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Nate Hayes is among the subscribers of the 1788 mailing list, and will surely present his own understanding of the matter.
Dear Forum Members,I have been working diligently on my paper to present the unique findings developed at Sunfish Studio in relation to the application of modal intervals to fields such as computer graphics and computer aided design. Members of this forum have admonished me to "do it right" the first time, so I am taking the time to do just that. I appreciate your patience.
As a technical summary, it can be shown that Arnold's recipe requires the same sequence of floating-point operations used to compute the lower and upper bounds of the modal interval linear interpolation xx+tt*(yy-dual(xx)). Therefore the linearInt() function calls things by different names but simply provides the same obvious recipe that is already required by the modal interval computation.
Since my role at Sunfish is President and CTO, it is my responsibility to deal with the technological aspects of our business operation. What Arnold has submitted reaches beyond mere technical matters and enters into the peripheral arena of corporate governance.
Therefore, I also submit a prepared response from the CEO of Sunfish, Robert Subby:
We at Sunfish Studio, LLC are extremely troubled by the recent e-mail posting on the IEEE 1788 public forum by Mr. Arnold Neumaier. In his post he describes what amounts to a reverse engineered solution of our patent-pending modal interval polynomial function. Though couched in somewhat dismissive language, what Mr. Neumaier has done is to essentially deny the unique status of our intellectual property, painting it as somehow irrelevant and/or disconnected from his own recipe to compute narrow bounds on interval polynomials. In fact the opposite is true. As is clearly stated in the last paragraph of our publication on this subject, our solution encompasses any obvious alternative methods that might be used to arrive at the same solution.
Even if one assumes Mr. Neumaier has charted another path to the same end, it is obvious his path does not meet the standards of patent law regarding what is defined to be an "inventive step" or "obviousness."
It is my hope that this brief e-mail summary will be helpful in clarifying both Nate's current involvement with the forum and our company's concern with the protection of intellectual properties.
Robert Subby, CEO Sunfish Studio, LLC