.1 -22%
Desolvation energy -41.7 -37.9 -9%
Restraints violation energy 159.1 104.7 -34%
HADDOCK score -161.5 -159.4 -1%
Buried Surface Area 2489.8 2416.7 -3%
@colbyford
colbyford / CC12.1_B.1.1.529_HADDOCK_results_table.csv
Created November 28, 2021 15:14
SARS-CoV-2 B.1.1.529 HADDOCK docking results with the CC12.1 antibody
Metric 6XC2 RBD w/ CC12.1 Predicted B.1.1.529 RBD w/ CC12.1 % Difference
Van der Waals energy -106.9 -90.7 -15%
Electrostatic energy -342.6 -284.9 -17%
Desolvation energy -37.5 -28.8 -23%
Restraints violation energy 143.2 152.6 7%
HADDOCK score -198.6 -163.3 -18%
Buried Surface Area 2778.5 2584.3 -7%
@colbyford
colbyford / spike_ref_vs_b11529.fasta
Created November 26, 2021 19:43
Spike protein amino acid sequences between the SARS-CoV-2 NC 045512.2 reference genome and the B.1.1.529 variant
>NC_045512.2:21563-25384 Severe acute respiratory syndrome coronavirus 2 isolate Wuhan-Hu-1, SPIKE
MFVFLVLLPLVSSQCVNLTTRTQLPPAYTNSFTRGVYYPDKVFRSSVLHSTQDLFLPFFSNVTWFHAIHVSGTNGTKRFDNPVLPFNDGVYFASTEKSNIIRGWIFGTTLDSKTQSLLIVNNATNVVIKVCEFQFCNDPFLGVYYHKNNKSWMESEFRVYSSANNCTFEYVSQPFLMDLEGKQGNFKNLREFVFKNIDGYFKIYSKHTPINLVR---DLPQGFSALEPLVDLPIGINITRFQTLLALHRSYLTPGDSSSGWTAGAAAYYVGYLQPRTFLLKYNENGTITDAVDCALDPLSETKCTLKSFTVEKGIYQTSNFRVQPTESIVRFPNITNLCPFGEVFNATRFASVYAWNRKRISNCVADYSVLYNSASFSTFKCYGVSPTKLNDLCFTNVYADSFVIRGDEVRQIAPGQTGKIADYNYKLPDDFTGCVIAWNSNNLDSKVGGNYNYLYRLFRKSNLKPFERDISTEIYQAGSTPCNGVEGFNCYFPLQSYGFQPTNGVGYQPYRVVVLSFELLHAPATVCGPKKSTNLVKNKCVNFNFNGLTGTGVLTESNKKFLPFQQFGRDIADTTDAVRDPQTLEILDITPCSFGGVSVITPGTNTSNQVAVLYQDVNCTEVPVAIHADQLTPTWRVYSTGSNVFQTRAGCLIGAEHVNNSYECDIPIGAGICASYQTQTNSPRRARSVASQSIIAYTMSLGAENSVAYSNNSIAIPTNFTISVTTEILPVSMTKTSVDCTMYICGDSTECSNLLLQYGSFCTQLNRALTGIAVEQDKNTQEVFAQVKQIYKTPPIKDFGGFNFSQILPDPSKPSKRSFIEDLLFNKVTLADAGFIKQYGDCLGDIAARDLICAQKFNGLTVLPPLLTDEMIAQYTSALLAGTITSGWTFGAGAALQIPFAMQMAYRFNGIGVTQNVLYENQKL