https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions tagged with Medical Sciences sorted by most likes. https://community.wolfram.com/groups/-/m/t/1872608 *Short URL to share this post*: https://wolfr.am/coronavirus ***JOIN*** *our* ***Medical Sciences*** *group for the latest updates & best networking*: https://wolfr.am/MedicalSciences ---------- This post is intended to be the hub for Wolfram resources related to novel coronavirus disease COVID-19 that originated in Wuhan, China. The larger aim is to provide a forum for disseminating ways in which Wolfram technologies and coding can be utilized to shed light on the virus and pandemic. Possibilities include using the Wolfram Language for data-mining, modeling, analysis, visualizations, and so forth. Among other things, we encourage comments and feedback on these resources. Please note that this is intended for technical analysis and discussion supported by computation. Aspects outside this scope and better suited for different forums should be avoided. Thank you for your contribution! ## ________________________________________ ## FEATURED CONTENT - [COVID-19 Livestream Notebook March 24][8] by Stephen Wolfram - [Agent-Based Networks Models for COVID-19][9] by Christopher Wolfram - [Live-Stream: Exploring Pandemic Data][10] by Stephen & Christopher Wolfram + guests - [Live-Stream: Exploring and Explaining Epidemic Modeling][11] by Stephen & Christopher Wolfram + guests ## ________________________________________ ## [CALL for Making COVID-19 Data Computable (*link*)][12] More pandemic-related information and data sets emerging every day. We invite people in the community to contribute to making more data surrounding this topic computable. Here is a call to action with some recommendations for people who want to do more, whether it's just pointing out relevant data sources, or taking the time to make some of that data computable and more instantly ready for other people to explore: https://wolfr.am/COVID-19-DATA . ## ________________________________________ ## [Curated Computable Data (*link*)][13] [FOLLOW THIS LINK][14] to see all available COVID-19 data repositories ready for computation in the Wolfram Language . [Changes in Updates to SARS-CoV-2 Sequences in the Wolfram Data Repository][16] We have published and are continuously updating the Wolfram Data Repository entries. Below are a few key ones. Follow the link above to browse all repositories. We encourage you to make [*your own contributions*][15] of curated data relevant to COVID-19. > **Pandemic Data for Novel Coronavirus COVID-19** > https://www.wolframcloud.com/obj/resourcesystem/published/DataRepository/resources/Epidemic-Data-for-Novel-Coronavirus-COVID-19 > **Genetic Sequences for the SARS-CoV-2 Coronavirus** > https://datarepository.wolframcloud.com/resources/Genetic-Sequences-for-the-SARS-CoV-2-Coronavirus > **Patient Medical Data for Novel Coronavirus COVID-19** > https://datarepository.wolframcloud.com/resources/Patient-Medical-Data-for-Novel-Coronavirus-COVID-19 > **COVID-19 Hospital Resource Use Projections** > https://datarepository.wolframcloud.com/resources/COVID-19-Hospital-Resource-Use-Projections > **OECD Data: Hospital Beds Per Country** > https://datarepository.wolframcloud.com/resources/OECD-Data-Hospital-Beds-Per-Country > **Hospital Beds Per US State** > https://datarepository.wolframcloud.com/resources/Hospital-Beds-Per-US-State ## ________________________________________ ## [Computational Publications (*link*)][17] We encourage you to share your computational explorations relevant to coronavirus on Wolfram Community as stand-alone articles and then comment with their URL links on this discussion thread. We will summarize these articles in the following list: ### ________________________________ ###FEATURED > **COVID-19 Livestream Notebook March 24** by Stephen Wolfram > https://www.wolframcloud.com/obj/s.wolfram/Published/COVID-19-Livestream-March-24.nb > **Agent-Based Networks Models for COVID-19** by Christopher Wolfram > https://community.wolfram.com/groups/-/m/t/1907703 > **Epidemiological Models for Influenza and COVID-19** by Robert Nachbar > https://community.wolfram.com/groups/-/m/t/1896178 > **Epidemic simulation with a polygon container** by Francisco Rodríguez > https://community.wolfram.com/groups/-/m/t/1901002 > **Distance to nearest confirmed US COVID-19 case** by Chip Hurst > https://community.wolfram.com/groups/-/m/t/1911583 ### ________________________________ ### EPIDEMIC MODELING: SIMULATION > **Epidemic simulation with a polygon container** by Francisco Rodríguez > https://community.wolfram.com/groups/-/m/t/1901002 > **Agent based epidemic simulation** by Jon McLoone > https://community.wolfram.com/groups/-/m/t/1900481 > **Modeling the spatial spread of infection diseases in the US** by Diego Zviovich > https://community.wolfram.com/groups/-/m/t/1889072 > **Geo-spatial-temporal COVID-19 simulations and visualizations over USA** by Diego Zviovich > https://community.wolfram.com/groups/-/m/t/1900514 > **Life, Liberty, and Lockdowns: cellular automaton approach** by Philip Maymin > https://community.wolfram.com/groups/-/m/t/2181433 ### ________________________________ ### EPIDEMIC MODELING: COMPARTMENTAL > **Teaching notebook on disease models** by Gareth Russell > https://community.wolfram.com/groups/-/m/t/2694698 > **Stochastic Epidemiology Models with Applications to the COVID-19** by Robert Nachbar > https://community.wolfram.com/groups/-/m/t/1980051 > **COVID19: Italian SIRD estimates and prediction** by Christos Papahristodoulou > https://community.wolfram.com/groups/-/m/t/1984320 > **Solver for COVID-19 epidemic model with the Caputo fractional derivatives** by Alexander Trounev > https://community.wolfram.com/groups/-/m/t/1976589 > **EpiPlay: using Mathematica to gamify education in epidemiology** by Rui Alves > https://community.wolfram.com/groups/-/m/t/2535927 > **Epidemiological Model for repetitive rapid testing for COVID-19** by Diego Zviovich > https://community.wolfram.com/groups/-/m/t/2075883 > **Phase transition of a SIR agent-based models** by Diego Zviovich > https://community.wolfram.com/groups/-/m/t/1977230 > **A simple estimate of covid-19 fatalities based on past data** by Kay Herbert > https://community.wolfram.com/groups/-/m/t/1959438 > **SIR Model with Log-normal infected periods** by Diego Zviovich > https://community.wolfram.com/groups/-/m/t/1946292 > **SEI2HR-Econ model with quarantine and supplies scenarios** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1937880 > **COVID-19 - Policy Simulator - Can you find the perfect policy?** by Jan Brugard > https://community.wolfram.com/groups/-/m/t/1931352 > **Epidemiological Models for Influenza and COVID-19** by Robert Nachbar > https://community.wolfram.com/groups/-/m/t/1896178 > **Exploring Epidemiological Modeling** by Jordan Hasler > https://community.wolfram.com/groups/-/m/t/1920119 > **SEI2HR model with quarantine scenarios** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1926505 > **The SIR Model for Spread of Disease** by Arnoud Buzing > https://community.wolfram.com/groups/-/m/t/1903289 > **COVID-19 - R0 and Herd Immunity - are we getting closer?** by Jan Brugard > https://community.wolfram.com/groups/-/m/t/1911422 > **Basic experiments workflow for simple epidemiological models** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1895675 > **Scaling of epidemiology models with multi-site compartments** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1897377 > **WirVsVirus 2020 hackathon participation** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1907256 > **An SEIR like model that fits the coronavirus infection data** by Enrique Garcia Moreno > https://community.wolfram.com/groups/-/m/t/1888335 > **A SEIRD Model For COVID-19 Using DDEs** by Luis Borgonovo > https://community.wolfram.com/groups/-/m/t/1996374 > **A Neat Package for Compartmental Model Diagrams** by Hamza Alsamraee > https://community.wolfram.com/groups/-/m/t/2078640 > **Redesign of didactics of S(E)IR(D) -> SI(EY)A(CD) models of epidemics** by Thomas Colignatus > https://community.wolfram.com/groups/-/m/t/2004784 > **COVID-19 SIR models: transmission, vaccination, herd immunity dynamics revealed** by Athanasios Paraskevopoulos > https://community.wolfram.com/groups/-/m/t/3008488 ### ________________________________ ### EPIDEMIC MODELING: LOGISTIC > **COVID-19 pandemic data in Italy** by Riccardo Fantoni > https://community.wolfram.com/groups/-/m/t/1909687 > **Predicting Coronavirus Epidemic in United States** by Robert Rimmer >https://community.wolfram.com/groups/-/m/t/1906954 > **Tracking Coronavirus Testing in the United States** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1902302 > **Logistic Model for Quarantine Controlled Epidemics** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1900530 > **Updated: coronavirus logistic growth model: China** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1890271 > **Coronavirus logistic growth model: China** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1887435 > **Coronavirus logistic growth model: Italy and South Korea** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1887823 > **Coronavirus logistic growth model: South Korea** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1894561 > **Logistic growth model for epidemic Covid-19 in Colombia** by Diego Ramos > https://community.wolfram.com/groups/-/m/t/2092786 ### ________________________________ ### GENOMICS > **Analyzing the spread of SARS-CoV-2 variants in California** by Daniel Lichtblau > https://community.wolfram.com/groups/-/m/t/2205357 > **Analyzing the spread of SARS-CoV-2 variants in Florida** by Daniel Lichtblau > https://community.wolfram.com/groups/-/m/t/2206874 > **Analyzing Nextstrain Data with WFR Newick Functions (COVID-19/SARS-CoV-2)** by John Cassel > https://community.wolfram.com/groups/-/m/t/1958952 > **Finding and analyzing a COVID subvariant in Australia** by Daniel Lichtblau > https://community.wolfram.com/groups/-/m/t/2342489 > **Analyzing SARS-CoV-2 Genetic Sequences** by John Cassel & Daniel Lichtblau > https://blog.wolfram.com/2021/08/19/newick-trees-proximity-resources-and-accessions-analyzing-sars-cov-2-genetic-sequences/ > **Estimating the number of times the SARS CoV-2 virus has replicated** by Carlos Munoz > https://community.wolfram.com/groups/-/m/t/1943243 >**From sequenced SARS-CoV-2 genomes to a phylogenetic tree** by Daniel Lichtblau >https://community.wolfram.com/groups/-/m/t/1961461 > **Genome analysis and the SARS-nCoV-2** by Daniel Lichtblau > https://community.wolfram.com/groups/-/m/t/1874816 > **Visualizing Sequence Alignments from the COVID-19** by Jessica Shi > https://community.wolfram.com/groups/-/m/t/1875352 > **A walk-through of the SARS-CoV-2 nucleotide Wolfram resource** by John Cassel > https://community.wolfram.com/groups/-/m/t/1887456 > **Geometrical analysis of genome for COVID-19 vs SARS-like viruses** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1878824 > **Chaos Game For Clustering of Novel Coronavirus COVID-19** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1875994 ### ________________________________ ### DATA ANALYSIS > **Optimal Annual COVID-19 Vaccine Boosting Dates Following Previous Booster Vaccination or Breakthrough Infection** by Jeffrey Townsend > https://community.wolfram.com/groups/-/m/t/3341399 > **Probability of early infection extinction depends linearly on the virus clearance rate** by Nóra Juhász > https://community.wolfram.com/groups/-/m/t/3307502 > **Detecting Global Community Structure in a COVID-19 Activity Correlation Network** by Hiroki Sayama > https://community.wolfram.com/groups/-/m/t/3056172 > **Analyzing trends of COVID-19 through public news feeds** by Silvia Hao > https://community.wolfram.com/groups/-/m/t/2569395 > **Deep neural network detection & clinical staging of COVID-19 chest X-rays** by Peter Riley > https://community.wolfram.com/groups/-/m/t/2389110 > **COVID-19 - The Swedish Experiment - Is it working?** by Jan Brugard > https://community.wolfram.com/groups/-/m/t/1974412 > **A simple COVID-19 spread model** by Daniel Lichtblau > https://community.wolfram.com/groups/-/m/t/1945196 > **COVID19: The performance of the Swedish strategy** by Christos Papahristodoulou > https://community.wolfram.com/groups/-/m/t/1990972 > **Exploring social trends on Covid-19 pandemic using WikipediaData** by Jofre Espigule-Pons > https://community.wolfram.com/groups/-/m/t/1931508 > **Google Mobility Data** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1946686 > **Understanding Aggregate COVID Curves** by Christopher Wolfram > https://community.wolfram.com/groups/-/m/t/2068457 > **Apple mobility trends data visualization** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1942813 > **Computing COVID-19 Spread Rates in US Cities** by Daniel Lichtblau > https://community.wolfram.com/groups/-/m/t/1930261 > **COVID-19 data and the Newcomb Benford Distribution** by Gustavo Delfino > https://community.wolfram.com/groups/-/m/t/1913908 > **Short-time trends for COVID-19**, by Fabian Wenger > https://community.wolfram.com/groups/-/m/t/1912710 > **What countries are hit hard by COVID19 outbreak?** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1904507 > **COVID19 in Iran: under-diagnosis issue** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1891140 > **Coronavirus analysis: descriptive statistics with SQL functions** by Damian Calin > https://community.wolfram.com/groups/-/m/t/2206078 > **Covid-19 vaccine campaigns efficacy analysis** by Damian Calin > https://community.wolfram.com/groups/-/m/t/2383314 > **Argentina: COVID-19 Data Analysis** by Tobias Canavesi > https://community.wolfram.com/groups/-/m/t/1932910 > **Analysis of the Change in Phillips Curve After COVID-19 with Regression** by Seojin Yoon > https://community.wolfram.com/groups/-/m/t/2055704 > **COVID wave alert: statistical analysis and visualization** by Antonio Neves > https://community.wolfram.com/groups/-/m/t/2115658 > **Predicting COVID-19 using cough sounds classification** by Siria Sadeddin > https://community.wolfram.com/groups/-/m/t/2166833 > **Covid-19 vaccination data analysis using SQL functions** by Damian Calin > https://community.wolfram.com/groups/-/m/t/2324474 > **Analyzing COVID-19 vaccine sentiment over time** by Arshaan Sayed > https://community.wolfram.com/groups/-/m/t/2317293 > **VAERS data analysis using SQL functions** by Damian Calin > https://community.wolfram.com/groups/-/m/t/2351726 > **Correlating COVID-19 government measures to biweekly/daily outbreaks** by Arshaan Sayed > https://community.wolfram.com/groups/-/m/t/2362327 > **Plotting Covid19 sentiment in different regions of Chennai** by Aditya Sairam Prakash > https://community.wolfram.com/groups/-/m/t/2388236 ### ________________________________ ### DATA VISUALIZATIONS > **CDC COVID19 vaccination data across US counties** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/2282418 > **Top 20 COVID countries HeatMap by absolute death and death in ppm** by Rodrigo Murta > https://community.wolfram.com/groups/-/m/t/2004800 > **COVIDWORLD app: current data and visualizations for SARS-CoV2 pandemic** by Rui Alves > https://community.wolfram.com/groups/-/m/t/2473065 > **US Counties COVID-19 confirmed cases by population density timelines** by Bob Sandheinrich > https://community.wolfram.com/groups/-/m/t/1992898 > **3D Modeling of the SARS-CoV-2 Virus in the Wolfram Language** by Jeff Bryant > https://community.wolfram.com/groups/-/m/t/1989540 > **California COVID19 Data** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/2132204 > **COVID-19 progress in Peru macro regions: coast vs mountain vs jungle** by Francisco Rodríguez > https://community.wolfram.com/groups/-/m/t/1965079 > **COVID-19 reopening criterion: a simple visualization** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1962615 > **100 Days of COVID19 Over US Counties** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1956368 > **Population Density Map** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1955760 > **Google Mobility Data** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1946686 > **COVID19 Case-Fatality Ratio, Income, and Age: Simple Visualization** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1939045 > **Data Analysis of Coronavirus in Mexico** by Ivan Martinez > https://community.wolfram.com/groups/-/m/t/1927657 > **Confirmed COVID-19 Cases in Catalonia** by Bernat Espigulé Pons > https://community.wolfram.com/groups/-/m/t/1919468 > **Distance to nearest confirmed US COVID-19 case** by Chip Hurst > https://community.wolfram.com/groups/-/m/t/1911583 > **COVID19 Confirmed Cases: US Counties** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/1950980 > **COVID19 data visualization across US counties** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/2119049 > **Maps for Visualizing Covid-19's Effect** by Eric Mockensturm > https://community.wolfram.com/groups/-/m/t/1934457 > **US Counties COVID-19 deaths plot** by Bob Sandheinrich > https://community.wolfram.com/groups/-/m/t/1918332 > **Comparing the spread of COVID-19 between countries**, Jan Brugard > https://community.wolfram.com/groups/-/m/t/1905992 > **NY Times COVID-19 data visualization** by Anton Antonov > https://community.wolfram.com/groups/-/m/t/1911668 > **COVID-19 cases for each administrative division in Spain** by Bernat Espigulé Pons > https://community.wolfram.com/groups/-/m/t/1910116 > **Propagation risk of COVID-19 by local contact in Spain (10 - 14 March)** by Bernat Espigulé Pons > https://community.wolfram.com/groups/-/m/t/1898126 > **Visualizing the Pandemic Data COVID-19** by Martijn Froeling > https://community.wolfram.com/groups/-/m/t/1899870 > **COVID-19 visualization of turning point** by Isao Maruyama > https://community.wolfram.com/groups/-/m/t/1899911 > **Mapping "Live" COVID Data on a Globe** by Gabriel Lemieux > https://community.wolfram.com/groups/-/m/t/1902102 > **Novel Coronavirus COVID-19 in Brazil** by Estevao Teixeira > https://community.wolfram.com/groups/-/m/t/1905950 > **Mapping Novel Coronavirus COVID-19 Outbreak** by Jofre Espigule-Pons > https://community.wolfram.com/groups/-/m/t/1868945 > **Ways to visualize COVID-19 simulation results?** by Kyle Keane > https://community.wolfram.com/groups/-/m/t/1962739 > **General and COVID-19 deaths in Sweden** by Oscar Rodriguez > https://community.wolfram.com/groups/-/m/t/2006377 > **COVID19 Tokyo per days of the week** Isao Maruyama > https://community.wolfram.com/groups/-/m/t/2133807 ### ________________________________ ### DATA PROCESSING > **Cov-Tell: Daily COVID-19 Updates with Alexa (made with Wolfram APIFunction)** by Jessica Shi > https://community.wolfram.com/groups/-/m/t/1958307 > **Build a COVID-19 Chest X-Ray Image Uploader with Cloud & Data Drop** by Jofre Espigule-Pons > https://community.wolfram.com/groups/-/m/t/1919770 > **Scraping OpenTable's "State of the Industry" page** by Aaron Enright > https://community.wolfram.com/groups/-/m/t/1911043 > **City-level Search Tool for Coronavirus (COVID-19) Confirmed Cases** by David Lomiashvili > https://community.wolfram.com/groups/-/m/t/1913247 > **Web Scraper: New York Times Coronavirus Data** by Robert Rimmer > https://community.wolfram.com/groups/-/m/t/1894426 > **TraCOV: Personalized COVID-19 Risk Analysis Tool** by Jessica Shi > https://community.wolfram.com/groups/-/m/t/1977700 > **Mobility changes data: transforming to Wolfram Language dataset** by Mads Bahrami > https://community.wolfram.com/groups/-/m/t/2160386 ### ________________________________ ### MASKS > **Effect of mandatory mask usage in COVID cases** by Diego Zviovich > https://community.wolfram.com/groups/-/m/t/1919060 > **Face mask detection: classifying image data** by Siria Sadeddin > https://community.wolfram.com/groups/-/m/t/2139499 ## ________________________________________ ## [Livestream Archives (*link*)][18] - Stephen & Christopher Wolfram + guests [Exploring Pandemic Data][19] - Stephen & Christopher Wolfram + guests [Exploring and Explaining Epidemic Modeling][20] - Robert Nachbar - [Epidemiological Models for Influenza and COVID-19][21] - Brian Wood - [COVID-19 Dashboard Visualizations][22] - John Cassel - [Behind the Genetic Sequences for Novel Coronavirus SARS-CoV-2][23] - Keiko Hirayama - [Patient Data Exploration for the Novel Coronavirus COVID-19][24] - Keiko Hirayama - [Pandemic Data Exploration for the Novel Coronavirus COVID-19][25] - Diego Zviovich - [Geo-spatial-temporal COVID-19 Simulations and Visualizations Over USA][26] - Anton Antonov - [COVID19 Epidemic Modeling: Compartmental Models][27] - Anton Antonov - [Scaling of Epidemiology Models with Multi-site Compartments][28] - Anton Antonov - [Simple Economic Extension of Compartmental Epidemiological Models][29] - Juan Klopper - [Coronavirus medical data analysis][30] - Juan Klopper - [Coronavrirus epidemiological data analysis][31] - Rory Foulger - [Coronavirus Data Exploration - Wolfram Livecoding with Students][32] ## ________________________________________ ## Other useful resources - Arnoud Buzing [GitHub][33] repository and [Notebook Gallery][34] for coronavirus - [Modeling a Pandemic like Ebola with the Wolfram Language](https://blog.wolfram.com/2014/11/04/modeling-a-pandemic-like-ebola-with-the-wolfram-language) - [Epidemics at Wolfram Demonstrations](https://demonstrations.wolfram.com/search.html?query=epidemic) - [IGSIRProcess - IGraph Epidemic models][35] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1China_c.png&userId=1624544 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1.5US_c.png&userId=1624544 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2World_c.png&userId=1624544 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3Genetic_c.png&userId=1624544 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4Patient_c.png&userId=1624544 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5Resources_c.png&userId=1624544 [7]: https://www.wolframcloud.com/obj/examples/COVID19Preview.png [8]: https://www.wolframcloud.com/obj/s.wolfram/Published/COVID-19-Livestream-March-24.nb [9]: https://community.wolfram.com/groups/-/m/t/1907703 [10]: https://youtu.be/Vs5APySGYnk [11]: https://youtu.be/kC6LHAv_lx0 [12]: https://community.wolfram.com/groups/-/m/t/1908923 [13]: https://datarepository.wolframcloud.com/search/?i=COVID-19 [14]: https://datarepository.wolframcloud.com/search/?i=COVID-19 [15]: https://reference.wolfram.com/language/workflow/SubmitToTheWolframDataRepository.html [16]: https://community.wolfram.com/groups/-/m/t/2238214 [17]: http://wolfr.am/StaffPicks [18]: https://www.youtube.com/playlist?list=PLxn-kpJHbPx3_hUbroRYC_7NxcOwZ1SWa [19]: https://youtu.be/Vs5APySGYnk [20]: https://youtu.be/kC6LHAv_lx0 [21]: https://youtu.be/pcFB6_yrxGE [22]: https://youtu.be/vUq8qx7kTYA [23]: https://youtu.be/HCJgv3N_kDo [24]: https://youtu.be/MlI_8o4A3BA [25]: https://youtu.be/P86ZY-znE64 [26]: https://youtu.be/Kjk-sYlg-U0 [27]: https://youtu.be/LRs9rYCXIzs [28]: https://youtu.be/b8oCNjRI0gY [29]: https://youtu.be/C-sjXQiPE7s [30]: https://youtu.be/gA0TPQZgNY0 [31]: https://youtu.be/I-n3zN4aU6c [32]: https://youtu.be/4xCfPIiredM [33]: https://github.com/arnoudbuzing/wolfram-coronavirus [34]: https://wolfr.am/JZNRriEE [35]: http://szhorvat.net/mathematica/IGDocumentation/#epidemic-models Vitaliy Kaurov 2020-02-04T15:18:14Z https://community.wolfram.com/groups/-/m/t/1868945 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4686Wuhan_Coronavirus_Outbreak_Jan29.gif&userId=95400 [2]: https://www.wolframcloud.com/obj/c2eafc69-4016-4e05-a8ad-b1d22a37379f Jofre Espigule-Pons 2020-01-29T02:18:52Z https://community.wolfram.com/groups/-/m/t/922544 Dear all, my data consist of a list of lists of points in 3D. After running the code ClearAll["Global`*"] SetDirectory[NotebookDirectory[]]; sliceData = << "SliceData.txt"; Graphics3D[Line /@ sliceData, Boxed -> True, Axes -> True] one gets: ![enter image description here][1] Clearly the data describe a 3D object (as "wire frame"). **QUESTION:** *How can those data be converted into a single 3D Mathematica object (graphics, mesh, ...)? Is there an already implemented way (a routine) I am missing?* ---------- NOTE on DATA: ------------- The data stem from our radiotherapy treatment planning system. There we are working with contours which are drawn on any single CT slice. Organs at risk and target volumes are defined by those contours. One special contour is the "BODY contour"; this is what is shown in my example data. Dose will be calculated only inside this BODY contour, therefore e.g. the volume around the ears and nose appears to be exaggerated (for being on the safe side). Those treatment plans can be exported as DICOM files and nicely imported in Mathematica. When high energy radiation is applied to a body it turns out that the dose next to the skin is highly diminished; this is due to the buildup effect of the dose. When full dose at the skin is wanted, one has to anticipate this buildup effect, and this can be realized by putting a "flab" onto the skin: A flab is a layer made of some tissue equivalent material. Optimal flabs can have quite irregular shapes. I recently learned at a conference that there is the possibility to 3D print those individual flabs - if one can provide the data ... So - probably to everybody's disappointment - I do not want to print any BODY contour, but I imagined a BODY contour might serve here as kind of a "honey pot". Best regards and many thanks! -- Henrik [1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=sliceImg.png&userId=32203 Henrik Schachner 2016-09-11T20:40:44Z https://community.wolfram.com/groups/-/m/t/1974412 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- ![enter image description here][1] &[Wolfram Notebook][2] [Old]: https://www.wolframcloud.com/obj/c29137dd-dcdf-4dd1-827e-3495b64a8436 [Original]: https://www.wolframcloud.com/obj/a9d60a60-4adf-41ec-ad5a-a666b1591cf0 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=image.jpeg&userId=20103 [2]: https://www.wolframcloud.com/obj/956d65fd-abfb-45d9-802d-9a79013e7b14 Jan Brugard 2020-05-14T15:04:02Z https://community.wolfram.com/groups/-/m/t/1907703 ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=animation.gif&userId=24497 [2]: https://www.wolframcloud.com/obj/111b7fc9-47f8-4d2e-90ff-fe71265746fd Christopher Wolfram 2020-03-25T06:40:12Z https://community.wolfram.com/groups/-/m/t/294122 ![enter image description here][5] When playing with Mathematica 10 I constructed this very simple example of an application of the NDSolve command, which I wanted to share. The objective is to model the growth of a special kind of brain tumour which affects mainly glial cells in a highly simplified way. I follow modelling ideas discussed in the excellent book ["Mathematical Biology" (Vol 2) by J.D. Murray][1]. It turns out that Gliomas, which are neoplasms of glial cells, i.e. neural calls capable of division, can be be modelled by a rather simple diffusion-growth model. $$\frac{d c}{dt}=\nabla\left(D(x) \nabla c \right)+ \rho c$$ where c is the concentration of cancer cells and $D(x)$ is the diffusion coefficient, which depends on the coordinates; $\rho$ models the growth rate of the cells. The following boundary condition has to be observe (even though will be ignored in the model I use later on): $${\bf n} \cdot D(x) \nabla c = 0 \qquad \text{for}\; x\; \text{on}\; \partial B.