Waiting a year or more for a virus fix may cost us many lives. Why not help solve such virus problems thru math modeling and Calculus-level software? With a math model, such software (free and available from my website goal-driven.net ) can solve (continuous) math problems in less than 2 days. Yes, it may require years to arrive at the final solution as the researchers must gain a new way of thinking about their virus problem. But, once there, their next virus problems will be solved in days!
From 1976 to 1979, eight problems from the silicon valley were solved in 2 to 4 hours. Watkins-Johnson (WJ) Co. (Palo Alto, CA) R&D dept. solved a problem in 2 hours that landed them a contract with the US government to build a black-box. This box had to solve 10 issues. WJ was the only bid that did all 10 issues; 2nd bid did 9 and all others did 8 or less.
A Bang-Bang Control problem, for my casebook, was solved 4 ways; 1a, 1b, 2a, & 2b. Both 1a & 1b ways were solved in some 15 minutes. But, 2a required some 24 hours to execute and come up with a solution. Due to this long run, I now say 2 days for a problem-solution.
When starting my casebook in 1991, 40 demo problems were available to be executed & tested on my PC. The average execution time was 5 minutes per problem. Today, the time for those same 40 demo problems is 30 seconds, nice!
Automatic Differentiation (AD):
AD is the key feature that gave NASA’s abandoned software the quickness to solving math problems. AD coupled with Operator overloading allows numerical methods (aka Solvers) to be stored in a library for all to use without knowing or understanding them. My FortranCalculus language/compiler has a dozen or two solvers stored in a library. One changes their solves name in their code and a new solver is ready to try solving their problem. This is very helpful (and quick) when trying to find the right solver for ones problem.
Each solver calculates either the Jacobian or Hessian matrix that is necessary to converge to a solution. Think of the US as possible solutions to your problem. Your chosen solver will seek peaks and valleys over this region and zero in on one. Say it picks Nebraska. You switch solvers and try again. It too finds Nebraska. Now you change some initial conditions and try again … Nebraska. Start your search in the four corners of the solution space (ie. USA) … all come back with Nebraska. This should give you confidence in the solution -or- that your model is wrong, if you know Nebraska is not correct. Someone new at this testing may have trouble getting it at first. But, in the end, should give them confidence in their solution.
Website Stats:
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Over the last few years, my website downloads for 30 to 80 users / day. Each user averages around 4 apps per download. 200+ visitors / day visit my site; China has the most visits. The following stats are for the month of March, 2020.
There is a downloadable slide presentation (2 mb) that is available and should answer most questions. Recommend downloading the (free) FC compiler and our Curvfit app. Run some demo files to get an idea of what I’m referring too.
Here is a short Bio:
My History
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I attended Oregon State U. and majored 3 years in Electrical Engineering. Then I switched to a Math major for my final years and graduated with a B.S. in Math (1967).
My first job was with Lockheed Aircraft Co. building the SR-71 (Black Bird). One assignment had me designing the pilot’s suit. It was to be 1/4″ thick consisting of 5 materials and required to drop the outside temperature from its high to 98 degrees next to the pilot’s body temperature. A great math problem!
Another job was at Memorex Corp. designing a “Matched Filter” for a 14″ disc drive. This electrical filter was to make a pulse more symmetric and slimmer. The more symmetrical and slimmer a pulse, would help minimize the “Pattern-Induced-BitShift” (PIB). Heavy math problem! (Main LaPlace transform equation took me 22 pages of hand written notes to derive the necessary equations. Oh, those little minus signs kept giving me trouble!)
Next job was at Lockheed Missiles & Space Co. Here I had different assignments. One assignment had me analyzing, what is called Digital Signal Processing (DSP), a plume from a space craft to try and label it as a “Friend or Foe”. If its a Friend no problem, but a Foe may require action to be taken or it may shoot you down. This job required understanding the Fourier Transform. (FFT algorithm was being used. That was a BIG math mistake. I switched to 10 other algorithms and partially solved the problem.) For more, see my SpectrumSolvers v. 6 app… goal-driven.net .
After a lay-off in 1991, I started writing my math textbook/casebook. 28 years later the book is done plus a website, 4 apps developed, & front-end for a compiler I developed in order to show a new computer language, FortranCalculus (FC), that makes solving math problems very easy. This ‘new’ language takes a ‘automobile’ level computer to a ‘airplane’ level computer. Design solution times drop by (around) 95%; i.e. what took 20 months is now done in less than 1 month and the solution is optimal.
1991-2020 Optimal Designs Enterprise
President/Consultant
Main objective is to train Engineers & Scientists to solve their own math problems without real programming. Most modeling, simulation & optimization problems can be solved in a page or two with the aide of a calculus level language/compiler.
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Here is a conoravirus volunteer project that I mentioned at our last Zoom meeting … Michelle gave me a contact lead that I pasted this on to:
Are you interested in solving viruses? If so, do you know anyone who has advanced math modeling experience with one or more viruses? Please pass this e-mail on to those who may help solve one or more of these virus problems.
I’m a retired mathematician/electrical engineer and author of a casebook titled “Engineering Design Optimization using Calculus Level Methods: A Casebook Approach“. In the 1960s, NASA’s Apollo Space project team hired TRW, Inc to develop a software program to solve their math issues, where math models (i.e. continuous equations) described the interactions involved, to getting to the moon and back. I have a derivative of the software they developed and used. Do you know anyone who is researching a health issue, e.g. coronavirus, that may be interested in some help solving their math model or developing such a model? (Engineers often call this type of software Rapid Prototyping. This developed software is known as a Calculus-level compiler.)
There is no charge for my service on health problems … it’s free. If you know of someone who may be interested, please pass my name and email address on to such people.
Let’s get these viruses solved before they do us in.
Thanks,
Phil Brubaker
opt-designs@goal-driven.net
Rotary Club of Medford
Oregon State University ’67
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Have you seen the movie Hidden Figures? If you haven’t, you should see it. My background has me working with engineers, who provide a math problem, and physicists who understand the interactions of electrons/molecules/etc. So when an engineer gives me a math problem to solve, I work on it for a few hours or days until computer simulations show that their math model is okay -or- needs improvement. Improvements come from the physicists in terms of more equations/parameters/constrain
Communication:
Hidden Figures movie may help one understand the communication problem between different types of people; e.g. NASA’s Engineers, Scientists, and Mathematicians. The movie shows engineers trying to solve some equations and getting no where fast! A mathematician comes along and solves their problem. But numbers say little to engineers. Near the movie’s end, the mathematician draws a graph showing a solution. The engineers finally get the ‘picture’ of what the equations are trying to say to them. Remember, a picture is worth a 1,000 words, right?
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These are a few topics that may fit what you want, let me know.
Phil