$$ In reality the diffusion coefficient will depend on the tissue type, i.e. gray matter vs white matter. I will use an image from a CT can to describe the different densities of the tissue instead. ![enter image description here][2] In the book by Murray great care is taken to estimate the diffusion coefficient but I just want to show the principle here. I use the attached file "brain-crop.jpg" and import it: img2=Import["~/Desktop/brain-crop.jpg"] Then I sharpen it and convert it to gray-scale. img3 = Sharpen[ColorConvert[img2, "Grayscale"]] Then I use that image to determine the diffusion coefficient, locally: diffcoeff = ListInterpolation[ImageData[img3], InterpolationOrder -> 3] I should now determine the boundaries using something like EdgeDetect. As the background is black and allows no diffusion at all, we can simplify this by just setting a larger (rectangular) boundary box like so: boundaries = {-y, y - 1, -x, x - 1}; \[CapitalOmega] = ImplicitRegion[And @@ (# <= 0 & /@ boundaries), {x, y}]; Next we can solve the ODE on the domain: sols = NDSolveValue[{{Div[1./500.*(diffcoeff[798.*x, 654*y])^4*Grad[u[t, x, y], {x, y}], {x, y}] - D[u[t, x, y], t] + 0.025*u[t, x, y] == NeumannValue[0., x >= 1. || x <= 0. || y <= 0. || y >= 1.]}, {u[0, x, y] == Exp[-1000. ((x - 0.6)^2 + (y - 0.6)^2)]}}, u, {x, y} \[Element] \[CapitalOmega], {t, 0, 20}, Method -> {"FiniteElement", "MeshOptions" -> {"BoundaryMeshGenerator" -> "Continuation", MaxCellMeasure -> 0.002}}] Note that we start with an initially Gaussian distributed tumour and describe its growth from there. Also I took the fourth power of the diffcoeff function, which changes the relation between grayscale and diffusion rate. You can change the coefficient to get different patterns for the growth. Interestingly, this integration gives a warning about intersecting boundaries in MMA10, which it did not say in the Prerelease version; if someone can fix that, that would be great. For any time we can now overlay the resulting distribution onto the CT image: ImageCompose[img3, {ContourPlot[ Max[sols[t, x, y], 0] /. t -> 2, {y, 0, 1}, {x, 0, 1}, PlotRange -> {{0, 1}, {0, 1}, {0.01, All}}, PlotPoints -> 100, Contours -> 200, ContourLines -> False, AspectRatio -> 798./654., ColorFunction -> "Temperature"], 0.6}] This should give something like this: ![enter image description here][3] Using frames = Table[ ImageCompose[ img3, {ContourPlot[ Max[sols[d, x, y], 0] /. d -> t, {y, 0, 1}, {x, 0, 1}, PlotRange -> {{0, 1}, {0, 1}, {0.01, All}}, PlotPoints -> 100, Contours -> 200, ContourLines -> False, AspectRatio -> 798./654., ColorFunction -> "Temperature"], 0.6}], {t, 0, 10, 0.5}]; we get a list of images, ![enter image description here][4] which can be animated ListAnimate[frames, DefaultDuration -> 20] to give ![enter image description here][5] This is only a very elementary demonstration, and certainly still far away from a "real" medical application, but it demonstrates the power of NDSolve and might, in a modified form, be useful as a case study for some introductory courses. Cheers, Marco [1]: http://www.springer.com/new+&+forthcoming+titles+%28default%29/book/978-0-387-95228-4 [2]: /c/portal/getImageAttachment?filename=brain-crop.jpg&userId=48754 [3]: /c/portal/getImageAttachment?filename=BrainTumor-still.jpg&userId=48754 [4]: /c/portal/getImageAttachment?filename=1473BrainTumor-frames.jpg&userId=48754 [5]: /c/portal/getImageAttachment?filename=BrainTumor.gif&userId=48754 Marco Thiel 2014-07-14T13:54:54Z https://community.wolfram.com/groups/-/m/t/2166833 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/cdf7d474-f4fb-4cbd-bbd5-f1fac8699f7a Siria Sadeddin 2021-01-18T22:46:11Z https://community.wolfram.com/groups/-/m/t/1896178 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- **Recent updates:** - [EpidemiologicalModelsForInfluenzaAndCOVID-19--part_1.nb][1] - [EpidemiologicalModelsForInfluenzaAndCOVID-19--part_2.nb][2] - [EpidemiologicalModelsForInfluenzaAndCOVID-19--part_3.nb][3] - [EpidemiologicalModelsForInfluenzaAndCOVID-19--part_4.nb][4] - [EpidemiologicalModelsForInfluenzaAndCOVID-19--part_5.nb][5] &[Wolfram Notebook][6] [1]: https://www.wolframcloud.com/obj/rnachbar/Published/EpidemiologicalModelsForInfluenzaAndCOVID-19--part_1.nb [2]: https://www.wolframcloud.com/obj/rnachbar/Published/EpidemiologicalModelsForInfluenzaAndCOVID-19--part_2.nb [3]: https://www.wolframcloud.com/obj/rnachbar/Published/EpidemiologicalModelsForInfluenzaAndCOVID-19--part_3.nb [4]: https://www.wolframcloud.com/obj/rnachbar/Published/EpidemiologicalModelsForInfluenzaAndCOVID-19--part_4.nb [5]: https://www.wolframcloud.com/obj/rnachbar/Published/EpidemiologicalModelsForInfluenzaAndCOVID-19--part_5.nb [6]: https://www.wolframcloud.com/obj/fcfa338d-3fd1-4918-8890-dad8b455ae16 Robert Nachbar 2020-03-11T17:39:06Z https://community.wolfram.com/groups/-/m/t/1888335 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- September 27: This site will now be updated about twice a month, middle and end. We will try to update the models. For the most part, the epidemics have run their modeling course and have taken a new turn in many places. We will maintain this site only as a source of information for a while longer, or until we compute new models for the renewed outbreaks. August 29: This site will only be updated on weekends or Mondays, from now on. We will try to compute new models based on fresh data if time allows. The Finland section will be changed somewhat. July 29: We now have a model for the world in the main section June 15, 22: (Notebook not yet ready today June 22, hopefully soon) -- As of June 22 I will be on holiday, or doing something else, until August 17. Some sections will not be updated on a daily basis. In the table of contents ("WHAT IS INCLUDED IN THIS POST" just below), I will indicate how often each section will be updated. I will also make a note to this effect in each of the corresponding sections. There are some forecasts which will be checked on the date that is given for the forecast. At times I will be in wilderness areas without electricity, so some updates at that time might not arrive promptly. Before June 22 (or a bit later, apologies) I will post a notebook which calculates parameters for some of the models automatically. There will be enough in it to get you started with your own data. The table of contents is updated now accordingly (and corrected) June 3-5: In a reply to the Europe section, a picture with forecasts for fatalities per capita for USA, UK, Sweden, and Italy, updated daily. Minor corrections in the text were made on June 5. May 29: contents have been reorganized slightly, the table of contents is now up to date again. See detailed update notices after the main text, and in each section (this post contains several sections where results are shown, see table of contents ("INCLUDED IN THIS POST") just a bit below. May 20: I have updated the table of contents ("INCLUDED IN THIS POST" below) NEW, May 10: Daily new cases forecast trends obtained from optimally fitted "TRUE" models (to learn about this, read the next paragraph and go to the response posted today at the bottom of the post ... it will be up in a few minutes). A notebook will be provided with some guidance as to how to obtain optimal fits almost automatically when I have time to finish putting it together. WARNING: There is a lot of details involved in what I am doing which gives rise to mistakes, especially when something new comes around. I just corrected some blatant ones. Hopefully they dwindle out to zero with time. On April 21, 26, and a importantly on May 3 and 4, I have tried to improve and restructure this presentation and make a note of various conceptual issues. I have also added "TRUE" (or truer) models of the outbreak (where the number of cases is matched to the R curve - read ahead). I realize that as it was before today (and maybe still), it was poorly and hastily written. I will continue to make improvements as I have time. If nothing else, please read this paragraph. Hopefully it is easier to read now and clearer. I specify where to find material in various sections, now close to the beginning and not in too many places. NOTE and DISCLAIMER: we are using a formalism to model data ... this is not exactly the same as having a model of the outbreak itself ... only an approximation that allows us to have some understanding the dynamics of the outbreak and make some forecasts with reasonable accuracy. Modulo the explanations of compartmental models ahead and in the linked post, for the purposes of modeling the outbreak, the only data we have is the number of detected cases. This corresponds to the R curve in the outbreak: each detected infection is an individual that de facto gets quarantined and removed from the infective process. We have no other data available. We don't have data that tells us when an individual becomes exposed or infectious. However, we are using a compartmental model differently: we are considering the R curve to be those individuals that have recovered from the infection or died. And the I curve as the number of detected cases minus those that have recovered and died. The point is, these definitions of our compartments are sound in the sense that they are disjoint (that is, true compartments); and the dynamics of how individuals move from one of our so defined compartment to another can be described with the equations of the SEIR and SIR models. And so, we have a model of the data which we are able to collect. To make this clear, we present in this section, along with other content outlined below, two models for the outbreak in Italy (for which the data is very good), a "TRUE" model of the outbreak, in which the data is matched to the R curve (removed individuals), and OUR VERSION of the model of the data as we have endeavored to look at it for the most part in this post. Without further ado: SEIR MODELS: For an explanation of SEIR (and SIR) models see Robert Nachbar's post: https://community.wolfram.com/groups/-/m/t/1896178 The equations of the slightly modified SEIR model are given ahead. It is possible to model the data by assuming a low enough susceptibility. I explain in the discussion with Robert Nachbar below why the main effect of containment measures is to lower the effective number of susceptible individuals when it is imposed (relatively speaking, at the beginning). Using this idea, it is also possible to model what could happen if you lift restrictions too early by letting the susceptibility increase (see picture) and you then reintroduced them (this is not a forecast, just a possible scenario). As a CAVEAT, these models are models using the DETECTED number of cases, not the TRUE number of cases, AT THE MOMENT THEY ARE DETECTED, not at the moment they are exposed or become infectious. Also, our compartments do not correspond to the compartments of a "true" model of the outbreak. We are taking the I compartment to be the number of detected cases minus the number of recovered and fatal cases, the sum of which is the R compartment. Our ASSUMPTION is that we can model the I compartment moving to the R compartment as individuals moving from being infected to being recovered or dead ... so intuitively we are tacitly assuming that our model gives us a picture of the outbreak with a delay, reflected in the data as it becomes available. Regardless of these considerations, our model allows us to understand how the disease evolves in time as it pertains to the data we have at hand. At least, we were able, in the Chinese model, to predict an end of outbreak time well in advance (the evidence is in Rimmer's response to this post where a similar prediction is made based on our model). INCLUDED IN THIS POST: 1) SEIR models for data from China. A SIR model for Italy. A "TRUE" SIR model for Italy and for the US. And a daily new cases forecast obtained from the "TRUE" model for the US. (The Finland model now lives in its own section (3) only, see ahead. The Spanish model has been replaced and lives in its own section (2). On the last weekend of May a new notebook will be available in the notebook section (5)). As of June 22 and until August 17, this section will continue to be maintained on an as frequent as possible basis, daily if possible. If not, in the updates below, I will indicate if there is to be a pause 2) In a response below, various models for Spain, UK, France, Germany, and Austria, see section for details. This section will be maintained once a week, on Mondays, starting June 22 and until August 17. 3) in a separate response below, two models for Finland (SIR and "TRUE"), a model as Norway, and "TRUE" models for Denmark and Sweden. In a reply to that section, there is detailed information for Sweden (case forecasts and fatality forecasts). From June 22 to August 17, both these section will be maintained on a daily basis if possible. Otherwise, you will be notified as to when updates will occur. 4) in a separate response, a brief discussion of SIR models (with models for China, Italy, and two more models for Finland) in a separate response. Also there, a document of cases/tests ratios for various countries in the SIR models section. This section includes a picture of positivity rates for several countries updated once a week. The positivity rates picture will be updated last on June 22, and again on August 17, weekly. 5) in a separate response, a notebook, towards the end of the post. This section includes a pdf document with dialy new cases for many countries updated once a week. By June 22, this section will contain a notebook which shows how to fit parameters automatically. From June 22 to August 17, the pdf document will not be updated. The notebook and pdf document are also posted in a reply to Kaurov, above the Scandinavian countries section. 6) Daily new cases forecast trends obtained from optimally fitted "TRUE" models in the latest response (May 10). Read more in the new section. Notebook will be provided to make automatic fits. From June 22 to August 17, this section will not be updated. 7) Fatalities per million for USA, UK, Sweden, and Italy. Details in the section, a reply to the Europe section. This section will be updated as frequently as possible between June 22 and August 17. SIR MODELS (see SIR section for equations) At the end of the post in a new response I discuss a simpler SIR-like model for the Chinese, Italian, and Finnish data which is practically as good - the equations are there. It has two advantages over the SEIR model: a) the classic SIR model has analytic solutions, so straightforward (somewhat) computational optimization can be carried out to estimate the parameters - although our equations are not the classical ones as they have a delay; b) it yields for the data we are trying to model values of R0 that are congruent to the observed ones, 5.43 for China - compared to 5.7 obtained in the just published study led by Steven Sanche and Lin Yeng-Ting, Los Alamos N. L. (arXiv:2002.03268) in Emerging Infectious Diseases, V26, Num 7 - (a note about this for the SEIR model below) without further ado (more on this ahead); and c) (UPDATE 3) if we look at the susceptibility curves (S in the diagrams), we see that they do not necessarily reach 0. If they are asymptotic to a positive value, that means there is a herd immunity effect - the value of the asymptote being the number of people who remain susceptible under containment that will not get infected; moreover, we can see that the susceptibility curve is very close to its asymptote near the peak of the infections curve (I in the diagrams), so that targeted testing is warranted as an effective measure of containment at that stage. That section contains a model of China (final) and a model for Italy (that is not updated), and a two models for Finland, one using the JHU data instead of the Finnish authorities data, and another one using another recovery schedule using an estimate based on the scant recovery data for Finland. A SIR model for Finland and the SEIR model alternate every so often here; the SIR model uses THL (Finnish health authorities) data. Both models are available in the Finland section, and the model for Germany in its section is, alternatingly, either a SEIR or a SIR model. We have removed, in the Finland, an SIR model that shows what it looks like to reach a plateau or steady state, rather than a peak; the equations for this are necessarily different than the simple SIR equations given in the SIR section, In the SIR section there are also other models for Finland, one using JHU and the other using a different recovery schedule. The newer models are adjusted quite frequently, especially with respect to the number of susceptible individuals, as they continue to grow. They tend to stabilize about three weeks after control measures have been in place. After the I curve peaks, it is possible to begin to get an idea of how long the outbreak will last. EQUATIONS and PARAMETERS OF MODIFIED SEIR MODEL Now the equations (for the SIR model, see the SIR section at the end of the post and after most of the discussions). s'(t) = -Beta * s(t) * i(t) / p, e'(t) = Beta * s(t) * i(t) / p - Sigma * e(t), i'(t) = Sigma * e(t - m) - Gamma * i(t - n), r'(t) = Gamma * i(t - n) The function s(t) is the number of susceptible people (the people that can get exposed to the pathogen) at time t. e(t) is the number of people that have been exposed to the pathogen and can become infected; i(t) is the number of people who are infected; r(t) is the number of people who have become resistant to the pathogen: they have recovered and developed immunity or died. Now the parameters. beta is usually considered to be the rate of infection or "force of infection"; sigma is the usually the rate at which an exposed individual becomes infective; gamma is usually the removal rate. We introduced m and n, shift or delay parameters to line up the model curves with the data. Here, we are operating with a delay. In our model, an individual is in the I compartment when it gets detected (a case of infection) and we continue to consider it infective until it gets "removed" when it has recovered or passed (not when it gets caught). In reality (in a true model of the outbreak, as in the second example for Italy in the pictures), individuals become infective before they get caught, and they get removed when they get detected. If we assume some kind of uniform delay in the process, we can try to fit the model to the data as we have compartmentalized it (cases and recovered+deceased). Thus we get a description of the dynamics of the outbreak as described by the data we can collect. IN ANY CASE, OUR MODELS ARE MODELS OF THE DATA ... the SEIR (SIR) formalism works well, and they have predictive value. The parameter values are in the titles of the pictures for each country. In general we assume e(0)=i(0)=1 unless stated otherwise in the model label. Also, s(0)=p, and r(0)=0. R0 in our SEIR-like and SIR-like MODELS: In the SEIR models, the basic reproduction number (R0) is constant and it depends on the parameters of the equations below. If we do the usual calculation (roughly beta/gamma in the equations below), R0 in our models is about an order of magnitude larger than the estimated-observed R0. There is an intuitive explanation for that. If we were to model the DETECTED number of cases using the BELIEVED or TRUE number of susceptible individuals, thought to be an order of magnitude higher than the detected ones, then we would need to scale down beta by an order of magnitude to get our results, among other things. That would give us the R0 that is being measured (my understanding is that R0 was estimated on DETECTED number of cases - but if this is wrong, then my explanation for the disparity is not correct). The main effect of lockdown is to lower the number of people that can be exposed to the pathogen when it is imposed, roughly at the beginning of the outbreak (see reply to Rober Nachbar's response for a thought experiment that explains this). Recall, the basic reproduction number (R0) is constant. The R0 numbers obtained in the SIR models discussed in a separate section are congruent with the values that are proposed in the research litereature (more about that in the SIR section). A NOTE ABOUT SOME DATA Some countries do not provide any or most data pertaining to recoveries. We have estimated this data, sometimes extrapolating from available data, sometimes using an estimating function based on average rates from countries that do provide the data, etc. It would take too long to discuss what we have done in each case where recovery data seems to be missing or partial. We explain the Finnish case. The THL (Finnish health authorities) data for the Finnish model comes from the Finnish Department of Health and Welfare (THL acronym in Finnish). There is a delay in the release of the data of 1-2 days. however, the recovery data comes from Johns Hopkins University and occasional reports from the Finnish authorities. According to the medical chief of staff of the infections diseases clinic at the Helsinki and Uusimaa hospital district, it was "important to define what people mean when they talk about recovery", and that "eventually it would be important to compile statistics to better understand the disease" and "was taking the numbers with a grain of salt" noting that "the criteria undrelying the data are not always clear and they are not always the same in each country". He also said that "tracking recovered patients was not a top priority". (quotes source is Yle news, the state run news agency). We have serialized the occasional recovery data according to how cases might have arisen in time to obtain a recovery rate function. We verify the accuracy of this function every time a new datum becomes available. We use this function also to estimate Norway recoveries. The US model now uses an alternative recovery schedule based on an average of the recovery schedules of countries which are providing these data, as the US recovery data seems lower than it ought to be. See my comment in the day's update (April 15). We also use an estimate for UK data which is not available. Some countries have changed the way they count in the middle of the process, and we have adjusted for this (or not) as we see fit - again, it would take too long to discuss this. For the most part, we use the data that is available and take it from there. SOME EXTRAS: In the notebook section, where there is space, I include a pdf document with a smoothened version (14 day moving average) of the daily tallies for several countries in Europe, as well as USA and South Korea. In the SIR section, where there is space, there is a picture of the current positivity rates (number of cases/number of tetsts conducted so far). It is a useful diagnostic of where a country stands in the process. August 29 - September 5,12,20,27: updated. We will update the US daily tally only once every two weeks now, during weekends. There is now sufficient data for a new model. We will try to compute it if we have time. Next update, in two weekends. August 22-28: updating ... We will stop updating the Italian model ... it has run its course, and Italy is on its way to new growth. We shall continue updating the US daily pictures and the weekly US and world models. There is now sufficient data to compute a new model for the US. Hopefully we have time to do this soon. August 2-21: Updated. Weekly readjusted today, 16th. The weekly models for the world and US are updated. It appears the situation in the US is now stable (no more growth) but there is a long tail ahead. You can see this from the daily case numbers as well. July 28-August 1: Updated. We are replacing the TRUE model for US with a TRUE weekly model based on the second rise in the outbreak, which is now starting to stabilize. We project 11 million detected cases in a stretch of about 60 weeks starting our count on June 7 (but the final number might be less if a vaccines becomes available before that). We will try to derive a forecast from this model later and combine it with the daily cases counting graph. We have removed one of the pictures for Italy and put up a new model for the whole world. More data is needed to get a good estimate on the projected number of cases - our guess, at least twice what this model suggests. June 19-July 27: Updated. Our model for the US will have to be recalculated once things stabilize. Right now there is very substantial growth in the number of cases. Results for Italy will be posted with a delay of one day. This section will continue to be updated daily after June 22, unless a note to the contrary is made, for example, during travel in the wilderness without access to electricity. June 13-19: Updating. It seems there is an uptick of cases in the US. We note there is a fatalities per Million model in a reply to the European section for several countries (Italy, USA; Brazil, Sweden, and the UK). This modeling, matching the R curve of a SIR model to fatalities per million cumulative provides a forecast of fatalities for those countries. Our forecast is compared to those of IHME and other institutions. Details are in that section May 29-June 12: Updating. I have removed the Finland model in this section, it can still be found in the section for Finland and the Nordics. And I move up to this section the daily new cases forecast that comes out of the "TRUE" model for the US. It might illustrative to show what you can get out of this model. At the very bottom of this post in their own section similar forecasts for Italy and the Nordics can be found. We also have a new fit for the "TRUE" model for Italy. May 28: There is a new model fit for Finland. There is also a new model fit for USA. At the bottom of the post, in the last section, there are new forecasts for the daily number of cases ... you can compare the old and the new model fits. May 23-28: Updating. We will wait until the end of May to fit a new "TRUE" model for the US. A semiautomatic, almost optimal fit for the Finland model has been obtained. We will try to fit models automatically from now one, slowly but surely. An automatically fitted, almost optimal SIR model for Italy is now posted. May 19-22: updating. On May 20 the table of contents above ("INCLUDED IN THIS POST" section) was updated. May 18: there is no data for Finland May 17 yet. May16-17: The Italy "TRUE" models has been fitted again this weekend; next weekend we do the U.S. May 10-15. Updating. The US and Italy "TRUE" models are now optimally fitted. The Italy model is fitted to 4 May when restrictions were lifted. A notebook to do this will be provided later. From these models one can derive the daily new cases forecast trends in the new section at the end of the post (for more info, read there, it will be up shortly). It takes about 2-4 hours of compute time to make some of these fits. These models will not be fitted again as restrictions are slowly lifting ... which changes the forecast, hopefully in a noticeable way (or hopefully not, from the state of things point of view). The Italy SEIR model has been replaced by a SIR model. Earlier on May 10 I had posted the wrong file for the US model ... it is now correct. And apologies, had the wrong label on the Italy "TRUE" model, now corrected (hopefully) ... May 8-9: I will leave the "TRUE" model for the US now. It is perhaps the most reliable picture of what lies ahead. One of my usual SEIR models forecasts a higher (4.4 million) susceptible population, but that number does not square with the "TRUE" model, although soon I will do an automatic and optimal fit of it, which might push this number up. Over the weekend, a new model for Italy will be forthcoming and "TRUE" models will start to be produced in a fully automated way (I will later post a notebook with the code that does the optimization; it is written withing the simplicity of built in Mathematica functionality, which means it is somewhat slow and NMinimize needs help. May 6-7: Updating. Soon we will have to update our standard model for Italy. The "TRUE" model looks very reliable now, enough to make long term forecasts and provide a picture as to what to expect in the longer run. May 5: The US SEIR models will now alternate with a "TRUE" SIR model (see first paragraph of text above and subsequently for explanation). Also, there is an SEIR model for Italy and now a "TRUE" SIR model as well. April 30 - May 4: updating, US model alternating every so often April 29: updating. Today I put back the US model with the actual recovery data that is provided. The two models will alternate. One of our alternative Finnish models squares with the latest THL recovery estimates, so we are showing that model instead of the model we had yesterday. This picture will be updated again at 2 PM EEST. April 28: Tomorrow I will start alternating the US model with the model obtained from the recovery data that is provided. I found a source of daily increments for the Spanish data. The Italian model has been stable now for weeks, since before the peak of the I curve. Their official data is quite good comparably speaking. April 27: updating. I will not update Spain after today until I get hold of the data from local authorities if I can. The JHU data is inconsistent both in number of cases and in recoveries. It seems the historical series is being updated retrospectively, but according to the Spanish authorities, it is not yet ready. The temporary lump sums provided temporarily make for very poor data. When it becomes ready, I will continue to update this model. If I can obtain reliable information from press reports, I will update my data thus by hand. April 25-26: updating. Today, April 26, the recovery data from Spain is highly anomalous, for the second time (in the past, counting method changed). Unless this datum is corrected, from now on I will use an estimate based on a recovery rate function that can be computed from the data up to yesterday, or constant adjustment as of today based on today's estimate. Using this function, we obtain today's picture. April 24: updating. It seems the model for Spain might require a steeper rise up again. April 23: updating. I have posted yet a new model for Finland which is probably more accurate. It is hard to say, as the entire time series changes each day due to delays in testing reports. The date in the Spanish model is now correct. I seem to have made, unfortunately, a correct forecast of the consequences of going back to work too soon! April 22: updating. Spain went back to work ten days ago. We see new growth and forecast it will continue so ... may we be wrong. April 21: updating. I changed the text above to improve it and hopefully make it more readable, and highlight important issues. I changed the standard SEIR Finland model for an SIR model that to me, seems more realistic, given the daily tally trends. The problem with Finnish data is that the entire time series gets corrected every day, not just the last day. While this makes for accuracy, it makes modeling difficult. I will alternate with the usual SEIR model. April 19+20: updating. There is yet another model for Finland using another estimate for the recovery schedule. At the end of the SIR section there is a picture of the current positivity rates (number of cases/total number of tests). This should be a useful diagnostic. I will start keeping a history of these data from now on (I only have a history for Finland). April 18: updating. There is an additional model for Finland in the SIR section using JHU data instead of THL data April 17: updating. This section now has the SIR model for Finland, we believe it is a more accurate model for the time being, and based on a just published estimate of recoveries. Our extrapolating function seems to be working quite well and we have adjusted it to reflect this last change. April 16: updating. The German model in its section is now an SIR model. In the Finland section there is a SIR model in which a plateau, rather than a peak, is reached April 15: updating. Today I will show an alternative model for the USA that uses an average recovery rate obtained from other countries rather than the reported data, which seem low (understandably so, it is not a priority to test people who have tested positive and are recovering at home). The daily tally in the US has slowed down somewhat, which would lend credibility to the model, which shows the infection curve getting close to a peak. Also, in the previous model, the number of susceptible individuals was probably too high. I will compute an estimated peak date tomorrow based on this model. I will continue to track the old model, but it doesn't fit here. I am thinking of adding another response to the post with a number of models which don't fit here, but I haven't made up my mind about it yet. April 13-14: Today is the last day the China model will be updated (April 13). April 14: I am adding a SIR model of Italy in the response with the SIR model for China. There is also a SIR model for Finland in the Finland section. It is possible to compute an effective R that is time dependent (but that won't be in the post, although I will make a notebook available in that section at a later time with this). I will add SIR models for other countries as well. I am working on an optimization program for the SIR model to further automate the determination of parameters - if I ever complete this it will also be in the SIR notebook eventually. On another note, I plan to add a section with models for other Scandinavian countries as soon as I have time. April 12: updating. Today I am adding a response with a section which discusses the simpler SIR-like model (which I managed to make work almost just as well as the SEIR model, although it is somewhat more difficult to get it to work). The SIR-like model has the advantage that analytical solutions are known for SIR models which might be modified for our specific instance of the model, and in the case of our investigations, it yields an adequate value for R0 without the need for any further explanations. April 11: updating. The daily tally pdf document in the Finland section is now per million inhabitants. Again note the disparity between European countries wishing to pursue an exit strategy at the moment, and South Korea, the role model country. I have added a picture which explores a scenario in which Spain lifts restrictions (as it has announced) today. We are able to model (with some mathematical ingenuity) the effect of this on the S curve, and subsequent effect on the number of infections. We hope this does not happen, but it might. April 10; updating. I added some explanations in the text and a picture that illustrates what could happen when restrictions are lifted too early and then reintroduced - this is not a forecast, just a plausible scenario. I moved the notebook to a new response at the end of the post. April 9: updating. In the Finland section there is a pdf document with the smooth version of the daily tallies for several Euro countries, USA, and South Korea. The Italy model seems very stable now. April 8. Updating. Today I added, in the main part of the text above, an "intuitive" note about the basic reproduction number (R0) in these models and why they are about an order of magnitude larger than the measured rates. April 6-7. Updating throughout the day. France and UK models temporarily suspended due to missing or inconsistent data, until more data is available April 5: Updating throughout the day. There is a new model for Austria in the Europe section. It's I curve has p Enrique Garcia Moreno E. 2020-02-26T16:43:12Z https://community.wolfram.com/groups/-/m/t/1911422 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- ## Are the measures taken getting us closer to herd immunity? ## In this post I will look at one simple, but very important, aspect of a pandemic, namely herd immunity and what's required to reach it. My ambition is to write something that does not require any mathematical experience and that hopefully leaves you with a positive feeling at the end. *If you already know how exponential growth and herd immunity work, you may skip the first two sections.* ## Exponential growth - What is R0 and why is it important? ## By now, most of you have heard about the R0 ,or basic reproduction number. To understand herd immunity you need to understand this number. R0 tells you how many people, on average, each infected person will infect. If one person infects two on average, then the number is two. Below you can test a few different values and see how many persons will be infected within four steps (even though not entirely correct, you can think about it as days if you like) depending on R0 number. Select the R0 number and then drag the slider to see how many have been infected at any given point in time. ![Initial stage with R0 2][1] Infection after three days with R0=2: ![Stage three of infection][2] For simplicity I have assumed that it takes one day before an infected person has infected everyone that they will infect. For COVID-19, just as for most it actually takes longer, so this slows down the process somewhat. However, the principle is the same. COVID-19 is believed to have an R0 number between 1.4 and 3.9 ([reference][3]). As you can see the number of infected grows incredibly fast already at the higher range, but a bit more modest at lower. If we assume no immunity, i.e. people can get sick again and again, then the growth for values between 1 and 4 would look like this: ![growth depending on R0 - linear][4] The red dashed curve represents R0 = 3.9, i.e. the upper range of COVID-19, and there is a green dashes representing the lower range, R0 = 1.4. This has a growth rate that is so close to zero, so it is hard to detect it. If we change to a a logarithmic plot it is easier to see: ![growth depending on R0 - logarithmic][5] ## Immunity - How does immunity impact the epidemic? ## Most people that get infected will recover and get immune. Let's look at the case of R0 = 2, with 50% of the population being immune. If you click the immune checkbox every second point will become green, indicating people that are immune. Now, the first infected will only infect one person, meaning that the first immune person is protecting every person on the left side. The first person at the right will be infected, but yet again he will only infect one person. ![illustrating immunity][6] Immunity will not spread equally of course. For instance, instead of the scenario I showed above we could imagine that everyone at the left side is immune and non at the right hand side. The the whole right hand side would be infected after 5 days. On the other hand it is enough that person 2 and 3 are immune to stop the entire disease. Of course the populations we are talking about are much larger than this example and people are connected in much more advanced network. However, the example above illustrates well the behavior one can expect in this situation. This can be summarized in a very simple equation: s = 1 / R0 where s is the proportion of the population that is susceptible to the virus. Thus for R0 = 2 gives a threshold of 50%, R0 = 3 gives 33%, and R0 = 4 gives 25%, meaning that 50%, 67%, and 75%, respectively, has to be immune in order to achieve herd immunity. The average estimated R0 for COVID-19 is 2.65 which corresponds to around the 60% immunity that you probably heard epidemiologists talk about. ## Current immunity and growth rates ## Let us look at the current development in a few countries and how many have been identified as infected this far. I will remove the initial phase, and start from the day that each country reached 100 confirmed cases. ![infected population - linear][7] This looks quite different from the graph *"Growth of infection for different R0 numbers - linear scale"* showed previously, so let's look at the data in a logarithmic scale: ![infected population - logarithmic][8] Instead of being straight lines as shown in *"Growth of infection for different R0 numbers - logarithmic scale"* the lines are flattening out over time. Why? There are basically two possible solutions - either the population is getting immune - or the policies taken are having effects. The graph, *"Percentage of population that has been known to be infected - linear scale"* showed that there has been so few cases yet, that there is probably no effect at all from herd immunity. At least assuming that the number of know cases are within one order of magnitude of the actual cases. Therefore the effect that immunity has on this policy dependent R0, let's call it RO^, can be neglected at this stage of the process (if we are lucky though there are a lot of unknown cases, that can help us get to herd immunity faster). Thus, the decrease of RO^ is likely due to policies. If we take the ratio between each days we will get the current RO^: ![daily growth rate][9] It is obvious that RO^ decreases over time for all three countries. This is actually the case for all countries, except for possibly the US. As seen it is very close to 1 in the case of South Korea, and even Italy is below 1.1! ## Herd immunity - and why we are closer to reach it then you think ## Remember that herd immunity is achieved when s = 1 / R0 If we consider the case that each country maintains it's current policies, the herd immunity under those conditions is: s = 1 / RO^ So let us look at which proportion of the population needs to be immune in order to get herd immunity. - Use R0 min and RO max to set an interval - The grey zone shows the R0 range (1.4 - 3.9) for COVID-19 according to current studies. - The orange will highlight your currently selected range (deactivated by default) - The blue range shows the current RO^ for countries with more than 100 cases (ranging from South Korea and possibly China to the US). - The horizontal lines show the immunity needed to reach herd immunity (i.e. between 29% - 75% for COVID-19) ![R0 and immunity][10] Setting R0^ = 1.02 (South Korea's current value) results in only 2% needed for herd immunity, given that the current policies are kept. Sweden's 1.05 corresponds to 5%. ![R0^ and immunity][11] Of course these estimates are a bit rough, but they clearly give more hope that the measures taken in different countries are actually getting us towards herd immunity, if nothing else at least a policy dependent herd immunity. I plan to make a new post regarding how to use these policy dependent herd immunity to get towards a real herd immunity. [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=h1.png&userId=149796 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=h2.png&userId=149796 [3]: https://en.wikipedia.org/wiki/Basic_reproduction_number [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=h3.png&userId=149796 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=h4.png&userId=149796 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=h5.png&userId=149796 [7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=h6.png&userId=149796 [8]: https://community.wolfram.com//c/portal/getImageAttachment?filename=h7.png&userId=149796 [9]: https://community.wolfram.com//c/portal/getImageAttachment?filename=h8.png&userId=149796 [10]: https://community.wolfram.com//c/portal/getImageAttachment?filename=h9.png&userId=149796 [11]: https://community.wolfram.com//c/portal/getImageAttachment?filename=h10.png&userId=149796 Jan Brugard 2020-03-27T17:00:17Z https://community.wolfram.com/groups/-/m/t/2437685 I'm very happy with the continued improvement of the Dicom import and export functionality and speed. However, there is one issue with the current implementation that makes it very unuseful if you do quantitative image analysis. It might be that I miss an option if not I think this should be fixed. In the Mathematica documentation and examples, Dicom data is typically shown and imported as images which I understand for display purposes. But I consider the information in Dicom files as data, very well curated and standardized. For many (MRI) applications, the actual quantitative values of voxels stored in Dicom actually have meaning, values, and even units. For example in the image below each voxel value is actually a quantitative measure of T2 relaxation time in the heart, where the values are stored in milliseconds as voxel values as is also mentioned in the metadata. ![enter image description here][1] ![enter image description here][2] To get from the stored values to quantitative values (WV, DV or FP) the fields from the header and the equations are well defined. Header values: - SV = stored value of DICOM PIXEL DATA without scaling - WS = RealWorldValue slope (0040,9225) "RWVSlope" - WI = RealWorldValue intercept (0040,9224) "RWVIntercept" - RS = rescale slope (0028,1053) "RescaleSlope" - RI = rescale intercept (0028,1052) "RescaleIntercept" - SS = scale slope (2005,100E) "ScaleSlope" Outputs: - WV = real world value - FP = precise value - DV = displayed value Formulas: - WV = SV * WS + WI - DV = SV * RS + RI - FP = DV / (RS * SS) So my first try was that I want to obtain the "RawData" to access the SV pixel data, which does not output anything. ![enter image description here][3] Eventually, if I import this Dicom file into Mathematica I have to use a lot of tricks to get to the correct stored values. The Dicom images I use are stored as 12-bit Integers but are converted by Mathematica to a Numerical array with type Int16. Also, I have to specifically specify that I don't want any "DataTransformation" which by default rescales the data and actually changes some voxel values!!!! In[1]:= << QMRITools` {meta, data, bd} = Import[file, {"dicom", {"MetaInformation", "Data", "BitDepth"}}, "DataTransformation" -> None]; dataT = Import[file, {"dicom", {"Data"}}]; {dd = ToExpression[ StringJoin @@ StringCases[NumericArrayType[data], DigitCharacter]], bd} {ss, rs, ri} = meta /@ {"2005_100e", "RescaleSlope", "RescaleIntercept"} {data, dataT} = Normal@{data, dataT}; svT = 2.^bd (dataT/(2.^dd)); pfT = (rs svT + ri)/(rs ss); sv = 2.^bd (data/(2.^dd)); pf = (rs sv + ri)/(rs ss); PlotData[pfT, pf] Out[3]= {16, 12} Out[4]= {1.99854, 0.500366, -2.} For my current research, I need the PF values and to get them correctly I have to: 1. Use "DataTransformation"->None, which is not really well documented what it actually does. But based on what I see actual values of the data are changed by clipping the histogram, which for default handling of medical data is never OK!! ![enter image description here][4] 2. As far as I am aware the only way to obtain the actual stored values of my Dicom data (the actual binary values stored in the file itself) I have to find the actual BiteDepth and the imported data type and rescale my data accordingly. Below are the obtained PF valued data I need with and without DataTransformation. Although the image on the right might look less appealing with default range and scaling it is actually correct when scaled apropriately. ![enter image description here][5] ![enter image description here][6] Am I missing a correct option for getting the actual data stored? If not this should definitely be changed. Dicom is the international standard to transmit, store, retrieve, print, process, and display medical imaging information. With the current implementation, it is impossible to Import and Export such files without actually changing the stored data. Thanks, Martijn [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=dcmtag.png&userId=1332602 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=T2map.png&userId=1332602 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=raw.png&userId=1332602 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=hist.png&userId=1332602 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=dataTrans1.png&userId=1332602 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=dataTrans2.png&userId=1332602 Martijn Froeling 2022-01-05T09:42:43Z https://community.wolfram.com/groups/-/m/t/568284 Wolfram Language has very detailed built-in data about Anatomical Structure. Here is an example of usage building an interactive models of brain. First we would need some data. Because anatomical parts constitute of smaller parts and so forth, we can visualize anatomical structures as trees, for instance: ![enter image description here][1] To get that I need to build a data crawler: crawler[root_, depth_] := Flatten[Rest[NestList[DeleteCases[Union[Flatten[ Thread[# -> DeleteMissing[EntityValue[#, EntityProperty["AnatomicalStructure", "RegionalParts"]]]] & /@ Last /@ #]], HoldPattern[_ -> Sequence[]]] &, {"" -> root}, depth]]]; start from brain and get down 3 levels of anatomical structure: edge = crawler[Entity["AnatomicalStructure", "Brain"], 3] ![enter image description here][2] Get edges, vertices, and labels as images of anatomical parts: g = Graph[edge]; vert = VertexList[g]; lblsT = Rasterize /@ vert; The image at the top is build with `ContextualizedHighlightedImage`: lblsI = Module[{tmp}, tmp = EntityValue[#, EntityProperty["AnatomicalStructure", "ContextualizedHighlightedImage"]]; If[ImageQ[tmp], ImageCrop[tmp], "N/A"]] & /@ vert ![enter image description here][3] we can also try just with `Image`: lblsI = Module[{tmp}, tmp = EntityValue[#, EntityProperty["AnatomicalStructure", "Image"]]; If[ImageQ[tmp], ImageCrop[tmp], "N/A"]] & /@ vert ![enter image description here][4] A quick way to get a non-interactive tree like plot: GraphPlot[edge, VertexLabeling -> True] ![enter image description here][5] But for fancy interactivity and to preserve Graph data-structure we write a short code and get the top nice image in this post: tltps = Tooltip @@@ Transpose[{lblsT, lblsI}]; TreeGraph[vert, edge, VertexLabels -> Thread[vert -> (Placed[#, Center] & /@ tltps)], ImageSize -> 700, GraphStyle -> "ThickEdge", GraphLayout -> "RadialEmbedding"] ![enter image description here][6] That was a good programming exercise and now we can appreciate how recent function [**NestGraph**][7] can make things much easier: NestGraph[Cases[EntityValue[#, EntityProperty["AnatomicalStructure", "RegionalParts"]], _Entity] &, Entity["AnatomicalStructure", "Brain"], 4, ImageSize -> 700, GraphStyle -> "SmallNetwork", GraphLayout -> "RadialEmbedding", VertexLabels -> Placed["Name", Tooltip]] ![enter image description here][8] We can also build a 3D interactive model app. For example, choose specific brain parts bParts = { Entity["AnatomicalStructure", "ParietalLobe"], Entity["AnatomicalStructure", "Cerebellum"], Entity["AnatomicalStructure", "PituitaryGland"], Entity["AnatomicalStructure", "OpticChiasm"], Entity["AnatomicalStructure", "Hypothalamus"], Entity["AnatomicalStructure", "ChoroidPlexusOfCerebralHemisphere"], Entity["AnatomicalStructure", "HippocampalFormation"]} ![enter image description here][9] and get their 3D models: bParts3D = EntityValue[bParts, EntityProperty["AnatomicalStructure", "Graphics3D"]]; And then we can build an app with just few lines of code: Manipulate[ Show[Graphics3D[], x, ImageSize -> {400, 400}, SphericalRegion -> True, Boxed -> False, ViewAngle -> .27], {{x, bParts3D[[1]], ""}, Thread[bParts3D -> bParts], CheckboxBar, Appearance -> "Vertical"}] ![enter image description here][10] You can also get MeshRegion ![enter image description here][11] to do some computational geometry, for example: RegionMeasure[%] `1482.164538484` Of course you can check for any anatomical part and also its properties: EntityProperties["AnatomicalStructure"] ![enter image description here][12] [1]: /c/portal/getImageAttachment?filename=sdfreqtwry6745etwrgafhsfnfbsd.gif&userId=11733 [2]: /c/portal/getImageAttachment?filename=ScreenShot2015-09-21at10.51.26AM.png&userId=11733 [3]: /c/portal/getImageAttachment?filename=trye75675rgtwrgfhsfhatq45.png&userId=11733 [4]: /c/portal/getImageAttachment?filename=ScreenShot2015-09-21at10.53.42AM.png&userId=11733 [5]: /c/portal/getImageAttachment?filename=sdsdfeqt546whr6w45.png&userId=11733 [6]: /c/portal/getImageAttachment?filename=sdf34t54y65uejythrtsgdfhadf.gif&userId=11733 [7]: http://reference.wolfram.com/language/ref/NestGraph.html [8]: /c/portal/getImageAttachment?filename=dsf45y6u5jhrtdgfas.gif&userId=11733 [9]: /c/portal/getImageAttachment?filename=ScreenShot2015-09-21at9.38.16AM.png&userId=11733 [10]: /c/portal/getImageAttachment?filename=ewr435trhsgfdas.gif&userId=11733 [11]: /c/portal/getImageAttachment?filename=ScreenShot2015-09-21at10.46.37AM.png&userId=11733 [12]: /c/portal/getImageAttachment?filename=ScreenShot2015-09-21at11.04.18AM.png&userId=11733 Vitaliy Kaurov 2015-09-21T14:40:23Z https://community.wolfram.com/groups/-/m/t/1887823 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- &[Italy and South Korea][1] [1]: https://www.wolframcloud.com/obj/ac179b9c-d365-4c8e-a3bb-9d4348a589ef Robert Rimmer 2020-02-26T02:18:26Z https://community.wolfram.com/groups/-/m/t/2927764 ![Introducing the Wolfram ProteinVisualization paclet!][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main2.bmp&userId=20103 [2]: https://www.wolframcloud.com/obj/353c8f22-23af-4a49-b43c-b0b0f1645249 Soutick Saha 2023-05-31T14:38:54Z https://community.wolfram.com/groups/-/m/t/1931352 *MODERATOR NOTE: Wolfram notebooks are attached at the end of the post. For more coronavirus resources, updates, and discussions see:* https://wolfr.am/coronavirus ---------- ![Pandemic model and one scenario][1] By now you have all heard that fighting the Corona virus is all about flattening the curve. It sounds easy, doesn't it? ![Flattening the curve][2] However, despite that the maths behind the scenes is rather simple, flattening the curve turns out to be quite complicated. What happens if you don't do enough? How important is timing? What's the risk of doing too much? With the help of System Modeler, the Wolfram Language, and my wonderful colleagues (thanks for having patience with me) I have developed a COVID-19 - Policy Simulator. The ambition is not to give any precise numbers, but to make it easier to understand how simple yet at the same time complicated it is to control a pandemic. While developing the simulator I realized that my intuition was far from correct in many cases. I doubted the results more than once, and was sure there were mistakes in the model, but most of the time it turned out that it was not the model faulting - it was my intuition. Will your intuition be better than mine? Download the recently released [HighSchoolBiology Virtual Lab 1.1][3] and use it together with this notebook to test your intuition! The screenshot below shows a naive attempt to set policies. As seen it leads to a disaster at the end of the year. ![Naive policy][4] I hope that using this simulator should give you a good idea of how complex it is to find the optimal path through a pandemic, and also to some extent why a recipe that works in one country does not apply to another. ## The simulator ## *Important: Let me repeat that the simulator is not exact. Many rather rough assumptions are made for several different reasons. Most of these , but not all, are mentioned and discussed in a separate notebook. The development notebook shows how I proceeded to roughly tune the default parameters, so they reflect the state in Sweden in the beginning of April 2020. As countries differ in population density, traditions, political structure, age distribution, healthcare system, and so many other things the impact of different policies will vary substantially between countries. Therefore, I made it possible to vary the impact of the policies I have chosen to use. Is your country already very socially distant? Then, further social distancing will probably not have as big of an effect as in other places, and so on. In most cases the simulator allows you to modify some of the assumptions by your self.* In this simulator you can enact the following policies: - Improved hygiene (washing hands, cough in elbow, don't touch your face, etc) - Social distancing (keep away from each other, no handshaking, work from home, etc) - Isolate the sick (even stricter social distancing when your sick) - Lockdown (close restaurants, schools, shops) - Seasonal effect (not really a policy, but something that you might hope for.., but will it always be beneficial on the long run?) - Close borders (when borders are closed, they are hermetically closed, so no infected persons at all enter the region) Applying policies will typically decrease the exponential growth rate. However, if you have already enacted lockdown, then social distancing will give no further effects. In reality it might actually do that, however to avoid making the simulator overly complicated I have chosen this simplified solution. Other things that I have omitted are e.g. testing, masks, and tracking apps (partially because I have limited data to tune the model with, but mostly to keep the simulator simple). ![COVID-19 Policy Simulator][5] On the right hand side of the simulator you can change several settings, including - Infection properties - Default is set to the currently believed mean values - Policy effects - The first five, will reduce the exponential growth - Close borders, when the borders are not closed the number shows how many persons per 100k susceptible that are infected by travelling abroad each day - Initial setting - Change population and current state, e.g. start with no infected - Vaccination - Enact a vaccination policy, setting start date and how many percent of the susceptible population that is vaccinated per day - Healthcare - Set the number of available beds - Additional plots - Default - Adds a plot using the default values, to make it easier to see the effect of your current policies and changed assumptions - No policies - Adds a plot using your current assumptions, but no policies - Beds - Show the number of beds - Susceptible, infected, and recovered - Add any of these three to the plot - Simulation end time - By default the plot is zoomed in to 120 days, to see what happens later (or to zoom in at earlier stages), you can change this. Note again that there are many measures that are not included, but I believe these are the most important in order to understand the dynamics of a pandemic. Furthermore, I am assuming that the effect of an active policy does not change over time. In reality, of course, a lockdown is likely to me more respected in the beginning then after a few months. Finally, I am completely disregarding both short and long term side effects that policies might have, e.g. effects on economy, education, and healthcare. Note that you can use the menus on the top right of the simulator to - Hide controls - Paste snapshot - Reset to default values Try to set your best policy, and comment on the strengths and weaknesses you see with it. If you like you can send us an email to virtuallabs@wolfram.com with your strategy or suggestions for improvements. Note, that by including a snapshot in your answer, you make it easier for us to see what you have done. Example strategies ---------------- Let's just conclude this by showing three strategies: - Do nothing - Complete lockdown -waiting for a vaccine - Compromise The first one, is shown in the default simulation. It shows that more than 40,000 people will need intensive care at the end of April if we follow this tactic. With a limit of 2,100 beds this is a disaster. ![No policies][6] Now let us enable improved hygiene,isolation of sick, social distancing, lockdown, and close border for a quarter and see what happens. It looks great to begin with, but as soon as the policies are lifted we have a problem that is almost just as big as in the first case. ![Delayed pain][7] Finally, let us try to be a bit more clever. Turning the first three policies on and off over time, and then finally turning all off I got something that looks a lot more promising. In this simulation I am turning of the last policy beginning of February 2021. I am assuming that no vaccine will be available during this time and that there are no seasonal effect. Of course turning policies on and off is probably not the easiest thing to achieve in reality, but it is possible, at least as long as full quarantines are not needed. ![A bit more promising][8] Alternative setups ------------------ As mentioned, the model has been roughly tuned to Swedish circumstances. In doing so I have assumed that Sweden has an R0 value of 2.65, i.e. exactly the mean value. In reality I would believe that we have a lower value (a pure guess would be 2). Changing this assumption will change other values as follows: ![Table][9] I recommend you to test these scenarios by yourself. Note that on April 7, the estimated range of R0 of COVID-19 went up to 3.8 \[Dash] 8.9 on Wikipedia. How does this affect the model? Find your best policy, or insight, and let send us an email to virtuallabs@wolfram.com with your strategy or suggestions for improvements. *I have attached two notebooks to this post. the first is the interactive version of this post and the second contains more details on the model, assumptions, and code. Remember that you will need the [pre release][10]) of the [HighSchoolBiology Virtual Lab 1.1][11] (or wait until it is available)* [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=p1.png&userId=149796 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=FlattenCurve.gif&userId=149796 [3]: https://www.wolfram.com/system-modeler/libraries/high-school-biology/ [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=p3.png&userId=149796 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=10624Covid-19-simulator.gif&userId=149796 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=p5.png&userId=149796 [7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=p6.png&userId=149796 [8]: https://community.wolfram.com//c/portal/getImageAttachment?filename=p7.png&userId=149796 [9]: https://community.wolfram.com//c/portal/getImageAttachment?filename=p8.png&userId=149796 [10]: https://download.wolfram.com/?key=FDW6Q5 [11]: https://www.wolfram.com/system-modeler/libraries/high-school-biology/ Jan Brugard 2020-04-09T15:58:59Z https://community.wolfram.com/groups/-/m/t/1903289 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/ea3730f2-681f-488a-8c9b-76857f000e80 Arnoud Buzing 2020-03-21T23:18:15Z https://community.wolfram.com/groups/-/m/t/1901002 *MODERATOR NOTE: coronavirus resources & updates:* https://wolfr.am/coronavirus ---------- ![enter image description here][1] &[WolframNotebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3687ezgif.com-optimize.gif&userId=11733 [2]: https://www.wolframcloud.com/obj/c443430b-2f0e-461a-ad95-801016802147 Francisco Rodríguez 2020-03-18T01:05:06Z https://community.wolfram.com/groups/-/m/t/3327934 ![Animating a human skeleton using motion capture data][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=AnimatedSkeleton.gif&userId=20103 [2]: https://www.wolframcloud.com/obj/6f5b2224-0792-4d8d-84a1-8bce5125c0f4 Catalin Popescu 2024-11-24T23:40:07Z https://community.wolfram.com/groups/-/m/t/1911583 ![enter image description here][1] The New York Times recently published [COVID-19 time series data for each US county](https://github.com/nytimes/covid-19-data). This gives us a very granular look at the spread of the illness over time. This will let us approximate the distance to the nearest confirmed COVID-19 case for any given location in the US. -------- To start this task, first we import the data, canonicalize each time series to start on Jan 21, and only keep the lower 48 states: COVID19CountyData = ResourceFunction["NYTimesCOVID19Data"]["USCountiesTimeSeries"]; COVID19CountyData = COVID19CountyData[All, "Cases", TimeSeries[TimeSeriesInsert[#, {DateObject[{2020, 1, 20}], 0}], ResamplingMethod -> {"Interpolation", InterpolationOrder -> 0}] &]; COVID19CountyData = COVID19CountyData[KeySelect[!MissingQ[#] && !MatchQ[#, Entity[_, {_, "Alaska" | "Hawaii", _}]] &]]; Next we'll sample points in the US by discretizing its polygon, and then interpolating distances from these samples: usstates = EntityClass["AdministrativeDivision", "ContinentalUSStates"]; usa = RegionUnion[BoundaryDiscretizeGraphics /@ usstates["Polygon"][[All, All, 1]]]; usatri = DiscretizeRegion[usa, MaxCellMeasure -> .05]; usasamp = GeoPosition /@ MeshCoordinates[usatri]; Here are the points we'll be sampling from: MeshRegion[TransformedRegion[usatri, ReflectionTransform[{1, 0}]@*RotationTransform[π/2]], MeshCellStyle -> {0 -> {PointSize[Small], Red}, 1 -> {Thin, Black}}] ![enter image description here][2] Here's the `GraphicsComplex` we'll be adding `VertexColors` to: usagcomp = GraphicsComplex[ GeoPosition[MeshCoordinates[usatri]], MeshCells[usatri, 2, "Multicells" -> True] ]; For each point, to find the `GeoDistance` to the nearest affected county, we'll approximate by finding the nearest `GeoPosition` of the county polygons. This will speed up calculations. countypolys = EntityValue[Normal[Keys[COVID19CountyData]], "Polygon", "EntityAssociation"]; Finally, we have a function that takes in a date, finds all counties that have confirmed cases then, uses their polygons to find distances to each point we chose in the US, then creates a `GeoDistance` heat map: COVID19DistanceMap[date_DateObject?DateObjectQ] := Block[{counties, polys, coords, dists, gcomp, map, legend}, counties = COVID19CountyData[Select[#[date] > 0&]]; polys = Lookup[countypolys, Normal[Keys[counties]]]; coords = GeoPosition /@ Join @@ Cases[polys, _List?MatrixQ, ∞]; coords = PositionIndex[Counts[coords]][1]; dists = Clip[QuantityMagnitude[Nearest[coords -> "Distance", usasamp][[All, 1]], "Miles"], {0., 100.}]; gcomp = Append[usagcomp, VertexColors -> ColorData[{"Rainbow", {-100, 0}}] /@ Minus[dists]]; map = GeoGraphics[ { GeoStyling[Opacity[1]], gcomp, {Gray, polys}, {EdgeForm[Black], FaceForm[], Polygon[usstates]} }, ImageSize -> 1024 ]; legend = makeLegend[date]; Legended[map, Placed[legend, {0.1725, 0.125}]] ] makeLegend[date_] := Framed[ Column[{ BarLegend[{ColorData[{"Rainbow", "Reversed"}][.01#]&, {0, 100}}, LegendLayout -> "Row", ImageSize -> 300, LegendLabel -> Style["\[ThinSpace] Nearest Confirmed COVID\[Hyphen]19 Case (mi), " <> DateString[date, {"Month","/","Day","/","YearShort"}], 13, GrayLevel[0.2]]], Row[{Spacer[24], SwatchLegend[{Gray, ColorData["Rainbow", 0]}, {"Affected area", "> 100"}, LegendMarkerSize -> 13, LabelStyle -> GrayLevel[0.2], LegendLayout -> "Row", Spacings -> {0.5, 10.5}]}] }, Spacings -> 0], Background -> GrayLevel[0.95], RoundingRadius -> 10, FrameStyle -> {AbsoluteThickness[1.5], GrayLevel[0.75]}, FrameMargins -> {{0, 10}, {10, 15}} ] Here's the result for March 16, 2020. Notice that we clip the distance at 100 miles. This will give a consistent scale over time. COVID19DistanceMap[DateObject[{2020, 3, 16}]] ![enter image description here][3] We can now create a graphic for each day and export as a gif. Note that this is somewhat time consuming, but multiple kernels help. frames = ParallelMap[ Rasterize[COVID19DistanceMap[#]] &, DateRange[DateObject[{2020, 1, 21}], DateObject[{2020, 3, 24}]], Method -> "FinestGrained" ]; Export["covid19_distance_map.gif", frames, AnimationRepetitions -> ∞, "DisplayDurations" -> Append[ConstantArray[.2, Length[frames] - 1], 3]]; [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=covid19_distance_map.gif&userId=46025 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2020-03-2720.49.34.png&userId=46025 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2020-03-2721.01.13.png&userId=46025 Greg Hurst 2020-03-28T01:07:51Z https://community.wolfram.com/groups/-/m/t/992466 This project was part of a Wolfram Mentorship Program. The classification of human motions based on patterns and physical data is of great importance in developing areas such as robotics. Also, a function that recognizes a specific human motion can be an important addition to artificial intelligence and physiological monitoring systems. This project is about acquiring, curating and analyzing experimental data from certain actions such as walking, running and climbing stairs. The data taken with the help of an accelerometer needs to be turned into an acceptable input for the Classify function. Finally, the function can be updated with more data and classes to make it more efficient and whole. **Algorithms and procedures** The data for this project was acquired by programming an Arduino UNO microprocessor with a Raspberry Pi computer, using Wolfram Language. An accelerometer connected to the Arduino sent measurements each time it was called upon, and Mathematica in the Raspberry Pi collected and uploaded the data. The raw data had to be processed for it to be a good input for the classify function. First, it was transformed into an spectrogram (to analyze the frequency domain of the data). Then, the spectrogram's image was put through the IFData function which filters out some of the noise, and finally the images were converted into numerical data with the UpToMeasurements function (main function: ComponentMeasurements). This collection numerical data was put in a classify function under six different classes (standing, walking, running, jumping and waving). *The IFData function and the UpToMeasurements functions were sent to me by Todd Rowland during the Mentorship. Both functions will be shown at the end of this post. **Example visualization** The following ListLinePlot is an extract from the jumping data ![Example data][1] Next, the data from the plot above is turned into a spectrogram by the function Spectrogram, i.e.: spectrogramImage = Spectrogram[jumpingData, SampleRate -> 10, FrameTicks -> None, Frame -> False, Ticks -> None, FrameLabel -> None] ![Example jumping data spectrogram][2] Finally, all the spectrogram images are used as input for the UpToMeasurements function, along with some properties for the ComponentMeasurements function: i.e: numericalData = N@Flatten[ UpToMeasurements[ spectrogramImage, {"EnclosingComponentCount", "Max", "MaxIntensity", "TotalIntensity", "StandardDeviationIntensity", "ConvexCoverage", "Total", "Skew", "FilledCircularity", "MaxCentroidDistance", "ExteriorNeighborCount", "Area", "MinCentroidDistance", "FilledCount", "MeanIntensity", "StandardDeviation", "Energy", "Count", "MeanCentroidDistance"}, 1]] Which outputs a list of real numbers, one for each of the properties: {0., 1., 1., 1., 1., 19294.9, 0.222164, 0.985741, 31011.8, 15212.5, \ 9624.42, -0.0596506, 0.724527, 190.534, 0., 42584.5, 0.364667, \ 42584., 0.453101, 0.315209, 0.232859, 0.169549, 0.00909654, 42584., \ 98.7136} These numbers are grouped in a nested list which contains data for all 5 human motions. All the data is lastly classified in a classifier using the Classify function. After several combinations of both properties and data sets, I was able to produce classifier functions with an accuracy of 91%, and a total size of 269kb. ------------------------------------------------------------ **Attempt on building a classify function using image processing** On the other hand, the image processing capabilities of Mathematica lets us extract data from images, hence it should be possible to create a classifier which recognizes the moving patterns in the frames of a video. First, I had to take the noise out of every image, this proved to be troublesome, since the background can vary greatly between video samples. Then, I binarized the image in order to isolate the moving particles in each frame, and extract their position with ImageData. Lastly, a data set can be formed from all the analyzed frames; this data can essentially be used in the same way as the accelerometer's, but the classifier was unsuccessful in separating the samples accurately. This was mainly because the accelerometer's data is taken at a constant rate and very precisely, whereas the images depend on the camera's frame rate, and many other external factors. This is what made the data different enough to fail being classified with accuracy. Furthermore, if a big dataset is made from videos of people performing certain actions, the data processing can follow similar steps as the ones explained in this report. Thus producing a similar classifier function. This can further increase the functions accuracy, but the process needs an algorithm that can effectively trace the path of "a particle" that moves through each of the frames of the video, and extract precise velocity data from said movement. ------------------------------------------------------------ Conclusively, the classify function is working very well with the data provided, its accuracy is about 91% for the SupportVectorMachine method. This is a very good result for the human motion classifier. The next step is to add more classes to the function, and test the classifier with data acquired from different sources, such as another accelerometer and various videos of human motion footage. ----------------------------------------- **Code:** - UpToMeasurements function UpToMeasurements[image_,property_,n_]:=MaximalBy[ComponentMeasurements[image,"Count"],Last,UpTo[n]][[All,1]]/.ComponentMeasurements[image,property] *Note: This function simplifies the exploration of properties to input in ComponentMeasurements, also, it outputs a usable list of numerical data retrieved from a given group of images. - IFData function: imagefunctions=<|1-> (EntropyFilter[#,3]&), 2-> (EdgeDetect[EntropyFilter[#,3]]&), 3->Identity, 4-> (ImageAlign[reference110,#]&), 5-> (ImageHistogram[#,FrameTicks->None,Frame->False,FrameLabel->None,Ticks->None]&), 6-> (ImageApply[#^.6&,#]&), 7-> (Colorize[MorphologicalComponents[#]]&), 8-> (HighlightImage[#,ImageCorners[#,1,.001,5]]&), 9-> (HighlightImage[#,Graphics[Disk[{200,200},200]]]&), 10-> ImageRotate, 11-> (ImageRotate[#,45Degree]&), 12->(ImageTransformation[#,Sqrt]&), 13->(ImageTransformation[#,Function[p,With[{C=150.,R=35.},{p[[1]]+(R*Cos[(p[[1]]-C)*360*2/R]/6),p[[2]]}]]]&), 14->( Dilation[#,DiskMatrix[4]]&), 15->( ImageSubtract[Dilation[#,1],#]&), 16-> (Erosion[#,DiskMatrix[4]]&), 17-> (Opening[#,DiskMatrix[4]]&), 18->(Closing[#,DiskMatrix[4]]&), 19->DistanceTransform, 20-> InverseDistanceTransform, 21-> (HitMissTransform[#,{{1,-1},{-1,-1}}]&), 22->(TopHatTransform[#,5]&), 23->(BottomHatTransform[#,5]&), 24-> (MorphologicalTransform[Binarize[#],Max]&), 25-> (MorphologicalTransform[Binarize[#],"EndPoints"]&), 26->MorphologicalGraph, 27->SkeletonTransform, 28->Thinning, 29->Pruning, 30-> MorphologicalBinarize, 31-> (ImageAdjust[DerivativeFilter[#,{1,1}]]&), 32-> (GradientFilter[#,1]&), 33-> MorphologicalPerimeter, 34-> Radon |>; reference110=BlockRandom[SeedRandom["110"];Image[CellularAutomaton[110,RandomInteger[1,400],400]]]; IFData[n_Integer]:=Lookup[imagefunctions,n,Identity] IFData["Count"]:=Length[imagefunctions] IFData[All]:=imagefunctions *Note: This function groups together several image filtering fuctions; it was used to simplify the exploration of functions to be used in the classifier. **This function was written by the the Wolfram team, but was slightly modified for this project. - propertyVector function (this function automatically evaluates all the prior necessary code needed to create the classify functions): propertyVector[property_]:={walkingvector=N@Flatten[UpToMeasurements[#,property,1]]&/@IFData[6]/@(Spectrogram[#,SampleRate->10,FrameTicks->None,Frame->False,Ticks->None,FrameLabel->None]&/@walk); jumpingvector=N@Flatten[UpToMeasurements[#,property,1]]&/@IFData[6]/@(Spectrogram[#,SampleRate->10,FrameTicks->None,Frame->False,Ticks->None,FrameLabel->None]&/@jump); standingvector=N@Flatten[UpToMeasurements[#,property,1]]&/@IFData[6]/@(Spectrogram[#,SampleRate->10,FrameTicks->None,Frame->False,Ticks->None,FrameLabel->None]&/@stand); runningvector=N@Flatten[UpToMeasurements[#,property,1]]&/@IFData[6]/@(Spectrogram[#,SampleRate->10,FrameTicks->None,Frame->False,Ticks->None,FrameLabel->None]&/@run); wavingvector=N@Flatten[UpToMeasurements[#,property,1]]&/@IFData[6]/@(Spectrogram[#,SampleRate->10,FrameTicks->None,Frame->False,Ticks->None,FrameLabel->None]&/@wave); stairsvector=N@Flatten[UpToMeasurements[#,property,1]]&/@IFData[6]/@(Spectrogram[#,SampleRate->10,FrameTicks->None,Frame->False,Ticks->None,FrameLabel->None]&/@stairs); walkingvectortest=N@Flatten[UpToMeasurements[#,property,1]]&/@IFData[6]/@(Spectrogram[#,SampleRate->10,FrameTicks->None,Frame->False,Ticks->None,FrameLabel->None]&/@testwalk); jumpingvectortest=N@Flatten[UpToMeasurements[#,property,1]]&/@IFData[6]/@(Spectrogram[#,SampleRate->10,FrameTicks->None,Frame->False,Ticks->None,FrameLabel->None]&/@testjump); standingvectortest=N@Flatten[UpToMeasurements[#,property,1]]&/@IFData[6]/@(Spectrogram[#,SampleRate->10,FrameTicks->None,Frame->False,Ticks->None,FrameLabel->None]&/@teststand); runningvectortest=N@Flatten[UpToMeasurements[#,property,1]]&/@IFData[6]/@(Spectrogram[#,SampleRate->10,FrameTicks->None,Frame->False,Ticks->None,FrameLabel->None]&/@testrun); wavingvectortest=N@Flatten[UpToMeasurements[#,property,1]]&/@IFData[6]/@(Spectrogram[#,SampleRate->10,FrameTicks->None,Frame->False,Ticks->None,FrameLabel->None]&/@testwave); stairsvectortest=N@Flatten[UpToMeasurements[#,property,1]]&/@IFData[6]/@(Spectrogram[#,SampleRate->10,FrameTicks->None,Frame->False,Ticks->None,FrameLabel->None]&/@teststairs);} Training:=trainingSet=<|"walking"->walkingvector,"running"->runningvector, "standing"-> standingvector, "jumping"-> jumpingvector, "waving"-> wavingvector, "stairs"-> stairsvector|>; Test:=testSet=<|"walking"->walkingvectortest,"running"->runningvectortest, "standing"-> standingvectortest, "jumping"-> jumpingvectortest, "waving"-> wavingvectortest, "stairs"-> stairsvectortest|>; - Example code for the acceleration data acquisition from image processing: images=Import["$path"] motionData= Count[#,1]&/@ (Flatten[ ImageData[Binarize[ImageSubtract[ImageSubtract[#[[1]],#[[2]]],ImageSubtract[#[[2]],#[[3]]]]]]&/@ Partition[images,3,1],1]) *Note: before this code can be used, the backgrounds of the frames of the video have to be removed, and the image has to be binarized as much as possible (some examples will be shown in the next section). - Example code for the retrieval of raw data from DataDrop: rawData=Values[Databin["Serial#", {#}]]; data=Flatten[rawData["(xacc/yacc/zacc)"]]; --------------------------------- **Please feel free to contact me or comment if you are interested in the rest of the code ( uploading the C code to the Arduino, the manufacturer's code for the accelerometer, C code switch that lets Mathematica communicate with the Arduino, and the Wolfram Language code used to start each loop in the switch that retrieves data ). Also, I could send the classify function, or any other information that I might have left out; all suggestions welcome. [1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=1.png&userId=602285 [2]: http://community.wolfram.com//c/portal/getImageAttachment?filename=2.png&userId=602285 Pablo Ruales 2017-01-11T01:15:04Z